METALLURGICAL PROCESS ENGINEERING Robert. D, Pehlke December 1960

Copyright 1960 Robert Do Pehlke ii

PREFACE The engineering of metallurgical processes is presently in a high state of fluxo The advent of the high speed computing machine has been a tremendous stimulus in promoting a re-examination of process design proceduresO In this regard, it has been recognized by most educators in the field of extractive metallurgy that a unit process treatment of the subject has much more to offer in its analytical approach than a descriptive presentation of current practice, This text is based on the unit process concept, and attempts to extend it to a consideration of the design of entire extractive processing systemso The future of metallurgical process engineering will undoubtedly involve, in addition to the advances in metallurgical sciencetechniques which are adopted from chemical engineering, instrumentation, computing economics, operations research, and other allied fieldso The metallurgical engineer should be acquainted with these areas, at least to the point of being able to evaluate possible contributions to metallurgical processing operations by specialists from these fields, Ideally, in a metallurgically oriented organization, the trained metallurgist should be prepared to assume a position of leadership in the engineering team which handles the many-faceted problems of metallurgical process design and operation, This book reflects an effort to expand the teaching emphasis in extractive metallurgy, and includes an introduction to some of the fields which are important in metallurgical process design and operation. Every effort has been made to develop an analytical approach to the engineering of metallurgical unit processes. In addition, the text includes iii

introductory material on the use of computers in process engineering, operations research procedures which treat system behavior in terms of queueing theory or linear programming models, as well as the mathematical simulation of processing systems, and consideration of the engineering of integrated systems. The experience of teaching a course entitled, "Metallurgical Process Design", to juniors and seniors at the University of Michigan has provided the material for this publication0 This course is preceded by courses in Process Stoichiometry, Chemical Engineering Thermodynamics, and Rate Operations which involve 3, 4, and 4 semester hours, respectivelyo This preparation and a one hour required course in digital computer programming is an excellent one for the present subject, Consequently, only a brief review of stoichiometry, thermodynamics and kinetics in the first chapters has been included. Furthermore, a knowledge of heat transfer and fluid flow on the part of the student has been assumed. In the event that additional reading in these areas is necessary, "Unit Operations" by Ao So Foust and "Heat Transmission" by Wo Ho McAdams are excellent reference textso In view of the fact that the presentation is primarily analytical, it is necessary that it be supplemented by descriptive material to provide the student with a clearer understanding of the environment in which the processes under consideration operate. The principal use of the descriptive material should be in consideration of metallurgical processing systems, following a development of the unit process approacho C, R. Hayward s "Outline of Metallurgical Practice", J. Newton s "Extractive Metallurgy", or the texts on nonferrous and ferrous production metallurgy by Jo L. Bray are possible sources of this material, In addition, iv

the references from the technical literature at the end of each chapter provide an excellent source of descriptive materialo The integration of example problems, both for classroom use and homework, is a vital part of the presentation of this material, The text itself contains only a few such problems, although a supplementary problem set is presently under developmento Thus it becomes the responsibility of the instructor to provide additional material which will develop the student's engineering judgement and analytical approach to design problemso "Metallurgical Problems" by Allison Butts is a possible source of additional problems The author is indebted to many of his colleagues and associates for their encouragement in preparing this text. The assistance of the Industry Program of the College of Engineering in preparing the final manuscript is gratefully acknowledged. Robert D. Pehlke December 1960 Ann Arbor, Michigan v

TABLE OF CONTENTS PART I Foundations of Metallurgical Design. Chapter Title Page I Introduction...oo,.,, ooo....ooo.0..0..0000 3 II Stoichiometry - Mass and Energy Balaices,......... 7 III Thermodynamics. o~... o o o a o o oOooooo.o o oooa 21 IV Kinetics..oa a aoooooo.oooaooaoaa.oDaoo...D.a oaa 3 37 V The Thermochemical Modelo o.o.oo.a.o oooaoao o.ooo 47 VI Equipment Design and Selection o............. o 57 PART II Materials Preparation, Treating, and Handling VII Sintering........................................ 63 VIII Roasting - Calcining - Dryingo.........,....0.. o 77 IX Hydro-Metallurgical Operations 0o0 o.o.o oo.oo.OO.o 87 X Melting and Pouring.........oooooo,ooo....0oo0oooo 97 XI Casting and Solidification 115 PART III Primary Metal Production XII Direct Reduction of Metal Oxides and Halides0..0.. 133 XIII Fluidized Bed Reductiono o o. o.. o... 000..o.. 141. XIV Reverberatory Furnace Smeltingo.,oo........oooo.... 157 XV The Blast Furnace.. ooo..............oo.o.......oo. 163 XVI Converting Processes.........oo00.....00.0000o0000 177 XVII Electrolysis of Fused Salts o o o o o o o. o,.o o o o 189 PART IV Refining Operations XVIII Electrolytic Refining o....... o.o. o oa oo o o. 199 XIX Distillation Processes.0o000. 0o....o o...o o o.. 211 XX Liquid-Liquid Extraction................oo..oooo 227 XXI Precipitation Reactions-Deoxidationo.....0........o 233 XXII Phase Separation, o........oooo o o......o.o....o.0 o 247 XXIII Degassing Operations o....... o o o o o o o o oo o 261 PART V Integrated Operations XXIV Electronic Computers in Process Engineeringo,,,..o 283 XXV Material Handling - A Queueing Theory Approach., o 293 XXVI Linear Programming..... o..........o o........... o 305 XXVII Process Simulation......0,.0........0o o0....... 0 321 XXVIII System Engineering,.,o..o.o o,,,o o o0..0.....oo 329 Index..o a b 000 0 0000.00. 000 a a a o0 a 337 Table of Physico-Chemical Constants o. o o o..oo. 345 vii

LIST OF TABLES Table Page Part I II-1 Metallurgical Balance for Dwight-Lloyd Sintering Machine ooooooooooo O........... 12 Part II VII-1 Fuel for Normal Temperature Distribution in Sinteringo o o o o.O.o.oo. o Do Oo..... o 67 X-1 Heat Content of Several Metals..o.o.o o. 102 XI-1 Segregation Coefficients for Alloying Elements in Iror"; a"ooo Oooo foo 122 Part III XII-1 Maximum Vapor Pressure of Mercur-........ 135 XII-2 Heat Capacity and Heat Content of Mercury- 136 XII-3 Free Energy Functions and Heats of Formation of Several Chlorides'.....,...... 138 XVI-1 Sensible Heat Contents at Selected Temperatures Relative to a 77OF Base Temperature 181 Part IV XIX-1 Vapor Pressure of the Elements- ^,... O.,,, 212,213 XIX-2 Vapor Pressure Data for Dilute Liquid Iron Solutions at 600o~C...,.... o * O o o 215 XXI-1 Standard Free Energies of Formation of Oxides, Sulfides Nitrides and Carbides at 1600~C o a o D o O O o 0 O o O O..*.Oo.O.o.Oo 238 239 XXI-2 Standard Free Energy of oSlution of Various Elements in Liquid Iron ^^,.. o...o 240 XXIII-1 Relationship Between Reynolds Number and Drag Coefficient for Bubble Flow.....oooo 269 Part V XXIV-1 Comparison of Analog and Digital Computers 290,291 XXV-1 Summary of Calculations for Multistation Queueing Example.,.........**...O.... *ao o 301 XXV-2 Cost Analysis for Service Facilities in Open Hearth Shop..... *o.... o..... o 301 ix

LIST OF TABLES (CONT D) Table Page XXVI-1 Simplex Method of Calculation 0oo0......... 310 XXVI-2 Simplex Method of Calculation-2,.....ooo 311 XXVI-3 Simplex Method of Calculation-3 000....0 0.. 311 XXVI-4 Simplex Method of Calculation-4 o.....o,,... 311 XXVI-5 Optimum Program for Alloy ProductionOO OO. 315 x

LIST OF FIGURES Figure Page Part I 9iJII-1 Process Flow Diagram oooooooooooo.oo o.... 9 III-1 Activity of Nickel in Liquid Iron Showing Ideal Behavior. 0 o o OO o o0.OOOOOo oo... 24 III-2 Activity of Silicon in Liquid Iron at 1600 0.0 0 0 0 0 0 0 0C 0 0 0 0 0 0 0 0 0 a 0 0 a a 0 0 a 0 a 25 III-3 Activity of Copper in Liquid Iron at 16oo C00 00C000000000000 a 0 o o 0 o o 26 III-4 Activity of Copper in Liquid Iron at 16ooC 00C 000000000000000000000000000000000 28 III-5 Activity of Silicon in Liquid Iron at 1600 C. O 0 0 O O DO OOO D0 a O 0 a O 29 III-6 Activity and Activity Coefficient of Carbon in Liquid Iron at 1600~C 000000000000000000 30 III-7 Activity-Composition Diagram Showing Factors Involved in Converting Activities from One Standard State to Another.. o ooooo...oo.. 32 IV-1 Potential Energy Path for a Chemical Reactiono..OOoo00000000.000o0oooooooo0oo0o o 39 IV-2 Concentration Profile in a Boundary Layer o 43 V-1 Schematic View of Dortmund - Hdrder Hflttenunion Vacuum Treating Processo....... 50 V-2 Removal of CO from Liquid Steel by DHHU Vacuum Treating Process oo.,,O0.....oooo..o 51 Part II VII-1 Schematic Diagram of Dwight Lloyd Sintering Systemo o.ooo.ooooooooooooooo...ooooo 000000 64 VII-2 Temperature Distribution for Two Sinter Mixes When Combustion is Occurring Approximately at the Midpoint of the Bedo,..oooooo 68 X-l Melting Furnaces, o o.o o.o o...o o0 o.. 98 X-2 200 Ton Bottom-Pour Ladle,..oo.0oo.ooo.... 106 X-3 Flow Rates from Bottom-pour Ladle for Various Nozzle Materials with Erosion Coefficient, o oll12 xi

LIST OF FIGURES (CONT D) Figure Page XI-1 Segregation Pattern in Hot-topped Killed Steel Ingot.. oooooo oooOOOO oOO oooo 120 Part III XIII-1 Effect of Fluid Velocity on Pressure Drop for Upward Flow Through a Bed of Closely Sized Particles....0 0...oo0a 0 0 0 0. 143 XIII-2 Effect of Reynolds Number on Porosity for Upward Flow Through a Bed of Closely Sized Particles aa... 9..........0 a a00a0 aa.. a 144 XIII-3 Equilibrium in the Systems Fe-0-H and Fe-O-C......................oO O ooo O 147 XIII-4 Distribution of Retention Times for Perfect Mixing in a Continuous System o..oo,,oo.00o 153 XIV-1 Reverberatory Furnace Smelting.........ao 158 XV-1 Cross Section of Blast Furnace.ooo.oo0 0ooo 165 XV-2 Solubility of Carbon in Iron-Silicon Alloys9.o o.o o.. a o oao 9 oo o....a.099 0 o 09 169 XVI-1 Operating Positions of Bessemer Converter o 178 XVI-2 Changes in Metal Bath Composition During Blowing Period of 25 Ton Bessemer Converter. ooooooooooooooooooOoooa o o oo o 182 Part IV XIII-l Concentration Polarization at Anode of Electrolytic Cello..o.oooo0.00ooo 9.oo9ooooo 205 XVIII-2 Electrical Connections for Electrolytic Refining Cells.......oo ooo 9...... o.o o o o 208 XIX-1 Relationship Between X and Y for Various Values of ao. o. o O O a O o o o D o O o o o o 218 XXII-1 Free Energy of Nucleus Formation as a Function of Nucleus Size o o....o..o...oooo 250 XXII-2 Phase Diagram for the Lead-Silver Systemo9o 254 xii

LIST OF FIGURES (CONT D) Figure Page XXII-3 Schematic Diagram of Zinc Recovery System for Zinc-Lead Blast Furnace o...... 255 XXIII-1 Removal of Hydrogen from Liquid Steel by Flushing with Argon........0000...0.. 268 XXIII-2 Vacuum Degassing of Liquid Iron in Magnesia Crucible..oooo.............OOO. 273 XXIII-3 Desulfurization of an 80%Ni - 20% Co Alloy at 1530C by Vacuum Treatmento o.... 274 XXIII-4 Schematic Diagram of Vacuum-Flow Steel Degassing Process 000000................. 277 Part V XXIV-1 Digital Computer Operation..ooo.....oo... 285 XXIV-2 Flow Diagram for Successive Evaluation of Polynomial aooo0ooooooooooo0000 0000000 ooo 285 XXIV-3 Flow Diagram for Solution of Differential Equation with Analog Computero o 0000000 288 XXVI-1 Graphical Solution of Two-Dimensional Linear Programming Problem.,,.....o0..oooo 307 xiii

Part I FOUNDATIONS OF METALLURGICAL DESIGN -1

CHAPTER I INTRODUCTION A treatment of the science and of the art of process metallurgical engineering may be approached in two wayso The first, and one which has been highly popular in past years, is that of treating the extraction and processing of each individual metallic element starting with the mined ore and ending'with a semi-finished product. The second approach, and one which has become necessary in view of the constantly expanding frontiers of metallurgy and the diversity of processing systems used in metallurgical industries, recognizes that each of these processing systems is made up of a number of unit operations and processes which possess general similarities independent of the material being processed. The terms, unit operations and unit processes, were first used by chemical engineers to designate the unit actions in the manufacturing processes of the chemical industry. A distinction may be made between unit operations and unit processes on the basis of whether or not the process involves physical or chemical changeso Unit processes are defined as those operations which involve chemical reactions and/or changes in state of aggregation while unit operations primarily do not involve either bulk reactions or changes in state. Met- u-rgieal unit operations would include screening, size reduction, handling of solids and fluids, classification, flotation, sedimentation, and other material separation processes. Metallurgical unit processes would include such gas-solid processes as roasting, calcining, and gaseous reduction. They would include as well, sintering, the reduction of oxides, smelting -3

-4operations, converting, refining, hydrometallurgical processes, electrolytic processes, and other metallurgical operations which involve chemical reactions or changes in stateo This text is devoted to the development of an engineering approach to the design and integration of metallurgical unit processes. It should be noted that there is a distinct need for several kinds of unit operations and unit processes in sequenceo This need arises from the fact that no single unit operation or process is capable of separating a metal from all of the elements associated with it. Consequently, a coordinated sequence of operations and processes is made up such that materials flow from one step to the next in an orderly fashiono These integrated processes may make up the entire plant or section of a plant in which the metal is being processedo Successful operation of an industrial process requires intimate knowledge of the relations of the large-scale process to its surroundings and careful coordination of those relations with each other and with the internal characteristics of the processo The engineer who has a sound foundation in the principles of metallurgical operations; i.eo, in stoichiometry, fluid flow, and heat transfer, as well as a good background in thermodynamics and kinetics, should be able to apply this knowledge and readily adopt himself to the mathematical analyses and practical applications of metallurgical unit processes. The material presented in this test assumes such a background, although the first section has been devoted to reviewing a part I0~ t.hat material. The goal here is not only an understanding of unit processes, but a preparation for an even more advanced state of metal

-5lurgical process design, the engineering and design of metallurgical processing systems. In recent years, the processing industries have come to realize more and more that they can no longer think of their plants as an assemblage of individual unitso It is becoming apparent that each of the separate units in a processing system influences the others in many subtle ways as well as the more obvious, direct ones. The principles of feedback systems have been recognized for some time, but little has been done to implement these principles for the purpose of process controlo Recent advances in the mathematical treatments of integrated systems coupled with a better appreciation for the interaction of units making up a system, have led to a new engineering technique, that of system engineeringo System engineering strives to optimize the operation of entire plants or systems contained within them, and prepares to do so by analyzing the operation of each of the individual units and integrating the analyses of themo The advent of system, engineering is undoubtedly the dawning of a new era in process engineering. This advance represents a challenge to the metallurgical engineer. The meeting of this challenge is the goal to which this text is committed.

REFERENCES 1o Schuhmann, R,, Jr. Metallurgical Engineering. 1, Cambridge, Mass o Addison-Wesley Press, 1952. 2, Williams, T. Jo "Systems Engineering and Its Potential in the Process Industry." Oil and Gas Journal, 57, No. 33, August 10, 1959, 93. 3. Goode, Ho H. and Machol, R. E. System Engineering. New York~ McGraw-Hill, 1957o 4o Williams, To J. System Engineering for the Process Industries. The 4th Schoch Lecture at the University of Texas, Austin, Texas, October 16 and 17, 1959o -6

CHAPTER II STOICHIOMETRY - MASS AND EENERGY BALANCES The basis of engineering analyses of metallurgical processes is the mass and energy balances which may be set up for a processo The stoichiometric relations which make up these mass and energy balances are in themselves quite simpleo They could be summarized by the old observation, "What goes in, must come out", or more precisely as, the input to a system is equal to the output from the system plus any accumulation within the system. This statement is based on the assumption that matter is neither created nor destroyed, and also that matter and energy are not interchangable. This assumption is contrary to the foundations of nuclear science, but is one of general validity in metallurgical process operationso Processes may be divided into two classes, batch and continuouso In the batch process the charge materials are placed in a tank or container and then permitted to react by interchange of materials between the charge streams or the interchange of energy between the charge materials themselves or between the container and the charge materials. When the charge of the batch process has reached the desired conditions, it is removed and new charge materials are placed in the containero In the continuous process the charge materials are passed continuously through the container, the reacting volume and the rate of flow being adjusted so that the materials leave the system at the desired conditions. Each of these classes of processes has certain advantages and the choice of the process to be used is the responsibility of the -7

-8engineero The batch process generally involves equipment which is simpier and easier to fabricateo It does not require as close control and the control is needed only toward the end of the processo The batch process is intermittent, and consequently, associated with such a process are the problems of storage facilities to absorb the fluctuations in the rates of productiono The continuous process, generally requiring more carefully designed equipment than the batch process, can usually be handled in a smaller space and with continuous operation which easily fits into a smooth flow of production through the planto The temperature in each part of the continuous process equipment will remain substantially constant during the operation. Thus the continuous operation has an advantage from the point of engineering designo Conditions will be different at different points in the continuous system, but will remain constant at each particular point. This is called a steady state process and is in many respects an ideal one. The mathematical treatment of the steady state process is generally much easier than that for a non-steady state processo The continuous process does involve nonsteady state conditions, however, during startup and shutdown periods, but throughout the course of operation, the continuous process is in what may be described as a steady state cond.itiono Mass Balances The materials balance for an unsteady system was stated previouslyInput Output + Accumulation II -l A steady system, however, will contain a fixed and unvarying quantity of any given element so that the balance simplifies to~

-9Input = Output 11-2 This simpler relation also applies to batch processes and other unsteady systems if the input and output are measured for period of time such that the system is in the same condition at the beginning and the end of that periodo For the process shown in Figure 11-1, the over-all material balance may be stated mathematically as: a1 + a2 = b1 + b2 11-3 where a1 = total mass of stream A1, a2 = total mass of stream A2 b = total mass of stream B1, b2 = total mass of stream B2. B1 B2 A2 Ai B Figure II-1 Process Flow Diagram If the process is a batch process the mass of the streams may be expressed in weight units. If, however, the process is a continuous one, rate of flow may be used, expressed as mass per unit timeo In the case where the reactions taking place in a process are purely physical, the material balance may be written for each material involved. If, however, a chemical reaction is taking place, the balance must be written in the form of an element balance. The principle of conservation of elements may be usedo This principle states that matter is composed of atoms which are unchanged during the course of a chemical reaction. Furthermore, this principle may be extended to state that when atoms combine to form molecules, these combinations are brought

abut such that the weight of the molecule is precisely equal to the sum of the weights of the atoms which make it upo In addition to the principle of conservation of elements, the ideal gas law is also an important consideration, especially since gas phases are involved in nearly all process operationso Boyle Vs law states that at constant pressure, the volume of a given mass of gas is inversely proportional to the pressureo Charles' law states that at constant pressure the volume is proportional to the absolute temperatureo These statements are strictly true only for an ideal gas and lead to the ideal gas law. The relationship for an ideal gas is thus: FV = NRT -I 4 where P = pressure, V = volume, N = number of moles of gas, R = gas constant, and T = absolute temperatureo Real gases closely approach the ideal behavior represented by the above equation at low pressures and high temperatureso Since these are the conditions under which most metallurgical systems operate, no significant errors are introduced by assuming ideal behavior for gases involved in nearly all metallurgical operations The law of combining volumes follows from the ideal gas law and affords a further simplification of engineering calculations. According to this principle, the volume of a mixture of two gases is equal to the sum of the volumes of the individual gases, and the volume fraction as well as the mole fraction are given by the partial pressure of one gas divided by the total pressure of the gas mixtureo When complete and accurate stoichiometric data are available for a process, a table is easily drawn up to show the balances for the

-11materials and for each important element. A typical metallurgical balance is presented in Table II-lo In principle, all of the quantities entering and leaving a process with no accumulation or loss can be calculated if complete analyses on all -streams- and the quantity of one of the materials in each stream are known. Simultaneous equations can be solved for the unknown quantities which may be either weights or analyses of streamso If N independent element balances can be written, N unknowns can be solved for. If there are more independent equations than there are unknowns, several sets of answers can be calculated and checked against each othero Solutions of simultaneous equations set up from practical data are often in error because small errors in the original data can greatly be magnified in the solution. Even negative answers may be obtained and such results are often due to the fact that solutions are obtained by a-method of difference, and large errors may arise in solving the equations where a small quantity is determined by the difference between two large quantitieso The engineer must be aware of this difficulty, as well as be able to recognize and avoid ito It is rarely necessary to formally set up and solve a list of simultaneous equations involving all of the elementso Examination of the problem will usually reveal a simpler procedure for solving the particular problem. One factor which may be of assistance can arise from the fact that one element may enter and leave the process in a stream unchangedo For example, nitrogen often acts as an inert material which enters as air and leaves in the gaseous product. If the percentage of nitrogen in the exit gas is available and either the volume of

-12TABLE' 1-l Metallurgical Balance for Dwight-Lloyd Sintering Machine Basis Per 1000 lbo of dry charge FEED PRODUCT Charge - lb Sinter - lb Gases(suction box) lb Lead Ore (645)~ PbS 387 Pb 335 S 52 FeS 26 Fe 12 S 14 SiO2 232 Sio2 232 Silver Ore (65)' PbS 3 P 3 S Ag2S 0.3 Ag 0o3 S 0 SiO2 61.7 SiO0 61o7 Spathic Iron Ore (129) FeCO 129 FeO 80 C02 49 Limestone (6l1)~ CaCO3 161 CaCO3 80o5 co2 35o5 CaO 45 Moisture (100)o H20 100 H20 100 Oil (5) C 403 C 403 H Oo7 H 0.7 Air (774) N 595 N 595 0 179 0 31 o 148; Total 1879 880o5 998 5 Fromo Ao Butts, Metallurgical Problems McGraw-Hill Book COo New York. 1943.- po 231.

-13air or of the exit gas is also available, the other volume is readily calculated without regard for other stoichiometric data on the processo A general procedure should be adopted for setting up and solving the mass balances around metallurgical processeso Such problems are rarely difficult, but are generally long and tedious and offer many opportunities for arithmetic and other errors which are not easy to find and correcto Hence, from the very start a logical procedure of problem solving should be adopted, clearly writing out all steps so the solution can be quickly retraced and checked by another person if necessaryo The procedure should include a simple line drawing of the system with indicating arrows showing the direction of each stream, the known stoichiometric data, and the assumptions which are valid for the process and which may serve as a basis for solution, the basis for the calculatior, and the balanced chemical equations which will account for specific compounds or elements. Once this has been done, the equations may be inspected and a procedure decided upon for the solution of the problemo The solution should then be carried out and the results tabulated in a metallurgical balance table. The solution should finally be checked to see that all conditions are fulfilled and that the required results have been obtainedo Energy Balances All processes involve the interchange of various kinds of energy with the surroundingso In most metallurgical processes, heat energy is the principal form of energy exchanged between the metallurgical system and its surroundingso The supply and utilization of

-l4 heat range in importance with the supply and utilization of raw materials in determining costs and thus the success or failure of a process" For example, the availability of fuel or of low cost power has in many cases been the primary factor in the choice of plant locationo Hencee the systen of energy accoutnting or an energy balance for the process showing nput and output o eat and otpt hea ad r forms of energy is one of the indispensable tools that the metaLlurgical engineer uses. Just as the principle of conservation of elements afforded a simple approach to the materials balancee, the principle of conservation of energy or the first law of thermodynamics afford.s a sound basis for setting up anr energy balance, Ir both cases, a complete accounting of what goes into and what comes out of the system. is made with litt.le conrcern for the reaction mechanisms which operate within the system during the process operation, The first law of thermodynamics may be written asAE =Q- W 1N-5 where E is the energy change of the system., Q is the heat absorbed by the system from the surroundings, and W is the wo.rk: done by the system on the surroundings. The heat content or enthalpy of the system, H is the thermodynamic property defined as0 H = E + PV I1-6 where E is the energy content of the system, P is the pres -are d and V the volume of the sytemo Combining with the previous equation, the first law may be -written as$ H -H Q - W + P - P, 7 2 1 2 i I,

-15For a constant pressure process9 i:. which all the work done by the system on the surroundings is the work of expansion, that is, the integral from 1 " 2 of PV, P2 = P = P and W = P(V2 - V1) Combining the two equations above, H2 - Hi =p or H = Qp, where Qp is the heat absorbed by the system in changing from state 1 to state 2 by path of constant pressure in which only expansion work is done on the surroundingso If the change in state is at constant pressure, but involves work other than expansion work on the surroundings, n= Q - W 11I-8 where W' is the work done by the system on the surroundings in the constant pressure process, but does not include expansion worko For example, in an electric furnace process at constant pressure, -WI = the input of electrical work to the systemo Since most metallurgical processes follow paths of substantially constant pressure, the previous equation is a very useful oneo Before introducing the energy balance itself, it would be best to first discuss the principles of thermochemistry which underlie the various aspects of that balance. Thermochemistry is a branch of science which is concerned with energy changes, usually in the form of heat which accompany chemical reactions. Thermochemistry as a.. aiaence can be summaiezed by several laws which form the basis for most of the calculations accompanying heat effects in chemical reactionso In 1780 Lavoisier and LaPlace stated that the heat evolved in a given reaction is equal to the heat absorbed in the reverse reaction. This law is merely an expression of the more general law of conservation of energyo In 1840, Hess, in his law of constant heat summation, stated that the heat of a chemical reaction at constant pressure is independent

-16of the number of intermediate steps involved. In other words, the total change in enthalpy of a system is dependent upon Only the initial and final conditions of the system and is independent of the number of intermediate chemical reactions involved. Systematic thermochemical data are readily available for the following simple thermodynamic changes in state, all at constant pressure 1. temperature changes in pure substances 2. changes in state for pure substances 3. formation of compounds from elements 4o formation of solutions, The variation of heat content with temperature is expressed for most substances by a number of empirical relations involving temperatures to various powers. The quantity calculated is not the absolute heat content, but the relative heat content, Ht - H298 The temperature 2980K or 25~C is known as the base temperature and the quantity (Ht - H298) is then the heat content above the base temperatureo The variation, in the sensible heat with temperature is called the heat capacity cp which is defined aso p [= p I-9 Integration of the above equation gives0 T2 H2 Hi= c dT 1-10 Values of the sensible heat are tabulated in various sources, After a solid is heated to its melting point, additional heat must be supplied to melt ito The heat required for melting at constant

-17pressure is equal to the increase in heat content from the solid to the liquid and is known as the heat of fusiono An equal quantity of heat is liberated during solidification, so that AH solidification = -AH fusion II-1 Similarly, heat effects accompaneying vaporization and other allotropic. changes in materials are measured by heats of vaporization and heats of transformation When a chemical compound is formed from its elements, heat is either liberated or absorbedo The heat of formation, designated by AHf, of a substance is the enthalpy change resulting from a reaction in which the reactants are initially in the elemental form at some specified temperature and pressure, and the product is obtained at the same conditions of temperature and pressure. The heat of formation is a special case of heat of reaction in which the reactants are pure elementso The usual conditions of temperature and pressure are at the base temperature 25~C and 1 atmosphere, in general, and the heat of formation under these conditions is termed the standard heat of formationo A compound whose heat of formation is negative is termed an exothermic compound while one whose heat formation is positive is termed an endothermic compoundo The heats of reaction may be computed from the heats of formation by the following equation~'H= L[zMIH of reaction products] [Z[f of reaetants] II-12 The above equation follows from the previously indicated fact that EH for any process depends only on the initial and final states and not on the path takeno Thus, if a process is divided into several steps and AH is determined for each step, the algebraic sum of the AHI values for all the steps must equal AH for the original direct processo

-18The enthalpies involved in the formation of solutions are functions of composition. The enthalpy changes accompanying the formation of solutions have been tabulated for a few systems. Fortunately, these heats of solution in many cases are small compared with other enthalpy changes in the process, so that they can often be neglected without introducing serious errors into the over-all heat balanceo The heat balance for a process is a statement of the energy balance in a form which is convenient. The heat balance, like the material- balance, accounts for heat quantities in two categories, input and output. The totals for the two categories must be equal All items in the heat balance are positive, so if simple rules are followed there is little confusion of negative and positive signs which is often experienced in thermodynamic calculationso No new principles are introduced in the heat balance; it involves the same principles utilized in the mass balanceo However, a few conventions and definitions are involved in order to insure proper classification of the energy input and output, It is necessary to select a single base or reference temperature. This base temperature is often 25~Co However, for high temperature processes one might select the temperature of the process as the base temperatureo Thus steel-making processes might be referred. to 16000C, or copper-converting processes to 12000Co. After selecting the refer= ence temperature, reference states at this temperature must be understood for each substance in the input and output streamso For most substances there is only one stable state at the reference temperatureO However, in many cases, particularly for solutions, a specification is necessary~

-19The sensible heat of an input or output material is the positive quantity of heat required to change the substance from the reference temperature and reference state to the actual temperature and. actual state in which it is present in the input or output of the processo Thus, if the reference temperature is 16000C, and the material enters the process at that temperature and in its reference state, the substance brings no sensible heat into the processo On the other hand, if the substance is brought into the process at ambient air temperatures, it brings a negative sensible heat into the process. The calculation of sensible heat is a calculation of AH for the heating from the reference state to the actual stateo Heats of reaction must have the values corresponding to the reference temperature, and not to the process or to other temperatures, and must be for the reactions between substances in their reference state at the base temperature. The heat balance thus includesInput o1 Sensible heats in input materials (positive) 2, Heats evolved in exothermic reactions 3. Heats supplied from outside the system. Output 1. Sensible heats in output materials 2. Heats absorbed in endothermic reactions 30 Heats absorbed in bringing input materials to reference temperature and state 4o Heat loss. to surroundings by radiation and convectiono The procedure in calculating a heat balance is essentially the same as that involved in calculating a material balance, Accordingly, a logical and standard procedure of calculation is desirable, and should be outlined prior to the solution of the problem,

REFERENCES l Coororan, W. Ho. and Lacey, W, No Introduction to Chemical Engineering Problems, Chemical Engineering Series, New York0 McGraw-Hill, 1960. 2. Littlejohn, C, E. and Meenaghan, G. Fo An Introduction to Chemical Engineering, Reinhold.Chemical Engineering Series, New York- Reinhold Publication Corpo, 1959. 3. $chuhmann, R. Jr, Metallurgical Engineering, Cambridge, Mass0 o Addison-Wesley Press' 1952o -20

C~HAPTER III THERMODYNAMICS The chemical behavior of materials and the influence of extensive properties on the reactions which take place between substances may be described in terms of thermodynamic relationshipso The total energy which is available from a chemical reaction to do reversible work is the free energy, a quantity which was defined by J. Willard Gibbs as~ F =H - T S III-1 Then for a chemical reaction at constant temperature~ AF = AH - T A S III-2 The free energy change, A?, is a measure of the driving force for the occurance of the reaction at a definite pressure and temperature When AF is negative the reaction tends to occur and conversely, when AFis positive the reverse reaction tends to occuro The greater the free energy change, the greater the tendency for the reaction to occuro When AF is zero, the reaction is said to be in equilibrium and there is no tendency for the reaction to occur in either direction. The free energy change does not determine the rate of the reaction and will not permit a prediction as to whether the reaction is fast or slowo Solutions The chemical activity, a, (the tendency of a component of a phase to react), is dependent upon concentration of the component in that phase. In an ideal solution, the chemical activity of a component is proportional to the amount of the component presento As an example, if liquid nickel and iron are mixed in equal mole fractions, the iron -21

wh.ich -is present would. have one half the chemical activity of pure liqyuid irono. If the solution were more dilute in iron, its activity would be less. A component whose activity is proportional to mole fraction is said to be ideal and to obey RaouLt s Law~ moles A NA aA = Total moles N I -3 At NA = N in Equation (III-3), a 1o Thus,s the pure phase is the reference concentration or the Standard State. The reference concentration could also have been chosen at some other point. For example, a 1 mole percent solution could be used as the standard state and the activities indexed from that pointO Then, an ideal solution would have component activities equal to mole percent, ie o, a 1 mole percent solution would have an activity equal to 1, whereas a puresolution of a component would have an activity (index) of l00o Other standard states are often used as wello For a gas, the standard state is usually taken as 1 atmosphere pressure of that particular gas component An ideal gas with a partial pressure of i millimeter of mercury would have an activity of 1/760o If however, 1 millimeter of mercury pressure had been chosen as the standard state, the activity would be equal to 1 if the gas component was at a pressure of 1 millimeter and equal to 760 at one standard, atmosphere0 In metallic solutions, a standard state is often chosen such that the activity is eq:ual to the concentration in weight percent at infinite dilutiono This standard state, referred to as the one weight percent solution, is often convenient since compositions are generally expressed in weight percento

-23Fivee,Energy and Activity The free energy of a component is related to the chemical activity of the component by the relationship~ F - F = 4o575 T log10(a) III-4 where F is the free energy of the component within the phase and oF is the free energy of the component in its standard state in which a~ = lo Nbn-IdeaL Soltxionlas Most real solutions are not ideal. In order that a solution be ideal, the atomic species of the component must interact with those of the other components in the same manner that they do with their own, If this is not the case, the chemical activity of the component is altered from ideal behavior. The activities of nickel and silicon in molten iron are shown in Figures III-1 and III-2. N1ickel, as previously discussed, behaves ideally but silicon does not. The silicon atoms are more strongly associated with the iron atoms than with other silicon atoms, thus lowering the chemical activity of silicon below the ideal behavior predictiono The strong association between silicon and iron atoms is indicated by the facts that (1) energy is given off (exothermic heat of solution) when silicon is added to iron, and (2) intermetallic compounds of iron and silicon are readily formed in the solid phase. Figure III-3 shows the activity of copper in iron. Unlike silicon, copper atoms do not associate as readily with iron atoms as with other copper atoms. Therefore, the chemical activity of copper is increased above that predicted on the basis of ideal behavior. This is also shown by (1) endothermic heat of solution of copper, and (2) the

-241.0. 0.8,J,0.6 G 0.4 X -i t0 / 0.2 0 0.2 0.4 0.6 0.8 1.0 MOLE FRACTION NICKEL Figure III-1. Activity of Nickel in Liquid Iron Showing Ideal Behavior. (Standard State: Pure Liquid Nickel)

-251.0'' — 0.8 z Q 0.6 0 1. 0.-/ 0. 04 ___^ ^-y0: 0.0072 0 0.2 0.4 0.6 0.8 1.0 MOLE FRACTION SILICON Figure III-2. Activity of Silicon in Liquid Iron at 1600~C. (Standard State: Pure Liquid Silicon)

1.0..4.6.. 0 S 0.8 w 0.6 0. i 6 I-A 0.4 S. / 0.2 0.2 ~0 0.2 0.4 0.6 0.8 1.0 MOLE FRACTION COPPER Figure III-3. Activity of Copper in Liquid Iron at 1600~C. (Standard State: Pure Liquid Copper)

-27tendency to form two immiscible liquids at temperatures near the li4uidus. Although copper and silicon do not behave ideally, it is observed that their activities are proportional to concentration in dilute solutions. This quasi-ideal behavior is described by Henry's Law which says that the activity is proportional to concentration in dilute solutions. For this case it is convenient to use the 1 weight percent solution as a reference state0 Figures III-4 and III-5 show Henry's law behavior for copper and silicon in molten iron. Few solutions are ideal, or even quasi-ideal, and it is necessary to take this into account when calculating activities from concentrations. This is done by means of an activity coefficient. Figure I11-6 shows the activity coefficient necessary to calculate the activity of carbon in iron on the basis of Henry s Law. The activity coefficient is defined as- ff%(wte.%) III-5 The activity coefficient of carbon is 1 in very dilute solutions, i.e, carbon obeys Henry's Law. As the concentration is increased, the activity coefficient exceeds 1 by increasing amounts. For deviations from RaoultEs Law, Equation (III-5) may be expressed ias a = Y(mole fraction) III46 Conversion from One Standard State -to Another It is frequently necessary to convert from one standard state to another in order to make use of data which may give AF' as a function of temperature relative -to a reference state which differs from the desired one. For example, the free energy of formation of a metal Oxide may be known for the reaction~

-284 /../ u. i 0! 0 i I0 2 3 4 5 6 WEIGHT PERCENT COPPER Figure III-4. Activity of Copper in Liquid Iron at 1600~C. (Standard State: Infinite Dilution Referred to One Weight Percent Solution)

-296 5 0 / Q 2 0 2 3 4 5 WEIGHT PERCENT SILICON Figure III-5. Activity of Silicon in Liquid Iron at 1600~C. (Standard State: Infinite Dilution Referred to One Weight Percent Solution)

-30u. 4 o 5 Ca0 I 2 3 4 5 6 WEIGHT PERCENT CARBON 12 10 w u_ 6 w 0 4 0 2 HENRY'S LAW fI, 0 2 3 4 5 6 WEIGHT PERCENT CARBON Figure III-6. Activity and Activity Coefficient of Carbon in Liquid Iron at 1600 ~C. (Standard State: Infinite Dilution Referred to One Weight Percent Solution)

-31M(pure liquid) + Op(gas) - MO2(solid) III-7 but the oxidation of interest occurs from solution in a liquid metal solvent, say liquid iron. The activity of the metal must then be expressed in terms of its concentration in solution in liquid iron. Figure III-7 shows the activity of the metal, M, in solution in iron as a function of mole fraction, NMoA It is seen that the free energy change involved in the transfer of M from the pure liquid State A, to the dilute solution in ironI State B, must be determined. The free energy change is given by the expression~ F - R T in (aM(solution)/aM(pure liquid)) III-8 The activity ratio for the two Standard States is given by the atom fraction ratio, provided that the atom fraction in the solution is modified by the activity coefficient, f, as shown in Figure 11-7. The atom fraction of component M in solution in iron is given by the expressions c NM....III....-9 + 100-c M 55.85 where c is the weight percent and M is the atomic weight of component M. Equation (IIS-9), when applied to a dilute solution. reduces to.. 0.5585:N = c -- - II-10o If the standard state in solution, State B in Figure- III-7, is chosen such that the activity relative to that standard state is equal to the concentration in weight percent, c may be set equal to 1, (the reference state of a one weight percent solutions i.e., a = 1 at one weight percent). Correcting the mole fraction in solution for deviation from Raoult s Law, and noting that' the activity in the pure liquid. State A

-32i___ _______ ________A(PURE LIQUID) 8! I- I 0! 0 ~IL ~ / ^ — * o IMOLE FRACTION COMPONENT, M Figure III-7. Activity-Composition Diagram Showing Factors Involved in Converting Activities from One Stsndard State to Another.

-33in Figure III-7, is unity, the free energy change corresponding to the conversion of standard states from the pure liquid to infinite dilution referred to a one weight percent solution is given as: AF = R T in (0o5585 7 /M) II- 11 Equation (III-11) is the free energy change for the reaction: M (pure liquid) = M (1 wto % solution) III-12 Subtracting Equations (III-7) and (III-12), M(1 wt. % solution) + 02(gas) = M02(solid) III-13 for which the standard free energy change iso AF~ = AF~III-7 - 4~575 T log (O~5585 70/M) III-14 The equilibrium constant for Equation (III-13) involves the concentration of M in iron in weight percento The development above is equally valid for other solutions and with suitable modifications may be adopted for other equilibria and for solvents other than irono Effect of Temperature on Equilibrium Constant The free energy change for a reaction was defined by Equation (III-2) which may be written for a reaction in which the reactants and products are in their standard states as0 AF0 - AH- - TAS~ III-15 Expressing Equation (III-15) in terms of the equilibrium constant: log K =-(AHO/4o575 T)+(AS~/4o575) III-16 At the high temperatures involved in most metallurgical processing operationsa AL0H and AS' vary only slightly with temperature, so slightly that experimental techniques are seldom sensiti ent nough to determine them, Consequently, the enthalpy and entropy changes may be assumed

-34to be independent of temperature over reasonably small temperature ranges Effect of Pressure on Equilibrium Constant Le Chatelier's principle stateso "any change of the factors controlling the equilibrium of a system produces a shift in. such a direction as to minimize the change of the factor concerned", In terms of temperature this means that-o 1o endothermic reactions are more complete at higher temperatures, and 2. exothermic reactions are favored by lower temperatureso A second aspect of this principle is encountered in, regard to pressure changeso They are1. higher pressures shift the equilibrium toward, smaller volmes, and 2o reactions with volume increases are favored by lower pressures. This generalization is most important for those reactions which have unequal numbers of moles of gas in their reactants and products.

