V' th—u : A mm 02? FAST mmom m A mamas m1 EAMEMEE FLi‘s-W mama 22mm Pm mamas 0? 93:3»ng mama ammm mar I!- ma Fm mmmmn es mmm Fm mama mm Tins}: Eoc- flm Degree of M. S. EMCEEESEE’ STATE UKEVERSETY ‘E‘ed A. Eiieimheaz 1-970 E" “I!" a—II' “AA-3"": 1‘73 LIBRARY 5 Michigan, Stew 5' ’ ' a, Universi as] V -—-- ”w * ‘_.'~y 'fl‘v".".flw—v “was: ABSTRACT A STUDY OF FAST REACTIONS IN A VARIABLE LENGTH LAMINAR FLOW TUBULAR REACTOR by Ted A. Kleinhenz The kinetic parameters of the PhSiCl hydrolysis reactions were 3 determined from data obtained with a laminar flow tubular reactor at 0°C and in solution with 1,2-dimethoxyethane. The experimental appar- atus was a continuous flow variable length tubular reactor connected in series to an infrared spectrophotometer. The overall hydrolysis reaction was deduced to proceed by the stepwise hydrolysis of each chlorine atom resulting in the formation of PhSiC12(0H), PhSiC1(OH)2, and PhSi(0H)3. The infrared absorptions assigned to the reaction species which were used for analysis were: PhSiCl 514 cm'l; PhSiClz(0H), 3’ 1 525 cmfl; PhSiCl(OH) 425 cm'l; PhSi(0H)3, 465 cm' . 2’ The PhSiCl hydrolysis reactions were modeled with three coupled 3 second order, first order with respect to each reactant, irreversible reactions. The forward reaction velocity constants were found to be 1500., 77.5, 1000. (liter/mole—seconds) for the first, second, and third chlorine atoms, respectively. The hydrolysis of the second chlo- rine atom was found to be the rate controlling step. The flow within the reaction zone varied between plug and laminar. The kinetic data were analyzed using both plug and laminar flow reactor models. Both models fit the data reasonably well with most of the data between the two models. A STUDY OF FAST REACTIONS IN A VARIABLE LENGTH LAMINAR FLOW TUBULAR REACTOR Part I“‘KINETICS OF PhSiCl HYDROLYSIS REACTIONS 3 Part II-PLUG FLOW APPROXIMATION OF LAMINAR FLOW TUBULAR REACTOR By ,QW Ted ALLKleinhenz A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1970 ACKNOWLEDGMENT The author gratefully acknowledges the Dow Corning Corporation. and the Division of Engineering Research at Michigan State University for their financial support of this work. Sincere appreciation is extended to Dr. M.C. Hawley for his invaluable assistance and guidance during the course of the project. Sincere appreciation is extended, also, to Dr. W.D. Larson (Dow Corning Corporation) and Mr. A.R. Bond (Dow Corning Corporation) for their technical assistance, Mr. Don Childs for building and repairing the experimental apparatus, Mrs. Beverly Oetzel for typing the papers for publication. 11‘ To Christine TABLE OF CONTENTS Page ABSTRACT ACKNOWLEDGMENTS 11 TABLE OF CONTENTS iii INTRODUCTION 1 PART I-KINETICS 0F PhSiC13 HYDROLYSIS REACTIONS 4 ABSTRACT 5 LIST OF TABLES 7 LIST OF FIGURES 8 INTRODUCTION 9 MATERIALS AND EQUIPMENT 11 Materials 11 Reactor 11 Apparatus 13 Temperature Control 15 DISCUSSION OF PREVIOUS WORK 16 DESCRIPTION OF EXPERIMENTS AND EXPERIMENTAL CONDITIONS 19 Conditions for Water-PhSiCl3 Reactions 19 Conditions for PhSiCl3-PhSi(OH)3 Reaction 21 INTERPRETATION OF SPECTRA AND DATA REDUCTION 22 Analysis of Infrared Spectrum of PhSiCl3 and Hydrolysis Products 22 Calculation of Concentration of Hydrolyzates 25 Example Calculation: Run 13 26 MODELING THE PhSiCl3 HYDROLYSIS REACTIONS 37 RESULTS AND CONCLUSIONS 40 iii PART NOMENCLATURE REFERENCES II"PLUG FLOW APPROXIMATION OF LAMINAR FLOW TUBULAR REACTOR ABSTRACT LIST OF TABLES LIST OF FIGURES DEVELOPMENT OF PROBLEM METHOD OF ANALYSIS Illustrative Example DISCUSSION OF RESULTS . Irreversible Reactions Reversible Reactions Comparisons With Other Work Conclusions APPENDIX I NOTATION LITERATURE CITED EXPERIMENTAL PROCEDURES Experimental Preparation Reactor Data Collection Hydrolysis Reactor Trouble Shooting Safety FORTRAN PROGRAMS AND DOCUMENTATIONS Numerical Solution for Plug Flow Reactor Example Result for Plug Flow Reactor Numerical Solution for Laminar Flow Reactor ' iv 41 42 43 44 45 46 47 50 51 52 52 52 55 57 63 66 67 68 68 70 7O 71 72 72 72 74 Example Result for Laminar Flow Reactor Application of Programs to Different Types of Reactions RESULTS AND CONCLUSIONS RECOMMENDATIONS FOR FUTURE WORK APPENDIX A Fortran Model of PhSiCl3 Hydrolysis Reactions APPENDIX B Example Result of PhSiCl Hydrolysis Model 3 APPENDIX C Fortran Model of Plug and Laminar Flow Reactor with Ph81013 Hydrolysis Reactions APPENDIX D Example Result of Plug and Laminar Flow Reactor with PhSiCl3 Hydrolysis Reactions 74 75 76 77 78 82 84 89 INTRODUCTION The primary objective of this work.was the determination of the kinetic parameters of the PhSiCl3 hydrolysis reactions. In order to achieve this purpose it was necessary to develop a reactor suitable for "fast" reactions, combine an analytical method capable of observing the silane reaction species, and formulate an accurate description of the hydrolysis reactions and the reactor. In order to measure these kinetic parameters, it was necessary to obtain kinetic data on the hydrolysis of each individual chlorine atom. Since chlorosilane hydrolysis reactions are usually considered fast, a continuous flow tubular reactor system was chosen for the experimental apparatus. Noting that the infrared absorptions of chlorosilanes vary depending on the number of chlorine atoms present, infrared spectrOphotometry was chosen for the analysis of the reactor effluent. The use of a continuous flow reactor presented an opportunity to observe the reaction species at fixed reaction times for extended periods of time. Throughout the experiments the various reaction times were obtained by adjusting the length of the reaction zone while keeping the flow rates constant. This research was a continuation of previous work done during the summer of 1967 by Dr. M. C. Hawley (Michigan State University), Dr. W. D. Larson (Dow Corning Corporation), and Mr. A. R. Bond (Dow Corning Corporation) and reported in Dow Corning Report, Project Number 605, 1968. Their efforts resulted in the development of a continuous flow variable length tubular reactor and an initial investigation of the PhSiCl3 hydrolysis reactions. Part I of this study is a revision with additional kinetic data of a previous paper based on the original Dow Corning report. Part II of this work is an analysis of the effects of the plug flow assumption on the kinetic parameters determined in a fully devel- oped laminar flow tubular reactor. This section was developed as a foundation for the analysis of the experimental laminar flow kinetic data. Parts I and II were prepared independently in publication form. Part I is a study of the kinetic parameters of the PhSiCl hydrol- 3 ysis reactions. The hydrolysis of chlorosilanes is a fundamentally important reaction in the preparation of siloxanes. Many publications have dealt with methods for obtaining various siloxanes, but only a small amount of work has been published on the hydrolysis reactions. The hydrolysis of alkyl and aryl chlorosilanes has been studied with conductometric titration by Shaffer and Flanigan (1957) in batch exper- iments. However, the conductometric titration method is limited to following only the disappearance of water or the generation of HCl with time. With this method only the rate controlling step of the combined hydrolysis and condensation of the chlorosilanes can be studied. Prince (1958) has described a continuous flow apparatus using electrolytic conductivity to study the kinetics of fast reactions. This method is limited in that only the rate of generation of HCl in the hydrolysis reaction can be followed. It was possible to follow the individual hydrolysis reactions of each chlorine atom in the kinetic study of the hydrolysis of phenyltri- chlorosilane, a fast reaction. A continuous flow reactor was used with infrared spectrophotometry being the analytical method used to follow the concentrations of the reactants. The reactions were carried out in 1,2-dimethoxyethane as the solvent and at 0°C. The use of a flow reactor is a convenient method of converting the time variable into a length variable. The ideal plug flow reactor would be one in which an initially homogenous reaction mixture moves through a tubular reactor with a flat velocity profile. The result would be a uniform residence time on any flow cross section. However, if the ex- periment is performed in the fully laminar flow region, the velocity pro- file will be parabolic and each element on any flow cross section will have a residence time given by the ratio of the length it has traversed and its velocity. In the case of a plug flow reactor the bulk concentration is inde- pendent of any reactor parameters. However, in the case of laminar flow the bulk concentration is determined by the integration of the velocity- concentration product over the flow cross section. Therefore, in order to determine the effect of the plug flow approximation, the plug and laminar flow bulk concentrations were compared at the same residence times using the same rate constants. PART I KINETICS OF PhSiCl3 HYDROLYSIS REACTIONS Revision of paper originally prepared for publication by