THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING PROPYLENE-PROPANE ADSORPTION IN A PACKED SILICA GEL ADSORPTION BED Robert L.o Norman A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1962 June, 1962 IP-575

Doctoral Committee: Professor Brymer Williams, Chairman Professor Stuart W. Churchill Association Professor Bernard A. Galler Associate Professor Kenneth F. Gordon Professor J. Louis York

ACKNOWLEDGMENTS The author wishes to offer his heart-felt thanks to the many individuals and organizations without whose aid financial, material and spiritual, this work could not have been completed. To the American Institute of Chemical Engineers whose Fellowship in the Tray Efficiency Project the author held for two years and to the Hercules Powder Company who aided through one crucial summer, many thanks, Special thanks too to the Natural Gasoline Association of America for its generous support while the author worked on two of their sponsored projects. The Phillips Petroleum Company supplied the propane and propylene used in the study. The work of William Hines, Cleatis Bolen, Frank Drogosz and John Wurster in preparing the various components of the equipment is greatly appreciated. A note of thanks is in order too to the University Computing Center and its staff for the use of the IBM 704 in the development of the mathematical side of the work. The encouragement of many friends and associates has been a continuous source of strength for which the author wishes to offer his warmest thanks, The encouragement and patience of my wife has been an indispensible help without which it would have been impossible to continue. Finally, to my parents for their encouragement over the years, their guidance, understanding and support, I dedicate this work. ii

TABLE OF CONTENTS Page ACKNOWLEDGM~ENTS. *** ii ACLSOWFTDGLETS,...................e................. i LIST OF TA:BLES.bLES0...00.......o~~..... *0***@@e o0 V LIST OF FIGURES,.......................................... vi LIST OF APPENDICES... *.........*..**............ eo.......... viii NOMENCLATU.RE *, e a 0...................... ix A;BSTRACT.. o....... e... e... e...e.e..................... xiii INTRODUCTION..ee..................................2........ 1 The Model........... 2 Background Material,............................... 3 A, Adsorption Rates............................ 3 Bo Saturation Behavior of Packed Adsorption Beds.. 4 EXPERIMEITAL METHOD AND TREATMENT OF DATA. o........ 5 APPARATUS S................7 APPARATUS ~ e o ~ o~ o o ~ ~ o ooo-o.e i e e e * I o e eo o o o eoo I o 0 I eo e a l I t ~ I 0 0 0 7 A. Adsorption Cells.................................... 7 B. Constant Temperatur Bath,,....,. Const T emerat ure Ba.....o......................... 11 CD Flowmeteroos................. 12... D. 13Thermocouple 13 E. Sampling System.................................. 14 EXPERIMENTAL MATERIALS.....................................16 EXPERIMENTAL PROCEDUREos..,,*...****o,.. 0v0@@e.ee0* 17 A. Preparation of New Silica Gel Beds...................... 17 B, Preparation of Beds for a Run,..................... 17 C, Run Procedure..................................... 18 x,. Analysis......................... 18 THEORYo...... e. oe...e.. o........ e..................... 21 A. Development of the Mass Transfer Model,.................. 21 iii

TABLE OF CONTENTS (CONT'D) Page 1o Assumptions.... o..... o........ o..... 21 2. Mathematical Formulation of the Diffusion Model...... 22 3. Development of the Gas Film Mass Transfer Relation... 27 4. Interface Relations................................. 29 B. The Plug-Flow Model o................................ 30 1o Basis. o......o.ooo c@ oo o..o..oo.oooo.oooeo 30 2. Development of the Differential Equations............ 31 3. Solution Along the Characteristics..,................ 34 EXPERIMENTAL DATA.... o.......... o....... o..................... 37 DATA PROCESSING.................................................. 54 A, Mass Balance Calculations............................ 54 B. Derivation of the Rate Equation Constants................ 55 C, Iterative Trial and Error Determination of the Diffusion Coefficient................................ 56 D. Summary of Data Processing Results..,................... 87 DISCUSSION OF THE DATA PROCESSING RESULTSa............... 88 A. Adsorptive Rel.tive Volatility....................... 88 B. Nature of the Diffusion Coefficient..o....,.............o 88 RECONSTRUCTION OF THE CONCENTRATION HISTORIESo......o o........ 90 CONCLUSIONS AND RECOMMENDATIONS................o.............. o 97 REFERENCES................................... 168 iv

LIST OF TABLES Table Page I Properties of the Silica Gel Adsorbent................. 16 II Experimental Data at Particle Diameter of.28 cm...... 38 III Velocity Data at Particle Diameter of.28 cm........... 46 IV Experimental Data at Particle Diameter of.117 cm...... 48 V Experimental Data at Particle Diameter of.198 cm...... 52 VI Typical Data Processing Run..................... 58 VII Summary of Data Processing Runs..............o....... 72 VIII Fifty Roots of the Equation tan P = P................. 110 IX Beattie-Bridgman Constants of Propylene and Propane.... 124 X Correlation Constants for Viscosity Function........... 125 XI Correlation Constants for j Factor Function.......... 127 XII Correlation Constants for Polanyi Characteristic Curves...........oe.................................. 128 XIII Correlation Constants for Fugacity Ratio Function for Propylene.............. 0 e..... a 129 XIV Correlation Constants for Fugacity Ratio Function for Propane.................................... 129 XV Correlation Constants for Liquid Specific Volume.....,. 129 XVI Correlation Constants for Saturation Temperature as Function of Pressure..............o............... 130 XVII Distribution of Volumes in System................... 139 XVIII Flowmeter Calibration Data........................ 4-1 XIX Calibration of Chromatography Results.................. 143 v

LIST OF FIGURES Figure Page 1 Flow Diagram of Apparatus............................. 8 2 Adsorption Cell Cap9.................................. 9 3 Adsorption Cell Body................................... 10 4 Adsorption Cell Conical Bottom Cap............. 10 5 Sampling Manifold. o.................................. 15 6 Typical Chromatography Trace........................... 20 7 Schematic Sketch of One Adsorption Bed Showing Terms Used in Mathematic Derivation of the Plug-Flow Model... 32 8 The Characteristic Directions of the Plug-Flow EqUationS o s eo.......... o................... o 35 9 Concentration Histories Reconstructed for Runs 3, 7, and 9.....e e..ee.,......... 92 10 Concentration Histories Reconstructed for Runs 6 and 17....o........... 93 11 Concentration Histories Reconstructed for Runs 45 and 47.......... * * 94 12 Concentration Histories Reconstructed for Run 56....... 95 13 Concentration Histories Reconstructed for Run 52....... 96 14 Comparison of Observed and Calculated Velocity Histories for Run 26................................... 99 15 Finite Difference Grid with Characteristics Shown for Plug-Flow Equations..........o............... 116 16 Specific Area for Mass Transfer...................... 131 17 Sketch of Adsorption Surface Showing Equi-Potential Curves e........ oo.....e.e............................. 133 18 Variation of Adsorbed Specific Volume with Adsorbed Volume for Three Typical Cases........................ 134 vi

LIST OF FIGURES D) Figure Page 19 Polanyi Adsorption Potential Characteristic Curve for Propane on Silica Gel.................... 136 20 Polanyi Adsorption Potential Characteristic Curve for Propylene on Silica Gel1..7...........,.......... 137 21 Predicted Isotherms with Experimental Points for PrOpane.oOO.OO..oo.~x.oe...................... 138 22 Data Processing Calculations, Computer Flow Sheets,.,, 145 23 Concentration History Calculation, Computer Flow Sheets O,.......................o... 157 vii

LIST OF APPENDICES Appendix Page A MATHEMATICAL DERIVATIONS........... e... 101 A. Solution of the Boundary Value Problem Posed in the Diffusion Model................1.. 101 B. Method of Characteristics for a General Set of Two Simultaneous Quasi-Linear First-Order Differential Equations............................ ll C. Finite Difference Approximation to Plug-Flow Model Equations.................. 115 D. Derivation of the Equilibrium Velocity Relation. 122 B PHYSICAL PROPERTIES CORRELATIONS...................... 124 A. Vapor Density................................ 124 B. ViscosityOo ~O......................e.e.e.. 125 C. Diffusivity............................ 126 D. j Factor for Mass Transfer..................... 127 E. Adsorptive Equilibrium Capacities............. 127 F, Fugacity Ratio.................................. 128 G. Liquid Specific Volume..................... 129 H. Saturation Temperatures......................... 130 Io Specific Area for Mass Transfer................. 130 C THE POLANYI ADSORPTION POTENTIAL THEORY.............. 132 A. Theory.......................................... 132 B. Application to Propylene and Propane Isotherm Data......,....... 135 D CALIBRATIONS............................ 139 A. System Volumes............,.,.................. 139 B. Flowmeters...................................... 139 C. System Pressure Drop......................,,,. 140 D. Analysis - Calibration of Chromatography Result s O......................................... 140 E COMPUTER FLOW SHEETS....,..................e.. 144 Ao Data Reduction Routine...................... 144 B. Plug-Flow Model Equation Solution...........w.. 156 viii

NOMENCLATURE Symbol Dimension a Beattie Bridgeman constant a coefficients for temperature dependent fugacity ratio correlation as cm2/gm specific area of adsorbent particle for mass transfer (area of equivalent sphere) ax cm2 cross-sectional area of column A0 Beattie Bridgeman constant ~b coefficients for pressure dependent crosscorrelation of fugacity ratio B0 Beattie Bridgeman constant c coefficient of liquid specific volume correlation c Beattie Bridgeman constant d coefficient of saturation temperature correlation D cm /sec diffusivity of mixed adsorbed gases in gel DAB cm2/sec gas phase diffusivity of propylene into propane Dass cm2/sec assumed value of D e coefficients of temperature function correlation (defined by Equation "(B4)) E error in a computed value F mg-mol/cm/gm rate function defined by Equation (A45) f cm /cm5 voids fraction in packed adsorption bed g coefficients of (Gy) power series fit G mg-mols/sec molar flow rate i a counter used in the computer flowsheets ix

Symbol Dimension j a counter used in the computer flowsheets jD j factor for mass transfer ky mg-mol/ mass transfer coefficient in concentration cm2/sec units k a counter used in the computer flowsheets L gm amount of silica gel in cell mAmB mg-mols/gm average bulk concentration of propylene and propane respectively on the adsorbent. m~,ml mg-mols/gm pure phase adsorptive capacities of silica gel for propylene and propane respectively. mg number of constants in power series fit to (Gy) data nan number of analyses in one data set nc number of series cells np number of points fit on each break-through curve during reduction to diffusion coefficients calculations. nr number of concentric shells used in the finite difference solution of the diffusion equation. PA'PPB atm partial pressure of propylene and propane respectively PA PY atm interface partial pressure of propylene and propane respectively. P atm total system pressure q coefficients of QA power series fit QAIQB mg-mols/ rate of increase of average concentration of gm/sec propylene and propane respectively on the.silica gel R atm cm3/ gas constant mg-mol/~K x

Symbol Dimension r cm radial distance of a point from the center of the adsorbent particle (considered as a sphere) r0 cm radius of the equivalent spherical particle Re Reynolds Number 2rOfvpM/kp R1 R2IR3 rates defined by Equations (56),(58) and (A82) respectively s mg-mols/gm total adsorbed gas concentration at any point within the equivalent spherical particle s* mg-mols/gm total gas concentration at r0 sA'sB mg-mols/gm concentration of propylene and propane respectively at any point within the equivalent spherical particle. Sc Schmidt number t sec time T ~K temperature Tc critical temperature TR reduced temperature u cm/sec ret'velocity of molecular species u variable defined in Appendix A, Sec. B only v variable defined in Appendix A, Sec. B only v cm/sec fluid free space velocity in adsorbent column V cm3/mg-mol specific volume y mole fraction of propylene in gas phase y* mole fraction of propylene at interface YO inlet mol fraction of propylene x cm distance through the beds X1X2, ~ 23variables used in the iterative determination of points on the plug-flow model grid, correspond to y, v and s* respectively, xi

Symbol Dimension z cm distance across the gas film a a group defined by Equation (A72) aAB adsorptive relative volatility of propylene to propane zeroes of Equation (A20) Y group defined by Equation (27) 5 group defined by Equation (28) a small amount e Kcal/gm-mol adsorption potential a cm2 term used in simplification of diffusion equation; defined by Equation (A2) gm/cm sec viscosity PM gm/cm3 mass density p mg-mol/cm3 molar density PA,P mg-mol/cm3 partial molar densities APB ps gm/cm3 bulk density of silica gel bed T dummy integration variable occurring in Equations (A32), (A33), and (26). CP cm3/gm adsorbed volume per unit weight of adsorbent viscosity function defined by Equations (B9) and (BlO) group defined by Equation (15) xii

ABSTRACT The kinetics of a binary gas-solid adsorbent system have been studied under the follwing flow system: A series of three shallow packed beds of silica gel were saturated with pure propane gas. A stream of pure propylene was then passed through the series beds at constant flow rate. Concentration histories were measured at the outlet of each bed as a function of time. Similar experiments were run with propylene initially on the bed and propane as the eluent gas. A range of pressures from one atmosphere to 403 atmospheres, temperatures of OOC,, 250Co and 490Co and particles of.117 cm,,.o198 cm,, and.28 cm, in diameter were employed both in propane desorption and propylene desorption runs, The results were analyzed in terms of a series resistance formed by gas phase film diffusion followed by homogeneous spherical particle diffusion. Gas phase film resistance was estimated from existing correlations and an average value of the effective diffusion coefficient of 3,65 x 105 sqo cm, per sec. was obtained in the partial diffusion model. This was within the experimental accuracy independent of temperature and pressure, The derived coefficient was used to reconstruct some of the concentration histories obtained experimentally and showed moderately good correlation, X.Z i i,

INTRODUCTION When a gas mixture is passed through a packed bed of adsorbent which is saturated with a gas of composition different from the equilibrium composition corresponding to that of the passing gas, each component of the mixture is adsorbed at a particular rate depending upon how much of that component is already on the adsorbent, Components not present in the gas but adsorbed on the solid are given off until an average composition of adsorbed gas is reached which is in equilibrium with the gas passing the particles. This equilibrium composition for hydrocarbon gases has been studied by Lewis et al. (14,156) but the kinetics of this type of 'tadsorptive displacement" seem not to be available. The purpose of this investigation was to examine the kinetics of a binary hydrocarbon (propylene-propane) displacement process on a solid adsorbent (silica gel)o The choice of a binary system seems to be justified by the same argument as is frequently mentioned in connection with vaporliquid mass transfer studies: i.e., the binary system is the simplest possible choice since only one concentration variable is needed, The equations for mass transfer across the boundary layer film, for example, can be solved explicitly for the rate of each of the two components in certain special cases, This would not be possible for ternary or higher systems, In addition, the analytic techniques are usually considerably easier than for multi-component systems. -1 -

-2 -The propylene-propane-silica gel system was chosen for investigation on several accounts. First, there was a fairly complete set of equilibrium data available over the range of pressures necessary, Secondly, the heats of adsorption and desorption for each gas were almost identical so that in the displacement reaction, isothermal operation could be assumedo Experimental evidence later backed this up. Thirdly, a very precise, convenient and rapid method of analysis was available in the form of gas chromatography. The potential value of a selective adsorption process for the separation of propylene and propane was also an incidental factor in the choice of this system. The Model Where the adsorbent saturated with a binary gas of one composition is contacted with the same binary gas of a composition other than the equilibirum composition in a constant pressure flow system, it does not seem likely that pressure gradients of any size will develop within the porous structure of the gel. Since the reaction is really one of displacement, the rates of adsorption and desorption would appear to be dependent upon the rates of diffusion of the two components past each other through the gel and across the concentration gradient or gas film on the outside of the particle. The actual adsorption reaction, as has been noted by various authors is probably very rapid compared to the diffusion step. The model was based upon homogeneous radial diffusion in the particle rather than diffusion along an idealized pore. It was

-3 -felt that both models would exhibit the same general behavior and the one chosen would be the most useful. Background Material Ao Adsorption Rates In his comprehensive review of the kinetics of chemisorption of gases on solids, Low(l7) mentions only one investigation of the "Rapid Sorption by Porous Solids", that by Sutherland and Winfield(22) These authors measured rates of gas uptake by various porous solids in a constant volume system by means of pressure decrease. The systems examined were isopropyl alcohol - A1203oH20, ethanol - thorium (IV) oxide, water - thorium (IV) oxide, water - A12030H20, water- -A1203 and methylvinylcarbinol - thorium (IV) oxide. Initial pressures of from 195 to 4 mm. Hg. were used. Sutherland and Winfield developed equations for the following three possible cases: 1) Transient Knudsen flow into pores of the adsorbent accompanied by adsorption on and desorption from the walls of the pores0 2) The special case of the above when adsorption and desorption were so rapid that adsorption equilibrium could be assumed. 3) Adsorption which is so slow that the transport processes cannot influence the rate at which gas is taken up by the adsorbent. The rate of adsorption and desorption thus determines the rate of gas uptake.

4'The data of Winfield indicated that case 2) was the realistic scheme. Ward(24) considered gas uptake in the hydrogen-copper system to be partly due to solution of the hydrogen in copper and then diffusion into the particles. He derived an expression for the rate q from the spherical diffusion equations. 00 4 3 8R3 1 exp(kn 2 t/R2)] q =A - gR5 -- C - exp(-kn2 itt/R) n=l where R is the radius of the copper spheres, and k is a constant. Glueckauf(8) assumes that particle diffusion is the controlling resistance in chromatographic displacements and with a solution of the diffusion equation examines several empirical rate equations as to their applicability with various types of isotherms, B, Saturation Behavior of Packed Adsorption Beds The problem of adsorption (or ion excharng on a packed bed where the component to be adsorbed is present only in small quantities has been solved by various authors with various simplifying assumptions. The stipulation of "trace adsorption", of course, ensures that the velocity of the gas through the bed is constant. Among these solutions should be mentioned the work of Hiester and Vermeulen(9) who made dimensionless solutions for a general class of problems where the kinetics of adsorption could be described by a second order kinetic equation and the equilibrium isotherms were linear. Acrivos(l) outlined in general terms the method of characteristics as applied to the adsorption in a fixed bed problem. It is this method which is pursued in the following mathematical work.

EXPERIMENTAL METHOD AND TREATMENT OF DATA The experimental apparatus used in this investigation consisted of three shallow(linch) beds of silica gel in series. Before the first bed and between each of the successive beds were located small orifice meters for flow-rate determination and sample points for the withdrawal of gas samples, Thermocouples were mounted just below the adsorbent bed support screen and just above the bed. These were used to check the designed isothermal operation of the.apparatus. A constant temperature bath surrounded the three cells and connecting tub ing. The general method was to saturate the three adsorbent beds with pure propylene and then introduce a measured constant flow of pure propane to the beds in series. Flow-rates were observed and samples taken for analysis by gas chromatograph at intervals until essentially pure propane was being taken off the last cell. Periodically during a run which lasted for an average of 25 to 30 minutes, temperatures were read in the gas stream by the thermocouples. After saturation with propane, the inlet gas was changed to propylene and the procedure repeated until essentially pure propylene was issuing from the last cell, In this cyclic way, concentration history data could be obtained for both propane desorption into propylene and propylene desorption into propane. The data so obtained were curve fit as the product of concentration and flow-rate (corrected for dead space in the columns)

-6 -and the curve fits differentiated with respect to time to obtain an expression for adsorption or desorption rates. These were then used to iteratively deduce a value of the diffusion coefficient consistent with a homogeneous spherical diffusion model, For a few cases, the value of the diffusion coefficient obtained above was tested by reconstruction of the concentration histories based upon a plug-flow bulk flow model and a rate governed by homogeneous spherical diffusion into the adsorbent particles.

APPARATUS The overall layout of the experimental apparatus is shown in Figure 1. Components of the adsorption cell are shown in Figure 2, 3 and 4. Following is a detailed description of the major components of the apparatus. A, Adsorption Cells Three identical cells were used in series. The body of the cell shown in Figure 2 is made from standard galvanized two-inch pipe machined out to receive a force-fit liner, The top of the body has twenty-four to the inch threads and is machined to a smooth gasket fit, The bottom of the body has standard two-inch pipe threads to receive the bottom conical cap. A clamping support of 3/4 inch angle iron is welded to the body, The liner is of two parts, one forced in from the bottom, the other from the top. Between them a fine stainless steel screen (200 mesh) silica gel support is held. The overall height of the body exclusive of the top and bottom caps is 3 and 3/4 inches, The screen support is mounted 1 and 1/4 inches above the bottom of the body. The top cap shown in Figure 3 is machined out of three-inch hexagon bar stock steel, It is one inch in height and is bored out to a depth of three-quarters of an inch, The inside surface is smooth machined for a gasket fit. One central hole is threaded to receive three-eighths inch copper tube fitting and four holes, ninety degrees apart are drilled on a circle whose radius is 3/4 inch and are threaded to receive one-quarter inch copper tube fittings. -7 -

MANOMETER SAMPLEE ORIFICE SAMP ORIFICE SAMPLE ORIFICE SAMPLET 1 2 1 $ 3 INLET NEEDLE VA LVE W" I - 132 3 ORIFICE t t t REDU3CING I VA LVE CYLINDER Figure 1. Flow Diagram of Apparatus.

-9 -2.343" Cc- -2.290" MACHINE THREADS 24/in. IiI I!, 3,3 0i ii 0 FINE SCREEN SUPPORT _I 4 l 2"STD. PIPE THREADS _ _2 _ _ g I" 2A Figure 2. Adsorption Cell Cap.

-10 -DRILL a TAP /\,1/4 PIPE TAP 3" HEX STEEL BAR STOCK 3/41" IIlI 3 —=1I 24/IN. THREADS MAJOR DIA. 2.343 IN. BOT DIA. 2.290 IN. Figure 3. Adsorption Cell Body. 2"NPT 15" RETAINER RING 16- /4" MESH DAMPING SCREEN 3 3 -1/2i I — Figure 4. Adsorption Cell Conical Bottom Cap.

-11 -The bottom cap shown in Figure 4 is a specially designed gradual enlargement. It is cast in iron and machined to receive a three-eighths inch copper tube fitting at the small end, the inside is cut to a smooth taper. At the top of the cap a fine (200 mesh) screen is clamped. The purpose of the gradual enlargement and damping screen is to ensure as flat a velocity profile in the entrance of the cell as possible. The top is threaded to fit onto the threaded lower part of the cell body. The overall height of the bottom cap is 3 and 3/4 inches. The gasket for the top cap is cut from one-eighth inch teflon. B, Constant Temperature Bath The constant temperature bath is 23 by 6 by 11 inches and is constructed from twenty-two gauge galvanized iron s.oft-soldered at all joints except the back removable panel. This is fastened by means of 3/16 inch sheet metal screws on a spacing of 2 inches, A gasket is provided for the back panel, This panel is also cut 3 inches from the top and hinged at that point so that the top can be loosened and swung down to provide easy access to the cell caps when they are to be removed, During runs at O~C., ice is packed around the cells mounted in the bath. At other temperatures water is in the bath and the temperature is regulated by a bi-metallic on-off type controlling device and a 500 watt immersion heater. The current supplied to the heater can be adjusted by means of a variable resistor supplied with voltmeter and ammeter. In this way optimum heating current can be found for each operating temperature.

-12 -In the bottom of the bath a coil of one-quarter inch copper tubing of length 64 inches is placed to serve as a pre-heater or cooler for the gas going to the first cello Thermocouple measurements showed that temperature never varied from the bath temperature by more than one-half a degree at any time during a run. C, Flow-meters Flowrates are measured at four points in the system; namely, at the inlet to cell number 1, at the exit of cells number 1, 2 and 3. Measurement was by means of the pressure drop across a small orifice of diameter,02 inches mounted in the lines, The orifice fixtures were machined from one-half inch brass round bar stock. A one-inch piece of the stock was bored from both ends to a depth of 17/32 inch, and to a diameter to provide a snug push fit for 3/8 inch copper tubing, The bottom of the hole was bored out square leaving a partition approximately 1/16 inch wide at the center of the pieces This partition was then carefully center-drilled and pierced with an orifice hole of diameter.02 inches. The orifice fixtures are fastened by sweating and soldering the 3/8 inch tubing into the bottomed holes in either end. The manometer taps are one-eighth copper tubing soldered into holes bored as close to the orifice fittings as possible. The manometer U-tubes are made of 1/3 inch OD by 2mm ID capillary tubing and are provided with a construction at the bottom to prevent oscillation. They are fastened at the top into fittings made from standard elbow type 3/8 inch copper tubing fittings with

-13 -the compression rings replaced with rubber O-rings. This type of fastening was found to be quite satisfactory at all ranges of pressure and vacuum. Needle valves are provided in each manometer connection so that they could be isolated when the system is under vacuum. The manometer fluid used is Acetylene Tetrabromide colored for easy reading with Methyl Red. This fluid has a specific gravity of 2.876 and provides the correct range of pressure drops over the required range of velocity measurements. All four flowmeters were calibrated with propane and propylene measured by downward displacement of water. D. Thermocouple s Thermocouple fittings were made from copper-constantan double wire passed through the center of a one-eighth OD stainless steel tube and then brazed into the tip. This tube was then mounted by means of a compression fitting bored out to let the tube pass all the way through and extend into the gas stream, Thermocouples are mounted below each adsorbent bed through the wall of the cell and above the bed through the top cap. Thermocouple EMF's were measured with a Leeds and Northrup Type K Potentiometer. A multipoint switch was provided to which all thermocouples were connected. This allowed rapid reading of all points.