1. Chipman, John. Basic Open Hearth Steelmakingo A.IM.E., Chapters 14 and 16, New York, 1951. 2. Darken, L. S. and Gurry, R. W., Physical Chemistry of Metals, Metallurgy and Metallurgical Engineering Series, New York- McGrawHill, 1953..Chapter 14. 3. Kelley, K. K. "Contributions to the Data on Theoretical Metallurgy: X. High Temperature Heat Content, Heat Capacity, and Entropy Data for Inorganic Compounds", Bulletin 476, U. S. Bureau of Mines, 1949. 4, Elliott, J. F. and Gleiser, M., Thermochemistry for Steelmaking Vol. 1, Reading, Mass., Addison-Wesley Publishing Company, 1960. -35

CHAPTER IV KINETICS Chemical kinetics is a study of the rate at which chemical reactions occur. Reaction rates are important in the design of processes because they determine the size of equipment and the time involved in processing material with it, and therefore have much to do with economic feasibility. There are two general scientific approaches to the problem of describing a metallurgical processo The first approach as outlined in Chapter III was the thermodynamic approach The thermodynamic method permits the process to be described in terms of an end point to which the process will eventually converge or one which it is approaching during its operation. The second approach which will be now considered is that of reaction kinetics. This implies a knowledge of the mechanisms by which chemical reactions occurring in the process take place and a mathematical description of the process reactions in terms of those mechanisms. The foundation of present rate theory goes back historically to Arrhenius, who found 6hat for many processes the specific reaction rate constant k may be written as a function of temperature in the following wayk AeQ/RT IV-1 Alternatively, log k is a linear function of 1/T. The quantity Q although usually determined only from the slope of such a plot is regarded as the heat or energy of activation of the reaction. This relatioinship iS parallel to the one cOrreSponding to the equilibrium const ant. -37

-38The Theory of Absolute Reaction Rates Many have contributed to the development of the theory of absolute reaction rates. An outstanding number of successful applications have been made Eyring and co-workers, Modern rate theory assumes that any observable process may be described adequately in terms of the energy of the atomic configurations involved. For any conceivable way the reaction might occur we may imagine a plot of energy versus a distance coordinate as shown in Figure IV-1. The curve of he e reaction coordinate involves a peak or a maximum through which the reaction must pass, corresponding to what is termed the activated complex. The two fundamental principles involved in the reaction rate theory are both concerned with the activated complex. They are~ 1. The activated complex has an exceedingly short life and is in equilibrium with the reactants~ A chemical equation for the formation of the activated complex may be written and an equilibrium constant determined. This equilibrium constant is related to the free energy of formation of the activated complex in the standard state in the usual way. zLF* -=BT in K* r7-2 2. The specific rate of decomposition of the activated complex into products is a universal rate independent of the nature of the particular reaction or complex involved. The rate is RT)/h, where R is the gas constant, h is Planck's constant and N is'!:o..s number

-39U. Oz >-0 W4 ZJw 0 /0c 0 o / V)~~~~~~~~~(-) wX w C) L, I >0. z C) 4Q 0 z 0 o 4 bNd z \ H \: U 0 M

-40The reaction rate may then be expressed as: reaction rate = [RT/h ] e-L*/RT e S*/R [YR 2...... * ] IV-3 [CR1 CR2.....] The following facts are to be noted about the terms of the above re actions1. The first term contains only universal constants and the absolute temperature. 2. The second term is the principal temperature dependent term involving the enthalpy of activation. 3. The third term depends upon the entropy of formation and it is expected if the complex is simple that A\S* is quite small, but that if the complex is complicated (as compared with the reactant) in atomic configuration *S is large and negative. 4. The fourth term involves the activity coefficients. 5. The fifth term is the product of the concentrations of the reactants. A complete description of the absolute reaction rate theory may be found in the literature and an excellent simplified treatment has been 2 presented by Darken. Classification of Reactions A reaction may be classified according to its molecularity, that is, the number of molecules or molecules plus atoms taking part as reactants in the formation of the activated complex. On this basis the elementary steps of any over-all reaction are designated monomolecular,

-41bimolecular, trimolecular and so forth. An over-all reaction involving many steps, however, cannot properly be classified in this manner, that is, only the individual elementary steps of an over-all reaction are suitably described in this wayo Over-all reactions are commonly classified empirically according to the number of concentrations to which the rate is proportional. The reaction order may be defined as the sum of the powers to which the concentrations of the reactants must be raised to give a satisfactory solution to the rate equation. In many simple cases, the observed over-all reaction proceeds principally by one chain or sequence of steps and one step is so much slower than the others that it alone is essentially responsible for the observed rate. This slow step involves, as do all steps, the formation of an activated complex and its decomposition. If this step is unimolecular, the rate of the over-all reaction will be of the first order. The reaction rate is the rate of disappearance of reacting species which is then proportional at constant temperature to the concentration~ -dC/dt = kC Iv-4 Upon integration, this gives In Co/C k (t - to) where C is the initial concentration at time to. For kinetic treatments of more complicated cases, the reader is referred to the sources given at the end of the chapter. Mass Transport as Rate-Limiting Step At the high temperatures which are usually involved in metallurgical processes the rates of chemical reactions are in general. very

-42largeo Consequently, the rate-determining step is most often that of mass transporto For the formal development of the fundamental diffusion equations, the reader is referred to the references at the end of the chapter. It should be noted that an excellent presentation of these equations and suitable boundary conditions for them are presented by 2 Darken Transport in solids is by diffusion and is therefore governed by Fick's laws If the rate of a reaction is limited by diffusion in a solid phase, the rate may be expected to be lowo In fluids (gases and liquids) transport occurs by diffusion and convectiono Generally forced convection is encountered and under these conditions the composition of the bulk of the fluid is practically uniform, with appreciable concentration differences only close to the phase boundary0 Thisis represented schematically in Figure IV-2 for a case where a reaction prod.uct denoted as i is being removed by the fluid. The rate of transport of i away from the boundary is in moles per secondcentimeters squaredo. = -i (x) + i IV-5 where Di is the diffusion coefficient, A the phase boundary area, c. the concentration of i and vx is the flow velocity of the liquid in the x direction, ivx represents the convection contribution to the transport; v cannot normally be evaluated, but at the boundary vx O0 Hence, dn =-Di -Ak ( Ci Vas Figure IV-2 shows Ci blk) - Ci xO)I -i =. C i ~~ )^ - (~ i/7 x\

-43Ci(x=o) zI w \ O U1 Ci(BULK) -.. -- DISTANCE FROM PHASE BOUNDARY, X Figure IV-2. Concentration Profile in a Boundary Layer.

-44so~ dni D- A [Ci (x=O ) - Ci (buk)] I-8 adt s where 5i is the effective boundary layer thickness. In general, 5 cannot be calculated except for a few cases, but its value depends upon D, being larger for larger values of D, and also on the convection conditions, being smaller for higher flow velocities past the boundary. When the reaction is between a gas mixture and a liquid solution or between two liquids, one must consider two boundary layers, one in each phase. Darken2 has applied the above general development to the carbon boil in the open hearth process, by assuming that the situation prevailing in the open hearth is essentially that of oxygen diffusion from a slag through a thin layer or film in the metal phase (neglecting the boundary layer in the slag phase) and mixing by convection beyond this film. Darken has calculated the rate of carbon drop estimating the film thickness to be about 0.003 centimeters and choosing a reasonable value for the diffusivityo From Fick's first law, it may be shown that the rate of carbon drop on the basis of this model iss -d[C]/d t =D ([ - [0]) r9 1x5 16 where 1 is the bath depth and 5 the film thickness, For conditions during oreing, the following average or approximate values may be used; [0] 0.23%s (solubility limit at 16000C), [0] = 0.04%, =-13.inches se -4 2 34 centimeters (average bath d.epth.) D = 1 x 10 centimeters2/second, and. 5 = 0.003 centimeters.

-45On this basis, d[C] = x 10 4( 0o23-0o04) 12 x 3600 = 050%/hr IV-10 dt 3 x0o003 T which is in good agreement with the observed carbon drop during heavy oreingo A similar calculation for the rate of carbon drop during normal boil conditions setting []se - [0] = 0o04 gives Oo.11 per hour, a figure se very close to the observed average rate. It should be noted from the above example that selection of suitable rate data permit the process designer to predict the kinetic behavior of a processo To B. King6 has presented a number of excellent examples which are applicable to metallurgical processes operating under vacuum conditions.

REFERENCES 1. Eyring, H. J. of Chem. Phys. (1934) 107o 2. Darken L. S. and Gurry_ R. W. Physical Chemistry of Metals, Metallurgy and Metallurgical Engineering Series. New York, McGraw-Hill, 1953. 3. Barrer, R. M. Diffusion in and Through Solids. Cambridge University Press, 1941L 4, Jost W. Diffusion in Solids, Liui-ds andi Gases. New York~ Academic Press, 1952, 5, Glasstone, Laidler and Eyring The TheTory of Rate Processes, New York~o McGraw-Hill Book Co., 19 41 6. King, T. B. Thermodynamics and Kinetics in Vacuum Metallurgy, Vacuum Metallurgy, ed. R, P. Bunshaw, New York- Reinhold Publishing Co,, 1958. -46

CHAPTER V TIE THERMOCHEMICAL MODEL A thermochemical model of a process is a dynamic description of the process taking into account mass and heat transfer, and kinetics, along with instrumentation and control. The model permits an accurate method of calculating the operating characteristics of a process under all possible conditions, including variations in process temperatures, pressures, flow rates, and feed compositions. The complete model is suitable for adaptation as a computer program program permitting simulation of the process and dynamic predictions of its operating characteristics or optimization of the process under a given set of limiting conditions. This will be treated in greater detail in Chapter XXVII. It should be noted that the thermochemical model, or often only a limited form of it, is the first step toward good process design. In order to merely specify the size of a process, a general knowledge of the desired input and yield are necessaryo This can be given [by a mass balance of the system, often based'on the experience with previous equipment of a similar type. In addition, the energy or fuel requirements are equally important. The completion of a mass and energy balance for a process is often sufficient to quantitatively evaluate the effect of changes in process operating variables on the performance of the process. Mass -Balaance The mass balance is the most important part of the thermochemical model. The mass balance may be written on the basis of previous -47

-48experience or on the basis of known equilibrium relationshipso The principles of writing a mass balance were outlined in Chapter IIo The purpose of this section is to introduce some of the difficulties which may be experienced in practice, and indicate some of the approximations which are often advantageous to make in order to achieve the goal of a reasonably accurate set of material relationships0 In practice, overlapping data are often available which permit a check on the mass balance. Data on an iron blast furnace, for example, might give the mass of the inlet and outlet streams$ as well as their composition. It is possible, hIowever, that the balance for a given element may not check.s' Once one has ruled out the possibility of accumulation or depletion of the element from somewhere inside the system (a real possibility under conditions where the burden is altered or new refractories are used to reline the process container), a decision must be made regarding the relative accuracy of the data, and on which part of the data the balance should be based. In making this decision, the methods used to determine the data must be given consideration. -rthermore, the alternative difficulty of having insufficient data may Occur. In this case, previous experience and the astute judgement 6f the process engineer are brought to bear on. the proble mO Lacking hot metal analyses, in the case of the blast furnace cited above, for elements which are strong oxide formers, one can safely assume that these elements report completely in the slag, Such elements would include calcium, magnesium, and aluminumj but would. not include silicon f The assumption that all elements which are not strong oxide formers report in the hot metal is also a reasonably valid one, Such elements would include iron and manganeseo

-49In the face of missing thermodynamic and kinetic data, the assumption that a given reaction goes to completion within the alloted process time is often a valid basi$ for design purposeso Consider for example, the Dortmund-Hdrder degassing process in which low carbon steel is drawn by vacuum from a ladle up into a vacuum chamber, and then released to flow by gravity back into the ladle. A schematic description of the process is shown in Figure V-1. Only a small fraction of the liquid metal in the ladle can be drawn up into the vacuum chamber. The question facing the process designer is- "How many cycles of the degassing operation will be required to lower the gas content of the metal in the ladLe to a desired level?". An approach to the problem which would appear feasible is to assume that the metal drawn up into the vacuum chamber is completely degassed, and that upon being returned to the ladle is completely mixed with the ladle material. For this case, the material balance for the degassing operation is given by the relations C = Co ( X)n V-l whereo n number of cycles C = concentration of gas in the metal in the ladle after the nth cycle. 3C initial gas concentration in the metal X = fraction of ladle material which is drawn into the vacuum chamber during each cycle. The results of actual data taken from the operation of the process are compared with Equation (V-i) in Figure V-2. The agreement between the two curves shows the assumption to be valid.

-50STEAM EJECTOR VACUUM SYSTEM CARBON ARC HEATER VACUUM VESSEL SUCTION NOZZLE-\ DEGASSING LEVELS ORMAL \EVEL LADLE Figure V-1. Schematic View of Dortmund - Hdrder Hfttenunion Vacuum Treating Process.

-5110 r....... 10 o OBSERVED CO CONTENT -CALCULATED CO CONTENT FOR X =0.1, EQUATION V-1 8 6 i -- - Figure V-2. Removal of CO from Liquid Steel by DHHU Vacuum I-' %% 6 I-. ) 0o 0 5 - 0 15 20 Figure V-2. Removal o CO from Liquid Steel by DHU Vacu Treating Process.

-52The success of the assumptions used to predict the perfortI mance of the Dortmund-Horder degassing process should not be taken as a justification for their use in all cases. It should serve, however, to indicate the possibilities which exist for the process designer WhO is aware of the behavior of metallurgical processes and of the limitations of idealized treatments of those processes. Heat: Balance The heat balance is founded on the mass balance and may be determined using the principles outlined in Chapter II. The difficulties encountered in specifying a complete enthalpy balance for a process often arise from problems encountered in the mass balance, i.e.,comaposition and mass of streams entering or exiting the process. The lack of accurate thermodynamic data often hampers the writing of a reliable heat balance. In the face of the difficulties indicated above, the process designer often lumps the error into a term called "heat loss" which includes in addition to the radiation and convection losses from the physical system, the cumulative errors in the other terms in the heat balance. It should be noted that the heat losses are quantities which may be calculated with a reasonable degree of accuracy in many cases. Hence, a better procedure is to estimate the accuracy with which each term in the heat balance may be determined. Shifts in the process variables could then be evaluated with a clearer picture of the limitations on the calculated result. Kineties The subject of process kinetics is briefly introduced here in order to complete the descriptive facets which make up the thermo

-53chemical model. The specific treatment and, a discussion of the limitations of the several approaches to the kinetic description of processes is reserved until Chapter)iU.H where specific examples will be introduced in connection with simulation of processes. The factors which are of importance in describing process kinetics and the rate determining mechanisms which play a role in determining these kinetics have been outlined in Chapter IV, The difficulties arise in integrating these rate determining mechanisms into the overall behavior of the process, i.e., of providing some quantitative and limiting description of the entire process on the basis of the behavior of the many components and multitude of reactions which generally make up a metallurgical process. There are three possible approaches to this problem. The first and most. difficult being an attempt to summarize the kinetic behavior of the process in terms of the rate mechanisms of all, or more reasonably, of the two or three most important ones, This approach, although the one which is most correct, is usually limited by either the lack of data on the kinetics of the system or a limited knowledge of the combined behavior of several reaction paths which may be competing or interrelated in some other fashion, In a simple case in which a single transport process is rate determining, this approach is a highly satisfactory one. The second and most promising approach from a commercial standpoint is the experimental determination of overall rate constants for the process. The determination of these rate constants is often difficult and requires the use of high speed computing equipmento If such constants can be determined for a range of operating conditions,

-54the process dynamics may be specified with a relatively high degree of accur acy without precise knowledge of the behavior of the reacting components of the process. This approach is often made from a less rigorous standpoint, that of averaging the known process data and estimating a reaction path for the process. This approach is often a fairly accurate one but lacks dynamic response to variations in process conditions, temperature for example, since the reaction path is predetermined. It is however, a conveenent assumption, and one which has some merit in predicting process behavior. The third and final treatment of process kinetics is the rather weak but often unavoidable assumption that the reactions go to completion or reach equilibrium in the time alloted, i.eo, the ideal. process. The limitation of this approach is obviousO The designer is faced with the predicament of proposing a process for which he has no sound foundation from which to recommend a process cycleo When such a stand is taken with regard to the rate of operation of a process on the basis of previous experience with similar systems, the limitation is not a great one. It should be pointed out however, that further improvement in the process operation will undoubtedly rest on a knowledge of the kinetics of the system and that lacking it, efforts should be made to obtain it from actual operation experience at the earliest opportunity. The importance of instrumentation and control cannot be overemphasized. The lack of suitable instrumentation can prevent an intelligent and informed operation of a process, and often at a strong economic penalty. Incorporated with the thermochemical model, and specifically related to its limitations and inadequacies, must be the

-55" requisite inStrumentation and provisiona for control of the process during its operating cycle, The thermochemical model can serve as a guide to design and operations but aite is t integrAtion with imaginative and sound instrumentation and control that will permit significant ad ances;in the proceas industries.

CIAPTER VI EQUIPMENT DESIGN AND fSET3SCTION An important area in which the process metallurgical engineer will be required to make decisions is that of equipment design and selection. The replacement, improvement, or construction of new facilities for the operation of metallurgical unit processes is an activity which is constantly being carried out in an industrial organization. To make such decisions it is fundamental that the metallurgical process engineer be completely familiar with all aspects of the unit process including a knowledge of the raw materials, products, and intermediate constituents which may be present; that he know the process temperatures, pressures, and concentrations throughovt the operation, as well 6s the physical characteristics and the chemical composition of the substances involved, and knowing these things and having in hand, energy and material balances, he will be able to make competent design decisions. While it is not proposed here to go into the details of the design of high temperature processing equipment, a brief description will be presented of some of the factors which must be considered. The first dediaion which the design engineer must make is the size and type of unit in which the process will be carried out, and how that particular unit will integrate with the overall processing.system. In general, since many variations are possible in the selection of equipment, it is often necessary to make an economic balance based on the operation of the process in the types of units under consideration. This economic balance will involve an analysis of the capital in estment required, the operating overhead, and other factors which enter into the determination of the total -37

-58cost of a given piece of equipment. The general design may depend u.pon several varying factors and often it is necessary to make a parametric study of the particular design possibilities in order to determine the optimrum one, High speed computers are often of great assistance in per-, forming such a tasko Once the size and type of vessel has been determined, decisions must be made, ones which are often not independent of the selection of the size and type of vessel, on the materials of constructiono These decisions require that the specific characteristics of the process be known in complete detail in order that materials may be selected on the basis of their strength, which of course, is influenced by the environment and temperature involved, their corrosion resistance or resistance to attack by the substances with which they will be in contact and the economics of the particular materials which are possible choices0 In the interest of economics, the materials of construction may vary throughout the piece of equipmLent in which a proces is i caried out0 The particular materials selected being a function of those point conditions which exist in a given region of the processo An exam.,ple in this regard is given in the construction of basic open hearth fiurnaces where a basic lining is used for the hearth of the furnace, but in general-, sil'ica (acid type refractory) is used for the roof~ Such a decision is based strictly on economics and may be modified according to current conditions0 In the particular instance cited, consideration is now being given to basic roofs for open hearth furnaces Improvements in the processes for the production of high quality alumina have significantly lowered its price and., although at the present time it is more expensive than. silica, it may be chosen as a suitable material on the basis of greater life,

-59The selection of specific materials for the construction of equipment in which metallurgical processes are carried out is often an art. The process metallurgical engineer who is working in the area of equipment design will undoubtedly rely on pre vious experience and on the results of studie both laboratory and plant which have been conducted with regard to interaction of various materials under different conditions of temperature, pressure and compositiono The problem of equipment design is an expansive one and often it is difficult to arrive at a suitable solution for the problem of selecting the optimum equipment and conditions under which to operate the process0 With due regard for this, it may be stated that one of the most important factors involved is a thorough knowledge of the unit process, itself, and it is toward this goal that the remainder of the text is devotedo Attention is called to the list of supplementary references below which treat in some detail the problems mentioned above.

METRENCES lo Basic Open Hearth Steel Making0 Physical Chemistry of Steel Committee, AIM, New York, 1951, Chapters 1, 3, and, l8o 2. Schuhmann, R o Metallrgical Engineering Cabrd.ge, Mass.o AddisonWesley Press, 1952, Chapter 10o 3o Brownell, Lo Eo and Young, Eo Ho Proes Euipent Designo New Yorks John Wiley and. Sons, 1959o 4. Trinks, Wo Industrial:Furnac-so 1, New York: John, Wiley & Son.s 1950o 5..Norton, F. Ho Refractories New York o McGraw-Hi.TiLI, 1.949o 6. Etherington, Ho Modern Furnace Technology, Charles Griffiran Londo 1944. 70 Buell, Wo C.o. Jro The Open Hearth Furnace -Its Design, Construction, and Practice0 CleTeland_ Pe.nton Publishing Coo, L939o 8. Lindemuth, Lo Bo Design, Construction, Operatson of Open Hearth mrnaces with Basic Roof Blast Furnace_ an Steel Planto 29, 194l, 11090 9o Camp, Jo M0 and Francis, C. Bo The Making., Shaping and Treating of Steel. United States Steel Coo, Pittsburgh, 1951. 10. Vilbrandt, F. Co and Dryden, C. Eo Chem ical Engineering Plant Design New York- McGraw-Hill, 1959o 11. Chemical Engineers Handbook John Ho Perry, Editor, New Yorks McGrawHill, 1950. 60o

Part II MATERIALS PREPARATION, TREATING AND HANDLING -61

CHAPTER VII SINTERING Sintering is a process employed to make fine materials useful by heating them to an elevated temperature such that the small solid particles in contact with one another adhere and agglomerate into large useful particles without the process of fusion taking placeo Sintering of fine materials occurs as a result of the driving force of the excess free energy of the powder over that of the dense solid by virtue of the different surface areas for the two states. Considerable research has been carried out to determine the mechanism of sinteringo(1,2) The sintering of large quantities of material is often necessary in the operation of a metallurgical plant~ This process provides an opportunity to use fines and of ten makes a particular process feasible by converting the fine materials available as charge material into a useful agglomerated form. Sintering is usually accomplished with the Dwight-Lloyd machine. A schematic diagram of a typical sinter strand is presented in Figure VII-1o For several years BISRA (British Iron and Steel Research. Association) has been. investigating the fundamentals of industrial. sintering processes o(37) It is principally from these sources that the following engineering design relations for industrial sintering processes is developed About 50 years ago Dwight and Lloyd devised their first continuous sintering machine to convert non-ferrous ore fines into a suitable size for further refiningo The basic features and. principles have -63

-64CHARGE HOPPER MIXER BURNER \\ [ FEED HOPPER MOVING GRATE L J O' IND BOX \( 0 SEPARATING SCREEN A D FAN Figure VII-1. Schematic Diagram of Dwight Lloyd Sintering System.

-65not changed during those 50 years. Originally, for copper ores, sulfide fines were distributed in a thin layer along a traveling belt made up of grateso They were ignited and the sulfur was burned out of the ore as air was drawn through by large fanso The fines fused together forming a strong sinter cake which was desirable for reverberatory or blast furnace chargingo The basic difference between the above process and. the process used for ferrous ores is the self-contained' fuel of the copperbearing sulfide materialo In the ferrous process carbon in the form of coal or coke has to be added to obtain a burning processo As shown in Figure VII-1 the material for sintering is taken to a primary mixero This mixer mixes the fines and. added fuel and perhaps water, depending upon the state of preliminary agglomeration desiredo The mix is then charged. onto the moving belt of the conveyor where it passes under a set of flame nozzles which ignite the bed. The fuel burned. in these nozzles is usually blast furnace gas enriched with coke oven gaso Air is drawn through the burning bed by the suction system below and at the end of the strand the sinter drops off the pallets onto a static screen where the large particles are taken off and the smaller ones are returned to the sintering process as recycleo Heat Balance In computing a thermal balance for the sintering process one needs only to account for the reactions taking place during sintering, particularly the burning of the fuel, the sensib.le heats of the input and output streams and the estimated heat losses during the processo Such a balance is presented in Reference 8 for the sintering of a lead

-66ore. The fuel requirements to provide a normal temperature distribution down the bed for a number of sintering mixes are shown in Table VII-1, together with the net thermal requirements which may be seen to be relatively independent of the material to be sintered. The net thermal requirement has been obtained by subtracting the heat needed for endothermic reactions from the heat input of the coke and dividing the resultant figure by the residual weight of the solid. The fuel, requirements given in Table VII-1 are for experimental materialso It is expected, however, that the actual metallic bearing ores which would be used in industrial practice have similar characteristicso The optimum fuel requirement varies slightly with different sintering mixeso One may account for this by consideration of the reactions which take place during sinteringo The composition of the ore also determines the peak bed temperature or the temperature at which the sintering actually takes placeo Variation of this peak bed temperature will cause a variation in the optimum fuel requiremento Variation in the carbonate or water content of the sinter mix will give a variation in the width of the hot zone, since the hot gases from the ignition process pass down through the bed, driving off the water vapors and decomposing the carbonates If the matching of the heat front, often taken to be the point at which the temperature rises above 1000~C and the flame front is different, the width of the hot zone will increaseo This is illustrated in Figure VII-2 which shows the broadening of the heat front in the sintering of marble (CaCi3) caused by incomplete calcination in advance of the flame fronto'Combustion is delayed in this case, giving rise to a broader combustion zone and an increased specific air volumeo

-67TABLE VII-I Fuel for Normal Temperature Distribution in. Sintering Net Thermal Requirement Material Water % Coke % BTU/ Alumina 3 5 580 Mullite 3 5 580 Silica 3 4~5 523 9 5 504 Alumino-Silicate 22 7.5 593 brick 32 9 558 4)0 10.5 540 Al-Si brick 83% 20 8.3 665 Marble 17% Al-Si brick 67% Marble 33% 20 8 3 580 Al-Si brick 50% Marble 50% 16 8.5 593 Al-Si brick 33% Marble 67% 16 9 558 From; E. W. Voice and R, Wild, Journal of Metals, p. 105, 1.958.

-680 —--- -----—,_ ALUMINO-SILICATE BRICK L —-- MARBLE In z 3 3.. — 0 / 0 / 4 _-, —--- # a 0 200 400 600 800 I00)0 1200 1400 1600 0010o~0 0 200 400 600 800 1000 1200 1400 1600 TEMPERATURE, C Figure VII-2. Temperature Distribution for Two Sinter Mixes When Combustion is Occurring Approximately at the Midpoint of the Bed.

-69It should be noted that the peak temperature is also reducedO Figure VII-2 also shows a reasonably well-defined flame front occurring during the sintering of alumino-silicate bricko In addition to the variations in the amoun.ts of water and carbonate present in different ore mixes, the specific heat; will also change Despite these factors, however, the net thermal requ.rement in general is about the same for a wide range of sinter mixeso The high temperatures which are reached during sintering are possible because a hot zone travels through the bed and full use is made of heat recuperation between gases and solidso Thus the fuel has to supply heat for endothermic reactions, sensible heat to the solid material in the sintering zone, and make up for heat losseso Since the width and temperature distribution of the sintering zone are substantially the same for all materials, and the heat capacity is proportional to the weight of the material as are the heat losses, there is a theoretical basis for the experimental fact that the net thermal requirement is essentially independent of sinter mixo Air Requirement There is a definite rate of travel of the hot zone down. through the bed which is independent of combustion. The heat generated in the top layers may arrive at a lower level in the bed. in the same instant as combustion is taking place giving rise to an increase in the bed temperature; or it may arrive before or after combustion in which case it will widen the high temperature zone without raising the temperature reachedo These two conditions may be termed matching and mismatc:hing since the

-70extent to which the heat front and flame front are coincident controls the temperature reached in the bed. Under optimum conditions, -the combustion zone will be a narrow high temperature areao The specific air volume required for the sintering process is controlled by heat transfer properties rather than combustiono Small additions of water to the bed delay the initial rise in temperature at any level but also increase the rate of rise above 100~C, Large additions of water cause a very pronounced delay in. the temperature rise above 1000~Cand thus a considerable increase in the volume of air requiredo The heat needed to evaporate the water and decompose the carbonat~es must be supplied by hot gases passing down throug:h. the bed; thus the presence of water and carbonate must delay the progress of the heat front to some extento In the sintering process, the temperature in the combustion zone is between 1300 and 1500~C. Thus the sensible heat of the gas leaving this zone is high and the delaying effect of endothermic reactions is minimizedo Lower down in the bed, calcination liberates more gas at a relatively high temperature which also carries heat down through the bedO Still further down the bed, water evaporation takes place. Thus both carbonate and water in a sinter bed will increase the required air volume but the presence of water should have a greater influence The specific air volume is determined by three factors~ (1) the mean air flow; (2) the rate of travel of the combustion zone through the bed; and (3) the bulk density of the mix These factors are interrelated. in such a manner as to produce a relatively constant air volume independent of sinter mixo

-71The specific air volume is controlled by heat transfer and, increases in its requirements with increasing quantities of water in the mix. It should be noted that in commercial sinter plants considerable leakage occurs at the pallet seals so that the actual amount of air going through the bed is usually only half of that drawn in at the fan,, and the plant operation should be designed on this basiso The minimum specific air volume requirement is approximately 25,000 standard cubic feet per ton. Importance of the Width of the Combustion Zone The combustion zone thickness depends on the extent to which the various fronts which travel down through a sinter bed are in phase First, there is a water evaporation front which must keep ahead of the combustion zone or the bed will go ou.t Secondly, there is a calcination front which will cause a marked broadening of the combustion zone if it lags it. Finally, there are the heat fronts and combustion frontso The extent to which these travel down the bed together will, largely determine the width of the combustion zone. A narrow combustion zone will give high fuel efficiency and is a condition which should be aimed at in normal iron ore sintering practiceo Engineering Relations for Sintering Operations The initial question facing the design engineer is the rate at which air may be drawn through the bed. This is determined by the bed permeability which is usually defined as the flow through a unit q of material under a unit pressure gradient, the units being self-consistento

-72This definition leads to the following equation5 (3) F (h)n p -F^ (n (VII-1) A s where p = the permeability given in British permeability units, F - the total sintering air flow in cubic feet per minute at 30 inches of mercury and 60~F A - the grate area for sintering in square feet h = the depth of the bed in inches (taken before sintering) s the suction under the bed n =coefficient equal to 1 if the flow is streamlined or o5 if it is turbulente A number of experiments carried, out on various sinter mixes before and after ignition have shown that the exponent, n, is independent of bed conditions and is approximately equal to 0o6. With change of pressure and temperature conditions, the permeability equation may be corrected. assuming ideal gas law behavioro Air Flow Rate The amount of air required, per ton of material can be found by the following relation. VI F - 60 (VII-2) where V, the specific volume of sintering air per ton of raw material in cubic feet at 30 inches of mercury and 60 ~F I = the input material rate in tons per houro

73Input Material Rate The material input rate depends on the pallet speed, the available volume for the material, and its densityo I h (v )w( -i-) (VII-3) 12 12 2000 where v the strand speed in inches per minute w the strand width in feet B the bulk density of the feed in pounds per cubic feeto The above equation gives the dimensions of the strand needed for any given input tonnage. Combining Equations (VII-l) and (VII-2) and rearranging terms, the input is found to be a function of the suction under the bed: 60 WL p (s)0o6 (VII-4) V h where L. strand length in feet This equation shows that the strand dimensions, specific volume and the permeability determine the input Output Material Rate The output of a sintering machine is the difference between the input and recyleo Q - I(y-c) (VII-5) where y = the yield as fraction of charged material which is discharged c = the circulating load as fraction of charged material which is recycledo

-74Fan Horsepower The power needed for the fan depends on the air flow that takes place through the wind legs, and. the suction. The theoretical power can'be obtained, E 6 55 (VII 6) th 6350 where Eth = the theoretical horsepower requirement for the fan operating on the sintering bed, The actual horsepower is larger due to the leaks in the system9 pressure losses in the air system, and the inefficiency of the fano Sintering Time The time from entering the sinter machine until the sinter is discharged at the other end. is: 12 L t >1 I-7) where t = the time in minutes to reach +he peak wind box gas temperatures. From Equations (VII-3 and VII-4), the required length of the strand for sintering iso 1o6 v BV(h)1.6 288000p (s )0 6 ( 8) Rearranging terms and combining Equations (VII-7 and. VII-8)o By(h).I"6 t =,.) 6 (-9) Equation (VII-9) shows that the depth of the bed greatl.y infl.uences the sintering timeo

-75Flame Front Speed The rate at which the flame moves through the sintering material and the depth of the bed are the determining factors in the sintering time: hf = (VII-10) Experiments have shown that the flame front velocity is linear with time as indicated by Equation (VII-10)o This equation may be rearranged in the form. 24000F f V A B (VII-11) The flame front speed is shown to be dependent on the air flow which is a function of permeability, the limiting factor in the flame front speedo The direct application of the derived equations above involve some knowledge of the processo Undoubtedly the design of a sintering operation will require laboratory or pilot plant experimentation~ The above relationships, however, should prove to be extremely useful in permitting a prediction of the desired variation in controllable parameters that should accompany a change in sintering practice at a given industrial planto The relationships derived apply as well to pelletizing processes.

REFERENTCES lo Roberts, JO Po "Mechanism of Sintering"o Meta ll.rgia, 42 (1950) 123 o 20 Kingery, D, (edo)o High Temperature Processes, Cambridge, Masso Addison-Wesley Press, 1959. 3. Voice, Eo W,, Brooks, So Ho, Davies, Wo, and Robertson, Bo Lo Symposim. on Sinter, Special Report No 53, Iron and Steel I:nstitute, London, (1955) 43 4o Voice, Eo Wo, Brooks, So Ho, Davies, W,, and Robertson, B, Lo'Factors Controlling the Rate of Sinter Production," Journal of the Iron and Steel Institute, 175, 1953o 5. Voice, Eo W,, Brooks, S. H,, and Gledhill, P. K'"The Permeability of Sinter Bedso" Journal of the Iron and Steel Institute, 174, (1953), 136o 60 Voice, E W,, Lang, C,, and Gledhill, Po Ko "Investigation of the Effects of Controlled Variables on Sinter Qualityo" Journal of the Iron and Steel Institute, 167, (1951), 393~ 7, Voice, Eo W, and Wild, Ro "How Theory Can Help Make More Sinter," Journal of Metals, 10, (1958), 105o 8, Butts, Ao Metallurgical Problems. Metallurgy and Metallurgical Engineering Series, New York~ McGraw-Hill, 1953, Chapo 14, 9~ Wendeborn, Ho Bo "Sintering as a Physical Process," Journal of the Iron and Steel Institute, 175, (.953), 280. -76

CHAPTER VTI ROASTING - CALCINING - DRYING A metallurgical unit process which is often very use~ful in an integrated operation is one which removes a volatile constituent from a solid material,~ The unit process may be termed roasting, calcining, or drying, depending upon. the particular operation which is being carried out, These unit processes, however, are quite similar, The term "drying" is applied to the removal of water from a material The water may be present either as a liquid or vapor or as chermically combined watero The nature of the process differs with these differing circumstances, but the basic operation is essentially the sameo, "Calining" defines an operation in which carbonates are decomposed'by heat, evolving CO2 gaso "Roasting" is a similar process except that it involves reaction between the charged material and. the combination gaseso This reaction is one of oxidation in which sulfur is removed from ores in the form of S02o Roasting requires, in addition. to the supply of hot-combustion gases, a free excess of air in amounts above those theoreticall.y re quired for the roasting operation in order that each particl —.e of ore may have sufficient contact with oxygen. In general, precise control of the amount of excess oxygen is necessary in order to prevent further oxidat-ion of the roasted material. Roasting and sintering are unit processes which are often carried out simultaneousl.y in a combined process "roastsintering", In view of the fact that the process equipment and engineering approaches to these operations are quite similar, the remarks of this chapter will be restricted to one, calcination. It should be kept in mind, however, that the treatment presented here is one which m.ay be suitably applied to all of these unit processes, -77

-78Lime and magnesia have long been important industrial materials. As is well known, the major tonage outlet for magnesia is in the refractories industry in which it is employed as "dead-burned grain magnesite." Lime is also used as a refractory material, since it has excellent refractory properties. However, it cannot be of service alone since exposure to the atmosphere after calcination will allow it to be slaked by the water vapor in the air, and fall to a useless powder. It should be noted that the use of burnt lime in the open hearth furnace has the advantage of decreasing the heat period and heat requiremento Calcination is carried out in many types of furnaces, both gas and electrically heated, and on hearths which are rotary, stationary or of the tunnel type in which the contents are carried through in small cartso Of particular interest'to the design engineer is the lime kiln performance, ioeo, the process cycle described in terms of the time required for calcination and the thermal requiremento Thermodynamics of Calcination The reaction that occurs in calcining a chemically pure limestone may be expressed asCaC3 = CaO + C0 VII-1 The equilibrium constant for Reaction 1 may be expressed asK = Pco2 VIII-2 The free energy of decomposition may be expressed as a function of temperature aso ZF~ = 42,490-37o7T -4o575 T log (PCO ) VI T-3

-79Equations (VIII-2 and VIII-3) may be utilized to predict the equilibrium pressure of CO2 in contact with heated limestone, and the temperatures at which appreciable calcination of the limestone can take placeo Kinetics - Mechanism of Calcination In addition to predicting the temperatures at which decompposition of the limestone can take place, it is necessary as well to consider the kinetics of the reaction. Although several experimental investigations have taken place to elucidate the exact manner in which the decomposition takes place, little success has been obtained in predicting a suitable mechanism for calcination. It has been found, however, that calcination of limestone takes place at a definite boundary plane, i e., the boundary of two solid phases, one of lime (CaO) and the other of limestone (CaCO3). This plane progresses from the surface of the piece of limestone being caine-. toward the center at a definite rate and is maintained in about the same shape as the external surface of the stone Other investigators have noted, however, that this particular mechanism does not always applyo In order to permit a precise description of the rate of calcination to be written in terms of the ratelimiting mechanism, further experimental investigation is necessaryo Based upon calcination data, Furnas derived the following equation that can be used to determine the progressive penetration of the zone of calcinationo log R = OoO03145T - 3.3085 VIII-4 Where R = rate of advance of the boundary line of calcination in centimeters per hour, T = temperature of the surroundings in degrees centigrade.

-80Equation (~VIlrT-4) is purely empirical, and, no d theoretical. basis should be attached to it.o The equation has been derived. on the basis of an. approximation that the line of calcination advances at a constant linear rate and is dependent only upon the temperature of the surroundings, and. is independent of the size and shape of the particle, the degree of calcination, and previous heating. Since the rate of penetration of the line of calcination is ass-med to be constant throughout the entire period, the length of time required to calcne is direct y proportional to the size of the pieceo Conley3 performed a set of experiments on the effect of temperature on rate of calcination of high calcium, limestone of cylindrical shape at one atmosphere pressure of carbon dioxide, On the basis of his data, he derived the equation R = Oo005254T - 4O702 VIII-5 In view of the differing resul.ts obtained, in these two investigations, it must be coneluded that the rate of calcination is highly dependent upon. the type and co ndition of stone as well as the -condiLtionrs pre-vailing in the kilnr Undoubtedly, in practice it would be necessary to conduct a set of tests to determine the rate of ca.cination of the material to be processed before one specifies a set of operatting condxitions for a given calcination process, Calcination time depends upon the prevailing external conditions of the stone, conditions which govern the heat su.pp.y to the stone surf ace, It is also a function of temperature of calcination, and. of preheating and calcining reaction heat requiremenntso t is, in addition, a matter of the

-81extent of external surface, of the exposure of the surface, of the thermal conductivity of the stone and lime, and the required calcining depth. Heat Balance Although the over-all heat requirement for the kiln may be specified by a heat balance for the process, it is often to the advantage of the designer to divide the kiln operation into several zoneso Consideration of the heat requirement, heat transfer properties, and behavior of the material in each of these zones can lead to a better design and a more effective calcining operation, The zones depend upon the type of kiln, and in many cases can be considered as a preheating zone where the material enters the kiln and where the combustion gases are withdrawn, a combustion or central zone in which the actual calcining operation takes place, and at the far end of the furnace, a postheating zone where the calcined charge is superheated or soaked at a specific temperature or where it may be cooled within the confines of the kilno Often, to increase thermal efficiency of the kiln, recuperative preheaters are utilized to heat the incoming air and perhaps the fuel. In improving the thermal efficiencies of the calcining operation, one is concerned primarily with heat losseso The loss of heat by transmission through the kiln structure, and radiation and convection to the surroundings from the structure surface, is generally less serious than the losses at the exit or entrance to the kilno In computing the loss of heat through the surfaces of the kiln structure, one can generally assume that the inner temperature of the wall is at the same tempera

-82ture as the operating process and perform a trial and error solution for convection and radiation losses from the exterior surfaces and balance this heat loss with the conduction loss through the refractory walls. There is a heat loss involved in the sensible heat of the hot lime which is withdrawn from the kiln. This is easily computed from. the specific heat of lime and the temperature at which the material is taken from the furnace. Imcomplete combustion of the fuel is also a source of inefficiency in the calcination operationo Heat may be lost by incomplete combustion, both from combustible material leaving the plant in the form of ashes, and combustible gases lost out the stacko Suitable control of the fuel-air ratios and also a well-designed combustion system may be used to reduce these losses, It should be noted that adequate control of the draft is often an important factor in introducing sufficient air and fuel and providing a uniform distribution over the kiln cross sectiono The greatest heat loss in. the kiln operation is the loss of heat in gases going out the stacko The amount of heat in the exhaust gases may be calculated from the specific heat of the gases and their exit temperature. Often, this heat loss is a sum of many of the poor engineering developments that have taken place in the process itself. However, exhaust heat loss can be minimized with the use of recu.perative preheaterso The heat balance of the lime kiln may be written in the following manners

-83Heat Input The source of heat in any calcining operation is the fuel, generally coal or coke, and it is therefore necessary to know its calorific value and the total weight usedo The heat input is then given by the product of the standard heat of combustion of the fuel times the pounds used. Heat Output Preheating limestone Decomposing limestone Further heating of lime Heat losses~ lo heat loss due to radiation and convestion 2o heat loss due to imcomplete combustion 3o sensible heat of the exit gases 4o sensible heat of the hot lime 5 other possible heat losses which might include the sensible heat of solid products of combustion or a change in the ambient temperature of the kiln structure itself, etco Thermal Efficiencies In discussing the thermal performance of a lime kiln, a common pr&ctice is to quote the ratio of lime produced to the fuel supplied for combustion. The true thermal efficiency of a lime kiln is expressed as the ratio of the heat theoretically required for calcination to the heat actually supplied to produce a ton of limeo The thermal efficiency varies from kiln to kiln and is a function of the stone, its size, the tempera

-84ture of operation, and other factors which are involved in the contact between the combustion gases and. the chargeo The normal kiln performance is of the order of 25% to 35% efficient with a heat requirement of from 8-10 million BTUPs per ton of lime produced,

REFERENCES lo Kubaschewski, 0o and Evans, E. L Metallurgical Thermochemistryo New Yorkl John Wiley and Sons, Inc., 1956. 2, Furnas, Co Co "he Rate of Calcination of Limestone'' Industrial and Engineering Chemistry, 23, (1931) 534. 3. Conley, J, E. Calcination Conditions for LimeStone, Dolomite, and Magnesite, Technical Publication Number 1037, Mining Technology 3, 19399 4o Lewis, W. K.,, Radasch, Ao H., Lewis, Ho Co Industrial Stoichiometry, Chemical Engineering Series. New York~ McGraw-Hill, 1954, Chapter 12, -85

CHAPTER IX HYDRO -METALLURGICAL OPERATIONS Hydro-metallurgy is a phase of metallurgical-process engineering which deals with operations taking place in aqueous solutiono These processes include solid-liquid extraction which is frequently referred to as leaching. Solid-liquid extraction is important in many phases of metallurgical engineering. A typical example is the recovery of copper from oxidized copper ores, which are generally low-grade ores containing less than 1,5 weight per cent copper, by extraction with solvents such as dilute sulfuric acido Extraction always involves two steps- (1) the contact of the solvent with the solid to be treated to transfer the soluble constituent to the solvent, and (2) the separation or washing of the solution from the residual solid, Liquid always adheres to the solids which must be washed to prevent either the loss of solution or contamination of the solids, depending upon which is the desired material, The complete process may also include the separate recovery of solute and solvento A separate operation is usually involved which might be evaporation, distillation, electrolysis, ion exchange, solvent extraction or precipitation, the latter being one of the more common ones in the metallurgical industries. An example of hydro-metallurgical operations is the extraction of gold and silver by cyanidation and precipitation of those elements from the cyanide solution with zinc, Leaching techniques are employed to obtain zinc oxide and copper oxide with acid, copper with ammonia, -87

-88alumina with caustic soda, and uranium with acid or carbonate The recovery of these solutes is then carried out by cementation or precipitation. processes. Copper is recovered from acid solu:tions by cementation with iron, uranium and vanadium are recovered from acid or carbonate solutions by neutralization, and often metallic ions can be precipitated from aqueous solutions as insoluble sulfides. In recent years, interest in hydro-metal Lurgical operations has been greatly intensified, This has been brought on in large measure by the necessity for turning to lower grade ore materials which must be concentrated in one manner or another before processingo Many of the new developments in-olve leaching and precipitation operations which are conducted at elevated temperatures and pressureso The advantages for operating under these conditions are (I) greatly increased rates of reaction, (2) favorable displacement of thermodynamic equilii'bria, and. (3) the possibility of using certainr. gaseous or high-y volatile reagents such as oxygen, hydrogen, and ammoniao Among the new processes wT.hich have resulted from the application of high-tempe rature and high-press ure techniques are direct leaching of nickel, copper, and cobalt sulfides with ammonia, carbonate leaching of pitchblend ores, leaching of certain sulfide ores with water, precipitation. of metallic nickel, cobalt and copper from. aqueous solutions of their salts by hyirogen red:ction, and precipitation of uranium and vanadium oxides from. aquWeou,s carbonate solution by hydrogen reductiono Although there is a demand for advances relating to the physical chemistry of some of the older hy dro-met al-Trgical processes, undoubtedly the employment of higher temrpera4res and. pressures in conjunction with new extralction techniqes will bring the greatest advances to the field.