M.C. Hawley, W.D. Larson, and A.R.Bond (based on Dow Corning Project Number 605, 1968) Revised paper by T.A. Kleinhenz, M.C. Hawley, W.D. Larson, and A.R. Bond Michigan State University Department of Chemical Engineering 1970 ABSTRACT KINETICS OF PhSiCl3 HYDROLYSIS REACTIONS By T. A. Kleinhenz, M. C. Hawley, W. D. Larson* and A. R. Bond* Michigan State University East Lansing, Michigan *Dow Corning Corporation Midland, Michigan The kinetic parameters of the PhSiCl3 hydrolysis reactions were determined using a continuous flow variable length tubular reactor connected to an infrared cell. The PhSiCl3 hydrolysis was carried out in l, 2-dimethoxyethane and the reaction was deduced to proceed by the stepwise hydrolysis of eadh chlorine atom resulting in the formation of PhSiC12(OH), PhSiC1(OH)2 and PhSi(OH)3. The IR bands assigned to intermediates and products which.were used for analysis are as follows: PhSiCl3, 514 cmfl; PhSiCl 1 l 20H, 525 cm? (corrected for PhSiCl3); PhSiCl(OH)2, 425 emf ; PhSi(OH)3, 465 cmfl. It was not possible to observe the siloxane region because of complete absorption by the solvent. To determine if there was reaction between chlorine on silicon and hydroxyl on silicon, solutions of phenyltrichlorosilane and phenylsilanetriol were reacted at 0°C. There was no evidence of any significant reaction. I The flow within the reaction zone varied between plug and laminar flow. Both plug and laminar flow models were used to analyze the kinetic data. The PhSiCl3 hydrolysis reactions were modeled by three coupled second order irreversible reactions (one hydrolysis reaction for each chlorine atom). The forward rate constants for the PhSiCl hydrolysis in l, 3 2-dimethoxyethane at 0°C were found to be 1500., 77.5 and 1000. liters/ mole-seconds for the first, second and third chlorine atoms, respectively. The choice of flow model had little affect on values of reaction velocity constants. The rate controlling step was the hydrolysis of PhSiC12(0H). LIST OF TABLES SUMMARY OF RUN CONDITIONS ABSORPTION COEFFICIENTS FOR REACTION SPECIES ABSORBANCE AND CONCENTRATION VALUES AT VARIOUS MEAN TIMES FOR HYDROLYSIS EXPERIMENTS LIST OF FIGURES Page Continuous flow tubular reactor 12 Hydrolysis experimental flow system . l4 Infrared spectra of PhSiCl3 hydrolysis products and. analogous compounds 23 Composite infrared spectrum of PhSiCl hydrolysis reaction species with increasing mean reaction times (Run 13) 28 Mole fraction of total silane versus mean reaction time of PhSiCl3 hydrolysis reaction species (Run 13) 29 Mole fraction of total silane versus mean reaction time of PhSiCl3 hydrolysis reaction species (Run 16) 30 Mole fraction of total silane versus mean reaction time of PhSiCl3 hydrolysis reaction species (Run 18) 31 Mole fraction of total silane versus mean reaction time of PhSiCl3 hydrolysis reaction species (Run 19) 32 Mole fraction of total silane versus mean reaction time of PhSiCl3 hydrolysis reaction species (Run 20) 33 INTRODUCTION The hydrolysis of chlorosilanes is a fundamentally important reaction in the preparation of siloxanes. Many publications have dealt with methods for obtaining various siloxanes from chlorosilanes, but only a small amount of work has been published on the hydrolysis reaction. The hydrolysis of alkyl and aryl chlorosilanes has been studied with conductometric titration by Shaffer and Flanigan (1957) in batch experiments. The conductometric titration method is limited to following only the disappearance of water or the generation of HCl with time. This means that one can only study the rate-controlling step of the combined hydrolysis and condensation of the chlorosilanes. Under the conditions of their experimentation with saturated HCl the overall reaction was observed to be quite slow. Half lives in the order of hundreds of seconds were observed. Prince (1958) has described a continuous flow apparatus using electrolytic conductivity to study the kinetics of fast reactions. Prince (1958) studied the hydrolysis of Ph3SiCl and Ph3SnCl as examples of fast reactions. This analytical method is limited in that one can only measure the rate of HCl generation in the hydrolysis reaction. It has been stated (Kuznetsova et.al; 1965) that hydrolytic condensa- tion of organochlorosilanes in an excess of water is accompanied by the formation of organosilanols which undergo further reaction in a variety of ways. No data were reported to support this statement. 10 Other workers (Allen et.al, 1957; Allen and Modena, 1957; Prince, 1959; Chipperfield and Prince, 1963) have studied the kinetics of hydrolysis of substances with only one chlorine atom. This paper reports a kinetic study of a fast reaction, the hydrolysis of phenyltrichlorosilane, whereby it was possible to follow the individual hydrolysis reactions. A continuous flow type reactor was used with infrared spectrophotometry being the analytical tool used to follow the concentrations of the reactants. The reactions were carried out with 1, 2-dimethoxyethane (Ansul Ether 1211) as a solvent at a temperature of 0°C. 1Ansul Company, Marinette, Wisconsin. MATERIALS AND EQUIPMENT Materials Phenyltrichlorosilane was fractionated under dry N2, bp l99-201°C, prior to use so as to remove hydrolysis products. Subsequent handling was accomplished by means of vacuum or dry N2 pressure apparatus. Commercial grade 1, Z-dimethoxyethane contained 3-4Z water and some peroxides. These were removed by shaking over several portions of KOH pellets followed by distillation under dry N2 from KOH pellets. Only the middle cuts, bp 84.0- 84.5°C, free of water and peroxides were used. Phenylsilanetriol was prepared by hydrolysis of phenyltrimethoxy-silane (Tyler, 1959). (The white crystalline product was dried under vacuum at room temperature overnight. Silanol analysis indicated slight condensation, nmr spectra in dimethylsulfoxide revealed no water present. Reactor Figure l is a sketch of the tubular reactor connected to the infrared cell (Hawley, M. C., Larson, W., Bond, A. R. 1970). The reactor was constructed of 2.16 mm inside diameter stainless steel and jacketed with a one inch copper tube. The water was added to the reactor through a stainless steel hypodermic needle. The end of the hypodermic was closed and the water was forced through two radial holes close to the end of the needle. The main feature of the reactor design is that the length of the reactor can be varied by just changing the position of the water inlet. The windows of the infrared cell were thallium iodide—bromide. The sample chamber was 0.1 mm thiCk, 25 mm high and 10 mm wide. The cell was connected to the reactor such that the flowing fluid had to make.a 30° turn before passing through the cell. 11 12 zoo mm L: a as was .uomomom .8153 30¢ moosfiusou A oudmwm _ seam ~~ k . 0mm _-.J L tam E0 m® _ PF T mamas V. 13 The residence time of fluid in the measuring cell was equivalent to about 3 mm of reactor length. Pressure drop through the apparatus limited the flow and runs were made such that the Reynold's Number in the reactor was in the range of 100 to 200. Therefore, plug flow did not prevail in the reactor during these experiments. Thus, it was necessary to vary reactor length rather than flow rate to make the kinetic studies so as not to superimpose the variation in flow problem on top of the kinetic problem. Apparatus Figure 2 is a schematic of the flow system used for this experimentation. The PhSiCl3 and l, 2-dimethoxyethane were mixed together in one of the stainless steel tanks while water mixed with l, 2-dimethoxyethane was contained in the other. Nitrogen pressure was used as the driving force for flow. Rotometers were calibrated and used to monitor the flow of the water and the chlorosilane solvent mixture. ’Temperature of the reaction was controlled by circulating water or other controlled temperature fluid from a constant temperature bath through the jacket of the reactor. The infrared cell was connected to the end of the reactor. A Perkin Elmer Model 337 spectrophotometer with solvent in the reference cell was used to record the spectra. Values of absorbance versus reactor length at constant flow rates were obtained at various inlet flows of water and PhSiCl3. These data were analyzed and converted to concentration versus reactor length from which kinetic parameters were determined. 14 Nitrogen Pressure i Water Ether PhSiCl3 Ether é— Rotometers —9 Reactor ———‘1 Constant Temperature Pump Bath Figure 2. Hydrolysis experimental flow system. IR Cell 15 Temperature Control Constant temperature control was achieved in the reactor by using an equilibrium mixture of ice and.water in a controlled temperature bath. Reactants were pumped through heat exchange coils submerged in the bath on their way to the reactor. Heat exchange media.was also pumped through the reactor. DISCUSSION OF PREVIOUS WORK The studies of Shaffer and Flanigan (1957) and Prince (1958) both used electrolytic conductance to follow the hydrolysis of chlorosilanes. Shaffer and Flanigan (1957) slowed the reaction by saturating the solvent with HCl and lowering the temperature so that it could be followed batch- wise with time. Prince (1958) designed a flow reactor and monitored the electrolytic conductivity as a function of reactor length. Both experimental methods yield only the concentration of HCl which allows one to study only the rate controlling hydrolysis step, and one is not able to determine whether hydrolysis or condensation is rate controlling.