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Crystallization kinetics of sodium sulphate in a salting out MSMPR crystallizer system Na₂SO₄/H₂S0₄/H₂O/MeOH… Mina-Mankarios, George 1988

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CRYSTALLIZATION KINETICS OF SODIUM SULFATE IN A SALTING OUT MSMPR CRYSTALLIZER SYSTEM Na 2 S 0« t/H 2 S 0 ^ / H 2 0 / M e 0 H By GEORGE MINA-MANKARIOS B.Sc., The University of Manchester Institute of Science and Technology, England, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Chemical Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1988 r © George Mina-Mankarios, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of CHEMICAL ENGINEERING The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date SEPTEMBER 5, 1988 DE-6(3/81) - i i -ABSTRACT The growth and nucleation rates of sodium sulfate crystals salted out from their solution in a 38% w/w sulfuric acid solvent by the addition of an 80:20 w/w methanol'.water solution, were determined from measurements of the steady-state crystal size distribution (CSD) generated in a continuous mixed-suspension, mixed-product-removal (MSMPR) salting out crystallizer, and the effect of the supersaturation, the crystal suspension density and the temperature on these rates was investigated. The effect of the Cr + + + impurity was also briefly studied. For the pure system, the power-law kinetic rate equations of crystal growth (G = K QS g) and crystal nucleation (B = K„S b) were fitted to the experimental data D and the fitting parameters were determined at each of 25, 30 and 35°C. In addition, the nucleation and growth rate data were fitted to the relative kinetic equation (B = K^G 1) to provide a basis for comparison between i and b/g. Secondary nucleation effects were investigated by testing, in parallel with the primary nucleation rate equation B = KgSb, the rate equation B = K^M^S11 which includes a nucleation dependence on the crystal suspension density. i v The relative kinetic equation B = K M^G was also tested for comparison (v compared with u/g). - i i i -No evidence of secondary nucleation could be shown. The fitted estimates of j were non-positive at all temperatures and statistically non-different from zero at 35 and 30°C, just approaching significance at 25°C with a negative point estimate for j. Primary nucleation was shown to be the dominant nucleating mechanism for this system. The growth rate kinetic order g was determined to be essentially unity (G = KqS 0' 9 7) and was statistically non-changing with temperature. The nucleation rate kinetic order b was similarly temperature independent and was determined as 2.1 (B = KgS 2* 1). The kinetic rate constants K and K were both a function of temperature and G . B were fitted to an Arrhenius type temperature dependence to give K n = 43960 exp(-24600/RT) and K = 0.064 exp(70870/RT) B where R is in kJ/kmole-K. The activation energy for growth was positive at 24600 kJ/kmole. The nucleation activation energy was negative and larger in magnitude at -70870 kJ/kmole. - iv -In the presence of the chromium impurity, the kinetic parameters K , g, K , b, and i were determined at three levels of the concentration of the impurity in the crystallizer feed. An increase in the impurity concentration was shown to cause an increase in the growth rate constant K Q but had no significant effect on the nucleation kinetics. The result was a decrease in the relative rate constant and therefore a larger crystal size. The kinetics of crystallization as determined for this system would indicate that a high temperature, high crystal suspension density and long residence time are conditions which are favourable for the production of a large sodium sulfate crystal. - V -TABLE OF CONTENTS Page ABSTRACT i ± TABLE OF CONTENTS v LIST OF TABLES viii LIST OF FIGURES x ACKNOWLEDGEMENTS xii CHAPTER 1 - INTRODUCTION 1 1.1 Introduction 1 1.2 Objectives 4 CHAPTER 2 - CRYSTALLIZATION REVIEW 7 2.1 Introduction 7 2.2 Salting Out Crystallization 8 2.3 Crystallization Phenomena 9 2.3.1 Crystal Nucleation Kinetics 15 2.3.2 Crystal Growth Kinetics 25 2.3.3 Relative Kinetics 33 2.4 The Steady-State MSMPR Crystallizer 38 2.4.1 The Population Balance 38 2.4.2 Crystal Size Distribution - (CSD).... 42 2.4.3 The Mass Balance 43 2.5 Previous Work on Crystallizing Systems 47 ! 