-14 -E. Sampling System Samples for analysis are taken in glass sample bulbs of approximately 30 cco capacity, They are fitted with one opening closed by a stopcock and a 10/30 ground glass joint is provided for fastening to the sampling manifold and to the gas chromatography unit. The sampling manifold as shown in Figure 5 is designed so that the sample bulb and the leads from the sampling valve can be evacuated prior to the taking of a sample. Four sample points are provided for: inlet to cell number 1, and outlets of cells 1, 2 and 3, Ea.ch sampling system is provided with a connection to the main vacuum header, a ground glass joint to fit the sample tube and a mercury manometer to measure the vacuum and to act as a safety valve. Connection from glass-ware tometal sampling valve at the cells is provided by tygon tubing. All other parts of the leads from the cell to the sample tube and including the manometer are made from 2 mm, capillary tubing to cut down on the volume of gas necessary in each sample. Vacuum is drawn on the main header by a Cenco Hyvac 7 pump. A cold trap is provided in the line to trap condensible gases~ The entire sampling assembly is mounted on a flexaframe and can be disconnected and removed en mass so that the back of the apparatus is accessible.

3 2 J I TO SAMPLE TOSAMPLE kTO COLD TRAPTO SAMP PT TO SAMPLE AND VACUUM PT. I PUMP NOT TO SCALE Figure 5. Sampling Manifold.

EXPERIMENTAL MATERIALS The propane and propylene used in this investigation were supplied by the Phillips Petroleum Company. They were supplied as 99 mol percent purity but subsequent analysis showed that the propane was at least 99.9 mol percent with undetectible impurities on the gas chromatograph, The propylene analyzed 99,6 mol percent pure with the only detectible impurity being propane. The silica gel was purchased from the Davison Company in several mesh sizes. These were further refined so that material used passed through the indicated mesh size or stuck in the screen but would not enter or pass through the next smaller screen, TABLE I Mesh Size 8 10 15 Bulk Density o706.700.700 Voids Fraction as Packed o.42.42.42 BoETo Surface Area sq.m./gm. 872 -- 830 (measured with Nitrogen) Pore Volume cc./gmo 47 -- 47 -16 -

EXPERIMENTAL PROCEDURE A. Preparation of New Silica Gel Beds Fifty cubic centimeters of gel as measured in a graduated cylinder were weighed and then put into each cell. Since the cross sectional area ax of the column is 20.3 square centimeters, the depth of gel in each bed is 2.46 cm. The bed is evenly distributed and then the cap is screwed into place and turned down firmly on the teflon gasket. After all connections have been made and pressure tested with compressed air, the system is put under vacuum. Care must be taken that the manometer valves are all completely shut so as to prevent the sucking of the fluid back into the pressure tap lines. The pressure gauge is shut off. The system is kept under vacuum and at a water bath temperature of about 800C. for 2 to 3 days. The system pressure usually quickly attains a minimum of a tenth of a millimeter of mercury as measured by a McLeod gauge and maintains this during the period of pulling down. B. Preparation of Beds for a Run Before a run, the beds are filled with one pure gas and allowed to come to equilibrium at whatever pressure and temperature the run is to be made. Experience showed that this need not be much more than an hour at any temperature or pressure used. -17 -

-18 -Just before the run, the connection from the pressure regulating valve to the main flow regulating valve is broken and the gas cylinders switched. The remaining gas in the leads up to the opening is then purged with the second pure gas and then the connection re-made. C. Run Procedure The timer is started and the main regulating valve opened at time zero. Since the volume of the leads and pre-heater is 300 cco, it requires a determinable amount of time, depending upon the flow-rate used, for the gas to reach the first cello During this period of time, the flow-rate and the pressure in the cells must be adjusted by use of the two valves upstream of the cells and downstream. It was found that once this was carefully done, the conditions remained adequately constant, usually without any further adjustment during the course of the run. Samples are taken according to a pre-determined schedule, It is important to keep the total volume of samples low, especially during low flow-rate runs, It was found possible to make replicate runs to fill in the concentration histories as the reproducibility was quite good. Pressure drop readings from the flow-rate manometers are recorded during some of the replicate runs, Do Analysis Gas samples are analyzed by vapor-solid chromatography, The column is of quarter inch copper tubing, three feet long and

_19 -packed with Burrel 200-mesh chromatography grade silica gel. The column is at room temperature, the carrier gas is helium and the flow-rate is maintained at approximately 250 cc./min. The peaks are recorded on a Brown 0-2 mv. recorder equipped with a mechanical integrator supplied by the Disc Integrator Corporation. A typical chromatogram is shown in Figure 6. One analysis requires 2 and 1/2 minutes.

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THEORY Ao Development of the Mass Transfer Model 1. Assumptions The model to be developed here considers two mass transfer steps in series; namely, diffusion across a gas film and then diffusion into the particle with a constant relative volatility at the interface, The actual adsorption reaction is considered to be infinitely rapid. The concentration of adsorbed propylen and propane are assumed to follow an expression of the form below which was found by Lewis(l4) to hold for average concentration at equilibrium. sA sB mA m where ml = average equilibrium capacity of adsorbent for the gas mg-mols/gmo s = point concentration of adsorbed gas (function of radius) mg-mols/gmo This equilibrium assumption is in a way related to the assumption of the infinitely rapid adsorption step since it is as consequence of that condition that all available adsorption sites must be filled at all times. Equation (1) says, in effect, that the fraction of available sites for adsorption of propylene actually filled with propylene, plus the fraction of sites available for adsorption of propane, actually filled with propane, must be equal to one, The number of available sites will be different for the two gases, being higher for the unsaturated one. The sites will, however, -21 -

-22 -be on the same adsorption surface and so if one gas is adsorbed, by stearic hindrance, the other gas is not adsorbed on that accupied surface. The assumption of pointwise equilibrium is consistent with the experimental relations of Lewis as shown below. By definition r0 2 r sAdr r 2 5 r=dr rr ( 0 with a similar expression for mn Hence r r mA mB 3 0 FSA SB]2 3 2O +A mB = + m r dr = r2dr = 1 mf[' r S Lmpm ir A rl~ 0o 0 o 0 It is further assumed that transport through the solid phase can be treated as Fick's Law type diffusion through a homogeneous sphere. The diffusion coefficient is considered to be independent of concentration. 2, Mathematical Formulation of the Diffusion Model The transport of propylene (component A) and that of propane (component B) are governed by the diffusion equations in spherical coordinates: -at r D ar A 2) L[2r~r

-23 -B D[ + (5) t ' Lr r 6r2 From (1) mB SB = mB - -I sA (6) mA Differentiate twice with respect to radius. B =_ -B A( mA Or 2 2 6r2 t 2 (8) br mA Differentiate (6) with respect to time. Bs - mB SA (9) at mA at Substitute (7), (8), and (9) into (5) and cancel. 6SA [ 2 SA 62SA] = D I~ (10) at B Lr r ar2 ] Equation (10) implies that for this model it is necessary to consider the diffusion coefficients equal DA = DB (11)

-24 -The result of (11) is that there is only one independent diffusion equation in the set (4) and (5), It may be written in terms of the concentration of either propylene or propane or in terms of the sum of the concentrations. We will use the latter. Define: s =sA + sB (12) Solve for sA and sB separately in the two equation system (12) and (1), s +mB A B (13) and s(* - 1) + mB = ( 1) mB (14) SB where t I mA mB (15) mA By definition, QA is the rate of increase of average propylene concentration (bulk basis) on the silica gel; QB is the rate of increase of average propane concentration. In other words: A 3mA (16) =A mB $ at (17)

-25 -A boundary condition on the diffusion equation showing the flux of material into the particle may be derived in terms of the total concentrations: 4Tcr02 s (4/) 5 K 3 r)r A + QB (18) (4/3) r r0 or US) rp(QA + QB) (19) Jr ro 3 D If we differentiate Equation (3) with respect to time and use definitions (16) and (17) we get the following condition which must hold between the rates: 1 1 QA + B b= (20) Substitute QB as can be solved for in Equation (20) into (19)o We then get a boundary condition in terms of one rate QA only. ro ~ ED A (21) We are now in a position to make a complete statement of the boundary value problem involved in the diffusion model. t = D r Sr + Srr(22)

-261 -Sr(r,t) -= QAr ()t) s(0,t) bounded for all t (24) s(r,O0) = SO (25) The method of Laplace Transforms(5) is employed to give an analytic solution in terms of an infinite sine series. Details of the solution are given in Appendix A; the series solution is given here. 00 s(r,t) = m(t) -2 r~ 1 Ynbnsin(Pnr/r0) (26) 3 D r n where Y = (3l)n X (27) 00 oo 2 n= exp(- PnDt/rO) n t r(_ QA (j)( n0 n QA (t) (28) and an are the successive roots of the equation tan Pn = Pn (29)

-27 -The notation "QA( )(t)" denotes the jth derivative of QA(t) with respect to t. The average concentration m(t) is given by t m(t) = S + r QA(T) dT (30) 0 3. Development of the Gas Film Mass Transfer Relation From kinetic considerations as outlined by Treybal(23) the partial pressure gradient across a gas film due to the interdiffusion of two gases may be written: -dp = PAPB(UA - u)dz (31) By definition, QA = UAPAas (2) QB UBP=BaS (33) Therefore, PA APB - QBPA dz (34) as- (AP Now if we assume that the Perfect Gas Law holds, PA = PA/RT (35) Now the diffusion coefficient DAB may be defined as follows: DAB = R T2/ P (37)

-28 -If we now substitute this into (34), we get -dpA RT (QAPB - PA )dz (38) A DABPas Now PA PB = P (9) Therefore RT _dPA D P [PQA - (QA + QB)PA]dZ (40) OABPa s Rearrange -dPA RT dz (40a) QA + QB DA Pas QA If now QA and QB are constant across the diffusion path z, we may integrate this expression. Q + Q PA * P-(I~lB~P 1 logT&A A] RT z By definition DABP = k (42) RT z Y Therefore QA + QB QA +QB = kS loage [A (43) lo(ge A + Q A + PA n A

-29. Now as a result of the equilibrium restriction imposed by Equation (20), rate Equation (43) can be written in terms of QA only, QA kyY loge (44) P *PA The mass transfer coefficient ky may be estimated from the Colburn jD factor correlation. ky(Sc)2/3 j = = f(RE) (45) f vp The specific area aS may be estimated from Figure 16 of the Appendix B. the source of which is Hougen and Watson, Chemical Process Principles, (12) 4, Interfacial Relations We assume adsorption equilibrium at the interface, Thus any resistance to adsorption will. be included in the effective difussion coefficient PA* SB* (46) * *. AB (46)A PB SA PA + PB =P Substitute for SA* and SB* values from (13) and (15) and for pB* from the above physical restraint into Equation (46). P_ s*( - 1) + mB P PA* s* mB AB

-30 -Solve for PA and substitute for r its definition from Equation (15)..C~ P p * = P | (47) m~(ma- s*) I 1+ m (s* - m') aAB A B B. Development of the Plug-Flow Model 1. Basis It was desireable to use the derived diffusion coefficient to predict the experimental concentration histories as an additional check on the consistency of the data processing step. As has been mentioned previously, the adsorption cells were designed with a long conical gradual enlargement and a fine damping screen below each bed. These were to ensure a flat velocity profile across the bed and the subsequent development of the flow model assumes no radial bed gradients in velocity or concentration. Flow rates used in this study were low with a maximum Reynolds number of 10. On this basis, eddy diffusion was not taken into consideration and no term for longitudinal diffusion was put into the flow equations. No temperature gradients were ever detected in the system during any run as might be expected from the very similar heats of adsorption of propylene and propane. These heats of adsorption were obtained as the slope of a Clausius-Clapeyron type plot of logeP vs 1/T at constant amount of gas adsorbed. The Lewis(14'15) equilibrium data provided values of 5260 cal. per gm. mol for propylene and 5480 cal. per gm. mol for propane.

-31 -As a result of the above, the equations were set up without heat effects. The rate of adsorption was governed by the diffusion of mixed gas in the particle. Gas film resistance is taken into consideration. All mass transfer processes were taken the same as those used in the previous section and all assumptions stated there apply equally to this section, 2, Development of the Differential Equations We take a mass balance around a differential volume of the adsorbent bed as shown in Figure 7 of volume axdx. Since the mass balance will refer specifically to propylene unless otherwise noted, we drop the subscript and write y for YA' etco The net amount of propylene added to the element in dt seconds through fluid flow is vpy - [vpy - a (vpy) dx]}faxdx (48) -- (vpy) faxdxdt ax The net amount of propylene added to the element in dt seconds due to transfer from the solid phase is -p Q a dx dt (49) The net accumulation of propylene in the vapor phase of the element in dt seconds is {[py + a (py) dt] -py} fax dx a=- ((50) A t (py) fax dx dt

-32 -dx VOIDS FRACTION: f X CROSS SECTIONAL AREA=aA Figure 7. Schematic sketch of one Adsorption Bed Showing Terms Used in Mathematic Derivation of the Plug-Flow Model.

-33 -The complete differential mass balance on propylene in the gas phase can then be assembled and common terms cancelled to give the following differential equation: (vpy) + (py) + S QA = ~ (51) Similarly a mass balance can be derived on the whole gas stream: (v) + s(52) 6x 6t f Equation (51) can be simplified. Expand the applicable terms to 6: 6p 6y 6y Ps Y [ (vp) + ] + (v) + + Q = (53) Substitute for the square bracketed term its equivalent from Equation (52) and rearrange. y +! vy = _ vPs [(1 - Y)QA - YQB] (54) 6x v 6t fv Finally substituting from Equations (15) and (20), we get 6y 1 (y + =R1 (55) ax v at where R 1 = y)Q (1 - 56) fv If we make the assumption that the molar gas density remains constant and substitute from (15) and (20) into Equation (52), the following equation develops.

3a = R 2.(57) where R pS A (58) 3. Solution Along the Characteristics(16'11) It is convenient to find a solution of Equations (55) and (57) along their so-called characteristic directions. Application of this method reduces the problem to one of solving the following simultaneous ordinary differential equations of first order along the socalled characteristic directions C+ and C- as shown in Figure 8. The theory of this method is covered in some generality in Appendix A. Gas Phase Concentration (d) + = R (59) dx C Velocity dx 2 The projections of the characteristic curves into the x-t plane are given by C*- dt =1 (61) dx x C-: -= (62) dx Solution of these equations involves now the simultaneous integration of Equations (59), (60) and (61) in order to obtain the values of y, v and t along the C characteristics as functions of xo

-35 -C+ X Figure 8. The Characteristic Directions of the PlugFlow Equations.

The actual integration is carried out by a numerical finite difference scheme, the details of which are outlined in Appendix A.

EXPERIMENTAL DATA Data observed during runs were analyses at various times, flow rates at the outlet of the three beds at various times during some runs, inlet flow rate and temperature and pressure. Temperatures within the gas stream were monitored periodically but in no case showed a detectible difference from the bath temperature. Only one temperature is reported for each run. In the following section, the data are grouped into blocks in which the particle size is constant and sub-blocks in which the temperature was changed. Pressure was changed within these blocks and is indicated for each run. Analyses are indicated in the following way in the tables to follow: time (secs)/mol fract. propylene. For example, 150/.620 indicates a mol fraction of.620 at time 150 seconds from start up. Flow rates are indicated similarly as time(sec)/flow rate (mg-mol/sec.) A. Block 1 Data During this set of runs, the following column data were standard: Amount of Silica Gel in Bed 1 35.3140 gm. 2 35.4280 gmin. 3 35.0310 gm. Height of each bed 2.46 cm. Particle Mesh size on 8 Particle nominal diameter.28 cm. Beds void fraction (meas. by Hg displacement).42 -37 -

TABLE II EXPERIMENTAL DATA AT PARTICLE DIAMETER OF,28 CMSo -38 -

-39 -TABLE II i., 1 3 L r=. 7 _ _ 8 'J rtu-l 0ol. lrll) Inlet ol.*:0o. ire; s.. i. '. iMolar to. A N A L S * atin 3T Fl. Rt. g-mol/ sec Bath Teinperature ( P' 3.993.80 1 (;J/.172 1"0/. 710 307)/. 866!20/.973 2 80(/.00 20/)0/. 3 32)/.6.36 )l0/. 825 3 100/.000 220'/.037 3)40/.255 l60o/.580 8.97.000.78 1 30/.608 150/.209 270/.101 390/.077 2 50/.897 170/.378 290/.258 10o/.183 3 70/.991 190/.6h2 310/.408 h30/.288 5 3.03.993.84 1 40/o.00 1607.36 280/.6 28 70 o/.829 2 6 0/.ooo 18 0 /4.1O 3007/. 06 420/.577 3 80/.000 200/.000 320/.069 hLo/.272 6.97.000.78 1 50/.570 150/.286 280/.157 320/.105 2 70/. 825 170/.1 50 260/. 308 30/. 21hL 3 90/.913 190/. 639 28o/. )859 360/. 388 7.9 7 *.993.80 1 30/. 030 Q0/.0O8 190/.7()8 27/. 867 2 l, O/. o oo/ o 17.5 20 o/.336 280o/.533 3 50/.000 110/. O00 210/.033 290/.162 8.97.000 1.07 1 30/.635G 90/.303 150/.17h 210/.155 2 o/. 881 100/.509 16o/.365 20/. 268 3 50/.970 110/.713 170/.521 230/.825 9.97.993.80 1 1/. o096 120/. 552 210/.758 330/. 893 2 60/.oo000 10/.12 230/.389 350/.710 3 80/.000 160/.000 ~50/.10o 370/.367 10.97.993.41L 1 100/.000 z2O0/.433 340/.69 5 51.0/7. 96 2 120/.000 2L/0.033 30o/.160 5)0/.5ZL1 3 14o/.ooo 260/.000 380/.000 580/.036 11 1.19.000 1.50 1 60/.556 160/.262 260/.157 4~07/.099 2 90/.870 18.)/.477 280/.206 L O/7.171 3 113o/.987 200/.698 30,)/.851 L6o/.08o 12 8.31.993 1.35 1 60/.065 120/.533 210/7.73 360/.866 2 70/. 000 lh/.129 260/. 72 3 8)/. 669 3 80/.000 160/.018 280/.239 800/.82 13 h1.31.(00.76 1 30/.988 120/,.820 210/.h81 330/.308 2 O/.0 85 180/7.980 230/.850 350/.573 3 70/.988 160/. 987 25/. 993 370/.795 18I 2.31.993 1.20 1 30/.082 120/.553 210/.773 330/.8815 2 70/.000 1)7O/.238 230/.525 350/.689 3 90/.000 1607/.061 250/.262 370/.533 *seconds/mole fraction C H6

-40 -TABLE II (Cont'd.) 10 11 12 13 1L 15 16 3 5!40o/. 973 660/.982 780/. 991 l80/.993 1380/.993 560/. 11i 680/.9)15 800/.969 1100/.987 1100/.993 580/.763 700/.870 820/.935 1120/.976 1920/.988 1 510/. 060 630/IKo 750/.031 105oo/NG 15o0/.0oo05 530/.111 650/.100 770/.06h 1070/.05L 1l70/.018 18o0/.005 550/.167 670/.15Q 790/.120 1090/.08t11 L90/. 0L3 1910/.033 5S 520/.9)09 6h0/. 9h13 760/.971 1060/.985 1360/.987 1660/.993 2360/.993 5)10/. 717 66o/.820 780/.9o?07 180/.954 1380/.973 1680/.980 2380/.992 560/.)59 680/.665 8(0/.788 1100/.900 llj00/.963 179u0/. 76 20o/. 985 6 h10/.078 570/.051 690/.061 850/.030 1130/.026 h30/.193 5907. i7 710/.086 870/.065 115/.0 o48 1450/.292 610/. 260 730/.166 890/.126 1170/.078 1h30/.057 1940/.038 7 350/.920 h30/.947 510/.965 590/.974 720/.988 90u/.989 360/. 721 )llho/. 82 520/.878 600/.918 730/.950 910/.979 111o/.987 370/.364 h50o/.55h 530/.706 610/.807 7140/.898 9o0/.945 1120/.970 8 270/.127 oo00/.072 500/.055 700o/.029 100oo/.009 1480/.o00 280/.182 O10/.1h2 510/7111 710/.053 1010/.029 1h90/.000 290/. 351 h20/. 2h0 520/.177 720/.117 1020/.060!00o/.036 9,50/. 96),i 780/ 983 1.70/. 38 650/.938 800/.965 1000oo/.982 ),o/. 659 670/. 57 8o0/.925 1020/.968 10 P) (/. 967 12)tO/. 986 1800/.99 3 2510/.993 86o/. 871 120o/.07(o l2o/.o 3 53o/.993 807/. <2 12 07,/. Qoo 1i),o/.981! 2550/.993 11 58/. 062 760/. 3 8o. 037 1100/.o 1 00/. oo 1,00o/.oo000 600./ 121 780/.076 900)/.06,5 110/.058 l)20/. 0311 1 8o0/. Ol0o 2220/.005 620/. 191 800/.123 9g0/.091 11O/.08lt lh0/.05~2?ho/.022 207O/.005 12 600/.950 9(0/o973 1200/.986 1500/.993 180oo/.993 620/.877 c20/.958 1270/. 97; 1520/. 985 1820/.993 6140/. 626 9l0o/. 87)L4.6o/. 959 1540/. 983 13 650o/. 210 600/7.152 800/.113 11o/.o.09 150/. 039 ~o00/lO 25uo/.ooo lt70/ 389 620/.262 820/.20o6 112O/.119 1520/.070 2020/.036 2520/.010 90o/.585 6ho/.h 151 80o/.329 114O/.193 1540/.113 2 0oo/.075 25;)40/.032 14 b50/.9)42 600/.978 800/.988 1100oo/.992 i500o/.993 000oo/. 993 670/.866 620/.916 820/.206 1120/.98h 1520/.993 2020/.993 )140/. 738 6)o/.8)18 8)0o/.930 111o/. 973 1540/.990 2060/.993

TABLE II (Cont'Td.) 1 2 1 3 1 6 I I 6 - 7 8 9 itun Col. Inlet Inet Col. o0. Press rn. f. Molar TAo. A A L Y S E S arm. C3id 6F1.Rt. mg-mol /sec Rath Temperatllur = OC 0 15 2.37.000 1.20 1 30/.797 120/.358 210/.175 330/.114 2 '07. 973 130/. 5 1 230/. 3)1h) 350)/.259 3 70/.98L 160/.739 250/. 53 370/.321 16.97.993.*1 1 150/.273 270/.579 )100/. 798 650/.9~0 2 160/.017 290/.101 h20/.~237 6707/.7)43 3 20.)/. (00 310/.000 4) t0/.023 690/.239 17.97.000.78 1 90/.1125 u0o/.209 350/.105 50 )/.7Oh 2 110/.6i2 2L0/.350 370/.239 520/. 47 3 130/.771 240/.519 390/.273 5i0o/.246 18.97.993.h11 1 90/hG 190/.450 290/.672 h40/.873 2 11()/.000 210/. 022 32O/.1Lhh4 707/.z4 4 3 130/.000 230/.000 340/7.O1 )490/. 051 19.97.000 1.07 1 60/.h98 170/.208 240/.13h 30o/.113 2 70/.669 150/.369 230/.257 340/.198 3 90/.765 130/.599 220/.415 320/.279 20.97.993.41 1 70/.060 2)10/. ~597 380/.820 600/.933 2 90/.000 260/.084 h00/.281 620/.718 3 110/.000 280/.005 L20/.020 6h0/.27) 21.97.000.50 1 )0/. 818 160/.43)4 380/.191 5k0O/. 092 2 60/.927 180/.632 LO0/0. 520/.210 3 80/.973 200/.800 l420/.)164 5)40/.346 22.97.993 1.17 1 30/.17)1 110/.686 170/.815 250/.917 2 50/.035 120/.386 180/.565 260/.758 3 70/.005 130/.070 190/.325 270/.515 23.97.000.50 1 100/.595 250/.236 4150/.150 550/.089 2 120/.780 270/. 128 470/.263 570/.202 3 1)40/.921 290/.677 490/.415 590/.347 24.97.993 1.17 1 50/.341 lho/.781 230/.869 310/.928 2 70/.075 150/.490 2)0/7.698 320/.838 3 90/.005 170/.21i4 50/.416 2h0/.697 25 3.70.000 2.04 1 40/.600 120/.215 200/.118 260/.087 2 60/.898 1l40/.399 220/.224 300/.159 3 8o/.970 160/.581 40o/.356 320/NG

