THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING EFFECT OF THE DISTRIBUTION OF RESIDENCE TIMES UPON THE PERFORMANCE OF AGITATED REACTORS.Gordn.... - A dissertation submitted in partial fulfil)ent of the req.uirenents for the degree of Doctor of Philsophy in the October, 1-958 IP..... Uie..;si.y o. M.c IP —332

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Doctoral Committee: Professor Robert R White, Chairman Professor Julius T. Banchero Professor Cecil C. Craig Professor Robert C. Elderfield Assistant Professor Kenneth F. Gordon ii

ACKNOWLEDGMENTS The author wishes to express his appreciation to all those persons who aided in this investigation~ In particular, he wishes to acknowledge the interest, guidance and criticism offered by Professor Robert Ro White, chairman of the doctoral committee. The interest and suggestions of the doctoral committee, Professors J. T. Banchero, C. C Craig, R, C. Elderfield. and Ko F. Gordon, were also sincerely appreciated. The author wishes to express his gratitude to Messrs. Francisco De Maria, W. J. Murray Douglas, and Richard C. Faulkner for their interest and aid during the course of this study. The shop and secretarial personnel of the Chemical and Metallurgical Engineering Department were most cooperative and helpful at all times The author is also indebted to the Horace Ho Rackham Graduate School and the Michigan Gas Association who made this work possible with financial assistance through fellowship grants. iii

TABLE OF CONTENTS Page ACKNOWIEDGN S N T........ o,,. o........ 4 o. o....,.. 4.4 4... iii LIST OF TABLEIS.4.*.,..*..,.,,,........ 4.,.... vi LIST OF FIGURES.,. * *.....*,.4.........,*..... vii STATEMENT OF THE PROBLEM,,. *,.,.*,* 44 44 44444.4 ix CHAPTER I INTJJRODUCTION,. ~.~ ~ ~. t ~. ~ ~. )~ o. ~. o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~. ~ *. * * W.* o *. ~ * 1 H6eated:-Data- in the Literature,....If444444.......... a II THEORY.. 44W44444444 ~.,~~.. a,44 44 4, aAts 4.o 3 Pulse Experiment. 4. 4 ** 4 * 4 4.4*. o *044 44o44 4.. 3 Step-Function Experiment.....,.,.,.............. 4 First Moment 4...,4.4..440**.. 4 444. - 4 7 Distribution of Residence Times Model.,,*,.,... 8 III, BATCH REACTION RATE CONSTANTS.......,........* <..*... 9 Description of the Reaction.,,.., *,,.,.,,..,.. 9 Materials.,.... 44444 44 4'44 444 4 4 4 * 4 4 444 10 Analytical Methods...................... 44.+.- * 11 Analysis of Tertiary-Butyl-Bromide Solutions.,, 11 Determination of the Concentration of Ethyl Alcohol in the Solvent..4,.,.,,.,,,,...... 12 Equipment,, 44*4444~44. ~444 *44-,. 4w 44*4.4i ~1 12 Procedure 14* 4 44444,, 4 * 4* 4... o,.,.3.... *.. 13 Calculations and Datae,,........^..*4.o. 4...4.*..~*4. 13 Correlation of Batch Constants 4....4,,,.. v. a 4. 17 Discussion..i......... -. i..... i4 4 4 21 IV. CONTINUOUS FLOW SYSTEMS,,..,.... 4*.t...4*4,.4,.** *... 22 Description of Dyes. 4..,,,,.,,,.,.. 22 Flow System4 44........ 44.... *......, 44*. 23 Equipment.4*44...4 4.44..4.* 4..4,4i.4.4 #.4........2 23 Reactor Inlet Flow System..*,,..*..o....23 - Reactors *~ ~~~~. 44*444...*......* 4.44.4444 4 4 25 One-Compartment Reactor* ^~8.- 4 ** ~ ~44. 26 Glass-Bead Reactor... 4:.. 4......,.. 28 Two-Compartment Reactor...,..,.,,,.. o.. 531 iv

TABLE OF CONTENTS CONT D Page Colorimeter, Recorder and Dye Injection,. *,,,,* 33 Reactor Outlet Flow System,,..,.*.......,4...35 Procedure ata......,,.. ~.....,...... - $......* 374 Preliminary.....o.,,. 4o,.o....444.s4.*.. *44... 40 One-Compartment Reactor..,,.,.,., 4,,,. 43 Glass-Bead Reactor...,., o,,.,...... t.. 84 47 Two-Compartment Reactor,..,... -,.4,......). 4, 50 V. DISCUSSION OF THE CONTINUOUS REACTOR DATA..,,*,,,,..... 53 Engineering Approach 3., o., o.. 4 * *. 4~ 53 Preliminary Data,,,...,,,...*.i4t.o o4$ 4 4 4 53 One-Compartment Reactor Data..,, o,.,,,,,, o,. 54 Glass-Bead Reactor Data,..4...,,.,.,,..~* 56 Two-Compartment Reactor Data,.,,,,,,,,,,....56 Statistical Approach 8.....,.......*.......... 58 One-Compartment Reactor Data,. *,..,., *,.* 62 Glass-Bead Reactor Data.~....,, o,,.,....,,.,.. 65 Two-Compartment Reactor Data..i., *.i..,*,... 6, 65 VI. SUMMARY AND CONCLUSIONS,.,... *....4..,.... 69 Summary, a.,,,,..,..,.0 o 4,.,...,,.,,.... 69 Conclusions.... 4,.* 4 4,,..., 4,,,,*4. - a.* I,4 69 APPENDIX I ADDITIONAL DERIVATIONS, a.A * 4... a.+ 4... 73 Calculation of Conversion which has Occurred Before Sampling....,. 4 a.... 44....... i..... 73 Maximum Error Caused by Using.a Mean k4,..,.,,$..* 73 APPENDIX II. DETAILED DATA AND SAMPLE CALCULATIONS..,.*.,**..,,,. 75 Calculations for Run 45,.*4;444. ss4 S 4 44.,.4# O,'s4 75 Sample Calculations for Statistical Testsb,,...,,..* 86 APPENDIX III. CALIBRATIONS.,. o, 4;4,, * O,..,.,.,,..o.,.,.,4 *, -4 91 Dye Concentration as a Function of Colorimeter Reading,,,.:.,,.,,.,....~ o,. 4 ~. *: ~.... 91 Thermometer Corrections'..,..,,,,,,,.o.,,, o.., 91 Aqueous Ethyl Alcohol Feed Bottles.,,..,. -:. 4:. 95 Tertiary-Butyl-Bromide Feed Bottle ^. *..4.,o,,,.4. *. 97 Twk Compartment Reactor Volume,,..... 4....... - 99 NOMENpLATURE......#.4..4., o..*.44 o..o4.# 44...4.444444...44.... 101 BIBLIOGRAPHY~ ~ o.,.. ~.. o. 4 a ~ ~ 4. 44 *. 4. 4 4o o...o ~ o o o,. ~ ~,. 104 v

LIST OF TABLES Table Page I Batch Kinetic Data,,,,,o., o4 oo.,,.,,.,4.,o,4,,,. 15 II Percentage Difference Between Confidence Limits and Value Predicted by Equation (10)....*8...... 18 III Batch Kinetic Constants at Various Initial Concentretions of Tertiary-Butyl-Bromide 4...,,.,....,.,,,. 20 IV Preliminary Data -- Distributi-on Functions under NonReacting Conditions -- One-Compartment Reactor.,,,..... 42 V Distribution Function:s under Reacting Conditions,**.,,,, 44 VI One-Compartment Reactor Data.o..,4,.o.:o. * 46 VII Glass-Bead Reactor Data...,...., o............. 49 VIII Two-Compartment Reactor Data, *,,4.,,.,........ 4 *,, 52 IX Sample Data of Tertiary-Butyl-Bromide Samples4..,.., 76 X Sample Data of Reactor Variables*.,,4 *,,.4., ^,,.,,,,, 78 XI Sample Calculation of the Distribution Function from a Recorder Trace,,4 * ** 44 4 4 4* i444 82 XII Sample Calculation of the First Moment and Conversion, 84 XIII Sample Calculations for Barlet ts Test,,,.,,,o, 88 XIV Sample Calculations for the Test of Nornality,.., ^.,,. 89 XV Thermometer Calibrations,... o.4,,...o,,,,.4,. o.r 93 XVI Calibration of Aqueous Ethyl Alcohol Feed Bottles.4,,,. 95 XVII Calibration of the Tertiary-Butyl-Bromide Feed Bottle... 97 XVIII Volume of the Two-Compartment Reactor,,. 444,.4. 4,,,,4.. 99 vi

LIST OF FIGURES Figure Page 1 Concentration as a Function of Time...444..*..4....... 3 2 F(G) as a Function of *,..4...,4..,*............ 6 3 Flow Diagram.,.,..,...... * * * * *..... *. 24 4 2One-Compartment Reactor ^..7~~^ ** * 27 5 Glass-Bead Reactor for Runs 27 to 30.444,.4o4.4o...... 29 6 Glass-Bead Reactor for Runs 37 to 41...................... 30 7 Two-Compartment Reactor......... 32 8 Modification of the Colorimeter Circuit................. 34 9 Reactor Level Controller<..........o............ 36 10 Sketch Showing the Inlet Stream Positions for the OneCompartment Reactor.,4.*,,, * 4 4 4.4*4 o o 9 41 i1 Distribution Functions for the One-Compartment Reactor,, 4 4., 4 4~-4 4*0 4 4 * 45 12 Distribution Functions for the Glass-Bead Reactor,..... 48 13 Distribution Functions for the Two-Compartment Reactor... 4... 4 V... *.4.. Wo o -,.,.. - 44***. *.. a 4 51 14 Fractional Conversions for the One-Compartment Reactor..., * o444444,44o.,4 4 4a44*~4X. 44 4 4* 4*4*4 4.44* 55 15 Fractional Conversions for the Glass-Bead Reactor,..*.. 57 16 Fractional Conversions for the Two-Compartment Reactor...4.. 4. 4.*444 4* *.* 4 4 * 4* 4 *... 44 *4 *44 59 17 Oe-Compartment Reactor Relative Conversion, Differences Based Upon the Perfectly-Mixed Distribution....4...... 63 18 One-Compartment Reactor Relative Conversion Differences Based Upon Measured Distribution Functions. 4.*.44* 4*.. 64 19 Glass-Bead Reaptor Relative Conversion Differences Based Upon Measured'Distribution Functions *..*... *.... *.. 66 vii

LIST OF FIGURES CONT'D 2Figure Page 20 Two-Compartment Reactor Relative Conversion Differences Based Upon Measured Distribution Functions.*.. * *,.,,, 68 21 Representative Distribution Functions.., o,*...,.,, 4 70 22 Sampling Model,.,,.* 0,,,,,,,*,,,,,,,,,,,.,-.. 73 23 Recorder Trace for Run Number 45,,,,,,,,***,4r*,***,.o 81 24 Calibration of Blue Black in Aqueous Ethyl Alcohol Reaction Mixtures.....,*.,...... o,,,,... *., o... 92 25'Thermometer'Calibrations,,*,.,,,,,,,. 4=,.,,,*,,,, 94 26 Volunes of the Alcohol Feed Bottles,,.,,,.....,.,,.. 96 27 Volume of the Tertiary-Butyl-Bromide Feed Bottle.,.^. 98 28 Two-Compartment Reactor Volume Calibration................. 100 viii

STATEMENT OF THE PROBLEM To evaluate the applicability of distributions of residence times for calculating the first-order conversion occurring in continuous, homogeneous, liquia-phase, flowsystems.

CHAPTER I INTRODUCTION Greater and greater use is being made -f continuous processes in the chemical industry~ A continuous process consists of a number of individual units of equipment through which materials are moving in a more or less continuous manner. The different units vary greatly in design from the point of view of flow behavior. Some units, which have a great deal of mixing in the direction of overall flow, behave like perfectly-mixed systems. Others, which have very little or no mixing in the direction of overall flow, behave like ideal slug-flow systems, Then there are others whose behavior is neither perfectly-mixed nor slug-flow. These are the pieces of equipment for which there is a great need for having general methods for predicting their performance. Danckwerts(lO) has suggested how the distribution of residence times for many of these systems could be used as a model for predicting their performance. There is yet very little data which has been taken to evaluate the distribution of residence times model as applied to many processes. Among these is chemical reaction. Very little experimental work has been published in the literature to determine whether or not the distribution of residence times model proposed for predicting the amount of conversion in homogeneous, first-order systems is valid. This research was undertaken in order to evaluate the distribution of residence times model for homogeneous, first-order, reacting systems. -1i

Related Data in the Literature In determining flow patterns and the amount of chemical reaction occurring in contiinuous systems some investigators have made measurements insi-de the systems, others have made measurements only on the outclet stream: In the former group are Aiba(l) who has measured flow patterns in stirred reactors and Prausrliitz25,26)9 who has measured concentration fluctuations in a packed column. In the latter group are Gilliland(16), who has measured the distribution of residence times and conversion occurring in fluidized systems; Cleland(6), who has predicted the distribution of residence times and has measured the amount of first-order conversion occurring in viscous-tubular reactors; Kawamura(20), who has measured the distribution of residence times and the amount of second-order conversion occurring in a horizontal cylindrical reactor: and Nagata(23) who has measured the distribution of residence times and the amount of first:order conversion occurring in columns with various numbers of compartments and stirrerso Danckwerts(9 ll 12) has suggested methods for measuring concentration fluctuations both inside a system and. the exit streamo Measurements made inside a flow system have the advantage that in general, they describe the flow system more completely than measurements made only on the outlet stream, but measurements made inside a system are in general more difficult experimentally and tedious than measurements made on the outlet stream0 In the experimental work which was performed for this thesis all measurements were made on the outlet stream~