2.5.1 Reported Kinetics 47 | 2.5.2 Effect of Supersaturation 50 ; 2.5.3 Effect of Residence Time 54 I 2.5.4 Effect of Crystal Suspension Density. 56 ! 2.5.5 Effect of Hydrodynamics 59 | 2.5.6 Effect of Temperature 61 ! 2.5.7 Effect of Soluble Ionic Impurities... 65 i 2.5.8 Effect of Salting Out Agent 67 CHAPTER 3 - EXPERIMENTAL SECTION 73 ? 3.1 Apparatus 73 | 3.2 Extent of Experimental Work 75 i 3.3 Preliminary Procedures 80 1 - v i -Page 3.3.1 Na2S0t+ Solubility in Me0H/H2S0i+/H20 Mixtures 3.3.2 Sieve Analysis 3.3.3 Time Required for Steady-State....... 3.3.4 Uniformity of the Crystal Suspension. 3.3.5 Shape Factor of Na2S0i+ Crystals 3.3.6 Mother Liquor Sampling 3.3.7 Methanol Loss During Crystallization. 3.3.8 Crystallization of NaHSO^.H20 3.3.9 Calibration of Rotameters 3.3.10 Densities of the Main Crystallizer Feed and the Salting Out Agent 3.4 Experimental Procedures 3.4.1 Preparation of Feed Materials 3.4.2 Continuous Crystallization Experiments 3.4.3 Crystal Sampling and Sample Treatment 3.4.4 Measurement of the Supersaturation... 3.5 CSD Instability CHAPTER 4 - DATA ANALYSIS AND RESULTS 4.1 Determination of the Growth and Nucleation Rates from the Steady-State CSD Data 4.2 Results for the Chromium-Free System 4.3 Results for the Impure System 4.4 Effect of Variables on the CSD CHAPTER 5 - DISCUSSION AND CONCLUSIONS 5.1 System Variables 5.1.1 Supersaturation 5.1.2 Residence Time 5.1.3 Alcohol/Feed Ratio 5.1.4 Crystal Suspension Density 5.1.5 Agitation Rate 5.1.6 Temperature 5.1.7 Concentration of the Cr + + + Impurity.. 5.1.8 Yield 5.1.9 Crystal Size Distribution 5.2 Relative Kinetics 5.3 Check on Data Accuracy 5.4 Conclusions 5.5 Recommendations for Further Work 80 89 95 96 98 102 103 104 105 106 107 107 107 108 110 112 117 117 121 142 161 168 168 168 171 175 179 182 182 186 193 194 198 199 203 206 - v i i -Page NOMENCLATURE 2 0 8 REFERENCES 2 1 3 APPENDICES 2 1 6 A Correlation plots of the nucleation rate corrected for suspension density at three temperatures 217 B Scatter plots for fitted growth and nucleation rate equations 224 C Detailed run conditions and CSD data from run numbers .1-77 249 D Loge population density versus crystal size plots for run numbes 1-77 327 E Computer program.... 348 F Input data to computer program. 364 G Rotameter calibration curves 369 H Densities of crystallizer feed and salting out agent 372 J Details of the crystallizer 375 K Analytical procedures 377 - v i i i -LIST OF TABLES Table Page 3.1 Solubility of sodium sulfate in mixed Me0H-H2S01+-H20 solvents 83 3.2 Crystal suspension density and mean size data at 600 RPM 99 3.3 Shape factor data for four crystal sizes.... 101 4.1 Summary of results for run numbers 1-21 (Dataset 1). 122 4.2 Summary of results for dataset 1 classified by residence time and average suspension density (T = 25°C) 123 4.3 Summary of results for run numbers 22-40 (Dataset 2) 125 4.4 Summary of results for dataset 2 classified by residence time and average suspension density (T = 30°C) 126 4.5 Summary of results for run numbers 41-62 (Dataset 3) 127 4.6 Summary of results for dataset 3 classified by residence time and average suspension density (T = 35°C) 128 4.7 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 25°C 131 4.8 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 30°C 132 4.9 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C 133 4.10 Summary of kinetic rate equations as determined by curve-fitting experimental data to the respective kinetic models at three temperatures 1 3 4 - ix -Page 4.11 Summary of results for run numbers 63-77 (Dataset 4) 146 4.12 Summary of results for dataset 4 classified by residence time and Cr + + + concentration (T = 35 °C) 147 4.13 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C - Cr feed concentration = 75 ppm 152 4.14 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C - Cr feed concentration = 150 ppm 153 4.15 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C - Cr feed concentration = 300 ppm 154 4.16 Summary of kinetic rate equations as determined by curve-fitting experimental data to the respective kinetic models in the presence of the chromium impurity (T = 35°C) 155 - X -LIST OF FIGDRES Figure Page 2.1 Solubility diagram 11 2.2 Nucleation versus supersaturation 19 2.3 Concentration profile of solute near growing crystal surface 27 3.1 Schematic diagram of the equipment 74 3.2 Solubility of sodium sulfate in mixed Me0H-H2S01+-H20 solvents 84 3.3 Concentration