-42 -TABLE II (Cont'd.) 10 11 12 13 1 1 15 16 15 450/.074 600/.053 80o/.031 1100/. 022 1500/.010 2000/.000 4o70. lh3 620/.104 820/.061 11207/.042 1520/.026 2020/.010 90/. 227 64)0/.173 840/.122 1140/.09 16 1ooo/.987 150 0/.9c3 1020/.0o6 1520/.985 lolLo/. 810 1507/. 958 17 650/.039 800/.031 9707/.018 1300/.003 1700/.000 670/.0095 820/.080 990/.042 1320/.021 1720/.002 690/.165 8ho/.139 1007/..103 1340/.0h5 1740/.026 18 650/.946 920/.983 1 20/.988 1370/.990 670/. 800 907/.936 1107/.961 1390/.978 690/.302 960/. 766 1160/. 884 1410/.9.3 19 o440/.053 620/. 011 80/. 013 110/.f005 1340/.002 154/. 000 460/.134) 600/.070 820/.047 1120/.026 1320/.014 1520/.o09 )830/.214 5907.145 800/.103 1100/.059 1300/. 01 1500/.026 20 780/.966 1060/.983 1300/. 987 1600/. 993 800/. 881 1080/.98 1320/. 978 1620/.988 820/.560 1100/.863 13l).O/.938 16o40/.975 2000/.988 21 620/. 063 71)-/.06), 900/.025 1100/.018 1300/. 00 1600/.00oo 6h0/.142 76%0/.'117. 920/.055 1120/. 057 132/. 037 1620/.022 660/. 279 7807/. 219 910/.161 1140l/.116 1340/.099 1640/.068 2000/.038 22 350/.9} )! -50/.96)1 600/.979 800,/. 98 1000/.990 370/.874 70o/.922 620/.958 820'/.977 1020/.986 390/.767 )00/. 866 607/.927 8140 /.965 100Lo.983 23 700/.067 820/.0).15 1000/0.032 1200/.010 11100/. 008 1700/.00()7 2200/.003 720.1b.9 840.123 11020. 085 1220/. 058 1)120/. 038 1720/.017 2220/.015 740/.2 61 860/. 217 10110/.157 1240/.120 1,l0/.101 17401/.073 22L0/.036 2h h00/.962 520/.976 7(0/.98h 900/. 992 1100/.993 1300/.993 420/.902 54o0/.940 720/.973 90/. 982 1120/. 988 132/.99o 1620/.991 44o/. 799 560/. 898 740/.953 940/. 972 1 il0o/. 8). 13410/.988 1640/. 990 25 370/.060 o ho 0.040 520/.034 600/.024 700/.)16 8oo/.0o5 looo7/.Oo0o 380/.118 460/NO 540/.071 620/ 05i 720/i. 80/.019 020) O 2 1o00/.215 48i0o/.159 560/.1i9 640/. lo6 7407/.069 &40/.049 1o104/.033

-43 -TABLE II (Cont'd.) X1 2 3 51 6 1 7 1 8 9 Run Col. Inlets:iA - I Col. No. Press. m. f. molar Nol ANA L Y S E S atm C3H6 Ft.Rt. m=-Zol ath Temperature, 26.0C 26.96.993.81 1 30/1151 150/,795 270/,954 390/.974 2 50/.o00 170/9539 290/. 852,410/.'935 3 70/.000 190/.168 310/.635 430/.854 27.96.000.40 1 30/,865 150/.343 270/.187 390/.098 2 50/.973 170/.591 290/.369 410/.192 3 70/.985 190/.818 310/.554 430/.409 28.96.993.81 1 50/.279 110/.731, 200/.884 330/.959 2 60/.012 120/.288 220/.710 350/.898 3 70/.005 130/.033 240/.344 370/.770 29.96.000.40 1 100/.553 200/NG 340/.177 450/.130 2 120/.817 220/.526 360/.296 470/.223 3 140/NG 240/.737 380/.489 490/.431 30.97.993.48 1 30/.027 100/.395 200/.768 300/.902 2 4h/.000 110/.016 210/.193 310/.558 3 50/.000 120/.000 220/.005 320/.067 31.97.uOO.77 1 20/.758 80/.346 140/.259 200/.137 2 30/.969 90/.663 150/.366. 210/.277 3 40/.989 100/.772 160/.574 220/.4h2 32.97.993 1 50/.038 150/.522 25o/.0o8 350/.914 2 60/.ooo 160/.029 260/.220 360/.557 3 70/.000 170/.005 270/.069 370/NG 33.97,'*OOX.77 1 50/.555 170/.180 360/.o68 450/.o39 2 60/.750 180/.310 370/.141 460/.111 3 70/.910 190/.505 380/.253 470/.205 34.97.993 97 1 501/.133 150/.698. 250/.869 350/.'947 2 60/.000 160/.260 260/.617 360/.806 3 70/.000 170/.025, 270/.200 370/.438 3th Temperature, 490C 35.97.000.8i 1 30/.700 100/.224 170/.1240 240/.056 2 40/.833 110./,359 180/.225 250/.109 3 50/.965 120/.548 190/.343 260/.260 36.97.993.67 1 30/.059 100/.698 170/.902 240/.965 2 40/.000 110/.178 180/.614 250/.845 3 50/.000 120/.008 190/.152 260/.503 37.97.00.83 1 50/.5024 130/.199 2vo/.078 300/.025 2 60/NG 14u/.295 210/.171 31O0.098... _ 3L 70/.807 150/.h90 220/.283 320/,16

-44 -TABLE II (Cont'd.) o10 11 12 13 1h 15 1 6 26 51o/.98h 630/.991 750/.992 870/.992 990/.993 530/.968 650/.980 770/.986 890/.989 10107/.990 1120/.99~ 1520/.993 55~/.93 670/.967 790/.985 910o/.985 lC30/.987 11a0/.98 1540o/.990 27 510/.098 630/.037 750/.030 870/.013 1100/.007 1L()0/.,)5 53)/.183 650/.129 770/.079 890/.072 11201.025 1L20/.021 550/.316 670/.253 790/.179 910/.162 1Lo/.093 1b240/.070 28 5/ 90/. 1o 700/. 90 85o/.0 7.3 1000/.993 )170/0 7 6iO/. 7, 720. 2 6 870/.903 1020/. 93!9p0/.7i)-~,';30/. 72 7?0/. 07? 890o/. 87 lOL10 o. 989 29 560/. 0V7 800/.034 1000/.022 1300/. -00) 580/.11 820/. 095 1020/.067 1320/.018 1620/.037 2020/.000 600/.281 81 0O/.202 1040/. 100 13140/.082 1640/.065 20110/.022 30 400o/.963 50()/. Q73 60o/.989 8o0/,.993 10/. (807 510/. 12 610/ 955 810/.98L 1010/. 99 121,/.993 b20/. 325 520/.653 620/.856 820/.9)18 1020/.981 1220/.969 ]610/.993 31 60o/.1i3 320/.( 09 90/. 081 500/.030 700/.o5 o100)/.00) 27(/.217 330/.158 l10/. 11 510/.066 7107/.03 L;910/.0 07 1309/. 005 2o0/. 3L3 380o/. 71 0/.207 520/.182 7'20/.o6O 1_o0/./ 35.1310/. O15 3~ 700/. 97 9007/. 9C9 1200/.992 1500/. 993 71./. 958 91iC/. C82 1 /107. I99z 1510/.993 720/. 877 2207/. 9 8 6120/.9814 1520/.990 33 6oo/.o025 8oo00/. 0oo5 900/. 00 120oo/. 00 610/.079 610/.7 3 1 c107/. 015 1210/.005 1510/.00 620/.138 820/.072 92 0/.OL7 1220/.025 1520/.005 31 1(50/.967 550/.978 650. 990 750/T-G 857)/990 950/. 93 6()6/.868 560/. 9l. 66/. 972 760/.9711 60o/. 85 960/.9t89 10)60/.990 1470/.737 <70/. 87. 67)/. 919 770/.958 870/.977 970/.981 1070/.987 35 35 )/.02 500/.o005 750/.o000 360Z.092 510/.025 760/. 0o5 1010/.000 370/.129 520/. 061 770/.016 1020/.005 13510/.0-o0 36 3107/.9 718 390/. 983 -60/. 98 7 600/.993 700/.993 320/.921 400/. 967 1170.973 61)o/. 97 710/.993 860/. 9'; 3 3307.758 8107/. 8379 480/.980 620/.976 70L 6/.8 7 737. 0/.Q8 3 1020/.993 37 10o/. o0 ()o7/.000 b20/.053 610/.013 910/. 000 430/.111 6'o/.odo 920/. 7.013

-45 -TABLE II (Cont'd.) 1 2 3 ix 5 7 I il Ctol. Inle tinet Goi. Lo. rress. m. f. Molar iAo. atm C3H f- Fl.Rt. rmg-mol /sec Bath Te;n,)era, ure - 490~C 38.6 0.67 1 60/.L31 137/. 798 20/. '35 2 70/.030 140/.369 lo0/.726 280/.882 3 80/. oo05 15o/.o 0/3 22o/.300 290/.6?$ 10 11 12 13 lh -5 360/.9) Lh3o/.9o68 ),o/.s85 3 70/. 8l)! ho/. 911 550/. 989

-46 -TABLE III VELOCITY DATA AT PARTICLE DIAMETER =.28cms. Run Col F L O W R A T E D A T A No. No. 26A 1 35/.631 55/.687 75/.717 95/.729 115/.73 135/.747 2 40/.638 60/.660 80/.675 100/.689 120/.69 1401/.713 3 25/.614- 45/.638 65/.653 85/.653 105/.66 125/.661 1 155/.749 175/.757 2 160/.720 180/.729 200/.736 220/.737 240/.741 260/.744 3 145/.662 165/.662 185/.663 205/.665 225/.674 245/.680 1 2 280/.746 300/.749 320/.752 340/.753 360/.754 380/.754 3 265/.682 285/.687 305/.692 325/.698 345/.701 365/.705 2 510/.769 540/.770 580/.764 610/.767 660/.767 710/.767 3 405/. 714 25/.714 515/.726 585/.730 615/. 732 715/.734 1 3 765/.737 815/.738 915/.743 965/.745 1015/.749 9 1 20/.428 35/.525 50/.488 65/.477 80/.)62 180/.)28 2 25/.467 40/.514 55/.496 70/.495 85/.485 185/.456 3 30/.493 45/.493 60/.)482 75/.482 90/.472 190/.458 1 320/.422 430/.421 540/.420 770/.418 980/.416 1280/.414 2 325/.442 435/.439 545/.437 785/.434 985/.429 1285/.424 3 330/.445 440/.444 550/.441 790/.439 990/.435 1290/.426 30 1 15/.401 95/.423 165/.451 255/.466 365/.472 465/.478 2 20/.403 100/.405 170/..408 270/.422 370/.443 470/.450 3 25/.390 105/.390 175/.390 275/.391 375/.392 475/.404 1 565/.479 865/.479 2 570/.460 670/.465 770/.469 870/.470 1070/.471 3 575/. 419 675/.436 775/.441 875/.444 975/.447 1075/.449 1 2 3 1175/.456 1275/.457 3 1 35/.854 125/.767 245/.761 305/.759 345/.757 425/.756 2 20/.849 40/.882 130/.814 150/.811 250/.796 310/.794 3 25/.849 45/.857 135/. 817 155/.815 255/. 800 275/. 798 1 575/.755 705/.751 985/.748 2 580/.785 710/.783 990/.776 1120/.774 3 315/.797 355/.7961 525/.791 715/.7785 995/.770

-47 -B. Block 2 Data Throughout the block of data composed of runs number 45 to 55 inclusive, the following column data were standard: Amount of Silica Gel in each Bed 1 33.5014 gm. 2 34;o806 gm. 3 32.'8644 gm. Height of each bed 2,46 cm. Particle mesh size on 14 Particle nominal diameter 1168 cm. Bed voids fraction (measured by Hg displacement).42

TABLE IV EXPERIMENTAL DATA AT PARTICLE DIAMETER OF.117 CMS. -48 -

-49 -TABLE IV 1 2 3 T 5 6 7 9 _ Hiun Col. Inlet Inlet Col. iFo. Fress. m. f. Molar Io. A N A iL S i S atm C3B6 Fl.Rt. 3 6 mg-mol sec Bath Temperature- O00 45.98.993.87 1 50/.020 iz0/.Lo5 190/.881 200/.966 2 60/.ooo0 130L/. 2)O7/. 00) 2 70/.57 ) 3 70/.000 ooo o/.o 210/.o00 280/.ooo 1t6.28.000.86 1 50/.85Q9 120/.0 l. lO0/.185 260/.109 2 60.981] 130/. 867 200/. 602 270/.414 70/.988 1)07/. 97)- (/.870 2 2/7. 6)19 1 7.Q8. 03.87 1 30/.000 100/.215 160/.705 230/. 958 2 lo0/.00( 110/.000 170/.000 210tO.181 3 50/.ooo 120/.00 18. o00oo 250/00ooo ) 8 2.30.ooo.88 1 50/.985 10o/.653 210/.7 33 290/. lb5 2 60. 993 1!0O/.982 220/.806 3007.566 3 70/.993 150/.993 230/.978 310/.888 Bath Teinperature 26C 49.96.993.63 1 30/.o00 110/.560 19o/.976 27o0/.988 2 4l).ooo L o20/. 0(J 200/.268 807j/.9 47 3 507.0O 130/.0o0O 107. o/o0 So90/. 027 50.96.000.63 1 50/.800 130/.266 210/.105 290/.0L3 2 60/.979 140/.708 220/.396 300/.206 3 70/.993 150/.921 230/.630 310/.379 51.97.993.63 1 70/.097 150/.870 230/.988 310/.993 2 80. oo0 160.000o 240/7.830 320/.979 3 90/.000 170/.000 250/.000 330/.450 Bath Temperature - 0~C 52.97.000.49 1 50/.974 150/.605 250/.231 350/.140 2 60/.993 160/.974 260/.760 360/.517 3 80/.993 170/.993 270/.970 370/.-810 53.98.993.52 1 30/.000 130/.068 230/.560 330/.952 2 40/.000 1h0/.000 240/.000 340/.076 3 50/.000 150/.000 250/.000 350/.000 54.98.000 1 20/.988 100/.581 180/.250 260/.107 2 30/.993 110/.905 190/.583 270/.353 3 40/.993 120/.985 200/.826 280/.554 55.98.993.52 1 100/.019 200/.467 300/.900 400/.986 2 110/. 000 210/.00 310/.005 410/.454 3 120/.000 220/.000 320/.000 420/.001

-50 -TABLE IV ( CONT'D ) 10 11 12 13 1 15 16 5 330/.990 l)oo/.991 h70/.993 600/. 993 310/.929 h10/.990 h80/.993 610/.993 760/.993 350/.030 120/.560 L90/NG 620/.991 770/.993 1020/.993 6 330/.o055 oo/. ol 870/.022 600/.008 700/.005 80oo/.oo looo/.ooo 3h0/.268 810/.188 890/.112 610/.076 710/.050 810/.022 1010/.011 350/.877 1120/.343 500/.251 620/.161 720/.108 820/. 07 1020/.041 87 300/.988 370/.993 0Lo/.993 310/.852 380/.976 850/.989 520/.992 320/.000 390/.833 460/.824 530/.982 600/.990 700/.993 88 370/.071 h85/.o83 600/.023 700/.005 900/.000 12oo00/.oo000 380/.358 460/.236 610/.117 71u/.066 910/NG 1210/NG 390/.772 870/.h81 620/.235 720/.127 920/.08h 1220/.038 119 350/.9o2 430/.993 510/.993 360/.992 l,0/. 993 520/.993 710/.9o3 370/.826 L50/.987 530/.989 720/.993 920/.993 50 370/.028 lO/. 00oo 530/.000 380/.119 h,60/.067 5l0(/.038 620/.010 710/.000 390/.210 470/.168 550/.119 630/.066 720/.037 51 390/.993 h70/.993 0oo.0991 880/.993 810/.97 l90o/.988 52 450/.096 550/.o56 750/.027 1050/. 002 1300/.000 460/. 365 560/.259 760/.123 1060/.049 1310/.036 1660/.001 470/.614 570/.462 770/.267 1070/.125 1320/.082 1670/.048 53 430/.987 530/.992 630/.993 800/.993 440/.688 540/.973 640/.992 810/.993 1010/.993 450/.ooo 550/.049 6o50.598 820/.982 1020/.989 54 344/. 069 420/.041 500/.021 600/.002 800/.000 000/.000 350/.228 430/.151 510/.118 610/.067 810/.054 1010/.013 360/.377 440/.261 520/.193 620/.132 820/.082 1020/.036 55 500/. 993 510o/.94 610/.989 710/.993 520/.013 620/.400 720/.928 900/.992

C. Block 3 Data Throughout the runs numbered 56 to 59, the following column data were standard: Amount of Silica Gel in each Bed 1 33.8562 gm, 2 33.5274 gm. 3 32.0713 gm. Height of each bed 2.46 cm. Particle mesh size on 10 Particle nominal diameter.198 cm. Bed voids fraction (measured by Hg displacement).42

TABLE V EXPERIMENTAL DATA AT PARTICLE DIAMETER OF o198 CMSo -52 -

-53 - TABLE V 1 2-2 3 5 6 8 9 u Col. Inlet Inlet Col. o. Press. m.f. molar No. A N A L Y S E S C3H6 flow rate Bath Temperature = OC 56.98 1.000.79 1 30/.906 120/.356 190/.175 260/.104 2 40/.993 130/.677 200/.497 270/.353 3 50/.993 140/.924 210/.756 280/.611 57.98.993.68 1 30/.014 100/.251 170/.584 240/.864 2 40o/.000 110/.000 180/.032 250/.158 3 40/.000 120/.000 190/.000 260/. 000 Bath Temperature - 25"C 58.98.000 1 30/.784 100l.250 170/.150 240/.088 2 40/.983 110/.667 180/.398 250/.277 3 50/.987 120/.868 190/.652 260/.477 59.98.993 1 30/.055 100/.608 170/.924 240/.978 2 ho/.000 110/.oh9 180/.447 250/.842 3 50/.000 120/.000 190/.028 260/.248 10 11 12 13 1 15 16 56 330/.087 400/.054 470/.050 600/.042 700/.011 900/.007 1100/.000 340/.284 410/.195 480/.142 610/.104 710/.067 910/.045 1110/.030 350/.477 420/.337 490/.305 620/.228 720/.173 920/.127 1120/.059 57 310/.940 380/.979 450/.983 600/.992 700/.993 900/.993 320/.h47 390/.750 460/.902 610/.964 710/.989 910/.993 330/.005 400/.082 470/.300 620/.828 720/.955 920/.984 58 310/.057 380/.026 450/.02o 6uO/.000 320/.176 390/.108 60o/.103 610/.035 800/.0)46 1010/.00 330/.354 ho00/.266 470/.201 620/.152 81 /.035 102/.054 59 310/.990 380/.993 320/.96 390/.983 460/.988 610/.993 810/.000 1010/.00c 330/.709 460/.91 h70/.975 620/.98q 820/.993__

DATA PROCESSING All calculations in the reduction of the data were programmed for the IBM 704 computer. A complete flowsheet of calculations is shown in Appendix Eo In this section the overall sequence and objectives of these calculations are discussed. The major objective of the data processing was to deduce the magnitude of the diffusion coefficient D involved in the homogeneous spherical diffusion model, As is shown in the Theory section, the diffusion equation may be solved with a boundary condition of an arbitrary input rate function of time, if this function is such that it has a finite number of derivatives. For this reason, use was made of polynomial curve fitting although this lead to considerable interpolation and smoothing to get enough points to make the polynomials describe the expected curves through the experimental points. A., Mass Balance Calculations The assumption of point-wise equilibrium results in the molar flow rate G being fixed at any point in space and time by a relation of the form: G = G (1 + ) (63) Derivation of this relation may be seen in Appendix A. From smoothed curves of the experimental concentration - time data, points are taken at frequent time intervals and the amounts of the desorbing gas passing each of the three sample points per -514 -

-55 -second (Gy) calculated and tabulated~ These values are then correlated as functions of time by a polynomial. The curves are next integrated by taking the analytic integral of the polynomial expression. From the difference of these integrals and after a correction is made for dead space, the loading of the desorbing gas on each bed initially is calculated. B., Derivation of the Rate Equation Constants The constants g of the (Gy) curve fits are differenced and divided by the adsorbent amounts in each cell to give the constants q of the rate functions according to the following relations: (Gy)o - gl,0 (64) L1 q =-l,n 2 <n< mg (65) l,n L- - q gi-ln - gi,n 2 < i < n (66) in Li 1 < n < m - _ g If the desorbing gas is propylene, the coefficients q are taken as the coefficients of the rate function QA. if the desorbing gas is propane, the coefficients are those of the function QB and they are transformed to those of Q via relation (20): E 1 < n < m() q. = m q l<n mg (67) qin l<i<n

-56 -C. Iterative Trial and Error Determination of the Diffusion Coefficient The rate equations derived above are average rates and as such apply most properly at the mid points of the adsorbent beds from which they are derived. As a result, in order to use them in the determination of the diffusion coefficient via the analytic solution, local conditions of molar flow rate and mol fraction must be interpolated at the mid-points. This is done by a standard three point formula. From these interpolated values, a mass transfer coefficient is computed from the jD correlation and then from the following rearrangement of Equation (44) I _ (1 -y) (*QA/kyas) y* -J — ) e (68) the interface mol fraction of propylene is computed, Next, from Equation (47) the following relation is derived: - y*/c + (1 - y) s (69) /CAB + (1 - *)/m (69) From this relation, the total gas interface concentration s* on the adsorbent surface is computed. Finally a value of the diffusion coefficient D is assumed and the interface total gas concentration is compared as the solution of Equation (26) at radius r = r0o The assumed value of the diffusion coefficient is then corrected as indicated by the discrepancy in the two computed values of s* and the iterative part of the calculation repeated until this discrepancy is less than an allowable error (usually 1%). The actual method of correction of the assumed value of D based upon this error is taken from a technique due to Gauss and recently described by Wegsteino(25)

-57 -This trial and error determination is repeated for four points on each of the break-through curves taken experimentally and finally the derived values of the diffusion coefficient are averaged. In the section to follow, the data reduction as performed by the computer is reproduced for one run in Table IV and is summarized for the remaining runs in Table VII.