CHAPTER II THEORY Suppose that to a continuous reactor of constant volume V the inlet and outlet flow rates are constant and equal to v. The bulk resiV dence time for the system is v Some elements of liquid will spend a time V V less than V in the system and others will spend a time greater than v in the system, that is, the elements will have a distribution of residence times in the system. Pulse Experiment In order to visualize the distribution of residence times suppose that at time t = 0 a pulse of tracer of quantity Q is injected into the inlet stream to the reactor, Let C(t) be the concentration of tracer in the outlet stream for such an experiment. A graph of C(t) against t might appear as shown in Figure 1. The rate at which tracer leaves the reactor is C(t) tl TIME, t Figure l1 Concentration as a Function of Timeo -3

-4vC(t) and the amount of tracer leaving during the interval O to t is f vC(t)dt. Then the fraction of tracer leaving during time 0 to t is t 6VC ) V,tv — C() adt. Since is the length of 1 residence time, then O = tv Q...V V the umber of residence times, Then t 9 /vC (t )dt Vf(Y ) dg O.Q O Q Q Iet V(): = lE(() be the distribution of residence times for a pulse input. Then the fraction of tracer leaving during 0 to Q resi-'0 dence times is r0 E(-)da. Let F(0) = E(:)d: (1) 0 so that F(.) is the fraction of tracer leaving during 0 to 0 residence times. If the reactor is under. steady-state flw conditions then F(Q) is also the fraction.f liuid thrughput which has been in the reactor residence times ranging fronm 0 to 0. When time becomes very. great all the dye has left the reactor. Therefore limit -0 o / E(Q)do = 1O (2) 0.''..' -.' Step-Function Experiment Sppose tracer-is fed to a continuous flow system as a stepfunction, For 0 < 0 no tracer has entered the system~ For > 0- all

the liquid entering is tracer, Let F' (@) be the fraction of liquid.in the outlet stream at residence time 0 which is tracer. But tracer is liquid which has been.in the system residence times ranging from 0 to 0 Therefore F' (Q) is the fraction of liquid in the outlet stream which has been in the system residence times ranging from 0 to; 0o But in the preious section the fraction of liquid in the- outlet stream which had been in the system residence times ranging from 0 to 0 was F(Q), Therefore F' (Q) = F(O) and from now on the prime will be omitted. Note that by Equation (1) 0 F() =- FE()d(9) o In the step-function experiment the rate at which- tracer leaves the reactor is vF(G) and the amount of tracer which has left during O to G residence times is t 0 IvF(Q)dt =V J F(Q)dQ 0 0 0 Let f0 I(Q)do be the fraction of liquid in the system at residence time 9 which is tracer, The quantity of tracer in the system at residence time Q is V J I(-0)dQo Upon Summarizing: Moles of tracer in during time 0 to 0 = vt = VQ VJ dO Moles of tracer out during time 0 to - = VJf F(G)dQ Moles of tracer in the system at time 0 = Vf0 I(Q)dQ Moles of tracer in the system at time 0" = 0

A material balance for the system for the interval 0 to 0 is: Tracer in - Tracer out = Tracer present at time 9 9 9 9 V /d V- V J F(O)dg =V I(O)d 0 0. 0./[1 - F(Q)] d9: = I(Q) -d4 0 0 but lim -~ co / I()a: _ oO (3) 0 that is, when time becomes great- only tracer is present in the reactor~ Therefore, 9 lim.o -,! [i- F(1)] O lo O (i4) 0 O F(9) might appear as shown in Figure 2. 1.0 F(G) Number of Besidence Times, 9 Figure 2, F(Q) as a Function of 0,

First Momentr The first moment of the distribution of residence times E(O) is.Q fO EE(Q)dGo But from Equation (1) it fellows that E(-)d = dF(Q)o Therefore O oo J E(Q)Q=' Q-dF(-) O 0 From Figure 2 it can be seen that the li f -dF(Q) is the cross-hatched area which was proven by Equation (4) to be 1., Therefore, e a f GE(o)d i J [1 - F(Q)] d = l (5) o o that is, the first mment about an abscissa of zero of the E(Q) function is 1,Go For any continuous flow system there are two material balances, The first is that the total fraction of material of all ages leaving the system in the outlet stream is 10-: This is Equation (2) The second is that the ttal fraction of material of all ages inside the system is lo.0o This is Equation (3)o Equation (5) shows that the first mont f EE(') is identical to the internal material balance, Thus either the two material balances or the outlet material balance an the first moment can be used to check to determine whetger tracer is actually behaving as a tracer, Capen(5) and Truesdale(29) have discussed the value of these equations as checks,

-8Distribution of Residence Times Model... -.. t...'. - -i... J.,: ~..'.'.-...v, Danckwerts(lO) has proposed the distribution of residence times model for predicting the amount of first-order conversion occurring in homogeneous, liquid-phase, flow systems. Suppose that for any system the distribution function E(@) and the reaction rate constant k.are known. By the distribution of residence times model any flow system is equivalent to a series of slug flow reactors in parallel in which liquid spends time G, where G may be anywhere from 0 to o,. The fraction of the total reactors in which liquid spends times ranging from 0 to 9 is, the fraction:of the liquid which has residence times ranging from 0 to 9 in the system and by Equation (1) equals fO E() dG. The conversion in each reactor is 1 - ek where T is the length of one residence time. The conversion for the system is then the average conversion for all the reactors 0 - SD =im,lim (1 - e-kT)E(@) da (6) 0 It is the object of this research to evaluate this model, that is, Equation (6), for calculating the amount of conversion occurring in first-order, homogeneous, liquid-phase flow systems.

CHAPTER III BATCH REACTION ATE CONSTANTS In order to predict conversion using the -distribution of residene tei8es model ift is necessary to know the reation rate constant; as well as the distribution functiono Reaction rate cn.stants were measured by a series of batch experints and. correlated over the range of.variables used for continuus runso ~-',' -: Description of the Reaction The reactn used.for all experimeal ork was the hydrlysis o tertiartyly.br omide. in aqueous ethyl alcohl. The mechanism of this reaction is simultaneous, nucleophilic, substitution and elimination (18,19,27) The first step, the ionization f tertiaryt-butyl-brolide, is the rate-c.ntrolliing step and is common to both substitution and elimination. (19) Br I + C - c -C3 - C - C*- + Br C. CH5 The bromide ions then react by any one f three fast reactions to form IiBr quantitatively. -.9

-10OH CH3 - C - CH3.+ Br + j Br + CH3 C CH3 I.{I-~ -''''3.c 21 1 CH5 C:3 c~3 Ci3 - IBr + C3 - C - 0 CH2CH3 CH3 According to Bateman(3) the amount f second order reaction is not measurable and so the reaction consists essentially of the unimolecular ionizatio -of tertiary-butyl-bromide fdll wedby rapid formation of EBr. From the mixing viewpoint the reaction is first-order and is the same as a radioactive decay reaction. Materials The aqueous ethyl alcohol was C.P- 95 percent alcohol which was diluted to the desired concentration with distilled water. Tertiary-butyl-bromide was prepared by a modification of the method of Sudborough (28) Silica gel was used in place of calcium chloride as the drying agent. Final purification of tertiary-butylbromide was by distillation, the fraction boiling between 73.1 and 73.60C/760 mm. being used for all kinetic work. Other materials which were used were C^Po acetone to quench the reaction, carbonate-free sodium hydroxide as the alkali for titrating the solutions and phenolphthalein as indicator.

-11Analytcial Metd Aalys is of Tertiary-But-Bromie Solutios Samples Of the tertiary-butyl-bromide in aqueous ethyl alcihil siobtion were remoed from the reacting system by a 25 ml,- pipette. The contents of the pipette were drained into approximately 250 ml. of cold acetone in order t qu t he reaction. While the tertiary-}utylbrmide- solution drainled intothe acetone the flask containing the acetioe was shaken Y:LgrBly in order to dissolve tbe tertiary-butyleomide solution in the acetone as quickly as possible in rer to obtain a rapid quench. The time at which the solution began and finished leaving the pipette was recorded and the arithmetic average time was used to cotute kinetic constantso Te quenched tertiary-butyl-bromide silution was then immediately titrated. with carbonate-free sodium hydrxide using phenolphthalein as the indicator A blank crrection was made fr the acidity of acetone and ethyl alcoho1. Using estimates of the maxim vaues f ftemperature of quenched solution time required for titration and water o0ntent of acetone, the maximm error in fractinal cersion by assuming zero cnversi to be ccuring while the s4lution was quenched was 0.0O. The actual errr in general was proba'bly cosiderably less becaue1 maximum estimates of each of the variables were used. In order to determine the initial quantity f tertiary-butylbromide in the solution samples were allwed to react to cpompletion

-12= during a period of from ten to twenty hours at 20 to 250Co The samples were then titrated, as described previously for the partially-reacted samples, with carbonate-free sodium hydroxide, Determination of the GCncentration.of Ethyl Alcohol in the Solvent The concentration of ethyl alcohol in th aqieous ethyl alchol used.in the reaction was determined by a Westphal balance. The balance was calibrated by solutions whose cnrcertrations were determined by a pycnometer.. Equipment The reactin vessel was a five hundred mn, three-necked, glass flask with two vertical creases each 1/2 in. deepo The flask was creased in order to increase the rate of mixing, Weissberger(30) has described the creasing of glass vessels, The stirrer was a bent glass rod and was 7/8 ino in diameter, The diameter of the vessel between creases was 2-3/8 in, The speed of stirring was approximately 1000 r.pm. Macnald(21) has sumnarized what several investigators hae found to be high enough stirrer speeds to ensure sufficient mixing for kinetic purposes. Using this discussion as a basis it was considered that 1000 r.po.m. was high enough for the creased reactor which has just been described. The stirrer was sealed by the glass tubing seal described by Morton. (2) Temperature was maintained constant by immersing the reaction vessel in a constant-temperature, water bath, The reactor temperature was measured by a thermometer which could be read to O 010C and was calibrated against a National Bureau of Standards thermometer,

m13Procedure Four hundred mlo of aqueous ethyl alchl were placed in te caed flask,described in the previous section, and broght to temperature in the constant temperature bath. After the teperature of the alciohl had remained constant for at least fifteen minutes 4 mlo f tertiary".butyle-bromide were injected into the aqveous ethyl alchol by a 5 ml. hpodermic, The mean time of injection was considered to be the time of start of reaction Periodically samples were withdraw by a 25 mi. pipette, quenched and titrated as described on page 11, The.greased flask was stirred except when samples were being withdrawn, Stirring was stopped. during sampling in order to prevent the pipette from being broken by the stirrer, The temperature of the reacting solution was recorded at least once between samples. Calculations and Data Batch reaction rate clpastants were calculated for the time intervals between successive samples using the integrated form of the first-order rate equation~ k 2.26 log1 (7) t 1 -f Since temperature changes up to + O,10C during the course Of the reaction the temperature for each interval was determined by plotting teperature as a function f time and using the average temperature for each interval. The average temperature for each inerval was the integrated. average temperature for the interval.

For the tertiary-butyl-bromide reaction rate of reaction varies greatly with both temperature and concetration f ethyl alcohol A series of batch runs at temperatures varying from 23 to 28C and aqueous alcohol concentrations varying fro.064 to 68 mass fraction ethyl alcohol were made. These data are presented in Table I. The colums are as follows: Column DescriptiOn 1 Run number 2 Temperature, ~C 3:Mass fraction alcohl in the aqueous ethyl alcohol IInitial concentration o tertiary-butlbromide, mles / 1. 5 Time between samples, sec. 6 Fractional cversion fr the interval, based upon there being zero conversion at the beginning of the interval 7 Reaction rate costant, sec,"l

, -15TABLE I. BATCH KINETIC DATA 1 2 3 4 5 6 7 Run Tempo C C Time Conversion iON Number TC, EtOH ~t, Sec. Sec J-7 25.02.6589.088 250.2600 1.204 J-7 25s14.6589 o088 440.4065 1.186 J-7 25.11.6589.088 450.4524 1.259 J-8 24.90 o6589.088 250.2429 1.113 J-8 25.03.6589.088 380 3.568 11o61 J-8 25.06.6589.088 390.3771 1.214 J~8 25006.6589 o088 4oo.4011 1.282 J-9 25.03.6434.088 260.3027 1.387 J-9 25.16 o6434 -088 340.3842 1.426 J-9 25.19.6434.088 390.4457 1513 J1O0 24.98.6434 o088 250 834 1.333 J-10 25008 o6434.088 410.4387 1o409 J-10 25.07 ~6434.088 360.4129 1,479 J-11 23 03.6434 o088 250.2380 1.087 J-l1 23014.6434.088 380.3463 1.119 J11 23.13.6434 o088 510.4498 1.172 J-12 22.99.6589.088 240.1912.o884 J-12 23.12.6589.088 360.789.908 J312 23,13.6589 o088 450 34FT5 o949 J-12 23.08.6589.088 470.3754 1o001 J-13 24.98.6612,088 262.2541 1.119 J-13 25o13.6612.088 390.3614 1.150 J-13 25.18.6612 0088 340.3436 1.238 J-14 24.90 06612.088 242.2310 10085 J-14 25007 o6612.088 288.2824 1.152 J-14 2513.6612' o088 350.3435 1.202.J-14 23,13.6612 ~o88 360.3463 1.181 J135 22.91.6612 o088 240.1875 -865 J-15 23.05 o6612 o088 320.2491.895 J-15 23.14.6612.088 420.3245.934 J-16 23,00.6788.088 260.1702.718 J-16 23.11.6788.088 340..2224.740 J-16 23 12.6788.088 330.2263 0778 J-16 23o04.6788.088 340.2270.757