‘ When Shaffer and Flanigan (1957) titrated trichlorosilanes, highly condensed polysiloxanes were formed at 0°C, while at -78°C they stated that (RSiC12)20 was a stable hydrolysis intermediate. They concluded that lowering the temperature of the reaction had essentially the same effect as increasing the HCl concentration in that both suppressed the hydrolysis of the silicon chlorine bond. Shaffer and Flanigan (1957) made the following generalizations about the chlorosilane hydrolysis rates: 1. The hydrolysis rates of members of the series SiCl4 - R SiCl 3 4 > RSiCl3 >>R281Cl2 > R381C1. 2. For any chlorosilane containing two or more chlorines on the are related by SiCl same silicon, the first chlorine reacts very much faster than those remaining. They assumed that the kinetics of the reaction of water with chlorosilanes could be expressed by 16 17 —d[HZO] m _ . n p -—-EE—- = k [H20] [:SlCl] [HCl] (1) Values of m and n were determined but the effect of HCl was not studied in enough detail to determine p. Based on Equation 1, Shaffer and Flanigan (1957) determined the order of reaction with respect to water as one. They showed the order with respect to chlorosilane of the RSiCl3 systems to be two. They also found that the hydrolysis reaction of (CH3)ZSiCl2 had an apparent order of -l/3. This observation was not under- stood, since the increase in rate of hydrolysis with decrease in initial chlorosilane concentration was not observed for any other R SiCl . 2 2 Most of Shaffer and Flanigan's (1957) hydrolysis experiments were carried out in l, Z-dimethoxyethane saturated with HCl. The rates of hydrolysis of CH381C13, PhSiCl3 and (Me)ZSiC12 were also measured in dioxane-HCl. They reported that the rates of hydrolysis of (Me)ZSiCl2 and MeSiCl3 were three times faster in dioxane than in l, 2-dimethoxyethane. The hydrolysis of PhSiCl3 in dioxane—HCl was slower than the hydrolysis carried out in 1, 2-dimethoxyethane HCl at the same temperature. It was shown that the hydrolysis of chlorosilanes was first order with respect to water. This observation was interpreted to mean that the rate controlling step involved only a single water molecule. The following chain of bimolecular reactions was proposed by Shaffer and Flanigan (1957) to describe the hydrolysis of chlorosilanes: H20 + HCl + s + H20 - HCl - 3 (2a) S refers to one or more molecules of solvent R SiCl + H 0'HCl'S + R SiCl (OH) + 2HC1°S (2b) x x x 3-x 4- 2 18 2Rx81C13_x(Oh) + (RxSlCl3-x)20 + H20 (2c) or Rx81Cl3_x(OH) + RxSlC14_x + (Rx81C13_x)20 + HCl'S (2d) It has been reported that only in the case of PhZSiC12 have indications of stable groups like =Si(OH)C1 been found and this was interpreted that for the other chlorosilanes studied, either reaction (2c) or (2d) is very fast compared to (2b) and (2b) is the rate determining step, or that the equilibrium for (2b) is far to the left. The observation that the hydrolysis of chlorosilanes is second order for chlorosilanes requires that two molecules of chlorosilane be involved in the rate controlling step, and this requires that reaction (2c) or (2d) to be slower than (2b). In the next section results of experimentation are discussed in which the concentrations of unstable intermediate chlorosilane hydrolysis products were determined. Data obtained by the described infrared method should yield more fundamental information about the hydrolysis and condensation of chlorosilanes. The hydrolysis reactions of chlorosilanes are "fast" at room temperature and low HCl concentration and the intermediate hydrolysis products are unstable. Therefore, conventional batch kinetic techniques are not suitable for study of these reactions. Fast reactions can be studied in a continuous flow system if a continuous method of analysis is available to measure the concentrations of the reaction species. In this manner, unstable intermediate species may be monitored. DESCRIPTION OF EXPERIMENTS AND EXPERIMENTAL CONDITIONS Conditions for Water-PhSiCl3 Reactions A11 PhSiCl3 hydrolysis reactions were run at 0°C. The reactants were cooled to 0°C in an ice-water bath and the heat of reaction was dissipated through the reactor cooling jacket. The desired initial reactant concentrations were obtained by setting the appropriate flow rates based on the solvent-reactant concentrations in each tank. The flow rates remained fixed for each consecutive set of data points during a run. Therefore, in order to follow the hydrolysis reactions as a function of reaction time the outlet of the hypodermic needle (carrying the water-solvent mixture) was carefully positioned at different axial distances from the reactor outlet. This technique effectively varied the length of the reaction zone and resulted in fixed mean reaction times for extended periods of real time. An experimental foundation for proposing any hydrolysis intermediate species and their rate expressions was provided by reacting several different molar ratios of water and chlorosilane. A summary of the initial concentrations of chlorosilane and water during the experiments is presented in Table l. The original concentration of PhSiCl3 prepared for each experiment is given as "total silane" in Table l. The presence of PhSiC12(OH) in the silane feed is due to hydrolysis prior to the mixing with water in the experiment. The initial concentration of PhSiCl was determined quantitatively 3 from the infrared spectrum of the initial change. The remaining silane was 19 20 mm.mq mm.HH m.mm No.H mqa. ammo. . omoo. ammo. ow H.oq o.m m.mm qfi.m can. wwoo. oooo. omoo. 0H H.0q H.o o.oq mq.m New. wmmo. ammo. memo. ma H.0q H.q o.mq mH.N mow. memo. ommo. memo. ca o.oq 0.0 o.oq Hm.m mmm. ommo. ommo. ammo. ma cwe\oo cwe\oo cwe\oo mcmawm pnmqu\mmflozvAmmmfiq\mmflozv Ammuwg\mmfiozv Ammqu\mmaozv mmmm 30am ucm>aom ucm>aom Hmuoe mmum3 mcmafim HmDOH Amovmaoflmmm maofimnm cam Hence lumen: Imcmamm \nmamz mo .ocoo mo .ocoo mo .ucoo wo .ocoo . mmumm 30am ucmuommm mnowufiesoo sneezimcmafimomofizu HmfiuwcH mZOHHHQZOU mam mo wm<flzbm I H mum_ §>_ m_ m>_ 2_ m—m_ m_ Oman 2;— m_ m_m_ ‘ 33 m_ magma. 2_ B_ m_m_ m_ 2_ m_ m_ osmium; 2_ 2_ j m_ m_ m_ 2_ m_m_ emammmimome. smears. . Naomi _ a _ _ so 24 During the hydrolysis of PhSiCl it was suspected that PhSiCl OH, 3 2 PhSiCl(OH)2 and PhSi(OH)3 were formed. Since PhSiClZOH and PhSiC1(OH)2 are unstable compounds, they have never been isolated and identified. The presence of PhSiClZOH was inferred from the occurrence of the bands at 1 and 525 cm-1. These absorptions are probably due to the anti- 570 cm7 symmetric and symmetric SiCl stretching vibrations of a silicon atom containing two chlorine atoms. A single peak at about 550 cmfl, effected for the monothloro species, was not seen. It was believed that the SiCl stretch of the monochloro species was superimposed on the 525 cm.-1 band of the dichloro species. It was also observed during the hydrolysis experiments that new peaks occurred at 485 cm.1 and 465 cm—1. Based on analysis of Figure 3 1 and following information, 465 cm-1 was considered due to PhSi(OH) 525 emf 3: to PhSiC120H and both 620 cm51 and 514 cm1 due to PhSiCl3. Although the monochloro species absorption was not noted during these experiments earlier experiments using a Perkin Elmer 521 spectrophotometer detected an absorption at 425 cm.1 that could be attributed to the monochloro species. Therefore, the monochloro species concentration was obtained by forcing a mass balance of the silane charge. This concentration was always low, thus it was subject to large error since it was the difference of large numbers. At this point, one may question the nature of these intermediate dichloro and monochloro species. Using 1, 2-dimethoxyethane as solvent, it was not possible to observe the siloxane region of the infrared spectrum because the ether totally absorbed in that region. Therefore, it was 25 possible that the intermediate species were condensed compounds with one and two chlorine atoms attached to the silicon atom. A separate experiment showed no reaction between PhSiCl3 and PhSi(OH)3. Since no reaction occurred between PhSiCl3 and PhSi(OH)3 this would indicate that condensation ' Cl Cl did not occur. Further, the spectrum of PhSiOSiPh shown on Figure 3 C1 C1 -1 indicates that this species has an absorption at 620 cm as does PhSiCl . During the hydrolysis experiments the disappearance of the 620 cm.-1 absorbance was observed. Also, it should be noted that the PhSi(OH)3 has no significant absorbance at 620 cmfl. Since the 620 cm"1 peak was not 1 and 525 cm.1 peaks were strong, it present at all times when the 570 cm. was believed that siloxanes were not formed at this point in the experiments. This argument substantiated the belief that the dichloro species was PhSiClZOH, and also makes the presence of PhSiCl(OH§during hydrolysis more plausible. Calculation of Concentrations of Hydrolyzates It was experimentally determined, using infrared spectrophotometry, that the difference of the absorbance of PhSiCl3 and the corresponding base line absorbance was proportional to the product of the concentration, c, of PhSiCl3 in the ether solution and the infrared cell path length, d (i.e. the Beer's law relationship is applicable). 