of sodium sulfate in the mother liquor solvent SIS ct function of the mass fraction of the salting out agent in the solvent 86 3.4 Yield of sodium sulfate as a function of the mass fraction of the salting out agent in the mother liquor solvent 88 3.5 Density of the crystal suspension as a function of the mass fraction of the salting out agent in the mother liquor solvent 90 3.6 Crystal mean size versus sieving time 92 3.7 Crystal growth rate versus sieving time 93 3.8 Crystal nucleation rate versus sieving time. 94 3.9 Effect of residence time on the crystal mean size 116 4.1 In n versus crystal size (T = 25°C, x = 80s, Mt = 34 gr/1) 120 4.2 Effect of temperature on the growth kinetics 136 4.3 Effect of temperature on the nucleation kinetics 138 I - xi -I 1 Page 4.4 Effect of temperature on the relative kinetics 141 4.5 Scatter plot for fitted growth rate equation G = 43962 exp[-24626/RT]S0'9707... 143 4.6 Scatter plot for fitted nucleation rate equation B = 0.064 exp[70870/RT]S2, 1 0 6 5 144 4.7 Effect of the Cr + + + concentration in the feed on the operative growth rate 148 4.8 Effect of the Cr + + + concentration in the feed on the operative nucleation rate 149 4.9 Effect of the Cr + + + concentration in the feed on the mean crystal size 150 4.10 Effect of the C r + + + concentration in the feed on the growth kinetics 157 4.11 Effect of the Cr+ + + concentration in the | feed .on the nucleation kinetics 159 4.12 Effect of the C r + + + concentration in the ' feed on the relative kinetics 162 i i I | 4.13 Effect of residence time on the CSD 164 | 4.14 Effect of crystal suspension density on ! | the CSD 165 j 4.15 Effect of temperature on the CSD 166 | ! 4.16 Effect of Cr + + + feed concentration on the i 1 CSD 167 i i j i ) 5.1 Photographs of Na2S0it plate crystals 196 j 5.2 Experimental versus theoretical suspension j density 204 . - x i i -ACKNOWLEDGEMENTS I would like to express my sincere gratitude to Dr. K.L. Pinder under whose supervision this project was carried out, for his patience, guidance, and suggestions which have been invaluable. The staff in the workshops, both main and electronics, and in the stores of this department have been very helpful in constructing and maintaining the equipment used to carry out this project. Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. Last but not least I would like to thank my mother Rasha Mina for her constant love, encouragement, and support. - 1 -CHAPTER 1 INTRODUCTION 1.1 Introduction The addition of a suitable agent, which is miscible with the solvent, and in which a salt is relatively insoluble, to a salt solution, causes the precipitation of that salt by reducing the solvent's capacity to retain the salt in solution. i.e., by reducing the salt solubility in the final mixture. This is commonly referred to as the "salting out" of solute from its solution by the addition of a third component (Murray and Larson, 1965). Salting out crystallization, with its relative operational simplicity, offers several advantages over the more conventional cooling or evaporative crystallization and there appears to be a growing industrial interest in this process as a possible means to increase yields and conserve energy. While considerable experimental work has been done on numerous crystallizing systems over the past two decades (Garside and Shah, 1980), there is still relatively little information available in the chemical engineering literature on salting out processes and there is a noticeable lack of data on the specific sodium sulfate crystallizing system. The salting out system relevant to this study is the Na2S04/H2S0i+/H20/Me0H system. Sodium sulfate is precipitated from its solution in a 38% w/w sulfuric acid solvent by the addition of 80% w/w aqueous methanol. The use of aqueous rather than absolute methanol is necessary to provide sufficient water in the crystallizer to precipitate the neutral anhydrous sodium sulfate; the neutral salt being the desired product for the purposes of this study. The addition of pure methanol causes the precipitation of the acid salt Na3H(SOi+)2 which carries with it 18.71% of its own weight of E^SO^ and therefore represents an undesirable loss of acid from the system. The main purpose of this process, in its industrial application, is the separation of sodium sulfate from sulfuric acid, prior to subsequent processing and eventual recovery