~i6TABLE I. BATCH KINETIC DATA (CONT'D) 1 2 3 4 5 6 7 Run Temp. CEtOH C Time Conversion 10ik Number T~C. 0 t. Sec. Sec-1 J-17 24,88.6788.088 250.1982.884 J-17 25.02.6788 0,o8 290.2376.935 J-7 25.03.6788 oO88 310.2537 o944 J-17 25.03.6788.088 370.2981 o957 J-18 24.96.6788.088 240.1938.898 J-18 25o06.6788.088 310.2475.917 J-18 25o06.6788.088 350.2877 *969 J-18 25.06.6788.088 360.2957.974 J-19 28.05.6788.088 230.2588 1.302 J-19 28.16.6788.088 250.2926 1.385. J-g9 28.07.6788.088 350.3870 1.398 J-20 27.78.o6612.088 220.2845 1.522 J-20 27.95 6612.088 320.4094 1,646 J=20 28.02.6612.088 320.4167 1.685 J-21 27.85.6612.088 220.2832 1.513 J-21 27.93.6612.088 260.3473 10635 J-21 27 97.6612.088 290.3881 1.694 J-26 24.97.6568.088 290.2841 1.152 J-26 25.10.6568.088 280.2872 1.209 J-26 25.09.6568.088 310.3200 1.244 J-26 25.05 o6568.088 390.3763 1.210

-17Correlation of Batch Constants Grunwald(l7) has suggested that the best way to correlate reaction rate constants for -tertiary-butyl-chloride over a wide range of alcohol concentrations is log k A' B' C' (8) ETOH where A' and B' are constants and C'ETOH is the mole fraction of ethyl alcohol~ Over the narrow range of alcohol concentrations used in this research mass fraction and mole fraction are nearly exactly proportional to one another. Therefore Equation (8) can be rewritten as log k A" -BC ETOH where A" and B are constants and CETOH is the mass fraction of ethyl alcohol. The variation of k with temperature is normally correlated by log k = A"' E R(T + 273.1) where A"' and E/R are constants and T is the temperature in ~Co The expression used to correlate data in terms of both alcohol concentration and temperature was logZ. k A. A-BCpn~ ~ (9) log k = A - BCETo - R(T + 273.1) This equation is the sum of the two previous equations. Since the ranges of variables were small it was not considered necessary to add the term DCETo/ T +E27H o The constants in Equation (9) were determined by a least ip'~ 0f7~JI

-18square fit of the data in Table I, and the equation became 4,641.22 log k088 = 15.9501 50223 CETOH T + 27310.64 < CETOH <.68 23 < T~C < 28 Co =.088 where T is the temperature in ~Co CETOH is the mass fraction of ethyl alcohol on the tertiarybutyl-bromide free basis. Co is the initial concentration of tertiary-butyl-bromideo The 95 percent confidence limits for the general type of correlation of which Equation (10) is an example are given on page 530 of Duncanl). Hence the 95 percent confidence limits for log k o are: o88 4.641.22, 15.9501 - 50223 C TOH T + 273*10 2957 (o182 + 134.7 (C -.6623)2 + 614.6 x105 (0 T + 27310 -.335436)2 + 1243 x 104 (C - 6623)(T + 2T00B5456) TABLE II PERCENTAGE.DIFFERENCE BETWEEN CONFIDENCE LIMITS AND VALUE PREDICTED BY EQUATION (10) CETOH ToC Percentage of k.6623 25.02 0.93.6400 25,02 2,01.6800 25.02 1,69.6623 23500 1.55.6623 28.00 2,01

-19At CETOH and T equal t.6623 and 25.02 respectively, the mid-point of the correlation, the confidence limit is narrowest* Most of the continuous runs were made very close to this point. Therefore the 95% confidence limits for the continuous runs would, in general, be the value predicted by Equation (10) + 1%. The multiple correlation coefficient r = 0.988. -1.23 A series of runs were made at various initial concentrations of tertiary-butyl-bromide. These data are presented in Table III. Columns 1 through 7 are the same as described on page 14 for Table I. Column 8 is the rate constant at 25.100C and was computed from the data in column 7 by using the activation energy given by Equation (10). All the data were taken in the same aqueous ethyl alcohol solution. By performing a least square fit of the data in Table III, the change in k is C- k.o88 k088(0580)(0880- C ) (11) O O where 0.580 is the constant determined by the least square fit and CO is the initial concentration of tertiary-butyl-bromide in moles/l. The slope of Equation (11) is significantly different from zero at a significance level of 5 percent. The 95% confidence interval for k - k 088 is 0 k 088(0580)(.0880 - CO) +.0425.0714 + 63.72 (C.0668)2 This is equal to kC -k 0o88 + 013% at the ends of the interval specified by Equation (11).

-20TABLE III BATCH KINETIC CONSTANTS AT VARIOUS INITIAL CONCENTRATIONS OF TERTIARY-BUTYL-BROMIDE 1 2 3" 4 5 -6 7 8 Run Temp. CEtO C Time Coiversion 103k 105 Number T"C t, Sec. Sec k-1 k25.10 ~ C J-26 24,97.6568.0880 290 o2841 1o152 1.172 J-26 25 o10.6568 o0880 280.2872 1.209 1.209 PC. ir 25.09 6568 o0880 310.3200 1.244 1^246 J-26 25 05.6568.0880 390 3763 1o210 12818 J-27 24.98.6568.0453 260.2678 1.199 1.217 J-27 25.06.6568.0453 320.3229 1.219 1.225 J-27 25.05 6568.0453 310.3230 1.258 1.266 J-27 25.01.6568.q453 370 13640 1.223 1.237 J-28 24.92.6568.0754 270.2700 1.166 1.193 J-28 25.05.6568.0754 280.2895 1.221 229 J-28 25003 o6568.0754 340.367 1.207 1.217 J-28 24.98.6568.0754 440 o4124 1o208 1.226 J.29 24.92.o6568.0584 288.2864 1 172 1.199 J-29 24.98.6568.0584 290.2998 1.229 1.247 J-29 25.01.6568 Q584 370.3694 1,246 1.260 J-29 24.96.6568.0584 460 14338 1.237 1,258

-221 Discussion For the hydrolysis of tertiary-butyl-bromide in aqueous ethyl alcohol a survey of the literature revealed that no measurements of reaction rate constants have been reported in 70 volume percent ethyl alcohol (3) Bateman has measured constants at 60, 80 and 90 volume percent ethyl alcohol. These data were later checked by Cropper(8. If Equation (9) is used to interpolate between the values at 60 and 80 volume percent alcohol then the following comparison can be made by using Equations (10) and (11) at 25,000C and Co =.05. Mol Fraction k k ETOH Bateman Equations % Difference 10 11i 4102 oo01479 o001499 + 1o33 o4316 o001179 o001190 - 0o60.4539.000959 o000946 1.41 When the approximate nature of the correlation is considered and also that Bateman did not indicate that he made more than one mesourement at each concentration, the agreement is within the generally accepted limit of 1 to 2% for reaction rate constants. Equation (10) gives an energy of activation of 21,240 compared to (3) the value of 21,700 reported by Bateman

CHAPTER IV CONTINUOUS FLOW SYSTEMS (32) (15) The pulse response technique, which was used by Yagi(, Ebach( (13) and De Maria, was used for measuring all distribution functions. The mathematics of the pulse technique is discussed in Chapter IIo From this point on in this thesis a distribution function or the distribution of residence times will always refer to E(G) rather than F(O) or 1(G). Also t will be time and 9 the number of residence times, Twill be the length of 1 residence time, so that, t = T Description of Dyes Pontamine Fast Turquoise 8GLD Conc, 150%, which was manufactured by EDI..du Pont de Nemours and Company, was used to measure some of the distribution functions in distilled water. For the remainder of the runs in water and.all the runs in aqueous ethyl alcohol, eosin bluish, manufactured by the National Aniline Division -of Allied Chemical and Dye CorpO of Pharmaceutical Laboratories was used as dye. The formula for eosin bluish is Br Br NH O COONH4 Eosin Bluish (4,5 - dibromo - 2, 7 dinitrofluorescein) For all runs in the presence of tertiary-butyl-bromide Pontachrome Blue Black RMo Conco was usedo This is a vegetable black and was manufactured by E,I, du Pont de Nemours and Company. -22

-23Flow. System The flow diagram for the continuous reactor system is shown in Figure 3 The system can be broken up into the 0o1lowing sections: 1o Inlet flow system which includes equipment to measure and control the rates of flow and the temperatures of the inlet streams to the reactor, 2. The reactors (a) One-compartment reactor (b) Glass-bead reactor (c) Two-compartment reactor. 5. Colorimeter, recorder and-dye injection system. 4.. The reactor outlet system which included level control, flow measurement and sampling. Equipment Reactor Inlet Flow System The feed to the reactor consisted of a solution of unreacted tertiary-butyl-bromide dissolved in aqueous ethyl alcohol, The tertiarybutyl-bromide and aqueous ethyl alcohol streams were combined just before entering the reactor. Before coming together each of the two streams was controlled with regard to flowrate and temperature. Prior to each run ethyl alcohol was diluted to the desired concentration, thoroughly mixed and pumped to either a 12 or 5 gallon glass bottle which was used as a storage and constant-head tank. Constant head (24) was maintained by the method described by Page The storage bottle was calibrated with respect to volume, and the flow rate was determined by the displacement from storage during an interval of time. An inclined

-24 TERTIARY- "' AQUEOUS BUTYL- ~~~BROMIDE a~ )ALCOHOL BROMIDE STORAGE STORAGE FLOWRATE " MANOMETER ROTAMETER. D 4TEMPERATURE DYE ) CONTROL COIL INJECTION LEVEL MANOMETER LEV - -' MIXING.r'/' COIL.~ "^ ^ ^ ^ EVEL REACTOR ~. CONTROLLER COLORIRECORDE METER RECEIVIN SAMPLING BOTTL Figure 3, Flow Diagram

-25manometer was used to indicate whether the flow-rate was constant. The flow-rate was adjusted by means of the stop-cock nearest the reactor. The aqueous ethyl alcohol was brought to the temperature of the constanttemperature bath by passing the aqueous ethyl alcohol through 16 feet of 7 mm. glass coils immersed in the constant-temperature bath. Either 1/4 in. inside diameter Tygon tubing or 7 mmo glass tubing was used for the ethyl alcohol lines from storage to the junction between the aqueous ethyl alcohol and tertiary-butyl-bromide streams. The tertiary-butyl-bromide storage vessel was a 1-3/4 in. I D. glass vessel which was 18 in, long. It was maintained as a constant head tank in the same manner as the aqueous ethyl alcohol storage tank. Flow was adjusted by the stop-cock shown in Figure 3 and the constancy of flow rate was indicated by a small rotameter which had a sapphire beado Flow-rate was measured by displacement from storage. The lines between the storage tank and the junction with the aqueous ethyl alcohol line were either 1/8 in. I.D. polyethylene tubing or 6 mm. glass tubing. Before entering the reactor the aqueous ethyl alcohol and tertiary" butyl-bromide streams were brought together by a 7 mm, glass Y joint. Following the Y was a short, irregularly bent glass coil, the diameter of which increased and decreased irregularly. This coil served to dissolve the tertiary-butyl-bromide in the aqueous ethyl alcohol. The volume of the mixing coil was included in the reactor volume. Reactors The reactor temperatures were controlled by placing the reactors in a constant-temperature batho The temperature of the bath was controlled

-26by a heater operated by a mercury-switch and Trimount Electronic Relay System~ Cooling water was passed through coils in the bath in order to help equalize the times of heating and cooling. An Eastern, model 8, heavy-duty laboratory stirrer was used for all reactors The number of revolutions of the stirrer in a measured time interval was measured by a mechanical counter which was connected directly to the upper end of the stirrer shaft. This eliminated any possibility of the stirrer shaft rotating a different number of times than the shaft of the counter. The voltage to the stirrer was maintained constant by a constant-voltage transformer. The shaft and propeller stirrers were 316 stainless steel. The space between the shaft of the stirrer and the reactor Plexi(22) glas cover was sealed by the glass tube seal recommended by Morton(p2) Some of the details of the seal are indicated in Figure 4, The seal consisted of a 1 1/4 in, length of 12 mm. glass tubing whose loD. was 10 mm, The glass tubing was held in place by a rubber stopper which served as a.shoulder to rest on the Plexiglas cover. The stopper was sealed to the reactor cover by Sauereisen cement and Pyseal. Vapor was prevented from passing up the narrow annulus between the glass tube and stirrer shaft by a piece of rubber tubing which on one end fitted over the end of the glass tube and on the other end pressed against the stirrer shaft. Also some Dow Corning stopcock grease was placed inside the annulus. One —Compartment Reactor The reactor which was used for all runs in which a one-compartment reactor was run under reacting.condit ions is shown in Figure 4. The reactor

-27 PYREX VZXI ^RUBBER 1j i2 | z "PLEXIGLAS SAUEREISEN 31. l1-/ 1'",- - -.BAdz -7 2 nj, ^ r ^ ~"tLi~ Figure 4 One-Compartment Reactor

-28was a 2000 ml. glass beaker with 7.mm glass tubes for inlet and outlet lines and a line to the reactor level-measuring monometer. The reactor cover consisted of 1/8 in. Plexiglas which. was sealed to the reactor wall by number 51 Sauereisen c!nment, The Plexiglas cover and. Sauereisen cement were coated with a 1/4 in. layer of Pyseal in' order to insure the tightness of the reactor. The cover contained two holes. One was for the stirrer shaft~ This seal was described in the previous section. The other hole was for the reactor thermometero The thermometer seal is shown in Figure 4. It consisted of a rubber stopper through which extended the thermometero The stopper was sealed to the Plexiglas cover with Sauereisen cement and Pyseal. Stirring was accomplished by a 1 1/2 in. diameter three-bladed propeller, which the Mixing.Equipment Co. claimed was a model of commercial propellers. The stirrer shaft was mounted vertically in the center of the reactor and the stirrer was 3 in. from the bottom of the reactor. Liquid volume in the reactor was measured by a calibrated inclined manometer. A calibration curve is shown in Figure 28. -.'': — Glass-Bead. Reactor The two glass-bead reactors, which are shown in Figures 5 and.6, were slightly different from each other in that the depth of the glass beads, the height of the side tubes and the height of the realtors were different. -Each reactor consisted of two concentric compartments. Each inner compartment was a 2 5/16 in. IoD..2 17/32 in, 0oD., glass tube in a 2000 mlo teaker, A space of 1/4 in. existed between the end of the tube and the bottom-of the reactor. The inner compartment in each reactor contained

*0^ orp^ Eln s^^H xalOJ ej ^oq ~ a~o^9H $ I p9:e'QT{ a e~n^T', 0 / L,, ar /U r iu~ "/ IU cW ^U / ^ ~,' i" i 0.9v -i^ix ~-abe/I ~'i ".~ P/1 B ^ ^I IA Y~ ~tC~i i X3^ 17771 7 0410 SVSX31d mg/l \\ \ ^^^\ // -6z

-.0i\ /\ // /k ^ / Z77z PYREX _pg'RUBBER 8^j: * jT,jPYSEAL a PLEXIGLAS X'~g, -B t t I " n I Figure 6. Glass-Bead Reactor for Runs 37 to 41.

a 1 in. diameter propeller stirrer while the outer compartment, which was the space between the tube and the reactor wall, was filled with 6 mm. glass beads. Overall flow in the reactor was down through the inner compartment and up through the glass beads, The reactor cover and method of sealing were the same as for the one-compartment reactor described in the previous section, Each cover contained four holes. One was for the stirrer shaft~ Two more were for reactor thermometers in both compartments. The fourth was for the inlet feed line. The seals on all four of these holes were the same as for the one-compartment reactor. The reactor level manometer was connected to the bottom of the reactor.': Two-.'Compartment Reactor, The two-compartment reactor, which is shown in Figure 7, was a 2000 ml. beaker in which a horizontal circular baffle divided the reactor into two compartments, one above the other. Flow was into the upper compartment and down through the four holes in the baffle, down through the lower compartment and out through the.reactor outlet at the bottom of the reactor. The upper compartment contained a l 1/2 in. diameter propeller stirrer which was mounted concentric to the reactor and 1 3/8 in, above the baffle, The reactor cover and seal were the same as for the onecompartment reactoro The cover contained three holes, One was for the stirrer and the other two were for the thermometersfor the two compartments. The seals for these holes were again the same as for the onecompartment reactor.