8 d c = A - A0 (3) It was assumed that the same relation was valid for each reaction species being monitored. [“r" L. 26 The above proportionality constant was determined for PhSi(OH)3 by an analysis of the hydrolysis end product of PhSiCl3 and an excess of water. The proportionality constant for PhSiC12(OH) was determined by an analysis of the hydrolysis product of PhSiCl3 and water in a molar ratio of approximately one mole of PhSiCl3 to one half mole of water. The absorption coefficients for the reaction species monitored and corresponding frequencies are summarized in Table 2. Figures 5, 6, 7, 8 and 9 are graphs of mole fraction of total silane charge (determined by dividing the logrithmetic intensity ratio by the appropriate d and the total silane charge) of all reaction species versus the mean residence time within the reactor. The points on Figures 5, 6, 7, 8 and 9 represent the experimental data. The solid and hatched lines were constructed from the digital computer simulation of the plug flow and laminar flow hydrolysis models, respectively. Example Calculation: Run 13 A composite sketch of the infrared spectrum recorded during Run 13 is shown in Figure 4. The composite drawing shows the region between 650 cm.-1 and 450 cm.l. The reference spectrum was recorded before the addition of water while the following spectrum represent the absorptions due to the reacting silanes. 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H. 2 auens I910; J0 uopomg 3pm '1“. .‘ .‘ ~l Ir... a. 1! ‘1 ul\d.- 33 .AON 51E mewuomm cowuummn 3930.6»: MHUHmAQ mo ocufl coflommn Emma mum??? mcmflm H33 mo noflomum 302 .o musmwm 0% .385. :83: w w .m. m. m. - o o maovfiowmnm \ \ magma \ o \ \ \ 0 O \A 1 v. «1.... 1.... mafia 0/ N / Fm. £9 6me 0/0/ m o r w. .8328 .«o .8“: 32. ”00 m2 13cwm|§d3 $38 . Es: 3% .3553 .. .. 1% 5338 we .23: mm 3.25 :38 $68 vmmo. n 2 552 303 warm auens [310$ J0 uonoexg 910W 34 E = L/Ub (4) The course of the reaction was followed by maintaining constant flow rates while varying the length of the reaction zone by either inserting or withdrawing a portion of the hypodermic needle carrying the water- solvent mixture. The net absorptions for PhSiC12(OH) and PhSi(OH)3 measured during Run 13 are listed in Table 3. The molar concentrations were found by apply- ing Equation 3 with the appropriate absorption coefficients of Table 2 and the appropriate IR cell path length of Table 3. It was noted in all experiments that the 514 cm“1 absorption due to PhSiCl had disappeared in 3 all reaction mixtures. Assuming that the reaction proceeded through a stepwise hydrolysis of each chlorine atom, all of the initial PhSiCl charge 3 could be accounted for by the four reaction species: PhSiCl PhSiC12(OH), 3’ PhSiC1(OH)2 and PhSi(OH)3. Therefore, knowing the concentrations of three of the four species present, the remaining component was found by forcing the silane mass balance. The results of this procedure are shown in Table 3 as the molar concentrations of the reaction species for several mean reaction times. 35 TABLE 3 - ABSORBANCE AND CONCENTRATION VALUES AT VARIOUS MEAN TIMES FOR HYDROLYSIS EXPERIMENTS A - A 0 Net Absorbance Concentration (Moles/Liter) Of E, sec 525 cm"1 465 cmfl PhSiC13 PhSiC12(OH) PhSiC1(OH)2 PhSi(OH)3 RUN 13 MHZO = .326 moles/liter d = .01154 cm .0000 .130 .000 .0754 .0236 .000 .0000 .0287 .300 .070 .0000 .0544 .022 .0224 .0765 .212 .170 .0384 .006 .0544 .124 .170 .187 .0308 .008 .0598 .196 .090 .242 .0163 .005 .0774 .244 .065 .255 .0118 .006 .0815 .339 .045 .282 .0081 .001 .0901 .482 .030 .280 .0054 .004 .0896 .625 .020 .305 .0036 .002 .0974 .911 trace .310 trace .0990 1.485 .310 .0990 RUN l6 MHZO = .209 moles/liter d = .0118 cm .0000 .164 .000 .0675 .0290 .000 .0000 .0621 .303 .074 .0000 .0547 .018 .0235 .1100 .299 .116 .0540 .006 .0368 .1575 .209 .131 .0377 .017 .0416 .205 .190 .159 .0343 .017 .0505 .277 .155 .183 .0280 .010 .0582 .468 .107 .215 .0193 .009 .0684 .706 .055 .241 .0099 .010 .0766 1.286 .026 .256 .0047 .010 .0814 RUN 18 MHZO = .247 moles/liter d = .0125 cm .0000 .195 .000 .0672 .0326 .000 .0000 .0477 .285 .170 .0000 .0476 .0021 .0501 .0954 .231 .160 .0386 .0472 .1431 .180 .230 .0302 .0018 .0678 .191 .150 .235 .0251 .0053 .0694 .2865 .145 .245 .0243 .0032 .0723 .429 .090 .280 .0150 .0022 .0826 ~669 .060 .300 .0100 .0013 .0885 1-00 .050 .305 .0084 .0014 .0900 1'955 trace .315 trace .0930 36 TABLE 3 - Con't. A - A 0 Net Absorbance Concentration (Moles/Liter) Of E, sec 525 cm'1 465 cm—1 PhSiCl3 PhSiC12(OH) PhSiC1(OH)2 PhSigOH)3 IWN 19 MHZO = .149 moles/liter ’ pd = .01295 cm .0000 .037 .000 .0926 .0060 .000 .0000 .0238 .520 .045 .0000 .0841 .002 .0128 .0477 .500 .065 .0808 .0185 .0954 .470 .087 .0760 .0248 .143 .430 .100 .0695 .001 .0285 .2385 .420 .101 .0679 .002 .0288 .3815 .400 .130 .0646 .0371 .763 .400 .111 .0646 .0026 .0316 RUN 20 M820 = .190 moles/liter d = .01295 cm .000 .035 .000 .0868 .0056 .0000 .0447 .470 .080 .0000 .0760 .0228 .0894 .400 .115 .0646 .0328 .134 .360 .130 .0582 .0371 .2235 .320 .155 .0518 .0442 .358 .270 .170 .0437 .0002 .0485 MODELING OF PhSiCl3 HYDROLYSIS REACTIONS The following reactions were assumed to represent the hydrolysis of PhSiCl : 3 k PhSiC13 + H20 +1 PhSiC12(OH) + HCl (5a) k2 PhSiC12(OH) + H20 + PhSiCl(OH)2 + HCl (5b) k3 PhSiCl(0H)2 + H20 + PhSi(OH)3 + HCl (5c) Furthermore, it was assumed that these reactions were first order with respect to each reactant, second order“ overall and irreversible. The proposed rate equations and mass balances are: d(PhSiC13) Eff—— = -kl (Ph31C13) (H20) (6a) d(PhSiC12(OH) = -k2 (PhSiC12(OH)) (H20) + (6b) dt . k1 (PhSiClB) (H20) d(PhSiC1(OH)2) -k3 (PhSiC1(OH)2) (H20) + 3 (6C) dt k2 (PhSiC12(OH)) (H20) (PhSi(OH)3) = (PhSiC13)o + (PhSiC12(OH))o + (PhSiC1(OH)2)o + (PhSi(OH)3)O - (PhSiCl3) - (PhSiC12(OH)) - (PhSiCl(0H)2) (6d) (H20) = (H20)o - (PhSiC12(OH)) - 2(PhSiC1(OH)2) - 3(PhSi(OH)3) (6e) (HCl) = (H01)o + (H20)0 — (H20) (6f) The flow system of the experimental reactor consisted of a well‘mixed entrance region, a developing laminar flow region, a developed laminar region, and a small mixing zone at the outlet. In this system the greatest deviation 37 38 from plug flow is fully developed laminar flow. The laminar and plug flow regions represent the extremes in expected flow conditions. Therefore, the kinetic data were analyzed using both plug and laminar flow reactor models. The effect on the reaction velocity constants of the plug approximation when laminar flow exists has been evaluated by Kleinhenz and Hawley (1970) for reaction orders between 0 and 3. Their analysis employed an integration of the concentration-velocity product for each model over the flow cross | section. ELJ" = Zn IE UC rdr b 2 (7) HR Ub C It was concluded for a second order irreversible single species reaction that the plug flow model rate constant required to predict approximately the same concentrations as the laminar flow model was 15 percent lower than the laminar flow model rate constant (the laminar model rate constant being the true rate constant). Since the rate controlling step in this work was second order and irreversible the rate constants determined using the plug flow approximation would be expected to be within 15 percent of the actual values. It is expected that this error can be reduced by choosing the k's such that the data is bracketed when treated with both models. - The results of the plug and laminar flow models can be seen in Figures 5,6,7,8 and 9 for runs l3, l6, l8, l9 and 20, respectively. The solid lines represent the plug flow model, the hatched lines the laminar flow model, and the enclosed points are experimental data. The hatched lines and solid lines for PhSiCl3 and PhSiC1(0H)2 nearly corresponded to each other 39 and therefore, only a solid line was drawn to represent both models. The differences in the laminar and plug flow model concentrations shows up in the PhSiC12(OH) and PhSi(OH)3 species, primarily. Using the same rate constants, both models fit the data reasonable well. Considering the actual system as a combination of plug and laminar flow, it was expected that the two models would bracket the experimental data, as occurred in mos t cases . The analysis of the plug flow assumption by Kleinhenz and Hawley (1970) concluded that the reactant concentration of a laminar flow reactor would be higher than that of the equivalent plug flow, and that the product concentration would be lower. The numerical analysis of the PhSiCl3 hydrolysis reactions showed this same trend for each reaction species. While the intermediate chlorosilanols were being formed as the major reaction products their laminar flow model concentrations were less than the corresponding plug flow model concentrations. However, when these intermediates became the major reactants their laminar