TABLE VI TYPICAL DATA PROCESSING RUN II -58 -

-59 -TABLE VI BINARY ADSORPTION KINETICS MASS BALANCE CLOSURE CALCULATIONS RUN NUMBER 1 NUMBER OF SERIES CELLS 3 INITIAL SYSTEM PRESSURE 1.0000 ATMOSPHtERES INITIAL SYSTEM TEMPERATURE (BATH TEMP.) O. DEGREES CENT. MOL FRACTION CF PROPYLENE IN BED INITIALLY U. BED VOIDS FRACTION 0.4200 BED CROSS-SECTIONAL AREA 20. 3000 SQUARE CM. ADSORPTIVE RELATIVE VOLATILITY 0.5000 SILICA GEL LOADED IN EACH CELL 1 35.3140 GRAMS 2 35.4280 GRAMS 3 35.0310 GRAMS DEPTH OF BEDS 1 2.4600 CM. 2 2.4600 CM. 3 2.4600 CM. MAXIMUM (EQUILIBRIUM) LOADING PROPYLENE 3.2131 MG-MOLS/GM. MAXIMUM (EQUILIBRIUM) LOADING PROPANE 2.5311 MG-MOLS/GM. ASSUMED INITIAL LOADING OF PROPANE 2.5311 MG-MOLS/GM. INLET MASS FLOW RATE 0.7961 MG-MOLS/SEC INLET VOLUMETRIC FLOW RATE 16.6419 tC/SEC INLET FREE SPACE VELOCITY 1.9526 CM/SEC AREA FOR MASS TRANSFER 18.5000 SQ. CM. PARTICLE RADIUS 0. 1400 CM. INLET MOL FRACTION PROPANE 0.0010 UNPROCESSED EXPERIMENTAL DATA WITH FLOWRATES OBTAINED BY EQUILIBRIUM MASS BALANCE DATA FOR CELL NO. 1 TIME G F V X Q SECS MG-MOLS/SEC CC/SEC CM./SEC PROPANE MG-MOLS/SEC 17.30 0.6168 12.8949 1.5124 1.0000 0.6168 20.00 0.6168 12.8949 1.51214 1.0000 0.61 68 50.00 0.6363 13.3027 1.5603 0.8650 0.5504 80.00 0.6611 13.8201 1.6210 0.7050 0.4660 110.00 0.6873 14.3697 1.6854 0.5480 0.3766 140.00 0.7121 1 4.8895 1.7464 O.1 100 0.2920 170.00 0.7305 15.2 38 1.1914 0.3140 0.2294 200.00 0.7596 15.4651 1.8139 0.2680 0.1982 230.00 0.750? 15.1002 1.8414 0.2130 O.1599 260.00 0.7588 15.8668 1.8610 0.1750 O. 1328 290.00 0.7654 16.0054 1.8772 0.1440 0.1102 320.00 0.7715 16. 1326 1.8922 0. 1160 0.0895 350.00 0.7759 16.2248 1.9030. 0960 0. 07 745 380.00 0.7806 16.3227 1.9145 0.0(50 0.0585 410.00 0.7837 16.3886 1.9222 0.0610 0.0478 440.00 0.7862 16.440U8 1.9283 0.0500 0.0393 1470.00 0.7878 16.474 1.9322 0.04.30 0.03.39 500.00 0.7891 16.5'124 1.936! 0.0350 0.0216 530.00 0.79 1 16.5461 1.9407 0.0280 0.0222 560.00 0.7922 16.5654 1.9429 ().0240 0.0190 590.00 0.7927 16.5751 1.91441 0.0220 0.0114 620.00 0.7936 16.5944 1.91463 0.0180 0.0143 650. 0 0.7940 16.6041 1604.9415 0.0160 0.0127 680.00 0.7945 16.6138 1.9486 O.0140 0.0111 710.00 0.7947 16.6187 1.9492 0.0130 0.0103 740.00 0.1952 16.6284 1.9503 0.0110 0.0087 770.00 0.7957 16.6382 1.9515 0.0090 0.0072 800.00 0. 7959 16,6430 1. 9520 O. 0080 0.0064 830.0 (0 0. 796 1 16.6419 1. 95.h26 0.0070 0.0056

-60 -860.00 0.7961 16.6419 1.9526 0. 0070 0.0056 890.00 0.7961 16.6479 1.9526 0.0070 0.0056 920.00 0.7961 16.6479 1.9526 0.0070 0.0056 950.00 0.7961 16.6479 1. 9526 0.0070 0.0056 980.00 0.7961 16.6479 1.9526 0.0070 0.0056 1010.00 0.7961 16.6479 1.9526 0.0070 0.0056 1040. 00 0.7961 16.6479 1.9526 0.0070 0. 0056 1070.00 0.7961 16.64/9 1.9526 0.0070 0.0056 1100.00 0.7961 16.64'9 1.9526 0.0070 0.0056 1130.00 0.7961 16.6479 1.9526 0.0070 0.0056 1160.00 0.7961 16.6479 1.9526 0.0070 0.0056 1190.00 0.7961 16.6479 1.9526 0.0070 0.0056 1220. 00 0.7961 16.64(9 1.9526 0.00(0 0.0056 1250.00 0.7961 16.6479 1.9526 0.0070 0. 0056 1280.00 0.7961 16.6479 1.9526 0.0070 O.0056 1310.00 0.7961 16.6479 1.9526 0.0070 0.0056 1340.00 0.7961 16.6479 1.9526 0.0070 0.0056 1370.00 0.7961 16.6479 1.9526 0.0070 0.0056 1400.00 0.7961 16.6479 1.9526 0.0070 0.0056 1430.00 0.7961 16.6419 1.9526 0.0070 0.0056 1460.00 0.7961 16.6479 1.9526 0.0070 0.0056 PRESSURE IN CELL 1 1.0510 ATMOSPHERES DATA FOR CELL NO. 2 TIME G F V X Q SECS MG-MOLS/SEC CC/SEC CM./SEC PROPANE MG-MOLS/SEC 17.30 U.6168 13.0886 1.5351 1.0000 0.6168 20.00 0.6168 13.0886 1.5351 1.0000 0.6168 50.00 0.6168 1 3.0886 1.5351 1.0000 0. 6168 80.00 0.6172 13.0976 1.5362 0.99 T70 0.6154 110.00 0.6198 13.1513 1.5425 O.97)0 0.6068 140.00 0.6256 13.2 755 1.557 1 0.9380 0.5868 170.00 0.6378 13.5342 1.5874 0.8550 0.5453 200.00 0.6566 1. -9333 1.6342 0.7330 0.4813 230.00 0.6755 14.3352 1.6814. 0.6170 0.4168 260.00 0.6927 14./7008 1.7242 0.5170 0.3581 290.00 0.7077 15.0186 1.7615 0.4340 0.3071 320.00 0.7208 15.2976 1.7942 0.3640 0. 2624 350.00 0.7332 15.5618 1.8252 0.3000 0.2200 380.00 0.7433 15.7747 1.8502 0.2500 0. 1858 410.00 0.7519 15.9580 1.8717 0.2080 0.1564 440.00 0.7590 16. 1096 1.8895 0. 1740 0.1321 470.00 0.7654 16.2451 1.9054 0.1440 0.1102 500.00 0.7706 16.3563 1.9 184 0. 1200 0.0925 530.00 0.7746 16.4403 1.9283 0.1020 0.0790 560.00 0.7779 16.5109 1.9365 0.0870 0.06(7 590.00 0.7806 16.5678 1.9432 0.075h0 O.0585 620.00 0.7826 16.6108 1.94'82 0.0660 0.0517 650.00 0.7844 16.6491 1.9527 0. 0580 0.0455 680.00 0.7856 16.6732 1.9556 0.0530 0.0416 710.00 0.7872 16.7070 1.9595 0.0460 0.0362 740.00 0.7881 16.7264 1.9618 0.0420 0.0331 770.00 0.7892 16. 7507 1.9647 0.0370 0.0292 800.00 0.7899 16.1653 1.9664 0.0340 0.0269 830.00 0.7908 16.7848 1.9687 0.0300 0.0237 860.00 0.7915 16. 7995 1.9(04 0.0210 0.0214 890.00 0.7922 16.8142 1.9721 0.0240 0. 0190 920.00 0.7927 16.8240 1.9733 0.0220 0.0174 950.00 0.7931 16.8338 1.9744 0.0200 0.0159 980.00 0.7936 16.8436 1.9756 0.0180 0.0143 1010.00 0.7938 16.8486 1.9761 0.0110 0.0135 1040.00 0.7943 16.8584 1.9773 0.0150 0.0119 1070.00 0.7945 16.8633 1o9779 0.0140 0.0111 1100.00 0.7947 16.8683 1.9785 0.0130 0.0103 1130.00 0.7950 16.8732 1.9790 0.0120 0.0095

1160.00 0.7952 16.8781 1.9796 0.0110 0.0087 1190.00 0.7954 16.8831 1.9802 0.0100 0.0080 1220.00 0.7957 16.8880 1.9808 0.0090 0.0072 1250. 00 0.7957 16.8880 1.9808 0. 0090 0. 0072 1280.00 0.7959 16.8930 1.9813 0.0080 0.0064 1316.00 0.7959 16.8930 1.9813 0.0080 0.0064 1340.00 0.7959 16.8930 1.9813 0.0080 0.0064 1370.00 0.7961 16.8919 1.9819 0.0070 0.0056 1400.00 0.7961 16.8979 1.9819 0.0070 0.0056 1430.00 0.7961 16.8979 1.9819 0.0070 0.0056 1460.00 0.7961 16.8979 1.9819 0.0070 0.0056 PRESSURE IN CELL 2 1.0357 ATMOSPHERES DATA FOR CELL NO. 3 TIME G F V X Q SECS MG-MOLS/SEC CC/SEC CM./SEC PROPANE MG-MOLS/SEC 17.30 0.6168 13.3341 1.5639 1.0000 0.6168 20.00 0.6168 13.3341 1.563' 1.0000 0.6168 50.00 0.6168 13.334 1 1.5639 1.0000 0.6168 80.00 0.6168 13..3341 1.5639 1.0000 0.6168 110.00 0.6168 13.3341 1.5639 1.0000 0.6168 140.00 0.6171 13.3402 1.5646 0.9980 0.6159 170.00 0.6185 135.3706 1.5682 0.9880 0.6111 200.00 0.6205 13.4 133 1.5732 0.9740 0.6043 230. 00 0.6240 13.4903 1.5823 0.94)0 0.5922 260.00 0.6292 13.6028 1.5955 0.9130 0.5745 290.00 0.6362 13.7526 1.6130 0.8660 0.5509 320.00 0.6464 13.9751 1.6391 0. 7980 0.5159 350.00 0.6619 14.3088 1.6783 0.7000 0.4633 380.00 0.6770 14.6369 1.7167 0.6080 0.4 116 410.00 0.6908 14.9346.7517 0.5280 0.3647 440.00 0.7035 1 5.2092 1.7839 0.4510 0. 3215 470.00 0.7144 15.4451 1.8115 0.3980 0.2843 500.00 0.7243 15.6592 1.8366 0.3460 0.2506 530.00 0.7328 15.8451 1.8584 0.3020 0.2213 560.00 0.7406 16.0135 1.8782 0.2630 0.1948 590.00 0.7471 16. 1544 1.8947 0.2310 0.1( 26 620.00 0.7542 16.3069 1.9126 0.19(0 0. 1486 650.00 0.7603 16.14392 1.9281 0.1680 0.1277 680.00 0.7657 16.5551 1.9417 0. 1430 0.1095 710.00 0.7702 16.6536 1.9533 0. 1220 0.0940 740.00 0.7746 16.7486 1.9644 0.1020 0.0790 770.00 0. 7784 16. 8501 1.9740 0. 0850 0.0662 800.00 0. 7810 16.8882 1.9808 0.0730 0.0570 830.0 0 0.7833 16. 9369 1.9865 0. 0630 0. 0493 860.00 0.7849 16.9711 1.9905 0.0560 0.0440 890.00 0.7860 16.9957 1.9934 0.0510 0.0401 920.00 0.7874 17.0252 1.9969 0.0450 0.0354 950.00 0.7881 17.0400 1.9986 0.0420 0.0331 980.00 0.7894 1(.0697 2.0021 0.0360 0.0284 1010.00 0.7901 17.0846 2.0038 0.0330 0.0261 1040.00 0.7910 17.1045 2.0062 0.0290 0.0229 1070.00 0.7915 17.1145 2.0073 0.0270 0.02114 1100.00 0.7922 17. 1295 2.0091 0.0240 0.0190 1130.00 0.7927 17.1395 2.0103 0.0220 0.0174 1160.00 0.7931 17. 1495 2.0114 0.0200 0.0159 1190.00 0.7936 17.1595 2.0126 0.0180 0.0143 1220.00 0.7938 17.1645 2.0132 0.0170 0.0135 1250.00 0.7943 17. 1745 2.0144 0.0150 0.0119 1280.00 0.7945 17.1706 2.0150 0.0140 0.011 1 1310.00 0.7947 17.1846 2.0155 0.0130 0.0103 1340.00 0.7950 17.1896 2.0161 0.0120 0.0095 1370.00 0.7952 17.1946 2.0167 0.0110 0.0087 1400.00 0.7954 17. 1997 2.0173 0.0100 0.0080 1430.00 0.7954 17. 1997 2.0173 0.0100 0.0080

-62 -1460.00 0.7951 1'7.204? 2.0179 0.0090 0.0072 PRESSURE IN CELL 3 1.0170 ATMOSPHERES CORRELATION OF Q CURVES AS POLYNOMIALS -IN rIME BED NO. 1 CORRELATION CONS -ANTS B( 1)'= 6.59 127079E-01 B( 2) = -1.80543028E-03 B 3) = -1. 78389500E-05 BC 4) = 1.38157107E-07 B( ) = -4.3236221 7F-10 B( 6) = 7.54037476E-13 B 7 ) = -.85644490E-16 B( 8) = 4.85t26790E-19 BC 9) = -1.64533921E-22 B(10) = 2.35100204E-26 COMPARISON OF FIT WITH DATA TIME COMPUTED EXPERIMEN AL 17.299 0.62383430 0.61682 197 20.000 0.61752134 0.61682197 50.000 0.53964930 0.55040489 80.000 0.45642506 0.46604356 110.000 0.3 610664 0.37663200 140. 000 0.30545699 0.29196978 170.000 0.24489143 0.22937234 200.000 0.19538049 0.19821931 230.000 0. 15614463 0. 15993238 260.000 0. 12571464 0. 13279313 290.000 0. 10260715 0.11022322 320.000 0.08498239 0.08949627 350.000 0. 07140798 007448854 380.000 0.06064859 0.05854496 410.000 0.05176080 0.047808 0 440. 000 0.04408-62 0. 0591209 470. 000 0.037226 19 0.03387696 500.000 0.0 3097926 0. 02763832 530.000 0.02529)98 0.02215569 560.000 0.02023523 0.01901212 590.000 0.01587387 O. 0 174384 620.000 0.01230683 0.01428451 650.000 0.00959031 0.01270415 680.000 0.00772560 0.01112316 710.000 0.00666343 0. 01033167 740.000 0.00628050 0. 00874729 770.000 0.00640941 0.00716106 800.000 0. 00685368 0.00636725 830.000 0.00 740827 O. 0055 7291 860.000 0.00787964 0. 00557297 890.000 0.00811862 0.00557297 920.000 0.0080 1 14 0.00557297 950.000 0.00755432 0.00557297 980.000 0.00676864 0.0055729-7 1010.000 0.00577084 O.00551297 1040.000 0.00473031 0.00557297 1070.000 0.00384530 0.0055729 1100.000 0.00327741 0.00557297 1130.000 0.00320190 0.0055729 1 1160.000 0.00365508 0.0055/297 1190.000 0.00460720 0.0055729V7 1220.000 0.00587731 0. 00557297 1250. o00on 0.0071560 00055(297

-635 -1280.000 0.00797145 0.00557297 1310.000 000 0.00801150 O.00551297 1340.000 0.00695560 0.00557297 1370. 000 0.00492854 O. 0055 '291 1400.000 0.002/5511 0 O.00557297 1430.000 0. 00259032 0. 00557297 1460.000 0.00825240 0. 0055 '29 7 INITIAL LOADING OF PROPANE, CELL NO.1 2.6430 MG-MOLS/(;M. PERCENT ERROR IN MASS BALANCE 4.4204 BED NO.2 CORRELATION CONSTANTS B ( 1) = 5. 9499464E-01 B( 2) = 1.08423200E-03 ( 3) = -6.85988104E-06 B( 4) = -4.09215873E-08 B( 5) = 2.61373848E-10 BR 6) = -5.91870731E-13 B( 7) = 7.05440629E-16 B( 8) = -4.72072154E-19 B( 9) = 1.680753075E-22 B(10) = -2.48296845E-2o COMPARISON OF FIT WITH DATA T I ME COMPUTED EXPER I MENTAL 17.299 0.61150853 0.61682197 20.000 0.61364(92 0.61682191 50.000 0.62840062 0.61682197 80.000 0.62581984 0.61539025 110. 000 0. 60668585 0. 60675884 140.000 0. 57346006 0.58683157 170.000 0.52948545 0.54531178 200.000 0.47839584 0.48127731 230.000 0.42369898 0.41618650 260.000 0.36850186 0. 35813204 290. 000 0.31535026 0. 30713044 320.000 0.26615186 0.262 37269 350.000 0.22220293 0.21997279 380.000 0. 18417429 0.18581515 410.000 0. 15224995 O.15639400 440.000 0.12619532 0. 13207116 470.000 0. 10546984 0.11022322 500.000 0 08933302 O. 09247 740 530.000 0.07694256 0. 07900881 560. 000 O. 06 744065 0. 0676 7903 590.000 0.C6002445 0.05854496 620.000 0.05399642 0.05165301 650. 000 0.04880116 0.04549678 680.000 0.04404008 0.0416'469 710.000 0.03946964 0.03620899 740.000 0.03498968 0.03309871 7 70.000 0.0306 1673 0.02920070 800.000 0. 02644985 0.02685645 830.000 0.022637 70 0.0232444 860.000 0.01933400 0. 02137063 890. 000 0.01666917 0.01901272 920.000 0. 0147 1 794 0.01743849 950.000 0. 01347(67 0. 01586242 980. 0.0 0 1 280 0 214 0. 01 42845 1 1010. 000 0.01272681 0 01349486 1040.000 0.01283024 0.01191419 1070.000 0.012926(1 0.01112316 1100.000 0.01275896 0.01033167

1130.000 0.01214982 0.009539(1 1160.000 0.01097295 0.00874729 1190.000 0.00929316 0.00795441 1220.000 0.00729873 0.00716106 1250. 000 0. 00536975 0. 007 16106 1280.000 O. 00393 795 O. 006346725 13 16.000 0.003632 17 0.00636725 1340.000 0.004 49036 0.00636725 13 10. 000 0. 0066 3794 0.0055 1291 1400.000 0.00898632 0.00557297 1430.000 0.00)22 171 O0.00557297 1460.000 0.00270089 0.00557297 INITI AL LOADING OF PROPANE, CELL 40.2 2.4119 MG-MOLS/GM. PERCENT ERROR IN MASS BALANCE -4.7099 BED NO. 3 CORRELATION CONSTANTS B( 1) = 6.43359333E-01 8( 2) = -1.64141883E-03 B( 3) = 2.42935443E-05 B( 4) = -1.38142559-E- O B ( 5) =.597105 7 7E-10 R( 6) = -5.17722636E-13 B( 7) = 4.43524992E-16 B( 6) = -2.25528366E-19 B( 9) = 6.28952211t-23 B(10) = - 7.406985,64E-27 COMPARISON OF FIT WITh DATA TIME COMPUTED EXPERIMENTAL 17.299 0.62154762 0.61682197 20.000 0.61919436 0.61682191 50.000 0.60677259 0.61682197 80.000 0.60963123 0.61682197 110.000 0.61715916 0.61682197 140.000 0.62245756 0.61586770 170.000 0.62150(2 1 0.61108338 200.000 0. 6 1239859 0. 60434865 230.000 0.59473237 0. 92214 72 260.000 0.569 1 1 14 0.54 149524 290. 000 0. 53685312 O. 5 509 1 230 320.000 0.49949309 0.51585955 350.000 0. 45875800 0.46330140 380.000 0.41630471 0.41162720 410.000 0.3 3 6 3011 0.36472990 440. 000 0. 33200329 O. 321482 18 470.000 0.29243085 0.28431 '15 50(1.000 0.25564999 0.25059381 530.000 0.22213869 0.22131992 560.000 0. 19214266 0. 1478601 590.000 0.16570865 0.17259002 620.000 0.14272391 0.14857505 650.000 0. 12295677 0. 12773090 680.000 0. 106096 16 0.10948860 710.000 0.09 178854 0.09596543 740.000 0.07966655 0. 07900881 770.000 0.06937916 0. 06616104. 800.000 0.06060553 0.05701650 830.000 0. 0530 (08 1 0. 049347(5 860.000 O. 0465522 7 0.'04395328 890.000 0.04087643 0.04008674 920.G00 0.03592350 0.03543209 950.000 0.0 5161512 0.033096e71

-65 -980.000 0.02789211 0. 02841974 1010.000 0.02471540 0.02607413 1040. 000 0.02207445 0. 02294029 1070.000 0.01991685 0.0213(063 1100.000 0.01819780 0.01901272 1130.000 0.01685088 0.01743849 1160.000 0.01577413 0.01586242 190.000 0.01486965 0.01426451 1220.000 0.01400496 0.01349486 1250.000 0.01310077 0.01191419 1280.000 0.01204027 0.01112316 1310. 000 0.01081936 0.01033167 1 40.000 0.00947040 0. 00953971 1370.000 0.00818022 0.00874729 1400.000 0.00 720008 0.00 95441 1430.000 0.00699103 0.00795441 1460.000 0.00823867 0.00716106 INITIAL LOADING OF PROPANE, CELL NO.3 2.4657 MG-MOLS/GM. PERCENT ERROR IN MASS BALANCE -2.5836 CONSTANTS FOR RATE EQUATION 1 DC 1) = 2.39581573E-02 D( 2) -6.61232311E-0O D( 3) = -6.53345102E-0O D( 4) = 5.05995411E-09 D( 5) = -1.58351102E-11 01 6) = 2. 76163504E-14 D ( 7) = -2. 8 7739456E- 17 D( 8) = 1.77i32309E-20 D( 9) = -6.025 99537E-24 D {10) = 8.61045992E-28 CONSTANTS FOR RATE EQUATION 2 D( 1) = -2.36317372E-03 D 2) = 1. 05492288E-04 D0 3) = 4.00810540E-07 DC 4 ) = -6. 53758794E-09 D ( 5) = 2.53260756E-11 D{ 6) = -4.91347861E-14 DC 7) = 5.44347274E-17 D( 8) = -3.49698135E-20 D( 9) = I.21424130E-23 ( 10) = -1. 76472735E-27 CONSTANTS FOR RATE EQUATION 3 DC 1) 1.78564951E-03 D( 2) = -1.00632428E-04 D 3) = 1. 15020046E-06 DC 4) = -3:.61160043E-09 D( 5) = 3.6306424fE- 12 D( 6) = 2.73758560E-15 D 7) = -9. b 7005956F- 1 8 D() = 9.10252297E-21 D( 9) = -3.8832203 E-24 D( 10) = 6.43254971 -28

-66 -REDUCTION OF DATA FOR BED NO. 1 DEPTH OF SILICA GEL TO MID-POINT 1.2300 CMS. POINT NO, I 'TIME POINT OF FI T 128.781 1 SECS. MASS FLOW RATE 0.7749 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.2000 REYNOLDS NUMBER 4.6411 SCHMIDT NUMBER 0.8225 MASS 'TRANSFER COEFFICIENT 0.0369 SEC-1 INTERFACE MOL FRACTION 0.2143 SURFACE CONCENTRATION (TOTAL) 3.1570 MG-MOL/GM. AVERAGE CCONCENTRATION (TOTAL) ON SOLID 3.0588 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 11.9158 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERKIV CORR 1 10.0000E-06 -2. 7585E-101 2 9. 5238E-06 -2.91 33E-0 1 3.2507E 04 -8.9622E-06 3 1.8486E-05 -'1.1666E-01 1.9489E 04 -5.9860E-06 4 2.4472E-05.-6.4093E-02 8.7822E 03 -7.2981E-06 5 3. 1770E- O -2.5298E-02 5.3158E 03 -4. 7590E-06 6 3.6529E-05 -8.1942E-03 3.5940E 03 -2.2800E-06 7 3. 8809E-05 - 1. 4986E-03 COMPUTED DIFFUSION COEFFICIENT 3.8809E-05 SQ CM/SEC PC.INT NO. 2 TIME POINT OF FIT 80.2120 SECS. MASS FLOW RATE 0. 551 MG-MOLS/SEC. MOL FRACTION OF GAS CCONSIDERED 0.4000 REYNOLDS NUMBER 4.2504 SCHMIDT NUMBER 0.8751 MASS TRANSFER COEFFICIENT 0.0361 SEC-1 INTERFACE MOL FRACTION 0.4214 SURFACE CONCENTRATION (TOTAL) 3.0334 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 2.9030 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 16.4909 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERIV CORR 1 3, 8809E-05 -1.2060E-03 COMPUTED DIFFUSION COEFFICIENT 3.8809E-05 SQ CM/SEC POINT NO. 3 TIME POINT OF FIT 68.8669 SECS. MASS FLOW RATE 0.7460 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.5000 REYNOLDS NUMBER 4.1951 SCHMIDT NUMBER 0.8160 MASS TRANSFER COEFFICIENT 0.035: SEC-1

-67 -INTERFACE MOL FRACTION 0.5236 SURFACE CONCENTRATION (TOTAL) 2.9660 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 2.8591 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 17.6422 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERIV CORR 1 3. 8809E-05 -3.0943E-02 2 3.696 1E-05 -3. 7407E-02 3.4980E 03 -1.0694E-05 3 4.7655E-05 -6.2t408E-03 2.9144E 03 -2. 1414E-06 4 14. 9796E-05 - 1.4625E-03 COMPUTED DIFFUSION COEFFICIENT 4.9796E-05 SQ CM/SEC POINT NO. 4 TIME POINT OF FIT 49.1272 SECS. MASS FLOW RATE 0. (290 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.7000 REYNOLDS NUMBER 4.321 0 SCHMIDT NUMBER 0.8311 MASS TRANSFER COEFFICIENT 0.0358 SEC-1 INTERFACE MOL FRACTION 0.7278 SURFACE CONCENTRATION (TOTAL) 2.8113 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 2.7756 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 19.6481 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL 0 ERROR DERIV CORR 1 4. 9796E-05 -8.0230E-02 2 4. 7425E-05 -8.5495E-02 2.2202E 03 -3.8507E-05 3 8.5932E-05 -3.2982E-02 1.3637E 03 -2.4185E-05 4 1. 1012E-04 -1.7838E-02 6.2615E 02 -2.8488E-05 5 1.386-1E-04 -6.6939E-0 3.9118E 02 -1.7112E-05 6 i.5572E-04 -1.9639E-03 COMPUTED DIFFUSION COEFFICIENT 1.5572E-04 SQ CM/SEC