-89Thermodynamics and Kinetics of Hydro-Metallurgical Operations The engineer who is faced with the problem of designing a hydro-metallurgical operation may ask two questionss (I) Can. a given chemical reaction or process be made to operate, and if so, under what conditions? and (2) What are the factors which determine the rate of the reaction, and how can this rate be controlled in practice? The answer to these two questions lies in an understanding of the physical chemiattcy of hydro-metallurgical processes. Thermodynamics attempts to answer the first question, and kinetics the second. Through the use of thermodynamics it is possible to define the equilibrium in a chemical system and to predict how the equilibrium will shift with changing conditions. An increase in the concentration or partial pressures of the reactants will shift equilibrium in the foreward direction while an increase in the concentration of the products will have the reverse effect. If any of the reactants or products are gases or highly volatile substances, the role of pressure becomes readily apparent, particularly, in view of the fact that many hydro-metallurgical operations take place in acid or basic solutions, Pourbaix has conveniently expressed the thermodynamics of these systems in the form. of potentialpH diagrams. A discussion of this thermodynamic treatment has also been 3 presented by Halpurn. The thermodynamics of hydro-metallurgical operations can also be treated by the procedures outlined in Chapter III. In general, hydro-metallurgical processes particularly leaching reactions, are conducted under conditions in which the thermodynamics are very favorable, that is, there is a large decrease in free energy associated with the desired process. The limitations are, therefore, largely of

-90a kinetic nature, Most of the heterogeneous reactions of interest involve the following sequence of steps lo Absorption of gaseous reactants by the sol-tiono 2, Transport of dissolved reactants from the main body of the solution to the solid solution interface, 30 Adsorption of reactants on the solid surface, 4o Reaction on the surface, 5o Desorption of the soluble products from the surface, 60 Transport of the desorbed products into the main body of the solution, Step 1 could be rate limiting only in cases where gaseous reactants are involved, Usually however, a relatively fast gas absorption can be maintained by providing sufficient agitation of the solution and also a high partial-pressure of the gas phaseo The transport of a dissolved reactant to the surface (step 2) or of a product away from the surface (step 6) is more often rate limitingo In each case, the rate of transport to or from the surface is determined by the diffusion of the species across a boundary layer of thickness 5, immediately adjacent to the surface of the parti.le at which it is consumed or formed, Within this layer, the concentration of the d.iffusing species can be represented to a first approximation as a linear function of distance while on the solution side of the boundary layer, its value is the same as for the bulk solution., A treatment of this kinetic model has been presented in Chapter IV, The diff.sion coefficient in aqueous solution is usually of the order of 105 cm2/sec, and. the boundary layer thickness is a function of the agitation, Its value

-91normally ranges from about 0,05 cm in an unstirred system up to about 0o001 in a vigorously agitated one, Using these values, it can be shown that the maximum attainable rate in a diffusion-limited system is of the -1 2 order of 10- mols per cm -hr, depending, of course, on the concentration of the diffusing reactanto Processes which are rate-limited by diffusion can be speeded up by vigorous agitation of the liquid solution, by an increase in temperature, although the diffusion coefficient is usually characterized by a low-temperature coefficient corresponding to an activation energy between one and five kilocalories per mol, and also by maintaining a high concentration of reactant in the solution, Low rates of diffusion can result with localized accumulation of products, eogo the formation of a precipitated oxide, The oxide, although soluble, might redissolve slowly and tend to passivate the surface where the reaction is taking place. Steps 3 through 5, those involving adsorp1tion, chemical reaction at the surface, and desorption vary greatly from system to system and do not lend themselves to consideration in general terms, In the event that a given hydrometallurgical process is rate limited by one of those steps, it would be necessary to make a specific investigation of the factors involved in order to adequately design the process in terms of the rate limiting mechanisms, The Engineering of Solid-Liquid Extraction Processes The equipment used for solid-liquid extraction may be classified according to the manner in which the first step is accomplished. A process in which the solid particles are kept in relatively fixed positions with respect to each other is denoted by the term. "solid bed1, It

-92is possible that the solid bed remains fixed relative to the earth and that the solution moves through it, or it is also possible that the bed may be moved through the solution by means of a conveyor belto Another type of solid-liquid extraction is the "dispersed contact"e There is a variety of equipment which may be used in this case where the solids are dispersed in the so-lvent, In order that tthe particles remain in suspension, they must be extremely fine. However, in many cases, the suspension is maintained by agitation of the solvent, or the solids are moved through the liquid by means of screw conveyors, rakes, or other mechanical devices, In general, the stationary solid bed extractor involves a minimum amount of handling and is often used where large amounts of material are required to be treated, For a more complete discussion of the particular equipment used, the reader is referred to any of the standard chemical engineering textso3,4 5 The simplest method of operation for a solid-liquid extraction which includes the washing of solids is to bring all of. the material to be treated and all the solvent into contact in one tank, This process is known as a single-contact batch operation.o It is used, in general, only for small scale systemso The main reason being that a low recovery of soluble material is obtained. The total amount of solvent to be used can be divided into portions and the solid extracted in stages with fresh solvent, This method of operation is called simple-munltiple contacto Although recovery is improved, the method is still not good because the product is relatively dilute in solute. This method is used where the soluble constitu ent is not a product, The most efficient

-93technique, and the one most often used, is the multiple-contact counter-current operationo In. carrying out a process in this manner, the product solution is last in contact with the fresh feed and the extracted solids are last in contact with fresh solvent. This process is characterized by a high solute concentration in the product stream. Ideal Stage Concept In most systems, the kinetics of leaching are not well defined, and consequently, calculations are based on the ideal stage. An equilibrium or ideal stage is defined for solid-liquid extraction as a stage from which the product stream le'aving is of the same composition as the solution adhering to the solids, leaving the stage. Since this condition is not always fulfilled, the ratio of the number of ideal stages to the number of actual stages required to accomplish the same result is called the overall stage efficiencyo The design engineer can compute the number of actual stages only if he has knowledge of, or some basis for estimating, the overall stage efficiencyo Often a kinetic analysis of the problem can be of assistanceo In order to perform a calculation of the number of ideal stages the following conditions are assumedo 1o The system is composed of materials which may be treated as three componentso a, Inert solids which are insoluble in the solvent or solids for which the solubility is known.o bo A single solute which may be liquid or solid, or in the event that several solutes are involved, the interaction effects are knowno

-94Co A solvent which desolves the solute, but has no effect upon or is saturated with the solidso 2o The solute is not absorbed by the inert solid or in the event that it is, the relationships are known as functions of concentration and temperature, 3. The solute is removed by simple solution in the solvent without chemical reactiono The computation of the number of ideal stages required is based on material balances. A knowledge of the quantity of solution retained by the solid and the definition of the ideal stageo A mass balance is made about each ideal stage and this process is carried out until the solute or solvent exiting from a stream reaches the desired concentration level. The number of actual stages may then be obtained by divi7ding the number of ideal stages computed by the overall stage efficiencyo Material balances can be made arithmetically but this approach is usually quite tedious, Graphical methods have been developed which greatly simplify the calcula'tions, reducing error and also indicating clearly the variables involved and their effect on the operation, A detailed presentation of4 the arithmetic and graphical solutions for various types of solid-l.i id exraction are presented in References 3, 4, 6, and 70

REFERENCES 1, Pourbaix, Mo Thermodynamics of Dilute Aqueous Solutions Londono Edward. Ainold & Co,. 1949, 2, Halpern, J, "Some Aspects of the Physical Chemistry of Hydrometallurgy." Trans, AoIM.E,, 209, (1957), 281o 3. BIrown, G, G & AssoCo Unit Operations New York~ John Wiley and Sons, Inc,, 1950o 4o Foust, Ao So etalo Principles of Unit Operations, New York~ John Wiley and Sons, Inc, o 1959, 5A Aldrich, Ho Wo and Scott, Wo G. "The Inspiration Leaching Plant " Trans. AoI,M,E,, 106, (1933), 650o 6, Ravenscroft, E, A, "Extraction of Solids with Liquids," Industrial Engineering Chemistry, 28, (1936), 851o 7 Baker, C, Mo "Calculation Methods for Counter-Current Leaching.'" Trans. AIChE, 32, 1936o 8, Newton, J. Extractive Metallurgy, New York~ John Wiley and. Sons, Inc,, 1959, Chapter 7, -95

CHAPTER X MELTING AND POURING The kinetic advantages of a molten phase at high temperatures make it desirable to produce and refine metals in the liqg.id stateo Since most metals are solids at ambient temperatures, it is necessary to supply them with heat to perform a m.elting operation.o Subsequent to this, the metal is poured into and permitted to solidify in a mold of desired shape as either a casting or an ingot form. The material in this chapter deals with melting and pouring operations, Me1lting Practice The minimum power required to raise a metal from. room temperature to above its melting point is represented by the enthalpy increase which the metal experiences in going from the lower temperature to the higher. The actual power requirements, however, are much greater than this, and may be determined from a heat balance for the melting process. In writing such a heat balance, one must consider 1) the power input, 2) the sensible heat of the metal before and after the operation, 3) the sensible heat increase of the melting unit itself, 4) the heat losses, which include not only radiation and convection from the exposed surfaces of the melting unit, but also any heat removed. by cooling watter which is often. used to protect critical areas of the melting unit. The heat balance is mostd conveniently written for a given period of time, The calculation of the power input depends unpon the type of unmit used Several melting units are schematical.ly represented in. Figure X-lo Sketch A of that figure shows a type of melting unit which is quite -97

-98CARBON ELECTRODE HIGH FREQUENCY CRUCIBLE / COIL O METAL o 0o~t <~o 0DIRECT ARC 0 0 o 0 0 0O (A) INDUCTION MELTING META[L BATTH ///////?//////////77/ INDIRECT ARC V////////////////// //,Z (B) ARC MELTING RESISTANCE E / HEATING o ELEMENTS 0 CRUCIBLE,o /, o/,' 7uCRUCIBLE 0 MELT MELT GAS BURNE (C) RESISTANCE MELTING GA FIE R (D) GAS FIRED RETORT Figure X-l. Melting Furnaces.

-99efficient in that the heat is generated in the metal The alloy is placed within a coil which is supplied with a rapidly alternating currento The current flowing through the coil supplies the metal with a varying magnetic inductive forceo This force produces electrical eddy currents in the metal which are dissipated in the form of heat. The power taken up from the coil by the metal is thus dependent upon the magnetic characteristics of the metal, and its electrical. resistance properties, Metals which are not easily melted by induction may be placed in a container made of a material such as carbon which is heated by the induction coilo If a reaction would take place between the metal and the carbon crucible, it is possible to surround a refractoryoxide crucible with a cylinder which is heated inductively. The cylinder, usually a high melting point metal, is called a susceptoro A material which is often used under protective atmospheres for such applications is molybdenum which will withstand the high temperatiures often involved in such an operation. Induction melting may be done in air, or in the case of metals which are easily oxidized or which are desired in a high state of purity, the melting may take place under a protective atmosphere or vacuum. Vacuum indu.ction mel.ting is often considered to be a refining operation, and a great deal of research effort has been expended in demonstrating that vacuum-melted materials are often superior to those which are air-meltedo Another type of melting unit using electric power is shown. in Sketch B. This is known as arc melting and may be either of the direct or indirect type, depending upon w hether the arc operates between electrodes and metal or between two electrodes in the system.,

-100Large melting units used in e-lectric furnace operation for steelmaking generally use three-pole direct arc systems which have melting capacities ranging up to 100 tonso In the case of indirect arc furnaces, the electrodes are often placed along the centerline of the furnace, and to avoid excessive attack of the refractory s'urfaces, the furnace is rotated to provide a cooling of the refractory surfaces by the liquid metal itself. Resistance heating is often used to melt metalso There are a number of different types of resistance melting units, but in general the power is supplied by radiation from. a heating element, For operation at low temperatures, high melting point metals are often used as heating elementso For slightly higher temperatures, the "Globar" furnace is often used, and for operation at even higher temperatures, carbon resistors may be employed~ These electrodies are attacked by oxidizing gases and consequantly must be protected by an inert or reducing atmosphere, usually argon or carbon monoxide. Melting furnaces often use low-cost fuel in the form. of natural gas, fuel oil or powdered coal or coke. Sketch D shows such a furnace which may either be of the retort or reverberatory type. The economic advantages of using these types of fuels are often overcome by the deleterious effects of contamination~ Coal and oil products generally contain sulfur which are undesirable in steels. Nevertheless, however, the major portion of the steelmaking industry in the United States is based on open-hearth operation., which is a gas or powdered coal fired reverberator. ytype furnace as shown in F-gure XI7-O The power input to these fuzrnaces may be compu.ted fom. the heatinrg val.ue

-101of the fuel and the heating value and sensible heat of the combustion gases Sensible Heat of the Metal The sensible heat of the metallic charge may be calculated. from a knowledge of the input and. output temperatures of the charge and its specific heat. A more convenient method for handling such data is to tabulate the enthalpy increments for a given amount of metal, one pound mole for exampleo Table X-l gives the enthalpy in1 crements for several metallic elements. In order to compute the rate of heating, one may assume that the total heat transferred, between the hot internal surfaces of the melting unit and the metal, or the heat transferred between the burning fuel or direct arc and the metal., takes place entirely by radiation. If such is the case, one must know the temperatures and total emisivities of the surfaces involved, and also the geometry of the heating system. The total emissivity of various surfaces ha've 2 354 been tabulated, and geometrical effects have been summarized 34 The rate of radiant heat transfer from a surface at Tt to a surface at T2 may be calculated from the relationdQ = a F A(T - T) X-1 dt where a equals the Stefan-Boltzmann constant, 1730 x 102 BTU/ft2 -hr- Ro, A1 is the area of radiating surface 1, F is a dimensionless factor which accounts for the geometric relationship of the two surfaces to each other, and to other reflecting or refractory surfaces

-102TABLE X-1 HEAT CONTENT OF SEVERAL METALS1 HT - H98,15 cal/gm atom Temperature OTK Aluminum Copper Iron Lead Magnesium Zinc 298 0 o(a) o o o 400 600 600 642 656 620 630 500 1230 1215 1318 1324 1256 1270 6oo 1890 1845 2044 2014 1920 1940 700 2580 2480 2832 3884(liq) 2610 4400(liq) 800 3310 3130 3703 4605 3330 5150 900 4o6o0 3800 4682 5318 4095 5900 1000 7330(liq) 4490 5819 6024 7010(liq) 6650 1100 8030 5190 7135 6723 7810 7400 1200 8730 5895 8347(P) 7415 8640 1300 9430 6615 9203 8100 9490 1400 10130 10480(liq)10059 8780 1500 10830 11230 1091.5 9450 i600 11530 11980 11771 10110 1700 12230 12730 12939(5) 10760 1800 12930 13480 13914 11410 1900 13630 14230 18658(liq)12050 2000 14330 14980 19714 12680 2100 15030 15730 20774 2200 15730 16480 21838 2300 16430 17230 22906 2400 17130 17980 23978 2500 17830 18730 25054 2600 18530 19480 26134 2700 19230 20230 27218 2800 20980 28306 2900 29398 3000 30494

-103in the system, and the emissivities and absorptivities of the two surfaces, and T is the absolute temperature in ~Ro Sensible Heat of the Melting Unit The temperature increase of various portions of the melting unit must also be included in the heat balanceo If the operation is carried out on a continuous or semicontinuous basis, the temperature distribution in the melting unit can be assumed constant In this case, the term is negligible, One may also consider the change in temperature distribution of the melting unit, and attempt to estimate the sensible heat increase. In order to do this, it is necessary that one know the temperature distribution and also the enthalpy increments as a function of temperature for the furnace materials involvedo A third approach which is often satisfactory, but less accurate, is to assign a factor to this quantity such that the sensible heat increase of the melting unit is represented by a fraction of the heat energy which is taken up by the metal. One may then multiply the sensible heat of the metallic charge by a factor which ranges from lol to 1 5 for most cases. Heat Losses The principal heat losses in melting operations are the radiation and convection losses from the exposed surfaces, These losses may be computed by balancing the heat loss through the walls of the furnace with that lost by radiation and convection from the surfaceo This may be represented by the relation: qc = Qr + Qconv X-2

-104A trial-and-error approach to this problem is necessary where one solves the following equation for the interface temperature To0 km (Ti - To) = hcAo(To - Ts) + eoAo(T - Ts ) -3'~~X where T. is the temperature of the internal surface of the furnace, To is the interface temperature between the outer surface of the melting unit and the surroundings, Ts is the temperature of the surroundings, k is the thermal conductivity of the furnace lining, Ax is the thickness of the lining, eo is the emmissivity of the outer surface, A is the outer area of the melting unit, Am is the mean of the inner and the outer surface areas of the melting unit, and hc is the convective coefficient from the surface of the unit which may be taken on 0.25 the average as being 0O3(Ti - Ts) a for plane surfaceso Other heat losses include the sensible heat of any gases or other products evolved from the unit during the melting operation as well as heat lost to cooling water which may be used to maintain low temperatures in certain critical areas of the melting unite In the case where the metal surface is exposed directly'to the surroundings, one may compute the heat losses on the basis of radiation from that surface assuming that black body conditions are approached by the surroundingso Samways and Dancy6 have reported on the temperature drop of liquid metal between tapping and teeming and have statistically derived quantitative relationships based on plant observations, Pouring Practice Liquid metals are transported in metallurgical plants in ladles, which are cylindrically shaped vessels consisting of a steel

-105shell lined with brick~ The type of brick in most common use is fireclay brick. Ladles vary in capacity from 10 pounds to 300 tons, The operation of pouring from a ladle may take place in three ways. The heat may be lip-poured, bottom-poured, or a tundish may be usedo Although lip-pour ladles are quite commonly used in plants producing small castings or pour large heats from one ladle to another (reladling), primary produced metal, particularly in the steel industry, is usually cast from the bottom-pour ladle, Figure X-2 shows a cross sectioned view of a bottom-pour ladle used for 200-ton open hearth heatso With this method of pouring, a stopper assembly acts as a valve to control the flow of metal through a nozzle at the bottom of the ladle. The size of the nozzle may vary in diameter from 1-1/4 to 3 inches, but it is of a length which is several times the diameter in order to provide a smooth, solid stream of metal free from turbulence. Nozzles are made from fireclay and the softening of the surface of the nozzle seat provides an adequate seal for the harder stopper-heado The stopper rod assembly shown in Figure X-2 consists of a steel stopper rod protected from the heat by a refractory sleeve and connected to an external. control lever which permits the operator to start and stop the flow of liquid metalo One of the most important factors affecting the surface of the ingot and the subsequent product is the rate of flow of the pouring stream and the resultant rate of rise of metal in the mold. This rate is determined by nozzle size, mold size, the temperature and fluidity of the steel, the height of metal in the ladle, and the erosion of the stopper and nozzleo The optimum pouring rate is determined by the grade of

-106STOPPER ASSEMBLY LIQUID STEEL CONTROL LEVER LREFRACTORY LINING NOZZLE Figure X-2. 200 Ton Bottom-Pour Ladle.

-107T steel, but is also dependent upon mold design and temperature of pour. In general, a slow pour minimizes ingot cracking but increases the tendency toward folded ingot surfaceso With fast pouring, however, the converse is true. The rapid rise of molten steel in the mold prevents a rippled surface. However, a large head is formed in. the shell, which shrinks away from the mold wall and looses its supporto Since the shell is very weak and cannot withstand the ferrostatic pressure of the liquid metal, it will rupture, permitting fresh liquid to break through to the mold surface, This produces a weakness in the ingot surface which may rupture on cooling or subsequent forming operations. Rather than casting metal directly from the ladle to the mold, an intermediate pouring vessel may be used. Such vessels are called pouring baskets, pouring boxes, or tundisheso This method usually involves pouring from the tapping ladle into a vessel which has a nozzle leading into the ingot moldo Tundish or basket pouring is more expensive than conventional top pouring, but has the advantages that there is a greater opportunity for separation of non-metal.lic inclusions from metal, and there is also less splashing in the moldo Bottom-Pour Molds Some of the disadvantages of top-pouring mentioned above may be eliminated through the use of a bottom-pour mold assembly, The metal is cast into a runner system and finally emerges at the bottom of the mold through a special outlet, In bottom pouring, the metal rises steadily in the mold with very little agitation, Bottom-pouring is much more expensive than top-pouring, but is often used to insure optimum surface qualityo,

-lo08Rate of Pouring The rate of pouring greatly influences the quality of a cast ingot By considering the flow of metal through the nozzle of a bottom-pour ladle in terms of the flow equation, the rate at which metal is entering the mold at any time during the pouring operation can be estimated. In view of the fact that the nozzle erodes, one must have some relationship which indicates the size of the nozzle as a function of the amount of metal which has passed through it, Such correlations may often be obtained from plant data. If one also has estimates for the orifice coefficients and friction factors, the rate of pouring may be computed, The gradual enlargement of the nozzle has an effect that is desirable, iceo, the rate of pouring does not decline gradually with the ferrostatic head in the ladle as it would if the nozzle opening remained constant While the head of metal has been decreasing, the diameter of the orifice has been increasing, and the rate of pouring can remain nearly constant or even increase slightly. Since the rate of pouring has important effects upon the structure of the ingot' this may be an important aspect in the design of the pouring operationo Knowing the behavior of several, materials which may be available for nozzles, the process engineer may select that one which provides a relatively constant pouring rate throughout the casting operation. Application of the generalized flow equation to the estimation of teeming rates from a bottom-pour ladle is illustrated by the following example proble lem,

-109Example X-1 A steel ladle of the type shown in Figure X-2 contains 200 tons of liquid metal,o The metal is poured out of the nozzle in the bottom into a series of molds below. The nozzle is 18 inches long and has an initial diameter of 2 inches. The nozzle erodes during pouring, however, and the eroded, diameter is given by the relationship~ DN = 2 + eN where DN is the diameter in inches, C is the linear erosion coefficient, 0o006 inches per ton, and N is the number of tons of metal that have passed through the nozzle. The flow of liquid metal through the nozzle is characterized by the friction factor of the nozzle, the entrance coefficient, and the exit coefficient, which may be taken as 0,04, 0o20, and 10, and assumed to be independent of flow rate. The initial depth of metal in the ladle is 10 ft, Calculate the rate of flow of liquid metal throughout the pouring operation, and comment on the suitability of the particaular nozzle materialo Solution The flow velocity can be calculated at any stage of the pouring operation by the flow equation, expressed in terms of the parameters of this problem, 2 2 g (z2 - zl) + V2 V + P2 - P =-lw - w 2 g P 2 2 2 - fNVNL + l N +x xVN w = 2 gc'D 2 gc 2 gc

-110where 1w is the lost work caused by friction in the nozzle, fN is the nozzle friction factor, and 0N and OX are the entrance and exit coefficients, respectivelyo The work done on the system, w, is zeroo Selecting point 1 at the upper surface of the metal in the ladle and point 2 just below the nozzle, the pressure drop (P - P2) is zero, and V1, the velocity of the surface of the metal in the ladle is negligibly small in comparison to that exiting from the nozzleo Then, gc1 l0(2oo)+Lj 2] c 200 -N' 1 [1 210( 200) + L 2 V2 = L(2 gc) -I + + DN V2, the exiting flow velocity in ft/sec can be converted to a flow rate by the relationship2 N (flow rate in tons per minute) = V2 (60) DN 2000 4 Then: O 200-N2 lo- + L 60 D = [(2 gc) O, It P. (1 + D N+ ) where DN = 2 + 0o006 N Evaluating the last two expressions at the start of pouring~ DN = 2 + 0o006 x 0 = 2 inches 10 ( 200-0 18 2 N = (2)(32,2) 200 1.2 ] (6o)(2) 2 42 0 1 + (o0o4) 18 + 0O2 + 1o0 (2000)(144) 4 2 2 11o5] 240 T (450) = (6,o 4) 2(2_000) (576)- = 5.00 tons/mm

-17 The expression can be evaluated at regular intervals of metal poured from the ladle in a similar manner, generating the curve shown in Figure X-3. In view of the fact that one of the most important criteria for a successful, pouring operation is a relati ely constant pouring rate, the nozzle material of the example problem is highly suited to its application. Also shown in Figure X-3 are the pouring rates for nozzle materials with various erosion coefficients used in the operation described in the example problem~ The results shown. in Figure X-3 may be suitably averaged to provide an estimate of the total pouring time,.sing an expression of the general formo - (Tons Poured in Interval m) i A(Average N^) The total. pouring time of the operation described in the example problem is about 34 minutes. The digital computer was especially useful in providing these results (See Chapter XXI.V)

-112I0 8.O 6 0_~ O 0 40 80: ).003 4 0 0 40 80 120 160 200 TONS POURED Figure X-3. Flow Rates from Bottom-pour Ladle for Various Nozzle Materials with Erosion Coefficient, e.

REFERENCES 1. Elliott, J. F. and Gleiser, Mo Thermochemistry for Steelmakingo Reading, Massachusetts0 Addison-Wesley Press, Inc., 196 0 2. Butts, Ao Metallurgical Problems. Metallurgy and Metallurgical Engineering Series. New York~ McGraw-Hill, Inco, 19430 3o Trinks, W. Industrial Furnaces, Volo 1o,, New York- John Wiley and Sons, Inc., 1956 4. Basic Open Hearth Steelmaking, Physical Chemistry of Steelmaking Committee, AIME, New York, 1951, Chapter 10. Camp, Jo M. and Francis, Co B, The Making, Shaping and Treating of Steel, U. S. Steel Company, Pittsburgh, 1951.o 56 Samways, No Lo and Dancy, To E, "Factors Affecting Temperature Drop Between Tapping and Teeming." Journal of Metals, 12, (1960), 331. 7o Elliott, Jo Fo Private Communication, 8. Computing Center, The University of Michigan., Ann Arbor. -113

CHAPTER XI CASTING AND SOLIDIFICATION Following completion of the final refining operation, the liquid metal is poured from a furnace into a ladle, The liquid metal is then teemed from the ladle into molds and permitted to solidifyo These solidified castings are called ingotso The eventual use of these ingots may be in any of several forming operations, including remelting and recasting in a desired shapeo The forming operations which are used in the metallurgical industries are extensive subjects in them1-6 selves Consequently, the discussion in the present chapter will be limited to the casting of ingot shapes for use in further forming operations. The material presented here will be concerned chiefly with the rate of solidification, ingot structure, and some considerations of the continuous casting process. Rate of Solidification Flinn6 has presented a mathematical analysis of the solidification rate of metal cast into a sand mold. based on the work of Ruddle 7'8 In this approach, it is assumed that the temperature of the finite(plane) boundary was instantaneously raised to and thereafter maintained at a temperature Ti at time t = 0 The temperature T at any point at a distance x from the finite boundary in a semiinfinte solid body is given by: Tm = To + (T - To) erfc (x/2at) XI-1 -115

-Il -6 where T = temperature at distance x from mold wal.l into moldo m To = temperature at t = 0 Ti = mold-metal interface temperature x = distance from mold wall = thermal diffus'vIty, K/pc t = time The rate of heat transfer across the mold-metal interface is given by the thermal conductivity multiplied by the temperature gradient. Differentiating Equation (XI-l) with respect to x, at x O i T (T! - To) T_ - (TT To) XI-2 axI and then: aQ K(Ti - To) XI-3 If the freezing time depends on removing a certain amount of heat, Q, then: 2K(T. To) \xt Q = - 1 ~ xi-4 Thus for a given metal and mold temperature~ Q -= /t XI-5 where p is a constant depending on pouring conditionso If the freezing time depends on removing a given quantity of heat, then the thickness of frozen metal measured from the mold wall is given by: d= xi x!-6 where y is a constant. A similar result has been derived by Feild9o

-117By considering an infinite plate, it may be shown that the total distance which the freezing plane must advance for complete solidification, one-half the plate thickness is also the volume to area ratio, Thus:, 2 t = (V/A) XI-7 where y' is a constant, and V/A is the volume to area ratioo This relationship has been shown to apply with reasonable accuracy to all casting geometries although it is only rigorous for infinite plateso Ingot Structure In addition to pouring conditions, ieo, temperature of the liquid metal, the nature and temperature of the mold, and its geometry, the rate of pouring, and other factors which affect the cooling rate, the most important factors which influence ingot structure are metal composition and gas evolution. Effect of Rate of Heat Removal A cast ingot will generally consist of three zoneso Near the surface of the ingot the structure is very fine, randomly oriented grains. This region is called the chill zone and its structure is caused by a rapid rate of solidification during the early stages after pouringo Inside this zone is a second zone where the crystals are thin and elongated, perpendicular to the mold wallo This zone is called the columnar zone and is caused by relatively rapid heat removal giving rise to directional solidification and grain growtho Inside the columnar zone, the ingot has a granular structure in which the crystals are randomly oriented but are much coarser than in the chill zone. This

-118zone is caused by a low rate of heat removal in the final stage of solidification All ingots which do not involve gas evolution, during solidification will. show these three structures, the extent of the zones being a function of pouring conditions, composition, and average rate of solidificationQ The rate of solidification shows a large variation being nearly infinite at the mold surface and decreasing to a very small value near the center of the ingot, It is this variation in cooling rate during ingot solidification that causes the three structural zones described aboveo Influence of Metal Composition Since most liquid metals involved in metallurgical operations are not pure, they solidify over a temperature range with the first liquid solidifying having a different composition than that which finally solidifieso Most alloying elements lower the melting point of a pure liquid, and consequently, the first crystals of solid to form would more closely approach the pure major component than the composition of the bulk liquido When the first crystals of sol.id form, they leave liquid next to them which is slightly less pure than the bulk liquido The solidification of such a metal may then be visualized as crystals separating out which are more pure in. the major component, and are separated from the bulk liquid by a film of liquid metal which is less pure than the bulk metal. Freezing may then proceed in any of three ways. (1) If the rate of solidification is very high, the less pure liquid solidifies so rapidly that the solidification process is indistinguishable from that of a pure liquid metal ( 2) If the rate

-119of solidification is slightly lower, the boundary layer of impure liquid may delay solidification slightly. (3) If the rate of solidification is very low, the bulk liquid beyond the impure film may reach its solidification point before the impure liquid.. Free crystals will then form in the liquid and settle out to the bottom of the ingot. As a result of the change in solidification rate during the freezing of an ingot, all three types of freezing take placeo These three freezing conditions produce the three zones described above. These three zones are also characterized to a certain extent by segregation 0 The segregation characteristics of an, ingot are determined by its composition, its rate of cooling, and the tendency of the alloying element to segregate between liquid and solid' A killed steel ingot is characterized by two zones of positive segregation (areas in which the composition is greater than that of the average) and one zone of negative segregation (concentration. lower than the average, These zones are shown in Figure XI-l. The conical zone of negative segration in the lower portion of the ingot is caused by the settling of free crystals which are purer and more dense than. the bulk liquid, As the free crystals settle, they cause an upward movement of less pure liquid along the sides of the ingot near the solidification interface leading to positive segregation in this area, Similarly the V-shaped zones of positive segregation in the upper central portion of the ingot are caused by the movement of less pure liqu id down into the ingot cavity by shrinkage during the final stages of solid. fication.

-120++ + + + +++ + + + ++ + + + + + + + + + + + + + + + \+++ + I + + + + + + + + + + + + r + + 4I1 + + + I+ + - + + + + + + + + + + -= — + + + + +Po si e + +- Negative Segregation Zone + Positive Segregation Zone __ _ _ __ _ _ Fiur X-1 egegtin aten______ppd ile _t _oitv _ e r o _ ___ _eatv _ erg o __ _ _

-121Examination of the equilibrium phase diagrams for most metallic systems reveals that- the alloy content of the solid bears a constant ratio to the alloy content of the liquid in the region near the melting point, Chipman1 calls this ratio k and has tabulated values of (1 - k), the segregation coefficient, for binary systems with irono These values are presented in Table XI-1, where it will be noted that the values of k for a given element differ depending on whether the solid is gamma or delta irono If the segregation coefficient is zero, this indicates no tendency to segregate since the alloy content in the solid and in the liquid would be the sameo If the segregation coefficient is 1, however, this indicates that no alloying element will appear in the first solid to form, and consequently, this alloy would show extreme segregationo Effect of Gas Evolution on Ingot Structure The presence of gas in an ingot during solidification may not only change the physical nature of the ingot because of the prescence of blowholes caused by the gas, but may also affect the segregation tendencies of the ingot since the presence of a less dense gas phase causes fluid flow in the ingot during solidification, The presence of gas in an ingot is often an advantage, however, since the gas evolution will compensate for shrink and reduce or eliminate the ingot pipe giving a higher yield, In the manufacture of steel, the carbon-oxygen equilibrium, and the influence of temperature on it, are of primary importance in the control of ingot structure by gas evolution, Carbon and oxygen react to form carbon monoxide whenever the equilibrium constant for

-122TABLE XIi 10 SEGREGATION COEFFICIENTS FOR ALLOYING ELEMENTS IN IRON Element Segregation Coefficient, 1-k Delta Iron Gamma Iron Aluminum o0,08 Boron o.95 0.96 Carbon 0,87 o064 Chromiim 0O05 0ol.5 Cobalt 0o 0 0.05 Copper 0O 44 0.12 Hydrogen o,68 0o55 Manganese 0o16 0 05 Molybdenum o 20 0 0.4 Nickel 0,20 0.05 Nitrogen 0 72 0o46 Oxygen 0 98 0 98 Phosphorus 0 87 0 o 94 Silicon Oo34 0.5 Sul1fur 0 o98 0 98 Titanium 0o 86 0 93 Tungsten 0.05 0 5 Vanadium o.10

-123the solution of the gas in liquid iron is exceeded, The reaction may be written C + 0 = CO XI-8 where: K = PCO/ac a XI-9 The equilibrium constant is thus proportional to the pressure of CO, which is a linear function of depth in the ingot moldo At atmospheric pressure near the top of the ingot, the equilibrium product would be one-half that which it would be at a depth of five feet in the ingot where the pressure is twice as great. In practice, ladle deoxidation is used to reduce the oxygen to near the equilibrium level with the carbon present As freezing proceeds, carbon and oxygen are concentrated in the liquid by the freezing out of pure crystalso This process results in gas evolution when the product of the carbon and oxygen activities exceeds that for the equilibrium valueo in a semi-killed ingot the concentration of oxygen is adjusted during the transfer in the ladle, and during the pouring operation in the mold, such that gas evolution compensates for shrinkageo As the steel shrinks during solidification the pressure is relieved,and additional gas is evolved. The top of the ingot then freezes over and gas formation in the lower part of the mold is controlled by the pressure. Rimmed steels are characterized by rapid gas evolution which begins during the solidification of the chill zone at the mold wall, With the first solidification, marked gas evolution begins at the liquid

-124solid interface and the rising bubbles cause the liquid metal to move upward along the sides of the ingot and down the center, The motion of the liquid prevents the formation of columnar crystals and keeps the interior of the ingot at a nearly uniform temperaturea Just inside the chill zone of a rimmed ingot is found a series of primary blowholeso The mechanism for the formation of these blowholes is described by Hultgren and Phragmen12o The formation of the elongated primary blowholes is caused by the formation of bubbles which are then swept away by the motion of the liquid. After the top of the ingot freezes over, enough impure liquid at the solid-liquid interface accumulates to start gas formation in much the same manner that it occurs in semi-killed ingots, This results in an interior series of spherical blowholes called secondary blowholes The upward motion of the liquid along the solidifying wall sweeps away impure liquid and mixes it with the unsolidified body of the ingot. This results in negative segregation in the rim zone of the ingot. There is then a large positive segregation in the upper central portion of the ingot, the last to solidify, Segregation in rimmed steel ingots has been discussed in some detail. 11 13 The presence of other gases in steel ingots may cause blowholes, these being principally hydrogen and nitrogeno In the case of copper, the evolution of hydrogen and water vapor or SO2 may also influence ingot structure, as hydrogen can in aluminum alloyso The control of gases in liquid metals is discussed in Chapter XXIIIo

-125-.ontinuous Casting Continuous casting processes have received a great deal of attention in recent years, and have come into wide use in the casting of light alloy slabs and ingotso Application is now being made in the processing of copper and steel, The purpose of continous casting is to reduce ingot castings to a form which is directly rollable on finish mills. There is good indication that there should be improvements in yield, in surface condition, and in internal quality of ingots which are cast by this processo The continuous casting of metal slabs involves the following operations~ (1) delivery of liquid metal to the casting strand; (2) flow of metal through a distributor into the casting mold; (3) formation of the cast section in a water cooled mold; (4) withdrawal of the casting from the mold; (5) further heat removal from the casting; e.go water spray beneath the mold; (6) cutting and removal of the cast bars. The rate of heat removal is the primary factor influencing the attainable casting rate. Obviously the casting rate could not be greater than one which makes it possible to remove the heat required for complete solidification prior to the time that the cast section is cut. Another more serious limitation on casting rate is the ability to develop a solid shell within the water cooled mold that can cont'ain the liquid metal as the section leaves the moldo The governing factor here is the thickness f the e shell emerging from the mold and this is determined largely by the rate at which heat is extracted in the mold. On this basis, then, the critical. phase of the continuous casting process is involved in removing heat in the water

-126cooled mold It is on this phase of the operation that the following analytical discussion will be concentrated. An analysis of the freezing of a continuous casting was made by Roth13 who assumed that (I) solidification does not begin until the metal reaches the mold (2) axial heat flow is negligible, and normal to the vertatiL axis, the temperature gradient is linear; (3) the surface temperature of that part of the ingot which is in the water-cooled mold is constant; (4) the metal is poured at the freezing temperature; (5) the thermal properties of liquid and solid metal areidenticalo On this basis the formula for the shape of the solidification front of a rectangular ingot is given as~ x = [ + 2 p p (p - )] I Xy o 2 (K G GS) where x vertical coordinate measured from. the top of the ingot mold, i e, depth of liquid sump y = horizontal coordinate measured from the side of the ingot, ie,, thickness solidified v speed at which ingot is moving vertically downward f = freezing temperature of metal G = surface temperature of ingot which is constant L = length of mold p = density of liquid metal (actually value averaged throughout mold volume) This result implies that the instantaneous freezing rate is proportional to the horizontal thickness already solidified and predicts

-127a wedge-shaped solidification front the sides of which are parabolic in sectionO The depth of the liquid sump should be proportional to v and to the square of the ingot thickness. The most serious errors in, this treatment are likely to arise from assumptions 1 and 2 aboveo A review of this and other studies of the solidification of continuous 14 castings has been presented by Ruddleo Savage and Pritchard15 investigated the rate of heat transfer in continuous casting by measuring the heat transferred to a water stream passing through the cooled copper mold, They found that up to about 40 seconds after casting their results may be represented by the relation~ Q = 64- 8 t cal/cm2 - sec X This equation gives for the average rate of heat transfer over a given period- ave 3 XI-12 0 In the case of a continuous casting whose withdrawal rate is v cm per second, the mold length being L cm, t may be replaced by L/v so that Equation (XI-12) becomes64 - 16 - (^s) -^-^/ x-13 Ft ave The prediction of this equiation that the average rate of heat transfer 16 increases with the casting velocity has been confirmed by experiment, where it was also shown that the rate of freezing is proportional. to the square root of t. The rate of freezing was found to be of the same order as that in an ordinary chill casting during the f irst stage

*-128of cooling, about 0~65 inches per minute2 A large increase in the rate of freezing takes place during the second phase of intense cooling by water spray beneath the mold, q now being equal to about 8044 inches 1j per minute, a value much greater than that applying in chill casting. The plot of thickness frozen against the square root of t thus consists of two intersecting straight lines. An investigation was performed at Inland Steel17 on the continuous casting of low carbon steel. The thickness of shell emerging from the water cooled mold was estimated by measuring the outer slab temperature as the casting emerged from the moldo Using these temperatures and assuming a constant temperature gradient across a uniform solidified shell, the thickness of the frozen outer skin at the time the casting emerged from a 24 x 6-~ inch mold was estimated. The thickness of the emerging shell was found to decrease with increasing casting rate, The results of the investigation showed qualitative agreement with those of Savage and Pritchard5 Although information at the present time is relatively limited, a heat balance for a continuous casting strand could be derived, based on a knowledge of the rate of heat removal during cooling in the chilled mold and in the water spray, and the amount of heat which must be removed which is specified by the metal and rate of castingO At the present state of the art, howeker, one would undoubtedly have to rely on pilot plant data in order to fully design a continuous casting processo The economics of continuous casting as well as a survey of the present status in a number f countries has bee pesened18 in a number of countries has been presented,

REFERENCES Io Underwood, Lo R, The Rolling of Metals, London Chapman and. Hall Ltdo,, 1950, 2, Sachs, Go and Van Horn, Ko Ro Practical MetallurgyO American Society for Metals, Cleveland Ohio, 1940o 3o Pearson, Co E, The Extrusion of Metals, New York~ John Wiley and Sons, 1944, 4, Goetzel, C Treatise on Powder Metallurgyo New York~ Interscience Pubblishers, In',, 19,49o 50 Seybolt, A, U, and Burke, Jo, E, Procedures in Experimental Metallurgy, New York gJohn Wiley and Sons, Inc,,, 1953o 60 Flinn, Ro Ao Modern Cast Metals Practice, College of Engineering, The University of Michiganr 1955, 70 Ruddle, Ro Wo The Solidification of Castings, Institute of Metals Monograph and Report Series, 7, Institute of Metals, London, 1957, 8, Ruddle9 Ro W. A Preliminary Study of the Solidification of Castings, Journal of the Institute of Metals, 779(1950> 1~I 9, Feild, Ao L, "Solidification of Steel in the Ingot Mold'J American Society for Steel Treating Transactions, 11, (1927), 2640 10, Basic Open Hearth Steel Making, Physical Chemistry of Steel Making Co-s itee, AMET, New York, 1951, Chapters 11 and 1.6, 1.o Hayes, A, and. Chipman, J o Mechanism of So1.idification and Segregation in a Low Carbon Rimming Steel Ingot, A21iE~9 Trans o. 1359 (1939), 85, 12 H ultgren, A, and Phragm.en, G. Solidification of Rimming Steel Ingots, AIMB Transo, 135, (1.939), 1.33 13. Roth, Wo, Aluminulm, 25, (1943), 283 14o Ruddle, R, W, ibid refo 7, Chap, 7, 15o Savage Jo and Pritchard, W, H. "The Probleg of Ruptaire of the Billet in the Continuous Casting of Steel'' Journal. of' the Iron and Steel Institute, 178, (1954), 269, 16. Lewis, D, M. and Savage, J. "The Principles of Continuous Casting of Metals," etatllurgical Reviews, _1, (1956), 650 -129%

-13017. Jaicks, F. D., Kraay, Lb E. and Tannenbaum, Me "Continuous Casting of Three Types of Low Carbon Steel," Journal of Metals, 9, -1957d 18o Journal of Metals, August and September, 1957o 19, Smart, J. So, Jr, and Smith, A, Ao^ Jr. Continuous Casting: The Asarco Process, Iron Age, 162, (1948), 162.