flow model concentrations became greater than the corresponding plug flow model concentrations. These trends were noted in the numerical analysis, but the concentration differences of the chlorosilanbls when they were major products were small as can be seen of Figures 5,6,7, 8 and 9. It was determined that both models fit the data reasonably well. In order to combine the two models the rate constants were chosen such that most of the data.was bracketed by the two models. The reaction velocity constants = 77.5, k = 1000.0, were determined and are as follows: k = 1500.0, k 3 1 2 liters/mole-seconds. RESULTS AND CONCLUSIONS It was demonstrated that infrared spectrophotmetry can be used to analyze the reaction species in the fast hydrolysis reaction of chlorosilanes. The hydrolysis reactions of individual chlorines on PhSiCl3 were followed at 0°C in solution with 1, 2-dimethoxyethane. It rvas observed that the first chlorine reacts nearly "instantaneously" at 0°C. It was shown that PhSiCl3 hydrolyzes to PhSi(OH)3 prior to significant condensation and chlorosilanol intermediates were observed in the reaction system and their concentrations were determined as a function of reactor length. It was determined that PhSiCl3 did not react with PhSi(OH)3 in l, 2-dimethoxyethane for reaction times less than 0.5 seconds at 0°C. This indicated that under these conditions, the hydrolysis reactions are considerably faster than the condensation reactions. The reactions of the three chlorine atoms of PhSiCl3 were found to be adequately described as first order with respect to each reactant, second order overall and irreversible. The problem of variations between plug and laminar flow was analyzed by calculating the differences in concentration of species for the plug flow and laminar flow models. The reaction velocity constants were determined to be as follows: k1 = 1500.0, k = 77.5, k 2 = 1000.0, liters/mole-seconds. 3 ACKNOWLEDGMENT The authors gratefully acknowledge the financial support of the Dow Corning Corporation. 40 NOMENCLATURE E (PhSiCl (PhSiCl base line absorbance absorbance bulk concentration concentration 3) 3)o IR cell path length rate constant length of reaction zone moles/liter reactor radius radius mean reaction time velocity bulk velocity frequency absorbance coefficient concentration of PhSiCl3 initial concentration of PhSiCl3 41 REFERENCES Allen, A. D., Charlton, J. C., Eaborn, C., and Modena, G., J. Chem. Soc., 3668, (1957). AUen, A. D., and Modena, C., J. Chem. Soc., 3671 (1957). mapperfield, J. R., and Prince, R. H., J. Chem. Soc., 3567, (1963). ltmley, M. C., Larson, W. D. and Bond, A. R., "Variable Length Reactor," Patent Applied for 1970. Ifleinhenz, T. A., and Hawley, M. C., Manuscript Submitted for Publication, 1970. Ihmnetsova, A. G., Andrianov, K. A., and Zhinken, D. Ya., Trans. Soviet Plastics, 4, 29 (1965). Prince, R. J., Trans. Faraday Soc.,_§4, (6), 838 (1958). Prince, R. J., J. Chem. Soc., 1783 (1959). Shaffer, L. H., and Flanigan, E. M., J. Phys. Chem., 61, 1591, (1957). Shaffer, L. H., and Flanigan, E. M., J. Phys. Chem., 61, 1595, (1957). Smith, A. L., Spectrochimica Acta, 12) 489 (1963). 2 Smith, A. L., Spectrochimica Acta, 23A, 1075 (1967). Tyler, L. J., J. Am. Chem. Soc., _1, 770 (1959). 42 PART II PLUG FLOW APPROXIMATION OF LAMINAR FLOW TUBULAR REACTOR Paper prepared for publication by T.A. Kleinhenz and M.C. Hawley Michigan State University Department of Chemical Engineering 1970 43 ABSTRACT PLUG FLOW APPROXIMATION OF LAMINAR FLOW TUBULAR REACTOR T. A. Kleinhenz and M. C. Hawley Department of Chemical Engineering Michigan State University East Lansing, Michigan An analysis was made of the application of a plug flow reactor model under the conditions of: laminar flow, uniform temperature distribution, and negligible radial diffusion. The steady state bulk concentrations predicted by plug and laminar flow models were compared at the same bulk residence times. Numerical solutions are presented for reaction orders between zero and three for single species reactions. The correction factor associated with the assumption of plug flow approaches an asymptotic limit for reaction orders greater than one. For reaction of order one or less the correction factor increases without limit as the conversion increases. It is concluded that reaction velocity constants can be determined from data obtained in a laminar flow reactor by applying a correction for the plug flow assumption. 44 LIST OF TABLES Igggg REACTIONS INVESTIGATED 49 EFFECT OF EQUILIBRIUM ON MAXIMUM DEVIATION OF THE CONCENTRATION RATIO: FIRST ORDER REVERSIBLE REACTION 56 RATE CONSTANT RATIO FOR IRREVERSIBLE REACTIONS 61 45 LI ST OF FIGURES Effect of reaction order on ratio of plug to laminar bulk concentration for irreversible reactions Effect of equilibrium constant on ratio of plug to laminar bulk concentration for first order reaction Comparison of plug and laminar models for zero order irreversible reaction Comparison of plug and laminar models for first order irreversible reaction Comparison of plug and laminar models for second order irreversible reaction 46 54 59 60 61 DEVELOPMENT OF PROBLEM The investigation of fast (half life between one second and one milli-second) reaction kinetics usually results in the abandonment of batch reaction techniques. The use of a flow reactor system is a convenient method of converting the time variable into a length variable. The ideal plug flow reactor would be one in which an initially homogeneous reaction mixture moves through a tubular reactor with a flat velocity profile. At a given cross section of an ideal flow reactor, every element would have a residence time equal to the ratio of the length of the reaction zone and the bulk velocity (mean time). I = L/Ub (1) The closest approximation to the plug flow case is the attainment of turbulent flow. Although the velocity profile is a weak function of radial position, the point velocity fluctuations provide enough radial mixing to validate the plug flow assumption. However, in many cases it is not feasible to build a small scale reactor for fast reaction studies in which plug (turbulent) flow can be attained. If the experiment is performed in the laminar flow region, the effect of the velocity profile must be considered. The well known parabolic velocity distribution is 2 V U = ZUb (1 - (r/R) ) (2) Each element in any cross section will have a residence time set by the ratio of the length and the point velocity. t . L/U (3) 47 48 Numerically, the velocity distribution can be considered as a weighting factor in the integration of the point concentration over the reactor cross section. ' R r r 2w f C(L,-~, U )U(— , U ) rdr b n Ub R2 Equation (4) is identical to the result that would have been Obtained uSing the concept of an exit age distribution. The above tdefinition of the bulk concentration represents the concentration that would be measured if the tubular reactor were cut across its cross section and the effluent instantly analyzed. In the case of a flat velocity profile, the bulk concentration becomes dependent upon a uniform residence time (i.e. it becomes the plug flow model). In order to determine the bulk concentration it is necessary to integrate the concentration-velocity product over the reactor cross section. In the case of a complicated rate expression, the rate can be integrated (numerically) simultaneously with Equation (4). The relationship between the bulk concentration in laminar flow given by Equation (4) and the equivalent plug flow model concentration has been investigated for several reactions. Constant physical properties were assumed. The reactions investigated are summarized in Table 1. Analysis of an irreversible ugh-order reaction yields a n-l dimensionless reaction parameter of I k Co . Each reversible reaction has to be analyzed for its appropriate dimensionless parameters. 49 TABLE 1. REACTIONS INVESTIGATED Dimensionless Order Rate Concentration Reaction Parameter ' a I— = - - 0 C k C Co(1 kt/Co) kt/Co 1/2 0' = -kCl/2 0 = 00(1 - kt/ZCol/2)2 kE/col/2 1 0' = -kC 0 = 00 exp(-kt) RE k'+k exp(-t(k+k') ) - v ___ _ v _ _.