of the acid for reuse. Clearly, then, the most desirable crystalline product is one that contains no acid. i.e., the neutral sodium sulfate. The kinetics of crystallization (crystal growth rates and crystal nucleation rates) in this system were investigated using a mixed-suspension, mixed-product-removal (MSMPR) test crystallizer. Growth and nucleation rates, under different steady-state conditions, were calculated from steady-state crystal size distribution (CSD) data using the MSMPR analysis technique. The theoretical interpretation of such data, obtained from MSMPR crystallizers, has been developed by Randolph and Larson (1971) to yield both the growth and nucleation kinetic rates simultaneously. In essence, the procedure involves the - 3 -curve-fitting of the experimental crystal size distribution, determined in this work by standard sieving techniques, to the form of crystal size distribution predicted by theory, and from the estimated parameters of the fit the kinetic rates are calculated. The separation of sodium sulfate from sulfuric acid solutions finds direct application in the pulp and paper industry where chlorine dioxide is used for bleaching. It is an essential part of the "acid recovery process" (ARP) (Lobley and Pinder, 1979; 1981) that was developed to treat chlorine dioxide generator effluents, which consist primarily of sodium sulfate, sulphuric acid and water, to recover and recycle the sulfuric acid from these effluents to the generator. In this process the sodium sulfate is precipitated from the acid by salting out with aqueous methanol. The working system in this study was chosen to be compatible with the crystallization system in the ARP process. The main acid-feed to the crystallizer was prepared as 25.0% w/w Na2S0it, 28.5% w/w H2SO4, and 46.5% w/w H20, which approximates a typical effluent from a Mathieson chlorine dioxide generation process. The salting out agent was prepared as 80% w/w aqueous methanol. The kinetic information determined here is therefore- immediately relevant to the design and operation of ARP salting out crystallizers. - 4 -1.2 Objectives The purpose of this investigation was to calculate crystal growth and nucleation rates for the salting out system described from steady-state crystal size distribution measurements, and to determine the effect of supersatura-tion, temperature, crystal suspension density, and the concentration of the Cr + + + ionic impurity on these rates. The kinetic rate equations to be used to model the experimental data were: For growth rate: G = K^Sg (1.1) and K q = A q exp[-EG/RT] G G (1 .2) For non-secondary nucleation: B = Kr,S b (1.3) and K„ = A exp[-E /RT] B B B (1.4) For general nucleation: B = K n MJ S U (1.5) - 5 -and K n = A n exp[-EN/RT] (1.6) The overall objective can therefore be subdivided as follows: - To determine the effect of the supersaturation on the growth rate by estimating the growth rate kinetic order g. - To determine the effect of temperature on the growth rate by estimating the activation energy.for growth e g. - To evaluate the dependence of the nucleation rate on crystal suspension density in order to determine either, (i) a significant effect of crystal suspension density on the nucleation rate and therefore the applicability of the general nucleation model (1.5). Or, (ii) a non-significant correlation of the nucleation rate with the suspension density and therefore the applicability of the non-secondary nucleation model (1.3), confirming the common assumption that secondary nucleation effects are not ordinarily significant in salting out crystallization systems. - 6 -- To determine the effect of the supersaturation on the nucleation rate by estimating the nucleation rate kinetic order b or u. - To determine the effect of temperature on the nucleation rate by estimating the activation energy for nucleation or E,. B N - To determine the effect of the concentration of the soluble impurity, the tri-valent chromium cation Cr + + +, which occurs in chlorine dioxide generator effluents, on the kinetic parameters of growth and nucleation. - 7 -CHAPTER 2 CRYSTALLIZATION REVIEW 2.1 Introduction In order for a solute to leave solution and precipitate, a certain degree of supersaturation of the solution has to occur. Under conditions of supersaturation, the solvent will contain more dissolved solute than it would at equilibrium, at the same