Part III PRIMARY METAL PRODUCTION -131

CHAPTER XII DIRECT REDUCTION OF METAL OXIDES AND HALIDES As an introduction to the smelting techniques used for the production of metals from their oxides, halides, or other compounds, this chapter will be devoted to the thermodynamics of reduction reactions. As a general rule one may consider the relative stability of the compounds of two metals as being indicative of whether one metal may be used to reduce the other. For example, calcium oxide is a more stable oxide than the oxide of titanium; thus under suitable conditions the addition of pure calciim metal to titanium oxide will produce titanium metal and calcium oxide. The concentrations of the components in the phases which are present determine the degree of completion to which the reaction will go. The standard free energy difference for the particular reduction reaction indicates the degree of success which one might preduct would result from an attempt to perform such a reduction. The kinetics of reduction reactions are important and it is necessary that the process be carried out under pressure and temperature conditions which are favorable. Unstable Oxides The thermal decomposition of mercuric oxide has often been sighted as a classic example of the use of temperature alone for the reduction of a metal from its ore. Mercury occurs in nature principally as cinnabar (HgS) and since mercury is not easily oxidized the roasting of the sulfide mineral results in the formation of metal. The reaction is: HgS + 02 = Hg + SO2 XII-1 -133

-134The sulfide may also be decomposed by lime or iron according to the reactions: 4HgS + 4CaO = 4Hg + 3CaS + CaS04 XII-2 HgS + Fe = Hg + FeS XII-3 The kinetics of the above reactions require that they be carried out at temperatures above the boiling point of mercuryo Consequently, means must be employed for the condensation of the vaporo Vapor pressure and enthalpy data for mercury are presented in Tables XII-1 and -2, respectively. These data may be used for computations involving the condensation of mercury vapors. The use of reduced pressures for reduction reactions is often advantageous. In the case of the reduction of mercuric oxide by heat alone, the advantage of operating in a vacuum is obvious, The reaction involved would be: IgO(s) = Hg(g) + 2 02(g) X.I-4 The standard free energy change is given by the relationship: PHg PO2 AF~ = -RT ln K = -RT ln aHgO XIIT-5 Metallic Reduction of Halides The excellent mechanical properties, low specific gravity, and resistance to atmospheric corrosion, along with the fact that it ranks ninth in abundance among the elements in the earth's crust, created a strong interest in titanium, Great difficulty was experienced in producing ductile titanium directly from the oxide, and research led by W, J. Kroll led to a process involving the reduction of titanium chloride (TiCl4) with metallic magnesium in a steel chamber. o The tetra

-135TABLE XII-1 MAXIMUM VAPOR PRESSURE OF MERCURY1 (In millimeters of mercury) CP c P C 0 P OC P -30 0.000005 120 0o746 270 123o 5 -20 0.000018 130 l,186 280 156o9 -10 O oooo60 140 i 84-5 290 197o6 0 0o 00185 150 2o807 300 246~8 10 0o000490 16o 4o189 310 305 9 20 0.001201 170 6 o28 320 376 3. 30 0o002777 180 80796 330 459,7 40 o00o6079 190 12 423 340 557 9 50 0o 01267 200 17 287 350 672 7 60 0o02524 210 23 72 360 806,2 70 o0o4825 220 32o13 370 960,7 80 0o08880 230 42.99 380 113804 90 0o1582 240 56085 390 1341o9 100 0.2729 250 74O37 400. 15741o 110 o 4572 260 9630 * 1 "International Critical Tables, " III, 1928 * 400-3100 OCo Log P 66 + 70752 T

-136TABLE XII-2 HEAT CAPACITY AND HEAT CONTENT OF MERCURY2 T Cpo HT - HIJ T_ ~~~~ ~HT 11298 o15 "K Cal/~k-mole Cal/mole 298 6,69 o 300 6.68 12 400 6,54 672 500 6.48 1323 6oo 6,49 1970 629'9(1) 6,49 2165 629~9(v) 4.97 16302 700 4097 1665o 800 4o97 1714o 900 4a97 17640 1000 4 97 18140 1100 4.97 18630 1200 4,997 19130 1300 4o97 19630 40oo 4,97 20120 1500 4.97 20620 6oo0 4.97 21120 1700 4 97 21610 1800 4 97 22110 2 Elliott, J. F. and Gleiser, Mo Thermochemistry for Steelmak'ing I, Addison-Wesley, 1960o * Referred to liquid from 298 to 629o9~K; ideal monatomic gas from 629o9 to 1800~Ka

-137chloride of titanium can be produced in the liquid state by the action of chlorine gas on titanium carbide which is made by heating titanium concentrates with carbon in an electric arc furnace The reduction process, called the Kroll process, provides for the introduction of liquid titanium chloride into a closed chamber, allowing it to drip on magnesium bars heated to 750~C in a reducing atmosphere, The reaction which takes place iso TiC1 + 2 Mg - Ti + 2 MgCl XII6 The relatively high stability of magnesium chloride makes magnesium desirable as a reducing agent for the production of metals from their chlorideso Table XII-3 gives the standard free energy and heat of formation of several metallic chlorideso The Carbothermic Process The large energy change involved in the formation of CO or CO2 and the insolubility of carbon in most nonferrous materials makes carbon a highly desirable reducing agent for the production of metals from their oxides, The retorting of finely ground, intimately mixed powders of an oxide material and carbon, resulting in the production of the metallic element and carbon dioxide gas, is termed a carbothermic process. The process is highly exothermic with most metals and often, as in the case of magnesium, produces a gas containing a metallic vaporo Unfortunately as the vapors cool the reaction reverses itself and the oxide is again formed, If, however, the gases are rapidly cooled from the maximum temperature, the metallic vapor may be condensed as a metalo A process based on this principle was developed by 2 Hansgirg for the production of magnesiumo0 The carbothermic process

-138TABLE XII-$ *xFREE ENERGY FUNCTIONS AND HEATS OF FORMATION OF SEVERAL CHLORIDES' (AF - AH298)/T, cal/mole -AH298 Compound 298.1~K. 500 K o 1000 0K, 1500K Kcalmole AgCl 13.9 1305 loil(liq) 9ol -30.3 AlC13 46 45(1iq) -166.8 AuC1 141414 11 8 BeCl2 32.6 32 28(liq) 112.6 CaCl2 36.1 35.8 34,2 31,9(liq) 190,6 CeCl1 56 55 54 49(liq) 260 CoCl2 34,7 35.4 32,8(liq) 29,5 74 CrC13 55.7 55.7 52.4 49.6(liq) 132 CuC12 34 35 33 53.4 FeC1l 31 30.9 28.8 24,3 81,9 HfCl4 72 70 255 KC1 22,1 22,6 22,8 20o5 (liq) 1044 LiC1 17 4 17.8 17,5(liq) 1.6,6 97-7 MgCl1 39.7 39,2 38o0(liq) 33,9 153.2 MnCl2 32.9 32.8 30,6(liq) 26.4 111o6 NaCl 21,6 21,9 22.0 19,6 98.3 NiCi2 34,8 35.0 3309 3l.2(liq) 73 PbC12 36,2 35.8 32.8(liq) 85.7 SnC14 56,8(iqi) 127,4 TiC14 52.8(liq) 52~ 3 181.4 ZnC12 37.4 37 29,6 99.6 ZrC12 36 36 33(lig) 145 Quill, Lo Lo The Chemistry and Metallurgy of' M',illaneous Materials, Thermodynarmics New York~ McGraw-Hill, 1950,

-139has been used for the production of many metals, Unfortunately, however, in some cases the formation of a stable carbide prevents this process frotm being a practical ones One such case is that of aluminum where the formation of the carbide occurs when, aluminum is held at high temperatures in the presence of carbon. The standard free energies of several metallic oxides and carbides are-presented in Table XXI-1, The Perrosilicon Process When calcined dolomite (a mixture of CaO and MgO) is heated under vacuum with ferrosilicon at about ll000C, the magnesium is reduced and volatilized, and the SiO formed in the reaction unites with the lime to form calcium silicateo This reaction forms the basis for the ferrosilicon process for the production of magnesium, usually referred to as the Pidgeon process. This process is typical of a number of reduction processes in which metallic elements are used for the reduction of oxides, Liquid aluminum may often be substituted for the ferrosilicon alloy. Calcium or sodium are often used for the reduction of uranium oxide, Although the standard free energy change may indicate that the reaction should go to completion, if two mutually soluble metallic elements are used resulting in the formation of an alloy, the activities, particularly of the primary reactant, are reduced, and the degree of reduction is limited, Provision in the process for making a separation of the metallic components may be of great assistance in carrying out the reduction process, Gaseous Reduction Processes The reduction of chlorides by hydrogen, or of oxides by hydrogen, carbon monoxide, or methane are processes which are being given

-140considerable attention by process research and development groupso The reaction involved in such a process may be represented as~ MO + H2 = M + H20 XII-7 The thermodynamics of these reduction processes may be derived from. the data presented in the tables of this chapter and Chapter XXIo Several techniques have been proposed for carrying out such reduction processes and in view of the advantages of a large suiJrface area in carrying out gas-solid reduction operations, both packed and fluidized beds have been proposedo Although the engineering problems are more difficult in fluidized beds, the advantages of operating under continuous conditions has led to a higher interest in this type of operation, Consideration of fluidized bed reduction and the derivation of relations which are also applicable to fixed bed reduction processes are treated in the following chaptero REFERENCES 1o Hayward, C. Ro An Outline of Metallurgical Practice. New York. Do Van. Nostrand Company, Inco, 1952. 2o Dungan, To A, "Production of Mg by the Carbothermic Process at Permanente"o Trans. AoI.MEo, 159, (1944), 308~ 3-o Cavanagh, P. Eo "Direct Iron Ore Reduction," Journal of Metals, 10, (1958), 804. 4o Newton, Jo Extractive Metallurgy, New YorkS John Wiley and Sons, Inco, 1959o

CHAPTER XIII FLUIDIZED BED REDUCTION The fluidization of solids in a moving gas stream in order to carry out chemical reactions is becoming an increasingly important metallurgical processo Such a technique may be employed in operations involving calcination, oxidation, reduction, roasting, chlorination, sulfitization, and many other processes, including heat transfer and the physical movement of particulate bodies, The engineering design of such processes involves a knowledge of the pressure drop required to maintain fluidization, as well as the thermodynamics and kinetics of'any reactions taking place in order that one can. specify the mass and heat transfer taking place in the operationo Such operations are often advantageously carried out in several stageso In this case the details of each stage as well as the overall performance must be determined Pressure Drop A pressure gradient which may be reasonably well defined is necessary to overcome friction associated with the passage of fluid upward through a bed of solid particleso The pressure gradient increases with flow rate, When the pressure drop approaches the weight of the bed over a unit cross-sectional area, the solids begin to move and fluidization sets in, This motion of solids occurs at superficial velocities which are far below the terminal free settling velocities of the solid particles0 As the velocity of the fluid and the pressure drop are increased the bed continues to expand until the porosity (fraction of the bed which is void space) reaches unityo -141

-142These effects are shown in Figues XIII-1 and 2o In Figure XIII-1 the superficial velocity is shown to increase with increasing pressure drop until the point of fluidization is reachedo At this point an increase in the superficial velocity does not involve further increase in the pressure dropo Figure XIII-2 shows that the porosity of the bed increases with Reynolds number up to the Reynolds number corresponding to the free settling velocity of the individual particles, At this point each particle behaves independently of other particles in the bed and the porosity may be assumed to be lo At the point of fluidization the forces tending to raise the particles are equal to the total weight, that is, the buoyant f6rce (including the friction force) is balanced by the force of gravity of the particleso A force balance gives: | (l-X)(LA)p + (-APf)A g (1-X)(LA) p5 XIII-1 gc gc where X = porosity of the bed A = cross sectional area of the bed L = thickness of the bed p =density of the solid particles pf = density of the fluid AP -= pressure drop required for fluidizationo Solving for -APf~ -Ap - X(l-X)I (p ) ( ) X1II-2 The pressure drop equation may be used with other considerations to estimate the size of a fluidized reactor. The reactor must be large enough to accomodate the bed in its expanded. fluidized stateo The

-143UNSTABLE PACKED BED - -- FLUIDIZED BED 0 / 0 / _ I LOG (v, SUPERFICIAL VELOCITY) Figure XIII-1. Effect of Fluid Velocity On Pressure Drop for Upward Flow Through a Bed of Closely Sized Particles.

-144t Z I O. W no - Figure XIII-2. Effect of Reynolds Number on Porosity for Upward Flow Through a Bed of Closely Sized Particles. C- Lii Dp p v c^~ ~ ~~~O Re, Fiur XII2 Efeto enlsNme nPrst ^~~~~ ~o Upward FlwTruha ^do lsl Sized Particles.

-145 diameter of the bed may be determined from the mass velocity of the gas under operating conditionso The mass velocity of the gas must be such that the Reynolds number at which the system operates is above that at which fluidization occurso The operating Reynolds number is often taken as 3 times the Ieynolds number at the point of fluidization0 The height of the reactor must be equal to the height of the bed in its expanded fluidized state. This may be determined from a plot such as shown in Figure XIII-2o The steps involved in the design of a fluidized reactor include- (1) Calculation of the Reynolds number at the point of fluidizationo This involves a trial and error procedure since the friction factor is dependent upon the pressure drop in porous beds, (2) Choice of a suitable operating velocity above that corresponding to fluidization in order to fix the diameter of the reactor, (3) Construction of the plot of log Reynolds number versus porosity to determine the porosity of the bed at operating conditions and thus estimate the height of the reactor. This approach to the design of a fluidized bed reactor is outlined in Reference 1o Process Thermodynamics Thermodynamic calculations should be performed on the reactants and expected products of the fluidized bed reactor in order to determine whether or not the process is feasible, and if so, at what temperature the operation should be carried outo Several processes have been proposed involving the reduction of iron oxides using hydrogen, carbon monoxide or mixtures of the two gaseso In addition, processes of chemical reduction, thermopyrolysis or disproportionation of halides in a fluidized bed have been proposed for the production

-146of Al, Be, B, Cr, Co, Cb, Cu, Ge, Hf, Fe, Mn, Mo, Nii Si, Ta, Sn, Ti, W, U, V, and Zro These processes are not restricted to halide and oxide feedso Sulfides or other compounds which can be produced with a satisfactory degree of purity at a lower cost may be substituted. A thermodynamic consideration which is often more important in terms of the rate of the process is the fact that several reduction steps occur, For example in the case of iron, a process might be carried out advantageously with several stages which would involve one for drying and conversion of Fe203 to Fe304, a second for reducing Fe304 to FeO, and a third for the final reduction of FeO to Feo An equilibrium diagram for the systems Fe-O-H and Fe-O-C are presented in Figure XIII-3o The gas composition of either CO/CO2 or HC/ 0 required for a reduction step in converting the iron oxide to a lower oxide or to pure iron may be determined from the figure. Similar diagrams may be plotted from equilibrium data in other gas-solid systems o Material Balances The material balances for a fluidized bed. reactor can-be written around each stage of the process, based on the fact that the gain of atoms by the gas stream equals the loss of atoms from. the solid stream, This may be denoted as0 G(ynn-ynL) = S(Xn+l - Xn) XIII-3 -where G is the mass.of the gas stream, S = the mass of the solid stream Yn = the composition of the gas leaving stage n, Y n = the composition of the gas leaving stage n-l or entering stage n,

-147100 H2/HO2 MIXTURES 90 - - CCO/CO2 MIXTURES w Fe c):: 70 - - a. ~) z 60 0 0 50 z X Fe Iu 40 a-J 0 2 30 20 2 0 ----------------— < —-— ^^Fe 3I0 500 600 700 800 900 1000 1100 TEMPERATURE, ~C Figure XIII-3. Equilibrium in the Systems Fe-O-H and Fe-O-C.

-148x denotes similar nomenclature for the solid stream. This basic equation may be applied to a column of n stages where n may range from 1 to a very large number, It is apparent from Equation XIII-3 that a multistage operation is quite similar to that employed in hydrometallurgical processes and a graphical technique 2 similar to that mentioned in Chapter IX has been proposedo This graphical technique is an adaptation of that developed by McCabe and Theile for use in distillation calculations Rate of Reduction The kinetics of the reduction reactions taking place in the fluidized bed reactor may be controlled either by diffusion or by the rate of the chemical reaction, The controlling mechanism is determined by the system and the temperature of the processo Considering specifically the reduction of iron oxide'by hydrogen, McKewan showed that the rate of reduction per unit area was constant with time and directly proportional to the partial pressure of hydrogen, This indicated that the reaction was controlled at.the oxide metal interface rather than by diffusion through the reaction product layerO In view of the foregoing considerations a rate equation can be derived to fit the reported data, Consider a sphere of iron oxide of- initial radius, ro and initial, density, p o Assume that the rate of formation of uniform reaction product layer is proportional to the receding surface area of the remaining oxideo If W is the weight of that part of the original material that has reacted thens dW T A XIII-4 dt

-149% -, -- where k is a proportionality constant having the dimensions, m 1 t and is a function of temperature, pressure and gas compositiono From this it follows thato r P f = kt XIII-5 where f is the ratio of the thickness of the reduced layer to the initial radios.o Equation (XIII-4) states that at the oxide metal interface the amount of oxide reacting per unit area per unit time is constant or that the reaction interface advances at a constant rateo The fractional reduction, R, is defined as the weight of oxygen removed divided by the total weight of oxygen originally present as iron oxide, The fractional reduction, R, bears the following geometrical relationship to the fraction thickness, f0 f 1 - (1 - R) Xl/3I-6 Substituting this value for f into Equation (XIII-5)~ rp [l- (!-R)1/3] kt XIII-7 The same eqiqation would apply to a cube whose side equals 2roo The reduction rate for any particle whose shape is similar to a sphere or cube can be approximated by Equation (XIII-7) Equations can also be derived to fit other geometrical shapeso The results of the above investigation were interpreted in terms of the theory of absolute reaction rates (Chapter IV)o The specific rate constant, k', may be defined aso kT -AH* S kg s h e FR e * XIIT-8 k' = ~- e RT e where K is the transmission coefficient initially taken to be unity, k is Boltzman's constant, h is Planckes constant, AH* is the entropy of activation., and -S-* is the entropy of activation.

-150For the case of hydrogen reduction of iron oxide the rate is directly proportional to the byd-rogen concentration where the hydrogen concentration [H2] is expressed in mols per liter, Therefore the rate of reduction of iron oxide by hydrogen will be~ AH* kT - W AS* Rate = ko - [H2] e e XIII-9 The data obtained in the foregoing investigation showed a break occurring at a temperature below which wustite (FeO) is no longer stable. The interface in the high temperature range is FeO/Fe and in the low temperature range it is Fe304/Fe, The equations for the two ranges are: -15,300 High Temp Rate = 7.32 T[H2]e RT gm/cm2-min XIII-10 -l49900 Low Temp Rate = 9,12 T H2 e P- - gm/cm2-min XIII-ll Another approach to the kinetics of reduction of a granular bed of iron ore was taken by Wiberg and Edstrom6 who showed that the reduction of iron ore in a gas stream tends to follow a first order reaction rate. The expression for this is~,-k c XIII-12 dt r The term dc/dt is the rate at which oxygen is removed. from the ore in pounds of oxygen per pound of iron per hour; c is the concentration of oxygen in the material in pounds of oxygen per pound of iron; k is the reduction constant in hours - Collecting terms and integrating between c at = and c at,time t co n = kr t XII-13 c

-151or the fraction of oxygen remaining at time t is~ f - e r XIII-14 As a first approximation it' may be assumed that the overall reduction rate of ore particles in a fluidized bed proceeds ac.ording to this type of equation. The actual value of the reaction constants kr should be determined in a small scale reduction bed in which conditions would be typical of those in the larger unit which is being designed. Residence Time In view of the highly dynamic characteristics of a fluidized bed, mixing of the solid particles is assumed to be perfect. Several 7,8 investigations have shown this to be approximately trueo With this assumption the residence time of particles entering a single stage can be determinedo The mean retention time (G) as defined below may be taken as a suitable measure of retention~ G = quantity in system/rate of treatment XIII-15 where G is in units of time and. the other aquantities are in a consistent set of unitso To estimate the retention time of solid particles in the reactor, let us assume at time t = 0 a small quantity, no, of tagged particles is added with the feed; let n = the number of tagged particles in the reactor at time t (n = n when t - 0)o The concentration in the reactor and in the exit stream at time t is n/V, where V is the volume of the systemo The number leaving the tank in a time increment dt, is then -dn which must equal the product of the effluent concentration, n/V and effluent volume, vidt, where v is the flow rate through the systemo Thus~ n -dn = dt XIII-16

-152Integrating, and noting that n = n when t - 0~ n ln Q = t XIII-17 r' V Since V/v is the mean retention time, G, defined preriously and n/nO may be defined as r, the fraction still remaining in the system at time t, then~ r ea XIEi-18 The fraction of the total number of particles discharging in the time interval from t to t + dt is -dr; ioe, -dr is the fraction of the particles with retention times between t and t + dto Differentiating the previous equation~ t dr. e XIII -19 dt G The normalized plot of -dr/dt vs t in Figure XIII-4, based on this equation, shows graphically the distribution of retention times, The total area under this curve from t = 0 to t oo is unity. The area under the curve between any two t'imes, t1 and t2, represents the fraction. of the atoms with retention times between t1 and t Using Equation (XIII-18) it can be shown that the fraction of particles retained in the reactor for a period less than. the mean retent tion me,, is (1 -1/e) or 0o63o When mixing predominates over direct displacement as the characteristic of flow through a piece of equipment, the above analysis shows that a substantial part of the feed material is retained for a very short time while another substantial part is retained for times much lon'ger than the mean retention time0~ Accordingly if a definite time of retention is required to complete a chemical reactisn, som.e substances may pass through unreacted while others are retained longer than necessary. One solution for this problem is to design the process as a

-1531.0 0.8 I_ l 0.6 \ 0.4 MEAN RETENTION TIME 0.2 0 I t,/0 2 te 3 4 5 t/e Figure XIII-4. Distribution of Retention Times for Perfect Mixing in a Continuous System.

-154multi-stage reactorO Another manner in which this difficulty may be overcome is through the use of a recycling stream, In the case of iron ores, a very effective method is to use magnetic separation of the completely reduced iron in the product stream of the reactor and to recycle the nonmagnetic materialO Separation processes may be used in a similar manner depending upon the physical and chemical differences which exist between the product which is completely reacted and that which is only partially reacted, Energy Balances From the viewpoint of thermal equilibrium. a fluidized bed qualifies quite well as an ideal stage, since gases and solids entering such a bed attain bed temperatures almost instantaneously. Temperatures are essentially constant throughout a fluidized bed and the solid and gas streams are consequently at the same temperature0 This is essentially true even when the gas and solid streams entering the bed are at temperatures very different from the bed, and also in cases where chemical reactions are occurring which involve large heat effects. On this basis, a heat balance may be written about each stage of a fluidized bed reactor As in any other heat balance, the terms to be considered are the sensible heats of the reactants and the products, the heat evolved by any reactions taking place in the process. the heat losses and any additional energy supplied to the processo A carefully drawn heat balance should permit the operator of the equipment to carry out the process very close to the optimum temperature0 In practice. the temperature of theprcess can be nt ed by the nadjustment of energy put into or taken out of the equipment itself or by control of the degree of preheating of the inlet materials,

_A_ 5 55 REFERENCES i, Brown, Go Go and Associates, Unit Opeat ionso New York~ John Wiley & Sons, Inco, 1950, Chapter 20, 2o Meissner, Ho Po and Schora, F, C. "Graphical Technique for a Multistaged Fluidized Bed Operatido as Applied to Iron Ore Reduction,"'Transo AoI MoEo 218, (1960), 1.2 3, McKewan, Wo Mo "Kinetics of Iron Ore Reduction" Trans. AoIMoE,, 212, (1958), 791. 4o McKewan, Wo M. "Kinetics of Iron Oxide Reductiono" Transo AoIoMoEo, 218, (1960), 2. 50 Wiberg, Mo "Reduction of Iron Ore by Carbon Monoxide-HydrogenMethane," Jerkonterts Annaler, 124, (1940), 7790 6. Edstrom, Jo 0o "The Mechanism of Reduction of Iron Oxides," Journal of the Iron and Steel Institute, 175 (1953), 289, 7. Gilliland, Eo Ro and Mason, E. A. "Gas and Solid Mixing in Fluidized Bedso" Industrial and Engineering Chemistry, 41, (1949), 1191 80 Gilliland, Eo R, and Mason, Eo Ao "Gas Mixing in Beds of Fluidized Solidso" Indo and Engo Chemo,, 44, (1952), 218, 9o Schuhmmann,R Jro Metallurgical Engineering9 Volo lo Cambridge, Mass,~ Addison Wesley Press, 1952, Chapter 2o 10o Leva, Mo. Fluidization, Chemical Engineering Series. New York~ McGraw-Hill, 1959o 11, Cyr, Ho Mo, Siller, Co Wo and. Steele, T, Fo "Roasting Metallic Sulfides in a Fluid Columno," Journal of Metals, 6, (1954), 900. 12o Bryk, P, et alo "Flash Smelting Coppe Concentrateso" Journal of Metals 0, (1958), 395~ 13o Stelling, 0o "Carbon Monoxide Reduction of Iron Oreo" Journal of Metals, 10, (1958), 290. 14o Oxley, Jo Ho and Campbell, Io E, "Fluidized Beds for Metal. Production," Journal. of Metals, 11, (1959), 135o 15o Brandt, Ho Ho and Marshall, Wo Eo "Rates of Reduction of Some Iron Ores in a Fluidized Bed," International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, 1959, 16o Henderson, J. BO "A Study of the Rate and Mechanism of the Hydrogen Reduction of Fine Hematite Ores, International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, 1959,

-1561.7. LangQtOn, B Go and Stephens, F Mo Jr "Self-Agglomerating Fluidized Bed Reductiono") Journal Of Metals, 12,(1960), 312o

CHAPTER XIV REVERBERATORY FURNACE SMELTING The reverberatory furnace is often employed for extracting metals from their ores. Ore and fluxing agents are charged to a furnace to which external heat is supplied, bringing about melting and at the same time chemical changes necessary to produce the metal (or sometimes matte) from compounds existing in the ore, A reducing agent, often in the form of powered coal such as used in tin smelting, is added. The charge materials are essentially those added to the blast furnace, but when the operation is carried out -in a batch process, the term used to describe it is simple smelting. Reverberatory furnace smelting is a key step in the extraction of copper from its ores. Ore and liquid slag from the converting step containing copper, iron, sulfur and oxygen along with gangue oxides such as silica, alumina, magnesia, etc. are charged to the furnaceo This mixture is heated to temperatures above 12000C so that the entire charge is molten0 Two liquid phases result (1) a copper matte consisting of copper, iron and sulfur, and (2) a slag which is a solution of iron oxide, silica, alumina, magnesia and other oxides but with a low copper contento These two phases separate under the influence of gravity, the heavier matte accumulating in the bottom of the furnace. These two liquids are tapped from the furnace, and are the principal products of the processo In addition, some reactions yield sulfur dioxide and other gases from the burning of the fuel which pass out through the flue The essential features of a reverberatory furnace for carrying out this process are shown in Figure XIV-lo1 -157

-158Q"~ 0 LL5 0 0. n" Q I IU IZ U) Q 0i0 cL5LL ~ ~ ~ ( -i -Jo(Z 0 ~ ~ ~ ~ ~ ( I irI! o~~a

-159For the successful operation of a smelting process9 it is important that the engineer understand the operation and be able to express it in terms of mass and energy balances. A knowledge of the equilibrium relationships involved in the process and consideration of the rates of reactions involved will permit a mass balance to be written for the process, Similarly the energy balance and specification of the fuel requirements may be determined from the sensible heat of the input materials, the heats of reaction, and a knowledge of the heat losses from the processo These factors which affect the smelting operation in the reverberatory furnace are considered below, and for illustrative purposes are treated in terms of copper smelting operations o Material Balance A metallurgical balance for the copper reverberatory furnace has been prepared showing the variations in charge requirements for several matte grades, The material balance often involves a number of assumptions, particularly regarding the products of combustion~ The compositions of the charge materials are usual.l.y know n., or may be assumed to'be typical of the practice usedo The products of the smelting operation may usually be assumed to be in equilibrir-,m. with respect to distribution of elements between slag and matte or metal, or to be typical of the smelting practice in volvedo On this basis and making the use of element balances, a material balance may be made for the reverberatory furnace, Depending upon the desired composition of matte to be produced, one may compute a smelting charge requirement6

-16oEnergy Balance A list of thhe reaction involed in the fusion of the. complex mixture which is charged to the reverberatory furnace in copper smelting would be extremely longo Any attempt to quantitat iel y relate the energies involved in that given list of. reactions with what actually takes place in the reverberatory furnace is essentially impossible, The ore charged into a reverberatory furnace may contain Cu2S, C-u2O,- CuO, CuSO4, FeS, FeS04, Fe203, Fe203, and Si02 together with various complex silicates of iron, aluminum, etCo In addition, the complex mixture of converter slag which is recycled to the reverberatory furnace is also added along with silica and other components in the fluxing agents.o On the basis of the assumptions used in making the material balanee, one might make a reasonable guess at the heat evolved by reaction duriing reverberatory smelting0 One diffi>culty over and above the complexity of the situation which exists in the furnace is the fact tha-t data in general are lacking on the heats of solution and heats of reaction for. most of the systems involved0 In view of this fact, an estimation of the energy requirements for reverberatory smelting might be made by neglecting energies of reaction for the system, The energy balance then becomes a summation. of the sensible heats of the products minus the sensible heats of the reactants and the heat losses from. the furnace, The figure resulting from the summation should be the fuel requirement, The sensible heat of the materials may be estimated from specific heatsO Although specific heats may not be available for the actual materials involved, they can be estimated by consideration of the specific heats of the

-16 1elements themselves in the quantities in which they are present or through the use of some overall. mean specific heat representing a material which is typical of the total charge in the furnaceo The heat losses may be estimated by consideration of the rate of heat conduction through the construction materials of the furnace, This heat loss must be equal to that lost by radiation and convection from the outer surfaces of the furnaceo Specific attention should be given to the heat losses from furnace openings during chargingo In view of the extremely high temperature of the interior of the furnace, heat losses through furnace openings for relatively short periods of time represent a major fraction of the total heat loss of the unit, Kinetics of Reverberatory Smelting In view of the fact that relatively little is known about the particular equilibria which exist in the furnace, relatively little may be said about the rate controlling steps involved in the smelting processo In view of the fact, however, that the product of a smelting process is two liquid phases, a slag and a metal (or matte), the rate of approach to equilibrium, when equilibrium is known, may be estimated from either the rates of the chemical reaction which iS involved or the rate of transport of a given species from one phase to the other, The principles involved in such a calculation are outlined in detail in Chapter XXo Heat transfer in the open hearth steelmaking process has been reviewed by Bo Mo Larsono

-162EERN CES 1, Benz, Mo Go Departmefnt of Metallurgy, M:T, unpublishedl 2o Schumann, Ro Jrr0, Powell, Ro Go and. Michael, E, Jo "Constitution of FeO-Feo20-Si02 System at Slag Making Temperatures " Journal of Metals, 5, Sept~ 195 3 30 Bray, J. Lo Nonferrous Production Metallurgyo New York~ John Wiley & Sons, Inc o,.94 —~ 4o Hayward, Co Ro An Outline of Metall:urgical Prac. tice. New York~ Do Van Nostrand Coo, Inc,, Chapter 1o 50 Ruddle, Ro Wo The Physical Chemistry of Copper Smelting. Institute of Mining and Metallurgy, London, L953 5o Butts, Ao Metallurgical Problems Metallurgy and Metallurgical Engineering Series,, New York.~ McGraw-Hill, 1943, Chapter 10o 7o Schuhmann, Ro Jro Metallurgical Engineeringo Cambridge, Mass o0 Addison-Wesley'Press, 195.2 8. Newton, J. and Wilson, C0 L. Metallurgy of Copper, NeW York~ John Wiley and Sons, nc, In, 1.942 9o SchumLnH.- Ro Jro, "A Survey of Thermodynamics of Copper Smelting, " Transo AOI.M.E.O 88, ( R950) 873 10 Johnson, Ro Ko "The New Hayden Smelter o" Journal of Metals, 11, (1959) 376. 11.'Operating Statistics for the Gaspe Smelter, Journal of ketals, 9, (1957), 1117i 12, Basic Openhearth Steelmakingo Ao.I.MoE, ew York 1951, Chapter 200 13o Newton, J. Extractive Metal.lugy. New York: John Wiley and Sons, Inc., 1959, Chapter 7.

CHAPTER XV THE BLAST FURNACE The blast furnace process consists of charging ore, fuel and flux into the top cfa shaft furnace and blowing heated air or blast into the bottom, This process is the backbone of the steel industry, producing a high-carbon. high-silicon., high-manganese cast iron which is converted to steel in the steelmaking furnaceso The process is also used for the production of leado In the case of the iron blast furnace, the approximate relations between -the reactants and products is such that per ton of iron produced, approximately 2 tons of ore, 0o9 tons of coke, 0o4 tons of a mixture of limestone and dolomite, and 3,4 tons of air is charged into the furnace, From these materials there is produced l10 tons of iron, 0O6 tons of slag, Ool tons of flue dust, and 5ol tons of blast furnace gaso This rough statement relates to the production of pig iron in Northcentral United States, about 75% of the production in the USoAo Iron is supplied to the furnace by ore in the form. of the oxide, either hematite (Fe203) or magnatite (Fe304) Pure hematite contains 70% iron, but the present ore being mined from the Lake Superior region contains about 50% iron, the difference being represented by ganguee, which consists mostly of silica and alumnina, and about 12% moistureo Iron is also supplied by charging mill scale, sinter, slag from open hearth furnaces or Bessemer converters, and scrapo The fuel to provide temperature and also the source of the reducing agent is coke, the solid produ.ct of the destructive distillation of coal. Limestone and dolomite are added to form a fluid- slag -163

-1.64and to restrict the amounts of silica sul.phur and phosphorus entering the pig irono The blast, which is heated air, sometimes enriched with oxygen, supplies oxygen to the process which reacts with the carbon of the coke to form. carbon monoxide, the gaseous reducing agento (Figure XV-1), The blast furnace plant consists of several components, the principal one being the blast furnace structure itself, The blast is compressed by blowers and passes through stoves, where it is heated to a temperature of about 1550~Fn The stoves involve regenerative heat transfer and fuel is supplied by the blast furnace stack gases, which have been treated to remove dust, In addition, the blast furnace operation requires charging equipment and ladles for the removal and transport of metal and slag, Secondary equipment includes a sinter plant where iron oxide from narious steel-making operations, as well as from the dust collecting equipment of the blast furnace, and ore fines are sintered into a usable product~ Coke ovens are necessary for the production of coke from coal, and often a fully integrated plant will also include production fac'lities for the manufacture of by-products from coke oven gases. A fully integrated steel plant will include in addition to these facilities comple te steemking facilities and all the auxiliary equipment involved therewitho Discussion in this section will be confined to the iron blast furnace It should be noted that the principles involved are the same in other blast furnace processes, Chemistry of the Process The principle reaction taking place in the blast furnace process is the reduction of iron oxide by carbon~, The actual mechanism for this process involves gaseolus reduction by carbon monoxide according to the reactions

-165DOUBLE BELL CHARGING SYSTEM FOR COKE, ORE, LIMESTONE EXIT GAS EXIT GAS V dJ ~ \ COLUMN -MOLTEN SLAG Figure XV-1. Cross Section of Blast Furnace. ~'K S T A. BUSTLE PIPE-' ^ BOSH SUPPORT ING O —----- COLUMN [ MOLTEN SLAG Figure XV-l. Cross Section of Blast Furnace.

-1663 CO + Fe203 = 2 Fe + 3C02 In the presence of an excess of carbon at a high temperature, CO2 is at once reduced to C0o C02 + C = 2 CO XV-2 The actual reduction of Fe2O3 by CO may take place in three steps, the Fe203 being successively reduced to Fe304, FeO and finally Feo In addition to reducing the oxides of iron, carbon also reduces the oxides of manganese, silicon and phosphorous according to the reactions~ MnO + C = n + CO XV-3 SiO + 2C =Si + 2 CO XV-4 P^5 + 5 C = 2 P + 5 C V-5 The water vapor in the blast also plays a role in the process~ I20 + C CO + H2 XV-6 The hydrogen liberated by the above reaction may react with iron oxide reducing it: FeO + H =- HO0 + Fe XV-7 The water so formed is again decomposed. It should be noted that relatively few of the reactions involved furnish the heat required for the process, but that it is the oxidation of carbon and some of the reduction reactions involving carbon monoxide that furnish the heat to dry the raw materials, decompose the limestone, melt the iron and slag and to replace the heat losses, Reactiam (XV5-3)through(-5)indicate that since the construction materials for the hearth are essentially pure carbon and the gas composi

-167tion in the region of the tuyeres is controlled. principally by the blast rate and temperature, and is not subject to great variation, that the distribution of the alloying elements, manganese, silicon, phosphorous and sulphur are controlled principally by the slag composition and temperature of the hearth, Between 50 and 75% of the total amount of manganese charged, principally in the ore, is found in the pig iron.o The highest proportion being obtained with high hearth temperatures and basic slagso The amount of phosphorous in the iron is Controlled directly by slag composition, A low temperature and a high basic slag are required to obtain lOw phosphorous. Sulphur which is carried into the furnace principally by the coke. and often by the ore, may be retained largely in the slag at high temperatures in the presence of carbon and a basic slag. The silicn onontent of the pig iron is controlled by the activity of silica in the slag. High temperatures and acid slags favor high silicon contents.0 In view of the extremely important role played. by slag composition in the blast furnace process, considerable research effort has been expended on studies of blast furnace slags~ The thermodynamic properties of blast furnace slags were recently reviewed by Chipman3 In addition to the role played by slag composition. the interaction of dissolved elements in liquid iron are also important with respect to blast furnace metal composition~ The equilibrium constants for Equations(XV-3) through (XV-5) involve the activities of the dissolved constituents in the liquid metal. These activities are a function of the liquid metal composition, that is, the amounts of other alloying elements present, A principal interaction which occurs in blast furnace metal is that between carbon and silicon in

-168solution. The solubility of carbon in liquid iron is greatly reduced by the presence of silicon as. shown in Figure CX7-2. Since the liquid pig iron leaving the blast furnace hearth is essentially saturated, ioeo at equilibriumm with pure carbon at the temperature of the hearth, the activity of silica in the slag, which is a function of silica content, slag composition, and temperature, controls the silicon content of the metal which in t-urn contr:oLs the carbon content, The influence of temperature on the solubility of carbon in iron silicon alloys is also shown in Figure X-22 The relationships between activities of slag components and slag composition, and temperature, as well as the interactions which occur in the liquid metal are relativel.y well knowno It follows that with this information, the heats of reaction and specific heats for the prodacts and reactants when combined with the mass balance may be used to calculate an energy blance for the blast furnace processo Blast:.Frnace Stoichiometry A mass balanace around te ablast furnace not only describes in detail the mass flow of the streasms going to and from. the system and permits an energy balance to be writ;en'based. on it, but is also very helpful in performing charge calculatifons, A material balance for the blast furnace requires a knowledge of the composi tion and amounts of each stream going to and from the blast furnace system. Often times this information is known with limited. accuracy and one m.st therefore estimate or make assumptions. concerning the dispositi.on of given materials between various streams0 The slag volume and theoretical slag composition may be calculated frOm lime, magnesia, silica and al.umina

-169z co 4. OII I, I-.I 43 Ow 4 690_ ___ a| 2 ____ ___1290~C -!I0 2 4 6 8 10 12 14 WEIGHT PERCENT SILICON Figure XV-2. Solubility of Carbon in Iron-Silicon Alloys.