-32[:I IAPYSEAL // I I[ PLEXIGLAS SAUEREISEN 31 — B! /.___ SAUEREISEN 31R -1 -e Figure 7^ Two-Compartment Reactor ^^1 ^^^^^l ^^^^^^ ^~~ SAUEREISE 31 -^ lJ'^- ^ 1 ^ I ^A

"33Colorimeter Recordei a'id D iictin: - -.-, r; ": = -' ". The dye concentration in the exit streaea leaving the reactor during the tracer part of each run was measured continuously by a Beckman Model C colorimetero This type of colorimeter is designed for measuring concentrations of solutions in test-tubes. The colorimeter was converted to a continuous colorimeter by running the 7 mm.n glass tube from the reactor through the space in the colorimeter where a test-tube normally is placed, The response of the colorimeter was fed to a Speedomax, Type G, one-secondresponse recorder so that a continuous record of the distribution function could be obtainedo The wiring of the colorimeter was modified as Shown in Figure 8 so that the output of the colorimeter could be fed to the recorder. The voltage to the colorimeter and recorder was controlled by a constantvoltage transformer. The calibration of the colorimeter in terms of dye concentration is described in Appendix III. Dye, the concentration of which was 60 go/l.,was injected through a piece of Tygon tubing into the inlet stream by a hypodermic at a point between the mixing coil and the inlet to the reactor. The volume of dye varied from 2 to 6 mon, depending upon whether the reactor volume was 1100 or 2200 ml., and on how high the peak in the distribution -of residence (21) times waso MacDonald used 3 mlo for a 1950 mlo reactor. The time of injection was from five to ten seconds, The dye was injected into the inlet stream nearly perpendicular to the direction of flow. The dye hit the tube wall and was dissolved in the inlet stream. If the dye had been injected in the direction of flow then the dye would have entered the reactor at a velocity much higher than that of the inlet stream The hypodermic needle was stainless steel.

METER 10 MV RECORDER A Figure 8. Modification of the Colorimeter Circuit. RA IRC WPE 2000 ohm potentiometer RB IRC BW 1/2 ohm resistor RC IRC BW 1/2 ohm resistor C

-35Reactor Outlet F Sytem'.,' All lines in which there wasz tertiary-butyl-bromide, that is, all lines from the Y to the end of the outlet line, were either 7 mm. glass tubing or 1/4 ino inside diameter polyethylene tubing. The only exception was the short length of Tygon tubing through the wall of which dye was injected. Samples of the outlet stream were removed through the T which is shown in Figure 3o The T was located vertically below the, reactor and at a low enough point so that the liquid would flow into a 25 mlo pipette at the same rate that liquid was flowing in the outlet stream, During sampling the outlet line was shut off Just beyond the sampling point and the sample was withdrawn at, as close as possible, the outlet stream flow-rate from the reactorO Before sampling the sampling tee was thoroughly purged in order to obtain a good sample. The conversion as measured in the samples was corrected for time of withdrawal and for the time required for flow of liquid from the reactor outlet to the sample point. This correction is described more fully in sample calculations on page 75 in Appendix II. The reactor level controller is shown in Figure 9. The bottom of the level controller was.a rubber stopper. Since the level controller was at least three feet beyond the sample point there was no possibility of the rubber influencing the sample compositions. The liquid from the level controller was collected and measured in order to measure the reactor outlet stream rate, Measurements were made during periods when no sampling or purging were occurring

-36~~~~~~~~~r:! -. 6 I ^. 9. I Le-e.. Contro.,e --- 12 mm ~ 7 me'F-Figure 9. Reactor Level Controller

Procedure In most runs both the distribution of residence times and conversion were measured. Before the run was begun the aqueous ethyl alcohol and tertiarybutyl-bromide feed tanks were filled. A sample of aqueous ethyl alcohol was taken in order to measure its ethyl alcohol content. The method for measuring the concentration of ethyl alcohol is described on page 12. The constant temperature bath, in which theieactor and coils preceding the reactor were immersed, was brought up to the desired temperature which in general was between 24~5 and 25,5~C. The stirrer, colorimeter and record amplifier were turned on so that they could warm up and reach steady-state conditions, After the bath had reached temperature the aqueous ethyl alcohol and tertiarybutyl-bromide streams to the reactor were beguno While the reactor was filling, flow-rates were checked and adjusted until they were approximately the desired values. Then the level controller was adjusted until the desired volume of liquid in the reactor was maintained. From time to time, while the system was approaching steady-state, flow-rates, reactor liquid level, reactor temperatures and concentration of reacted tertiary-butylbromide in the exit stream wre checked After the system had reached steady-state the following measurements were made, A sample set of data isshown in Table X in Appendix II, Time of reading Level of aqueous ethyl alcohol in the feed tank Level of tertiary-butyl-bromide in the feed tank Aqueous ethyl alcohol flow manometer

-38Tertiary-butyl-.bromide rotameter Reactor level Reactor temperatures Bath temperature Propeller speed..Flowrate of the outlet stream from the reactor Room temperature Samples from the outlet stream were then taken. Sample data are presented in Table IX on page 76. The following readings were taken. Time of start of sampling Time of completion of sampling Time of start of quenching Time of completion of quenching Total rilo of standard akai to neutralize the partially reacted. sample less blank correction Total ml. of standard alkali to neutralize the copXLetely reacted sample less blank correction. The remaining columns in Table IX were quanties calculated from these measurements. All the measurements Saown in Tables IX and.X were then repeated. The distribution of residence times for the system was then measured The recorder trace for run 45 in the two-compartment reactor is shown in Figure 23o Before dye was injected recorder traces corresponding to 0 and 100% transmittance were made. Zero % transmittance occurred when the

-39colorimeter light was turned off. One hundred % transmittance was the transmittance of clear solution~ The time corresponding to a mark made on the recorder trace was recorded, At the end of the distribution function a second such measurement was made. These two readings not only served to relate the time of pulse injection to the recorder time but also served to check the recorder speed. The mean time of dye injection into the inlet stream to the reactor was recorded. Further details of dye injection appear on page 33. From time to time whiLe the tracer experiment was being run checks were made on temperatures, flow-rates and liquid levels to see that the system was remaining at steady-state. The distribution function was run until the recorder did not change value for approximately one residence time. The traces corresponding to 100 and 0% transmittance were again made. The colorimeter and recorder were then shut off, Then two more sets of readings as shown in Tables IX and X were made of flowrates, temperatures, etc. This completed one run~ Each run consisted of one measurement of the distribution of residence times and four measurements of reactor composition and reactor variables. The calculations for obtaining the distribution of residence times and material balances are shown in Appendix II. The procedure for runs in which the distribution of residence times was measured under non-reacting conditions was the same as described in the previous paragraph, except that no outlet compositions were measured. The procedure for runs in which the distribution of residence times was not measured, but reaction was taking place, was the same as described in the previous paragraph except that the tracer experiment was omitted.

Data Preliminary Twenty-one, preliminary, pulse runs were.made to determine whether the distribution of residence tim s,E(G), in a one'compartment reactor was changed appreciably by changing reactor variables such as length of residence time, propeller speed, etc.- The data for these runs are presented in Table IVo Column Descript ion 1 Run number 2 Volume of liquid in the reactor, ml. 3 Flowrate, ml/min. 4 Length of one residence time, min. 5 Reactor temperature, OC 6 Propeller speed, r..p.m. 7.Dye used as tracer 8 Liquid 9 to 29 Distribution of residence times, E(9), as a function of the number of residence times, 30 Internal material balance or first moment 31 Conversion predicted by the measured distribution of residence times using kT = 1o0. 32 Conversion predicted by the perfectly-mixed distribution using,kT = 1.0. 33 Conversion in column 31 -conversion in column 32.

(b) (e) {d) Figure 10. Sketch Showing the Inlet Stream Positions for the One-Compartment -Reactor.

TABLE IV OHE-COMPARHMES REACTOR 1 2 3 4 5 6 7 8 10 11 12 13 16. 15 16 "7 A 19 20 21 22 23 26 25 26 27 28 29 30 31 32 3!v Distribution of Residence Times E((). Q Hun V v Tp. First f f Humber MI.: m./Mla. Min. C BP.M. Dye Llquid -.1.3.5.7.9' 1.1 1.3 1.5 1.7 1.9 3.2' 2.6 3.0 3.) 3.8 4.2 4.6 5.0 5.6 5.8 6.2 tonent M.D. P.M.D 1 P.M.D. T71 1980 91.1 21.7 26.7 287 Taurquois Water'.899.727.596.485.394.323.263.212.182.152.111.081.051.040.030.020.014.010.007.006.002 1.062.5110.50.0110 15 1963 83.8 23.2 ~ 163 Water.871.719.585.479.393.326.268.220 -192.163.125.086.058.038.029.023.015.011.267.004.002 1.062.5170.50.0170 16 1976 88.2 22.4 27.0 172 Water.906.732.604.497.401.319.252.202.167.140.111.081.059.040.030.021.015.013.011.007.003 1.059.5083.5000.88 19 1906 139.0 13.70 24.9 9T Water.921.756.612.499.410.331.271'.226.188.153.110.061.050.033.022.014.010.007.005.003.001.986.4969.5000.0031 20 2149 155.4 13.83 24.7 61 Water.915.714.593.491.399.326.265.215.176.149.114.075.052.035.027.017.013.009.007.004.002 1.001.4973.5000.0027 21 2D74 160.7 12.92 25.2 76 Water-.900.734.599.496.405.330.274.229.192.159.118.078.058.841.024.011.004.003.002.001.001 1.023.5047.5000.0067 22 2107 162.6 12.97 25.0 69 Water.860.692.555.463.384.324.277.238.204.172.137.099.069.044.025.014.0ol.008.005.003.001 1.080.5256.5000.0256 23 2126 162.4 13.11 25.3 69 Water.864.705.592.489.408.338.274.220.179.19.112.080.057.041.032.024.015.012.008.826.005 1.074.5169.50.0169 24 2093 78.2 26.77 25.2 78 Water.857.716.585.480.396.328.273.224.184.150.111.075.o61.043.032.023.016.012.008.006.003 1.097.5205.3000.0205 25 2123 159.2 13.35 24.7 209 Water.882.706.587.488.403.330.266.218.182.152.118.085.058.038.026.020.015.011.006.004.002 1.074.5155.5082.0155 26 2128 166.3 12.86 24.4 47 Eosin Bluish Water.906.720.594.491.410.335.276.225.182.152.113.076.052.061.030.016.011.007.004.003.00? 1.021.5073 -5000.0073 27 2086 157.5 13.26 24.6 66 0Water.910.762.601.482.395.327.272.223.180.146.110.078.055.039.029.019.010.006.04.002.001 1.004.5025.5000.0025 28 2112 166.6 12.68 24.1 72 " Water.909.725.590.494.414.343.280..226.183.151.115.075.054.037.026.018.010.005.003.002.001.999.5050.50.0050 29 2077 162.7 12.83 24.3 89 Water.855.700.585.490.403.332.273.231.193.162.120.083.60.01.030.021.012.008..005.003.002 1.067.5199.5000.0199 30 2099 160.6 13.08 24.4 93 Water.870.706.591.495.412.348.289.234.192.159.121.083.059.040.021.013.006.004.002.001.001 1.007.5118.5000.0118 31 2058 158.2 13.00 24.6 113 " Water.881.712.586.481.400.338.282.234.192.155.l09.082.060.062.031.019.012.009.006.003.002 1.046.5142.5000.0142 [0 7I 2D55 176.7 11.63 24.6 71 2ETO.656.856.676.535.429.344.279.228.189.150.109.076.050.033.022.017.010.006.004.002.001 1.009.5157.5000.0157 2 2045 110.3 16.54 24.7 50 " 288.940.765.625.495.394.321.260.213.179.151.112.072.047.031.023.016.010.007.005.004.002.982.4947.5000 -.003 3 2085 175.5 11.89 24.7 217 " 2IO8.902.745.609.305.411.332.272.224.187.150.110.074.050.031.020.014.009.007.005.4.003 -997.5012.5000.0012 4 2068 178.2 11.61 24.8 59 2E20.906.789.631.514.410.323.273.215.176.146.106.070.045.030.02.015.010.008.006.004.003.979.4946.5000 -.0054 5 2085 176.7 11.95 24.4 59 220H.946.767.616.505.415.334.268.218.179.149.108.069.046.030.021.013.007.004.002.001.001.942.4902.5000 -.0098 Reactor was as s.own In Figu- lO0 excep2.. T27 - Two propellers ~ T28 - Vertical Inlet near center. Figure loc 729 - Vertical Inlet near wall., Figure lOb T30 - Horizontal outlet at top, Figure 1Od T31 - Sane as 30 except propeller wBS I In. from the bottom of the reactor.