temperature. The difference between the actual and equilibrium concentrations of dissolved solute (w - w e q ) is the supersaturation, S, which provides the driving force for precipitation. The state of supersaturation is thermodynamically unstable and, unless operation is such that a constant level of supersaturation is maintained, e.g., by continuous crystallization, a supersaturated solution will always move towards a new state of equilibrium by shedding its excess dissolved solute. Solutions are most commonly brought to a state of supersaturation by cooling, evaporation or salting out. Generation of supersaturation by cooling, which is employed in what are accordingly called cooling crystallizers, is utilized when the solute solubility shows a strong positive temperature dependency. Supersaturation - 8 -is induced upon cooling an initially saturated solution, because of the reduction in the solubility of the solute, causing the solvent to become supersaturated in solute material at the lower temperature. Cooling is achieved by direct or indirect contact heat exchange or by flash solvent evaporation under reduced pressure (adiabatic vacuum cooling). More substantial evaporation of solvent reduces the amount of total solvent available to keep the solute in solution and increases the solute concentration beyond that required for saturation at the boiling temperature, thus producing the supersaturation in evaporative crystallizers. 2.2 Salting Out Crystallization A less conventional type of crystallization but with potential advantages over more common processes is salting out crystallization. In salting out crystallizers a solution is supersaturated by the addition of a third component, the salting out agent, which causes the solute to leave solution by reducing its solubility in the resulting mixture. The salting out agent is thought to "compete" with solute molecules for available solvent molecules and as a result inhibiting the capacity of the solvent to maintain the solute in solution. The added agent- should be miscible with the solvent and, for good solute recovery, the solute - 9 -should be relatively insoluble in it. A high recovery of solute can be achieved by the choice of a suitable additive. Salting out processes allow operation at or near room temperature and eliminate the need for vacuum and/or heat exchange equipment. Additionally, the mixed-solvent mother liquor often has a high retention capacity for impurities and very pure crystals result. Probably the only disadvantage in a salting out process is the need for a recovery unit to separate the mixed solvents. Salting out has been employed for the crystallization of organic substances from water-miscible organic solvents by the addition of water, and for the crystallization of inorganic salts from aqueous solutions by the addition of an organic solvent. 2.3 Crystallization Phenomena The starting point for a crystallization operation is to attain the state of supersaturation. Once a state of supersaturation is achieved, crystals will have to form (at "zero" size) before they can grow. The rate of formation of crystals at "zero" size (rate of birth) is called the rate of crystal nucleation, B, and is defined as the number of nuclei formed per unit volume per unit time. Crystal nucleation proceeds under the influence pf the supersaturation driving force. However, it has been - 10 -observed that a perfectly clean solution, i.e., one that is totally free of suspended solids, which is gradually driven to increasing levels of supersaturation does not nucleate until a certain minimum supersaturation is reached. The solution then "bursts" into a sudden and abundant shower of nuclei relieving itself of unsustainable supersaturation. This supports the concept of metastability with respect to primary nucleation. The idea of metastability was first introduced by Ostwald in 1897 and was subsequently elaborated upon by Miers who suggested that two types of supersaturation can be recognized, the metastable and labile (unstable) states, where primary nucleation exhibits two very different kinds of behaviour. In the region of metastable supersaturation no appreciable crystal nucleation occurs. When the level of supersaturation reaches an upper metastable limit bordering on the labile zone of supersaturation a sudden rapid increase in the rate of nucleation takes place. The different states