-170balances, an iron balance is used to calculate the mass of the metal stream, and carbon, oxygen and hydrogen balances are used to determine the exit gas volume and composition. Several examples of this type of calculation have been presented in the literature5, 6 Energy Balance The total enthalpy balance for a blast furnace operation during a given reference period may be written in the form~ blast + Hburden + Hstone + Hcoke ot metal + Hlag +Htop gas + heat loss XV-8 It is necessary to solve the equation for the term, Hheat loss" In doing so. the sensible heat of the burden, stone and coke are taken as 0, since these components may be assumed to enter at 77~F, the base temperature, The sensible heats of the blast and hot metal may be computed directly. The sensible heat of the top gas may be computed ursing the reported CO-CO2 ratio and assuming the ratio H2/H20 = 4. For normal operation, ie, without high blast moisture or hydrocarbon injection at the tuyeres, the latter assumption has little or no effect on. the over-all enthalpy balance. It is often necessary to assume a temperature for the exit gases. 400OF is often selectedo In calculating the sensible heat of the slag, the stream is assumed to be a mixture of 2 CaOSi02; 2 CaOo 0a7 Ha oi8 A1203; SiO2; CaO SiO2; 2 MgO.SiO2; and CaSo Heats of formation for these compounds and their specific heats9'10 may be used to compute the sensible heat of the slago It is a reasonable assumption to neglect the heats of mixing of these slag components and then whether the slag actually consists of the compounds or not is of no significance in the calculation. The heat loss term of Equation (XV-8) can now be computedo

-171Heat transfer in the blast furnace has been examined in some detail by Ceckler and LanderL who concluded that furnace height should not influence the coke rate. Thermochemical Model of the Blast Furnace Recently a method of calculating the changes in blast furnace performance brought about by burden and./or blast modifications was 7,12 developed. The method is based on three simultaneous equations derived from the material and heat balances, These equations involve the computation of the moles of blast required to produce 1 pound atom. of iron, the moles of carbon per pound atom of iron which act directly with oxides in the furnace, and the change in carbon rate per pound atom of iron as compared to the reference period carbon rateo The equations used to relate these three unknowns are a carbon balance an oxygen balance and an enthalpy balanceo These three simultaneous equations are set up on the basis of the initial and final states of the various elements and their corresponding temperatures plus a furnace characteristic k defined by the equations k = Hheat loss/ mole of nitrogen per pound atom of iron for the given reference periodo XV-9 The thermochemical model is especially useful in problems connected with production planningo If an increase in the hot metal production is required from a group of blast furnaces, it. is necessary to assess the costs involved and attain the desired production rate by various combinations of blast and/or burden modification, Performance data calculated using the model can provide information on Thich cost comparisons can be based, In view of the complexity and nbumber of equations which are

-172involed, this model is most conveniently handled by a digital computer as outlined rin Chapter XXIVo The variation in hot metal cost resulting from the use of various blends of available raw materials can be assessed. using linear 13 programming techniques. This approach was first used by Bailey who incorporated into his linear program the statistical information devel14 oped by Flint, A linear program inrvolving the thermoche mical model and in addition r estrictions on the quality requirements for input and output streams and the economics of operating and freight costs can be used to optimize the blast furnace burden at different locations with regard to cost and productiono Development of a thermochemical model and its use on the digital computer has resulted in the prediction of blast furnace performance with reference to the additions of water vapor, natural gas and oxygen in the blast, ~ Blast Furnace Kinetics The rate of production of hot metal from a blast furnace installation may be dependent upon many factors It would appear, however, that the principal rated-imiting conditon is fixed by the rate of supply o~ - reactants and removal of products from the furnaceo For given blast furnace dimensions, the rate is primarily limited by the supply blast9 the maximum rate of blast being that which would be necessary to fluidize the blast furnace chargeo This limit may be computed ussing the techniques outlined in Chapter XIII For most blast furnace installations, the capacity of the blowing system is usually far below this limit, except for cases where the burden consists of extremely fine matearial., It has often been stated that in actual production facilities the real limriting

-173factor which controls the blast furnace production is the ability of the material handling systems to supply reactants and remove products from the furnaceo Successful integration of such auxiliary equipment as cranes, skip jack hoists, unloading and conveyor belt systems is discussed from the theoretical standpoint in Chapter XXVo Numerous correlations have been drawn between furnace dimensions and daily production rateso The results of these correlations indicate that the rated daily production of a furnace is given by the hearth area in square feet multiplied by a factor which ranges from 2.0 to 2,6, the actual value depending upon the particular furnace burden. The daily production rate has also been related to the coke burned per day which is in turn determined by the area in square feet of an annular ring six feet wide in front of the tuyeres multiplied by the factor 6300~ These relationships may also be used to indicate the proper number of tuyeres for a given hearth diametero Such correlations are based on present practice and often serve as a guide to the design of blast furnace installationso A further limitation on blast furnace produ.ction rate could be the kinetics of the reduction processo This has been discussed in some detail in Chapter XIII and. will be considered only qualitatively here due to the mathetical problem of dealing with a strong temperature gradient throughout the furnace bedo One can, however, estimate the rate of reduction assuming that the process is carried out by pure carbon monoxide gas at the prevailing temperature of the furnace chargeo Integration of this rate equation throughout the bed height would then give the required furnace height and the necessary residence time for the charged materialo

-174Improvements in Blast Furnace Operation In addition to design improvements the principal advancements in blast furnace operation have been. ontrol of the blast humidity, oxygen enrichment of the blast, natural. gas or other fueS enrichment of the blast, pressure operation and the increased use of beneficiated materials, Over one-half of the material. entering the blast furnace is airo Consequently, relatively small changes in humidity are important with regard to the amoun-t of water carried into the Jfurnace, The endothermic decomposition of the water vapor in the hot zone adjacent to the tuyeres absorbs considerable heato This additional heat absorbed in the hearth of the furnace increases the amount of fuel required in the form. of coke, Considerable fuel saving can be accomppl.ished by drying the blast-stream either by a refrigeration cycle or by passing the air throu.gh suitable 15 drying columns, This bears out the importance of the humiidity of the blast with regard to blast furnace performance, Controlled humidity has been proposed as a means of regulating the blast furnace 15 Oxygen enrichment of the blas as a means of increasing furnace output has been proposed. for some time, The availability of large supplies of low-cost oxygen as the res-ult of advan ced developments in steelmaking processes has made this proposal even more feasible, It has been predicted that a 6% oxygen enrichment of the blast would increase production. rates from 20 to 25 per cent, The effect of oxygen enrichment is to decrease the nitrogen content of the blasto This should result in less heat being carried from the furnaces by the top gas, a decreased volume and. velocity of the reacting gas with a corresponding reduction in flue dust production, and an increased rate of combustion of the coke with higher hearth temperatures,

-175The amount of oxygen passing through the furnace for a given gas velocity may be increased if the furnace is operated under pressureo Modifications to existing blast furnaces were made at the time of World War II and showed a 15% increase in production with a decrease in coke rate of about 12-2 and in flue dust of about 33% Top pressures approaching one atmosphere gauge have been obtained, although there is often considerable mechanical difficulty connected with the operation of a blast furnace under pressureo Enrichment of the blast with natural gas has also been shown to result in a lower coke rate, The beneficiation of materials improves burden properties by concentration and enrichment, and may also improve the physical form of the burden as wello The washing and sizing of the burden is a very important aspect in obtaining optimum furnace performance, Considerable economy is also obtained with regard to transportation of charge materials to the furnace site if they are beneficiated at the mineo In addition, sizing of material prevents channeling of the gaseswith, resulting efficiencies in mass and heat transfer in the furnace shaft, and also promotes a more uniform movement of the burden down through the furnaceo

- i76-E REPRENCES lo Camp, J. Mo and Francis, C Bo The Making, Shaping, an Treating of Steel, PitLtsbhurgh U, So Steel Corporation, 195.1 2, Hayward, Co Ro An Outline of Metallurgical Practice, New York0 Do Van Nostrand Co, 1952o 30 Chipman, Johnr "Thermodynamic Properties of Blast Furnace Slags, International Symposirmm on the Physical Chemistry of Process Metallurgy, Pittsburgh (1959) o Proceedings to be published, 4. Chipman, J et al, "Activity of Silicon in Liquid Iron-Silicon and Iron —Carbon-Si7ion Alloys," Aeta Metallurgica, 2, (1954) 439, 5, Lewis, W, K,, Radaschb Ao Ho and Lewis, H, Co Industrial Stoichiometry, Chemo Eng, Series, McG raw-Hill^ 1954^ Chapter 10o 6, Butts, Ao Metailu.rgical Problems, Metallurgy and Metallurgical Engineering Series, MCGraw-Hill., 1943., Chapter 5 7' Landers Ho No,, Meyer, H W, and Delve, F, D, "A Thermochemical Model of the Blast Furnace," AI.E Annual Meeting, FebO 1.960 New York, 80 Joseph, To Lo and Newstatter, K. "The Use of Carbon in the Blast Furnace Heat Balances," Blast Furnace and Plant Proceedings, 35, (1947), 824 and 944, 9, Richardson, F, Do and Withers, Go "Thermodynamics of Substances of Interest in Iron and Steel Making, Part II," Compounds Between Oxides Journal of thoe on and Steel Inst-+tute, - 66 (1950) 2.13 10, Umino, S Science Reports of Tokyo Ip erial U nier_ it, 1!6, (1927), 575 o 11o Ceckler, Wo Ho and Lander, Ho N, "An Approach to the Problem. of Heat Transfer in the Blast Furnace," AooMoEo Annual Meeting, 1960, New York, 12, Lander, H, No,, Meyer, H, W,, and Delve, F, Do "Prediction of Blast Furnace Performance from Operating and Thermal Datao" To be publishbed, 13o Bailey, Do Ro "Burdening a Blast Furnace for Minimum Costs," AIME Proceedings of the Blast Furnace, Coke Oven. and Raw Materials Conference, 16, (1956), 1.5, 14, Flint, Ro V "A Multiple Correlation of Bla F urnace Variables,' AIME Proceedings of the Blast Furnace, Coke Oven and Raw Materials Conference, 11, 1952, 150 Hodge, A Lo "Computer~ Key to Predicting Blas+ Furnace Behavior," AISI Meeting, New York, May 25, 1960 Als.o Iron Age, June 2, 1960,

CHAPTER XVI Converting Processes The term "converting" is used to denote a further operation in producing a metallic element from the output material of a smelting operationo Converting has come to be used. almost exclusively in connection with processes which involve the-further refining of primary smelted material by blowing an oxidizing gas through ito Strictly speaking, however, in the case of steelmaking operations, converting could also be applied to the open hearth and electric processes which involve the oxidation of primary smelted pig iron to steel. The operation is carried out for these two processes in a closed furnace and oxidation is provided by the addition of iron oxideo The discussion of this chapter, however, will be confined. to converting operations in which an oxidizing gas is usedo The Bessemer Process Sir Henry Bessemer of England patented the pneumatic converter process in. 1856. Although the process has undergone several developments and considerable modification over the past century, it still maintains its essential featureso Liquid pig iron, the product of the blast furnace, is charged to a vessel and air is blown through it, oxidizing the dissolved carbon, silicon and manganese to very low impurity levelso The product, which is essentially pure iron containing low levels of alloying elements, is termed steelo The operation of a Bessemer converter is presented schematically in Figure XVI-Io In specifying the operating conditions for the Bessemer converter the engineer is interested in the oxygen. requirements, i oeo, the -177

-178WIND BOX -TUYERES ______\___. o...*.O***..* *... L. CHARGING 8 POURING BLOWING Figure XVI-1. Operating Positions of Bessemer Converter.

-179blast, the temperature of the metal, which determines the amount of scrap which may be added to the converter, and the time of operationo These operational features of the process may be specified by mass and energy balances and a consideration of the kinetics of the processo Material Balance The blast and flux requirements for'the converting process may be determined from the initial and final compositions of the batho Two items in the material balance which are particularly difficult to specify are~ (4) The composition of the exit gaseso Analyses of exhaust gases dubring the progress of a Bessemer blow indicated that early in. the blow large amounts of carbon dioxide and some pure oxygen were evolved10 As the silicon content of the iron was reduced, however, the amount of CO in the exhaust gases increasedo During the last two-,thirds of a heat the exhaust gases then. consisted essentially of carbon monoxide and nitrogeno Toward the end of the heat after the carbon had been removed, no composition data were reportedo An assumption in this regard which is often made is that the blast is 100% effective and. the exhaust gases contain carbon monoxide and carbon dioxide in the ratio of 4 to 1, as an average for the entire blowing period, (2) The loss of metal from. the bath is difficult to specifyo One often assumes that a frac tion of the charged metal is lost from the mouth of the converter as iron oxide dusto This percentage varies with different practices but may be of the order of 2 or 3 %. On the basis of typical hot metal charge analyses and typical end point steel analyses, a material balance may be written as outlined aboveo Similar material balances for copper converting have been presented0

-180o Energy Balance The energy balance for a converter is particularly important in determining the bath temperature. Since no external fuel is supplied, the process is completely autogenous. Consequently, an accurate specification of the amount of scrap to be added in order to prevent the converter from overheating is extremely important in converter operation. The energy balance for a converter process may be written in terms of the sensible heat of the reactants and products, the heat generated by reactions during the process, and the heat losses, The sensible heat of the materials involved in the process may be determined by the data presented in Table XVI-i. In order to specify the energies evolved by reactions taking place during the converter process, it is necessary to know the details of the chemistry of the blow. The Bessemer blow may be roughly divided into three parts ~ the silicon blow, the carbon blow, and the after blow. This is illustrated in Figure XVI-2. The silicon blow begins immediately. The oxygen in the air units directly with the iron to form iron oxide which dissolves in the bath and combines with silicon and manganese0 These reactions may be represented as: 2 Fe + 0 2[eeO] XVI-1 2 [FeO] + Si = SiOi + 2 Fe XVI-2 [Fe] + Mn = MnO + Fe XVI-3 The oxides of silicon and manganese form a slag with the excess iron oxide, evolving heat: 2FeO + 3i02 = 2FeO.SiQ2 XVI - 2 MnO+SiO - 2Mn XVI- 5 2 Yln-SiO2

-181TABLE XTI! Sensible Heat Contents at Selected Temperatures Relative to a 77'Fo Base Temperature4 Heat Content Material Tem Bperature'F. BTU per Lb o Preheated Steel Scrap 1250 172 Hot Metal. lo00 % Silicon 2440 527 Hot Metal, 1o20 % Silicon 2500 540 Hot Metal, lo40 % Silicon 2560 553 Blown Metal, Steel 2950 606 Basic Slag 3000 880 Gases Temperature O"F Heat Content BTU per Lbo Mole CO 3000 23,200 CO2 3000 37,400 CO2 3500 44,700 N 3000 23 000 N2 3500 27,9300

-182o 4 w Li W 3 ~z 2 -- - - - - \ 0.020 0 z z I^ I-M4 ~-0 SAs ~^ ^ ^'~f -^_ 0.005 0 ~0 2 4 6 8 I0 1 12 14 TIME, MINUTES Figure XVI-2. Changes in Metal Bath Composition During Blowing Period of 25 Ton Bessemer Converter.

-183This particular phase of the blow lasts about f iLre minutes during which the concentrations of silicon and manganese in the metal are markedly reduced. Toward the end of the silicon blow the carbon concentration begins to fallo Carbon may be oxidized either directly by the oxygen of the blast or by the dissolved oxygen in the metal, These reactions evolve heat and may be written aso 2 C + 02 CO XVI-6 C + 02 = C02 XVI-7 C + 0 CO XVI-8 C + 20 - CO XVI-9 -..L2 These reactions account for the presence of both CO and CO2 in the exhaust gases during the first phase of the silicon blowo At the beginning of the blow, carbon monoxide is subject to reduction by both silicon and manganese, especially if these elements are present in high concentrations, The reduction reactions may be expressed aso 2CO + Si 2C + Si0 XVI-10 CO +Mn C + Mn0 XVI 11 The temperature of the bath rises considerably during the silicon blow and this marks the onset of the second period or carbon blow, This period last six or seven minutes and the principal reactions occurring are represented by Equations (Xvi-T6, 7, 8, 9)and~ FeO + C = Fe + CO XVI-12 2FeO + C = 2Fe + CO2 XVI-13 The two reactions above combined with Equation (XVI-8) may be used to account for the rapid final burnout of the remaining carbon, The remainder of the blowing period is referred to as the after blowo

-184On the basis of a mass balance and the heats of reaction, the heat evolved by oxidation of the metal.loids from the bath can, be computed, (Tables XXI-1, -2), The principal source of error in writing an accurate heat balance for the converting proces s is n specifying the heat losses, An assumption which is often made is that the heat loss is equivalent to 20% of the heat evolved by the combustion of carbon to CO and C02o An experimental method 2 has been suggested for determining the heat losses by allowing the converter to stand for a short period and measuring the change of temperature with time, Such a technique would permit a reasonable estimate of the heat losses A heat balance for the oxygen converting process has been presented in detail, including consideration of blast rate and bath composi4 tion on... the scrap which may be added to the process,~ One principal adiantage which the open hearth process holds over the Bessemer converter is in its ability to handle a wide variation in types of charge. In order to generate more heat in. the steel converter processes and thus utilize a higher fraction of scrap, ferrosilicon is often added to the converter, the oxidation of which supplies more heat units for the melt4 ing of scrap, The Oxygen Process The availability of large quantities of oxygen has greatly altered the picture with regard to converting processes, Oxygen enrichment of the blast for the converting of copper mattes or the use of pure oxygen in the 6 LD process for steel have received considerable development attention in recent yearso The amount of available heat is increased greatly by removing

-185the necessity of blowing nitrogen through the batho Nitrogen behaves essentially as an inert except for some absorption toward the end of the blow in the Bessemer processo It does, however, remove considerable amounts of heat from the process which could have been used for the melting of scrap. Fu.rthermore, the ability to supply larger quantities of oxygen to the process has increased the production rates thus reducing the cost per ton of material. produced. The mass and energy balances for the oxygen process are essentially the same as outtlined above for the Bessemer process except that the sensible heat carried away by nitrogen in the exit gases is now available for melting of scrap. Considerable expansion for the;,.ses of oxygen in the basic metals industries is predicted5' 7 Rate of Converting The refining time required for the conversion of hot metal to steel in. the Bessemer process is controlled by the rates of oxidation of the elements dissolved in the iron bath. These rates of reaction are controlled by the rates at which react-ants arrive at the reaction site It is possible that the process kinetics may also be controlled by the rate of the chemical reactions involved, However, in view of the high temperatures, it is most probable that the rate of the reaction is controlled by mass t~ransport; of the reacting specieso Several mechanisms for the oxidation processes involved in the converter operation are suggested by the equations aboveo Most of these reaction steps involve oxygen either in the gaseous or dis solved stateo Consequen.tly, a I 1most likely rate limiting process is the transport of oxygen to the reaction siteo Parlee, Seagle, and

-18610 Schuhmann have studied the rate of the carbon-oxygen reaction in liquid iron, Based on their experiments, they concltaded that oxygen transport is rate limitingo They expressed their results in the forms dvco _ Do A t oo 28 i XI4 - = -~ (C 0 ~~' T o00 dt 5o M - where dVrc/dt is the rate of evolution of carbon monoxide gas in grams per secondo DO is the diffusion coefficient of oxygen in li quid iron which may be taken as 2-3 x 104 cm /sec at temperatures near 1600~Co 50 is the boundary layer thickness. A is the area of the reaction interface, which in the case of the Bessemer converter may be taken to be the surface of the bubbles of gas passing through the melto VM is the volume of metal in cubic centimeters, CO is the concentration of oxygen in weight percent, Similar expressions may be derived for reactions involving the oxidation of silicon and manganese, For these elements, however, one must consider in addition transport phenomena between slag and metalll1 12 Larson, in considering the rate of the carbon reaction in the open hearth process showed that the rate of carbon removal was a direct function of the rate of boilo The rate of boil was shown to be a function of oxygen potential which Larson expressed aso Rate of boil = (a constant) x (an oxygen potential [ZAS]) x (A/zL) o The constant may include such things as a mobility or diffusion rate of some reactant in either a slag, metal, or gaseous phase, The driving force is a concentration gradient of oxygen across a phase boundary or diffusion film and the term A/AL is the ratio of an area such as slagmetal surface per unit weight of metal to the thickness of a transport

-187or diffusion filrmo The interfacial areas and diffusion film thicknesses vary with turbulence in the system. It was concluded that a moderate increase in the potential or driving force term tending to deliver oxygen into the metal solution can greatly increase the boil rate, It was shown then that the minimum boil rat;e with oxygen s-upplied from air or combustion gases to a slag surf ace or through the metal, as in the case of the Bessemer converter in'volves a series of many transport and reaction rate steps but is controlled essentially by a diffusion process of oxygen, CO2, or H20 through nitrogen (mainly) in. a film zone of the order of a centimeter in thickness just above the bath surfaceo The importance of supplying oxygen to the converting process on the overall:rate is shown quite clearly by th.e fact that steel may be produced at a higher rate in the oxygen process than in the Bessemer process. Lack of highly precise data and the difficulty in determining the geometrical conditions which exist in a metal bath prevent a highly accurate picture to be drawn of the kinetics of converting processeso In specifying the operation of a converter with regard to time and blowing rate, one generally relies on prev-ious experienceo The technisaes outlined in Chapter V for specifying the kinetics of a unit process are applicable here.

-188REFE ENCES o Work, Ho Ko "Photocell Control for Bessemer Steel Makingo" Trans. AIME, 45, (1941), 132, 2, Butts, Ao Me+tallurgical Problems. Metallurgy and Metallurgical Engineering Serieso New York~ McGraw-H ll, Inc, 1943, Chapter 15, 3o Camp, J, M, and Francis, C, B, The Making, Shaping and Treating of Steel, Pittsbugh, U, S. Steel Company, 1951, Chapter 9, 4, Philbrook, W, O( "Thermochemistry of Oxygen Steel," Joournal of Metals, 10, (1958) 477o 5o Kurzinski Eo F, "New Techniques for Copper Refiningo" Journal of Metals, i0, (1958), 533, 60 One Year LD-Oxygen Refining Process, VereinigteOesterreichische Eisen-:iid Stahlwerke, AGC(Voest), Linz-Donau, 1.954, 56 pages, 7, Wright, E, C "Potential for Oxygen in. Steel Making," Metal Progress, 76, N o 3, (Sept, 1959), 101o 8, The Iron and. Steel Institute, Special Report No, 42, Report on the Bessemer Process, The British Iron and Stee- Research Association, London, May 1949, 9, Le;roy, P, Jo, Galey, J. G,, and Cawley, Fo D, "Control in the Acid Bessemer eProcesso" Journal of the Iron and Steel Institute, 183, (1956), 208, 10, Parlee, No A,, Seagle, So R, and Schuhmann, R,, Jr. "Rate of the Carbon-Oxygen Reaction in Liqu.id Irono" Trans. AI!E P (1958), 132 11 Darken, L, So and Gurry, R, W, Physical, Chemistry of Metal So Metallurgy and Metalul1rgi al Engineering Series, New Yor:ko McGraw-Hill, Ine,, 1953, Chapter 19. 12o Larsen, Bo M, and Sordahl, Lo 0 "Some Mechanisms in the Refining of Steel " International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, April 1959,

CHAPTER XVII ELECTROLYSIS OF FUSED SALTS An important process for the production of reactive metals is the electrolysis of fused salts. Such processes are carried out at relatively high temperatures, and consequentLy, are quite distinct from electrolytic processes carried. out in aqueous solutionso The principles involved are essentially the same9 howevero The engineering approaches to processes used for purification or the recovery of metals from leaching solutions are parallel to those which, will be described under fused salt electrolysis in the present chaptero In view of the fact that the chemically strong metals tend to react at high temperatures with most materials involving other metallic elements, a straightforward method for producing them is first to purify the salts of the reactive metals and then electrolize these salts for the recovery of the metallic elemento This process is used for the production of aluminum, magnesiumn. berylli.um. cerium, lithium9 sodiun., potassim., and caalcium It could also be used to produce less reactive materials, however, usually without economic advantage The electrolysis of a fused salt bath involves a container for the bath with some type of collection device available to handle the metal produced, and a cathode ard an anode to supply the electric power for decompositiono A direct current is passed through the molten bath which may be the pure salt or the salt of a more reactive metal in. which a compound. involving the desired metallic element is dissolvedo Exarmples of these two cases would be the production of sodium from pure liquid sodium chloride, or the production of alurinnum, from a -189

190fused cryolyte bath (A1Fg-3NaJ) in which a small amount of alumina is dissolvedo If a fused salt bath contains several metallic elements which have similar decomposition potentials9 a fractional decomposition of the bath is possible in wThich one may produce, first a pure metal, a, and then a pure metal, b, or in. the event that the decomposition potentials are the same, an alloy of a and b may be produced o Because of the high temperatures involved ii these processes, it is often necessary to supply external heato Lhis depends on the nature of the bath, In the case of alwominum produotion, the electronic conductivity of the fused salt is such that sufficient resistance heating of the fused bath itself occurcs to maintain the temperature of the process o In the case of the electrolysis of mnagnxesi-um from a chloride bath, the electronic conductivity of the salt is quite low and consequerntly external heat must be supplied. Thus, from the aspect of efficiency of the process, one is interested. in having a bath in which the conductivity is purely ionic, but it is often ad. avantage to have a fused bath in which he conductivitLy is partially electronic in order that the process may be self sustaining and not require external heat for the maintenance of temperatureo The Hall process for the production of aluminum is one such example. Since the conductivity of fused salts, in general, increases with increasing temperature9 it may be desirable to select a higher operating temperature in order to take advantage of the heating effect of the electronic conductivity of the salt. A further advantage of operating the bath at a higher temperature is the fact that the decomposition potential will undoubtedly be lowero T:he

-19Ladvantages, of course, are offset by the fact that the heat losses increase markedly as bath temperature is increased, a consideration which may all but wipe out the advantages mentioned previously. Process Calculations The process design engineer is particularly interested in the amount of metal deposited by a given currento Faraday's laws of electrolysis apply, defining the maximum theoretical quantity which may be liberated by a given amount of currento Faraday's laws may be summarized in the statement: "The mass of a substance involved in reaction at the electrodes is directly proportional to the quantity of electricity passed through the solution and to the equivalent weight of the substance." The actual recovery of metal for a given current may be less than theoretically predicted if part of the electrolytic action of the current is expended in some other wayo There are very few cases where the current efficiency is 100. The loss of ionic transfer because of electronic conduction through the salt, the presence of gas overvoltages, the loss through other resistances in the circuit, such as those where contacts are made between bus bars, and the presence of some polarization in the bath can result in the deposition of less metal, than that which is theoretically predictedo If the overall average efficiency of the process is known, however, one may predict the amount of metal deposited for a given current. From Faraday's law; M it W = - (XVII-1) N F W = weight of metal deposited, in grams M -- atomic weight of metal deposited

-192a N = valance of the metallic ion in the bath i current in amperes t -time in secords F = Faradayes constant, 96)496 abs coulombs/equivalent Equation (XVII-1) gives the weight deposited at 100% efficiencyo If the actual current efficiency of the process is known. the equation may be modified to the formn W(actual) W( theoretical) x efficiency (XVII-2) The considerations involved in predicting a current efficiency for a process are discussed in detail in the next chaptero An important aspect of the process is the voltage required to carry out the electrolysis. This may be computed from the free energy of decomposition of the metallic compound involvedo Consider the Hall cell for the production of aluminumo In the Hall process, virtually pure alumina is added to a bath of liquid cryolite containing some fluorspar (CaF2)o This molten bath is contained in a carbon lined vesselo The carbon lining serv-es as a cathode for the electrolysiso Carbon is also used for the anodes which are inserted into the bath from aboveo Although it is contended that the sodium and fluorine ions pl.ay an important role in the process, the overall effect may be summarized by the anode and cathode reactionso At the cathode pure alulminum (99% +) is deposited as a liquid. At the anode, pure oxygen gas is liberated which immediately reacts with the carbon anode material giving off a mixture of carbon monoxide and carbon dioxide gases. These reactions may be summarized as: 2A1 (1) + o ~2 (g) = A1203 (s) (XVII-3)

-193z F~ -40 o400 + 77O0T cal/mole (XVII-4) C (gr) + 1/2 o2 (g) = CO (g) (XVII-5) AF0 = -26,760 - 20o98T cal/mole (XVII-6) It may be shown that at a temperature of 10000C the CO/C02 mixture in equilibrium with graphite is essentially pure COo In calculating the theoretical minimum voltage at which aluminum will be deposited at the cathode in the Hall process, it may be assumed that the anode gas is essentially pure carbon monoxide and that the salt bath is saturated with aluminao Calculating the free energy of the sum of the reactions given in Equations (XVI-3) and (XVII-5)o A1203 (s) + 3C (gr) 2A1 (1) + 3C0 (g) (XVII-7) Fo = 320,120 - 139o9T cal/mole (XVII-8) The decomposition potential, E, is related to the free energy of reaction by the relation0 Z^0 - -njE (XVII-9) where ZLF is the free energy of the decomposition reaction, n is the nunmber of equivalents taking place in the decomposition reaction, J is Faradayes constant, 96,500 ampere seconds per gram equivalent or 23,060 cal per volt-gram equivalent, and. E~ is the reversible decomposition potential in voltso For the above case at 1,0000C the result iso E = 1l06 volts (XVII-10) There is still considerable speculation about how much the reaction voltage of the aluminum cell is affected by the oxidation of the carbon anodeo The problem concerns the influence of the energy of formation of the carbon monoxide and carbon dioxide formed at the anode. In actual practice, the operating voltages of the Hall cell are of the order of five or six voltso

-194The discrepancy between the theoretically predicted value given above, and that actually obtained is the result of factors which are discussed in detail in Chapter XVIIIe The current efficiency of the cell, however, is of the order of 80% or bettero An additional quantity in which the process design engineer is interested is that of the power requirement~ From Equation (XVII-l) and the example given above, it may be shownr that the theoretical power requirement for the production of one pound of aluminum at 1^,000~C is about 1.4 kw hourso In actual practice, however, the power requirement is about 807 kw hr/lbo From a heat balance of the electrolytic process, and a knowledge of the electrical conductivity of the bath at the temperature of operation, one may predict the rate of energy input necessary to maintain. that temperature. This heat requirement may be in the form of a determination of the required current density to maintain the operating temperature, or having selected the current density, it may be in the form of the burning of a given amount of fuel, within the cell vessel, itself. In the case of magnesium, the metal is recovered by electrolizing the chloride in a steel pot which serves as a cathode~ The anode is made up of carbon rods inserted in. the bath and external heat is supplied by burning natural gaso The magnesium is recovered as a liquido Since it is lighter than the bath, it floats on the salt and is protected from oxidation by a fluoride flux or molten sulphur.

REFERENCES 1. Butts, A. Metallurgical Problems o Metallurgy and Metallurgical Engineering Series, New York~ McGraw-Hill Book Coo 1943o 2. Hayworth, C. R. An Outline of Metallurgical Practice, New York~ E. Van Nostrand, Inco, 1952o 35 Bray, Non-Ferrous Production Metallurgyo New York~ John Wiley an.d Sonso 4o Lidell, Handbook of Non-Ferrous MetallurgyO New York~ McGrawHill Book Coo 5. Mantell, C. Lo Industrial Electrochemistry New York McGrawHill Book Coo 1950o 6o Newton, J. Extractive Metallurgy. New York. John Wiley and Sons. Inc., 1959.

Part IV REFINING OPERATIONS -197'

CHAP'E XVIII LECR'OLYT!C REFINING The electrolysis of solutions containing metallic ions is often employed to refine metals or to recover them from the products of leaching operations. Solutions containing metallic ions are electrolized to precipitate out the element in metallic form.. Because of the difference in electrode potentials set up by different metallic ions in solutionl, it is often possible by electrolytic means to separate several metallic elements from the same solution. The principles involved in electrolytic refining are essentially the same as those which were outlined in the previous chapter dealing with the electrolysis of fused salts. The basic differences arise from the fact that the processes are carried out at different temperatures and that the electrolyte is a molten salt in one case and an aqueous solution in the othero A form of electrolytic refining which is often used is that in which a partially refined anode is placed in an electrolyte, a current is passed through the solution and at the cathode is plated out a highly pure elemental form of the desired material' In this particular case, since the anode and cathode. are essentially the pure element being refined, the reversible cell potential is zero. The actual cell potential, however, is greater than this, the result of factors which will be discussed later. The design engineer who is dealing with electrolytic processes is interested in the power and voltage requirements to plate out a given amount of material, and also in the size of the operation, that,is the number of tanlks, the volume of solution, -199

-200number of cathodes and anodes which would be involved, etc. The relationships which will yield these are merely an extension of the basic engineering material presented in the previous chapter, Cell Voltages: The cell voltages are comprised of several components, These may be summarized as~ (1) the IR drop to overcome the resistance of the electrolyte, bus bars, connections, etco (2) the reversible cell potential, (3) the polarization or over-voltage0 The total cell voltage is the sum of these three potentials. Ohmic Resistance From Ohm-s Law, E = IR, the contribution of Ohmic resistance of the solution to the cell voltage may be computed. R, the resistance of the electrolyte in question, may be calculated from the equation0 R = r where 1 = the average length of the flow path ss = cross ectioal area r = te resistiity o the electrolyte The resistivity, r, may be determined by direct experimental methods and this is the general technique used, Often, resist iities or conductivities, the inverse of the resistivities, are tabulated for different electrolytesa In the case, however, where the solution is a cOmplex one, it is seldom accurate to iuse the weighted average of the conductivities. Furthermore, it is nearly always necessary to consider the temperature dependence of the resistivity. The length of path of current flow, 1, may be taken as the distance between the electrodes in the cello For simple geometries, s may be taken as the size of the electrodes0

-201If, however, the electrodes are of different sizes, the average value is. often a reasonable approximationo If the plates are relatively far apart, s can be assumed to be the size of the cross section of the tank or cell, independent of the size of the plateso Reversible Cell Potential, The reversible cell potential may be calculated from Equation XVII-9o E = —- XVIII-.2 Equation XVIII-2 is often approximated by substituting eH~ for ZF~ when the heat of reaction is known, but the free energy is not. This approximation is often referred. to as Thomson s ruleo Equation ZXIII-2 would then become~ 2AH~. TZLS~ tE + - XVIII-3 and Thomson Is Rule would ignore the second term of that equationo As an example the reaction potential. for the electrlys-is of water where n=2 may be calculated from the heat of reaction, -Ho = 68,370 calories giving E~ =1.4 l8 volts. The correct value, however9 calculated from the free energy changes -F = 56F 484 calories is E 1~225 volts. The error resulting from the use of Thomson Is Rule is a function of the temperature of operation of the cell and the entropy change for the reaction. The error resulting may range as high as a vo.lt or more in the calculated value of the reversible cell potential. As indicated above, it is oftenl necessary to. use this approximation.o One should, however, be aware of its limitations. Polarization In general, it is not possible to compute accur-ately the value of'the polarization or over-voltage o In practice, it is usually.

-202estimated from experience or data on similar electrodes o cells, but may often be modified with reasonable aiccuracy by considering the factors which influence it. The chief contribution to the polarization potential of the cell is that of over-voltages, usually caused by gases, which is related to the potential required for the evoltution of gas on an electrode. It has been found that over-voltages are functions of current density given by the Tafel relationship: 1 p A log vIIi-4 lo where i is the exchange current density and p is the Tafel slope g the over-voltage may be estimated from this relationship if the coefficient p is known for the particular cell and electrolyte involvedo The hydrogen over-voltage on an electrode has been found to be lower at higher temperatures. This is believed to be related to the activation energy for the reaction at the surface. The rate of this particular reaction is given by the Arrhtnius equation Rate Ae -a XVIII-5 RT If the over-voltage itself is related to the reaction at the surface, suitable experiments should specify the coefficients in the Arrhenius equation and permit a prediction of the influence of temperature on the rate of reaction at the surf ace. The over-voltage is also a function of the nature of the electrode. The hydrogen over-voltage is high for lead, mercury, zinc, and tin, metals which are poor catalysts for the reactiono H 2H + 2e XVII-6 This over-voltage, howeer, is quite low for platinum, iron, and. silver, metals which are good catalysts for the above reaction, The over-voltage

-203is also a function of roughness of surface. A rough surface has a low over-voltage, presuwmably because of the ability of the su rface to act as a nucleating agent for the formation and evolution of the gaso The hydrogen over-voltage is also influened by impurities in the electrodes, and the over-voltae t s torer-voltage tes ad he of those impurities which are present. The source of impurities may lie, not only in the electrodes themselves, but in t:races of metals. in the electrolyte which may plate out at the cathode. The hydrogen owver-voltage is also influenced by the electrolyte. However, this effect is generally quite small. Another important source of the polarization potential is caused by concertration polarization in the neighborhood of the electrode. This polarization potential arises from the fact that the concentration of ions in the neighborhood of the electrode may be different from thosf in the bulk of the electrolyte solutiOnh The concentration of ion in the bulk phase may be measured directly and that which exists at the surface may often be estimated, permitting a calLculation of the concentration polarization potentialo The relationships by which this polarization potential may be computed are shown in the following manner0 Consider, for example, a cell, of the type Cu(au=l) | Cu (+a) Cu (a2) I Cu(ac,,) XT-7 consisting of two pure copper electrodes emersed in solutions of coppercontaining electrolyte in which the activities of the copper ion are eqpual to a1 and a2. The electrode reaction on the left is~ Cu(pure) = Cu (al) + 2e- XVIII-8

-204with E given byRT E8 = Ecu- 3 ln (al) XVIII-9 Again, for the reduction on the right hand side; we haves Cu (a ) + 2e = Cu(pure) XVIII-10 2 E o=E0 RT E E -ll111^)n II 11 10E cu - 2-ln a) 0 0 where EC = E We obtain, therefore, for the cell reaction~ ++ Cu (a1) Cu (a2) XIII ( - 12 and for the cell EMF~ RT an ) E8 + EO E12 nT ln (a2) XVIII-13 The equivalent of such a concentration cell may exist in an electrolytic processing operation if the solution near the anode becomes depleted in metallic ions or if there is a build-up of ions in the solution at the cathode, The case of depletion of ionic concentration at the anode is illustrated in Figure XV II - The concentration difference between the bulk solution and the solution near the electrode creates a potential difference which must be overcome and acts to increase the total cell voltage. From Equation (XIII-13). it is evident that.the EM of this concentration cell arises from a transfer of copper ions from the solution where the activity is a, to the solution where the ionic activity is a2. Furthermore, it is shown that this EMF depends only on the ratio of the activities of copper ion in solution and n.ot on the absolute value of the cospper ionic activity In the finala cell EF,

-205T Z BULK CONCENTRATION ^ a2 ------ 3 / M I. a I' E CONCENTRATION AT ANODE X, DISTANCE FROM ANODE -- Figure XVIII-1. Concentration Polarization at Anode of Electrolytic Cell.

-2o6Equation (xV7II-.3) E does not appear, Ths is itrue of all. concentrat ion cells. It may be concluded therefore that for concentration cells, E is 0. and the EM equation takes on the simplified form, E lT In (aL) XIII-14 a2 Since in cells of the type under discussion, a ad an refer to the activities of the metallic ion. in soltion. we may assum. that, for dil-ute solutions, these are essentially equal to or are proportional in the same manner to the concentrations c and c 2 Thus, Equation (XVIEI-1.4) may be written approximately as, RT ET -- n ('cn ) XVIII-15 The equation in this form may be used to cal.cul.ate the concentration polarization potential of a cell where c refers to the su.rface concentration of the metallic ion in sol-u.tion and c, refers to the bulk concentration. Since we are interested. in the ratio of the two concentrations, any consistent units may be used to express ito Film Resistance A further contribution to the polarization potential, is caused by the Ohmic resistance, ie eo the I drop thro'u.gh the films at the elec. trode surfaceo Although the thickness of the film. may only be estimated the area is known and the current is know. The resistivity of the film is often difficult to evaluate, since there is a concentration gradient existing through it and the resistivity is a function of that concentration. The IR drops in the b. u bu ars the con'tac% resistanrces and other Ohmic resistanes which were includQd0 in the firft term of the total cel.

-207potential are often lumped together with the IR drop through the surface films and the entire potential drop is often evaluated as the difference between that which is calculated and that which is actually measured in practice. It is therefore necessary that these contributions to the total cell potential be evaluated experimentally. Computation of Total Voltage and Current Several basic electrical systems are possible in electrolytic process equipment, depending upon how the connections are made. The two priciple systems, parallel and series, are shown in Figure XVIII-2. A parallel system is one in which the electrodes within each tank are connected in parallel so that the voltage drop across the entire tank is the same as that between any pair of plates in the tank. The advantage of this system is that there is a smaller voltage drop, consequently, fewer losses due to short circuits$ A series connection is one in which the plates within the tanks are connected in series. Consequently, the voltage drop across the cell is the sum of the voltage drops between each electrode. In the series system, each plate acts as an anode on one side and a cathode on the other, whereas in the parallel system, each electrode behaves as either a cathode or an anode, the reaction taking place on both surfaces0 In general, less space is required'. Also, there is no necessity for preparing special starting sheets for the series system, The tanks themselves, are usually connected in series, however, with the total number in the circuit being determined by the supply voltage and power of the generator. Although the pure series system is used in a few large refineries, the system which is most commonly employed in metallurgical

-208+ + I.1[I I' | —-- MULTIPLE SYSTEM (PLATES IN PARALLEL) SERIES SYSTEM (PLATES IN SERIES) Figure XVIII-2. Electrical Connections for Electrolytic Refining Cells. Ref ining Cells.

-209 planf.ts is the multiple system, in which the plates within each tank are connected in parallel, but the tanks themselves, are connected. in, series, The computation of the total voltage and current, then, for the plant^ can be made using the principles of elementary electrical engineeringo Engineering relationships concerning the amount of metal theoretically deposited by a given. current, the amount of c.urrent required to deposit a given amount of metal, and the reversible cell voltage requirements are presented in Chapter XVII. Details concerning the specific operation of electrolytic refining processes in the various metallurgical industries are presented in Reference 4. It should be noted in passing that electrolytic refining may also be carried out in -a fused salt electrolyteo

-210REFERENCES 1. Blum W. and HogabO66m GC Princ iples of EleetrOplating and Electroformingo New York~ McGraw-Hill' Ixco, 1930 2. Butts, A. Metallurgy and the Metallurgical Engineering Series. New Yorke McGraw-Hill, 1943 3. Mantell, C. Electrochemical Enginreering New York~ McGraw-Hill, 1960. 4. Hayward, C. R. An Outline of Metall rgical Practice0 New YorkD. Van Nostrum Co,, Inc,, 1952o 5. Newton, J. Extractive Metallurgy. New York~ John Wiley and Sons, Inc., 1959o

-21l CHAPTER XIX IST~LLATION IRO~ MEOSES Distillation is the separation of the constituents of a liquid mixture by partial vaporization of the mixture and separate recovery of vapor and residue. Distillation processes conducted under vacuum are an important aspect of process metallurgical engineeringo This process plays the principal role in the extractive metallurgy of zinc and mercury, and has been used to remove these volatile constituents from. other metals, such as liquid lead. With the improvement in materials of construction and research advances, there is a growing interest in distillation processes for the refining of many metals including steelso The case of arsenic, for example, is of particular interest since there are many iron ores which contain arsenic and no suitable method has been developed to lower its content in the liquid iron produced. Fractional distillation has been shown to be a fpasible method for the removal of this element from liquid iron. The engineering design of a vacu'mr. distillation process requires that the vapor pressures of the constituents above the melt be known. Unfortunately, relatively few data are available on. the vapor pressures of elements abo-ve liquid metallic soluitons0 However, the vapor pressures of pure elements are known with a relatively high degree accuracy, and the vapor pressures of a number of e.ements are presented in Table XIX-1.2 If the vapor pressure of the pure element is known, the partial. pressure of that element above a metallic solution may be computed if the activity coefficient is Zknown, using the relations Pa = Pa a Xa XIX-l

-212TABLE XIX-I VAPOR PRESSURE OF THE ELEMENTS* Species 10o6 atm 105 atm 104 atm 10atm 1 atm A 8743(1) Ag 1200(s) 1305 1442 1607 1816 2485 A1 1290(1) 1405 1545 1725 1940 2600 As4 477(s) 517 563 622 708 895 At2 270(s) 320 350 390 500 Au 1570(1) 1720 1896 2112 2388 3239 B 1500(s) 1600 1750 1900 2150 2800(1) Ba 810(s) 890 985(1)) 1116 1295 1911 Be 1390(s) 1505 1655(1) 1830 2070 2780 Bi 873(1) 960 1060 1190 1360 1900 LBra ^173(s) 186 203 222 245 331(1) C 2720(s) 2920 3170 3450 3800 4775 Ca 790(s) 867 961 1075 1231(1) 1755 Cb 2820(1) 3050 3340o 700 420 5400 Cd 485(s) 530 585(1) 657 744 1038 01 1450(l) 1550 1700 1850 2100 2800 C12 114(s) 123 139 153 169 259(1) Co 1750(s) 1900(1) 2100 2500 2260 3370 Cr 1350(s) 1465 1600 1755 1960 2495(1) Cs 383(1 425 476 544 634 963 Cu 1400(1) 1530 1685 1875 2117 2868 F2 58(1) 85 Fr(87) 49o(1) 950 Fe 1550(s) 680 1837(1) 20553 2277 3008 Ga 1225(1) 1550 1500 1690 1920 2700 Ge 1370(1) 1500 1670 1880 2150 2980 BH2.20<5.39(l) He4 22(1) EHf 2850(1) 3100 3350 3750 4150 5500 Hg 287(1) 16 351 394 449 634 12 241(s) 26o 282 308 34i 456(1) In 1100(1) 1210 1550 1510 1730 2440 Ir 258o(s) -28oo(l) 3o4o 3350 3700 48oo K 439(1) 475 534 605 702 o152 Kr 119.9(1) La 15Q0(l) 1650 1800 2000 2250 3000 Li 705 () 775 865 980 1130 164o Mg 653(s) 715 789 881 1000(1) 1399

2ABE X3IBLE XIX-I oant' d) Species 10 am am 104 am 1 tm 103 atm 10 2 atm 1 atm Mn 1140(s) 1240 1360 1570(1) 1750 2370 Mo 2530(s) 2740 3000(1) 3330 3750 5077 N2 77,4(1) Na 510(1) 558 623 705 813 1187 Ne 27,3(1) Ni 1630(s) 1765(1) 1930 2130 2380 3110 o0 90o2(1) Os 2700 (s) 2900 3160(1) 3470 3850 4900 P4(yellow) 244(s) 268 296 334(1) 382 553 Pa 2250(1) 2450 2700 2950 3300 4500 Pb 887(1) 975 1088 1226 1408 2010 Pd 1660(s) 1800 2000(1) 2240 2530 3440 Po2 660(s) 750 835(1) 945 1300 =Pt, 2160(1) 2340 2550 2820 3140 4100 Ra 650(s) 700 770 850 965 1410(1) Rb 403(1) 445 496 561 650 952 Re 2900(s) 3150 3450(1) 3850 4300 5800 Rh 2200(s) 2400(1) 2600 2850 3200 4150 Rn 211(1) RH 2480( s) 2670 2900(1) 3180 3500 4500 S2' 500(1) Sb2 860(s) 940(1) 1025 1160 1340 1890 Sc 1540(s) 1680(1) 1850 2050 2300 3000 Se2 525(1) 568 620 679 755 1000 (2 atm Se6 and. 104 atm Se at 1000lK) Si 1480(s) 160o 1740(1) 1920 2140 2750 Sn 1300(1) 1450 1600 1850 2150 3000 Sr 740(s) 810 900 1010 1150(1) 1657 Ta 3300(1) 3600 3900 4.5o 4800 6300 T(e43) 2550(1) 2750 3000 3300 3700 5000 Te2 655(s) 700 758(1) 825 907 1130 Th 2250(1) 2450 2700 2950 3300 4500 Ti 1640(s) 1800 1990 2210(1) 2500 3400 Ti 795(1) 870 965 1082 1235 1730 u 2000(o ) 2150 2350 2580 2900 3800 V 1970(1) 2140 2340 2550 2900 3800 W 3230(s) 3490 3780(1) 4150 4625 5950 Xe 165 1(1) Y 1750(s) 1900(1) 2100 2300 2700 3500 Zn 560(s) 610 672 750(1) 852 1180 Zr 2070(s) 2250 2450(1) 2700 3000 3850 * L, Brewer-, Report for the Manhattan Project, MDD0C438G, 1946,

-214where P is the vapor pressure of pure component, a, at the temperature under consideration, 7a is the activ'ity coefficient of component a in. the solution and x is the mole fraction, For dilute sol:utions, a the activity coefficient of the solvent may be taken as one. If the solution is known to have ideal behavior, the activity coefficient of the solute is also one, Otherwise specific experimental data are required to determine the activity coefficient of the soluteo The vapor pressure of several alloying elements over dilute solutionrs in liuid iron at 1600 C are presented in Table XIX-2o Clausius- Capeyron E quation From the combined statement of the firs, and second, laws of thermodynamics, one may derive for a vapor-!iquid equilibrium the relationshipo (S- SI) dT (V ) dP XIX-2 -or ^ _ ^v _ ^ xEx-3 dT ~'7 T. Vv v This relation is knowna as the Clausi!us- lapeon equat'ion Its integration reqTires an experimental knowledge of L:' and z&T If the V v volume of the li qud is small in compari son with thawt of the vapor,y AV =S V and if the vapor is ideal, V R -/p s assumptions which are reasonable for metals at elevated temperat&u.res Substi",.ution in Equation (XIX-3) gives dP = ZI dT ^ ^v xiX-4 P. assuming that the right hand side of Equation (XIX-4) is _on tant; that isa aH, the enthalpy change aeomparying the change from the

-215G) rd 0 c o o 4 O. - O L(n rH -r-I -P 0 0 cx i l - Nc) (l O0 S H 0 C) H 0 0 0 0) 0 0 ~ kO H \10H ~ O0 (Y) P H L0 HQ O L0 ( L- 0 C') o (1 C c O O 0 0 0 0 0- 0 0 c.O r- O 0 0 0 0 0 0 0 OS o o O o O O O 0 o o O O O "- - \1 c H O C H 0 0 0 0 s ( O O O O I H O ^ O o r~ a ) 0- 0 00- 0 0C efl o o o o o o o 0 ~ p O O O O L o o o O H u) o C U) H 0Z: a ) 0 0 0 0 I H o0 0 R 3 ^ ^ u og O o 8 g!q H > o o o o o o o o H H HxU 0 O. I- 0 0 H &<- 0 0 0 0 H CC) 00 0 k 0 0 4 0 j-P 0 C riO O 0 O O 0 0 0 i a) o 0 -P H (P HP-0H 0 H 0 C 0 C,C; 0 0 0 0 4 0 0 0 0 0 o o o o o oe o o o o p C o a ( ~ CC)\Q CU ) ea Hl 0, o +C O G -U C\J 0 CD 0 H 0 D 0 01 0 0 0 0 O + )0 H o-p -+ - H -- LN o- rH H co 0 o O ON 0 c O Ln cO O [- C') o - O kG ^ 00 C\J oo L\ -- >- C 00 -pa) c N LN k L L\ LN 01 H -p ~ l? 0-~ r-~ < 0 0 O i PrCO-C 0 0 O ^ ~ ~do~oc

-216liquid to the vapor state at equilibrium is essentially equal to that accompanying a change from one standard, state to the other AH, the equation integrates to the familiar form: P2 AHv i \ ln ~p - T) XIX-5 This relationship may be used to extrapolate the data of Tabl.e XIX-1 to any desired temperature. Equation (XIX-4) may be integrated'to the general forms -A log P = + B XI-6 where A and B are constants whose values depend upon the units in which the vapor pressure, P and the absolute temperature, T, are expressed. This relationship permits the vapor pressures of materials to be tabulated in the form. of two constantso Such tabulations are available in several'sources.3 4 Relative Volatility The term. volatility is used to compare the vapor pressure of one pure substance with anothero However, the vapor pressure alone does not define the ease of separation of the components from. 1i quAd. mixtures, since the vapor pressure is a function of the presence of the other components. The partial pressure ratio of two components ov-e: a liAqid solution is given by the relationship~ 7axaPa Partial Pressure Ratio b~~ XIX-7 The criterion for a successful distillation is that the molar (or mass) ratio of a component to be separated must be greater in the vapor phase than in the liquid phaseo The coefficient of the molar ratio in. solution in Equation. (XIX-7) may be termed a where~

-2170 a Y7aa XIX-8 7bPb'O The relative volatilityj, O, is a direct measure of the ease of separation of components by a distillation processo Substances that are readily separated show large values of Io If C- is unity, no separation is possible since the concentration of the two components in the vapor will be the same as in the liquid soliutiono The relative volatilities of elements in liquid iron solutions1 are included in Table XIX-2o The computed values of Q, indicate that lead, manganese' copper, tin and chromiuLm may be removed from liquid iron; but that it would be impossible to remove silicon, nickel or cobalt from liquid iron, that is, that the relative volatility of iron is greater than that of the alloying element in these solutions0 The calculations lso indicate that aluminum has a relative volatility of one and would not be separatedo The relative volatility of two components changes with temperature. Viewed from the standpoint of ease of separation alone, the optimum temperature. range in which to conduct the distillation is that in which the value of a is maximumn Equation (XIX-7) may be u.sed to derive the following relationship between the concentration of the.volatile component in the vapor phase, ya and in the liquid phase, xao Y a VXIX9 X~e:t~ O~~ Xa Ya' —- xa (a'-1) rX9 Figure XIX-1 shows a plot of y versus x for various constant values of 4 of Q~'o

-2181.0 0.8 0.6 0.2 0 0.2 0.4 0.6 0.8 1.0 X Figure XIX-1. Relationship Between X and Y for Various Values of cf.