One.-Copiment 1.eactQr Following the oqne-comp.rtment reactor reliminary runs under non-reacting conditions, a series of rs under reacting conditions were perf d in the on-copartmnt reactor The details of the reactor are dscribed -on page 26.d the procedvre is discussed on page 37 The data for these rus a-e giren in Tables V and VI. he headings for Table' are: Column I Run number 2 - 44 E(9) as a function of the numbrer of reidence tlmes 45 Internal material balance or first moment 46.'fMBat'erial balance for all the liquid entering and leaving the reactor 47 Material balance for tertiary-butyl>bromide The distribution functions are shown in Figure 11, In Table Vi the headings are Column 1 Runnumber 2 Volume of liquid in reactor, ml. ~3 Mean overall flow-rate, ml o/min. # tLength of one residene time, min, 5 Reactor temperature, ~C 6 Propeller speed,. r.p.m. 7 Mass fraction of alcohol in the aqueous ethyl alcohol.

~azv (o) vC~.qO.l.a.~..1,.5.6.?.e x.o z.1 z.a l.} =.~ 1.5 ~.6 x.T ~.e z.~ a.o a.= 2.2 _. 2.~ a.6 a.o ~.o }.a ~.1, ~.6 ~.s ~.o ~.a 1,.1, ~.6 u.e ~.o ~.2 ~.~, 5.e 6.a ~.~?.o s~,~ O,~r,.U. ~-ala~, o..o,~.~o.V'~.~SS.~.~.Xe.~.zaS.xe~.z~.am.oTx.oso.o~.oa9.o2.~.o.~.ola.oo,~.ooa,.oo~.ooa.cox x.o~ mo.~a.~ m.w,6.~.~.ac~.~6.aoo.~.xe~.x~e ~xo?.o~.o~.0~.o~.ox?.wa.oo'(.cos.oo,,.oo~.oo~.oox ~.o.~e.~ ~.oo9.~,.~o6.~.'r~.em.~a~.~,o.~.~,.wss.~,.~.a'ra.a.~..z~o aae.,,,z,oax.o6s.osx.o.~.o~.oxx.~.co/,.oo~.oo~.co/..~.s~ ~o.1~.~.W~ z.~ z.n.x ~..0~ o~0.&~.~o?.~s.1,~.~o.}xe.~,.alx.x~o.~u.loo.o~.u,~.ca~.o~o.oao.olas.o.~.oo~.oo~.oo~.oox x.o.~.~0~.~rr~ /,o.o'r2.~.s~./o9.~'r.eoa.~ oT/,;.~.~.~o9.~.~.~.~a.~.aso.z~.~.z?3.:tug.1.~?.o~.oo~,.oo~.oox ~.o-to.s~.s~,.x~.~Te.e~ x.o~ z.ose x.oes.~.&~-t.~0~.s'r~.~.~,~.~z.~x.x~.~v.lou.oex.o~.o~o.o~.oao.ola.ooa.oo2.oox.~r}.sex.s~9 ~s.oaa.~eo.~n.6~.?,~2.ao~.a.~.a~,.em ~wa6.~a..~.~,~.~6~.~o~.~,9.~oo.x57.lm.o~.ow.osa.o~.oas.o~o ~ox~.om.oo8.oos.oo~.ooz:t~,.5s-~.9~s - a~./,~.s-co.61o.6~.~.~o.6~?.6~.sa~.~.1~..1,~.~e.~e.~.z/e..g~..ma.x57.laa.on.o~9.o~o.oax.ozu.o,.~.oo~.oo?.oo~.oo~.oo~.oo~.cox x.o~.~.s~, ~ 1~.~,~.~x6.s'ra.61o.6~, ~.~7o.ex.6~.6ol,.am.yr~.~,~,.~ex.~.urn.x~x.,,,~.o~.oso.o}?.o,~.o.~.o1~.oo9.oo~ x.oo~.~.sa~.ooo.~.~,9.~1,o.~oo.6~.es.~.6~.6~.s6o.~o~.1,~.~.~9.-~a.~,.z./~.2~o.2~..x6x.lax.o~.os~.o~.oa6.ox~.o~.o1.~.oo~.oos.o0~.ooa.ool x.o,~ x.oo6.~.uax.:.s~.~..~.&~.~.~ss.6s~.~.6~.s.~.5~.~0.~.~o.~,e.~oe.~'r3.~s.~.z~.lay:o~6.o~.~9.o1.~.oo8.oo?.oo~.co~.oo~.oo~ x~o~.~9a.~e~ ~.ooo.~}a.1~.s~.,~s.~s.~.c~.66s.r.~.5~.sll.~s9.a, ao.~.~.~eo.~.~o~.1~o.1~.o~.oc~.o~x.o~o.om.~.o1.~.oo~.oo?.oo6.oo5.ool,.oos.~.cox.oox x.o~.~.~ I I ~,s

l.0 1k^^~~ -~ ~ ~ ~PERFECTLY- MIXED DISTRIBUTION.OQ~si~~~8L ^.~ ^RUN NUMBER, —- 12 i 13 o>1 -- - 0.6 --- 33 >l 0.68 \ 0.4 02 0. I 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 32 NUMBER OF RESIDENCE TIMES, 6 Figure li. Distribution Functions for the One-Compartment Reactor.

TABLE VI ONE-COMPARTMENT REACTOR DATA 1 2 3 4 5 6 7 8 9 10 11 12 13 Mass Was Run Volume Flowrate T = V/v Temp. Fraction Dye Number V M1. v M1/Min. Mi. T'C R.P.M. ETOH Present? f p. M. FPM FM P.M.D. fM.D. p.M.D. M.D. 11 2028 182.4 11.12 26.50 257.6536 No.5019.5036 -.013 2068 170.8 12.11 26.52 240.5161.094 2007 184.0 10.91 26.45 245 5079.032 1991 179.4 11.10 26.43 256.5022 -.011 12 2023 168.5 12.01 26.35 268.6565 Yes.5168.5085.5201.061 -.024 1991 168.9 11.79 26.35 263.5143.043 -.043 1995 168.1 11.88 26.37 264.5202.086.001 1994 167.3 11.92 26.40 268.5119.025 -.060 13 1950 181.7 10.73 26.77 274.6556 Yes.5004.4990.5059.011 -.042 1984 178.5 11.11 26.74 273.5020.023 -.032 1975 180.3 10.95 26.84 284.4917 -.055 -.108 1974 179.1 11.02 26.66 269.4973 -.013 -.065 14 1953 182.6 10.70 24.69 323.6697 Yes.4081.4050.035 ~..... __ _-.4185.152 1955 170.3 11.48 24.69 322.413..100 1988 172.1 11.55 24.70 302.4165.130 15 2015 175.2 11.50 24.90 376.6635 No.4473.4380.090 1980 172.6 11.47 24.89 344.4409.028 1976 167.2 11.82 24.89 355.4409.028 1982 166.0 11.94 24.90 364.4426.044 16 1978 163.3 12.11 26.36 329.6566 Yes.5140.5061.059 1932 161.7 11.95 26.37 311.5101.030 1917 161.7 11.86 26.36 271.5120.044 1902 162.3 11.72 26.37 269.5100.029 17 2004 174.3 11.50 25.86 351.6613 No.4739.4699.034 1995 174.7 11.42 25.86 340.4838.118 1995 171.5 11.63 25.87 331.4890.162 2004 171.3 11.70 25.89 337.4833.114 33 2127 139.8 15.22 24.74 492.6552 Yes.5311.5198.5191.080.085 2113 142.0 14.88 24.74 496.5313.081.086 2112 143.4 14.80 24.74 463.5216.013.018 2121 143.4 14.79 24.74 487 MEN..053 -.017

-47Column 8 -Was a tracer experiment attemepted? 9 Measured. fractional conversion. 10 Fractional cnversicon calclated by using the perfectly-mixed distribution of residnce times 11 Fractional conversion calculated by using the measured distribution of residence times 12.Relative conversion difference based upon the perfectly-mixed distribution of residence times, 13 Relative conversion-difference based upon the measured distribution of residence times, Gl!assBead Reactor The glassj-bead reactor is discussed in detail on page 280 Figures 5 and 6 show sketches of the reactors used in runs 27.through 30 and 37 thrugh 41 lrespectively. The distribution functionsare given in Table V and are shown in Figure 12. The remainder of the data for the glass-bead reactor is given in Table VII. Te che adings are: Column 1 Run number 2 -Volumei of liquid in reactor, ml, 3 Mean overall flow-rate, ml^/min* 4.xLength of one residence time, min. 5 Inlet reactor temperatur'e, ~C 6 ~Outlet reactor temperature, C

RUN NUMBER 27 IV^^\ 1.0- -- 2 ^^\ ---— 29 6 - -— \ -30 QB -— ~~~~~~~~~~~~~~~37 Q8 /// 3Joe, ~~~~~~~~~~~~~~~39 U O~~~~~~~~~~~~~~~~~~4 /~~~~~~~1 - ~~~~~~~~~~41 0.6 I) 0 co0. 4 NUMBER OF RESIDENCE' TIMES llgure-12. Distribution Functions for the Glass-Bead Reactor. 1J61 O1 2~~' 0.0 Q.O 0.2 0.4 0.6 0.8 1.0 1.2 ~.. 0 2 NUMBER -OF RESIDENCE~ TIMES * Figure 12. Distribution Functions Thr the Gla~ss.-Bead Reactor.

TABLE VII GLASS-BEAD REACTOR DATA 1 2 3 4 5 6 7 8 9 10 1 Mass Run Volume Flowrate T = V/v Temperatures ~C Fraction Number V M1. v M/Min. Min. Inlet Outlet R.P.M. ETOH f fMD 30 1107 142.1 7.79 24.89 400.6536.4127 1080 147.5 7.32 24.92 421.4218 131 1107 149.1 7.42 24.76 423.4194.096 1102 147.1 7.49 24.84 420.4234.154 39 1150 1155.8 9.93 25.0o4 25.20 444.6560.5205.5229 -.025 1149 113.6 10.11 25.04 25.20 444.510 -.131 1155 116.2 9.94 25.03 25.19 463.5106 -.127 1149 116.8 9.84 25.00 25.19 445.5089 -.144 41 1144 97.6 11.72 24.92 25.07 396.6543.5561.5660.-084 1144 95.8 11.94 24.91 25.07 383.5622 -.032 - 1143 96.4 11.86 24.89 25.06 393.5562 -.083 1143 96.8 11.81 24.91 25.07 409.5589 -.060 27 1111 91.6 12.13 25.05 349.6542.5971.5777.158 1082 89.4 12.10 25.12 342.5885.088 1095 90.2 12.14 25.03 312.5887.090 1081 88.4 12.23 24.97 288.5820 035 40 1139 58.8 19.37 25.22 25.29 409.6584.7248.7199 028 1149 57.8 19.84 25.22 25.29 413.7097 -.059 1140 57.8 19.72 2515 25 4389.7243 026 1147 56.2 20.41 25.13 25.24 402.7423.130 28 1111 55.9 19.87 25.25 303.6563.7108.7294 -106 1078 53.7 20.07 25.27 306.7261 - 019 1100 58.7 18.74 25.23 314.7367 042 1068 56.7 18.84 25.23 298.7312.010 37 1146 66.7 17.18 25.22 25.30 410.6443 7351.7214.077 1148 66.3 17.32 25.29 25.36 417.7396.103 1149 65.9 17.44 25.19 25.30 409.7432 123 1142 62.5 18.27 25.17 25.28 402.7401 106 29 1098 61.0 18.00 25.24 292.6556.7364.7214 o087 1121 57.7 19.43 25.24 288 7498.164 1110 59.0 18.81 25.25 304.7508.170 1093 58.0 18.84 25.2 328.7428.124 MEANi.034

-507 Propeller speed, r.p.m. 8 Mass 8fraction of alcohol in the aqueous ethyl alcohol 9 Measured fractional conversion 10 Fractional conversion calculated by using the measured distribution of residence times.. l1 Relative conversion difference based upon the measured distribution of residence tinies. Two-Compartment Reactor The two-compartment reactor is described on page 31 and shown in Figure 7, The distribution functions are given in Table V and are shown in Figure 13* The remainder of the data for the glass-bead reactor is given in Table VII. The columns headings are the same as those for Table VII and are given on page 47*

0.8 TWO PERFECTLY - MIXED REACTORS IN SERIES /\~ /^^^^ ^^~~RUN NUMBER 42 0.6 CI^~~~~~ 7^^ ~\`\~~~ ^^^^44 48 o0.4 0~~~~~~~~~~~~~~~~~~~~~~~ 0.0 0.0 04 0.8 1.2 16 2a0 2.4 2.8 32 NUMBER OF RESIDENCE TIMES Figure 13. Distribution Functions for the Two-Compartment Reactor.