___ v o l C kC+k (Co C) C Co k+k' (k+k )t, and k/k 3/2 C' = -kC3/2 C = Co/(l + .SktCol/Z)2 kao I 8 — = 2 C. kc C Co/(l + ktCo) ktco 3 0' = -kC3 C = 00/(1 + 2ktC02)l/2 k‘t'co2 METHOD OF ANALYSIS The analytical solution to Equation (4), when possible, requires an integrated rate expression and the results are Often cumbersome for further use. Thus, a numerical approach was employed because it allowed a general solution to Equation (4) applicable to any single reaction rate expression (integrated or differential). The numerical solutions were Obtained through the use of a short Fortran program. The trapizoidal rule was used to integrate the concentration- velocity product over the circular cross section. The product was evaluated at the midpoint of each interval in order to remove the zero point at the center line and, in the case of irreversible reactions, at the wall. The Fortran program used is presented in Appendix I. The program consists of three READ statements that supply initial conditiOns-and physical data. The rate equation (i.e. integrated or differential) can be supplied. An outer DO loop steps the reactor length, and an inner DO loop performs the evaluation of the point velocity-concentration product along with the integration of Equation (4). After the completion of each cross sectional integration, the equivalent plug flow concentration is computed using the bulk residence time. The laminar and plug flow model bolk concentrations are-printed along with the ratio of the laminar and plug flow model concentrations and the dimensionless reaction parameter. The program is flexible enough to integrate any reaction rate expression if the proper rate expression is supplied. The rate can be supplied in either integral or differential form (FUNCTION .FUN 1 or FUN 3). The variable ITYPE defines the form of the supplied rate. An ITYPE of 0 indicates an integrated rate while 1 indicates a differential rate. The use of the program 50 51 is illustrated with a first order single irreversible reaction. Illustrative Example: First Order Irreversible Reaction In this case the reaction rate is given by Table 1. The point residence time and resulting concentration at any radius and length are derived from Equations (2) and (3) as t = L/2U (HI->2) (5) b R C = C0 exp(-.5fk/(l -(§)2) (6) It can be seen from Equation (6) that kf is the appropriate dimensionless reaction parameter for this case and a similar analysis for other reactions yields dimensionless parameters as given in Table l. Inserting Equations (2), (5) and (6) into Equation (4) yields: Cb 3 4CD I: (l—zz)z exp(-.5kf/(l-zz))dz (7) where z =-% (8) The above integral can be determined either numerically or analytically. The analytical solution is given and it can be compared with the Fortran results Of Figures 1 and 4. Making the proper substitutions, Equation (7) becomes: = — 2 w_ exp (-u2 Cb .5C0(kt) IKE. 3 du (9) 2 Evaluating the integral, Cb - .50o (RE)2 [(exP(‘;5kt)(2 ' kt) - .5 Ei(— 1%)] (10) (kt) The function Ei(-x) is known as the Exponential Integral and is commonly tabulated. 'I'_"’ ' ‘ 52 For the case of kf = 2.0, Cb/Co = 0.21938 when calculated from Equation (10). The numerical solution of Appendix I yielded a value of 0.2194. DISCUSSION OF RESULTS Irreversible Reactions The results of the irreversible reactions investigation are summarized on Figure l as a set of curves depicting the ratio of the laminar to plug flow bulk concentration versus the appropriate dimensionless reaction parameter of Table l. The concentration ratio (a measure of the deviation of the plug flow model) depends largely upon the reaction order and the degree of conversion. The laminar flow model concentration is always greater than the corresponding plug flow model concentration. This trend increases with the conversion and approaches an asymptotic limit for reaction orders greater than one. The concentration ratio approaches 0.63, 0.79 and 0.89 for the three-halves, second, and third order reactions, respectively. For orders of one or less, the ratio goes to zero due to the concentration reaching zero in the plug flow model before that of the laminar mOdel. Reversible Reaction The conCentration ratio of plug to laminar flow is plotted versus the appropriate dimensionless reaction parameter of Table l for a first order reversible reaction (see Figure 2). In the reversible case the concentration ratio is also a function of the equilibrium constant. The results are presented as a single curve for each equilibrium constant. Cb (Plug Flow) I Cb ( Laminar Flow) '01 #- n=0 Figure 1. 53 n: 1/2 Effect of reaction order on ratio of plug to laminar bulk concentration for irreversible reactions. Cb(PIUg Flow)/Cb ( Laminar Flow) 54 * k=1.25 k=2.5 k=5 k=lO k20 Figure 2. f14 60 (Io/Cb 4 _ Plug Model Laminar Model ka' Figure 5. Comparison of plug and laminar models for second order irreversible reaction. 61 TABLE 3. RATE CONSTANT RATIO FOR IRREVERSIBLE REACTIONS Zero Order First Order Second Order 0/00 Kp/Kl Kp/Kl E/Kl 1.0 1.0 1.0 1.0 .9 .98 .96 .92 .8 .95 .91 .88 .7 .92 .88 .85 .6 .89 .85 .82 .5 .86 .83 .81 .4 .82 .81 .80 .3 .78 .78 .78 .2 .73 .74 .77 .l .66 .72 .76 Avg. .86 .85 .85 62 It is interesting to note that the greatest correction required for the plug flow model rate constant of the reactions presented in Table 3 is 1.515 (i.e. K - 1.515 KP, for zero order reaction at 90 per cent conversion). L However, a better overall estimate of the average correction is given by the average of the ratio of the laminar to plug flow rate constants which are 1.163, 1.176 and 1.176 per cent for the zero, first and second order reactions, respectively. It appears that the reaction velocity constants determined using a plug flow model in the case of laminar flow are reasonably good estimates of the actual constants. In addition, the plug flow model approximation becomes better with increasing reaction reversibility (see Figure 2). These constants are easily corrected to account for laminar flow by the method presented in this paper. This procedure can be extended to more complex reaction schemes. Therefore, meaningful kinetic studies of fast reactions can be carried out in a laminar flow tubular reactor. Acknowledgment This work was supported by the Dow Corning Corporation. ll. .‘ APPENDIX I FORTRAN PROGRAM FOR DETERMINING BULK CONCENTRATION IN FLOW REACTORS REAL KI9K8 DIMENSION HEAD(100) COMMON OEL ’ROGRAM TO DETERMINE BULK CONCENTRATION IN TUBULAR REACTOR WITH LAMINAR FLOW IN = d 10 = 3 READ(IN999) (HEAD(L)9L=I916) REAU(IN9100) ITYPE9LONO9NSTEP9DR9DEL REAU(IN9I0I) CO9KI9K29UB9UMAX9Z9DZ WRITE(IO999) (HEAD(L)9L=I9Ib) WRITEIIO9102) 00 2 L=I9LONG Z = Z * OZ TRAPEZOIUAL RULE INTEGRATION. EVALUATIONS AT INTERVAL MIUPOINTSo S = 0.0 T0 = 000 CL = C0 00 I N=I9NSTEP RN 3 N U = UMAX“(I.’(UR*(RN‘.S))*“20) T = l/U IF(ITYPE) 39394 3 fl.= FUNI(KI9K29T9CO) 00 T0 8 ‘9CL = FUNZIKI9K29T9TO9CO9CL) BIG 3 T IS = S + CL*U*(HN'65T CLB = C0”2.*S*OR*DH/UB TB 3 Z/UB IF(ITYPE) 59596 U3: CO*FUNI(KI9K29TB9COT 00 T0 7 CP = CO*FUN2(KI9K29TB90609CO9CO) A = KI*Z/UB K = K2 IF(K) 999910 98 = 10.**106 60 T0 11 l0 8 = Kl/KZ llRATIO = CP/CLB 2 WUTE(IO9103) CLB9CP9RATI09A9B 99F0RMAT(16A5) 00F0RMAT(3IS94F1060T 01FORMAT(8FI0.0) 00F0RMATIIH0910X9I3HC LAMINAR 95X9 7HC PLUG 98X918HC PLUG/C LAMIN TAR 92X96HK TBAR9IZX95HKI/KE) U3FORMAT( 2X95E1364) CALL EXIT END U1 NO‘ 63 l— -- raw—~— P.‘ 64 FUNCTION rONl(K19K39T9CO) REAL K19Kd INTEROHATEO RATE EOUATION. FUNI = EXP(-K1*T) IFTFUNI) 19192 FONl = 0.0 RETURN END FUNCTION FON2(K1.62.I.IO.CO.CONC) REAL K19Kd COMMON DEL FIRST ORDER HONOR-KOITA INTEUNATION TECNNIQUL. C = CONC IJT = T-TO DS = OT/OtL NS = US IF(NS) 29(93 NS = 1 OT = T-TO GO TO 4 DS = NS DT = UT/US IN) I I=I9NS AN = UT*FUN3(K19K29COQC) EN = OT*FON3(KI9K29C0.C+.3*AN) CN = DT*FON3(KT9K29CO.C+.S*HN) ON = UT*FUN3(K19Kd9CU9C+CN) C = C +(AN+Zo*dN+d.*CN+DN)/0.0 CONTINUE FUNE = C RETURN EZTJL) FUNCTION TON3(K19NZ~C09C) REAL KI9Kd DIFFERENTIAL RATE tOOATION. FUNJ = -K1*C RETURN END 65 Cs?fifléfifiéfifl’fifififififififiGfififififiififibfl§§ ifGi’d’fi§§§§§§§§§§§§§§§§§§§§§§§§*fl'fififiififififififi HEAD REPRESENTS AN ¢A¢ FIELD HEADING IDENTIFYING THE PROBLEM IN = INPUT TAPE NUMBER IO = OUTPUT TAPE NUMBER ITYPE= I DIFFERENTIAL RATE EQUATION. ITYPE= 0 INTEGRATED RATE EQUATION. DEL= TIME INCRIMENT FOR RUNGE'KUTTA INTEGRATION = INITIAL CONCENTRATION IN LAMINAR MODEL 3 AXIAL LENGTH = AXIAL INCRIMENT = POINT VELOCITY = BULK VELOCITY = FRACTION OF RADIUS PER STEP = FORWARD REACTION VELOCITY CONSTANT = REVERSE REACTION VELOCITY CONSTANT CL = POINT CONCENTRATION IN LAMINAR MODEL = Z/U POINT RESIDENCE TIME = Z/UB MEAN RESIDENCE TIME = INTEGRATION SUM = BULK CONCENTRATION IN LAMINAR MODEL = BULD CONCENTRATION IN PLUG MODEL = REACTION PARAMETER = NUMBER OF AXIAL STEPS NSTEP= NUMBER OF RADIAL STEPS o9a§§§§§§§§9§§§«*9§9§§§**9§9§§999§9§§¢§§§§§§§§§9§9§§§§§99¢§§§§§§#§§§§§9 ##tfittttfiflttttttfittttfit C C C C C C C C C C C C DR C C C C C C C C C C C C I-QI' ' NOTATION concentration initial concentration bulk concentration first time derivative of concentration forward rate constant reverse rate constant k/k' equilibrium constant plug flow rate constant laminar flow rate constant point radius tube radius mean time time velocity bulk velocity r/R dimensionless radius 66 LITERATURE CITED L. T. Fan and R. C. Bailie, Chem. Eng. Sci., lg, 63 (1960). D. M. Himmelblau and K. B. Bishcoff, Process Analysis and Simulation, Chapter 5, Wiley, New York, 1968. 0. Levenspiel, Chemical Reaction Engineering, Chapter 9, Wiley, rr‘_ New York, 1962. L. S. Merrill, Jr. and C. E. Hamrin, Jr., A.I.Ch.E. Journal, $6, 194 (1970). G. I. Taylor, Proc. Roy. Soc., A219, 186 (1953). l- C. G. Wan and E. N. Ziegler, Chem. EngggSci., 22, 723 (1970). 