-219Equilibrium Distillation The principal method of distillation used in metallurgical processes is simple batch distillation. In this process increments of vapor are removed upon their formation from contact with the residual batch of liquid solutiono If the operation is not conducted under high vacuum conditions and one may presume that the vapor coming off the solution is in equilibrium with the bulk liquid, the following mathematical analysis may be applied. The mass balance of such a process may be written in terms of a differential equation as was first done by Rayleigho' The Rayleigh equation may be derived as follows: Assume a solution of two components, a and b, the total moles of which are L. Let the mole fraction of the more volatile component in the liquid be x, and the mole fraction of the same component in the vapor be yo Let dL moles be vaporized, The liquid will lose and the vapor will gain a differential quantity of the more volatile component. By a material balance, (L - dL) (x - dx) + (y + dy)dL = Lx XIX-10 Neglecting differentials of a second order and rearranging, dL dx 17 y-x XIX-11 Integrating Equation (XIX-11) between limits, L1 jXl dx Ln 1 " Jx, X y'x XIX-12 2 2 where L1 = moles of original charge, L2 = the moles of residual charge after L1 - L2 have been distilled off, xl = the mole fraction of more volatile component in the original charge L1, x2 = mole fraction of

-220more volatile component in the residual charge Lo Consistent weight units may be substituted for the molar units in Equation (XIX-12). If experimental data giving the relationship between y and x are available, the right hand side of Equation.(XIX-2) may be integrated graphicallyo If a mathematical relationship exists between y and x, the integration may be carried out analytically as in the following casesO DuAing a simple batch distillation at constant pressure, the temperature rises as the residual liquid becomes poorer in the more volatile componento If Q; does not vary with temperature, Equation (XIX-9) may be substituted in Equation (XIX-12) with the integrated result: T1 ( i 1n Lx2) XIX-13 ^2 4 1 X " 1-xi If Henry s law applies to the solute which is being removed from the solution in the distillation process, the relationship y=kx may be substituted with the result L 1 x 1 ln = ln - XIX-14 It should be noted that Henry's law is also an isothermal relationship, and in order to assure validity of Equations (}IX-13 and XIX-l4), one should be aware of any influences of temperature on the relationships involved. One may also consider the application to multicomponent 4 mixtures. In the event that only one of the components of the complex solution is highly volatile, one may consider the solution as a pseudo binaryo In the event, however, that two or more components have a volatility of the same order, one may compute the concentrationso The mathematics are more involved, but the principles are the sameo

-221Mglecular Distillation In most metallurgical distillation operations, particularly those carried out under high vacuum conditions, the rate of distillation is such that it is controlled by the rate of evaporation of atoms from the surface of the melt, and one may not under these conditions presume that equilibrium is maintained between the concentrations in the vapor and in the liquid. A process conducted under these conditions is termed molecular distillation the quantitatie rat distllat and he un t re distillation under conditions of complete nonreturn condensation is given by the Langmruir Equation which may be derived as followso At any given temperature there is a maximum at which a volatile substance will evaporate from an exposed surface. This rate is very difficult to calculate from kinetic theory, but it can be estimated from the observed vapor pressure of the volatile substance. From kinetic theory, the rate of collision of molecules of vapor with the surface can be calculated from the pressure of the vapor. The mass of vapor molecules striking a square meter of surface per. second, A, is given by the relation, p. = -pvi XIX-15 4 where pi is the density of the vapor and v is the average molecular velocity. It may be shown, however, that v = 4 2M XIX-16 thus assuming the ideal gas law to hold: 4 =Pf t2RT XIX-17

-222where.- the pressure of the vapor and R is the gas constant, and M is the molecular weight of the vapor specie. In general, the number of molecules returning to the surface will be the same as the number striking it. At.equilibrium, this will be the same as the maximum rate of evaporationo Therefore, W = P xIX-18 where wO = the rate of evaporation in grams per square meter per second, P is equal to the saturation pressure in millimeters of mercury at the solution temperature, T is the absolute temperature in degrees Kelvin, M is the molecular weight. Evaporation can occur at a rate of w0 only in a perfect vacuum, and when the rate of evaporation is so small that the mean free path of the vapor molecules exceeds the distance between the evaporating and condensing surfaces. At appreciable rates of evaporation, the vapor molecules will collide with each other. Some will rebound to the surface, so the actual rate of evaporation will be the difference between Wp and the rate of return to the surface wlo The rate of that evaporation will then beo W = v. - w, XIX-19 The two rates w,o and w! are related to the pressures PQ and P1o Therefore, the net rate of evaporation is given by M W - (Po - P) 2jg XIX-2 where P1 is the partial pressure of the vapor at the evserrating surface o

-223The ratio between P and P' is the degree of saturation of the vapor, (, it varies from, 0 to 1 as the evaporating conditions vary from molecular to equilibrium evaporizationo The degree of saturation is related in the following way to the relation between w, the observed, and wo, the maximum, rates of evaporation. q O= 1- Lw_ XIX-21 W Vo The actual rate of distillation is determined not so much by the rate of evaporation from the surface as by the rate of transfer of the vapor away from the surface, This rate of transfer is not as easy to calculate as the rate of evaporationo The factors which must be considered areO 1. pressure gradient of vapor 2. effective pressure of permanent gas in the system 3. dimensions of still and condensing system Further discussion of these factors is presented in Reference 6. Observations on Liquid Iron Alloys Under conditions of molecular distillation, one must consider the influence of the molecular weight of the component on its rate of evaporation. If one does this, the relative volatility coefficient, x, Equation (XIX-8) may be modified to the forms.. _ 7A P MFe a == - -o Q \Ig -XXIX-22'PFe PFe \ MA where M-e is the molecular weight of iron in the case under consideration, and MA is the molecular weight of the solute. Under conditions of a dilute solution, iron obeys Raoult's law and 7Ae is unityo

-224Also, the solute A at low concentrations obeys Henry's law, and A is nearly constant and equal to y It would be equal to one if the solution were ideal, Under such conditions, c' become's0 t o' P~ 55 8,a A ~ ~ 586 5 e~XIX-23'. e VMA A comparison is made in Table XIX-2 between the computed values of c' and those measured experimentally on liquid iron solutions 0 Although there is some discrepancy, it should be noted that the comparative evaporation coefficients are in the same order as computed, The unusual results obtained for silicon and also for aluminum, where it was noted that in some cases aluminum was highly volatile and in other cases did not distill at all, are explained in terms of- the formation of the highly volatile suboxideso This effect.has also been noted by Floridis7 who showed that the vacuum distillation of sulfur from liquid iron was greatly enhanced by the presence of silicon, presumably resulting in the formation of a volatile silicon sulfide, which assists in removing both elements from. solutiono Recoveries by Condensation Recovery of the distillate from distillation processes conducted as refining operations on liquid metals may be made by condensing the vapor to either the solid or liquidd form. If a solid is formed, the efficiency of the recovery is essentially 100 provided that the solid condensate is in a form such that it may effecti vely be collected. In the case where the condensate is collected as a liquid, one may estimate the efficiency of the recovery from equilibrium conditionso The vapor

-225pressure relations derived in Equations (XIX-6 and XIX-7) may be used to compute the partial pressures of the components over the condensed liquido If it is assumed that the temperature of the gases leaving the condenser is the same as that of the condensed liquid and that equilibrium concentrations prevail, the fractions of vapor constituents escaping condensation may be readily computed from. the partial pressures of components in the-vapor phases entering the condenser and exiting from it0

-226REFERENCES 1o Olette, M, "Vacuum Distillation of Minor Elements from Liquid Ferrous Alloys," International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, April 1959 2o Darken, L. S. and Gurry, Ro Wo, Physical Chemistry of Metals. Metallurgy and Metallurgical Engineering Series, New York~ McGraw-Hill, Inc.,, 1953. 3. Butts, Ao Metallurgical Problems Metallurgy and Metallurgical Engineering Series, New York~ McGraw-Hill, In.c,, 1943, Chapters 22 and 23. 4. Perry, John (ed,)o Chemical Engineers Handbooko New York~ McGrawHill, Inco, 1950, Section 9, 5o Rayleigh, Philosophical Magazine, 4, (1902), 521o 6o St. Clair, H. Wo "Distillation of Metals Under Reduced Pressureso," Vacuum Metallurgy, Bunshah, R, Fo (edo), Reinhold R.blishing Corp,, New York, 19580 7o Floridis, To Po "Vacuum Desulfurization of Liquid Iron Alloyss, Transo AoIMEo, 215, (1959), 870o

CHAPTER XX LIQUID-LIQUID EXTRACTION Liquid-liquid extraction is an operation which is often used in the'chemical processing industries for removing one constituent of a liquid phase by equilibrating it with a second liquid phase which absorbs the desired constituent from ito The liquid phases must be essentially insoluble in each others and it is desirable that the extracting phase have a higher solubility of the desired constituent, ie., a lower activity coefficient The high temperatures at which most metallurgical operations are carried. out. presents an equipment problem in carrying out liquidliquid. extraction procesess Qonsequently, most extraction processes are carried out in batch operations, eog,, slag-metal or slag-matte equilibria are used for selective removal of constituents in steel and copper processingo The two-slag processes can be considered to be simple multiple-contact extraction processeso Thus, the mass and energy balances are straight-forward and directly obtained by consideration of the concentrations and weights of the phases involvedO The use of liquid-liquid extraction processes involving aqueous ororganic solvents may also form a portion of an integrated metallurgical operation-. The engineering approach is essentially the same as that outlined for other hydrometallurgical operations in Chapter IX. Equipment and mathematical treatments are described in 1 2 several standard chemical engineering unit operation texts 1 The focus of this chapter will be brought to bear on the equilibria and kinetics of high-temperature extraction processes0 -227

-228Heterogeneous Equilibrium Under equilibrium conditions, the free energy of each of the constituents is the same in all of the phases of a system. Thus, it can be shown that at constan.t temperature, the activity of a constituent in one phase bears a constant ratio to its activity in the other phase or phaseso Consider, the distribution of iron-sulfide, FeS, between liquid iron and a slago The constant activity ratio requires that~ FeS(in slag) a constant XX-1 aFeS(in metal) If the activity in the slag phase is taken as the mole fraction, and that in the metal as the weight percentage, the ratio becomes~ NFeS(in slag) e i eSin metal) 2 Equation (XX-1) is an exact expression of the Nernst Distribution Law, and Equation (XX-2) represents an approximation to it based on the observed behavior of the phases involved, where L is the distribution coefficient. The equilibrium constants of reactions in one phase of a two phase equilibrium. may be related to those in the other by means of the distribution coefficientso At 1600O~C FeO distributes itself between liquid iron and a slag consisting of MnO and FeO in a constant ratio which may be expressed as~ (FeO) XX-3 T-( eLFO = 4.4 -3 The constant of the reaction of manganese with FeO is given byo Mn + FeO(in slag) = Fe + MnO(in slag) XX-4 K - )(F =23 xx5

-229When Equations (XX 3- and XX-5) are combined, the equilibrium constant for manganese reacting with oxygen dissolved in the metal is found, to be: Mn + 0 = MnO(in slag) XX-6 K =.'1 (-. l0oi XX-7 Kinetics of Liquid-Liquid Reactions At the high temperatures involved in slag-metal or slag-matte processes, the rate of the exchange reaction is so great that equilibrium conditions may be assumed at the reaction interface, and the chemical reaction itself may be eliminated as a potential rate. limiting step, The controlling mechanism then becomes a mass transport process in one of the phases presentO The constituent which is present in the lowest concentration is usually the one with the slowest transport rate, since the driving force for transport is the smallesto 4 Darken has considered the transfer reaction between manganese in steel and iron oxide in a contacting slag layers The reaction is a straight-forward exchange reactions +2 +2 x8 Mn + Fe'2 = Mn+2 + Fe XX-8 If the rate of one of the steps in the transport process is much lower than the others, then this step may be treated as the rate limiting one, In the process above, the concentration of iron in the metal is so high that its transport cannot be limiting. Generally, the concentration of manganese in the metal is much less than the concentrations of iron or manganese ionBS:.in.:.the. slag, so that the transport of manganese from the bulk metal to the reaction interface through a boundary

-230layer in the metal may be assumed to be rate limiting0 The process may be kinetically described as: d(CMn) DM A - (dt, s V (CMn(bullk) CMln(boundary)) XX-9 The concentration of manganese at the boundary (slag-metal interface) is the concentration in equilibrium with the slag since mass transport in the metal is rate limitingo This concentration may be calculated from equilibrium relationships, considering the bulk concentrations of the other reactants to prevail at the interfacee Converting from molar concentrations to weight percentages, Equation (XX-9) becomes: d(_Mn) DMn A - dit = 5_ o [M Mn (bulk) - % Mn (equilibrium)] XX-10 which may be integrated toa V [Mn Mn t i0)- ai (eUilibrum)] t=2 3 - log [~ {~ XX-ll 9 A DMn o t Mn t( Mn equilibrium) Darken has estimated the practical result observed in openhearth furnace operations using Equation (X-1ll)o Assuming that: V the bath depth is 34 cmo'SMn, the boundary layer thickness is 0 003 em, DMn the diffusion coefficient for manganese in -4 2 liquid iron is l1O'x 10 cm-/seco The time required for a 90% approach to equilibrium, i eo. when log rIj - %Mn(equil)to 1 -.n. -_- l(equ~i. - ] 1, is about 40 minuteso L7M 7oMn(equil) This is in reasonable agreement with the observation that one half hour or more is required to reestablish manganese equilibrium after it has been disturbed by a major addition,

-231A similar analysis could be used to estimate the kinetics of other appro&ches to equilibrium, eogo, sulfur, chromium, etCo REFERENCES lo Brown, G. G. and.Associates~ Unit Operations0 New York- John Wiley and Sons, Inco, 1950O 2. Foust, A, S, Principles of Unit Operationso New York~ John Wiley and Sons, Inc, 1959o 3. "Basic Open Hearth Steel.making!" AoIMEo,9 New York9 1951, Chapter 14o 4o Darken, L.oS and Gurry, R, Wo Physical Chemistry of Metalso Metallurgy and Metallurgical Engineering Series, New Yorko McGraw-Hill, 1953, Chapter 19a

PRECIPITATION REACTIONS - DEOXIDATION One of the principle methods of refining liquid metals is based on the insolubility of non-metallic compounds in li.quid metalso The addition of materials to the liquid metal which result in the formation of an insoluble compound by reaction with an. impurity element permits a refin;ng separation to be carried outo The calculation of addition requirements to effect a precipitation is based on the solubility product for the separating compound, or more precisely in terms of the equilibrium constant for the reaction involving- its formation from solution by the dissolved reactants Equilibriumn Constant for Deoxidation In view of the fact that oxygen is almost a universal reactant in high temperatture metallurgical process operations, equilibria between dissolved oiygen and other elements in the base material being refined are of prime importance in describing liquid metal processeso It should be noted that the formation of insoluble oxides may serve as a refining step in removing either oxygen or,the metallic component of the oxide. In addition, the formation of a nitride, sulfide- carbide, or other insoluble compound is also a refining operation which may be described in the same mannero The equilibrium between oxygen, a dissolv ed element, and the oxidation product which is usually a non-metallic "slag", or a gas in the case of carbon, hydrogen, or sulfur, may be expressed by the equationr -233

-234x M + y O = MXOy XX-1 where M represents the element dissolved in the bulk metal, 0 is the dissolved oxygen which may be present as oxygen atoms or in combination with bulk metallic atoms (eogo, oxygen dissolved. in liquid iron may be considered to be present as dissolved FeO), and MxOy is the oxide reaction producto The equilibrim constant for Equation (XXI-l) is: aMxO K = x y XXI-2 aMo aO The influence of temperature is given byo AF F= H - T S XXI-3 and, A F - RT In K XI-4 Experimental determinations of deoxidation constants involve not only the thermodynamics of the formation of the oxide product, but the formation of the solutions of oxygen and the reacting element in the bulk metal as well. Aluminum Deoxidation of Steel Consider the deoxidation of liquid steel by the addition of aluminum. The reaction isO 2 Al + 3 Al3 XXI-5 with equilibrium being specified by the constants A1203 EI.0 K = a- - 3 XXI-6 aAl o.a

235~ 0.-AH AS thenr log K - + 4575 T- xx 57 I FORMATION OF AL203 FROM KLE ELEENTS 2A1(1) + 3/2 02(g) = Ai203 (s) xx-8 At high temperatures, ie,,o near 19000~Ko0 El.iott and Gleiser giveo A F0 -255,200 Al H~ = -401,400 A So (A Hl - A F)/T = -77o0 thus the free energy for Equation (XXI-8) is given bys A F — 401,400 + 77o0T XXI-9 II, SOLLTION OF ALUNJMIUM IN IRON The activity of aluminum in liquid iron has been determined by combining the activity of aluminum in liquid silver with the results of measurements of the distribution of aluminum between liquid layers of silver and ironr The distribution measurements were reported'by Floridis and Chipman2 who computed a free energy of solution of aluminum in iron where the activity of aLuminium is expressed in weight percent, The chemical equation and the thermodynamic relationship s given aso Al (1) = Al (in liquid iron) XXI-10 A FII - 912900 -7o70T XXI-}1 III. SOLUTION OF OXYGEN IN LIQUID IRON The equilibrium between H2/H20 gas mixtures and oxygen dissolved in liquid iron have also been measured by Floridis and Chipman3o The equilibrium may be expressed as~

-236H2(g) + 0 n (in liquid iron) = (g) I-12 where K = H2O XXI-13.2 a o It was found that: A F -32 200 + 14,63T XXI-14 However, the formation of water from the pure elements is given aso Hg (g) + H (g) XXI-15 and A F0 -60,180 + 13.93T XXI-16 The difference between Equations (XXI-15 and XXI-12) gives: ~O2(g) = 0 XXI-17 21012 -2 with a free energy change; A FI - -27,980 0- 70T IXXL8 IV COMBINING I, II, AND III Combining: Al,03(s) = 2A1() + 3/202(g) (I) 0 A F = 401,400 - 77o0T 2Al(l) - 2Al(in liquid iron) (If). F nFI~ 25, 800 - 15.40T 3/202(g) = 30(in liquid iron) (III) A FI =-83,940 - 2.10T one obtains the result: AgP23(s) = 2A1 + 30(both in liquid iron) X.XI-19 A F =.291,660 - 94,50T XXI-20

-237or expressed in terms of. the deoxidation constants log Ki = -63,700/T + 20067 XXI-2 The deoxidation constant may then be calculated at any temperature in the steelmaking range, eogc KIV @ 16000C c 4o7 x 1 -14 Summary of Deoxidation Data A srnmmary presentation of the free energies of formation of oxide compounds is given in Table XXI-l " Also included are data for nitrides, sulfides, and carblides, compounds which may also be formed upon removal of an impurityo In addition to the standard free energies of formation of the insoluble compounds^ the standard free energies of formation of the solution contaniing the reactants is also rere re Table XXI.2 presents the free energy relations for the formation of dilute sol,,tions 4 in libquid iLon* The data for other solvent metals is less complete'9 with only a few values being scattered throughot the literatur.:eo In many cases, an estimation of the deoxidizing power of an. element may- be made by assuming that an ideal solution is formed beween. the element and the solvent metal (ioe, tthe mole fraction of the dissolved element'may be s'ubstnitated for its activity) If the free energy of formation of the soltion between oxygen and the solvent metal is'unknown9 however, the eqluilibrrium oxygen act ivity mnay only be specified. in terms of an equivalent oxygen partial pressure in the gas phaseo This information may be useful to the process engineer if the oxygen potential of the system. is determined by other conditions which are known

-238TABLE XXI-1 STANDARD FREE ENERGIES OF FORMATION OF OXIDES, SULFIDES NITRIDES AND CARBnIS AT 1600 ~c ASO Cal AH~ Cal per moleNo. Reaction per mole per deg g. OXIDES 1 2Al(l) + 3/2 02 = A1203 (S) -4b01,400 -77.00 2 Be(l1 + /P 02 = BeO (S) -142,360 -23.36 3 C(graphite) + 1/2 02 = C0(g) - 26,760 +20.98 4 C(graphite) + 02 = C02(g) - 94,260 + 0.27 5 Ca(g) + 1/2 02 = CaO (S) -187,980 -46.21 6 2Qb (S) + 5/2 02 = Cb205 (S) -417,770 -8158 7 Co(l) + 1/2 02 = CoO(S) - 57,380 -18,65 8 2Cr(S) + 3/2 02 = Cr203 (S) -271,300 -61.82 9 Gu(l) + 1/2 02 = Cu(1) - 33,110 -18.21 10 Fe(1l) + 1/2 02 = FeO(l) - 57,070 -11ii60 11 H2(g) + 1/2 02 = H20 (g) - 58,850 -13.12 12 Mg(g) + 1/2 02 = MgO(S) -176,060 -49.84 13 Mn(l) + 1/2 02 = MnO(S) - 97,360 -21.12 14 Mo(S) + 02 = Mo02(S) -131,530 -33.95 15 Ni(1l) + 1/2 02 = Ni(S) - 57,370 -22.09 16 Si(1) + 02 = Si02(S) -217,780 -46.91 17 Sn(1) + 02 Sn02(S) -138,500 -48.92 18 2Ta(S) + 5/2 02 = Ta205(S) -480,030 -96.65 19 Ti(S) + 02 = Ti02(S) -224,080 -41.93 20 2V(S) + 3/2 2 = v2o03(s) -291,350 -56,49 21 W(S) + 02 = wb2(S) -136,750 -40.93 22 Zr(s) + 02 = ZrO2(s) -258,170 -42.87 SULFIDES.. 23 2Al(1) + 3/2 S2(g) = A12S3(S) -164,400 -69.0 24 Ca(g) + 1/2 S2(g) = CaS(S) -169,600 -47.4 25 2cu(1) + 1/2 S2(g) = Cu2S(1) - 29,300 - 6.2 26 Fe(1) + 1/2 S2(g) = FeS(1) - 34,000 -10.4 27 Mg(g) + 1/2 S2(g)= MgS(S) -132,300 -45.7 28 Mn(l) + 1/2 S2(g) = MnS(S) - 68,700 -19.1 29 Mo(S) + S2(g) = MoS2(S) - 76,300 -33.3 30 Si(1) +:S2(g) = SiS2(S) - 73,200 -44~0 31 w(s) + S2(g) = WS2(S) - 69,800 -32.9

-239TABIE XXIJ3- (cont Dd) STANDARD FFRE ENERGIES.OF FORMATION OF -OXIDE4 SULIDES NITRIDES AND CARBIDES AT 1600 ~C LAS' Cal AH' Cal per mole No. Reaction per mole per deg K NITRIDES 32 Al(l) + 1/2 N2 = A1N(S) - 62,300 -30.1 33 B(S) + 1/2 N2 = BN(S) - 27,7Q0 -10o4 34 3Be(l) + N2 = Be3N2(S) -133,500 -40,6 35 3Si(1) + 2N2 = Si3N4(S) -209,000 -96.8 36 Ti(S) + 1/2 N2 = TiN(S) - 80,300 -21.0 37 V(S) + 1/2 N2 = VN(S) - 43,000 -21o4 38 Zr(S) + 1/2 N2 = ZrN(s) - 82,200 -22,0 CARBIDES, 39 4A1(l) + 30(gr) = A14C3(S) - 35,700 -28.1 40 Ca(g) + 2C(gr) = CaC2(S) - 59,800 -21.6 41 3Cr(S) + 2C(gr) = Cr3C2(S) 8,550 + 5.0 42 2Mo(S) + C(gr) = Mo2C (S) + 4,200 + 4.8 43 Si(l) + C(gr) = SiC(S) - 38,400 - 8o5 44 Ti(S) + C(gr) = TiC(S) - 57,300 - 2,5

-240TABLE XXI-2 (4) Standard Free Energy of Solution of Various Elements in Liquid Iron Standard state is the infinitely dilute solution in pure liquid iron, referred to a 1 weight percent solution such that the activity of the added element is equal to its concentration in weight percento Element l A cal/mole A1(1) =- 0o031 -12,900 - 7.70T C(gr) = C 8,900 -11010T Co(Y') = Co 1 - 926T Cr(s) = Cr I 4,350 -1l.11T Cu(l) = Cu 8 99300 - 9.40T H2(g) = H 79640 + 7.68T Mn(l) = Mn 1 911T Mo(s) = Mo 1 6,280 -12o32T Ni(l) = Ni 1 - 921T 2N (g) = N 860 + 5o7QT 2o (g) 0= 27,980 - 070T Si(l) = Si 0O0072 - 29,000 - 030T 2(g) = S - 31,520 + 5027T Ti(s) = Ti 0o05 - 7,000 -1100T V(s) = V 012 - 3,900 -11o07T W(s) - W 1 7,640 -1362T Zr(s) = Zr 0 05 - 7,000-12.20T

-241The equilibria presented have been derived for the pure reactant phase, eogo pure solid A1203l The relationships apply however, in all cases, and the deoxidizing power of an element may be computed under conditions of equilibrium with complex slag mixtures provided that the activity of the product in the slag is known. In fact, the deoxidizing power of an element increases as the activity of the compound formed decreases, as shown by Equation (XXI-2)o The use of silicomanganese as a deoxidizer is an illustration of this facto The deoxidation product is an iron-manganese-silicate slag in which the activities of the reaction products is much lower than what it would be If either pure silicon.or manganese were used. In this manner, the deoxidation is more completes and requireid less deoxidizing material for the same degree of deoxidationr Application of vacuumw ~ -systems where a gaseous reaction product is formed, (eg5, CO), permits the reaction to reach a greater degree of completion~ These principles apply as well to the formation of nitrides9 sulfides, carbides, and other insoluble compoundso Interaction in Alloy Systems The equations presented in Table XXI-2 have been developed for dilute, binary systems, and strictly apply only to these solutions~ The activities in solutions which do not follow Henry's Law for the solute, or are multi-component, usually, must be expressed as the product of a coefficient and concentration, and not concentration alone, The activity coefficient depends upon the degree to which the activity differs from the concentration. Activity is then expressed aso AM = fM (.4) XXI-22

for solutions whose concentration is expressed in weight percento If the standard state is defined as the infinitely dilute solution, and the activity is referred to a 1 weight percent solution, "fM is unity, ioe the activity is equal to weight percent, when the solution follows Henrjt Law for the solute. The activity coefficient, fSM depends upon the concentration of the solution, deviating from unity to a greater and greater extent as the solution becomes more concentrated in solute0 The coefficient is also a function of alloy concentration, and is influenced by the presence of other elements, as well as increasing amounts of atoms of its own type. The atomic interactions of alloying elements in liquid iron and the factors which influence the activity coefficients in multi6 component iron alloys has been discussed and tabulated in the form of interaction parameters6' 7 8 In solutions which are sufficiently dilute, Henry s Law behavior may generally be assumed, In addition, the influence of other alloying elements on the activity coefficients of the reacting elements is minimized in dilute solution.o, Under these conditions., activity coefficients may be assumed to be unity, and concentrations may be substituted for activities, Precipitation Stoichiometry The amount of reacting material which must be added. to remove an impurity from solution consists of two parts. First, a portion of the material added reacts with the impuarity and forms arn insoluble precipitate which separates from the li.quid alloy^ A second portion is represented by the added material which remains in solution in sufficient quantity to satisfy the solubility product relationship.,

-243Problem: A 100 ton ladle of steel at 1600 C contains 003 weight percent oxygen Compute the amount of pure aluminum which must be added to reduce the oxygen content of the steel to OQ001 weight percent' Assume Henry's Law behavior for both aluminum and oxygen n isolution9 and that equilibrium conditions are reached. Solutiono The deoxidation constant for alxminum. assuming the conditions given above and that pure alumina is the reaction product, was determined for 1600oCo using Equation (XXI-21)o K = 4o7 x 10-4 = (f) 2 (/)3 The equilibrium aluminum content is theno 4 7 x: to-1 A.7(oooi)- 8 3 The residual aluminum in solution in pounds iso (100) x (2000) x 6 ~5 x L-3 13o7 lb. 100 The aluminum which reacted is given by the p9unds of oxygen removed times the weight ratio in the reaction product o-r (Oo03 - 0,00l) x (1oo) x (2000) x (54) 65o2 lbo 100 (5) The total aluminum required is given, by the sum of the two amounts, or 78 9 lbo Kinetics of Precipitation Reactions The rate of approach to equilibrium for this type of refining reaction is controlled by nucleation and growth of the precipitateo A kinetic model may be derived in the same manner as that for phase

-244separation processes which are discussed' in the following chapter. The two refining processes are analogous, the phase separation process involving a reduction in solubility by a change in temperature, whereas the present consideration of precipitation involved changes in composition~

-245RF'ERENCES 1o Elliott J. FS and Gleiser, Mo Thermochemistry for Steelmaking, I Reading, Masso~ Addison Wesley, Ineo 1960o 2o Chipmaan John and Floridis, To Po "Aetivity Qf Al aimn in Liquid Ag-A, Fe-A-C, and Fe-Al-C-Si Alloys," Acta Metallu.rgica, 3,9 1955, 456. 3o Floridis, T0oP and Chipman,. Johno "Activity of Oxygen in Liquid Iron Alloys, Transo AoIoMoE, 212, (958), 5 499 4o;.Basic Open Hearth Steeimakingo AoIoMoSo New York:, 1951 Chapters 14 and 16' 5. Coughlin, J. P. Cont ribution of the Data on Theoretical Metal lurgy, XII Heats and Free Energies Of Formation. of Inorganic Oxidesa Bureau of Mines, Department of the Interior Bulletin3 5~42 6o Chipman, Jo "Atomic Interaction. in Molten Alloy Steels " Jo Iron & Steel Int0, -180o (195 5) 970 70 Elliott, J. F. and Gleiser, Mo "Thermochemistry for Steelmak.ing " IL, Reading, Mass.,o Addison Wsliey, Inco 1960o 83 Ohtani, M. and Gokeen, N. A. "Thermodynamic Interaction Parameters of Elements in Liquid Irono," Transo AoI.MoEo 218, (1960), 533S

CHAFEE XXI PHASE SEPARATION The refining of a metal by phase separation is accomplished by decreasing the temperature of a solution, until the solubility limit of a dissolved constituent is exceeded If t he phase wh ich separates out from a liTuid is a solid. the process is termed crystallizationo The phases are then separated by physical meansy thus effecting a re.. fining of the liquid. or recovery of a desired component from solution, Thermodynamics The equilibrium relationships for the separation of phases may be considered in terms of a phase tranrsition and the distribution of the components of a binary solution between the phases0 The transfer of one component from one phase to another may be expressed as0 (Component 1) (Cor-iponent I) XXJI-i phase I phase II The equilibrium constant for the reaction above iso a, K ^ _ XXII-2 A similar expression may be written for componen t 2 and the equilibrium relationship expressed byo II a2 K2 - - XXII-3 a2 It is convenient to choose a stand.ard state fo componen.t 2 such that a approaches N2 (mole fraction of component 2) as N2 approaches 2'

-248zero in each phase o Expressing the relationships above in terms of the activity coefficient and the mole fraction where a, is equal to N if the major component (component 1 in this case) follows Raoult's Law, a valid assumption if the solution is dilute in component 2: K (4l N2 )xxii4 N272 K -E$-( XI 2 II II 2 72 The equilibrium constants may be measured experimentally or calculated from free energy relationshipso If the standard free-energy change for the transfer of a component from one phase to the other is known, then -I or K2 may be determined from the relationo A F -RT Kln.K If the phase transition is defined for the solvent in terms of transition temperature, heat of transition, and known heat capacities o for the phases involved, A F1 may be computed The free-energy change for component 2 is not readily obtainable by this means since the, pure solute generally does not undergo the'saie transition as the solvent, Thus K2 must be determined empirically, and if values can be specified at two temperatures, an assumption of a linear relation between log K2 2 and 1/T will permit'extrapolation to other temperatures2 Kinetics The principle barrier to reaching equilibrium often manifests itself in the rate of nucleation of the separating phase0 This is particularly true for crystallization processes, where large degrees of supercooling have often been noteda The surface energy between the

-249precipitate and the solution must be considered particularly for solids, in addition to the differences in free-energies of the bulk phases3 The total free-energy change may then be expressed as3 2 A F - a Fv + 6a2 XI-6 where~ A F is the bulk free-energy change y is the surface energy of a unit area of interface between the parent liquid and the crystal. nucleuso 3 2 a, and 6a2 are the volume and surface area, respectively for a cube of side a, and it should be noted that these terms vary with the specific geometry of the nucleusb The geometrical factors introduce a size effect into the problem and since A F is negative for a supercooled melt, these factors determine v the critical size for a nucleus0 When the nucli are small the positive term predominates, and the curve shown in Figure IXII-1 rises to a maximum as the size increaseso A nucleus is stable if the size is greater than ao, the critical nucleus size, since the free-energy decreases if the nucleus grows, The free'energy change for the formation of a nucleus of critical size is called the work of nucleus formation0 The nucleus of critical size, ao, is in unstable equilibrium with the parent phase since any change in its size results in a decrease-.in free-energy, and a tendency to either grow or disappear The work of formation is determined by a which may be 0 evaluated by maximizing A F. 2 6(AF)/=a 3 a * + S12a = 0 XXII-7 a = 4y/A.% XXII-8

-250Z 0 IXXII 1.r f 0F o LL d Wr NUCLEUS SIZE XXII-1. Free Energy of Nucleus Formation as a Function of Nucleus Size.

-251Substitution in Equation (XX-i6) give.s AF* F (aao) "(4 7/ r) 3 F 647/AF) 7 XXII-9 nAWF = 7/(AE2 XXII-10 where the coefficient = 32 for a eubeo If the nucleus were spherical 3 would be equal to 1,6 1/3a The value of A F which corresponds to the critical size represents an energy barrier that muast be overcomoe by a nucleus before it is stable The energy required can ecme only from momentary~ local fluctuations of both concentration and energy~ The energy fluctuations are statistical in, nature and are of the usu.al kinetic type that gives rise to homogeneous reactions. The concentration flactuation requires transport by molecular diffusion of the requisite number of molecules close enough to one another to form a rucleus large enough to equal, or 4 exceed the critical size. Becker proposes the following equation for nucleation rate, =ce-Q/kT e -A(T)/kT XXII-11 dt where~ dN/dt = nucleation rate, number/unit volme-unit time Q = activation energy for diffusion A(T) = work required to form the surface of a nucleus T = absolute temperature c = a constant k = Boltzman constant The work of nucleation, A(T), increases markedly with decrease in supersaturation and is infinite at the saturation point, The term e -Q/kT decreases with increase in supersaturationo. The N versus T

-252curve thus has a pronounced maxim um that corresponds to a definite supersaturation, However, theoretically if time enough is allowed, homogeneous nucleation will eventually occur at any supersaturationo The presence of foreign particles or of seed crystals can appreciably increase the nucleation rate by innoculation. The alteration of surface energies, caused for example by the presence of trace anmomts of surface active elements, can also drastically affect the rate of nucleationo These effects occur becae.' of the change in the surface energy term of the nucleation rate equation, A more complete discussion of the kinetics of phase precipi2.9 tation is provided in the Supplementary References It may be concluded from the foregoing discussion that heterogeneous nucleation caused by the presence of seed crystals or innoculating agents which promote nucleation will occur prior to homogeneous nucleation, This is desirable in phase separation processes since a rapid nucleation of the precipitating phase promotes the kinetics of phase separation, and prevents nucleation of the precipitant from becoming rate limiting0 In practice, it is often necessary to "seed" the melt with foreign particles to promote heterogeneous nu.cleation0 Agitation in the form of vigorous stirring or vibrating techniques have also been used to promote nucleationo If growth of the precipitate is rate limiting,, the kinetics of phase separation may be described in terms of the rate model developed for liquid-liquid extraction in Chapter XX.

-253Processing Operatiors - Lead-Silver System Recovery of silver from lead may be accomplished by cooling the silver-containing lead batho Consider a lead-silver alloy containing, 20 weight percent silvero As shown in Figure XXII-2, leadsilver solutions will precipitate out a solid of very high silver content on cooling, The composition of the liquid solution will follow the liquidus line of the diagram if equilibrium conditions are maintained O-t cobling, the alloy will begin to precipitate a silver solid solution at a temperature of 540 Co and will continue to do so, until the eutectic point is -reached at 2~5 percent silver and 304 Co At this point, the liquid -can be filtered or the solid skimmed off (the lighter silver floating on the liquid bath) resulting in [(20 - 25)/20] x 100 87-5 percent recovery of the silwvera Further purification can be accomplished by the Parkes Process in which silver is removed in a sil-ver-zinc layer when. zinc is added to the leado This technique is also a phase separation process except that it. is more accurately described in. terms of precipitation reactions as described in the previoug achaptero Zinc Recovery by Phase Separation An example of the commercial application of phase separation is in the recovery of zinc from the zinc-lead blast furnace operating at AvonmouthJ England o This process is shown schematically in Figure XXII-3. Ores which are high in zinc are smelted in a lead blast furnace, producing a stack gas containing up to 6% zinc,, The stack gases.are passed through a splash-condenser containing lead which absorbs the zinc from the vapor phase0 It is reported that under

-254I000 960.5 ~~___ ___800 L __ ___. ___ _____ __ 0 F 600 - 400 - 327./ a + L 3040 -a a/3 CZ+, 200 ---- 0 20 40 60 80 100 Pb Ag WEIGHT PERCENT SILVER Figure XXII-2. Phase Diagram for the Lead-Silver System.

-255ROTORS E EXIT GASES 0.24% Zn 4500C -- ------' /^\ ^ ^\\ //<^- ^^ Pb AT 450 OC 6%0 Zn. {^ I ooo000 0 LEAD BATH Pb AT 56dfC SPLASH CONDENSER 2.4 %O Zn LEAD PUMP WATER RETURN COOLED SYSTEM LAUNDER l X \< ~BAFFLE 450 ~C ZINC LAYER Zn RICH ALLOY LEAD LAYER ZINC HOLDING SEPARATOR BATH TANK Figure XXII-3. Schematic Diagram of Zinc Recovery System for Zinc-lead Blast Furnace.