-68 -REDUCTION OF DATA FOR BED NO. 2 DEPTH OF SILICA GEL rTO MID-POINT 3.6900 CMS. POINT NO. 1 TIME POINT OF FIT 326.4326 SECS. MASS FLOW RATE 0.7535 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.2000 REYNOLDS NUMBER 4.5134 SCHMIDT NUMSER 0.8227 MASS TRANSFER COEFFICIENT 0.0364 SEC-i INTERFACE MOL FRACTION 0.2078 SURFACE CONCENTRATION (TOTAL) 3.1607 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 3.0679 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 6.3698 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERIV CORR 1 1.5572E-04 8.0484E-02 2 1.6350E-04 8.1080E-02 7.6516E 01 1.0596E-03 3 1.0900E-04 7.5069E-02 1.1029E 02 6.8066E-04 4 7.2668-E'05 6.5832E-02 2.5422E 02 2.5896E-04 5 4.8445E-05 5.1501E-02 5.9166E 02 8.7045E-05 6 3. 2297E-05 2.9065E-02 1. 3893E 05 2.0920E-05 7 1.1377E-05 -9.9634E-02 6.1520E 03 -'1.6195E-05 8 2.7573E-05 1.7190E-02 7.2134E 03 2.3831E-06 9 2.5189E-05 9.4217E-03 3.2597E 03 2.8903E-06 10 2* 2299E-05 -2.3184E-03 COMPUTED DIFFUSION COEFFICIENT 2.2299E-05 SQ CM/SEC POINT NO. 2 'TIME POINT OF FIT 209.2422 SECS. MASS FLOW RATE 0.7137 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.4000 REYNOLDS NUMBER 4.0176 SCHMIDT NUMBER 0.8754 MASS TRANSFER COEFFICIENT 0.0351 SEC-1 INTERFACE MOL FRACTION 0.4 136 SURFACE CONCENTRATION (TOTAL) 3.0.83 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 2.8423 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 10.2044 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DER IV CORR I 2. 2299E-05 6.4867E-02 2 2.3414E-05 7.0647E-02 5.1842E 03 1.3627E-05 3 9.7867E-06 -6.8546E-02 1.0214E 04 -6.1109L-06 4 1.6498E-05 2.4194E-02 1.381E 04 1.7507E-06 5 1.4747E.-05 6.7538E-03 9.9616E 03 6.7798E-07 6 1.4069E-05 -9.5206E-04 COMPUTED DIFFUSION COEFF 1C IENT 1.4069E'-05 SQ CM/SEC

-69 -POINT NO. 3 TIME POINT OF FIT 189.0098 SECS. MASS FLOW RATE 0.6)'53 MG-MOLS/SEC. MOL FRACTION CF GAS CONSIDERED 0.5000 REYNOLDS NUMBER 3.9100 SCHMIDT NUMBER 0.8163 MASS TRANSFER COEFFICIENT 0.0347 SEC-I INTERFACE MOL FRACTION 0.5144 SURFACE CONCENTRATIOiN (TOTAL) 2.9723 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 2.7949 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 1(0.4206 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERIV CORR 1 1. 4069E-05 -1.4241E-02 2 1.3399E-05 -2.1960E-02 1.1522E 04 -1.9060E-06.3 1. 5305E-05 - 1.4487E-03 COMPUTED DIFFUSION COEFFICIENT 1.5305E-05 SQ CM/SEC POINT NO. 4 TIME POINT OF FIT 142.7455 SECS. MASS FLOW RATE 0.6609 MG-MOLS/SEC. MOL FRACTION CF GAS CONSIDERED 0.1000 REYNOLDS NUMBER 3.9176 SCHMIDT NUMBER 0.831.3 MASS TRANSFER COEFFICIENT 0.o0341 SEC- INTERFACE MOL FRACTION 0.7146 SURFACE CONCENTRATION (TOTAL) 2.8224 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 2.6870 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 9.8705 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERIV CORR 1 1.5305E-05 -.4043E-02 2 1.4576E-05 -1.9631E-02 7.6681[ 03 -2.5601E-06.3 1. 7 136E-05 -- 1 6755E-03 COMPUTED DIFFUSION COEFFICIENT 1.7136E-05 SQ CM/SEC

-70 - REDUCTION OF CATA FOR BED NO. 3 DEPTH OF SILICA GEL TO MID-POINT 6.1500 CMS. POINT NO. 1 TIME POINT OF FIT 515.6765 SECS. MASS FLOW RATE 0.7535 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.2000 REYNOLDS NUMBER 4.5133 SCHMIDT NtIMBER 0.8230 MASS TRANSFER COEFFICIENT 0.0364 SEC-1 INTERFACE MOL FRACTION. 0.2070 SURFACE CONCENTRATION (TOTAL) 3.1611 MG-MOL/GM. AVERAGE CONCENTRATION (TOTAL) ON SOLID 3.1194 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 5.7324 MMG-MOL/GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TR IAL D ERROR DERIV CORR 1 1.' 1 36E-05 -6.8556E-02 2 1.6320E-05 -7.4435E-02 7.2045E 03 -1.0332E-05 3 2.6652E-05 -2.7027E-02 4.5886E 03 -5.8901E-06 4 3.2542E-05 -1.3847E-02 2.2376E 03 -6. 1883E-06 5 3.8730E-05 -4.4874E-03 1.5125E 03 -2.9668E-06 6 4. 1697E-05 -1.0265E-03 COMPUTED DIFFUSION COEFFICIENT 4.1697E-05 SQ CM/SEC POINT NO. 2 TIME POINT OF FIT 386.0540 SECS. MASS FLOW RATE 0.71.39 MG-MOLS/SEC. MOL FRACTION OF GAS CONSIDERED 0.40000 REYNOLDS NUMBER 4.0186 SCHMIDT NUMBER 0.8757 MASS TRANSFER COEFFICIENT 0.0351 SEC-1 INTERFACE MOL FRACTION 0.4113 SURFACE CONCENTRATION (TOTAL) 3.0398 MG-MOL/GM. AVERAGE CONCENtRATION (TOTAL) ON SOLID 2.9054 MG-MOL/GM. RATE OF ADSORPTION OF PROPYLENE 8.5074t MMG-MOL./GM/SEC RESULTS OF ITERATIVE DETERMINATION OF DIFFUSION COEFFICIENT TRIAL D ERROR DERIV CORR 1 4. 1697E-05 7.4038E-02 2 4.3782E-05 7.6907E-02 1.3762E 03 5.5886E-05 3 2.9188E-05 4.8429E-02 1.9514E 03 2.4818E-05 4 4.3704 E-06 -3.077 1E-01 1.4350E 04 -2. 1 4 3E-O 5 5 2.581 3E-05 5. 7432E-02 1.606E 04 2.3256E-06 6 2.3488E-05 2.8116E-02 4.0059E 03 7.0187E-06 7 1. 6469E-05 -1.4456E-02 6. 0656E 03 -2.3833E-06 8 1.8852E-05 3.2347E-03 7.4228E 03 4.3577E-07 9 1.8417E-05 3.0896E-04 COMPUTED DIFFUSION COEFFICIENT 1.8417E-05 SW CM/SEC POINT NO. 3

-71 -r I "'C[' N~ T F(' F ' 41.7' '6 St-F. U"~[Jt. FKAC I I 0 F GAS C iS F t. () S( rLM. IJ C; ' r K 0, l, F66,AS I t<FI ' 0 C( " F F.. " AI N N I(. I1 U ' (C N!, P. A( (T AL) 2. 9'3 t -MOL/ M. A V -A(;F C (,:-; tT ll( * ( ' l CL ()1' 0 S Q L IC 2 I.1 3 P,, L / G G. ~ 'a E OF Ait 'Pfl )'T " (: ''R(PYLrE 8. (310 M'l!O-MOL/GM/SEC ~P-, SilL!', C t' f i;F^'l l 'st i- I I)F ')IFFUSION COEFFICIE' t;T - V., I AJL I' t- k: ~ g Cr 0V L 2t l.','~'~F!: —i).J.Ou33 6 E-02 6.! OU F 03 4.9666E-06 3 1,,l~.S, '{- f - [.11 0 11452E-0[3 1.546(8 0.7 -9.4680E-07 14 7..3 1.F I i- 5 1. b 8 7 -0: 0 3 U COlV!-'T/. ilFO ':iFf'US ION. 0eFF C I [EN I 1. 531 E-('35 S4 C! SECL F01 T C l '. 4 V I T/C PCINT C)F FIT 277.5500 SECS. MASS FLO' R4TI 0.6616 MG-MOLS/SEC. "OL F tACT I O-N CF GAS CONS I )EP. D 0.10i0 R: YNOL. CS NUM t: R 3.921 1 %C'.- -"i' I li, NUTi'/Fl'' R 0.83 1 6 " S S r F, C F F FFICI E N T 0.03 4 1 S ECINTE'[<FACE MOL FIRA(CTI(ON 0.71 1 7,(!JF A'4 C CNCL E\TRA T,ION ( TOTAL) 2 82N48 MG-MOL/GM. VFA C f:: TRA I ON ( TOT AL ) ON SOLID 2.6954 M OL/ GM. PAI: OF AU SORFPTI 1ON OF PROPYLL: E '7.89g, 7 MMG-MOL/GM/SEC Uf'L. S C:F ITERATIVE IETERINArION CF DIFFUSION COEFFICIENT l', IAL -) ERROR DER I V CORR!; Cl1.5.I 1. lf.I — 5 3. 7936E-03 2 1.608.3E 3-()5 8.6103E-03 6.2891E 03 1.3691E -06: 1.,4 7 1 N4E-.) -2. HO80E-04 COT'i'iU rFE! i r I 00.l8FO F FI C I EN T 1.47 14 E-05 SQ CM/SEC AViRAGEL VAL;:Et 'F COCMPUTEU I lFF. COEFF. 3.6841 E-( SQ CM/SEC E',D[ OF DATA P'...CESSiN(; RUN NC. 1

TABLE VII SUMMARY OF DATA PROCESSING RUNS -72 -

-73 - I I CHH oI \) cC C - C r4 \ - CM (M t- L\ - cc) o \\D I CC) Xt CH a) 0 |( CO c\ \ V3 0d L(-\ t_ r 4 Co Ll ' I \) n\ r4 C! CY r-4 C\j C\J CC, H ccxL CO* C O cc~~ — q k mt+e -- **** CO ) OC o L — I e o 4. o QI O V O X ) ) M _ t L CO) CCy)) 4 C-Y -i' (O ~ CCO C J i- r-4 C ]c - 01 O A. ** ) CL-z cO t — h"' [L-' CN '-C co -- CNr C \) CNCO C-C LC,\ L(-\ LCL) ~ ) CQfC \ ) N r KcC t- \ - COr Cr 4O (r\L\Oa 0CM Lr 0_ ON CC) r- r-I ( Cg. L r- - I4 r-I!C I - II I I f I J C D 0 rr q! O (Ca,\) D L, CJ a-) \ID r \ CA cn0 w O 0z M CrJ r-A r ---0 C\j r-4 O CC, 4 Cr) O~j Oj N r', - CC, j C CCJC, CO') 00 c'Q Od C.O C COCOCOC\ MO 'V C_ U) xLRO) LrK 'CJ C -J (h O ad C- C bD I O CrM)O (r0M COj " - (.Y) ON OCt ' 01 -C |0 ~ooo I OQ no 0 C orC aO- ) \,oC r-4 Co (o o o r-4 c -0 ON o 0 CO\ 4 V C * u\x )r~O, —4 ) 0'3 b- C ~J '-4 o i cC ) 0\, _N L.C,D. c n \ID Lr C, C'coo c.COC " C ' C O. 0 " 'J." COO C'J C) COCOC C M ', COCO.I C'. 0C '-C ~* ',\ *. ', C d4 kC\ LcR Cr 'M\ CJ C > —) I-, rq co I Lr\ -4 O L — O'\co L(o' C O c t* -- t- - 0C Ccr a (D a0 a - z- 0t 0 - C O C r Oi O C-4 r-i C OC C rN - C O CO,_q- CO - CO- q CO,' L. C C - C CO C',O - Cr CO- -- CO CD CLr-,. 0 000 000 000 0)0-C 00 0 0 0 0 i -- H S i * * * *.... * * * ~..,] c' C \\D 4 LO CY)\D C\) I L, kO, -4 ( '-) L- r-! c- kC) \D tO.C o o 12 cN- '-. b- -. n eI It C,) " --? (: (L b — ) N-j L- OC)t C) t Jt N y n C-) o) I 9 uc; >COO UCO -c O CO:C) O O O O CO O MO - CO c CO CO cO CO CO cO CO CO ' —i CM C). t -' LC, J7t-t- C O CC O O ChO —CO -'-C O CM'O - O- C - zO 1 L~ N C - L-M 0CM r- C!j 3 ~1 CM CCO u ( \LI- C) r t- C.T\ Or') C O C (OO\ '~q __ -:.1.>1~ - -: C L,,o- _LO QO-,O CY -,-C O, — _COOCN ',O 0 0 ) (0 00 0 CL) 0 (000 0 t- C) 0 i 00 00C 00 0-) 0 ~ 0 00 000 0 00 0 0 0 0 ~, L.- (,, '-t,, t -4 \, -,C-t Od C - ) 40- t - LC,,\ O — CO'j H a- C) Oc (, \ \L O \ C)" C Lf- CD 4r \ | N a) O C C \ O Ch - I O 4 - 01 4 141 -1rd 1 - ( - C\I |O i O I i — L | i | LI ~ AO+ I >U F-|C D 3() m \rC) (vc\(: 6L pAX _......

I 3 4 5 6 1 - o g —l -1 _ ~- 1 _2 3 7 5 6 7 9 IC 1i 12 3 L4 Da ta Infol. imeBulk Mass 1.f Surf. Avg. Ads. Diff. Infe. r~ul k ~ las s. _I.f. Proc.. int.f. Re SC Trans. Conc. Cont. Rate Coeff fromrr Flo mCT~.fr. Re Se 'Trans. m.fr. R W of..1n on ('3L6 X0o5 I o. of 7Bate 02H Coeff. C3 H6 3 ~ ~X0 ~o~. ~vunsFit 1Sol. l. Gi Y kSk Vy* S* A D 3 8,19 1 17.9 1.9.800 7.11.822.0453.832 3.183 3.113 -32.8 24.3 1.15.600 6.48.875.0442.631.o66 3.068 -29.2 31.7 1.13,500 6.39.875.0440.528 3.001 3.022 -25.5 33.9 59.3 1.11.300 6.56.831.0437.318 2.849 2.895 -15.7 11.4 26.6 1.30.800 7.79.822.0473.807 3.169 3.46 -7.01 1.13 53.5 1.23,600oo 6.95.875.0457.610 3.053 3.193 -9.80 1.22 69.0 1.20.500 6.76.876.0452.511 2.989 3.158 -10.2 1.23 148-.4 1.15.300 6.79.831.0444.307 2.840 3.001 -6.53 1.29 3 67.4 1.30.800 7.81.823.0473.809 3.169 3.210 -9.15 5.55 105.1 1.23.600 6.95.875.0457.610 3.053 3.127 -9.90 3.79 142.7 1.20.500 6.77.876.0452.509 2.988 2.047 -8.76 4.48 259.9 1.15.300 6.79.831.0444.305 2.839 2.878 -4.44 3.52 - avg. value of D 3.73 4 10, 1 220.0.396.800 2.375.823.0267.211 3.138 3.002 6.85 1.64 16, 158.2.386.600 2.174.876.0261.584 3.016 2.888 8.65 2.09 18, 136.7.382.500 2.125.877.0260.483 2.945 2.844 9.25 2.69 20 96.7.373.300 2.10.832.0259.280 2.796 2.755 10.3 7.38 2 565.6.385.800 2.308.823.0263.792 3.139 3.053 4.74 1.81 434.7.365.600 2.054.876.0254.588 3.018 2.885 6.28 1.39 391.8.356.500 1.999.877.0251.512 2.952 2.823 6.458 1.39 306.7.338.300 2.002.832.0247.288 2.802 2.700 6.04 1.52 3 878.6.385.800 2.308.823.0263.793 3.140 3.064 4.28 1.74 737.9.365.600 2.054.876.0254.590 3.019 2.902 5.62 1.44 692.1.356.500 1.999.877.0251.489 2.953 2.8L2 5.75 1.48 597.0.333.300 2.002.832.0247.289 2.803 2.720 5.38 1.71 avg. value of D 2.19

2 3 64 5 8 9 10 11 12 13 Data Time I.f. Surf. Avg. Ads. Dff Proc. Col. Point MoR. SM.f. Con. Con Bate off frs~~~~ Flow m~f, rnCef Bun fP-rom No. of Bate M H NO. No. Trans. Son Sol. 3H6 C No. Runs Fit 3 6 Coeff. Sol. Soln X106 x105 G y k y* 3* m QA D 5 11 1 34.9 1.57.80I 9.40.775.0539.836 4.985 4.860 -38.9 45.9 1.55.600 8.72.824.0531.632 4.908 4.818 -34.0 68.8 1.53.4oo 8.77.811.0529.425 )L.813 4r.745 -25.9 121.8 1.51.200 9.52.738.0534.215 4.688 4.635 -14.6 2 60.9 1.64.800 9.81.775.0550.814 4.978 4.999 -15.7 3.60 93.2 1.60.6oo 9.01.824.0539.617 4.901 4.939 -18.6 3.78 148.5 1.57.400 8.957.81i..0535.416 4.8o8 4.834 -16.2 6.09 300.0 1.53.200 9.62.739.0536.204 4.68. 4.682 -4.08 6.09 3 138.4 1.64.800 9.81.775.0550.811 4.976 4.981 -11.8 6.1o l9l.6 1.60.6oo 9.01.825.9539.625 4.899 4.909 -13.1 6.09 265.1 1.57.500 8.95.811.0534.511 4.806 4.811 -11.6 6.og 485.4 1.53.200 9.62.739.0536.204 4.681 4.64o -3.68 avg. value of D 5.40 6 13 1 102.4.797.800 4.77.773.0390.826 5.ol4 4.808 -20.2 131.9.788.600 4.43.823.9384.624 4.937 4'.750 -17.9 170.3.779.400 4.46.810.0383.420 4.844 4.683 -15.1 273.8.771.200 4.84.737.0386.213 4.722 4.553 -9.21 2 187.8.832.800 4.98.773.0398.8io 5.009 5.026 -7.74 3.10 251.4.813.6oo 4.58.823.0390.611 4.932 4.972 -8.25 3.10 356.2.796.400 4.55.810.0387.410 4.839 4.886 -7.14 3.10 625.5.779.200 4.89.737.0388.204 4.716 4.749 -2.86 3.10 3 309.6.832.800 4.98.774.0398.807 5.008 5.008 -5.43 416.4.814.6oo 4.58.823.0390.608 4.931 4.940 -6.32 3.10 562.9.795.400 4.55..810.0387.407 4.838 4.847 -5.49 3.10 953.3.779.200 4.89.737.0388.203 4.715 4.709 -i.85 avg. vaLue of D 3.LU

1 2 3 4 5 6 7 8 10 II 12 13 14 Data Time roc. nf o Mol. BEuk Re Sc Mass I.f. Surf. Avg. Ads. Diff. ' romun ol. Pon Flow m.f. Trans. m.f. Conc. Conc. Rate Coeff. fron C Y ky y s* m fA D 7 21,23 1 38.6.554.800 3.32.823.0314.822 3.168 3.099 -157.. 59.1.538.600 3.03.876.0307.620 3.050 3.032 -13.3 74.7.530.500 2.98.877.0305.519 2.985 2.987 -11.8 78.8 129.1.517.300 3.06.832.0303.313 2.835 2.867 -7,83 7.83 2 60.4.607.800 3.64.823.0328.804 3.158 3.242 -3.25.375 138.3.577.600 3.24.876.0317.607 3.042 3.164 -4.957.844 167.5.562.500 3.16.877.0313.508 2.977 3.131 -4.96.715 303.9.535.300 3.17.832.0308.305 2.829 2.999 -3.29.598 3 164.4.609.800 3.64.823.0328.806 3.159 3.191 -4.14 3.42 252.9.577.600 3.25.876.0317.607 3.041 3.102 -4.54 2.22 313.2.562.500 3.16.877.0313.507 2.977 3.040 -4.32 2.01 515.4.535.300 3-17.932.0308.305 2.828 2.875 -2.84 2.01 avg. value of D 2.00 8 22,24 1 85.3 l.14.800 6.83.822.0444.785 3.156 3.017 15.-4 3.69 49.5 1.1L.600 6.25.875.0435.576 3.032 2.865 22.5 4.10 40.0 1.10.500 6.18.875.0433.472 2.963 2.814 24.9 4.99 27.3 1.07.300 6.37.832.0431.266 2.807 2.737 28.6 12.3 2 221.9 1.11.800 6.65.822.0438.792 3.161 2.975 7.49 1.35 133.2 1.05.600 5.92.875.0223.587 3.039 2.781 11.6 1.11 107.1 1.02.500 5.76.876.0418.486 2.973 2.710 12.2.95 69.4.974.300 5-77.831.041.287 2.823 2.609 10.9.71 353.4 1.11.800 6.65.823.0438.794 3.1]62 3.100 5.88 3.02 243.3 1.05.600 5.92.876.0423.589 3.040 2.900 9.86 2.12 205.9 1.02.500 5.76.876.0418.488 2.974 2.814 10.5 1.79 148.5.975.300 5078.832.041L.288 2.825 2.681 9.60 1.53 avg. value of D 3.14 _-~~~~~~~~~~~~~~~~~~~~~31

41 2 4 6 7 8 9 10 11 12 l~ 14 Data Time 1Mol. Bulk QCfas I.f. S ff Avg. Ads. Diff. Proc. In Uo. Col. Point FLow M.f. Be c r Conc. Conc- Rate Coeff. from Nranso. m. o Non Buns Fito. o6 Rate 3H No. No. Coeff. C3H6 on on Cl3H6.105 NTo. Fit Sol. Sol. x106 G yJ' ky y3 S m QA D 9 25 1 28.3 2.15.8oo 12.8.781.0622.844 4.843 4.636 -55.4 34.4 2.12.6oo 11.9.831.06i3.639 4.762 4.601 -47.1 45.5 2.09.400 11.9.818.611.429 4.774 4.550 -34.8 77.5 2.07.200 12.9.745.0616.213 4.532 4.465 - 1a4.9 2 33. 0 2.25.800 13.4.782.0636.805 4.829 4.905 -6.78.i6 63.4 2.19.600 1 2.3.831.0623.612 4.751 4.866 -14.3 1.00 69.7 2-14.400 12.2.818.o617.413 4.655 4.856 -14.9.42 177.6 2.09.200 13.1.745.o6i9.208 4.529 4.690 -9.62.83 3 90.3 2.25.800 13.4.782.0636.813 4.832 4.828 -L7.4 122.9 2.19.600 12.3.832.0623.614 4.752 4.762 -17%6 8.28 101.0 2.14.400 12.2.819.617.415 4.656 4.806 -17.8 1.24 317.5 2.09.200 13.1.750.0619.206 4.527 4.506 -6.76 avg. value of D 2.00 10 26,28 1 84.3.781.800 4.29.862.0375.787 2.216 2.095 11.9 4.51 53.5.751.6oo 3.88.917.0365.581 2.083 1.958 16.1 5.44 36.4.726.400 3.81.903.0360.375 1.938 1.862 19.0 l0.6 25.6.705.200 4.o6.822.0369.170 1.768 1.792 21.1 2 204.5.747.800 4.11.862.0367.793 2.220 2.027 6.26 1.47 136.3.688.6oo 3.55.920 -.0350.589 2.089 1.859 8.95 1.47 96.9.637.400 3.35.903.0338.387 1.947 1.742 9.39 1.35 68.2.593.200 3.42.822.0331 1-87 1.784 i.66o 8.23 1.62 3 223.9.747.800 4.11.863.0367.793 2.220 2.180 6.25 5.99 238.9.688.600 3.55.918.0350.582 2.088 1.964 9.31 3.23 192.8.637.400 3.34.904.0338.387 i.947 1.823 9.33 2.77 152.3.593.200 3.42.823.0331.188 1.785 1.712 7.67 3.49 avg. value of D 3.81