67 EXPERIMENTAL PROCEDURES Experimental Preparation Prior to the start of the preparation for the hydrolysis experiment sufficient time should be spent determining the proper flow rates and storage tank concentrations. The first step in preparing for experiment is a check on the condition r—- ~ of the following: the Perkin—Elmer spectrophotometer, the reactor and all connections, all reactant lines, rotometers, storage tanks, the KRS-S infrared windows and the reference infrared windows. If the general appearance and operating condition of the reactor system is satisfactory, bleed off any I ."1.i"'-Z__ x storage tank pressure and evacuate both tanks. Draw a sufficient amount of acetone into both tanks to allow a thorough washing of the tanks and reactor lines. Pressure both tanks with dry nitrogen and wash the acetone through the rotometers, lines, and through the reactor into a.waste container. The washing process should be repeated until the acetone flowing into the waste container is clear. Using recently distilled solvent, silane, and water carefully weigh the solvent for both reactants into suitable containers (polyethylene or polypropylene). The silane and water should be weighed using an analytic balance. Each reactant should be thoroughly mixed with its solvent before proceeding. Fill the cooling bath with tap water and add enough dry ice to create an ice-water equilibrium. Discharge any remaining acetone from the storage tanks and purge the tanks with dry nitrogen. Evacuate the storage tanks and draw the reactant-solvent mixtures into the proper tanks. 68 69 Withdraw the hypodermic needle from the reactor replacing it with a plug and pressurize the storage tanks. Purge both reactant lines. The approximate purge times can be estimated from the volume of each reactant line and its flow rate. Nitrogen bubbles must be purged from both lines. The silane-solvent mixture can be followed with the infrared spectrophotometer until a homogeneous mixture is observed. Start the nitrogen purge to the spectrOphotometer and the sample chamber (the sample chamber should be enclosed using Saran Wrap). Check the condition of the icedwater mixture and start the coolant circulation pump. 70 Reactor Data Collection Obtain a silane reference spectrum after the reactor has been cooled to the proper temperature. Remove the plug from the hypodermic inlet and connect the hypodermic needle to the reactor. A reference length should be obtained by inserting the hypodermic needle until it is flush against the reactor outlet. Withdraw the hypodermic needle to the first reactor length and set the predetermined reactant flow rates. Record the reactor length and flow rates in the lab notebook and corresponding identification on the infrared spectrum. After obtaining stable flow rates, start the infrared spectrophotometer. The slow scan is best for quantitative results. The above steps can be repeated as desired. At the end of the experiment, discharge any remaining reactants and bleed off the nitrogen pressure. Evacuate the storage tanks and draw a sufficient amount of acetone into each tank to remove traces of each reactant. Pressure both tanks and wash out the reactor system. Turn off the spectrophotometer and remove the sample and reference infrared cell windows. Drain the cooling fluid and leave the storage tanks under slight nitrogen pressure. Hydrolysis Reactor Trouble Shooting Problem: Coolant pump looses suction. Action: Turn pump off and blow back through the pump outlet. Loss of suction may be due to CO2 bubbles or ice in the pump intake. 71 Problem: Inability to maintain set flow rate. Action: Check appropriate valve positions. If the valves are all right, close the tank outlet valve and remove the rotometer needle valve. Check it for dirt in the orifice. If the orifice is not dirty, check the KRS—S cell for accumulated dirt. Problem: Inability to realize desired flow rate. Action: Remove and check the position of the orifice valve in the rotometer needle valve. It may be positioned too far forward. Problem: Low IR spectrum base line. Action: Check the nitrogen purge on the KRS-S windows. Water vapor may be condensing on the cold IR cell windows. Safety All distillation should be carried out in a well ventilated area. In the case of 1, 2-dimethoxyethane,KOH pellets should be added before distilling and the distillation should not be allowed to proceed to dryness. A11 distillations made under dry nitrogen pressure should have a Hg trap with the pressure not more than a few mm of Hg. Care should be taken after the completion of a distillation to avoid creating a strong vacuum in the apparatus. The necessary dry nitrogen pressure on the reactor system should be less .than 15 psig. A higher required pressure would indicate a restriction of the flow system. 'Ihe KRS-S infraredgwindows are toxic. Care must be taken to avoid unnecessary contact and to wash with soap and water after handling. Also, try to avoid breathing I, 2-dimethoxyethane vapors. FORTRAN PROGRAMS AND DOCUMENTATIONS Numerical Solution for Plug Flow Reactor The three coupled second order rate equations describing the PhSiCl3 hydrolysis reactions were evaluated numerically using the FORTRAN program listed in Appendix A. The program employs a Runge-Kutta integration technique to solve the differential rate and mass balance equations representing the hydrolysis reactions. The program consists of a main program that sets the initial conditions and two subroutines that supply the differential rate and mass 'balance equations and contain the Runge-Kutta integration scheme. The main program reads the initial conditions, prints an identification of the problem, and enters a DO loop which calls an integration scheme and prints the numerical solutions and corresponding reactions times. subroutine RUNGE contains the integration sCheme and subroutine EQN contains the appropriate differential rate and mass balance equations. Example Result for Plunglow Reactor The FORTRAN program presented in Appendix A is set up to model a plug flow reactor with three coupled second order irreversible reactions. The accompanying data cards contain the initial conditions of run 13 (see Table 3, Part II) and program controls in the following order: card 1, initial concentration (moles/liter) of PhSiCl PhSiC12(OH), PhSiCl(OH)2, PhSi(OH)3, 3, H20 and HCl; card 2, forward and reverse rate constants for the first, second and third chlorine atoms, respectively; card 3, time increment for the integration scheme and the number of integration steps requested; card 4, number of integration steps requested between printout of reactant 72 73 concentrations and corresponding times; cards 5 through 16, identification of problem. An example of the above FORTRAN program, initial conditions, and output is presented in Appendix B. The results are presented as reactant concentrations and corresponding reaction times. The program.with appropriate input is in Appendix A. 74 Numerical Solution for Laminar Flow Reactor The laminar flow reactor numerical analysis was made using the FORTRAN program listed in Appendix C. The program was intended to model a reactor with fully developed laminar flow and negligible diffusion. The main features of the program are the following: a determination of the residence time at a point on the flow cross-section and a Runge-Kutta integration of the appropriate rate equations up to the point residence time; and, the simultaneous Trapezoidal Rule integration of the concentration- velocity product over the flow cross section. The above program is very similar to the plug flow model. The main program reads the problem's initial conditions, prints an identification of the problem, and enters a DO loop which increments the reactor length and results in the following: the point residence time and the rate equations are integrated up to that time and the results are incorporated into a.Trapezoidal Rule integration of the concentration-velocity product over the flow cross section. The above procedure was repeated at set radial increments. Example Result for Laminar Flow Reactor The FORTRAN program presented in Appendix C is set up to model a laminar flow reactor with three coupled second order irreversible reactions. The accompanying data cards contain the initial conditions of run 13 (see Table 3, Part II) and program controls in the following order: card 1, initial concentration (moles/liter) of PhSiCl PhSiC12(OH), PhSiCl(0H)2, 39 PhSi(OH)3, H20 and HCl; card 2, forward and reverse rate constants for the first, second and third chlorine atoms, respectively; card 3, number of problem identification cards; card 4, problem identification; card 5, flow 75 rate (cc/min) of reactant 1, flow rate of reactant 2, reactor radius (cm), initial reactor length (cm), reactor length increment (cm), integration time increment (seconds), dimensionless reactor radial increment, number of axial increments, and number of radial increments. An example of the above FORTRAN program and initial conditions is presented in Appendix D. The results are presented as the plug flow model concentrations, the laminar flow model concentrations, and the plug and laminar flow model concentration ratio for the hydrolysis reaction species. The corresponding mean reaction times and reactor lengths are printed with the above concentrations and concentration ratios. Application of Programs to Different Types of Reactions It should be noted that the Fortran programs of Appendices A and C may be adapted to any reaction scheme involving reversible and irreversible reactions. The rate and mass balance equations of subroutine EQN can be replaced by any desired reaction scheme by inserting the proper differential equations for variables AN, BN, CN, DN, YN, and ZA (representing PhSiCl3, PhSiC12(OH), PhSiCl(OH)2, PhSi(OH) H20 and HCl, respectively). 