-256typical onditions the gas entering the condensers contains 5o9 percent zinc at a temperature of 1000~Co The gas leaves the condenser at a temperature of 450~Co and contains about 4 percent of the entering zinc, The lead enters the condenser at 4500Co. and leaves at about 5600Co It is saturated with zinc on entering, 2o15 weight percento During the condensation, the lead is heated and dissolves an additional 0O25 percent zinc The lead is then circulated through a cooling launder, The concentration of zinc 2o4 percent, is far below the saturation point on exiting from the condenser, 4o4 percent at 5600~C However, on cooling essentially pure liquid zinc begins to precipitate- out from the lead at o 470 Co where the solution becomes saturated0 Cooling is continued to 450~C. and the additional 0o25 percent absorbed in the condensers separates outo The upper liquid layer of zinc is then separated by means of a weir, and the underflow of lead-rich alloy is recirculated~ Engineering Design The major considerations of a phase separation which concern the engineer areo lo The yield of a given product. 2 T Te pit o he purty of the producto 3o The energy requirementso 4. The -rate of production~ Process Yield The yield of the product may be estimated by constructing a material balance for the system, ass-ming that equilibrium conditions prevail, This would represent the maximum yield, a quantity which.is

-25 7given in pounds byo I 0 c2 ^c2 Y = W XXII-12 2 2 where - W is the initial weight of the charge in pounds 0 2 is the equil ibrium concentratiorn in. weight percent of component 2 in the parent phase at the lower temperatureo 0 c is the concentration in weight percent of component 2 in the parent phase initially. II c2 is the equilibrium concentration in weight percent of component 2 in the precipitated phase at the lower temperature o Equation (XXII-12) is an expression of the "lever-rule" Mole fractions may be substituted for weight percentages and N t, the total number of moles of initial solution. substituted for Wo The yield is then expressed in moles, and the weight may be computed from the molecular weights of the solute and solvent and the concentrations in the producto When. the process involves a highly volatile solvent or reactions occur between the lining of the process container and the material being processed, a correction must be made to the yield ellation given above for the losses o. TPrity of Product The purity of the product for the equilibrium case is given directly from the phase diagram, In practice, the adherence of the parent liquid to the precipitated crystals' or the entrainment of one phase within the other often decreases the purity of the recovered materiala The purity can usually be improved by repeating the phase

-258separation on the producto In the case of crystals precipitated from aqueous or organic solutions, washing with fresh solvent can greatly improve the purityo Thermal Requirements The energy requirements for a phase separation can be calculated from a heat balance on the process. The cooling energy represents heat which must be removed from the system and is given by the sum of the sensible heat change in the solution, heat evolved during the separation of phases, (a quantity which may be either negative or positive, and is often approximated by the heat of solution for dilute solutions whose composition does not vary greatly during the operation), minus the heat losses to the surroundings, and any other cooling effects, eogo, vaporization of the solvent. Process Kinetics The rate at which a phase separation can be carried out may be limited either by the kinetics of the process, or the capacities of the equipment, or both may play a roleo The kinetics of nucleation have been briefly introduced in a previous section, and may be applied to the case where the rate limiting step is the nucleation o f the second phase. The growth of the phase may also be rate limiting, in which case the relationships of Chapter XX may be used to define the process rate, The ability of the equipment to extract heat from the solution. at a rapid rate may be a primary factor in the rate of the processo Alsso the removal of the material from the equipment, or the charging methods ioe,, material handling, may limit the operation. Consideration of these factors are of major importance in the engineering design of phase separation processes,

-25 9 RE EFREI ES 1o Darken, Lo S. and Gurry,,R Wo Physical Chemistry of MetalsO Metallurgy and Metallurgical Engineering Series, New York- McGraw-Hill, Inc,, 1953, Chapter 12o 2, Cottrell, Ao Ho Theoretical Structural Metallurgy. New York~o Sto Martin's Press, Inc,, 1955, Chapters X, XI, and XIVo 3. Mehl, Ro Fo and Jetter, Lo K. The Mechanism of Precipitation from Solid Solution, the Theory of Age Hardening, ASM Symposiium on Age Hardening of Metals~ (1939), 342 4, Becker, Ro "On the Formation of Binary Alloys, Ze ito Metallkunde, 29, (1937)s 245. 50 Volmer, Mo and Weber, Ao "Nucleus Formation in Super Saturated Systems " Zeit, Physo Chemo, 119, (1926), 277. 6. Zener. Co "The Role of Statistical. Mechanics in Physical Metallurgyo" Thermodynamics in Physical Metallurgy, ASMl, 1950o 7o Turnbull, D, and. Fisher, J. Co "Rate of Nucleation in Condensed Systems o Jo Chem. Phys,, 1, (1949), 71o 80 Borelius, Go "Kinetics of Precipitation in Supercooled Solid Solutionso" Trans, AoIoMoEo, 191, (1951), 477. 9o "Liquid Metals and Solidification," ASM, 1959o 10o Morgan, So W o K, and Ltmsden, JT "Zinc Blast-Furnace Operationo" Journal of Metals,.i, (1959), 270, 11o Perry s Handbook, New York0 McGraw-Hill, Inco,,(1950), 1050,

CHAPTER XXIII DEGASSING OPERATIONS One of the principal quality problems that faces the metalmaker in producing a suitable product is that, of control of gases. Hydrogen is a particularly troublesome gas causing bleeding ingots, embrittlement, and low ductility as well as the presence of blow holes. Nitrogen is also a gas which may have a desirable or undesirable effect on the properties of a metal, particularly steel, depending upon the composition, subsequent treatment, and the use of the producto Oxygen, of course, is a principal refining agent, and, consequently, plays a role in determining the properties of metalSo In addition to these simple gases, there are also complex gases, those which contain more than one type of atom in the molecule; principally, CO, C02, and H20o In the design of processes to control these gases in metals, solubilities, rates of solution, and the chemical reactions involved in their formation or decomposition in the metal are required, particularly in the liquid state. Much of this data is presently available, and an attempt will be made in this chapter to show its application in the design of degassing operations as a refining procesSo, Fundamentals of Gas-Metal Reactions The solubility of a gas in a metal is a function of the pressure of that gas above the liquid metal. The solubility of a diatomic gas, nitrogen for example, is proportional to the square root of the pressure of nitrogen, which is in equilibrium with the melto This relationship has come to be known as Sieverts Law, It follows directly from consideration of the equilibrium of the reaction~ -261

-2621/2 N N XXIII!1 where the equilibrium constant may be expressed as: 1 21 z) 2 %) XXIII-2 K =pN2) ~=N2 p Rewriting the expression for the equilibrium constant, and taking the activity coefficient of nitrogen in pure liquid iron as being equal to one: _ = Kl142 XXIII-3 A similar relationship may be written for hydrogen. The rate-limiting step for the removal of gas from a liquid metal is generally diffusion through a boundary layer in the metal. The rate process for the removal of a gas from a liquid metal may then be written in terms of the diffusion model given in Chapter IVo The reactions between gases dissolved in metals and other constituents in solution are expressed in terms of the reactions taking place, and equilibrium constants may be written') for them.;For example, the equilibrium partial pressure of CO over liquid steel. is determined by the product of the carbon and oxygen activities in the liquid metal. This may be seen from the expressions C + 0 CO XXIII-4 Where the equilibrium constant may be written as: Peo K4 ac ao XII.I-5 This expression may be rewritten in the- f=rni PCO Kgoacoao XXp!II-6 PCO = K1o aco aoxIwhich indicates that the partial pressure of CO in equilibrium with the steel is determined by the equilibrium constant and the product of the activities of carbon and oxygen in solution,

26-)3 One might also consider the sol.ubiliy product of a compoundi which contains the atomic specie of a gaseous componento For example, the solubility product of al:r?,inum nitr.ide is given by the reaction~ AI = A + N. XXIII-7 where the eTailibriim. constant may be exp re ed aso aAi aN K ^ - xXIIl-8 7 aA2 Combining this expression with Equation (XXIII 3)l onre san. compute the partial pressure of nitrogen in in equlibri. with a merlt containing a given weight-per cent a~'amlinm. and in contact- with aluminum nitride at a given activity, provided the.activity coefficients for the solution are knrowni The reaction would be expressed aso 1/2 N2 + I = N XX II-9 where the equilibrium reelationship is given by~ K K = ai tl, 9 FK (P^ ) 12 fa ( Al) XXIII-l.O The acti1vities of onerstitent in solution are influenced by the presence of other a'lo ing elements. The magnitude of tb, is influence is determined by the in'teracti on paraMeter (See Chapter E.I), which is defined 2 as O where n is the alloying element under consideration, and j is another alloying element. in solution whose presence influences the activity coefficient of no A complete list of the therm.odynamic interaction parameters of elements in liqumid iron has been prepared and correlated with the periodic table3

-264Inert Flush Degassing Inert flush degassing is a process carried out by bubbling an inert or insoluble gas through the li.quid metalo Since the solubility of the gas in the liquid metal is a function of the partial pressure of that component in the gas phase with which the metal is in contact, the presence of an atmosphere which is very dilute in the dissolved gas and sufficient time, will provide a means for eliminating the dissolved gas. The removal of dissolved gas from liquid metal involves diffusion through a boundary layer in the melt and the reaction of evaporation from the surface, and consequently, any process which shortens the diffusion path or provides a greater surface area should provide a more rapid means for reducing the dissolved elemento The blowing of an inert flush gas throubgh the liqunid metal in finely dispersed bubbles is such a process0 An.Equilibrium Process The process engineer is interested in the rate at which inert flush degass ng will remove a dissolved gas. If one cons iders that the flush gas'i in equilibriu=m. with the melt when it 2ea:ves the metal surface, that is, that the partial pressure of dissolved. gas in the exiting bubble is equal to the equilibrium. partial pressure for the concentration of dissolved gas in the melt at that instant, one may write the following relationLhipo P~ N, N Ck X QIXI -Bl G (f F c ) (P7' ^ ) G I:E7-il wnere NG is the liters of dissolved gas, N. the liters of flushing gas, and PG and PF represent the respective partial pressures in the

-265exiting gas bubbleo Since the total pressure on the system is one atposphere, PG + PF is equal to 1, and Equation (XXIII-ll) may be rewritten as i+PG dNL. - -rG ( P ) XXIII-12 Converting from liters of dissolved gas to parts per million by weight: 20 24W'+PG dip N-F - (- - (?)d XXIII-213 NF ( M d P CG where W is the tons of metal and M is the molecular weight of the dissolved gaso For the case where the dissolved gas is diatomic.- the equilibrium pressure of dissolved gas, PG, is related to the concentration of dissolved gas by Sieverts' Laws CG KG (P) XXIII-14 where the concentration is expressed in parts per million and the pressure in atmospheresO The SieVerts' Law constant is given in the units, 1 ppm/(atm) The partial pressure of dissolved gas is then: CG 2 P = ) XXIII-15 Equation (XXIII-13) may be integrated in the form: NF= ( c2 ) dC + KG2 G XXI-16 O0' o The volume of flush gas in liters, V, required to reduce the dissolved gas content in ppm from Co to.~ iss V F M (C0o C) (2 + C ) /c c XIII17 Boundary Layer Model 4 There is some evidence to indicate that the bubble is not in equilibrium when it leaves the liquid metal~ The tranusfer of dissolved

-266gas from the liquid melt to the inert flush bubble is controlled by difrfusion of the dissolved specie through a boundary layer surrounding the bubble, Since the diffusion coefficient is finite and the residence times for bubbles are relatively small, it is quite conceivable that the exiting bubble would not have sufficient time to reach equilibrium0 If it is assumed that the melt remains homogeneous throughout the flush process, and that the concentration of dissolved gas in the flush bubble exiting from the melt is quite small, i,e, that the concentration gradient through the boundary layer film surrounding the bubble is essentially given by the concentration of the bulk metal divided by the boundary layer thickness, a reasonable model may be derived, It should be noted that this selection of the concentration gradient through the boundary layer film assumes that the concentration in the boundary layer at the bubble surface is zero Under these conditions, the concentration gradient, approximated as Ac/Ax, is equal to (c - 0)/5o The kinetics of inert flush degassing are described by the relation0 d" c D AB F tR c XXIII-18 dt 5 where D is the diffusion coefficient of the atomic specie of the gas in the metal, AB is the average area of a gas bubble, VM is the volume of the liquid metal phase, F is the flow rate of the flush gas, tR is the residence time of the average gas bubble, and c is the instantaneous concentration of dissolved gas in the metal. The expression integrates to the form: log(-c) = k t XXII-19

-267where kg is a constanmt which may be evaluated from the factors given on the right-hand side of Equation (XXIII-18)o In general, these factors may be determined from the geometry of the degassing equipmen.t It should be noted that t t the residence time, is a constant which represents the time required for a gas bubble to leave the source which is injecting the flush gas and rise to the surface of the melto The boundary layer model, which expresse the concentration of dissolved gas in the melt in the general, form of ETqation (XX:II-19), 4 is.in excellent agreement with the experimental results shown in Figure XXIII-l0 Caculation of Residence Time The residence time may be computed by assuming that the bubble is a sphere and writing a force balance about the bubbleo The forces on the bubble are the bouyant force, its weight and the friction force caused by viscous dragd Thua ~ F = ma = wg mg Fd XXIII-20 where g is the acceleration due to gravity9 w is the mass of fluid displaced by the bubble,9 loe,, having the same vol'ume9 and m is the mass of the bubble0 Henc.e wg is the?sioyant force on the bubble, mg is the gravitational force, and F is the resisting for.-e caused, ~' d by friction effects in the viscous fluido or~ 2 dv LPB 3 fD PL I:-2 t - g ~XXIII - 21 dt PB 4d where d is the diameter of the bubble and p its density, v is the velocity of the bubble in the vertical direction, pL is the density of the liquid metal, and fD is the drag coefficient which is given as a function of Reynolds number in Table XXIII-I0

-2681.0 0 6.0 0O o W 0.4 3E 0.2 w 0.1 0 rw 0.064 0.02 0 20 40 60 80 FLUSHING TIME, MINUTES Figure XXIII-1. Removal of Hydrogen from Liquid Steel by Flushing with Argon.

-269TABLE XXIII-1 Relationship Between Reynolds Number and Drag Coefficient for Bubble Flow* d Re -6 107 2 x 10 106 2 x 105 105 lo8 x 10-4 104 1o75 x 10 3 103 2 x 102 10 1o8 x 10 10 2o0 1 35,2 200 ol8 300.2 350.3 400 9 900 2o5 2000 2 5 10,000 ~ Reported by David Taylor Model Basin, Department of the Nary

-270If a bubble is assumed to instantaneously reach a terminal velocity and to rise with no rapid changes in acceleration, the velocity at any point is given as, r do=; [ - I = I X -22 ( tP L L 3 p f D -1 Where h is depth in the melt, and the residence time, tRs is given by the integral: t = r LB.f XXIII-23 where H is the depth at which the flush gas is dischargedo Equation (XXIII-23 may be evaluated in either of two ways. First, average values for the density of the gas and the diameter of the bubble may be selected. and the average velocity computed using a trial and error solution involving the drag coefficient and the Reynolds number, A more rigorous approach may be taken~ The density of the gas may be expressed as a function of atmospheric pressure and depth in the melt, and perhaps temperature as well, since the bubble is heated during is passage through the liquid metal, The diameter of the bubble is expressed in terms of the density and mass of gaseous material, in the bubbleo These may be substituted in the integral of Equation (XXIIN-23) which is then evaluated graphically. Alternatively, using these expressions for bubble diameter and density, the velocity may be determined at several depths in the melt using Equation (XXIII-22)o The average of these values would-giv~ a reasonable value for the velocity up through the melt, at least one which is of higher reliability than one calculated using the first procedure outlined. In the event that

-271the velocity remains essentially constant, the assumption of neglegible aceeleration is valid and the residence time is given by the expressiont XXIII;-24 R v Vacuum Degassing An Qperation which is capable of producing liquid metals containing extremely low concentrations of dissolved gases is that of vacuum degassingo The liquid metal is held in a closed container under extremely low pressureso The mechanism by which the dissolved gases are removed is essentially the same as that previously described, diffusion through a boundary layer-at the surface and evaporation from that surface into the vapor space above. Since the partial pressure of dissolved gase above the ace the u ce o he melt is extremely low in the vacuum and remains that way throughout the operation, this is a very effective way of removing dissolved gases, Assuming the rate controlling step to be diffusion-of atomic specie. of the gaseous component through a boundary layer in the metal, the kinetics of vacuum degassing processes may be described by the equation~ dc -_ D A XXIII-25 dt'- V where A is the area of the gas-.'metal interface, generally taken as the cross-seetional area of the crucible or furnace hearth, V is the volume of the melt-.and c is the concentration of dissolved gaso Since the concentration at the gas-metal interface is assumed to be in equilibrium with the gas phase, in this case a vacuum, the concentration gradient is given by the ratio, c/5o If the process is carried out at reduced pres

-272sures rather than under a vacuum, the gradient is given by (c - c)/6 where.ce is the concentration of dissolved gas in equilibrium with its reduced partial pressure in the process atmosphere. Equation (XXIII-25) integrates to~ c D A Log ( —) = -o-3 V t XXIII-26 It should be noted that according to this model, as long as the reaction taking place at the surface of the melt is much more rapid than the rate of diffusion through the liquid boundary layer, the degassing rate is independent of the molecular form of the gas specie formed in the vapor space above the melta Figure XXIII-2 shows the concentration of hydrogen in, a melt of steel as a function of time under vacuumo The slope of the curve k', i eo the reaction rate constant for degassing, is given by the coefficient of Equation (XXIII-26) D A t' = 2.38 V XXIII-27 Assuming that D equals 6 x 10 3 cm2/min, 5 equals 0.003 cmo,, and A that V is 50 cm, the predicted rate constant is~ 6 x 10o -' (2o3)(00.00350) =007 m n which is in approximate agreement with the average slope of the line in Figure XXIII-2, about 0o02 minutes o The desulfurization of a liquid 80% Ni-20% Co alloy under -5 a vacuum of 10 atmospheres is shown as a function of time in Figure XXIII-3, The melt was 10 centimeters deep, and if a diffusion coefficient for sulfur of 3 x 10 5 cm2/sec and a boundary layer thick

-2730.006 0.004 ~' 0.002 0 O.t9 0 0.001 z _.1 0 0.0006 c1 - 0.0004 0.0002 0 20 40 60 80 100 TIME UNDER VACUUM, MINUTES Figure XXIII-2. Vacuum Degassing of Liquid Iron in Magnesia Crucible.

-2740.06.-.-____ 0.04 0 00 0 0.02. 0 N^0 ^ 00 a,"3 0 -J Z 0.01 Z 0.006 L. D0 0.002 0.001 20 40 80 0 20 40 60 80 TIME UNDER VACUUM, MINUTES Figure XXIII-3. Desulfurization of an 80oNi- 20%Co Alloy at 1530~C by Vacuum Treatment.

-275-5 3 x10 -4 - ks = (2,30,003)( 10) 4,3 x 10 sec, -4 An average observed value of 21l x 10 seconds - is in reasonable agreement.with the predicted resulto These examples serve to illustrate the general validity of the assumption that diffusion through a boundary layer in the melt is the rate contrplling step in the kinetics of vacuum degassing processes at high temperatureso Other Degassing Processes Numerous vacuum degassing processes have been proposed which attempt to produce a larger gas-metal surface area, and consequently, an increased rate of degassing. This is particularly important in the treating of liquid metals since the metal temperature decreases during the operation and a limited amount of time is available for ito One such process is the Dortmund-Harder process which was described in Chap7,8 ter V (Figure V-l)o, Recently, a new process has been developed in Germany called the Ruhrstahl-Heraus Continuous Vacuum Processo This is used exclusively in ladle degassingo The ladle of molten steel is placed in a pit in the teeming shed, and the vacuum apparatus positioned by an over-head craneo Tubes are lowered into the melt while the vacuum chamber is being Dp&ped -:t by a multiple stage pumping system~ Argon is introduced into one of the tubes, and the liquid steel moves up in this tube. The metal then splashes into the vacuum chamber where it is degassed,:: The time required to degas 100 tons of liquid steel is 15-20 minutes, and the temperature

-276drop during this period is only about 30~ Co If necessary, it is possible to heat the liquid steel by auxiliary equipment during the vacuum 9,10 treatment A schematic diagram of the process is presented in Figure XXIII-4o Knowing the volume of argon introduced and the geometry of the system, it should be possible to predict the decrease in concentration of dissolved gases in the liquid metal, providing one assumes something about the degree of degassing performed in the vacuum chamber, Several other vacuum degassing techniques include vacuum degassing in the ladle, a process deVisid by Ao Finkl and Sons Company, Chicago o Vacuum stream degassing is another method of bringing more of the surface of the melt in contact with the vacuumo In this process a ladle of steel to be degassed is placed over a vacuu chamber and the liquid metal is permitted to flow into the vacu m chambero The reduced pressure causes the gases to diffuse from the metal, which is received in another ladle below from which it can be repoured into an ingot moldo The thin stream, of molten metal allows an excellent, chance for- the vacuum to degas the melt quickly and efficiently, and results by this method have been as low as two parts per million residual hydro12 gen 0 Other vacuum degassing techniques include the consunmable electrode melting process in which an ingot of material is similtaneously melted and degassed in a vacu:am, Another effective method of controlling dissolved gases particularly for oxygen and nitrogen is that of adding a scavenging element such as titanium or zirconiumo' These elements form stable nitrides or oxides which are insoluble in liquid metalso The principles involved here are the same as those outlined in Chapter XXI o

-277VACUUM PUMPING SYSTEM GASES ARGON LIQUID STEEL LADLE Figure XXIII-4. Schematic Diagram of Vacuum-Flow Steel Degassing Process.

-278Inert flush degassing.may also be accomplished by placing a volatile solid in the liquid melt which then forms purging gases that are evolved in the bulk of the metalo An. engineering analysis of the effectiveness of such a method. may be accomplished in a manner similar to that outlined above under Inert Flush Degassingv The high effectiveness of the methods outlined here and the perfection of the processes a well a a the development of economic equipment for accomplish lng them will. undoubtedly see a greater and greater use of degassing methods as a refining operation in the metallurgical industrieso Temperature Drop of the Melt During Degassing The temperature drop of the melt during degassing may be computed di$rectly'by a consideration of the radiation and convection losses from the metal and its container during the degassing operationo The principal source of heat loss especial.y for steels is by direct radiation from the exposed metal surfaceSo The heat effect caused by the removal of the dissolved gas from so>.tion and in inert flush degas sing the sensibSle heat l.ost to the flush gases is also negligible in comparison.0 The time available for the degassing operation may then be computred directly by consider;ng the heat losses and any energy which may be supplied to the ope:ration0o1l3

-279REFERENCES io Pehlke, R, Do and Elliott, J, Fo "Solubility of Nitrogen in Liquid Iron Alloys," Part I, Thermodynamics, Trans, AOIM.E, to be published. 2o Wagner, Co Thermodynamics of Alloys. Addison-Wesley Press, 1952, 51-53o 3~ Ohtani, M. and Gokcen, No Ao "Thermodynamic Interaction Parameters of Elements in Liquid Irono" Trans AIoMoEo, 218, (1960), 533o 4, Sims, Co Eo "Flushing Molten Steel with NeutralGaseso" Electric Furnace Steel Proceedings of the A.IoMEo, 1949, New York, 302 5 Aksoy, Ao Mo Thermodynamics and Kinetics in Vacuum Induction Melting. Vacuum Metallurgy, Bunsah, Ro So(ed), New Yorko Reinhold Publishing Corp,, 19580 6. Machlin, E, S. "Kinetics of Vacuum Induction Refining-Theory," Trans. AI.MoE,, 218, (1960), 314, 7. Harders, FoKnuppel, H. and Brotzmann, Ko "The DHHU Process for Vacuum Treating Molten Steelo" Journal of Metals, 12, (1960), 3980 80 Wooding, Po Jo and Sieckman, W, "Vacuum Treatment of Molten Steel in Germany." Metals Progress, 77, (1960), 116, 9, Balster, H, Wo "Degassing of Steel by the Ruhrstahl-Heraus Continuous Flow Vacuum Process, Elect. Furnace Steel Proco" AoIoMoEo, 16, (1958), 192o 10o Starratt, Fo Wo "Vacuum Flow Steel Degassingo" J of Metals, 10, (1958), 4650 11o Finkl, Co Wo "Vacuum Degassing in the Ladle o o o A New Technique in Steelmakingo" Metals Progress, 76, (1959), 111. 12o Tix, Ao "Production Scale Degassing in a Vacuum," Electo Furnace Steel Proc, AoIoMEo, 1955, 70o 1.30 Samways, No L, and Dancy, T. E. "Factors Affecting Temperature Drop Between Tapping and Teeming" Journal of Metals, 1, (1960), 331o

Part V INTEGRATED OPERATIONS -281

CHAPTER XXIV ELECTRONIC COMPDUTRS IN PROCESS ENGINEERING One of the major developments in the rapid advances made in the scientific field in the last 15 years has blen the perfection of the electronic computer in both its analog and digital formsz The ifportance of electronic computers in the engineering of system.s has been established, and they shall undoubtedly take preeminence as the major tool. of the process design engineer. There are two basic types of large-scale calculating machines in use today, the analog or continuous variable machine and the digital. or discrete variable machine. An analog computer is a physical system, mechanical, electrical or optical, which is designed. in such a way that the variables of the system satisfy the same mathematical laws as do the variables of the problem. of interesto The physical process of computation is replaced by a measurement of the physical. quantities corresponding to the values of the unknown variables Digital computers, in contrast, pe-form their operations by counting in a ma;ner similar to a desk Calcu' latoro The Digital.a Comp-uter The large-scale digital calculator will perform only the simplest types of operations. First of all., it will. read. i.oe, assimilate inforiation whiach is supplied to it on punched cards, punched, paper tape, magetic tape, or by other similar techniqueso Secondly, it will. remember what it has read. The memory cells of most digitaL computers consist of magnetic cores, mercury d.ez.ay lines, cathode-ray-tubes, magnetic drumsa banks of relays, or electrostatic storage tubeso A retlay computer remembers information by having certain relays in an -283

-284energized cnonditlon wbile. others are in the urenergized. condition.o Irnformation is stored in a similamx yes-no manner by other basic: eLetrical components. Thirdly, the digital maehine will perform arithmetical operations. Most computers will add, subtra,~ct, mul.tiyply, and diviadeo By combination of these basic operations., s-uibroutines may be developed to'take roots, raise numbers to pow.ers or evaluate other commmon.ly used. functionso Fourth, the largge-scale digital computer may exercise choice~ It is able to follow a set of logical expressions, choosoing between one set of operations and. another on the basis of re. ative magnitufdes of quantities stored within'its memoryo Finallyl the computer can write0 Based on instructions given to it. xt may record on ptnched cards, tape~ or other output devies~ the values of quantit0es stor.ed w'ithin i ts memory. Figure XXIv-. ilulstrates the performance of a digital computero The computer reads data and instructions which are presented to it, and then performs the operations upon the data according to the instructions. In performing these operations the computer may use anj.y of the five facilities which it possesses. These'faciliti.es are i.dicated n the square of e of Fiurho the cXV whic shows the.mpter as a black boxo A detailed examination of the inaternal workings of a digital, computer. as well as references on the subject has been prepared by Goode and Machol.o The output of the computer is then the n u.erical su>.Jrts, called for by the original machine instructionso A simple example may serve to iltlustrae the way in which a digital computer may be used. Suppose one wishes to eval uae the polynomialo = a0 + apx + a2 x +a3 + o.oo+a x i..'-l at each integer value from, 0 to 100.

-285DATA TNSTRUCTIONS READ REMEMBER EXERCISE CHOICE ARITHMETIC OPERATIONS WRITE NUMERICAL RESULTS Figure XXIV-1. Digital Computer Operation. I III COMPUTE R(X) r- _- - L - STORE I R(X) I iII X=X + 1 V PRINT IV RESULTS is R(O...R() )YES > 1 N Figure XXIV-2. Flow Diagram for Successive Evaluation of Polynomial.

-286The overall organization of the computation is. shown by a Flow Diagram in Figre XXI)-2. The instructions and initial data are read into the machine in Input Box I. The machine has been instructed to compute the result, R, for the present value of x which has been initialized at zero, Box IIo The machine then stores the result, R(x), in its-memory, Box IIIo The value of x is then incremented by one and the -computer is asked to exercise choice, Box IVo If the value of x exceeds 100, the limit of the range for calculation, the computer proceeds to print the results, Box V; if not, the loop contaming instructions for computation and storag II and III is repeated,9 and the test at IV again imposed When.the value of x exceeds 100, the computer will call the values of R(O) o RB(00) from memory and write them as Output Vo The flow diagram includes all of the operations which the digital computer is capable of performing I Read, II Compute, III Remember, IV ExercLse Choice, and V Writeo The Analog Computer A particular for of the analog comp uter which is fiinng Vide application in engineeAing is the electronic analog computer or 2 electronic differential analyzer o This device uses operational ampl.i fiers to add, integrate, change sign. and multiply by econstants greater thal Io Linear potentiometers are u.sed to miultiplyy bconstats1 less than one, sand aervo-driven potentiometers are used to multiplyo Amrpli fier-servo combinations a sre used to divisde one variable byT another, and thfe devcee often includes special generators to provide certain typea of functionso, These components are connected to provide an electrical circuit with the sa mathematical description as the problem to be

-287soled. The circuit forms a complete loop, one ariable being soled for in terms of the remainirng variables and then fed. back into itself. Consider an elementary eexample a second-order, linear, ordinary differential equation of the forms d2x dx Aa~ + B Ct + Cx + D = 0 XXIV Using dot notation and solTing for the highest deri vative 00 B C D x = - xJ x- XXi"-3 A flow diagram may be drawn indicating the solutAion to Squation"(<XIV-3), as shown in Figure IVT-3. If x is know P x and x may be foand by integration. By performing the appropriate additions and multipliC-ations indicated by the right hand side of EBqati.on (QXXI3), x is obtained and fed back into the input. This type of feedback loop is basic to solutions of equations on analog computerso Th7e initial conditions place constraints on the voltage in the loo in order of satisfy the conditions of the problem, an r and the resu e obtained. by output voltages in the ciLr-uito Applications of Electronic CompUter. The applications of analog and digital compuaters hase, in general, been in keeping with the characteristics of the two types of machines3 T e anal.og machinre s more suited to. pereorming dynamic simulation of processes, partic'luarly systems which are described in terms of differentatial relaionshispt to time Conseqtenrtly, applications of analog computers in pro ess design have been prim.arily 4 in process simulation, and in the solution of problems inv olvng rate equations5' 6 7

-288TX INITIAL CONDITIONS;__ INITIAL A < XCX CONDITIONS ABX r ox - A.j(_ C -LX A A g-~ + A A A_ Figure XXIV-3. Flow Diagram for Solution of Differential Equation with Analog Computer.

-289T ie digital computer $ more suited to algebraic or logistic problems, as well. as to data reduction and. proeessing0 Applications include the solution of linear programming models (Chapter.XXlv), statiatical analyses, and process simulations wbich are too large or complex 8 for the analog machine o Several applications of a small e7ectronic digtal compater to problems in metallurgical. research have recently been noted9. A set of 45 problems with detailed. solutions by digital a.nd analog co mpaters has been prepared by a Ford Foundation Project at the UJnlversity of Michigan.o Comparison of Analog and Digital Machines The question as to whether analog or digital, techniques should be emp.loyed to obtain a given problem saoution often arises, o -e decision is not an easy one, since the advantages of one over the other may be essentially lost in practice. The decision should be based on effectiSenessr an.d cost, but other factors such as flexibility for use in other. potential applications. ease of procurement, and considerations which are relatingle to the implementation of the machine should, be weighed~ In generall, the analog machine is less expensiveo But wbereas both computers can solve any sol.uble mathematical probl.em, the digital machine is more suitable for problems which involve logic or massive sets of data. The relative desirability of analog or digital. machines for use in solving particular classes of mathematical. problems has been discussed in some talL 12 ae presents a comparison of the two techniques for application to process design problemso

-290TABLE XXIV-1 IF you are thinking of using analog computers for process simulationsHere are the advantages relative to digital computers Oo Analog Computer Digital Computer Simulates behavior of any system by Performs arithmetic operations action of easily manipulated and with numbers measured variables Simulation is continuous, permits Operates discontinous$ly; can inclusion of concepts such as dis- only approximate hig-he order tance, velocity, acceleration effects Results presented as family of graphs Results presented as tables of of variation of dependent variable numbers; must be plotted (same data obtained with recorder connected to process) Speed of problem solving is direct Speed is direct function of function of actual speed of physical problem complexity and size, system, is independent of size or relatively independent of complexty of system operating speed of process Programmed so that parameter magni- Flexibility not present withtudes are entered as settings on out special programming precauvariable potentiometers; parameter tions values can be changed at will BUT there are disadvantages, too...o Analog Computer Size of computer (number of computing Problem size reflected in comcomponents) determines size of problem puting time; no limit to size of which can be solved; simplifying assump- problem if time is available tions often made to reduce complexity Specifically designed for solution of Useful in nearly all types of ordinary differential equations; other problems0 Complex partial difproblems —eogo, solution of simulta- ferential equations more amenaneous algebraic equation-made by trail ble to solution by digital equipand error. Less complex partial dif- ment ferential equations solved if converted to ordinary diffeerntial equations and one variable assumed constant; family of solutions for different values of variable results

-291NOW —-if you think the advantages outweigh the disadvantages, here are some of the things that analog computers can do for you as compared to digital computers...... Analog Digital Equipment and Show great promise for work- Superior for details plant design ing out relative sizes of of mechanical design — plant equipment by solving e>g,, stresse, sizing dynamic equations of plant of members, costsperformance which are trial and error arithmetical problems Instrumentation Small, special purpose anaand data reduc- logs important in converting tion and plotting single variable and directly correlated multiple variable data in form of graphs Process control Best tool in existence for Simulations (re- studying resulting phenomenon; search) limitation on system complexity imposed by computer size Chemical plant Definite promise as final con- Flexibility and accu applications trol elements for units of racy of digital cormhighly automated chemical puters better for conplants trol of whole plants Research in basic Well suited to simulation of Better for determina processes chemical reaction kinetics tion of kinetic parameinvolved in chemical process ters by statistical development data reduction where necessary Research in unit Well suited for study of Better suited for operations transient state such as heat steady-state studies transfer, distillation which are usually arithmetical or statistical Plant operations Better here because and management statistics and arithtechnique studies metical operations predominate

-292REFERENCES 1. Goode, Ho H. and Machol, Ro Eo System Engineering, Control Systems Engineering Series, New York: McGraw-Hill Book Company, Inc,, 1957, Part 4. 2, Philbrick, G, Ao A Palimpsest on the Electronic Analog Art. Paynter, H. M, (ed.), Boston, 1955. 3, Williams, T, Jo Systems Engineering for the Process Industries, Fourth Eo P,Schoch Lecture at the University of Texas, Austin, Texas, October 16 and 17, 1959, 4. Meyer, H. W,, Simcic, No F,, Ceckler, Wo Ho, and Lander, Ho No "Blast Furnace Stove Analysis Using Special Temperature Measurements," AIME Blast, Furnace, Coke Oven and Raw Materials Conference, Chicago, April 4-6, 1960o 5. Howe, Ro Mo Application of Difference Technique to Heat Flow Probleis Using the Electronic Differential Analyzer0 Engineering Research Institute, University of Michigan, Ann Arbor, May 1950. 6. Chien, Ko Lo, Hrones, Jo A., and Reswick, J, Bo "On the Automatic Control of Generalized Passive Systemso" Trans, AoSoMEo, 74, (1952), 175. 7o Acrivos Ao and Amundson, No Ro "Solution of Transient Stagewise Operations on an Analog Computero" Industrial and Engineering Chemistry, 45, (1953), 467~ 80 Hodge, Ao L0 "Predicting Effects of Oxygen, Moisture, and Fuel Additions on Blast Furnace Operations with a Computer," AIME Fall Meeting, New York, October 17-20, 1960o 9o Leary, Ro J,, Smith, Ro W,,o Jr and Mitchel, Bo Jo "Applications of a Small Electronic Digital Computer to Pyrometallurgical Research," Bureau of Mines Information Circular 7959, U, So Department of the Interior, 1960o 10. "Electronic Computers in Engineering Education " First Annual Report.of:aiFbDrdc Found:ation Prject;in the. College of Engineering, The University of Michigan, August 26, 1960o ll Rubinoff, Mo "Analog vs Digital Computers - A Comparison," ProCo IRE, 41, 1953, 1254, 12, Forrester, Jo and Vance, A, Institute of Radio Engineers Meeting, New York, 1951o 13, Williams, T, J. "Analog Computing in the Chemical and Petroleum Industries " Industrial and Engineering Chemistry, 50 (1958), 1632,

CHAPTER )XX MATERIAL HANDLING-A QUEUEING THEORY APPROACH.... C _ _~..~._-..-. Although material handling is not a unit process in the strict sense it nevertheless plays an important role in the interrelationships of these processes. The transport of materials to and from unit processes particularly when t e path is between two integrated processes plays a direct and important role in determining the overall behavior of the integrated operation. Consequently, the dynamic behavior of integrated processes is not thoroughly described without a knowledge of the handling system which takes care of the transport of materials throughout the integrated operation. The importance of material handling ia born out by the fact that the rate of production of many integrated operations is truly limited by the transportation of materials to, from and within the system. The following discussion is presented as an introduction to some of the theoretical approaches taken regarding the movement of items within a system. The presented material is not intended to be complete but only to lay a foundation for the metallugical engineer, and outline some of the methods and procedures which are available to him when considering the design of systems which involve the transport of materials. Discussion of the types of equipment employed, the procedures and economics involved in material handling in metallurgical plants, and the design engineering-of such equipment is omitted. A sound approach to plant design engineering1 and a discussion of some of the details involved in material handling2 are readily available in the literature. The present purpose is to encourage the metallurgical process engineer to think of a metallurgical plant, as highly complex as it may be, as a system made up of -.293

-294individual units, and stimulate his interest and engineering approach to metallurgical process design from the standpoint of system engineering, Queue ing Theory Queueing theory is used to describ the mathematical approaches to problems arising whenever delays occur or priorities must be arranged regarding the sequence of a given operation. The mathematical models and solutions of the problems are the same whether the individuals or things are waiting or whether a gate is moving arosand to the waiting persons or objects. Applications of queueing theory have been made to a large nuJmber of-9bQl Ig,~ in which waiting time is involved, including the landing of aircraft, the loading and unloading of ore ships, the design of automobile parking, waiting and traffic facilities, the passage of travelers through customs, pedestrian movements, servicing and machine breakdowns, 3 4 etc. In the development of a queueing model one must provide for1. Gate or service points 2. An input process 3. Some queue discipline 4. Some service mechanism The model then describes the situation n which ustomers arrive at a gate of service point, are serviced, and then leave the service area. The arrival of customers is the input process, and may be described in terms of the distribution of arrivals at the service point. As the product of the input process arrives at the service point and joins a queue, it is termed a customer. The behavior of the customer is described in terms of a queue discipline which determines how the customer reacts to the existing condition of the queue. If the queue is too long, the

-295customer may leave the service area and be lost to the system. In the case of a multiple channel servicing system, the customer may join the queue of shortest length. Or the customer may be required to remain in the que ue irregardless of the apparent waiting timeo The service mechanism is a description of the service provided. in terms of the service time involved, which may be a constant or may de rease slightly with increase in queue length, or even be daistributed in some manner~ The elements of interest in a an alysis of the qieueing problem are~ 1o Waiting times for the customers 2 The number of customers in the queue 3 The ratio of waiting time to service time The purpose of seeking a model which describes the queueing problem is to provide for the servicing of as many customers with as few facilities as possible. Generally, one optimizes the economics of the situation by seeking the minimum cost in.volved for some balance of waitingltime between servicing unit and customer. Single Station Queueing Problem et us consider the problem of determining the probability of a giren qoieue-length and the expected queue length for the case of a single station for which both input and-output are assumed to be randonm The quaue discipline is assumed to be that each arriving unit takes the last position in the queue and that the units which make up the line are serviced in order of appearance in the lineo It may be shown5 that the probability of a waiting line of length n units, P.n is given byo Pn s r~(lA~-X/~l) xx~-i

-296if X/i is less than one, where X is the mean arrival rate, and i the mean service rate. The ratio, X/u, is sometimes called "traffic intensity" and is the average number of arrivals per unit of service. The mean length of a waiting line is given by the expressions - =[-k - if X/a is less than one. XXV-2 The expected waiting time of arrivals at a single station with random iaput can be formulated as followso Let - = expected waiting time and ts expected time spent in service; then O + Es = total expected time consumed in both waiting and service. When the mean arrival rate is XC i' X (t + ts). XXV-3 from which tw= -. XXV-4 It can be shown that: = l/pi. XXV-5 By substitution in a previous expression, Equation (XXVW-2), we obtains = [l/(-X)] l- XXV-6 as an equation for expected waiting time at a single station. In order that the real life situation be more closely approached by the queueing model, specific distributions for the probability of arrival have often been substituted in the model. Data taken under actual operating conditions for a sufficiently large sample have been shown to be very closely approximated by exponential or Poisson distributions in several cases.

-297Example of Single Station Model Consider the case of a heat treating section consisting of a singlle furnace which provides service for the many areas of a manufacturing plant. The job requirements vary in a random manner as do the arrivals of parts for heat treating^ The section is operated as a closed system and parts arriving remain until they are treated It is further assumed that each job is handled in the order in which it arrives. This idealized situation corresponds very closely with the queueing model derived above. If the mean arrival rate X is 5 jobs per day and the mean service rate p is 10 jobs per day, the traffic intensity x\/ 5/ / = 2The probability of a waiting line of given lengthn ns is0 P = (1) n l )?7 and the average number jobs waiting is~ )'=1 xxv-8 If the traffic intensity X/i, increases, the average queue length increases' becoming infinite as the service time.approaches the arrival time i e, (1.- X/ ) ~o The. analysis above is important to the management of the manufacturing firm in determining the optimum heat treating facilities for handling a given distribution of job requests. In the simplified case above, an increase in the' arrival rate to a level approaching 10 jobs per day would require that either the service times be decreased or that a multiple station arrangement be substituted, ioe., that the capacity of the facilities be increased.

-298Multistation Queueing Problem Consider the case in which customers arrive at a service station and receive service from several units, S, under the assumptions made for the single station model. The probability of having to wait in line which is the sum.of all probabilities that all service facilities are being used or that $ or more customers are in line is given by the expression: 00oo S Po w P= 8s (1 -xx where W is the probability that all service facilities are being used and P is the probability that zero customers are being served, The average waiting time for the case of multichannel servicing facilities iseS t w s(V 2-(x/> xx710 and it also may be shown that the probability of no customers being served, Po, is given by the expressions P. -. __ -____ 1___ ^__ p ~ 1 Example of Multist-ation Model The crane facilities provided in an open-hearth shop for tapping, teeming, and other pouring floor service requirements may be optimized by application of the multistation queueing model derived aboveo While strictly speaking, the behavior of the handling system in a steelmaking plant does not follow the assumption of random input and output, (in fact in most plants a large' staff of people are engaged in preventing it from becoming $so.X), the model permits some examination

-299of the problem and represents a situation more extreme than normalo It may be assumed that the facilities, one, two, three, or more cranes, are the service gates which provide service to the customers (the furnaces), and do so on a basis which permits any free crane to handle the service requirements of a furnace, the furnaces queueing until service may be provided. This last assumption is also not accurate since the cranes usually operate on the same track and are not free to move around each other to change their relative position. The assumnption.may be justified, on the basis that a crane which has received a ladle of metal may transfer that ladle to the next crane and then proceed to provide service to a furnace further down in the shop. Consider an open hearth shop consisting of twelve 200 ton furnaces which average 10 hours per heat. The service times for tapping, pouring, and removing the slag ladles average 1.0 hours per tapO The average time between arrivals is 0.833 hours since in a 10 hour period, an average of 12 heats would require.servicing, In a 24 hour period, an average of 28.8 arrivals would occur, requiring a total of 28.8 hours of service. This service requirement dictates that at least two cranes are necessary. Evaluating the expected waiting times for the furnaces for two cranes may be done as follows. From Equation (XXV-!l), where the traffic intensity, k/M = 1/0.833/1/1.0 1'.2 heats per average service time0? 1 0 - 2..- XXf.!.12' ~ (,2)n1/:. +: [(ia2)2'/2~[.1-(12/2)]. 12 (1 + 1.2) /f (( 2)/0.8)= 0.250 W - (1) (2) (2) [10.2502 20.250 - XX~-l3

-300One may thus prepare a table indicating the waiting times for the furnaces in average service time units as shown in Table XXV-lo The average waiting times of the furnaces are given in Table XXV-lo The total waiting time of the furnaces is given by the average waiting time per heat times the number of heats per day, 28080 The total waiting time of the cranes is given by the available hours, 24 times the number of cranes, minus the required hours of service, 28080 Assuming an operating cost of $300 per hour for the furnaces and $50 per hour for the cranes, the total cost of idle time may be computed as shown in Table XXV-2. The optimum service facilities are indicated by the minimum cost and in this case are shown to be 3 cranes, a result in keeping with practice in the industryo Other Approaches to Queueing Problems The analytical methods presented above are relatively straightforward and the examples used to illustrate them have been greatly simplified. Only a restricted number of cases can-be validly treated by these methods. There are however, techniques for determining the characteristics of a queueing system when the ar rival and service distributions are not convneniently expresses mathematically. These methods are described in the literatire under several headings which includes 1. Monte Carlo techniques 2. Theory of Games 3. Stochastic Processes The problems involved in analyzing queueing situations which arise in actual integrated plant operations are extremely complex and often prohibitively difficult. However, advances are coming rapidly and

-301TABLE XTV-1 Summary of Calculations for Multistation Queueing Example Average Furnace Waiting Time Arrivals per Service No. of Ave, Sero servie time time Cranes Time Units Hours S -. 1o2 1.0 2 0.250 0.561 0.561 1.2 1.0 3 0.294 0.078 0,078 1i2 loo 4 o.300 0.013 0.01.3 TABLE XXV-2 Cost Analysis for Service Facilities in Open Hearth Shop No, of Idle hr. Cost of Idle hr. Cost of Total Cost Cranes Cranes Cranes Furnaces Furnaces per 24 hr. 2 19.2 $960 16.2 $4860 $5820 3 43.2 2160 2.25 675 2835 4 67.2 3360 0.38 114 3474

-302new applications are being generated at a high rate. Consideration of these concepts is inherent to the system approach in metallurgical process design, and greater emphasis will undoubtedly be placed on the queueing theory approach to'material transportation problems.