of supersaturation can be represented on a solubility diagram as in Figure 2.1. The solid line denotes an arbitrary solubility curve for an arbitrary solute-solvent system defined as a function of temperature. Clearly the area below the solubility curve represents undersaturated and therefore stable solutions. The area above the solubility curve represents supersaturated states - 11 -TEMPERATURE Figure 2.1 Solubility diagram - 12 -of a solution and is divided into the metastable and labile zones. According to Miers there is a definite relationship between the concentration of a clean solution and the temperature at which crystal nuclei will spontaneously form. This relationship was defined as a supersolubility curve which is the (broken) line dividing the metastable and labile areas below which no appreciable nucleation occurs (metastable) and above which excessive crystal nucleation takes place (labile). Miers theory (Perry and Chilton, 1973) received considerable experimental support. However, it has been suggested in light of later work that it is probably more correct to think of the supersolubility curve as a zone over which the transition from a very low nucleation rate to a very high nucleation rate takes place rather than a well defined line at which the nucleation rate increases sharply. In industrial crystallizers crystal nucleation is often mostly due to nucleation mechanisms other than primary (discussed later). However, in order to avoid the danger of excessive primary nucleation, which becomes dominant at high supersaturations, and maintain a stable crystallizer operation the solute concentration in the crystallizer should be kept well into the metastable region of supersaturation. The second kinetic process that occurs simultaneously with crystal nucleation during the course of a - 13 -crystallization operation, subsequent to the formation of initial crystal nuclei is crystal growth. Once a nucleus has been formed, growth of the nucleus takes place by the addition and integration of solute molecules into the solid crystal structure of that nucleus. As with nucleation, the driving force for crystal growth is the supersaturation. Unlike spontaneous nucleation, however, growth is possible at any level of supersaturation. Thus a clean metastable solution will sustain its supersaturation without nucleation but a seed crystal introduced into the solution will grow as long as the solution is supersaturated. The growth rate of a crystal can be defined as a linear growth rate, G (length/time), which is the rate of increase of a characteristic linear dimension of the crystal with respect to time, or a mass deposition rate per unit surface area of the crystal, (mass/time • surface area). By considering the growth of a crystal of characteristic size L, a relationship between G and R Q can be obtained, thus Volume of crystal, V = k L 3 (2.1) o v Surface area of crystal, A = k L (2.2) O <x where k and k are volume and surface area shape v a factors defined by Equations (2.1) and (2.2) respectively (k = 1, k = 6 for cubes), v a - 14 -By definition, and, p ^ ^ c _ ^ V c . dL RG A "dt , T 2 dt , T 2 dt k dt c k aL k aL a (2.4) therefore, 3k p R G - • G (2.5) a It is common to talk about the linear growth rate G when reporting and correlating growth rate data. Crystal nucleation and crystal growth are the two kinetic processes which describe the general overall kinetic behaviour of a crystallizing system. Their relative magnitude is a major factor in determining the product crystal size and crystal size distribution from a crystallization operation. The rate of nucleation determines the rate of particle formation and the growth rate determines the rate of deposition of solute on existing particles. To control crystal size the relative rate of crystal formation to the rate of crystal enlargement is of - 15 -great Importance. In general a large crystal size is desirable and therefore nucleation should be suppressed relative to growth. Knowledge of the kinetics of nucleation and growth is fundamental to the proper design, operation and control of crystallizers. 