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Data Time Mol. Bulk Mass I.f. Surf. Avg. Ads. Diff. Inf o. Proc. fo Col. Point Flow M.f. Re Sc Trans M.f. Conc. Conc. Rate Coef f ~un fo N. of Rate C3H6 No. No. Coeff. C3H6 on on ( 3H6 xlo5 No. 'Runs Fit Sol. Sol. X1o6 G y ky S* Sy m QA D 11 27,29 1 39.9.466.800 2.56.863.0293.819 2.226 2.106 -14.2 57.7.446.6oo 2.30.919.0283.618 2.098 2.032 -11.7 82.1.427.400 2.24.904.0278.415 1.957 1.951 -8.94 138.1.411.200 2.37.823.0277.209 1.792 1.831 -4.91 5.44 2 84.1.536.800 2.95.863.0313.806 2.218 2.279 -4.89 2.99 124.8.492.600 2.54.919.0297.608 2.091 2.209 -5.61 1.79 184.7.456.400 2.39.904.0287.4o8 1.952 2.105 -5.04 1.35 341.4.425.200 2.45.823.0282.204 1.787 1.939 -1.81.+72 3 157.7.534.800 2.94.863.0312.806 2.217 2.244 -4.37 4.99 224.8.492.6oo 2.54.919.0297.607 2.090 2.146 -4.62 2.88 334.7.456.400 2.39.904.0287.406 1.951 1.993 -3.86 3.65 -1 597.0.425.200 2.45.823.0282.203 1.788 1.761 -1.88.. avg. value of D 2.98 12 31,33 1 22.0.907.800 4.92.867.0494.827 2.143 2.001 -27.5 32.0.864.6oo 4.42.923.0391.625 2.015 1.917 -23.0 51.5.826.400 4.29.908.0382.420 1.873 1.791 — 16.4 92.3.794.200 4.53.827.0381.211 1.709 1.630 -8.45 2 40.3 1.04.800 5.68.868.0432.8o6 2.130 2.195 -6.77 2.91 57.9.956.6oo 4.89.923.0410.6o8 2.003 2.152 -7.77 1.36 133.8.884.400 4.6o.909.0396.4o8 1.865 2.011 -6.77 1.82 222.4.821.200 4.69.827.0388.203 1.702 1.855 -2.39 1.00 3 74.1 1.04 4.800 5.68.868.0432.807 2.131 2.179 -7.55 5.4o 118.4.958.6oo 4.90.923.0410.609 2.004 2.960 -8.14 5.40 188.4.884.4o0 4.60.909.0396.407 i.864 1.893 -6.02 7.71 355.5.821.200 4.69.828.0388.204 1.702 1.675 -2.76 avg. value of D 3.66

2 3 4 5 6 7 8 9 10 1 121 Data MTime mz O Buk Mass I.f. Surf. Avg. Ads. Diff. Po. Info. Tie M. Bl Proc. Col. Point F low n.f. Re Sc Trans. m.f. Cone. Conc. Rate Coeff. from No. of Rate C3H6 No. NO. Coef f. 3H6 on on C3H6 X105 No. Runs it Sol. Sol. 3 y ky YX S* m DA 13 12 1 164.5 1.34.8oo 8.01.773.0500.786 4.999 5.075 14.3 94.8 1.32.6oo 7.44.823.0493.575 4.917 4.942 23.8 67.2 1.31.400 7.49.809.0491.367 4.816 4.863 30.9 58.3 1.30.200 8.14.737.0496.164 4.687 4.833 33.9 2 392.5 1.32.800 7.92.773.0497.792 5.002 14907 7.99 1.22 236.1 1.29.6oo 7.28.823.0487.586 4.921 4.738 13.4.88 161.1 1.27.400 7(.23.810.o483.382 4.824 4.618 16.8.67 103.9 1.24.200 7.77.737.0483.184 4.702 4.519 15.0.13 3 627.4 1. 32.8oo 7.92.773.0497.793 5.003 4.983 6.56 2.49 415.2 1.29.6oo 7.28.823.9487.591 4.923 4.812 9.06 1.35 297.3 1.27.400 7.23.810.0483.389 4.828 4.691 lo.o 1.00 207.1 1.24.200 7.78.737.0485.191 4.707 4.604 7.89.72 avg. avlue of 1.06 14 36,38 1 71.8.627.800 3.18.900.0342.788 1.525 1.464 11.5 10.0 50.0.595.600 2.84.958.0330.582 1.394 1.351 14.5 16.6 38.1.569.400 2.76.943.0324.377 1.259 1.268 16.4 29.3.548.200 2.91.859.0323.173 1.111 1.206 17.6 2 176.6.587.800 2.977.901.0331.792 1.527 1.412 7.62 3.97 219.9.521..6o0 2.48.958.0310.588 1.398 1.243 9.34 3.14 98.4.468.400 2.27.943.0295.386 1.265 1.121 3.90 2.62 75.0.424.200 2.26.859.0285.187 1.122 1.041 7.32 3.46 3 292.1.587.800 3.00.901.0331.793 1.528 1.522 6.76 31.1 227.4.52i.6o0 2.48.959.0310.589 1.398 1.313 8.35 5.42 191.7.469.400 2.27.944.0295.388 1.266 1.190 7.90 5.42 158.7.425.200 2.26.859.0285.189 1.12_3 1.090 6.42 9.03 avg. value of D 6.63

1 2 3 4 5 6 7 9 10 11 12 13 -F Data Time Surf. Avg. Ads. Proc. Info. Mol. Bulk Mass Ifif ~TColn Point Conc. Cone. Rate Run from No. o Flow m Re Sc on on C3H6 o No. Runs Ft Rate C3H6 No No. Coef 6 Sol. Sol. X106 G y ky y* s* m QA D 15 35,37 1 19.8 1.04.800 5.29.900.0437.828 1.540 1.288 -33.6.. 27.5.970.600 4.63.958.0418.626 1.422 1.101 -27.2 38.2.914.400 4.43.943.0407.422 1.289 l.086 -20.2 65.7.868.200 4.62.859.0403.212 1.141.922 -9.82. 2 31.7 1.24.800 6.31.900.0475.807 1.537 1.617 -8.67 3.13 52.4 1.10.600 5.27.958.0445.610 1.412 1.532 -10.4 3.76 75.7.995.400 4.82.943.0424.410 1.281 1.435 -9.25 3.02 156.6.905.200 4.82.860.0411.203 L.13.4 1.249 -2.62 1.98 3 55.9 1.24.800 6.30.901.0475.808 1.538 1.583 -10.7 10.8 85.9 1.11.600 5.28.958.0445.610 1.412 1.445 -10.6 15.1 113.4.996.400 4.83.943.0424.407 1.279 1.270 -6.93 244.8.905.200 4.81.859.0411.204 1.135 1.071 -3.048.. avg. value of D 6.30 91L.8oo.82'~ 3.054.30 16 45,47 1 94.5.843.800 5.05.823.0384.775 3.132 3.054 21.7 8.52 79.2.821.600 4.62.876.0376.510 3.009 2.974 23.8 20.5 73.2.812.500 4.56.876.0374.468 2.941 2.941 24.5 62.8.793.300 4.70.831.0372.266 2.786 2.082 25.2 2 232.9 ~820.800 4.91.823.0379.777 3.133 3.013 19.4 5.05 207.6.776.600 4.37.876.0366.572 3.010 2.892 21.7 5.33 197.4.756.500 4.25,877.0361.471 2.943 2.842 21.8 6.05 180.2 ~719.300 4.26.832.0355.270.2790 2.757 20.9 ]8.1 3 374.1.820.800 4o91.823.0379.774 3.131 3.097 22.5 19.6 247.5.776.600 4.37.876.0366.569 3.008 2.954 23.8 13.7 337.1.756.500 4.25.877.0361.469 2.941 2.898 23.5 15.6 326.5.718.300 4.26.832.0355.268 2.787 2.842 22.8 avg. value of D 12.4

2 3 4 5 6 7 8 9 10 11 12 13 14 '-)ata Inf 0 Time Mol. Bulk Mass I.f Surf Avg. Ads ]iff -IL-roc from Col. Point Flow M.f. Trans. Conc. Conc. Rate Coeff. Proc. from No.w m~sof B m)f. Bate Bun Fo. o. e oc eff on x~o5 Buns Rate C3H6 36oe f c36 o Sol. 36 X10 G I kk y Sg m Q D 17 46 1 36.8.942.800 5.64.823.0405.830 3.163 2.975 -27.8 49.7.914.6oo 5.14.876.0396.629 3.045 2.898 -24.6 56.3.902.500 5.07.876.0396.528 2.981 2.862 -23.0 77.0.878.300 5.20.83i.0390.324 2.834 2.764 -18.6 2 103.7 1.02.800 6.19.823.0424.816 3.155 3.081 -15.4 128.0.980.600 5.51.876 0409.618 3.039 2.993 -16.1 157.9.956.500 5.37.877.0404.510 2.975 2.884 -15.7 230.8.909.300 5.39.832.0398.315 2.827 2.650 -11.9 3 193.5 1.04.800 6.21.823.0424.800 2.151 3.100 -9.35 247.8.981.6oo 5.52.876 0410.611 3.035 2.978 -10.0.. 283.9.956.500 5.37.877.0404.511 2.970 2.897 -9.40 389.1.909.300 5.39.832.0398.308 2.820 2.711 -5.89.. avg. value of D 18 48 1 72.8.938.800 5.62.803.0411.822 4.174 3.498 -50.4 86.7.922.600 5.19.855.o4o4.620 4.080 3.402 -44.2 108.6.907.400 5.19.8411.0402.418 3.968 3.316 -37.9 135.5.892.200 5.60.766.o4o4.212 3.825 3.1-56 -24.2 2 166.2.996.800 5.97.803.0423.806 4.167 4.667 -14.4 212.8.965.600 5.43.855.0412.6. 4.075 4.532 -23.8.13 260.2.934.400 5.24.841.0414.41i4 3.966 4.343 -29.5 99 360.4.906.200 5.69.766.0407 3.828 3.864 -33.4 13.8 3 292.5.997.800 5.97.804.0423.805 4.167 4.114 -10.8 366.8.965.6oo 5.43.855.c413.606 4.042 3.983 -12.4 437.5.934.400 5.34.841.0407.405 3.961 3.858 -11.0 568.1.906.200 5.69.766.0407.202 3.817 3.699 -5.14 avg. value of D 5.00

1 2 3 4 5 6 7.8 9 LO0 11 12 13 14 Data Time Surf. Diff. Proc. Col. Point Mol. Bulk Mas. If Conc Avg. Ads. Codff Roc from f. o Flow m.f. Re Sc Trans. m.f. Conc. Rate 5 Run No. oRe SC No. Runs Fit Rate C3H6 Coeff. C3 H6 Sol. Sol. C3H6 G y ky y* s* m QA D 19 14 1 107.9 1.19.800 7.11.802.0o460.784 4.182 4.077 15.2 2.86 68.i 1.17.600 6.57.854.0453.575 4.082 3.968 22.5 3.77 51.8 1.15.400 6.58.840.0451.370 3.964 3.910 26.5 7.69 37.9 1.13.200 7.13.765.0454.165 3.812 3.852 30.5.. 2 277.2 1.16.800 6.99.803.9457.794 4.186 3.881 5.63.29 116.2 1.13.600 6.36.854.0445.592 4.090 3.712 7.58.090 85.7 1.09.400 6.26.840.0440.492 3.978 3.680 6.55.090 63.5 1.06.200 6.67.765.0440.194 3.835 3.660 5.17.099 3 464.4 1.17.800 6.99.803.0457.796 4.187 3.963 3.21.305 237. 133 600 6.37.854.0445.593 4.090 3.802 6.62.305 144.9 1.09.400 6.26.841.0440.392 3.978 3.708 6.70.173 89.1 1.06.200 6.67.765.0439.194 3.836 3.659 4.85.08L avg. value of D 1.15 20 15 1 38.2 1.28.800 7.67.802.0477.834 4.222 4.048 -34.6 52.1 1.26.600 7.09.853.0469.631 4.028 3.983 -29.6. 68.6 1.24.400 7.08.840.0467.427 4.017 3.918 -24.4 108.5 1.22.200 7.65.764.0470.217 3.874 3.804 -15.4 2 64.1 1.36.800 8.15.802.049L.807 4.209 4.260 -6.69 1.00 85.3 1.32.600 7.40.853.0479.608 4.117 4.237 -7.94.51 121.5 1.27.400 7.29.840.0473.410 4.007 4.192 -8.85.51 277-9 1.23.200 7.77.764.0473.206 3.865 4.018 -5.54.70 3 89.3 1.36.800 8.14.802.0491.806 4.209 4.275 -6.39.70 146.7 1.31.600oo 7.41.854.0479.609 4.117 4.21o0 -8.50 1.14 237.2 1.28.400 7.30.840.0473.408 4.006 4.100 -7.55 1.44 463.8 1.23.200 7.76.765.0473.203 3.863 3.938 -2.93 1.06 avg. value of D.76

1 2 3 4 5 6 7 b 9 10 11 12 13 14 Data mime Surf Avg. Ads. Diff Proc. Info. Col. Point Mol. Bulk Re Sc Mass. I.f Conc. Conc. Rate Coeff. from Flow m.f. Trans. m.f. Run N. oCfNo. of on on CfH6 XIo5 Run Runs Fit Rate C3H6 Coeff~ C3H6 Sol. Sol. G Y ky Y S m QA D 21 30 1 120.5.458.800 2.49.868.0290.789 2.119 1.963 8.09 2.35 87.4.440.600 2.25.923.0282.584 1.988 1.863 10.1 3.51 63.4.425.400 2.21.909.0278.380 1.844 1.777 11.5 7.29 43.6.412.200 2.35.828.0278.177 1.679 1.798 12.6 2 308.9.437.800 2.38.868.0284.792 2.121 2.009 5.77 2.61 238.5.401 o600 2.05.923.027.588 1.990 1.854 7.34 2.21 181.1.370.400 1.92.909.02650.387 1L849 1.712 7.29 1.95 134.4.344.200 1.96.828.0255.188 1o689 1.608 5.88 2.41 3 502.1.437.800 2.38.868.0284.793 2.122 2.044 4.97 2.83 413.7.401.600 2.04.924.0270.589 1.991 1.875 6.44 2.21 347.0.370.400 1.92.909.0260.489 1.850 1.730 6.30 2.21 289.6.343.200 1.96.828.0255.19 1.690o 1.621 5.02 2.58 avg. value of D 2.92 22 34 1 114.1.947.800 5.15.851.0417.785 3.023 3.010 13.9 15.6 76.6.923.600 4.72.905.0409.578 2.907 2.873 19.2 15.6 57.9.902.400 4.69.891.0405.372 2.775 2-787 22.3 44.4.883.200 5.04.811.0oi06.169 2.717 24.6 2 279.1.921.800 5.02.851.0412.792 3.027 2.929 (7.69 2.72 186.4.874.600 4.47.906.0398.546 2.913 2.729 11.5 1.79 137.3.831.400 4.31.891.0389.385 2.783 2.600 11.8 1.38 97.6.792.200 4.52.812.0386.186 2.627 2.501 10.1 1.38 3 440.1L.921.8oo 5.02.851.0412.793 3.027 3.090 t6.64 324.3.874.600 4.47.906 ~0398.586 2.912 2.862 10.8 5.44 265.2.831.400 4.32.891.0389.386 2.784 2.715 11.2 5.44 207.5.792.200 4.52.812.0386.186 2.628 2.579 9.47 5.44 avg. value of D 6.0o8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Data Time Surf. Avg. Proc. Inf. CoMLo. oint Mlo. ulk Be Sc Mass I.f. Conc. Conc. Ads. Run from No. F low m.f. Trans m.f. on Rate Coeff. Run No. Run s.. N Buns RuFit ate C3H6 Coeff. C3H6 Sol. Sol. C3H6 X105 G y ky Y* Sm A D 23 49,51 1 78.3.607.800 3.32.866.0333.792 2.161 2.045 17.5 6.21 66.8.584.600 2.99.921.0323.591 2.032 1.976 18.9 13.4 60.9.564.400 2.94.907.0319.390 1.891 1.939 19.3 55.5.547.200 3.13.826.0318.189 1.728 1.905 19.4 2 186.5.580.800 3.17.866.0325.807 2.162 1.887 15.3 2.31 165.3.533.600 2.73.922.0309.609 2.031 1.774 16.9 2.31 150.6.492.400 2.56.907.0298.390 1.892 1.693 16.4 2.66 144.3.457.200 2.62.826.0292.190 1.729 1.660 15.7 7.88 3 301.8.580.800 3.17.877.0325.792 2.161 2.043 17.2 5.72 281.0.533.600 2.74.922.0309.591 2.032 1.922 18.1 6.56 265.7.492.400 2.57.907.0299.390 1.891 1.833 17.3 11.0 254.1.450.200 2.62.827.0292.190 1.729 1.770 15.9 avg. value of D 6.45 24 50 1 35.9.746.800 4.07.866.0367.810 2.164 1.937 -24.3 49.5.711.600 3.65.921.0356.609 2.036 1.836 -20.8 65.8.681.400 3.55.907.0349.409 1.896 1.760 -17.2 89.4.655.200 3.75.826.0347.207 1.736 1.022 -12.3 2 83.7.856.800 4.67.866.0392.804 2.160 2.168 -11.1 23.2 122.1.787.600 4.04.922.0373.605 2.033 2.018 -12.1 161.7.728.400 3.79.907.0360.405 1.894 1.868 -10.6 230.6.677.200 3.88.826.0353.203 1.733 1.677 -6.30 3 149.4.858.800 4.68.866.0393.802 2.160 2.112 -8.38 203.4.788.600 4.05.922.0374.604 2.032 1.959 -8.40 258.7.728.400 3.80.907.0361.403 1.892 1.821 -6.36 366.9.677.200 3.88.825.0353.202 1.731 1.662 -3-17 avg. value of D

1_ 2 3 4 5 6 7 8 9 10 11 12 13 14 Data Time Surf. Ave. Proc. Info Co1. point Mol. Bulk Re SC Mass. I.f. Conc. Cone. Ads. Diff. from Flow r.f. Trans. m.f. Rate Coeff. Runs Rate C HR6 Coeff. C3H6 Sol. Sol. C H x6oS No. Fi ol o. 3= G y ky m D 25 52 i 64.2.551.800 1.38.823.0491.8o6 3.140 2.961 -17.1 87.1..534.600 1.25.876.0479.606 3.021 2.876 -1-5.3 110.6.520.400 1.24.862.0474.405 2.886 2.799 -13.3 149.8.307.200 1.33.785.0475.204 2.721 2.693 -10.1 2 1y74.6.605.800 1.51.824.0514.803 3.140 3.092 -8.86 233.4.573.6oo 1.35.876.0497.603 3.020 2.965 -9.71 311.4.545.400 1.20.862.o485.403 2.884 2.797 -8.77 436.1.519.200 1.36.785.0480.202 2.719 2.594 -5.30 3 309.8.696.800 1.514.824.0514.802 3.1.38 3.1 04 -5.66 403.7.574.600 1.135.876.o496.602 3.019 2.975 -6.04 527.2.545.4oo 1.300.863.0485.402 2.883 2.818 -4.83 436.6.519.200 1.359.785.0480.201 2.71a8 2.645 -2.48.. avg. value of D 26 53 1 152.2.505.800 1.26.823.0471.795 3.143 3.040 13.5.776 131.9.492.699 1.16.876.o46o.595 3.024 2.975 14.5 1.35 113.8.481.400 1.15.862.o456.606 2.887 2.914 15.1 94.6.470.200 1.23.785.0458.194 2.721 2.847 15.2 2 367.3.491.800 1.23.823.o464.796 3.144 2.953 11.5.34 332.6.465.6oo 1.09.876.0447.595 3.024 2.856 12.9.34 299.9.442.400 1.05.862.0437.395 2.888 2.758 12.9.44 264.8.420.200 1.09.785.9433.195 2.723 2.658 11.5.76 3 570.2.491.800 1.23.824.0464.795 3.143 3.057 14.1.76 537.9.465.6oo 1.09.876.9447.594 3.024 2.949 14.9.95 508.9.442.400 1.05.862.0437.394 2.887 2.851 14.5 1.44 476.9.420.200 1.10.785.9433.194 2.722 2.749 13.0 avg. value of D.80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Data Time Surf. Avg. Dataroc. Info. Col. PoBulk Re Sc Mass f Surf Avg. Ads. Diff. Fro. from Col. Point Flow M~f. Re SC Conc. oRe ScC Run No. of on on Rlun fromf Flow m.f. Trans. m.f. on on Pate Coeff. No. Runs PaFi t e C 3H6 Coeff. C3H6 Sol. Sol. C3R6 X105 G y ky y* s* m QA D 27 56 1 30.8.877.800 2.19.823.0616.813 3.153 3.031 -259 44.7.851.600 1.99.875.0601.611 3.035 2.954 -22.0 61.6.828.400 1.98.862.0595.410 2.899 2.877 -17.9 98.2.807.200 2.11.785.Q596.207 2.733 2.755 -11.6 2.04 2 72.4.965.800 2.41.823.0645.805 3.149 3.186 -10.6 2.04 115.2.913.600 2.14.876.0622.606 3.031 3.072 -12.1 2.04 174.6.868.400 2.07.862.o608.406 2.896 2.917 -10.3 2.04 286.7.826.200 2.16.785.0603.203 2.730 2.716 -5.71 3 144.9.965.800 2.41.823.0645.804 3.148 3.123 -8.63 219.4.914.600 2.15.876.0622.605 3.031 2.962 -9.59 323.2.868.400 2.07.862.0608.404 2.895 2.758 -7.41 535.5.826.200 2.16.785.0603.202 2.729 2.502 -3.98.. avg. value of D 2.04 28 57 1 114.9.657.800 1.643.823.0535.792 3.142 2.993 14.6.56 96.1.641.600 1.504.876.0524.590 3.021 2.926 16.4.87 77.5.625.400 1.492.862.0519.389 2.884 2.853 17.8 2.45 54.9.612.200 1.602.785.0521.1_87 2.715 2.758 19.1.. 2 306.3.639.800 1.597.823.0528 -793 3.142 3.059 11.9.90 258.0.605.6oo 1.420.876.0509.591 3.022 2.914 13.9.70 221.6.575.400 1.371.862.o498.391 2.885 2.797 13.8.70 178.4.547.200 1.434.785.0493.192 2.720 2.671 11.3.97 3 502.6.639.800 1.597.823.0528.793 3.142 3.145 11.8 449.3.605.600 1.421.876.0509.591 3.022 2.986 13.9 1'45 40o.3.575.4oo00 1.371.862.0498.391 2.885 2.832 13.6 1.45 354.6.547.200 1.434.785.0493.192 2.720 2.698 11.1 2.07 avg. value of D 1.17

-87 -D. Summary of Data Processing Runs The 25 useable data processing runs yielded an average value of the diffusion coefficient D of 3.65 x 10-5 sq. cm per sec. The standard deviation was 2.59 x 10-5 and the 95% confidence limits on the expected value of D as computed by the Student "t" method(3) for 25 observations were determined as (3465 + 1.06) x 10-5 sq. cm, per seco No effect of temperature or pressure was observed over the range of those variables obtainable in this apparatus, The averaged value of D reported is for all three particle sizes used and for all temperatures and pressures used,

DISCUSSION OF THE DATA PROCESSING RESULTS A. Adsorptive Relative Volatility Lewis et al.(14, from a series of equilibrium studies reported values of adsorptive relative volatility defined by Equation (46) for the system propylene-propane-silica gel of from.31 to.5. This was for a pressure range of 1 to 7.85 atmo At atmospheric pressure and above, the reported relative volatility of.31 could not be used in the data reduction step because it consistently gave particle boundary propylene concentrations which indicated extremely high diffusion coefficients (io.e - very flat, even inversely sloped gradients in the particle) for propylene desQzoption runs and very small coefficients for propylene adsorption runs. On the assumption that the value of D should be independent of the direction of propylene flow, the adsorptive relative volatility was adjusted to a value of.5, This was used throughout the data processing runs as reported above, The average of D for 13 propylene 'adsorption runs was 3.96 x 10-5 sq. cm. per sec. and for 12 propylene desorption runs 3,32 x 10-5 sq. cm, per sec, BO Nature of the Diffusion Coefficient Gaseous diffusion coefficients fall normally in the range.1 to 1. sq. cm. per sec, Liquid diffusion coefficients are usually in the range 0.3 to 5. x 10'5 sqo cm. per seco(20) Coefficients for diffusion of -gaseous species through solids are normally much smaller -83 -

-8 9 --10 of the order of 10 sq. cm,. per sec. The value determined in this investigation falls as might be expected in the liquid range. The lack of effect of the four-fold change in pressure obtained in this study also indicates that the diffusion is taking place in a highly compressed adsorbed state which amounts to essentially liquid diffusion.

RECONSTRUCTION OF CONCENTRATION HISTORIES Plug-Flow Model Calculations In the following section the results of recalculating the concentration histories according to the plug-flow model with adsorption rate controlled by homogeneous particle diffusion with an average D of 3.69 x 10-5 sq0 cm,/sec are shown for several runs, some composite. Figure 9 shows the results of calculations on a composite of runs 3, 7, and 9, These runs were made on adsorbent of average diameter "28 cm,, with a flow rate of.80 mg-mols/sec at the inlet and at a temperature of 00~C The pressure was approximately atmospheric, Propane was being desorbed, Figure 10. contains the graphical results of calculations on 6 and 17, These were at a temperature of 0~C, adsorbent diameter of.28 cm a flow-rate of.78 mg-mols/sec and a pressure of *97 atm, Propylene was being desorbed, The above two runs were made at the.-same temperature and pressure with almost identical flow-rates, It is interesting to note the difference in the shape of the curves caused by the relative volatility being different from a value of one, Figure 11 indicates the results obtained from runs 45 and 47, Conditions here were; temperature - 0~C, pressure -.o98 atm,, particle diameter -.117 cm, and flow rate - o78 mg-mols/seco Notice the considerable steepening of the curves due to decreased particle size and thus increased adsorption rates,

-91 -Figure 12 contains results from run 56 at 0~C, ~98 atm., particle diameter of.98 cmd and flow rate of 479 mg-moles/sec., Figure 13 presents the results of calculations on run number 52. This run was at.98 atm. pressure, OOC temperature for a particle diameter of.111 cm, The flow rate at the inlet was.495 mg-mols/sec.