TABLE VIII TWO-COMPARTMENT REACTOR DATA 1 2 3 4 5 6 7 8 9 10 1 Mass Run Volume Flowrate T = V/v Temperatures ~C Fraction Number V M1. v M/Min. Min. Inlet Outlet R.P.M. ETOH FM D. f M. D. 44 2074 176.8 11.73 24.79 25.01 116.6570.5354.5043.278 2076 174.8 11.88 24.77 25.04 116.5197.138 2077 176.4 11.77 24.76 25.00 112.5172.116 2077 177.0 11.73 24.76 25.00 101.5375 ~297 48 2091 164.2 12.73 24.88 25.17 159.6661.5600.5135.420 2091 162.0 12.91 24.88 25.17 150.5378.219 2090 161.8 12.92 24.94 25.18 146.5276.127 2095 164.2 12.76 24.95 25.17 150.5461.294 42 2097 161.3 13.00 24.88 25.09 167.6606.5885.5365.434 2090 158.9 13.15 24.87 25.09 161.5525.134 2098 158.4 13.24 24.87 25.07 163.5495.109 2093 160.1 13.07 24.87 25.09 173.5742.315 43 2095 176.5 11.87 24.73 24.95 289.6573.5178.5124 049 2099 176.1 11.92 24.74 24.97 303.5166.038 2091 177.5 l 11.78 24.68 24.91 304.5215.082 2080 175.9 11.82 24.68 24.91 307.5127.003 45 2084 173.1 12.04 25.03 25.19 378.6539.5676 5452.184 2086 -176.5 11.82 25.05 25.19 374.5579.105 2080 175.7 11.84 25.06 25.19 372.5573.100 2079 174.9 11.89 25. 07 25.19 380.5747.244 EAN.5436.5224.184

CHAPTER V DISCUSSION OF THE CONTINUOUS REACTOR DATA The data.are discussed.from.both an engineering. approach and from a statistical approach. The engineering approach is to discuss whether the differences between measurei.f conversions and conversions calculated from the measured distributions are of engineering importance while the statistical approach is to show whether the differences are real, Engineering Approach Preliminary Data The distributions of residence times, E(s), for twenty-one preliminary runs under non-reacting conditions in the one-compartment reactor / are presented in Table IV and ^the column headings are described on page 40. Using an arbitrary value of kT = 1.0 the conversions, calculated by using.these measured distributions of residence times in Equation (6), are shown in column 31. The conversion assuming a perfectly-mixed distribution and kT = 1l0 is 0.5000. Column 33 is the difference between conversion as calculated by the measured distributions and the conversion calculated by. a perfectly-mixed distribution, From an engineering..iewpoint these differences are small and their effect is generally not important compared to the uncertainty in kinetic constants and the ability to control reactors. These data indicate that in general f s l r a s one-compartment reactor in which the diameter and height are approximately equal that the distribution of residence times from the engineering viewpoint is rather insensitive to: changes in propeller speed provided that the speed is greater than 30 r.p.mo; changes in residence time for residence times -53

greater than eight minutes; differences in the position of the feed entrances to the reactor as shown in Figure 10; changes in baffling arrangements provided that the baffles do not essentially divide the reactor into two or more compartments; changes in the number of ppopellers on the same shaft; and ahanges in the distance of the propeller from the bottom of the reactor. One-Compartment Reactor Data Following the one-compartment reactor preliminary runs under non-reacting conditions a series of runs under reacting conditions were performed in the one-compartment reactor, The distributions of residence times, E(g), are presented in Table V and are shown in Figure 11. The conversion data are presented in Table VI and. are shown in Figure 14. In addition to the measured conversions, included also are conversions calculated by Equation (6) from the perfectly-mixed distribution and from the measured distributions of residence times, From Figure 14 it is seen that conversion level varies from run to run. These differences in level are not important because they are caused by differences in temperature, residence time and ethyl alcohol concentration between runs. The important part of the figure is the differences between measured and calculated conversions. The measured conversions are, in 27 out of 31 samples, higher than conversions calculated by making the assumption of perfect mixing, Based on complete conversion being 100% this difference averages (0-5 + 0.2). See page 90 for the calculation of 0.2, the 95% confidence interval, From an engineering viewpoint this difference is unimportant,

-550.6 o.5 > + o 9 0 U! 0.43 O AVERAGE MEASURED CONVERSION + PERFECT- MIXING CONVERSION X MEASURED - DISTRIBUTION CONVERSION 0.2 0 12 14 16 33 0.0 I I.1I.1I,~1 ~ 10 11 12 13 14 15 16 17 33 RUN NUMBER Figure 14. Fractional Conversions for the One-Compartment Reactor.

56For the one-compartment reactor, measured conversions and those calculated from the measured distributions are presented.in columns 9 and 11 of Table VI. In four out of eleven samples the measured conversions are higher than the calculated conversions. Based. on complete conversion being 100% the average difference in conversion is (-O.2 + 0..4)% and is of no engineering importance. Glass-Bead Reactor Data -.,,,,I. I' I. ~..,, I.. The details of the glass-bead reactors are described on page 28 The data for these reactors are presented. in Tables V and..VII and. the column headings for these tables are described on pages 43 and 47, Figure 15 shows conversion as calculated by the measured. distribution of residence times as afunction of measured conversion where the measured conversion is the average of 4 samples for the run. Upon comparing measured and calculated conversions in columns 9 and 10 of Table VII it is seen that for 20 out of 31 samples the measured conversions are higher than those calculated by the distribution of residence times. The difference between measured and calculated conversions is even smaller than that shown in Table VII, because the calculated conversions are based upon the temperature of the first compartment which was cooler than the second compartment. The difference in temperature, when measured, was not more than 0.25~C. In any case the difference between measured and calculated conversion is not of engineering importance. Two-Compartment Reactor Data The two-compartment reactor is described on page 31 and a sketch of the reactor is shown in Figure 7a The distribution functions for these

-570.80 0.72 _. 0.64:3 4 0 5 O56_ 0I' I o E X MEASURED- DISTRIBUTION 0.40 CONVERSIONS.. O LOCUS OF EXPERIMENTAL UL L I CONVERSIONS. 0.32 0.24 0.16 0.08 0.00 I I I I 0.40 0.45 0.50 0.55 Q60 0.65 0.70 0.75 0.80 EXPERIMENTAL FRACTIONAL CONVERSION Figure 15. Fractional Conversions for.the GlassBead Reactor.

-58riuns are presented in Table V and.are shown inFigure 13, The remainder of the data for these runs are presented in Table VIII, The column headings for these tables are described on pages 43 and 50. The average of the 4 measured conversions for each run and the conversions calculated by the measured distributions of residence times are shown in Figure 16, Based upon complete conversion being 100% the measured conversions are on the average (2.1 + 0,7)% higher than the conversions calculated by the measured distributions of residence times. In addition all 20 measured conversions are higher than the corresponding calculated conversions, The difference in conversion for the two-compartment reactor is much larger than for the other reactors and may be of engineering importance, Statistical Approach In the previous section differences between measured and calculated conversions were discussed from the viewpoint of engineering importance. In this section the statistical significance of the differences will be discussed, In order to evaluate statistically the differences between measured and calculated conversions it is desirable to.consider a difference which would be expected to be constant for all runs, If such a difference is used then there is the possibility of considering all the data at once in one statistical test, The continuous reactor conversions being considered in this thesis vary in level from run to run. Differences between measured and predicted conversions would be. expected to vary with conversion level. A quantity,

590.6 O 0 0 0 X X z x 2 0.5 x tx * W O 0.4 | O0 AVERAGE MEASURED CONVERSION cl:N X MEASURED- DISTRIBUTION CONVERSION L I 0.3 0.2 0.1 0.0 I.I I.....I. 100 140 180 220 260 300 340 380 PROPELLER SPEED, R.P.M. Figure 16. Fractional Conversions for the Two-Compartment Reactor,

460o F., which will be called the relative conversion difference based upon the distribution of residence times i is defined as F. = fi fS.oFoDo fP.MoD.e where f is the measured conversion fo is the conversion calculated by using the distribution of residence times i in Equation (6). f F is the conversion calculated by using the slug-flow disS.FOD. tribution of residence times in Equation (6) fP.MD is the conversion calculated by using the perfectly-mixed distribution of residence times in Equation (6). Conversion level was varied much more widely for the glass-bead reactor than for the other reactors. Figure 19 shows relative conversion differences based upon measured distributJons for the glass-bead reactoro The slope of the least square straight line is not significantly different from zero at a significance level of 5 percent. Since conversion level was varied much more widely for the glass-bead reactor than for any other reactor, then relative conversion difference is a satisfactory quantity to use for statistical tests when conversion level varies from run to run. The statistical procedures for testing and evaluating relative conversion differences for each reactor were: (1) An X-chart, Duncan(1) page 285, was used to determine whether the mean value of F for any run was significantly different from the mean, F, for all the runs. In no case was the difference sufficiently great to reject the null hypothesis that the means came from the same

universe of values. The upper and lower limits were 3aF + where F is the mean value of F for all runs N is the number of samples per run o is an estimate of ao, the universe standard deviation of means of all runs The universe standard deviation of means is the standard error of F, (2) Bartlett's test, Duncan(1) page 470, of homogeneity of variances was used. to determine whether the variances for each run came from the same normal universe. The null hypothesis was that the variances were a homogeneous set. Using a significance level of 5%, for no series of runs was the hypothesis rejected. (3) After the two previous tests had shown that the hypotheses, that the means and variances for each run were from the same universe, did not need to be rejected, then aX test, Duncan ) page 412, was performed to determine whether the data were approximately normally distributed. The null hypothesis, that the values of F were approximately normally distributed, was not rejected at a significance level of 5%. (4) Tests (1) through (3) indicated that it was reasonable to assume that the data for each reactor were homogeneous and approximately normally distributed. The data were then used to estimate a universe variance and mean. This variance and mean were used in evaluating the null hypothesis that the relative conversion differences were zero. A 5% significance level was used. The results of these tests will be discussed in the sections which followo

-62One-Compartment Reactor Data The relative conversion differences based upon the perfectlymixed and the measured distributions of residence times are shown in columns 12 and 13 respectively of Table VI. In some of the runs dye was present and in others it was not present. The mean values of relative conversion difference based upon the perfectly-mixed distribution when dye was present and not present were.060 and.049 respectively. At a 5 percent significance level tHe difference between these means was not significantly different from zero. Thus it was not necessary to reject the hypothesis that dye does not have a significant effect upon fractional conversion. The data were then combined and treated together. The relative conversion differences based upon the perfectlymixed distribution are shown in Figure 17. Tests (1) through (4), as described in the previous section, were performed upon this data, The mean value of relative conversion difference was.053 and the estimated universe standard deviation was.052 and the number of samples was 31. For the test of the null hypothesis that the mean -value of relative conversion difference was not significantly different from -zero the value of Z was 5.7. (See page 102 for the definition of Z.) Upon using,a 5% significance level the null hypothesis was rejected and it was concluded that measured conversions were significantly higher than those predicted by the perfectly-mixed distribution for the one-compartment reactor. Relative conversion differences based upon the measured distributions of residence times are shown in Figure 18. Tests (1) through (4),

0.20 0.16 x X X, 0.12 X X X X x x o.04 x X X x' o ^ X x x x e X X, & 0 x # ~~~~X - 0.04 x -0.08 -0.12 I II 12 13 14 15 16 17 33 RUN NUMBER Figure 17. One-Compartment Reactor Relative Conversion Differences Based Upon the Perfectly-Mixed Distribution.

-640.12 0.08 0.04 j U.1i -0.04 X X x x -0.08 -0.12 -0.12...._______________________. ________________________ 12 13 33 RUN NUMBER Figure 18. One-Compartment Reactor Relative Conversion Differences Based Upon Measured Distribution Functions.

-65which are described in the previous section, were performed on these data. For the test of the null hypothesis that the mean conversion d.ifference was zero, the mean value of relative conversion difference was -oO7 and the standard deviation was o060. For a sample size of 11 this difference was not significantly different from zero at a significance level of 5% when using a t-test. (See page 102 for the definition of t.) Therefore the differences between measured conversions and those calculated by the measured distributions of residence times were not significantly different from zero for the one-compartment reactor. Glass-Bead Reactor Data The relative conversion differences based upon the measured distributions of residence times for the glass-bead reactor are presented in column 11 of Table VII and these data are shown in Figure 190 Tests (1) through (4) described on page 60 were performed upon these data. The mean value of relative conversion difference was.034 and the estimated universe standard deviation was.099. The number of samples was 31. At a 5% significance level the mean difference was not large enough tomake it necessary to reject the hypothesis that the difference was zero, On page 56 it was discussed why this mean difference is actually even smaller than ~034. Therefore, for the glass-bead reactor, measured conversions were not significantly different from those calculated by the measured distributions of residence times. Two-Compartment Reactor Data ~-,. -'..',.._.. v The two-compartment reactor relative conversion differences based upon the measured distributions of residence times are presented in column

-660.20 016 x x Q12 X oox IXX XX 0.08 0.0412.000, x x -0.08 -0.12 X -0.16 I I x I: 0.32 0.40 0.48 Q56 0.64 Q72 080 MEASURED FRACTIONAL CONVERSION Figure 19. Glass-Bead Reactor Relative Conversion Differences Based Upon Measured Distribution Functions.

6711 of Table VIII and are shown in Figure 20, All 20 relative conversion differences are greater than zero. The null hypothesis, that the mean value of relative conversion difference was zero, was rejected and it was concluded for the two-compartment reactor that the measured conversions were significantly higher than those calculated by the distribution of residence timest

0.48. X x 0.40 0.32 X X X' X iU X X x x 0.08 X 0.00 1... I.. I.. 100 140 180 220 260 300 340 380 PROPELLER SPEED, R.RM. Figure 20. Two-Compartment Reactor Relative Conversion Differences Based Upon Measured Distribution Functions,

CHAPTER VI SUMMARY AND CONCLUSIONS Conversions calculated from the measured distributions of residence times for the one-compartment reactor were about five percent of the distance between conversions calculated by the perfectly-mixed and slug-flow distributions. Similarly conversions calculated from the glass-bead and the two-compartment reactor distributions were 80 and 55% respectively, of the distance between the perfectly-mixed and slug" flow conversions. For the reactors with distribution functions relatively close to perfect-mixing or relatively close to slug-flow, measured conversions were not significantly different, at the 5% significance level, from conversions calculated by the measured distributions of residence times. For the reactor with a distribution function intermediate between perfect mixing and slug flow, measured conversions, at the 5% significance level, were significantly higher than those calculated by the measured distributions of residence times. Representative distribution functions for the three reactors are shown in Figure 21, Conclusions (1) A preliminary survey of the distributions of residence times for a small, stirred, one-compartment reactor in which height and diameter were about equal indicated that differences between conversions calculated from the measured distributions and conversions calculated by assuming a -69

1,2 ONE- COMPARTMENT REACTOR 1.0 GLASS- BEAD REACTOR 0.8 Q6 04 TWO -COMPARTMENT REACTOR 0.2 0.0 0.0 0.4 0.8 12 1.6 2.0 2.4 2.8 3.2 3.6 4.0 44 NUMBER OF RESIDENCE TIMES, Figure 21. Representative Distribution Functions.