2.3.1 Crystal Nucleation Kinetics Crystal nucleation is the process by which crystal nuclei are produced during the course of a crystallization operation. Three main categories of crystal nucleation can be distinguished. Primary homogeneous, primary heterogeneous and secondary nucleation (e.g., Randolph and Larson, 1971; Garside, 1985). Homogeneous nucleation is the spontaneous formation of new crystals from the liquid phase, induced by the state of supersaturation alone. Heterogeneous nucleation is influenced by the presence of foreign insoluble material in the crystal suspension in addition to the supersaturation. It is thought of as a catalysed homogeneous nucleation process in which the inert foreign particles act as catalysts by providing nucleation sites on which crystals will preferentially form because of reduced energy requirements. Heterogeneous nucleation therefore requires lower levels of supersaturation than homogeneous nucleation - 16 -and so reduces the width of the metastable zone for the given crystallizing system. Secondary nucleation refers to nucleation induced by the presence of the suspended solute crystals themselves, given the state of supersaturation. "Contact" secondary nucleation is a phenomenon in which new crystal nuclei are generated upon contact between growing crystals and/or crystal-equipment (e.g., crystal-agitator). "True" secondary nucleation is thought to be similar in mechanism to heterogeneous nucleation where the solute crystals act in a similar manner to the inert foreign particles that promote heterogeneous nucleation. Evidence suggests that contact secondary nucleation is not only the most significant secondary nucleation mechanism but probably the most important nucleating phenomenon in many industrial crystallizers (e.g., Bennett et al., 1973; Larson, 1984). Nucleation due to crystal attrition is a somewhat trivial process in which pieces and chips broken off existing crystals become growing crystals. It is believed to have little or no contribution to the overall nucleation rate in a well designed crystallizer. Despite the uncertainties about the exact mechanisms of the different nucleation processes, and therefore the lack of an adequate theoretical basis on which to model experimental results, nucleation rate data have successfully - 17 -been correlated using empirical or semiempirical relations such as equations (2.7), (2.11) and (2.13). The classical theories of primary homogeneous (spontaneous) nucleation assume that nucleation in a supersaturated solution requires that a minimum number of solute molecules combine in a series of bimolecular reactions to produce ordered crystal embryos. The free energy of such embryos goes through a maximum at some critical size which decreases with increasing supersaturation (McCabe, 1946). Embryos larger than this critical size are "stable" nuclei whereas embryos smaller than the critical size can only decrease their free energy by redissolving. Accordingly, the effective rate of nucleation would be determined by the rate at which the crystal embryos surmount the maximum in the free energy curve. The resulting functional dependence of nucleation rate on supersaturation is of the following general form (Mullin, 1979): B = k x exp[- k2(logcr)~2] (2.6) where a is the supersaturation ratio w/wori and kj. and k 2 are constants which will depend on the operating conditions in the crystallizer. Because of the difficulty of preparing perfectly clean solutions in an industrial atmosphere (and even in the - 18 -laboratory), most primary nucleation that occurs in practice is likely to be heterogeneous and not homogeneous. Nucleation rate equations proposed for heterogeneous nucleation are essentially the same as equation (2.6) but with a smaller effective k 2. This has the effect of reducing the critical supersaturation, S m a x , at which the model predicts a rapid increase in nucleation rate, consistent with the view that the presence of foreign surfaces in a supersaturated solution catalyse the nucleation process and therefore reduce the range of supersaturation where little or no nucleation occurs (the metastable zone) - Figure 2.2a. Nucleation models such as (2.6), however, bear little relation to the nucleation rates observed in industrial (and experimental) crystallizers which do not follow the behaviour predicted by these models; that is negligible nucleation in the metastable zone of supersaturation and very high nucleation beyond that. Such behaviour is probably well approximated by nucleation from solutions when they are not being stirred, which is a condition that is not satisfied in many crystallizers. Most crystallization operations utilize some form of mechanical energy input to fluidize the crystal suspension. Under these conditions significant nucleation is observed even at relatively low levels of supersaturation. Mechanical energy input appears - 19 -Metastable _ (Heterogeneous) LLI (— < en < LLI O Me tastabFe (Homogeneous) !