'.0 0~.9.8 0~~~~~~.7 w z w.6 0> a0~ z L.R w 0.3 D:.000037 cm/e.2 G0.80 mg- mol/sec 0 _ _ _ _ I _~~~~~~~~~~~~~~~~~~~~~~~~~~__ 0 00 200 300 400 500 600 700 800 900 1000 ELAPSED TIME, SECONDS Figure 9. Concentration Histories Reconstructed for Runs 3, 7 and 9.

1.0 aJ I I I I RUNS # 6,17 0.9 0 - BED# I X - BED# 2 x y I I I A- BED* 3 2 0.8 D = 0000037 Cm/Sec A I I ( I Go = 0.78 mg -mol/Sec T = 0 OC P = 0.97 atm. 07 DIA. = 0.28 Cm. w z x w 0.6 0~ 0.5 z 0 I0~~~ LL 04 w~~~~~~~ Q3 y 0. 0.3 0.2 0.I 0 x 0~~~~~~~~~~~~~~ 0 x 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 ELAPSED TIME,SECONDS Figure 10. Concentration Histories Reconstructed for Runs 6 and 17.

-94 -I.0 0.9 o.9 j }t x / ] RUNS # 45,47 / / Q / 0 - BED- I 0.8 X - BED# 2 A - BED # 3 D - 0.000037 Cm/Sec Go = 0.87 mg-mol/Sec 0.7 T = O O~C P = 0.98 atm. DIA. = 0.117 Cm. w z w 0.6 0a. z o I0r LL 0.4 0 100 200 300 400 500 600 700 800 900 ELAPSED TIME, SECONDS Figure 11. Concentration Histories Reconstructed for Runs 45 and 47.

1.0 RUN # 56 0.9 0 0 - BED# I X - BED # 2 A - BED# 3 D = 0.000037 Cm/Sec 0.8 Go = 079 mg-mol/Sec T = O0C ~~A ~~~~~P = 098 atm. DIA. = 0.198 Cm. 0.7 x w Z 0.6 w 0~ Qr_ 0 0.5 LL I4 w 0 0.3 X\J E~~~~~~~ 0.4 0~~~~~ 0.1 0~~~ 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 ELAPSED TIME,SECONDS Figure 12. Concentration Histories Reconstructed for Run 56.

1.0 x 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ RUN # 52 09 0 - BED# I X - BED# 2 A- BED* 3 2 D = 0Q000037 Cm/Sec 0.8 Go= 0.49 mg-mol/Sec T= 0 OC P = 0.98 atm. DIA.- 0.117 Cm. 0.7 w z W 0.6 O~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~k 0. z 0.5 0 oo ~~~~~~~~~~~~~~~x CL LL 0.4 LL 0.4 w 0 0.3 Q2 x 0.1 0 0 I00 200 300 400 500 600 700 800 900 I000 1100 1200 ELAPSED TIME, SECONDS Figure 13. Concentration Histories Reconstructed for Run 52.

CONCLUSIONS AND RECOMMENDATIONS The purpose of this study was to examine the kinetic behavior of a binary gas-solid adsorbent system; propane-probylene-silica gel being taken as an example. Two separate processes were considered in the adsorption process; namely, passage of the gas through the so-called gas film and diffusion of the adsorbed gases in the particle. The former process was studied from existing correlations. The later process was reduced to a mathematical analysis yielding a coefficient of diffusion of 3~65 x 10-5 Sq. cm. per seco with a standard deviation of 2~06 x 10 5 sq. cmo per sec. During this process, the interface relations were assumed to be governed by a constant adsorptive relative volatility (defined by Equation (46)) of,o5 The use of this diffusion coefficient in the plug-flow model equations led to reconstructed concentration histories in fairagreement over most of the range except the initial few minutes where the adsorption or desorption rate was highest. It was in this region that the most difficulty was encountered in the data reduction step as well, The difficulty in clearly defining the adsorptive relative volatility mentioned earlier may be involved here. Under high transfer rate conditions, it is most unlikely that equilibrium at the interface is really attained at allo As indicated by the results of this study, the effective relative volatility may be a function of mass transfer rate and certainly different from its equilibrium value, -97 -

The diffusion model is not the only one which will fit the data. A first order kinetic equation of the following type: -QA k2(YA" mA/Kads) (70) where kI and k2 are velocity constants in the reaction kl 3 6 gas C3H6 adsorbed and Kads = kl/k2 = (YA/nmA) @ equilibrium will correlate the data to almost the same degree. This result may be expected if the radial particle concentrations gradients are close to linear, since for D = constant, the diffusion equation may be reduced to an equation of the type (70). The flowrate data obtained in the study were unfortunately unreliable, They showed, in general, a qualitative adherence to the predicted behavior but not a quantitative one, The comparison of flowrates obtained experimentally and those computed via relation (63) for run number 26 are shown in Figure 14o It is felt that the capillary tube manometers used with the orifice meters were too sluggish in response to allow accurate readings at these low flow rates; Future Work An important part of any further kinetic studies of this kind must be an elucidation of the interface relations under conditions of high fluxo The use of a constant relative volatility in this work seems to be one of the most important factors in the scatter of the determinations.

1.0.8 BED I,., (/) O A0 E E I I I I I I I RUN 26 E.4 1 EXPERIMENTAL POINTS 0 BED No I X BED No 2.2 A GBED No 3 SOLID CURVE FROM EQUATION (63) 100 200 300 400 500 600 700 800 SECONDS Figure 14. Comparison of Observed and Calculated Velocity Histories for Run 26.

-100 -The methods used here could theoretically be extended to multicomponent systems. However, ternary or higher systems present great experimental difficulties both in controlling the experiment and in interpreting the results. For example, a tentative attempt at a nitrogen-propane-propylene-silica gel experiment was made. It was found that with the bed initially saturated with nitrogen, and propane-propylene mixtures passed into it, the whole experiment was over before any readings could be taken. In general, all the components would have to be about equally adsorbed by silica gel in order to get adequate experimental durations. The method used here to calculate concentration histories could be extended to multicomponent systems, It is probable that some form of first order kinetic equation could be substituted for the complex diffusion equation, The accuracy obtainable would probably be sufficient for design purposes and the attendent saving in computing time would be quite great0 Here again, some better relation for unsteady state interface conditions is needed.

APPENDIX A A, Solution of the Boundary Value Problem Posed in the Diffusion Model(5) In the Equations (22) to (25), make the substitutions, U = r(So - s) (Al) 9 = Dt (A2) The problem then becomes UG = Urr (A3) u(o,9) = o (A4) 1 1 r2 U(rO, G) - Ur(ro,9) = -F(G) (A5) g r rO ro 0 U(r,O) = 0 (A6) The method of attack will be to first solve the case where boundary condition (A5) is replaced by a constant input function, Let the solution of this case be V(r,9). Then,. = Vrr (A7) V(0,@) = 0 (A8) V (r Vr(ro, ) = -1 (A9) r - r 0 0 V(r,O) = 0 (A10) This solution will then be used via Duhamel's (5) formula to get the solution of the original problem, -101 -

-102 -Taking the Laplace Transforms of the above set, we get SV = Vrr (All) v(O,s) = 0 (A12) 1 v(rOS) - 1 Vr(rO S) -S (A13) ro r0 The solution of(All) subject to the boundary conditions (A12) may be written v(r,s) = B sinh (is ro) (A14) Substitution of this into the other boundary condition (A13) and rearrangement gives v(r s) =- rr sinh( Is rO) ( ) s(sinh( Is ro) - s rOcosh( Is ro)) If now the hyperbolic functions are expressed in terms of the first few terms of their series expansion forms, we get r3-s r5s2 r7s3 Ea + 2r --- + -r5- + 0-4 1 3' 5 7 ' 54 5J Ti From (A16) it can be seen that the function has a pole of order 2 at s = O. Carrying out the division indicated, we can now obtain an expansion in the neighborhood of s = 0 00 3. 2 r r 2 2 2(3;' 2 v (r,s):= r + s (r0 52 ) + E an(r) sn (A17) 2rOs2 2s r0 L n-0 The first two terms of the solution arise from the first two terms in (A17) as the residue of eztv(r,z) at z = 0 The terms are

-103 -3r + r (r2 2(3')2ro (A18).2r0 2 ro 51 Equation (A15) contains an infinite number of simple poles at the roots of the equation sinh( fs ro) - -s ro cosh( Is r0) = 0 (A19) If we assume pure imaginary roots of the form ip/r 0 Equation (A19) simplifies to tan Pn = Pn (A20) Tables of the first seventeen of these roots are available(13) and they have been extended up to fifty. Table VIII contains the first fifty roots, The remaining infinite number of terms in the solution come from the residues of eztv(r,z) at z = ipn/r0. 2 zt rI8 r0~ sinh( Iz r0) e 1 2 dz z(sinr cosh( z r) - z ro )) ( A2) r0 -2r0 sinh(iPnr/r) e n /r(A22), (A22) An sinh(iPn) Now since sinh(ix) = isin(x) we may replace the ratio of hyperbolic sines by the ratio of circular sines. Also in view of the fact that tan Pn = fn) we have the two following relations, one of which we use directly and the other will be useful in a subsequent section:

-104 -sin(n) - (A23) and cos(Pn) = (A24) The residue is then Pn(Q): -2(-l) r0.. sin(nr/rO)e n (A25) The solution for V(r,Q) may now be written: 002 2 =Vr{+r 2 3ro 2 G/r0 V(r,) ( 2rO+ - ) - 2rO Ynsin( nr/rO)e n 0 V'~ 2r0 2r0 10 n=z (A26) where Yn is defined by Equation (27). Substitution of this formal solution into the Equation (A7) and its boundary and initial conditions (A8), (A9), and (AlO) shows that they are satisfied. We now return to the complete problem. Applying the Laplace Transforms to Equation (A3) and its boundary and initial conditions (A4), (A5), and (A6), the following equations arise: su(r,s) = Urr(r,s) (A27) u(0,s) = 0 (A28) 2 u(r-0s) - ur(rOs) = -f(s) (A29) rng ~ rn

-105 -A solution of these equations is u(r,s) = -f(s) r02 sinh( Is ro) (A30) sinh( Es r0)- Is r cosh( Is rO) or, in terms of the other solution, u(r,s) = sf(s)v(r,s) (A31) Duhamel's(5) Formula applies here in the form U(r,@) = F(O)V(r,) - F() -VT)V(r)) -F' (A32) Now if F(t) can be adequately represented by a power series whose derivatives converge to the corresponding derivatives of F(t), the integration in (A32) can be carried out by integration by parts. The resulting solution for U(r,@) is as follows: Co 2 3r U(rQ) = 3r F(T)dT + r( + 0 ) F(G) - 2r ZYnn in(nr/O) r0 lro 10 nn s n (A33) where 7n is defined by Equation (27), page 26, and 6n by 2 2 2 ~ r 2 '= e-nF/rO X (- 2 F(: (0) - (- ) F (Q) n p jo In j=l Pn (A34) It can be readily verified that this formal solution satisfies the differential Equation (A3) and the boundary conditions (A4) and (A5), However, in order to show that the solution fulfills the initial condition (A6), it is necessary to prove that for G = 0, the second and third terms in (A33) cancel. Note that verification of (A33) can be made by an

-106 -alternate route. Since V(r,Q) can be verified as a solution of (A7), (A8), (A9) and (A10) and since in general it can be proved that if U(r,G) is obtained from this solution via Duhamel's Formula, then U(r,0) is guaranteed to be a solution of the whole problem (A3), (A4), (A5) and (A6), We choose the longer route since it leads to a uqeful simplification of the expression (A33), It must first be proved that the second term may be expanded in a Sturm-Liouville type series of the sine terms appearing in the third term. We first show that the set sin(Pnr/ro) n = l,2, 3, 40,.o (A34) is orthogonal over the interval 0 to rog Proof of the Orthogonality of Set (A34) When m ~ n, we evaluate the expression: S.in( mrro}).o sin(n2r/ro) = 2 cos[ (m-n)rr/ro]dr 0 0 r 1 - o cos[ (m+n)r/ro]dr 0 r rO rin[(sm-n)r/r] _ rsin[(Pm+Pn)r/ro ] 1 2(m,-Pn) 2(Pm+Pn) j 0 ro(singmcosgn - cospmSingn) 2(pm - En) r0(sinmcOsin + cosmsinn) (A 2(8m + Bn)

-107 -S4stitution of relations (A23) and (A24) into the right hand side of (A35) gives: r ro m (_) (-l) (-l) n) rO /(-l)mpm (-l)n (-1) (-l)n n n Pm - Pn P1 + m2. 1+ B2n + 2 l + n2 0o (A36) When m = n, we evaluate the expression: r 0 r 1 1 i sin (nr/r 0) - 2 I[- cos(2pnr/ro)] dr 1 1 = ~rO- rO / n sin(2~nr) 2r - 4/ nn sin($n)C~S ( n) (A7 ) Substitute from iEquations (A23) and (A24): r sin2(Pnr/ro) = r 1 ro (l)n ()n 2 o 20n F17 Fl+Pn 2 Pn (4) ~~(A38) n The set (A34) is thus seen to be orthogonal over the interval 0 < r < rO. The norm of the functions sin(Anr/ro) is shown to be the last expression in (A38) and is non-zero,

Expansion of the Second Term in Equation (A33) in Terms of Orthogonal Set (A34) In order to complete the proof that solution (A33) satisfies the initial condition (A6), we expand the second term therein in terms of the orthogonal sine functions occurring in the third term. We wish a series representation of the form r +3r0 = AlSin(plr/r0) + A2sin(P2r/r0) + 0ooA (A39) Since the functions are orthogonal, we know that the coefficients An are given by: -r(r + 3 ) sin(Pnr/ro)dr An = (A40) sin 2(nr/ro)dr 0 Integration by parts gives the following: ~ An (_l-1) n2r2 (A41) Thus 00 r + 10 2r02o nsin(pnr/rO) (A42) If this series representation of the second term in series solution (A33) is placed into the equation, we get the following simplified expression: r X U(r) = F(T) dT - 2r n sin(nr/r) (A4) ro n=l

-109 -where 8" = e ( ) j ( () n L j=0 n=O Pn (A44) The series solution in form (A43) is easily seen to fulfill initial condition (A6). Re-introduction of Original Variables From Equation (21) F(G) = F(Dt) = r~ QA(t) (A45) The derivatives of F(G) with respect to G can be evaluated in terms of derivatives of QA(t) with respect to t by successive application of the chain rule. Thus: F( 1)(O) dF(g) ro dQA dt _ ro dQA 1 r0o 1 (1) dG 3D dt dG 3D dt D 3D D 'A F(2)(g) r= o 1 (2) (t) 5D D2 F(n)(G) = O 1n IQA(n) (A46) D Dn A (t) Substituting these relations and re-substituting for U from Equation (Al) into (A43), we get the final form of the solution (26). t 3 00 (26)

-110 -TABLE VIII FIFTY ROOTS OF THE EQUATION TANn = An n Pn n Pn n An 1 4.4934 18 58.1022 35 111.5176 2 7.7253 19 6162447 36 116.6595 3 10,O9041 20 64,3871 37 117o.8013 4 14'0662 21 67 5295 38 12069431 5 17.2208 22 7066717 39 124, 0949 6 20 3713 23 73o8139 40 127,2266 7 23.5195 24 76,9570 41 130,3685 8 26,6661 25 80,0981 42 1335 5103 9 29, 8116 26 83, 25 03 43 136, 6520 10 32.9564 27 8663824 44 139,7937 11 36,1006 28 89,5243 45 142o 9354 12 39,2444 29 92 6662 46 146, 0772 13 42,3979 30 95,8081 47 149.2189 14 45 o5311 31 98, 9501 48 152, 3607 15 48,6741 32 102o0920 49 155,5024 16 51.8170 33 105 2339 50 158,6441 17 54, 9597 34 108, 3757

-111 - B, Method of Characteristics for a General Set of Two Simultaneous Quasi-Linear First-Order Differential Equations(6,11) Consider the set AlUx + BlUy + ClVx + Dlvy =R1 (A47) A2ux + B2u + C2v + D2vC = R2 (A48) We assume that these equations have integral surfaces on which u and v are at least sectionally continuous. We are interested in the intersection of these two to form n.one.which -is the solution':surface of the simultaneous e:quations.. In particular, we are going to look for a space curve or family of space curves on this integral surface along which the derivatives in the above equations may be discontinuous, Provided that u and v are continuous along space curve C on the integral surface, infinitesimal changes in u and v along C may be obtained from infinitesimal changes in x and y along the projection of C into the x-y plane via the relations duC = uXdx + uydy (A49) dvc = vxdx + vydy (A5o) Now Equations (A47), (A48), (A49) and (A50) constitute four equations in four unknowns - the derivatives ux, uy, vx and vyo By Cramer's Rule, these equations provide a unique solution for ux, uy, vx and vy unless the determinant of the coefficients is zero, Now since we are looking for an indeterminancy which may allow

-112, ux to be discontinuous, let us set this determinant equal to zero. A1 B1 C1 D1 A2 B2 C2 D2 = o (A51) dx dy 0 0 0 0 dx dy After expansion, rearrangement and division through by -dx2, this determinant yields the following quadratic equation in dy/dx which must hold along the curve C on which the equation set is indeterminate a( dy) 2.+ b(4-) + c =O (A52) dx dx where a = A1C2 - C1 (A53) b - (A1D2 A2D1 + B1C2 - B2Cl) (A54) c = B1D2 - B2D1 (A55) Hence, the slopes of the projections of characteristics C+ and C are given by the respective roots of (A52), dy: -b + b - 4ac (A56) dx 2a Along the lines in the x-y plane defined by Equation (A56) the set (A47) - (A50) does not possess a unique solution and in particular, the set cannot be solved for uxp hence no solution exists unless the numerator determinant in Cramer's Rule is also zero, In that case there are an infinite number of solutions; hence the required indeterminacy on uwo

An important classification of equations follows from (A56). If b2 - 4ac < 0, the equation set is termed elliptic and there are no characteristic directions in the real plane, If b2 - 4ac = 0, the set is parabolic and there is only one characteristic direction through a point in the x-y plane. In the most important case where b2 - 4ac > 0, the set is termed hyperbolic and there are two characteristic directions through each point in the x-y plane. By equating the numerator determinant of Cramer's Rule for ux to zero, we can now derive an equation which provides a restriction on the total derivatives of u and v with respect to x along C+ and C-. R1 B1 C1 D1 R2 B2 C2 D2 = (A57) = 0 (A57) du dy 0 0 dv 0 dx dy After expansion, rearrangement and division through by dx2, (A57) yields the following expression: e(d) +f( ) + g =0 (A58) dx C dxC where e = [(B1C2 - B2C1)(dy) - (B1D2 - B2D1)] (A59) f = -(C1D2 - C2D1) (CY)C (A60) g = (CR2 - C2R1)(~)~ - (D1R2 - D2Rl)()dY) C (A61)

Application of the Method of Characteristics to Equations (355) and (57) The coefficients take on the following values: Al = 1 A2 = B1 = 1/v B2 = C1 = 0 C2 = 1 D1 0 D2 = 0 Hence a = 1 b = -l/v c = 0 The discriminant b2 - 4ac is positive and non-zero, hence the set is hyperbolic and has two characteristic directions given by 1 2 ct v (-) dx 2 dit 1 along C (61) dx v d t= 0 along C (62) dx Equations involving the total derivatives of y and v along the characteristics are now obtained from (A58). Refer to Figure 8. ot- 11 1 C+ e =1 1=1 vv vT f =0 g=- (v)

-115~ Hence a)C+ = R(55) C o e O f =0 g =0 Since Equation (57) involves only the derivative of v along the characteristic C- already, it introduces a degeneracy into the equations at this point. That is, along C o~ d (d y) 0 dx C dx C We thus take Equation (57) as the correct expression of the total derivative. of v with respect to x along the direction C. C. Finite Difference Approximation to Plug-Flow Model Equations(lO) For solution along the characteristic lines, we choose a finite difference grid constructed as in Figure 15,which is a straightline segmented approximation to Figure 8. The grid lines parallel to the t axis are separated by distances Axi; they need not be equally spaced. Increments Atj are chosen arbitrarily along the t axis and need not be equally spaced. The points so formed are the generating points for the C characteristic lines. The value of a variable at the ith space point and on the jth characteristic (C+) will be denoted vijo The characteristic curves shown in Figure 15 must be replaced by straight line segments whose slopes between points (i-l,j) and (i,j)

-116 -i:2 j:i i=O::2 i:3 1:4 Figure 15. Finite Difference Grid with Characteristics Shown for Plug-Flow Equations.