-71perfectly-mixed distribution were not important in most engineering applications. The ranges of conditions investigated were for propeller speeds greater than 30 r.p.m.; for residence times greater than 8 min.; for entrance positions of the feed as shown in Figure 10; for any baffling arrangements in which the reactor was not divided essentially into two or more compartments; and for either one or two propellers on the same shaft at various distances from the bottom of the reactor. (2) For the one-compartment reactor, measured conversions, at a 5% significance level, were not significantly different from conversions calculated from the measured distributions of residence times. The conversions were about 5% of the distance between conversions calculated for a perfectly-mixed and a slug-flow distribution of residence times. (3) For a reactor in which conversions were about 80% of the distance between conversions calculated for a perfectly-mixed and a slugflow distribution of residence times, measured conversions, at a 5% significance level, were not significantly different from conversions calculated from the measured distributions of residence times. (4) For a reactor in which calculated conversions were about 55% of the distance between conversions calculated from a perfectlymixed and a slug-flow distribution of residence times, measured conversions, at a 5% significance level were significantly higher than conversions calculated by the measured distributions of residence times. Based upon complete conversion being 100% this difference between measured and predicted conversions, at a 50% conversion level, was (2.1 + 0.7)% and may have been of engineering importance.

-72(5) The reaction rate constant for the hydrolysis of tertiarybutyl-bromide in aqueous ethyl alcohol was given by the following correlation log k88 = 15.9501 - 5.Q223c- 4,64122.o88 T + 273,10 over the following ranges of conditions.64 < C < 68 ~23 <'TC < 28 Co =.088 For other initial concentrations of tertiary-butyl-bromide the following correction was applied to the reaction rate constant kC - k 088 o88 (.580)(.0880o C).045 < 0o <.o88

APPENDIX I ADDITIONAL DERIVATIONS Calculation of Conversion which has Occurred Before Sampling 0 r O ~~~f f + I f ~ ~ Reacfor Sampling Figure 22. Sampling Model Let f be the fractional conversion occurring in the reactor and A f the additional conversion occurring during sampling time At. If the conversion occurring during sampling is assumed to be equal to the conversion occurring in a batch reactor in time At then Af = (- f)(le ) (13) and therefore -kAt -- (f + a) -(1- e ) (. e Maximum Error Caused by Using a Mean k The temperatures in the two-compartment reactor differed by a maximum of 0.250C4 The maximum error caused by using.a mean k instead of k's for each compartment will now be estimated.. From Figure 13 it can be seen that the distributions of residence times for the two-compart.ment reactor are approximately that for two perfectlymixed reactors in series. The error caused by using a mean k will be estimated by using the distribution for two perfectly-mixed reactors in series' -73

-74-. Using the data of run 44 t = 24.77~C k =.001187 sec. t2 = 25,02"C k2. 001222 sec, T1 = T2 = 5.89min. Conversion Using k's for Each Compartment kL _ _.001187 x 60 x 5.89 2 2 f ( - *29552 f 1 1+ kl.rl 1 +.001187 x'60 x 5.89 k2 T2 T001222 x 60 x 589 1 + kI T2 1 + 001222 x 60 x 5.89 f f+f2 (1- f) = 50800 Conversion UVing an Average k f = f k1 T. 0012045 x 60 x 589 2985 1 2 1 + kT1 1 +.0012045 x 60 x 5 89 f = fI + f2 (1 -f) = 5o8o01 % error =. =.002% 50,800 Therefore the error caused by using a mean k for the two-compartment reactor is negligible.

APPENDIX II DETAILD DATA AND SAMPLE CALCULATIONS Calculations for Run 45 In this section detailed data and sample calculations for run 45 are presented. Also sample calculations for the statistical tests are given on page 86, For Table IX the column headings are: Column Description 1 Sample number -2 Time of start of sample withdrawal from the system. 3 Time of completion of sample withdrawal from the system. 4 Time of start of quench of sample, 5 Time of completion of quench of sample, 6 Sampling time, sec. 7 Net ml. of NaOH required to titrate the sample. 8 Net ml, of NaOH required to titrate a sample which has completely reacted. 9 Product of reaction rate constant and sampling time, 10 Conversion occurring in the reactor and during sampling. 11 Calculated,conversion occurring in the reactor. The volume of the system between the colorimeter and the sampling point was 14 ml, The total volume of liquid withdrawn during sampling was 28 ml. The sampling time equalled the average time for liquid to flow from the reactor outlet to the sampling point, plus the difference between the average quenching time and. the average time for sample withdrawal -75

TABLE IX SAMPLE DATA OF TERTIARYr-BUTYL-BROMIDE SAMPLES 1 2 3 4 5 6 7 8 9 1011 Sampling Net* Sample __ Time: Hrs,, Mins,, Secs, Time cc Infinite* Number 1 2 3 4 At Sece NaOh Titer kAt f + Af 1 3.03:00 3 o03 13 3.03:23 3 40346 3,5 23.70.40,45.0433 5859 576 2 3.18:00 3.18:15 3.18:26 3 91:49 37.5 23.55 40,73.0470.5782.5579 3 4.38;00 4.38:13 4.38:23 4.38 47 350 23.48 40.74.0440.5763.5573 4 4.58:00 4.58:14 4.58:23 458:46 34.5 25,06 42.28.0433.5927.5747 NEAN 41.05 * Blank correction alsQ maade

-7714 x 46 23); (13 + 0) A-t 28^ x 13+ Q4~6+ ~( ~ =5 34.5 sec. 28 2 In column 9, k =.001281. See page 85 for the calculation of k from the batch correlation* In column 10, f + Af = 43 7 =.5859 4o.45 From Equation (14) (f +Af) (1 eUt) -kAt e = 5676 For Table.X the column headings are: Column Description 1 Time corresponding to the measurement in column 2 or 3. 2 Level of aqueous ethyl alcohol in storage. 3 Level of tertiary-butyl-bromide in storage, 4 Reading of the inclined manometer indicating the aqueous ethyl alcohol flow-rate. 5 Reading of the tertiary-butyl-brormide rotameter, 6 Reading of the inclined manometer indicating.'liquid level in the reactor. 7 Temperature of compartment 1, ~C. 8 Temperature of compartment 2, C, 9 Temperature of bath, ~C. 10 Propeller speed, r.p.m. 11 Flow rate of liquid leaving reactor, ml./min. 12 Room temperature, O~F

TABLE X SAMPLE DATA OF REACTOR VARIABLES 1 2 3 4 5 6 7 8 9 10 11 12 Time,, Level in Storage Outlet Room HxC. Aqueous t-BuBr Bath Fio.w- Tep M.., EtOH Cm. EtOH t-Bu-Br Reactor Reactor TemoGC Temp rate F Sec. Cm, Flowmeter Rotameter Level 1 2 0C RoP.M. Ml./Min. -255-3.00 9.0 35.0 53.9 24.96 25.21 25.00 377.8 172.0 79.1 2.55:30 32.0 256:00 1586 3,10-3.15 90 34.0 54,1 24.98 25,21 25.01 374.0 175.4 793 3.10:30 29.9 3.11:00 14.6o 3.45:0 Tracer Injected 4,30-4.35 9.0 33.4 53.6 24.99 25,21 25.03 371.8 174,.6 78.7 4630:30 18o.65 4 31:00 7.84 4.50-4.55 9.0 32.1 53,.5 25.00 25.21 25.00 380,1 173.8 78.9 4.5030 15.8 4,51:00 6.13 MEAN 53.8 24,98 25,21 2501 375.9 173.9 79.0 Thermometer Correction-.09 0-.2 04 CORRECTED MEAN 53.8 25.05 25.19 24,97 375.9 174.0 79.0

-79Aqueous.Ethyl AlcGol Flowrate The aqueous ethyl alcohol flowrate was measured by the displacement from the storage bottle. Time Level Volume 2,55:30 32,0 31.40 4,i50: 0 15.8 11,30 155:00 20.10 The volume of liquid in the storage bottle was obtained from the level in storage by the calibration given on page 95, Aqueous ethyl alcohol flowrate =,10 = 14.8 ml./min. 11500e Tert iary-Butyl-Bromide Flowrate The tertiary-butyl-bromide flowrate was also measured by the amount of liquid leaving the storage bottle. Time Level 2.56:00 15,86 4.51: 00 613 1,55:00 9*73 The volume of the storage bottle was calibrated in terms oi.. liquid level, The calibration on page 97 showed that volume was directly proportional to level. Tertiary-butyl-bromide flowrate,4 95 - 1.408 ml./min. 11500' Reactor Material Balance Total flowrate to reactor = 1748 + 1.4 = 176,2 ml./min, Outlet flowrate from reactor = 174,0 Volume out 174,0 Overall material balance = Volume n = 17 =.988 Average overall flowrate = 175,1 ml./min.

-80o Bulk Residence Time The reactor volume was calibrated in terms of the height of liquid in the reactor inclined manometer. From the calibration on page 99 the reactor volume was 2085 ml. V 2085 Bulk residence time = = 15 11.91 min. 175.1 TertiaryByl-tyl-Bromide Material Balance Concentration of tertiary-butyl-bromide in the combined inlet l. 4o x 1.186.06961 moles/l. stream to the reactor- = 1 6 = o6961 moles/. 137.0 x 175.1 Concentration of tertiary-butyl-bromide in the outlet stream from the reactor =4105 x 04204,06903 moles/1. 25.00 Tertiary-butyl-bromide material balance Material out.06903 992 Material in.06961 Calculation of t;he Distribution Function from the Recorder Trace The data and calculations of the distribution function from the recprder trace, shown in Figure 23, are presented in Table XI, Points read off the recorder trace are shown in columns 1 and 2. Column Description 1 Number of chart divisions and proportional to time. 2 Height of trace. 3 Relative height of trace or fractional transmittance. 4 Concentration of dye in outlet stream; obtained from column 3 by the calibration on page 92. 1,664n 5 Number of residence times 9 11, where the chart speed was 1,664 divisions/min. 6 Distribution of residence times E(@) = VC(~)

-81-. i.;. 1 -- ~ — ------------- ~~:j -.- ~~~i-. iL~~~^ ~4". - We ^ -: ^ ^ ~ ~ ^: I'LLI:m-U~ll ~!=-T:l~ II' ~i::i;^i:^.:^^^i^^lil~~~~~~~~~~~~~A tS ZL j1~7 lAillll~~lll ~- ^- ~l ~ —"~ ~~~^ I^-^ ^T — ^-:8 j!^!: l;~:.:~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~..... R ~g "~~-~'F^m l]:^l:^^^lpjj I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ^ ^^111^11 ll''~~~~~~~~~~~~~~~~~~~~~~~~~~~~7 i^ ~lefeall 1. ~~~~~~~7P I.^EpllllU 8^~~~~` 71-~i -it i

-82TABLE XI SAMPLE CAICULATION OFI HE DISTRIBUTION FUNCTION FROM A RECORDER TRACE 1 2;-' /- ~:3' ~~: 4 6 n I I/IO C(0):= 1.6664n E(Q) 116 91 0.38,83o 10 0 0000,03 o000 1 381.460.0680,. 354 2.270.326.0988.25 513 3.212.256 1207 -39.626 4 o188,227.1311.53.682 5.181.218.1348.67 o700 6.199.240.1261.81.656 7 o230.277 1138.95.590 8.268.323.0996 1.09 513 9.318.384 o0840 1.23.437 10.365.440 0720 1.37.374 11 i419.505.0601 1.51.312 12.473.570.0494 1. 65.257 13 524.631.0405 1.79.210 14.568.684.0337 1-93 o174 15.611.736.0271 2o07 ol41 16.649.781.0218 2.21.113 17.682.821 0171 2.35.089 18.711 o0856.0139 2,49.072 20.750.904 0089 2677.046 22 o 780.940 o0053 3o05.028 24,799.961.0034 3,32.018 26,810o 976.0022 3.60.011 28.816.984.0015 3092.008 30.820.8987.0012 416.006 32.822.990.0009 4.45.005 34 -825.994 oo00o6 473.o03 36.827 996 o0004 5.o0 o 02 38 828 o 998.0002 5,28.001 40.829.999.0001 56.001

-83If the chart reading for clear liquid was arbitrarily set at 00000, then the reading for 0% transmittance was 0.830. The relative height of trace height of trace =.83 The values of E(G) in column 6 were obtained by normalizing the C(G) curve given.in column.4 First Moment In Table XI, E(G) is given at non-integral values of..E(O) was plotted as a function of G and values were read off at integral values of,9 These values of E(G), along with other quantities used in calculating the first moment and conversion, are given in Table XII, which has the following column headings, Column Description 1 = The number of residence times. 2 - krG where k = the reaction rate constant. V T = V, the length of 1 residence time G = the number of residence times. 3 e 4 E(9) = () 5, A9 The first moment of the distribution function was calculated from E(G) in column 4 and 9GO in column 5 of Table XII. 9 o o For runlimi the t moment was 1.o.. o E(G) dG =.4 0 0 For run 45 the first moment was LO44.