-303B'ENCES l.o Vilbrandt, F. C. and. Dryden, C. E, Chemical Engineering Plant Design, Chemical Engineering Series, New York~ McGraw-Hill, Inc,, 1959, 2, "Session on Materials Hkandling, Electric Furnace Steel Proceedings." 7, 19499 5. 3o "Marshalling and Qaueeing,e Operational Research Quarterly. 3, Noo 1, March 1952. 4. Kendall. Do G. "SI6e Problems in the Theory of Queues." Journal of the Royal Statistical Society, Series B, 13, No. 2, 1951, 151 5. Churehman, C. W., Ackoff, R. L,, and Arnoff, E. L. Introduction to Operations Research. New York, John Wiley & Sons, Inco, 1957. 6. McCloskey, J. F. and Trefethen, F. N. (ed.), Operations Research for Management, Baltimore~ The John Hopkins Press, 1954. 7o Morse, P.M. Queues Inventories. and Maintainance. New York John Wiley & Sons, InCp, 1958 8. Feller, Wo An Introduction to Probability Theory and its Applications. Newr YorkO John Wiley & Sons, 19500 90 Brisby, M. D. J. and Eddison, R, T, "Train Arrivals~ Handling Costs and the Holding and Storage of'Raw Materials," Journal of the Iron and Steel. Institute, 172, 1952, 171. 10. Gaver, D. P. "The Influence of Servicing Times in Queueing Processes, Journal of the Operations-Research Society of Americaa, 2, No, 2, May I.o Eddie, L C "Tra. Delays and Toll Booths." Journal. of the Operations Research Society of America, 2, No. 2, May 195i4, 107 o 12. Goode, Ho Ho and Machol, R. E. System Engineering Control Systems Engineering Series, New Yorko McGraw-HHil1, IncO, 1957. 1.3 Fry, T, C, Probability and Its Engineering Uses. Princeton, NoJ. Do Van Westrand Co,,Inc,,o 1928. 14o Sassieni MO, YBapan, Ao, Friedman, L, Operations Research, New YorkJohn Wiley and S6ns, Inc., 1959,

CHAPTER XXVI Linear Programming is a mathematical procedure used for solving a general class of optimization problems which inmolve a combination of a number of interacting factors to produce a maximum or minimum resulto In order to apply linear programming, the following criteria must be mets 1) There is$ some function that is to be made a maximum or minimum. 2) There is a variety of solutions, each of which is subject *to a set of well defined restrictions which may be expressed as equalities or inequalities. 3) Among the variables of the problem, the relationship between any two may be represented by a straight line or linear relationship at least to an acceptable degree of approximationo The use of the linear programming model may be illustrated by the following example. Consider a metallurgical firm which wishes to produce an alloy steel of the following specifications~ Vanadium - 008% Minimum Chromium - l.8% Minimum Manganese - 0.6% Minimum In addition, the firm possesses a supply of two alloying materials of the following compositions1o Alloy 1 Alloy 2 % V 40% 10% % Cr 40% 30% % Mn 10o 30% % Fe Balance Balance where Alloy 1 costs $4 per pound and Alloy 2 costs $2 per pound, -305

-306On the basis of the production of one hundred pounds of the desired alloy steel, let xl equal the number of pounds of Alloy1 used and x2 equal the number of pounds of Alloy2 used. A combination of x1 and x2 will produce a solution to the problem if and only if that combination satisfies the specifications for the alloy steel. This may be expressed as: 0.4 Xi + 0.1 x > 0,8 XXVI-1 0.4 x+ 0.3 X2 1.8 XXVI-2 0.1 x + 0.3 x2 > 0.6 xxVI-3 Where: M >_ 0 XXVI-4 0 XXVI-5 It is possible to show graphically the feasible solutions which satisfy the set of inequalities presented aboveo The shaded region of Figure XXVI-1 contains all the allowable solutionso The solution to the problem is found in the optimum combination of alloying additions which minimize the cost function: C = 4x + 2x2 XI-6 The cost function may be plotted as a family of parallel lines whose parameter is total cost. The family of parallel lines may be superimposed on the graph as shown in Figure XXVI-1 from which it may be coneluded that the optimum alloying addition will occur at the vertex of the line bounded region of feasible additions. Since the firm seeks the lowest cost, the optimum alloying addition occurs at the point (0.75,5) indicating that the optimum addition consists of: 3/4 lb. of Alloy 1 per 100 lb. of steel 5 lb. of Alloy 2 j at a cost of: (3/4) 4 + (5) 2 = $13 /100 lb. of steel

-30710 9 8 7 XI REGION OF FEASIBLE SOLUTIONS 4 3 I 3 X AVERTEX OF MINIMUM COST!~~~~s~~~ ~13 " 0 1 2 3^ 4 6 7 8 9 10 X2 Figure XXVI-1. Graphical Solution of Two-Dimensional Linear Programming Problem.

-308The linear programming model in three dimensions is illustrated by the following problem.o A metals.lrgical firm is considering the production of three high speed. tool steelss Tool Steel % Si % C_ % V % W % CO VD! oo8o 8 030 0 25. 4oo 200 0 15 0 500 DV3 o8oO 0 30 o025 4o00 2 00 18.0 9 0 VD4 o080 0.30 025 4.00 2o00. 2000 12.0 Under a government rationing plan the "critical" alloying materials tungsten and cobal.t are available to the firm in the amnonts ofS 1000'.bo Tuigsten ) per month 500 Ibo Cobalt The return to the company on the three products indicated above iso Xl - $-o00/lb VD3 - $1o20/lb BD4 - $10 50/lb These conditions may be summarized in the following equations~ 0.l5 x. + 0.18: x + 0o 23- <K 1000 XxVI-7 0.05 x- + Oo09 x, + 0O12,x3 < 500 xI-8 where x1, x:.29 an.d X., are the pounds o f ol1, VDR, and VD4, to be produce-d, respectiSvelyo The profit function which.is to be maximized is~ Profit = x. + 1o2 x2 + o 5 x Max X -9 In this case, the region of feasible solu.tion. s isfomnd in three dimensions and is represented by a polygon bounded by the planes corresponding to the equations aboveo As in the two-dimensional case, the optimum solution will occur at a vertex of the poly.hedrono In this case, the cost f'unction will define a family of planes0 It is obvious that as ti. n. mbe of

-309variables increases, the geometry of this method becomes more and more complex. As a result, it is necessary to turn at this point to an algebraic approach which may be applied to any number of variables,, the Simplex technique The Simplex Technique The general maximization problem may be stated asO n C Ci cxi XX -10 1=i where C is the function which must be maximized, subject to the restrictionso, aijxi b XXVI-11 i =l and x.i 0 XXTI-12 A parallel set of equations may be written for the general minimization problem, and it may be shown that the solution to every maximization problem is equal to the solution of the dual minimization probleman and that the converse is also true. The problem above is phrased in the form given in Equation ("jXV9), with the restrictions to the problem being given by Equations (XVI-7 and -8), andx1 > O XX7I-13 x >O o0 X -14 x3 0 X7I -15 The restrictions of Equations (XXVI-13, -14, and -15) simply state that a negative quantity of high-speed steel cannot be produced, whereas those of Equations (XXVI-7 and -8) state that the amount of alloying materials

-310used to manufacture the alloy products must not exceed the total amount available to the firm. To proceed toward a solution by the Simplex method, the system of inequations is reduced to an equivalent system of equations by introducing new non-negative variables, x4 and x5, so that: 0.15 xl + 0.18 x2 + 0.20 x3 + x4 = 1000 XXVI-16 0.05 xl+ 0,09 x2 + 0.12 x3 + x = 500 XXVI-17 These new variables, x4 and x are called "slack variables". In this problem it can be seen that the positive values of these slack variables represent the amount of alloying element which is available to the firm but which is not consumed. The profit function which is to be maximized is thus Equation (XXVI-9), the profits associated with x4 and x being zero. The equations are now set up in the form of a matrix or table, as shown in Table XXVI-1, where the coefficients of xl.o. X5, i.e. the a.i s of Equation (XXVI-il), and of xo, the bi's of Equation (XXVI-ll), are listed. TABLE XXVI-1 x x x3 x x x 1 2 3 5 0.15 0.18 0.20 1.0 0 1000 0.05 0.09 0.12 0 1.0 500 The Simplex method of calculation is based on this matrix, arranged as shown in Table XXVI-2. A column labeled "Basis" is placed to the left of the x column in which the basis vectors are listed, in this case, the slack vectors. A row of P."s are added above, where these' ~

-311TABLE XXTI - 2 P. 1 1 2 1.5 0 0 J ~ Basis P. x x 2 x3 4 x5 x4 0 1000 15 o 8 2 1 0 x5; 0 500 o05 009 o12 0 1 K.0 0 0 0 0 0 0 K-P. -1 ~1 2 -lo5* O 0 a a TABLE XXVI 3 "x4 0 166-7 o0667 o03 0 1`67 - x 1 5 417 167 417 75 1 0 8a33 K 6500.625 1.125 1o5 0 125 K,-P. -.375* -~075 0 12.5 TABLE XXVI - 4 *> x, 1 2500 1.45 0 15 -25 X3 1i5 3125 0 o5625 1 -6 25 18.75 {cj 7187o5 1 1,294 1l5 5~625 35125 K.-P. 0 oo94 0 5~625 3o125 a J

-312are the coefficients of the corresponding x.js in Equation (XXVI-9), the profit function. A column of Pi's are added, corresponding to the P.'s i a but being subscripted with an i to indicate row instead of column. The profit function is then: 5 Profit = K = i Pjxj XXVI-18 j =1 Next, a row of numbers, indicated by Kj, is entered where j refers to the appropriate column. The coefficients of the x..'s, the element in'a the ith row and jth column, are used to compute K. as the sum: Kj = Pixi XXVI19 i iJ A row labled K - P is added to the table, a value which is determined j J for each column. This listing constitutes an initial feasible solution which is given by the column vector xo in terms of the basis vectors, x4 and x5. 4 = 1000 x 500 XXVI-20 The initial feasible solution thus consists of doing nothing, io.eo, use none of the available materials, which results in a profit of K - 0. Criteria for Optimization The problem, once having obtained a feasible solution, is to determine whether or not a more profitable solution exists, This may be decided on the basis of the following possibilities: A. The maximum profit is infinite and has been obtained by the present program. This is true if all x.i are less ija

-313than or equal to zero in a column where Kj - P. is negativeo B. The maximum profit is finite and has been obtained by means of the present pro'gram, This' condition may be recognized when all Kj P. are positive or zero0 C. An optimal program has not yet been found, iOe., larger values of K existo This case requires further calculation anid is identified if some xij are positive when Kj - P. is negative. Procedure for Calculation When situation C exists, choose the most negative K. P.. J a In the present example, this is K - P3 1.5, as indicated by the asterisk in Table XXVI- 2 This determines which of the xj s will be entered into the Basis column in Table XXVI-3o To determine which vector will be replaced, divide each of the positive x. s appearing in the i ~ 1ij selected column into the corresponding xid which appears in the same row under xO. The smallest of these ratios then determines the vector to be replaced. In the present example, the ratios xlOl/Xb 1000/0o2 and X20/x23 = 500/0.12 are considered,, the second being the smaller and indicating that the second'row, eector x is the one to be replacedo This is indicated by the arrow in Table XXVI-2, and a new basis is formed consisting of x4 and x3. The elements of the row to be entered are calculated by dividing each'element of the row being removed by the element in the selected columno Thus as shown in Table XXVI-3, x3, the row corresponding to x5, has been formed by dividing each element of X5 by x23 of Table XQ~I-2, 0.12 in the present case

-314The remainder of the table is formed in the following manner. Select a constant which when multiplied by the element of the row to be removed in the selected column gives the negative of the element in another row of that same column. Multiply each element of the row to be removed by that same constant and add the element to the element in the other rowo Repeat this procedure until all rows have been thus modified, the result being that the selected column will consist of zeroes except for a one in the row which was entered as shown in Table XXVI-3 for column x3, In the problem under consideration, each element in row 2 of Table XXVI-2 was multiplied by -1o667 and added to the corresponding element in row 1, thus generating row 1 of Table XXVI-3. In the general case, this procedure would be carried out for all of the several rows which might be present. The K js are then computed by Equation XXVI-19, and the values of K - P. determined, The procedure is then repeated until 3 J either situation A or B exists. In the present case, the solution is obtained after two iterations. The optimal solution is presented in terms of the pounds of alloys produced, pounds of materials used, and the profits in Table XXVI-5. The example selected has been intentionally simple in order to present the basic procedures involved in the Simplex technique, In general, applications of the linear programming model involve very high order matrices which are treated by the iterative procedure indicated above. Such a situation immediately brings to mind, the use of a large scale digital computer, And in fact, digital computers have been used to great advantage in the solution of several linear programming problemso

-315TABLE XXVIT-5 Optimum Program for Alloy Production Alloy lb. produced lb. W lb Co Profit VD1 2500 375 125 $250000oo VD~3 0 00'00 VD 4 3125 625 375 4687.50 Total 1000 500 $7187.50 This table indicates-that the optimum profit is obtained when only alloys VD1 and VD4 are produced in the amounts of 2500 and 3125 Ib., respectively. The entire allotment of tungsten and cobalt is used in the production of these two alloys, to the exclusion of alloy VD3.

-316Applications of Linear Programming Linear programming has found considerable application in the field of business planning and operationo. Problems which have been solved by linear programming techniques include personnel assignments, the blending of aviation gasesJ, contract awards6, allocation of manufactured products7'8, and the long-range planning of coke-oven replacements9^ as a few examples. The use of linear programming for control of technical processes has been developing rapidly in all fields of science, particularly in the chemical industriesl0 1i, 12 Fabian13 has proposed the use of linear programming to determine the least cost rate of input of materials into an integrated steel millo Although Fabian s treatment of the problem is relatively limited, it clearly illustrates the potential of the method and represents an excellent approach to a very difficult problem. 14 Hilty et.al. have used linear programming to predict the minimum materials cost for stainless steels. It should be noted that the foregoing discussion is by no means complete. In addition to the Simplex technique which was introduced in this chapter, a very powerful and simple approach to the problem termed the transportation technique is desirable for use whenever possible for large-scale problems since it involves the simplest arithmetic operations. The transportation technique will not, however, handle the general class of linear optimization problems as will the Simplex technique 5 The use of linear programming, particularly in conjunction with large-scale digital computers, should offer an excellent means of utilizing the vast amount of fundamental data that is being produced in various areas of process metallurgical engineeringO By combining these data with the

-317available operating and economic data in the form of linear programming models, many problems both economic and operative which face the metallurgical process engineer may be greatly clarified and suitable solutions worked out using this technique.

-318REFEBRENCES 1. Churchman, C. W., Ackoff, Ro L. and Arnoff, E. R. Introduction to Operations Research, New York~o John Wiley and Sons, Inco 1957, Chapter 11. 2. Charnes, A., Cooper, Wo Wo and Henderson, A, E. An Introduction to Linear Programming. New York: John Wiley and Sons, Inco, 1953 3. McCloskey, J. Fo and Trefethen, Fo M. Operations Research for Management. Baltimore: The Johns Hopkins Press, 1954, 217, Linear Programming and Operations Research by J. 0. Harrison, Jr. 4. Project SCOOP, "Symposiim of Linear Inequalities and Programming' Headquarters, U. S. Air Force, Washington 1952. 5. Charnes, A., Cooper, W. W. and Mellon, Bo, "Blending Aviation Gasolines-A Study in Programming Interdependent Activities," In reference 4, 60 Goldstein, L., The Problem of Contract Awards, in The Theory of Gains and Economic Behavior.. Princeton- Princeton University Press, by J. Von Neumann and 0. Morgens-tern, 1947o 7. Arnoff, E. Lo, "An Application of Linear Programming' Proceedings of the Conference on Operations Research in Production and Inventory Control, Case Institute of Technology, Cleveland, 1954. 8. Cooper, W. W. and Charnes, A. and Farr, D,, Linear Programming Models for Scheduling Manufactured Products, Carnegie Institute of Technology, Pittsburgh, September 1, 1952. 9. Truan, T. D. and Porco, D. A., An Application of Linear Programming in Long-Range Planning of Coke Plant Operations, Management Science, 4, No. 3 April 1958, 337. 10. White, W. B., Johnson, S. M., Dantzie, Go B. "Chemical Equilibriutm In Complex Mixtures", Journal of Chemical Physics, 28, (1958), 751. 11. Stillson, P. "Operations Research." Application in the Chemical Industries, Industrial and Engineering Chemistry, 48, (1956) 402. 12. Henderson, J. M. "A Short-Run Model for the Coal Industry," Review of Economics and Statistics, 37, (1955), 336o. 13. Fabian, T., "A Linear Programming Model of Integrated Iron and Steel Production," Management Science, 4, (1958), 415. 14. Hilty, D. C., Taylor, Ro Wo and Gillespie, Ro Ho "Predicting Minimum Materials Cost for Stainless Steels," Journal of Metals, 11, (1959), 458.

-31915o Charnes, Ao and Cooper, W. W. "The Stepping-Stone Method of Explaining Linear Programming Calculations in Transportation ProblemsTt Management Science, 1, No 1, Appendix, October 1954. 16. Taborek, J. J. "Optimization in process Equipment Design" Chemical Engineering Progress, 56, No. 8, 1960, 37. 17o Berg, C. "Optimization in Process Development," Chemical Engineering Progress, 56, No, 8, 1960, 42, 18. Goode, H. H. and Machol, R. E. System Engineering Control Systems Engineering Series, New Yorko McGraw-Hill B6ok C6o, Inc.o 1957T Chapter 25. 19o Sasieni, M,, Yaspan, Ao, Friedman, Lo Operations Research, New York~ John Wiley and Sons, Inc., 1959,

CHAPTER XXVII Process Simulation One of the principal applications of computers to process metallurgical engineering is in the area of process simulationo A detailed computer simulation of a process to determine the effect of all process parameters on yields and on by-product formation requires the derivation of a complete reaction model. An accurate simulation of a process permits optimum processing conditions to be specified before any final plant design or plant tests are made, thereby eliminating many of the difficulties of scale-up and the requirement of pilot plant tests, The derivation of an accurate dynamic model is often not an easy task, and one is faced with the alternatives outlined in Chapter V~ 1. A description of the dynamics of the process in terms of a series of differential equations which describe the mass and energy transfer processes which occur in the reactor. 2. A description of the process dynamics in terms of the operating results of similar reactors which are already in commercial use. A detailed description of the change in chemical concentrations, temperatures, flow rates, etc., as functions of time may be reduced to descriptive functions by numerical analysis with the assistance of a digital computer, or by trial and error techniques using an analog computer 3. The system may be described in terms of the average operating characteristics for the particular type of reactor -321

-322based on the observations made on commercial-sized units, The particular reactor may present a characteristic concentration-time relationship, or may involve temperature dependences which are easily observable. In this case, the average operating results may be applied to the system which is in the design stageo This model is not entirely a dynamic one, but is certainly highly descriptive of the process and may be used to some advantage. 4. In the case of metallurgical reactors in which the mechanisms of the processes being carried out are not at all understood, one may neglect the process dynamics and select a process time for a batch unit or a suitable flow rate for a continuous unit on the basis of either previous experience or good engineering judgement. Although this final choice is far from a satisfactory one, the reduction of the process model to a mass and energy balance does permit the evaluation of many of the process variables and furnishes a basis on which the dynamics of the process may be either estimated or evaluated after construction of the pilot plant or commercial-sized unit. The set of simultaneous equations describing the process system includes one for each separate chemical species formed or utilized in the chemical reactions comprising the process. The mass and energy balances. for each chemical species are interrelated in the forms dQ = 4 dr AE XmI:I dQ,V ~ aXXVII -1 dt dt where V is a factor which converts concentration to weight units, C0i:..-he c. ce.tinn:h e.fproduct, AE is the change in thermal

-323dQ energy during the reaction for each weight unit formed9 and is the rate of heat gain to the complete reactor, system, As outlined in Chapter II, heat transfer equations may then be set up to includes 1s The energy manifested, as a temperature change in the reaction mass, 2, The energy representing that appearing as a temperature change in the. reaction vesselo 3~ The energy transferred to or from the surroundings~ Having expressed the process variables in such a set of simultaneous d.ifferential equations, the daynamics of the system may be included in the process model in the form of a differential equation involving the changes in concentration with respect to time as functions of process geometry and chemical driving, forceso Consider for example the reaction which takes place when a reactive gas is contacted.with a liquid metal~, The differential equation describing the solution of gas in liquid metal has been presented in Chapter IV and may be expressed ass de D A(e) XXII-2 dt 5 v If the particular gas under consideration is nitrogens and the melt is pure liquid iron, the mass and heat balances may be interrelated by the relationship~ dQ [dc W 86o ~dlt~ L[~ 100 7~XRTII -3 dQ dc where dt is energy transferred to the system in cal/sec, d is the rate of change of concentration in wto %/sec, W is the weight of the melt in grams, (860/14) is the heat of solution in cal/gmo

-324The dynamics of the process may then be expressed in terms of equations XXVII-2 and XXVII-3. These equations, when coupled with the mass and energy balances may then form. a process model suitable for simulation. The dynamics of this simple process are very well understood, and the computer simulation of such a process would yield highly accurate results. This particular model would correspond to the dynamic process, Model 1 indicated above. Process model 2 would involve the observation of the behavior of the system with respect to mass changes; that is, gas going into solution in the metal and temperature changes along with the variation in those quantities entering into the mass and energy balances0 Such data could then be reduced on a computer to a dynamic model which would yield a highly accurate simulation of the process, accuracy of course, depending upon the reliability and extensiveness of the data takeno Process model 3 would involve the.averaging of data observed on many systems involving gas-metal equilibria, and the application of such generalized gas-metal behavior to the system under consideration. One might assume, for example, that the gas content of the metal varies linearly with time and that the average time of solution is given by a certain number of minutes. Such a model, of course, is not highly accurate, but does permit a reasonable prediction of the behavior of such a gas-metal equilibration process. The final dynamic model, which was essentially to ignore the variations in process variables with respect to time and merely examine the overall results, can also be applied to this particular process. If the equilibrium state of the system is known, and one has reason to

-325believe that suff icient time will be allowed. to approach this equilibrium condition, the mass and energy balances of the system may be written on this basis. The example system selected above was a highly simplified one. In the general case, there are a large number of concentration variables as well as many ill-defined thermal and geometrical parameters involved. In most metallurgical process operations, one is faced with the relatively difficult task of not only evaluating each of these variables, but also attempting to write a descriptive model which involves their interactions as wello Much of this data has become available in the last few years and considerable work is presently being expended in this directiono It is thus expected that approach 1 will become more and more important as metallurgical process operations are better understood. In the present situation, the availability of highspeed computing equipment as well as the installation of better instrumentation and control systems in metallurgical plants should permit veryadvantageous use to be made of approach 2o The development of data processing techniques and the success with which simulation of processes has been used, particularly in the chemical industries, should be an indication to the practicing me"allurgist that considerable clarification may be brought to bear on the operation of metallurgical processing plants. In attempting to write descriptive models for the purpose of process simulation, one should bear in mind some of the basic elements of process dynamics. It may be noted that the dynamic behavior of a chemical process depends upon the kinetics of the reactions involved.

-326upon the manner in which the environment variables change with time, and upon the geometry of the system, To relate these factors quantitatively requires that differential equations be formed to express the interrelation which exists between physical variables~ As indicated above, these data are generally not available; or if available, are not easily solved by means of arithmetical methods because they are non-linear equations~ However, it is often unnecessary to make a precise study of the dynamics of the process in order to sufficiently approximate the reactor dynamics to a degree that may be useful in obtaining engineering resultso The rates of metallurgical reactions may range from very slow to very rapid. The relative speed of the reaction with respect to the residence time in the system determines whether the chemical reaction process or the material handling process has the dominant role in the process kineticso When mixing lags are small and reaction rates are slow, the dynamic behavior of the system may be determined largely by the chemical kinetics, However, when reaction rates are high and material handling lags large, the situation reverses. Instantaneous conversion of charge material into product can be assised and the kinetics of the process treated on the basis of the material handling dynamics of the product emerging from the system. If material handling is the rate controlling step, static material balance equations may be used to describe the conversion of raw ritterial into product in an "ideal system"o These equations can be then modified by the appropriate functions to describe mixing and transportation of material0

-327In addition to the above concepts, a number of assumptions are often made to facilitate the formulation of a descriptive process mode. Batch and continuous stirred systems are generally considered to be perfectly mixed, that is, there are no temperature or concentration gradients existing in the reacting materials. The heat transfer coefficients throughout the system are considered to be constant at the ambient operating temperatures of the system. The heat transfer coefficients used, although assumed constant, would be characteristic of the particular media involved. That is, the heat transfer coefficient between the charged material and the reactor walls and the heat transfer Qoefficient between the system walls and the surrounding are assumed to be constant although most probably of a different magnitudeo The temperatures~ within the system are assumed to be constant although possibly different in different areas, or different media within the system. The use of these assumptions of course involves their justification in the application for which they are used, and in this-regard, one must often rely on engineering judgement, particularly in the case where previous experience in the area is not availableo

-328REFERENCES 1. Williams, T, J, Systems Engineering for the Process Industries, The Fourth E. P. Schoch Lecture at the University of Texas, Austin, Texas, October 16-17, 1959. 2o Campbell, D. P. Process Dynamics, New York~ John Wiley and Sons, Inc., 1958. 3. Goode, H. H. and Machol, R. E, System Engineering, Control Systems Engineering Series, New Y6rk McGraw-Hill, Inc o, 1958. 4. Hougen, 0. A. and Watson Ko M. Chemical Process Principles Part IIIo Kinetics and Catalysis, New York~ John Wiley and Sons, Inc., 1947. 5. Smith, J. M, Chemical Engineering Kiretics. Chemical Engineering Series, New York~o McGraw-Hill, Inc,, 1956. 6. Eckman, D. P. Automatic Process Control, Chapter II, New Yorks John Wiley, and Sonsa, IncS, 1958.. 7o Project Cyclone Symposium I on Reac Techniqus. Port Washington, N. Y., March 15-16, 1951, SDC, USN. 8. Project Cyclone Symposium II on Simulation and Computing Techniqueso Port Washington, No Y,, April 28-May 2 1952, SDC, and BUAER, USN. 9, Symposium III on Simulation and Computing Techniques, Port Washington, No Y., October 12-14, 1953, BUAER and NADC, USNo 10o Proc. Natl. Simulation Conferenceo Sponsored by Institute of Radio Engineers, Dallas, January 19-21, 1956, 11. Goode, H. H. Simulation - Its Place in System'Designa Proca IRE, 39, 1951, 1501o

CHAPTER XXVIII The goal of this text to the present point has been, to provide a basic understanding and an engineering approach to the unit processes involved in metallurgical process engineering. This is the foundation of metallurgical process engineeringo But, as a goal itself, it is inadequateO In recent years, the processing industries have come to realize more and more that they may no longer think of their plants as an assemblage of unit processes interconnected by material handling and mass transport systems. The individual components of a metallurgical plant should not be designed for a specific operation view of the fact that each of the separate units in such a plant influences the others in subtle as well as direct ways. In the face of such a situation, the engineer is forced to view the metallurgical plant and each of its component unit processes as an integrated system, The system viewpoint or approach to engineering design is rapidly being demonstrated to be vastly superior to an approach which evaluates each unit process on its own merits and then attempts to connect the several "best" processes into an integrated operation. It is also becoming apparent that control instruments need to be specified with the process as a whole in mind rather than merely the specific processing unit alone on which the instruments are to be installedo System engineering may be defined in terms of the enginqering approach to plant and process design which it involvesS lo Consideration is made of all aspects of the design of the proposed plant as a single unit including kinetics, heat and -329

-330mass balances, and process dynamics as well as instrumentation and automatic control. 2. Recognition is made of the fact that the relationships which are involved in such a comprehensive approach may be numerous and complex and with this in mind the use of electronic computers, both analog and digital, is given full consideration. 3. The assistance of basic and applied research organizations are sought to provide the greater amounts of basic data which are necessary for such an approach to design of process operations. 4. The inclusion of automatic control concepts in the integrated system design is considered to be almost a necessity in order to provide optimum operation of the system as a whole. Any processing system for the handling of chemical or mineral raw materials may be described as a network of alternating reaction and separation zones. Raw materials and energy are supplied to a reactor from which flows the product in the form of a mixture of desirable and undesirable materials. The products leaving the reaction zone are usually hot and must be cooled down before they can enter succeeding operationso From the product stream, energy is extracted. This operation may occur before or after the separation operation in which the desired products are removed from the product stream of the reactor. In view of these considerations the system engineer would favor reaction systems which provide a means for exchanging energy between the cooling down of the product stream and the heating up of the input feed stream. Certain

-331types of metallurgical process systems possess distinct advantages on this basis aloneo In addition to the specific reaction vessels which make up the system, the process metallurgical engineer must consider waste removal and material handling problems, and should evaluate the reactor type and the particular components of the system as part of an orderly system design studyo One must also consider factors which are exterior to the system design. Such problems would include the choice of raw materials and the ability of the system to handle the wide variation in raw material properties, which the feed might possess. Waste disposal problems are also a factor which must be considered with the view of the entire system in mind. Economic factors such as depreciation procedures, tax situations, public relations, and other forces which bear upon the business decisions the management of the firm may make must also become an integral part of the system design. In order to accomplish this large and formidable task of providing an adequate system design, the process metallurgical engineer will be required to draw upon basic scientific information relating to the process under consideration, to the use of analog and digital computers, as well as to the use of advanced mathematical techniques in order to evaluate and describe the numerous and complex relationships which exist between the components of a system. The engineer must be well founded or at least familiar to the point that he is able to make use of the rapidly-developing techniques of operations research in order that he might provide for an orderly flow of materials, equipment9 and labor to produce the maximum product at the minimum costO Having developed relationships regarding the inrfluence of the components of the

-332system on one another, the system engineer may provide an adequate description of the system in terms of the integrated models for each of its components. The techniques of linear programming will be of considerable advantage in seeking the solution to such a problem.. System engineering is a rapidly developing and highly advanced approach to process designi It is expected that in the future by system.. procedures, processes may be designed from fundamental kinetic data with the design yielding specifications for optimum operating conditions. Based of course on the accuracy of the models derived, it is expected that economic evaluations can be made with confidence7 and cost may be predicted more accurately than at the present time. If proved, system design, based on a knowledge of process dynamics can trim down the design, of particular units and yield a less expensive but improved system which is able to operate at optimum conditions under the guidance of improved control systems. Capital investment could then be reduced.and maximum production obtained from anly given equipment with improved quality. as a result of improved control. Computer simulation of processes has been demonstrated to be feasible and to be economically advantageous. Research into process system'behavior and the mathematical representation thereof have resulted in improved control systems, as for example, in the petroleum industrys -.computer controlled- plants. The process metallurgical engineer is presently placed in a position which requires that he be familiar with the techniques of system engineering, for just as it is possible to design and build a computer controlled plant with highly complex but very effective control, it is just as easy to design a system involving extensive and

-333costly control systems which are computer oriented but are not economically justifiable. The computer might be Over-taxed as a control element and essentially become an expensive data recorder, or be required to carry out duties which could be just as easily handled by much simpler and cheaper standard controllers, The metallurgical process engineer engaged in such system design has a great responsibility in seeing that proper installations are specified.

-334REFERENCES 1. Skelly, J. F, "How to Choose the Best Metallurgical Reactor,... A Syatem Viekpoint," Journal. of Metal s,, 1959, 841. 2. Willians, T, J - Systems Engine'ring for the Process Industries The Fourth E, P. Schoch Lecture at the University Of Texas, Austin, Texas, Octber 16-17, 1959. 3. GoOde, H. H, and Machol, R. E. system Engineering, New Yorko McGraw-Hill, Inc., 1957. 4. Campbell, D. P. Process.Dynami~s., New YorkX John Wiley and Sons, Inc., 1958.

INDEX -335

INDEX Activated Complex 38-41, 149-150 Activity 21, 23 See Thermodynamics Activity Coefficient 21-33, 211, 214-217, 223, 241-242, 248, 261-263 Air flow in sintering 72 requirement for sintering 69-71 Arrhenius equiation 37 See Reaction Rate Batch process 7-8, 3229 327 Bessemer process 177-184 Blast Furnace 163-175 Chemistry of iron 164-168 Improvements in operation 174-175 Mass balance: 48 Production of lead 253-256 Boundary layer 42-45, 90-91, 186-187, 230, 265-266, 271-273 Boyle's Law 10 Calcining 3, 66-71, 77-84 Carbothermic process 137-138 Casting 115-128 Charles I Law 10 Classification of reactions 40-41 Clausius- Clapeyron Equation 214-216 Combustion, in sintering 66-71 Compu<ters 53-54, 111, 172, 283-291, 324 Analog 2839 286-291, 330-331 Application of 287-291 Comparison of Analog and Digital 289-291 Digital 283-291, 314, 321, 330-331 Continuous casting 125-128 Continuous process 7-8, 322, 327 Converting processes 177-187 Crystallization 247-252 Current, in electrolysis 191-192, 194, 207-209 Degassing of ingots 124 operations 49-52, 261-278 Deoxidation data for 237-241 of steel with aluminum 234-237 Diffusion 42-45, 90-91, 186, 266 271-273 of oxygen in liquid iron 44, 186 of manganese in liquid iron 272 of sulfur in liquid Ni-Co alloy 230 -337

Tndex Distillation of liquid iron alloys 223-224 processes 87, 211-225 Dortmund-Horder Process 49-52, 275 Drying 77 Dwight-Lloyd sintering machine 12, 63-65 Electrolysis 87 of fused salts 189-194, 199-209 Elements, Law of Conservation of 9 EmissiTity 101, 104 Energy balance 13-19, 321-323, 327, 329-330 See Heat balance for Bessemer Process 180-184 for fluidized reactor 154 for phase separation 258 for Reverberatory smelting 16o-161 Equil ibriumr constant for deoxidation 233-237 effect of pressure on 34 effect of temperature on 33 Equilibrium Distillation 219-220 Equipment design. 57-59 Evaporat ion 87 Extraction processes 91-93 Fan, horsepower in sintering 74 Faraday s Laws 191-192 Ferrosilicon Process 139 Fick s Laws 42 lame front, speed in sintering 75 Fluidized. Bed Reduction 14l.154 Free energy 21 See Thermodynamics in electrolytic processes 192-194 Fuel,. requirement in sintering 66-69 Gas evolutionr, effect on ingot struct'ure 121-124 Gas-Metal reactions 261-263, 324 Gaseous reduction 3, 139-140 Growth 252 Hall Process 189-194 Heat balance 18-19, 52, 65-69y 97 See Energy balance for Blast Furnace 170-171 for Calcination 81, 84 for Continuaous Casting 128 for Degassing 278 for Electrolysis 194 for Melting 100-104 -338

Index Heat of Formation 16-17 Heat of Solution 16-17 Heat treating 297 Henry Law 27 See Thermodynamics Heterogeneous Equilibrium 228-229 Hydro-Metallurgy 87-95 Ideal Gas Law 10 Ideal Stage concept 93-94 Inert flush degassing 264-271 Equilibrium 264-265 Mass transport controlled 265-271 Integrated operations See System Engineering Interaction, in alloy systems 167-169, 241-242, 263 Interaction Parameter, defined 263 Instrumentation 54-55, 330 Ingot structure 117 effect of composition on 118-121 effect of rate of heat removal on 117 Ion exchange 87 Kiln lime 77-84 Kinetics 37-45, 52-55, 92 of Blast furnace 172-173 of Calcination 79-81 of Converting 185-187 in Hydro-Mtallurgy 88-91 of Liquid-liquid reactions 229-231 of Phase Separation 248-252, 258 of Precipitation reactions 243-244 of Reduction 133 of Reverberatory smelting 161 Ladle, bottom-pour 104-111 Langmuir Equation 221-222 Le Chatelier's Principle 34 Lead-silver system 253-254 Leaching 87-95 Linear Programming 305-317, 332 Applications of 316-317 Liquid-liquid extraction 227-231 See Hydro-Metallurgy Mass balance 7-9, 11-13, 47-52, 94 Bessemer Process 179 Blast furnace 168-171 E tr olys is 191-194 Fluidized Bed Reactor 146-148 Reverberatory smelting 159 Sintering 12, 73-74 -339

Index Mass Transport 42-45, 323 in aqueous solutions 90-91 in converting 185-187 in degassing 265-267, 271-275 in slag-metal systems 229-231 Material balance See Mass balance Material Handling 173, 293-302, 326, 329-331 Melting arc 99-100 induction 98-99 practice 97-101 resistance 100 retort 100 Mold, bottom-pour 107 Molecular Distillation 221-224 Monte Carlo techniques 300 Nozzle, bottom-pour ladle 108-111 Nucleation 248-252 rate of 251-252 Open Hearth, Basic Process 58 rate of carbon reaction in 44-45, 186 heat transfer in 161 material, handling for 298-300 Optimizaltion 305-317 Criteria for 312-313 Overvoltage See polarization Oxygen. enr.ch.mlent of blast 174-1759 184-185 Oxygen Process 184-185 Oxides, unstable 133-134 Parallel system, for electrolysis 207-209 Permeability, of sinter bed 71-72 Phase Separation 247-258 Engineering of process 256-258 Process kinetics 258 Parity of product 259 Thermal requirement 258 Yield 256-257 Zinc recovery by 253-256 Pidgeon Process 139 See Ferrosilicon Process Polarization 201-207 Potential See Cell voltage Pouring practice 104-108 rate of 108-111 -340

Index Precipitation 87-88 reactions 233-244 stoichiometry 242-243 Pressure drop in fluidized bed 141-145 Process dynamics 321-323, 325, 329-333 economics 57-59 kinetics 52-55 See Kinetics simulation 321-327, 332 See Simulation Queueing Theory 293-302 multistation model 298-300 single station model 295-299 Raoult s Law 27, 31, 33 See Thermodynamics Rayleigh Equationi 219-220 Reaction Rate Theory 37-41, 88, 148-150, 202 Recoveries by condensation 224-225 Reduction Direct 133-140 Gaseous 3, 139-140 of Halides 134-139, 145-146 of Oxides 3, 133-140 rate of 148-154 Reference State 18-19 Reference Temperature 18-19 Refining, electrolytic 199-209 See Electrolysis Relative Volatility 216-218, 220, 223-224 Residence Time in Fluidized Reactor 151-154 of gas bubble in melt 267-271 Resistance Ohmic, in electrolysis 200-201 Film, in electrolysis 206 Retort 100 Reverberatory furnace 100, 157-158 smelting in 157-161 Reynolds Number 142-145, 268-270 Roasting 3,T7 Ruhrstahl-Heraus Continuous Vacuum Process 275-276 Segregation 119-122 Coefficient 121-122 Sensible heat 16-19, 101-103 Series -system, for electrolysis 207-209 -341

Index Simplex technique 309-316 Simulation 52-55 See Process Sintering 3, 63-75 time for 74 Slag Blast furnace 48, 163-164, 167-170 Converter 177-184 Heat content of 181 -Metal distribution 228-229 -Metal Transfer rate 229-231 Reverberatory smelting 157-161 Solidification 17, 115-117 rate of 125-128 Solutions 21-27 Non-ideal 23-27 So1vent extraction 87 Specific Heat, definition of 16 Standard State 22-33 Conversion of 27-33 Steel Killed 119-121 Rimmed 123-124 Semi-killed. 123 Stoichiormetry 7-19 Stochastic processes 300 Surface energy 249-251 System Engineering 4-5, 13, 302, 329-333 Tafel relation 202 Thermochemical Model 47-55 of Blast furnace 171-172 Thermochemistry 15 Thermodyamics 16, 21-34 of Calcination 78-79 of Deoxidation 233-237 of Electrolysis 192-194 First Law of 14-15 of Fluidized Bed Reactor 145-146 of Hydro-Metallurgy 88-89 of Phase Separation 247-248 Theory of Games 300 Transportation technique 316 Tundish 105, 107 Unit Operations 3 Unit Processes 3, 59 -342

Index Vacuum degassing 271-276 Stream 276 Vapor Pressure of Elements 211-213, 215 of mercury 135 Vector, slack 310-312 Voltage, in Electrolysis 193-194, 199-201, 207-209 Volumes, Law of Combining 10 -343

TABLE OF PHYSICO-CHEMICAL CONSTANTS Acceleration of gravity, standard 32.17 ft. sec-2 Atmosphere, standard 760 mm Hg 14.7 psi Avogadro's number, N 6.02 x 1023 mole-1 Boltzmann constant, R/N, k 1.38 x 10-16 erg degree-1 British Thermal Unit 252 g-calories 778 ft-lb Calorie, gram 4o183 int joules Coulomb 1 ampere-sec Electronic charge, e 4.80 x 1010 esu 16 x 10-19 abs coulomb Electronic Mass, M 9o106 x 10-28 gra Faraday, F 96,496 abs coulomb equivr1 23,060 cal volt-1 equiv-1 Gas constant, R 0.730 cu ft-atm ~R-1 lb.-mole-1 1,987 cal ~K-lg-mole-1 8.314 x 107 erg ~K-1 g-mole-1 Horsepower, 1 hp 33,000 ft-lb min-1 Ice point, 0~C 273o16 ~K 320Fo 491.7 ~R Kilowatt, kw 1.341 hp Neutron mass 1.6745 x 10-24 gram Planck s constant, h 6.62 x 10-27 erg sec. Protron mass 16723 x 10-24 gram Stefan-Boltzmann constant, o 5.672 x 10- erg cm-2 sec degree4 0 173 x 10-8 Btu ft-2 hr1 oR4 Velocity of Light in Vacuum 2,998 x 1010 m sec-1 Volume of ideal gas, STP 22o414 liter g-mole-1 359 cu ft lb-mole-1 -345

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