-117 -are given by dt = 2 (A62) dx Vi + v Define three rate functions appearing in the equations to follow: 1 *i- Yi; ) i, QAi,j (A63) ij = -fvijP R: QAiiJ (A64) i;J fp Rij QAij (A65) J1 Gas Phase Concentration Equation (59) is used between point (i-l,j) and (i,j) to give the mole fraction Yi j in the form x. i1j Yi-1,2 j (A66) y. y + Rdx(A66) xi-l A modified Euler method is employed here to approximate the integral, Thus an iterative scheme is set up, since the Euler method uses the average of the rate at point (i-l,J) which is known and that at point (i,j) which is unknown since it depends upon the variables at point (ij) y~~~1k ~k + (R.1 + I.A)X I(A67) Yi,j Yi-lj 2

-118 -2.. Velocity Similarly, the velocity relation (60) is integrated along characteristic C-, However, note from Figure 15 that it is in general necessary to interpolate to the velocity and the rate R2 at the base point for integration along the characteristic to point (ij). Linear interpolation is used, x. V. * = vi.1 ( ) + R dx (A68) 1i3j =il(t ) + Xi-l where the notation vi l(t) is intended to represent the velocity on x grid line i-l and at the time point corresponding to the point (i,.j)9 The Euler formula for the velocity integration is then: 1 2 k V. V. (A69) vk =i.l(t j) Ri jv, + 30. Time The time at point (i,j) where i ~ 0, is obtained iteratively from the following modification of Equation (A62): ik = + 2i +i (A70) i-lj i~j and At, is obtained from k k At t t (At71) i.l T 1

-119 -4. Solid Phase Concentration The diffusion equation was set up in a difference form for inclusion in the plug-flow model calculations. Choice of this scheme over the analytic solution employed in the data reduction step was made on two accounts. Firstly, the rate function at grid point (i,j) is not known as it is in the data reduction scheme. The analytic solution requires knowledge of this rate function as an explicit function of time and it makes use of the derivatives of the function as well. In the PlugFlow Model calculations the rate is an unknown at point (i,j) and in order to obtain it as a function of time, curve fitting would be required over several previous points and the assumed value at (ij). In view of the linear interpolation used elsewhere in the finite difference solution, this does not seem justified. The finite difference approximation to the diffusion equation uses the equivalent of the function and its first derivative. Secondly, the finite difference equations can be solved much more quickly than the infinite series of the analytic solution; especially where a method of solution described by Richtmyer(21) and developed below for this case is used. Since the plug-flow model calculations require a considerable amount of computer time for solution, this was an important consideration, Balanced against this, of course, is the question of the accuracy and stability of a finite difference approximation. The stability of this finite difference form of the diffusion equation is quite good as is shown by various authorsiO')l By trial of several grid dimensions, One was

-120 - chosen which gave a satisfactory compromise between accuracy and time for solution, A difference approximation to Equation (22) arises from the use of backward time and space differences as follows: nm nm —D 2 Sn n-l SnS+lm - 2Sn,m + Sn-l,m AT 1' 4)' (A72) The integration here extends along the ith x-grid line from t to ti o Subscripts i and j will be omitted for the sake of clarity~ In place of the boundedness condition on s (24) we require that the gradient of s at the center of the particle be zero. The following set of difference equations then arises: - sm + sO = 0 0<m<nT l,m 0,m n =0 - a5sn2+l,m+ n,m - ( n Snn,m O < m < n T O < n < nr nrm = nr-m = QA (ti-l,j + m AT) 0 < m < nT n = nr (A73) where DAT (A74)

-121 -and Ati AT i = i (A75) nT Equation set (A70) may be written -Ansn-l,m + Bnsn,m - Cnsn-l,m = Dn (A76) where An = 1 n= 0 =~ O<n<nr 0 n = nr (A77) Bn =1 n = 0 {n-1 = 1 + 2r) a O < n < nr 1 n =nr (A78) Cn =0 n= 0 n-2 = (n-) 0 < n < nr n <n = 1 n = nr (A79) Dn =0 n = 0 Snm-l 0 < n < nr r QA(ti-lj +m ) n = n=n (A80) Richtmyer(21) shows that because of the special form of this set of equations; i.e., the matrix of coefficients contains elements only on the major diagonal, on one diagonal immediately above and one immediately below the major diagonal; one can reduce the implicit dependency of snm upon Sn+lm and Snlm to an explicit form

-122 -in which it depends only upon Sn+l nm This relation is of the form n,m = EnSn-l,m Fn O < n < nr (A81) (Rn, j + mR3)Ar + F n r Sn,,m 1 + nr 1 R =' r 0/(3D) QA(xitj) (A82) where the coefficients E and F are obtained recursively from the following relations~ E = 1 E n 0 n nr (A83) Bn - CnEn-l F0 =0 0 n < n< (A84) Dn + CnFn_1 n Bn C nEnl As is shown by Richtmyer,(21) use of these relations minimizes the nunmber of arithmetic operations required and hence ensures the best possible solution scheme as regards round-off error and time~ D. Derivation of the Equilibrium Velocity Relation From Equations (60) and (58) we get (d )C- fp QA (A85) () = f" QA From (59) and (56), we get that dvp (dy)c+ (A86) Ps(l - ry) dx

-123 -Now substitute for QA in (A85). (d) - = + - (dy) + (A87) dx C 1+ *y xx C This is now a separable expression which may be rewritten. and integrated. v y v0 l+=ry dy (A88) V + VO;Y+YO or loge (/vo ) = loge 1 + * y 0 1 + ty If the density is constant this, of course, may be written G = Go(+ (63) It may be shown by somewhat more general derivation that Equation (63) holds even if the density is not constant. This is not developed hereo

APPENDIIX B PHYSICAL PROPERTIES CORRELATIONS A. Vapor Density The volume-explicit form of the Beattie-Bridgeman(2) equation of state was used to obtain the specific volume of propane and propylene vapors V =[ + B(1 - ]bP[l cP] p [ AO][ aP (Bi) -RT P [RT RTI Table IX contains the constants for propylene and propane TABLE IX Propylene Propane A0 12,o 25 11o,92 B0 o192.181 a o07 o0732 b.o6 o 0429 c 1000000o 1198845., Additivity -of specific volumes was tested against the rules for mixture coefficients of the Beattie-Bridgeman equation as developed by and was found to be quite adequate in the range of temperature and pressure in question, The molar density p and mass density p n were calculated from the following equations: 1 (B2) YVA + (1 - y)VB -124 -

-125. YMA + (1 - y)MB n (B3) YV A+ (1 - Y)VB B. Viscosity The equation of Bromley and Wilke(20) for viscosity is rewritten in the form 1/2 0,00333(MTc ) fl(l.33TR) 2/3 The temperature function fl(1l33TR) was correlated as a power series function of TR from a tabulation given in Sherwood and Reld, fl(1.33TR) = ei(TR)i (B5) i=O The correlation constants are given in Table Xg Table X i e 0 - 092678353 1 -1, 0754612 2 -.1622960 3 -.,014580901 After insertion of the appropriate critical constants and molecular weights into (B4) and rearrangement into the dimension system used; i,e,, mg/cm sec, the following two relations were obtained and used for pure phase viscosity: Propylene: A =.12825 fl(l.33TR) (B6)

-126 -Propane: O IzgB = 12618 fl( 133TR) (B7) Since the effect of pressure on viscosity over the range used was small, it was neglected0 The effect of composition was allowed for by means of Wilk&'s equation in the form ktA I'B ~'mixt + ( - Y + 1 BA/(l (B8) where [1 + (LA/bB)l/2 (MB/MA)i /4]2 AB = (Bg) = 2 [1 + MA/MB]/2 1/2 1/4 2 1 + (~B/7'A) (MA/MB)1/412 >gA = B t A B ^(B10) BA = 21 F2 [1 + M/MA.l/2 Co Diffusivity(20) The Gilliland semi-empirical equation was used in the form: O oo43 T3/2 [(MA + MB)/MAMB ]/2 D (B_1) PAB (VbAl/3 + Vb 1/3) where Vb is the molal volume of pure substance at the normal boiling temperature. This molal volume is estimated by Schroeder's method based upon the additivity of apparent atomic volumes, The values used here were obtained from a table given by Reid and Sherwoodo (20) Propylene: Vb = 66 6 Propane Vb = 74

-l27 -If these values and the appropriate molecular weights are substituted into (B1l), the following expression for the diffusivity of propylene into propane cr vice versa, in cm /sec is obtained. DAB o.ooo00001364 T3/ / (2) D. j Factor for Mass Transfer (23) From curves given by Treybal, a correlation of jD as a function of Reynolds ' number was made. loge (j) = hi (log Re) (B13) i=O Constants of the correlation are given in Table XI. TABLE XI i h 0 o62562545 1 -. 50637400 2 -o 0070036931 3 0011111660 E. Adsorptive Equilibrium Capacities The isotherm data of Lewis et al(5) were reduced to Polanyi type distribution curves, See Appendix C for details of the Polanyi Adsorption Potential Theory from which this correlation method arises. These distribution curves were then correlated as power series fits - adsorption volume as a function of adsorption potential.

-128 -5 c = A - propylene ~o = ~ bcizc (B14) i=O b = B - propane Coefficients of the correlation are given in Table XII. TABLE XII i Propylene Propane 0 4.0674661 x 102 3.7845195 x 102 1 -246774164 x o10l -2, 7165051 x 10-1 2 7.4111129 x 10-5 1o8987394 x 10-5 3 -1,1470834 x 10-8 3,6440492 x 10-8 4 1,0611762 x 1012 -12226315 x 10 5 -4,7175589 x 10-17 1,1776570 x 10-15 F, Fugacity Ratio Data for the correlation of the logarithm of the fugacity ratio were taken from Maxwell(l8) and a curve-fit made in the form log (P ) = ai(1o8 x 10-3 T) (B15) 2 ij ai = bi.(P) (B16) j=0 Coefficients bij are tabulated below in Table XIII and Table XIV.

-12;9 -TABLE XIII Propylene i j 0 1 2 0 -3.1687540.20078375 -.018708807 1 5,1288900 -1,o0621171.10345047 2 10o o002484 1,o 9768422 -. 18864216 3 -8.1783705 -1o2394364.11365675 TABLE XIV Propane i O0 1 2 0 -1 1057091 -.61418538 o016313069 1 -6.1122970 3,2934058 -. 08325437 2 29 151559 -5, 6777008.13939543 3 -18.863775 3 2003745 -,076787776 G. Liquid Specific Volume Data for liquid specific volume of the two components was taken from Maxwell(18) and correlated in the form c = A - propylene vc = cci(l8T) (B17) = B - propane i=0 TABLE XV i Propylene Propane 0 -55, 129320 -28,362340 1 873o32809 697,91541 2 -2179o 3799 -1716, 5041 3 1922, 4285 1535 5613

-130 - H. Saturation Temperature Data was taken from vapor pressure curves in Maxwell(l8) and correlated according to the following equation: c = A - propylene (1/108T) = ci (log P) (B18) = B - propane Coefficients for this correlation are given in Table XVIo TABLE XVI i Propylene Propane 0 o 24625632 o24071426 1 - 024189387 -o 024266756 2 -,000616167607 -.0002237322 3 - 0000045771307 o 000005 9156969 I. Specific Area for Mass Transfer The following chart (Figure 16) is constructed from a table given by Hougen and Watson,(12) Chemical Process Principles, Volo 3, pa 9879 Figure 194 for mass transfer to packed bed particles,

-131 -I0 SOURCE: HOUGEN 8WATSON,CHEMICAL PROCESS PRINCIPLES, VOL 3 P 987, FIG. 194 SILICA GEL DENSITY=706 gm/cc 210 1 o IC 10 f0=20 d, cm Figure 16. Specific Area for Mass Transfer.

APPEND IC C THE POLANYI ADSORPTION POTENTIAL THEORY A. Theory (4,7,19) According to Polanyi, an adsorbent particle exerts a strong attractive force upon molecules of the surround fluid, this force giving rise to adsorption, Since succeeding depths of adsorbed material will contribute to the compression of underlying material, the density of this material will range from highest at the adsorbent surface to the bulk density at a sufficient distance from the particle. Eucken was the first to describe the adsorptive force in terms of an intermolecular potential gradient and later Polanyi quantitatively described this potential at a point as the work done by the adsorptive force in bringing a molecule from the gas phase to that point. For an isothermal system, the reversible work of compression is given by P2 W = VdP = AF between point 1 and point 2 (C1) -R _. P1 By definition the Polanyi adsorption potential at a point near the particle is this reversible isothermal work of compression or the difference in free energy F between that point and the adsorbent surface, P =i -S V dP (C2) Pi. -132 -

2 E- 1 Figure 17. Lines of Constant Potentials~ Thus we can visualize shells of constant adsorption potential surrounding the adsorbent particle (Figure 17)4 The value of the potential on any one of these surfaces will be a function of the volume of material adsorbed and so we can find a.relationship of the for e - f(~)o This is the so-called adsorption "characteristic" or distributiOnt curve,.Since the adsorption potential expresses the work of temperature-independent forces, the distribution curve should be independent of temperature. Computation of the adsorption potential requires a knowledge of the equation of state for the fluid in question both' in the gaseous and in the adsorbed (liquid) state0 As shown by Brunauer, we can visualize the variation of specific volume V for three typical systems as in the following Figure 18.o Case I represents a system far below the critical temperature and near saturation pressure so that practically all the adsorption volume i is filled with liquid.

-13 4. I I II Vt ~0 8at Omax Figure 18. Variation of:Adsorbed Specific Volume with Adsorbed Volume for Three Typical Cases. Case II represents a gaseous system above the critical temperature so that practically all the adsorption volume contains material of; high specific volume. Case III represents a gas intermediate to the other two. In this case:sat contains adsorbed liquid and the volume ~max csat contains gas, For clase I, the integral /VdP is adequately represented if we consider only that part of the integral arising from compression of the gas to the point of condensation, That is, we consider the liquid to be incompressible, Even for case II, it can be seen that if that part of the adsorption space containing gas is large compared to that containing liquid, the specific volume of the liquid is so much smaller that

-135 -the largest mass of the adsorbed material is in the liquid phase and the same method of computing the adsorption potential may be useful. B, Application to Propylene and Propane Isotherm Data In this work, the gases are well described by case I and so the adsorption potential was taken as e = RT loge( fs) (C3) where fs is the fugacity of saturated liquid at adsorption temperature, f is the fugacity at adsorption pressure. The adsorbed volume is computed from the following relation: NV = s where N is the amount adsorbed in mg-mols per gm of adsorbent and V is the molal volume of saturated liquid at adsorption temperature. The data of Lewis et alo were recomputed to obtain the data on the distribution curve of Figures 19 and 20, A power series fit was then made of the two distribution curves as shown in Appendix B., section Eo The resulting correlation was then tested by recomputing the isotherms shown in Figure 21 and Figure 22, Points plotted are the original Lewis data~

o O C -LEWIS 3000 - X 25 ~C -LEWIS & 40~C -LEWIS + 1000C-LEWIS O 28 ~C-MILLS — i 400C- MILLS SOLID LINE MACHINE CORRE LATION 2000 1000 100 200 300 400 Figure 19. Polanyi Adsorption Potential Characteristic Curve for Propane on Silica Gel.

O 0 C LEWIS ~~~X~~~~~~~~ ~~~~X 250C LEWIS 3000 \a 40~C LEWIS k< | I + 280C MILLS +\ | 40~C MILLS SOLID LINE-MACHINE CORRELATION 2000 1000 100 200 300 400 Figure 20. Polanyi Adsorption Potential Characteristic Curve for Propylene on Silica Gel.

-138 -2,,-0Xn PFRO CORRELATPYLENEION x 400C + IO O~C 2 PI ( I (I FROM CORRELATION 0 5 1 1.5 2 2.5 3 OX 4o00C Figure 2'1. Predicted Isotherms with Experimental Points for Propane.

APPENDIX D CALIBRATIONS A. System Volumes Total system plus one sampling manometer 1 1194 cc. 2 ll91o 6 ave. 1193 cc. One sampling manometer and leads 37 cc, Total volume of system 1156 cc, TABLE XVII DISTRIBUTION OF VOLUMES IN SYSTEM 1, Inlet valve to bottom of bed in cell 1 300 cc, 2, Top of bed 1 to sample point in cell 1 64 cco 3. Sample point 1 to bottom of bed 2 223 cc, 4, Top of bed 2 to sample point in cell 2 64 cc, 5o Sample point 2 to bottom of bed 3 223 cc, 6, Top of bed 3 to sample 64 cc, 7o Sample point 3 to outlet valve 104 cc, 8, Volume of beds 150 cc, B,. Flowmeters Flowmeters were calibrated by passing propane or propylene through the system, recording readings simultaneously from all four manometers and measuring the actual flowrate by downward displacement of water timed with an electric counter, The results of the calibration -139 -

-140 -runs are given in Table XVIIIo These results were correlated least squares to obtain the coefficients in the four equations following. The form of the equations comes from the orifice formula W = K p (AP)a (D1) It is -likely that the positioning of the pressure taps some distance from the orifice resulted in the exponent a differing from the theoretical value of 1/2o Inlet manometer W/fp = o l693(AP) ~5531 (D2) Manometer #1 W/jp = o1567(AP)5655 (D3) Manometer #2 W/ rp = 1607(AP))532 (D4) Manometer #3 W/p = o 1814(P )4 5124 (D5) CO System Pressure Drop By actual measurement the pressure drop through the system was the sum of the orifice pressure drops within the experimental error, That is, the resistance of the beds was negligible at the flow rates used, Do Analysis - Calibration of Chromatography Results Since the gas mixtures to be analyzed are simple binaries containing only propylene and propane, and since these two gases are very similar in physical properties, a simple ratio of peak areas to total of the two peak areas was used as a measure of the mol fraction of each gas,

-141iTABLE XVIII FLOWMETER CALIBRATION DATA Orifice Bar, Sys Coll Vol. Elapsed Gas Pressure Drops Press Temp, Tempo Collo Time mm Acet, Tetrabromide mm Hg OC ~C cc. sec. I 1 2 3 CQ.H8 20.0 21,5 25,5 23.0 737,4 25,0 25.0 1 1860 168,4 2 1855.168 9 3 186o 169.5 CH8 47.0 48,o 64,0 56.5 737o4 25,0 25,0 1 1866 102.4 2 1933 104.5 3 1882 101 8 C H8 89.0 92.5 119.5114,5 737,4 25,0 25,0 1 1815 69. 7 2 1840 70.7 3 1840 71.0 C3H8 140.0o 150,0 1920 192,0 737,4 25 0 25 0 1 1840 54.3 2 184o 54.2 c3H8 10,5 12,0 1500 1350 737,1 25eo 250 1 1825 221.5 2 1830 227.0 C3H8 30,0 5330 41.0 0370 736,8 25,0 25,0 1 1820 127.5 2 1835 129,0 05118 28,0 29,5 3605 32 7 736 8 25,0 20,0 1 1980 144 4 3 8 2 1980 142, 4 3 1965 14o 3 C3H6 98,5 o4.o 14.5 129,0 746.8 250 20.0 1 194o 70.1 2 1960 70 2

-142 - Synthetic mixtures of known proportions were made up and analyzed. The comparison of the analysis and known composition is given in Table XIX for the calibration analyses,

TABLE XIX CALIBRATION Ot CHROMATOGRAPHY RESULTS Mol Fraction Propylene Analysis Known Deviation Percent Dev..558.539 - o019 - 3,4. 374.389.015 4, o.688:703 o015 2,2,568.565 o003 - 0.5,528.557.029 545. 256 o 255 -.001 - o 4.867.894.027 3.1.133.142 oo009 6.7.427. 404 -.023 - 5,4.149 160.011 70 o.921.924 003 0. 3.457.448 - 009 - 2,0.268,282 o016 6,0.891.921 o 030 3 4 o275 o290.015 5,5.930 938 008 o g.786 809,023 2 9.904.898 -.00oo6 - o 6.667 o690.023 3,5.0843.09og4 010 ll, 9 933.942 9011 1.2.0658.0624 - oo.0034 - 5.0 Average absolute percentage deviation 3o7%6

APPEND IX E COMPUTER FLOWSHEETS A. Data Reduction Routine The detailed flowsheet for all calculations as performed by the IBM 704 in reducing the break-through curves to values of the diffusion coefficient D is here given,.144_ -

FIGURE 22 DATA PROCESSING CALCULATIONS COMPUTER FLOW SHEETS

MASS BALANCE CLOSURE CALCULATIONS LOAD 1st CORE LOAD READ INPUT DATA TRIG OFF AND STARTT / TRIGPRI0 INPUT Pk =Pk+l + eAPk DATA YES k > 0 Yi,l =initial COMPUTE GAS HOLDUP i <n IN DEAD SPACES < NO COMPUTE Wo i Go Wo/Wave - < COMPUTE mA & mB vo m|Go/pfa COMPUTE minitlal I ( =

-147 -PRINT COM-PUTE c ---- sA init. 4B A Yo - Yinitial Go = GoYinitial Yo Yinitial o(l - Yinitial) ~~PR. GINTo, COMP tj 0 0~~~0 'l 1 - *Yinet] t i 0 PRINT tj G. v. - _~Yi~J yG Gi j/,fax G l pt,. (i YES ~IYES -e' n- <n ii+ lO I~(N

-148 -k k 0 ` n YES j < n —~ ~i-= ti ti + tiN NO ti = ti/(nan + 1) PERFORM POLYNOMIALl CURVE FIT OF Gi, YES OF ORDER mg TO. tisc FOR O < j < nan COEFF'S gi <m<NO. 3m <m_ N O YYES

-149 -PRINT COEFFIC OENS gi E~~~~~G~t~) =~ gi,n(j j)n gi,n n PRINT YES t j <n 1/ I~~i(ti,j) NO /i limit i = Go ti 1 + I Ui(t)dt- faxdi -(dead space corr.)i till RINT sl'init = ( i-Gootim)/L YES Mi init. NO si,init = ( i )/L PRINT Ei = (mi, init mc, init)/minit} YES 1 E ax ax = max( IEi I),1< <n i< >E a NOI NO ON ~~~~~~~~~~~~~~~~~,, ho OTRIG 3 \ ~B

-150 -YE" ~~ init - Ui init G ), 1 NO 3F ~ ~ I ~PRINT b ti 5 ti b ti-.i NO o ti~~jt = ti + b ti YES j <11 PRI~NT " EXCESS IVE 3 ~ TIME SHIFT -

YES ~ ~ YE i n N~~~~iln2(g-l -ij)L 2 --— ~~~~~c ql 9,)/ 1 O~~~~~~~~~~~~~~~~~~~~~~~~11 NO~~~N ql~~~n -(mA/m )qingi~)/n YES ~ ~ ~ ~~E i < nr" NO ~ ~ ~ ~ N

-152 -PRINT x0 Xi-1 + (Axi)/2 ~YE ~YES NO mt = xG + (i/ int Q.G + (1- Q)* Gint = G Yi = iiJ1 +(1 i j _ i1 Gf

-153 -YES 1 yinnt /(tkjl - tkj)| =.Gk j_1 + (1 + Q) Gk k> int k-n 1 I Yk Ykii,-i (j-1 'Yi, j USE THREE POINT INTERPOLATION FORMUILA ON YES Gint AND yint, k = nc, nc -1, nc - 2 TO OBTAIN G AND Y AT X AND T USE THREE POINT INTERPOLATION FORMULA ON Gknt NO AND ynt, k = i+l, i, i-1 TO OBTAIN G AND y AT X AND T COMPUTE y* I H COMPUTE ky C OMPUTE sj C OMPUTE m

-154 -=1 y l B d = s* - m c A YES {> >~~~~~~~c PRINT < n, T, NO G, yy Re|, SC., ky,q S*L] YES NO o D1 =Dass COMPUTE s- Do = Da i = D2 D1 = D2 NOO~ k

-155 -N 1 YES NO i\ PRINT 11 Da~e = Dave = Dave + T2 D OFF )~ I NO ~/ I IONO ~~~~~PRININT "ve NEATve/(ncop) a PRINT "EXCESSIVE 1 ITERBATO TRIG 1 ON

-156 -B. Plug-Flow Model Equation Solution The following pages contain a detailed flowsheet of all calculation sequences used in the coi puter solution of the equations as detailed in the Theory section,

FIGURE 23 CONCENTRATION,HISTORY CALCULATIONS COMPUTER FLOW SHEETS -z157 -

-158 -PRINT LOAD C INPUT PROGRAM - READ INPUT DATA DATA AND -r - ro/nr L~, /r t Yin YO'Vin= Vo ON TRIG 2 OFF > 1 krr> krfl kr>lr Skr x; = ~ So NO =0 "AV0/(f.a.v0) — l x = OkE0 lj F0 0

-159 -PRINT COMPUTE 01210211 x COMPUTE PHYSICAL PROPERTIES, IE\TERR,l R2 = 72 FACE MOL FACTIONN RJ=R Rj y* AND RATES R. O -2 33 R AND Rj GPI YES JC~'./~. OR~ J COMPUTE SAs | A OR s < ~ a t~OR |~ NO ~~~~~~COMPUTE si, J I US~~TING FUNTIN ( Iterato suJb-R R2 R ENOR SO Sn s,,-sO~)/Snr>-OllNO C OMPUTE sil E USING FUNCTION 3 (Iteration sub- +1 routine) ) = 3 y = Yo v = vltJ = t- l + At

-160 = i YESY 0kr rz kX >PRINT =<~\NO/ YE YES j xAxX = > o COMPUTE X (y), YES x1 < o YES < ~ AND X2 (v) USIN) G OR>a12 NO x >_ (ITERATION SUBR COUTINE) COMPUTE X1 (y), X2 (v) ANDX3(s*) USING FU NCTIONS 1, 2 AND 3 (ITERATION SUBU.rTI. )

— 3 R 2 T2 3 = T O R R YES S 'O~ V.1 'X2 Yj = X, NO YES ti ti + (At) ON npr T` G 1 ~~NO OFF tj t +~ (Lt) TAPE 4 0*00s nr. YES NO PRINT COMPUTE s*C S*C Y*, 1-y~ey A) B 1~ 3 Al~ B) j 'R2. R3 _ k

-162 -< ( o0) OR1 ES (sj < 0) AND YES B YES IT1 I> Rli NO n n NO I INO YES I i4~~R 2 I~ojn~j \ ~ NO YES r | | Rlt> 2+> Tkr s k, r>n NO YES "NOFCYES ~~~~~~Y1=Yin H " 1 \~ > vj i >, inx NO I INO t5 t +A. (f H H + hi YES 3 Yjl n

-163 -YES 9 YES ~~~~~~~~~tjl =tjl + (,Ax)/vin < n t =t 1 +(A~ J1 LOAD PARTICLE CONC. PROFILE ON LISTING ROUTINE TRIG A~ND TRANSFER 8 TRIGYESEN

-164 -Function 1 COMPUTE PHYSICAL PROPERTIES, INTERFACE MOL FRACTION y*, MASS TRANSFER2 COEFF. ky, RATES -1 -2 — 3 R1, R2, R GRPI RETURN Function 2 COMPUTE PHYSICAL PROPERTIES, INTERFACE MOL FRACTION ENTRY 1 MA y% MASS TRANSFER COEFF. ky RATES RT, i GRP I COMPUTE PHYSICAL PROPERTIES, ITERENTRY 2 FACE MOL FRACTION y*, MASS TRANSFER COEFF. kyR - 1 -2 YRt GRP3 I YES No > tj + At NO YES g = (t - ta-l )/(te -

-165 -v =.vg + (i - ).v_1 R =OR + (1 - ).Rl RETURN X2 i= + + 1 )/2] Function 3 COMPUTE PHYSICAL PROPERTIES, INTERFACE MOL FRACTION i = AENTRY t* MASS TRANSFE At' = 2(A)/(X2 + vj ) COEFF. ky, RATES 11 -2 73 R1, I2 K3GRP I COMPUTE PHYSICAL PROPERTIES, INTERFACE MOL FRACTION y, MASS TRANSFER COEFF. k RATES

-166 -D. AT (Ar)2 C n = n-2)Ct 1 n~~~~ En a/Dn Dn 1 + 2 n )a -n,, En_, YES n n~~< 1.n < n~r AL n S AR 3 R -3 3 n m~~~ n ----— c ~ F (s f+C F -)/Dnn~ 1 1~~~~~~n n - YES n <n r n-r-mIL~ NO YES S s E + Fn> n n n+ 1' n n - TT

-167 -YES 7; m ~< nTON X3 = NO OFRETURN 1 rr RETURN 1 RETURN 2__

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