-84TABLE XII:.. SAMPLE'. CAULATIONO.i0F.LTIE FIRST. IOMEN.TAND COVERSION. 1 2 3 4 5 4 k3'1 e"-k TQ E(O) -.A o.05 023 o977.0.1.1.092.912.33.01.2. 183.834 479.02.3 q275.759 572.,03.4 366 093.635,.5 *458.633.676 005 o6.550.577.706.06.7 64.527.695.07.8.733.480.665 o08.9.824.438.621 o09 1.0. o.915.400.566.1.1 1.01.364.511.ll 1,2 1.10.333 459 o2 lo3 1.19 o 34.410.13 1,4 1.28 o278 362.14 1.5 1.37 o254. 32.15.1,6 1.47 2.23 0 216 1.7 1 56.210.243 17 1.8 1 65.192.201.27 2-.0 1.83 ol60 160 o 40 2,2.2..133 o0 44 2.4 2.20.o11 o 8.48 2,6 2,38.093.061.52 2,8 2*56.077 041.56 3.0 2.75.064.030- o 3,2 2- 93 -053.i.64 3.4 3 o11.05 o016,68 306 3. 30.037.011.72 3.8 348.031 o009 76 4.0 3.66.02 6.007,80 402 3.85 o021.006 84 4.4 4o03.018.o.88 4. 6 4.21 o 01.004 92 4. 8 440.012.,03 096 5.0 4.58.010.00 1.00 5.2 4.76.009.1 1,04 5o4 4. 95.07.0 O 108

-8q 8 As discussed on page 7 the first moment or internal material balance served as a check of a measured distribution function. Conversion Calculated by the Measured Distribution of Residence Times The conversion as calculated by the measured distribution of residence times was given by Equation (6). 0 1 iia / ek E(G) 0 ~Z -1 e-k+ E(@) S For this run fM D = 0,5452 Calculated Reaction Rate Constant It was shown on page 73 that a mean reaction rate constant could be used without introducing error. T 25.05 + 25 19 25.120C mean 2 CETOH' 6539 Uo.n..making these substitutions in Equation (10). log k 088 = 159501- 5.0223 (.6539) - 4,641.22 / (273.1 + 25.12) k088 =.001267 sec. where k o88 was the reaction rate constant for an initial concentration of tertiary-butyl-bromide of.o88 moles/liter. For an initial concentration of.0696 mo 4es/liter, by Equation (11).

-86k0696- ko88 = 001268 (.580) (0880 -.0696) k 0696 =.001281 sec Conversion Calculated by the Perfectly-mixed Distribution.kT - 11.91 x 60 x.001281 4 PM.D..1 + kT 1 11+ 91g x 60 x.001281 Conversion Calculated by the Slug Flow Distribution -kT f 1-e =.5998 S.FD. Relative Conversion Difference Based Upon the Measured Distribution - -., -- t.,r...;-... [.. _, _,, _,, -... Function F ='f fM.D. 5676-.5452 184 MsD = fSFD fPMD.5998 - 4779 S F.D. P.M.JD. Sample Calculations for Statistical Tests Effect of Dye The relative conversion difference data inl Table VI was tested to determine whether dye had an effect upon conversion, The null hypothesis was that the difference between relative conversion differences in the presence and absence of dye was zero. Let 1 and 2 be subscripts denoting the presence and absence of dye respectively. For the data in Table VI Fl o06oo4 F2 =,04902 1 2 o2 = 400272 52 =.00227

-87The variances were close enough to being equal to assume that the variances for the two universes were equal. Since the samples were small the t-test described by Duncan(), page 394, was used. N1 2 S -.0510 N + N2 - 2 1 2 t =..585 1 1 Using a two-tailed test and a 5% significance level the critical t was 2.045. Therefore the hypothesis was not rejected and the data did not indicate that dye had a significant effect upon conversion. X - Chart The tests described on page 60 were then performed upon all the data used in the previous section. The null hypothesis was that the means of all runs were the same F =.0533 a =.0359 Hence an unbiased estimate of the standard error 0- =.0398 F N 31 The upper limit was A F + - s.1130,N

-88The lower limit was F o- o- =- 60063 None of the means for the runs were outside this interval, Therefore, the hypothesis was not rejected. Barlett' s Test -Bartlettt'sTest which was described on page 61, was used to test for constant variability. The null hypothesis was that the variances for the individual runs were a homogeneous set, TABLE XIII SAMPLE CALCULATIONS FOR BARTLETT'S TES Run Number log a2 11,001859 7,2693 10 12.000511 6.7084 - 10 13.000891 6.9500 - 10 14 o001941 7,288- 10 15 o000642 64,8075..10 16 o000l47 6,1673 - 10 17.002129 73282 - 10 33,001025 7-0107- 10 - -2 Arithmetic mean = a = +0011437 _2 log = 7.05832- 10 log geometric mean = 6.94117 10

-89Let p = the number of variances Then p = 8 and n = N-1 = 3 G = 2.3026 pn (log arithmetic mean log geometric mean) (14) = 6474 H=- + P+ == 1.125 (15) 3np G 5.755 H For n 7X2 = 16.0.05 The hypothesis was not rejected 2 X Test of Normality From the results of the last two tests it was reasonable to assume that the means of the runs could be used to.estimate a universe mean and the variance of the runs could be used to estimate a universe. variance, The null hypdthesis was that the data were normally distributed with F =.0533 and a =.052 N = 31 Let X = the theoretical frequency and y = the actual frequency TABLE XIV SAMiLE CALCULATIONS FOR THE TEST OF NORMALITY Upper limit ( )2 of class Z Y y y or ~J&$$ Z Y 3y.00 1.05 4C557 4.068,03 -.46 5,766 8.865.06.13 6*789 7.007.09'.75 6.66 5.416.12 1,32 4.340 4 *027 oo 00 2.883 3 o005

-90(Y' y)2 z. Y = 1.39 For 3 degrees of freedom %o = 7.82.0' The hypothesis was not rejected. Significance of the Mean The previous test had shown that the data can reasonably be assumed to be approximately normally distributed. The null hypothesis for this test was that the mean, F, of the relative conversion differences based upon the perfectly-mixed distribution was zero. N 31 F =.0533 = =.0520 z=, 5-.7 For a 5 percent significance level Z 1.96. The hypothesis was rejected and it was concluded that the relative conversion differences were significantly different from zero. Confidence Interval for the Mean The 95 percent confidence interval for F is -- 1.96 at Ft + 1 - =.0533 +.0183 But f fM..0052 M. POM.D* Therefore the 95 percent confidence interval for f - f.0183 x.0052 =.0052 +:..533 = (o.5 +.2)

APPENDIX III CALIBRATIONS Dye Conceerration as a Function of i Coimter Reading n * i --.r tI -.: -. The amont of dye in the stream leaving the reactor was measured by a clorimeter which was calibrated by solutions of dyes mixed up to desired concentrations. A calibration urve for "Ptachrome" blue black rem, cLnc. in aqueous ethyl alcohol containing 0575 molesof HBr per liter is shwn in Figure 24. The calibration followed Beer's Law very closely log - -K C where I1 = the intensity of incident light I - the intensity of emergent light C the concentration of de K = the absorption coefficient Therimoiete Correcti.ons The thermometers when totally immersed in liquid were calibrated against thermoeters which had been calibrated by the National Bureau of Standards. The calibrations a reesented in Table XV and are shown in Figure 25, The standard thermameter for reaings through 9 was PRICO 460641L and for readings 9 thrugh 15 was PRINCO 461707.In Table XV correction was trui temperature minus the thermometer reading.

-92100___ 90 80 70 60 50 40 z o\ X. _ 30 z a. 20 15......I.I I..........I... 0.00 0.04 0.08 0.12 0.16 DYE CONCETRATION, GRAMS PER LITER Figure 24. Calibration of Blue Black in Aqueous Ethyl Alcohol Reaction Mixtures,

-93TABIE XV THERMOMETER CALIBRATIONS Correct.ions OC Reading Temperature AMINCO PRINCO - EXAX E XAX EXX Nmber ~C 4002 224273 7478 7375 760 1 16.32 -o 07 - 13 -.7 2 16.59 +o13 3 19.67 -. 04 o6 -02 4 24.93 -.04 - 02 -.0 5 25.12 +.07 6 29.38 -.03 +05 -o 7 35.76 +.10 8 45. 69 +03 9 51.63 -.05 -.04 10 50051 -.04 11 59.8 -^4 12 70.30 -.13 13 79.97 -.12 14 990.10 -.15 15 99.26 +.o6

0*16 + AMINCO 4002 012 L^ PRINCO 224273.O sooo ^^ ^^^ 0~~~~~~~~ EXAX 7478 ^y^^ N^ D ~~~~~~~~XAX 7601 0^~~~~~~~~~~~~~~~~ EX^ AX 7375 - ~t x~~~~ 0 ~ -0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' 1^8, 04 + / taj (U W-0.12 -016 1III1II 10 20 30 40 50 60 70 80 90 10O TEMPERATURED C figure 25. Thermometer Calibrations,

-95Aqueus Ethyl Alcohol Feed Bttles Thevolumes of the aqueous ethyl alcohol feed bottles were calibrated in terms of lquid levele These data are presented in Table XVI and are show in Figure 26. TABLE XVI CALIBRATION OF THE AQUEOUS ETYL ALCOHOL FEED BOTTLES Volume Liquid Level Liters 3.gal. bottle.gal, bottle 12 galo bottle 1 3.92 3.60 2 6.60 5 64 7.8 3 9.25 7058 4 11.91 9.39 9.6 5 14.53 11,28 6 17014 13009 11.4 7 19078 14o90 8 22,39 16.71 13.1 9 24.99 18.55 10 27059 20037 14o7 11 30o56 22.19 12 24,02 16.4 13 25085 14 27.67 18.0 15 29.51 16 31.30 19.6 17 33.20 18 35.23 2103 19 38.63 20 22.9 22 24.5 24 26.1 26 27.7 28 2903 30 3009 32 32o 5 34 341o 36 35-o7 38 37.4 40 39 2 42 41.4

-9644._..... W..... 1. 22 40 _ 20 36 18 32 _ _ 16 28.. 14 0 W O I I-'12 4 8 16 3 8 - / y Q 3 GALLON BOTTLE 4,dt,~fi fg 0 5 GALLON BOTTLE 4 _ /a 12 GALLON BOTTLE _ 2 0.~.~-, l,... 0. 0 4 a e2 16 20 24 28 32 36 40 LIQUID LEVEL Figure 26. Volumes of the Alcohol Feed Bottles.

-97Tertiary-Butyl-Bromide Feed Bottle The volume of the tertiary-butyl-bromide feed bottle was calibrated in terms of liquid level, These data are presented in Table XVII and are shown in Figure 27. The volume level relation was found to be linear and the slope was 16,64 ml./cm, TABLE XVII CALIBRATION OF THE TERTIARY-BUTYL-BROMIDE DT BOTTLE Liquid Level Volume Cm. Mlo 25.56 505.1 24.00 47801 22.73 457.1 21.02 429.4 19.80 409.3 18.27 382q3 16o88 359.3 15.59 337.1 14.09 313.2 12.43 283,8 11.18 263.2 9.70 238.8 8o35 216o7 6o77 188 9 %541 16605

* 814409 pOO& 9^Jmoa;TA~ nq-.Xjvj-ea j 9PtIn4 j uToA *5 L natTg'*__ O 13/\31 Whlomt)i -~ 8 o z ~5 l 8~ 0 9 1 0C)2 9OO -9^

-99Two-Compartment Reactot Volume The liquid level in the reactors was measured by an inclined manometer. The reactor volumes were measured as a Function of liquid level. For the two-compartment reactor the calibratin is presented in Table XVIII and shown in Figure 28& TABLE XVIII VOLUME OF THE TWO-COMPARTMENT REACTOR Liquid Reactor Level Volume, mL. 39.9 1930 42.8 1962 44~0 1979 48,1 2025 49,7 201 57.0 2116 7 02 2119

-1002120.... 2080 =S 2040 2000.c 1960 1920!, 36 40 44 48 52 56 60 LIQUID LEVEL Figure 28. Two-Compartment Reactor Volume Calibration,

NNOMENCLATURE A, At A"' A"" Costants B^ B' Constants C Initial Concentration of tertiary-butyl-bromide moles/l..C-OEp:EMass fraction of alcohol in the aqueus ethyl alcohol C(Q) Concentration Of tracer in the exit stream for a pulse experiment, grams/ml, -D Constant ~E ActivatiOn energy, cal./mole E(O) Non-cumulative distribution function for the outlet stream, dimensionless f Measured fractional conversio dimensionless f Fractional conversion calculated by using any distributin of residence times, dimensionless fj^"o HFractiona conversion calculated by using a measure distribution of residence times, dimensionless fPoM-rD" Fractional conversion calculated by using the perfectlymxed distribution.f r esidence times, dimen-. siOenless fSooDe:Fractioal conversion calculated by using the slug-flow Sdistribution of residen ce timfsf dimensinless Fi Relatie conversion difference based upon the distrlbutiOn function i dimensionless F(1) Cumulative dstribution function fr the outlet stream, dimensionless G RD)efined by Equation (14) H Defined by Equation, (15) I Intensity of the emergent light beam -101

~!02I. JIntensity of the incident light beam!I(.) ]Non-cumuliative distributin function for the reactor, dimensionless k First-.order reaction rate onstant, sec.k"c^, l'First-rder reaction rate nst in a solution whose initial cncentration f,tertiary-butyl bromide is CG moles/1., s-ebK Absorptioni coefficie ent nDegrees of freedom N Sample size P lNumber of variances Q iQu.rntity of tracer injected in the pulse, grams rj. jk MuJltiple correlation coefficient R Gas constarnt 1^987 cal/mole ~KO t Time measured from the intro-ction of the sig.na in a tracer experiment, sec. t Deviation of a variable from its mean divided by an estimate of the universe standard.viation based on the sample standard deviatipn, dimensionless t-b.' point of a t distribut in dimensionless T TesmperaatreT, rC:VY Volume of flow system, ml. y Actual frequency Y Theoretical frequency Z A variable measured from.the universe mean in terms of the universe standard deviatio

"103ther Symb.ols a'.y Level of significance A l Number.of resi dere times, dimensim.less T Mean residence time, p sec, 02 Variance a' Stand.ard error ^.L An estimate of F F X!; SfStandard. error of F F X2 S~Sample sum of squares divided by the universe variance o0 Infinity

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/3 9013 @,~2 7880 THE UNIVERSITY OF MICHIGAN DATE DUE. __i