3’ ‘5 CU ._ t (I. RESULTS AND CONCLUSIONS It was demonstrated that infrared spectrophotometry can be used to analyze the reaction species in the fast hydrolysis reactions of chlorosilanes. The hydrolysis reactions of individual chlorines of PhSiCl3 were followed at 0°C in solution with l, 2-dimethxyethane. It was observed that the first chlorine reacts nearly "instantaneously" at 0°C. It was shown that PhSiCl hydrolyzes to PhSi(OH)3 prior to condensation and 3 chlorosilanol intermediates were observed in the reaction system and their concentrations were determined as a function of reactor length. It was determined that PhSiCl3 did not react with PhSi(OH)3 in l, 2-dimethoxyethane fbr reactions times less than 0.5 seconds at 0°C. This indicated that under these conditions, the hydrolysis reactions are considerably faster than the condensation reactions. The reactions of the three chlorine atoms of PhSiCl3 were found to be adequately described as first order with respect to each reactant, second order overall, and irreversible. The problem of variations between plug and laminar flOW‘WaS analyzed by calculating the differences in concentration of species for the plug and laminar flow models. The reaction velocity OCISJ>U’. APPENDIX B Example Result of PhSiCl Hydrolysis Model 3 82 SIMULATIO A + Y 8 8 + Z 8 + Y a C + Z C + Y = 0 + Z A = PHSICL3 (HOLES/LITER1 B = PHSICL2(0H) C = PHSICL(0H)2 D = PHSI‘OH13 Y = H20 Z = HCL T = SECONDS K1 = 1500.0000 K2 = 0.0000 K3 = 77.5000 K4 = 0.0000 K5 = 1000.0000 K6 '3 000000 T A 8 0.0000 0.0753 0.0236 0.0050 0.0093 0.0826 0.0100 0.0015 0.0826 0.0150 0.0002 0.0769 0.0200 0.0000 0.0711 0.0250 0.0000 0.0659 0.0300 0.0000 0.0613 0.0350 0.0000 0.0572 0.0400 0.0000 0.0536 0.0450 0.0000 0.0503 0.0500 0.0000 0.0473 0.0550 0.0000 0.0446 0.0600 0.0000 0.0422 0.0650 0.0000 0.0399 0.0700 0.0000 0.0379 0.0750 0.0000 0.0360 0.0800 0.0000 0.0342 0.0850 0.0000 0.0326 0.0900 0.0000 0.0311 0.0950 0.0000 0.0297 0.1000 0.0000 0.0284 0.1050 0.0000 0.0272 0.1100 0.0000 0.0261 0.1150 0.0000 0.0250 0.1200 0.0000 0.0240 0.1250 0.0000 0.0230 0.1300 0.0000 0.0221 0.1350 0.0000 0.0213 0.1400 0.0000 0.0205 0.1450 0.0000 0.0197 0.1500 0.0000 0.0190 83 C 0.0000 0.0040 0.0057 0.0060 0.0058 0.0054 0.0051 0.0048 0.0044 0.0042 0.0039 0.0037 0.0035 0.0033 0.0031 0.0030 0.0028 0.0027 0.0026 0.0025 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.0018 0.0017 0.0017 0.0016 0.0016 (LITER/MOLE-SECONDS) 0 0.0000 0.0028 0.0089 0.0156 0.0218 0.0274 0.0324 0.0368 0.0407 0.0443 _ 0.0475 0.0504 0.0531 0.0555 0.0577 0.0598 0.0617 0.0634 0.0651 0.0666 0.0680 0.0693 0.0705 0.0717 0.0728 0.0738 0.0748 0.0757 0.0766 0.0774 0.0782 Y 0.3280 0.2521 0.2305 0.2157 0.2032 0.1923 0.1827 0.1742 0.1666 0.1597 0.1536 0.1480 0.1429 0.1382 0.1339 0.1300 0.1263 0.1230 0.1198 0.1169 0.1142 0.1117 0.1093 0.1070 0.1049 0.1030 0.1011 0.0993 0.0977 0.0961 0.0946 2 0.0236 0.0994 0.1210 0.1358 0.1483 0.1592 0.1688 0.1773 0.1849 0.1918 0.1979 0.2035 0.2086 0.2133 0.2176 0.2215 0.2252 0.2285 0.2317 0.2346 0.2373 0.2398 0.2422 0.2445 0.2466 0.2485 0.2504 0.2522 0.2538 0.2554 0.2569 APPENDIX C Fortran Model of Plug and Laminar Flow Reactor with PhSiCl3 Hydrolysis Reactions 84 \I\I\I\I\I\I\l\. ()()t)£)\2\1\1\; 85 REAL K19K29K39K49K59h6 DIMENSION HEAD(50920) COMMON AO9BO9CO9DO9YOoZO9KI9K29KJ9K49K59K69DT9AN9BN9CN9DN9YN9ZN9DE 1LT IN READ TAPE NUMBER IO WRITE TAPE NUMbER X INITIAL REACTOR LENGTH DX REACTOR AXIAL INCRIMENT DT INTEORATION TIME INCRIMENT DELR RADIAL INCRIMENT NSTEP NOMUER OF RADIAL STEPS LONG NUMBER OF AXIAL INCRIMENTS NSTEP NUMBER OF RADIAL INCRIMENTS QB FLOW RATE OF REACTANT TWO QA FLOW RATE OF REACTANT ONE U POINT VELOCITY OB BULK VELOCITY SX INTEGRATION SUM FOR COMPONENT X XL LAMINAR MODEL CONCENTRATION OF COMPONENT X T POINT RESIDENCE TIME XP PLUG FLOW MODEL CONCENTRATION OF COMPONENT X XR RATIO OF PLUG FLOW MODEL TO LAMINAR FLOW MODEL CONCENTRATION X TAV MEAN RESIDENCE TIME HEAD AN A FIELD FOR PROBLEM IDENTIFICATION NC NUMBER OF CARDS CONTAINED IN HEAD KX RATE CONSTANT X XO INITIAL CONCENTRATION OF COMPONENT X REAOIIN999) AO9BO9CO9DD9YO9ZO 99 FORMATI8F10.2) READIIN999) K19K29K39K49KS9K6 REAUIIN9100) NC 100 FORMAT(1615) DO 3 I=19NC REAUIIN9101) (HEADII9K)9K=I916) WRITEIIO9101) (HEAD(I9K)9K=1916) 3 CONTINUE 101 FORMATIIéAS) WRITEIIO9102) K19K29K39K49K59K6 102 FORMATI10X9SHK1 3 9F15.495X920H(LITER/MOLE’SECONDS)9/910X95HK2 = 9 1F15.49/910X95HK3 = 9F15.49/910X95HK4 = 9F15.49/910X95HKS 3 9F15.49 2/910X95HK6 = 9F15.4) READ(IN9103) 0A9QB9R9X9OX9DT9DELR9LONG9NSTEP 103 F0RMATI7F10.09&IS) AREA = 3.14*R*R Q=QA+QB OB = Q/(60.*AREA) UMAX = 2.*UB WRITEIIO9104) QA9QB9Q 104 FORMAT(10X929HREACTANT 1 FLOW RATE (CC/MIN)9F10.49/910X929HREACTAN 1T 2 FLOW RATE (CC/MIN)9F10.49/910X924HTOTAL FLOW RATE (CC/MIN19F15 2.4) WRITE(IO9105) 105 FORMAT(29X93X91HA 9 8X91HB 9 8X91HC 9 8X9IHD 9 8X91HY 9 8X91HZ ) WRITEIIO9110) AO9BO9CO9DO9YO9ZO 110 F0RMATI10X916HINITIAL CONC 96F9.4) 86 DO d L=I9LONb X = X + DX SA = 0.0 58 = 0.0 SC = U00 SD = 0.0 SY = 0.0 $2 = 0.0 T0 = 0.0 AL = A0 BL = bO CL = CO DL = DO YL = YO ZL = [O ' DO 1 N=19NSTEP RN = N U = UMAX*(1.-(DELR*(RN-.S))**2.) T = X/O ' CALL CONC(T9TO9AL9HL9CL9DL9YL9ZL1 T0 = I SA = SA + AL*O*(RN-.S) $8 = Sb + BL*U*(RN-.S) SC 3 SC + CL*O*TRN-.S) SD = SD + DL*U*(RN-.5) SYy= SY + YL*U*(RN-.S) $2 = SZ * £L*U*(RN-.5) 1 CONTINUE AL = SA*2.*UELR*DELR/UD BL = SU“2.*0ELH*DELR/uu CL = SC*2.*DELR*DELR/UH DL = SD*Z.*DELR*DELk/Ud YL = SY*2.“DELR*DELR/Ud ZL = SZ*2.*DELR*UELR/UH AP = A0 BP = HO CP = CU OP = DO YP = YO ZP = [O TAV = X/UB CALL CONCITAV9O.09AP9DP9CP9UP9YP9ZP) AR = AP/AL HR = BP/BL CR = CP/CL OR = DP/OL YR = YP/YL ZR = ZPIZL WRITEIIO910b) TAV9X 106 FORMATI1H09 9X924HMEAN REACTION TIME (SEC)9F10.497X919HREACT0R LEN IGTH (CM)9F10.4) HRITEIIO9107) AP9BP9CP9DP9YP9LP 107 FORMATI10X916HC PLUG FLOW 9bf9.4) WRITEIID9108) AL9BL9CL9DL9YL9LL 103 FORMAT(10quoHC LAMINAR FLOW 9hF9.4) WRITEIIO9109) AR98R9CR9DR9YR9LR 109 FORMATIIOX916HC PLUG/C LAMINAR96F9.4) 2 CONTINUE END ‘ U 87 SUHROUTINE CONCIT9TO9A9B9C9D9Y9I) REAL K19K59K39K49K59K6 COMMON AO9BO9CO9DO9YO9ZO9K19K29K39K49K59A69DT9AN9UN9CN9DN9YN9ZN9DE 1LT DELT = T - TO DS = DELT/OT NS = US IF(NS) £9293 NS = I DELT = T-TO GO TO 4 DELT = DELT/OS DO I I=I9NS CALL RONGEIA9B9C9D9Y9Z) CONIINUE RETURN END SUBHOUTINE RUNOETA9B9C9D9Y9Z) REAL K19K29K39K49K59Kb - COMMON AO9BO9CO9DO9YO9ZO9K19K29KJ9K49K59K69DT9AN9BN9CN9ON9YN9ZN9DE 1LT CALL EON(A9B9C9O9Y9Z) A1 = AN 81 = BN C1 = CN 01 = 0N Y1 = YN Z1 = ZN CALL EQN(A+AN/2.98+BN/2..C+CN/2..D+DN/2.9Y+YN/2.9Z+ZN/2.) A2 = AN 82 = BN C2 = CN 02 = DN Y2 = YN 22 = ZN CALL EQNIA+AN/2.9U+BN/2.9C+CN/2.oD+DN/2.9Y+YN/2.oZ+ZN/2.) A3 = AN 83 = 8N C3 = CN 03 = ON Y3 = YN 23 = 2N CALL EQN(A+AN.B9BN9C+CN.D+0N.Y+YN.Z9ZN) A = A + (A1+2.*A2*2.“A3+AN)/6.0 B = B + (81+2.*BZ*2.*83+BN)/6.0 C = C + (Cl+2.*C2+2.*C3+CN)/6.0 D = A0 + 80 . C0 + 00 - (A + B + C) Y = Y + (Y192.*Y2+2.*Y3+YN)/6.0 Z = [0 + Y0 -Y RETURN END 88 SUHHUUTINE EUNIA9B9C9D9Y9Z) REAL K19K89K39K49K59fib COMMON AU9HD9CU9DU9Y091O9K19hd9KJ9K49K59K69DT9AN9BN9CN9DN9YN9ZN9DE 1LT AN = (-K1*A*Y)*OELT HN = (-K3*B*Y+K1*A*Y)*OELT CN = (-Kb*C*Y*K3*b*Y)*OELT [N0 = -(AN+BN+CN) YN = -Y*(K1*A+K3*B+KS*C)*DELT [N = -YN RETURN END .0236 .0 .0 .328 .0236 .0 77.5 .0 1000. .0 SIMULATION OF LAMINAR FLON TUBULAR REACTOR PHSICLJ HYUROLYSIS REACTIONS A 9 Y = B + Z PHSICL3 (MOLES/LITER) PHSICLEIOH) PHSICL(OH)2 PHSIIOH)3 H20 HCL 13 6.0 .108 .0 .10 .0005 lllllIllllll+§ N-(COIDOI I. C 2 .02 50 APPENDIX D Example Result of Plug and Laminar Flow Reactors with PhSiCl3 Hydrolysis Reactions 89 90 SIMULATION OF LAMINAR FLOH TUBULAR REACTOR PHSICL3 HYDROLYSIS REACTIONS A + Y = B + 2 B + Y = C + Z C + Y = D + z A = PHSICL3 (HOLES/LITER) B = PHSICL2(0H) C = PHSICLIOHTZ D = PHSI(0H)3 Y = H20 Z = HCL RUN 13 K1 = 1500.0000 K2 8 0.0000 K4 = 000000 KS 8 1000.0000 K6 3 000000 REACTANT 1 FLOH RATE (CC/MIN) REACTANT 2 FLOH RATE (CC/MIN) TO IN ME ME ME ME TAL FLOH RATE (CC/MIN) A ITIAL CONC 0.0753 AN REACTION TIME (SEC) PLUG FLON 0.0112 LAMINAR~FLOH 0.0135 PLUG/c LAMINAR 0.6079 AN REACTION TIME (SEC) PLUG FLOH 0.0018 LAMINAR FLOH 0.0053 PLUG/c LAMINAR 0.3419 AN REACTION TIME (SEC) PLUG FLON 0.0003 LAMINAR FLOP 0.0017 PLUG/c LAMINAR 0.2265 AN REACTION TIME (SEC) PLUG FLON 0.0000 LAMINAR FLON 0.0006 PLUG/c LAMINAR 0.1289 TLITER/MOLE-SECONDS) 40.0000 6.0000 46.0000 8 C D. Y 0.0236 0.0000 0.0000 0.3280 0.0047 REACTOR LENGTH (CH) 0.0814 0.0037 0.0023 0.2554 0.0749 0.0030 0.0024 0.2633 1.0878 1.2444 0.9635 0.9701 0.0095 REACTOR LENGTH (CM) 0.0830 0.0056 0.0083 0.2321 0.0816 0.0048 0.0071 0.2389 1.0179 1.1710 1.1684 0.9715 0.0143 REACTOR LENGTH (CM) 0.0781 0.0060 0.0143 0.2184 0.0792 0.0055 0.0123 0.2243 0.9859 1.0865 1.1607 0.9738 0.0191 REACTOR LENGTH (CM) 0.0722 0.0058 0.0206 0.2056 0.0752 0.0057 0.0172 0.2130 0.9604 1.0275 1.1936 0.9649 Z - 0.0236 0.1000 0.0961 0.0883 1.0882 0.2000 0.1194 0.1126 1.0596 0.3000 0.1331 0.1273 1.0454 0.4000 0.1459 0.1385 1.0533 CH GAN STATE UNIVERSITY LIBRARIE ImIIIIIIII IIII IIIIII