/ 1/ -•max, ° m a x , heterogeneous homogeneous SUPERSATURATION a) Primary Nucleation (Classical theories) SUPERSATURATION b) Nucleation in agitated suspensions Figure 2.2 Nucleation versus supersaturation - 20 -to influence the nucleation rate such that primary nucleation is permitted at essentially any level of supersaturation within the metastable zone. Under such conditions, it has been observed that the dependence of primary nucleation rates on the supersaturation is closely approximated by a power-law relationship of the form, B = K B S b (2.7) where S is the supersaturation driving force (w - w e q), b is the kinetic order of nucleation with respect to the supersaturation and K 0 is the nucleation rate constant with a temperature dependency usually modelled as an Arrhenius-type relationship, Kg = A B exp[-Eg/RT] (2.8) in which T is the absolute temperature, R is the gas constant, Eg is the activation energy of nucleation and Afi is a preexponential factor (representing the approach of Kg as T tends to infinity). Kfi has been found to be also dependent on the hydrodynamics and the concentration of impurities in the crystallizing solution. Activation energies of nucleation have been found to vary amongst different crystallizing systems and positive or negative activation energies have been reported for different substances. - 21 -A power function which recognizes that occur at very low supersaturations was as B = Kd(S - S . ) b B mxny which assumes the existence of a lower metastable limit of supersaturation, S mi n, below which the nucleation rate is zero and above which nucleation can be correlated with power-law kinetics. Experimental evidence suggests that for most inorganic materials S mi n is very close to zero so that the model reduces to (2.7). It has been shown (e.g., Nyvlt, 1971) that the nucleation rate equation (2.6) can itself be approximated by a power-law function of supersaturation. Such an approximation however requires very large power-law exponents which is not in agreement with the experimentally determined values of b commonly in the range 1-3. It might therefore be concluded that primary nucleation in realistic mixed-suspension crystallizers deviates considerably from that predicted by classical primary nucleation theories, and is at present best modelled with power-law kinetic equations such as (2.7). Conceivably there exists a truly lower metastable limit (approaching zero) below which the nucleation rate is zero as well as an upper metastable limit at (and above) which nucleation is driven to excessive nucleation does not originally proposed (2.9) - 22 -uncontrolled levels (Figure 2.2b). All stable crystallizers, however, operate between these two limits where nucleation is described by low-order power-law kinetics. Miers concept of supersolubility assumes, in non-agitated solutions, the convergence of the two limits at one point corresponding to the location of the supersolubility curve. In the general case, the overall rate of crystal nucleation from a crystallizing solution is the summation of the contributions of the different nucleation mechanisms that are operative in the system, Rate of Primary Rate of Secondary Nucleation Nucleation Nucleation = + Rate (homogeneous or (Contact and/or True) heterogeneous) ( 2 .10 ) In systems where secondary nucleation effects are not ordinarily significant (e.g., salting out or reaction crystallization), the nucleation rate is predominantly due to primary mechanisms and is adequately correlated with the simple power-law nucleation model B = K-S*3. This model, D however, is not suitable for the representation of the general nucleation rate which is influenced by secondary (as well as primary) nucleation mechanisms. A general nucleation model must also include a dependence on the - 23 -frequency of crystal-crystal contact and crystal-agitator contact which promote (contact) secondary nucleation; contact nucleation is thought to be easily the most significant secondary nucleation mechanism in agitated suspensions. Such a dependence has been proposed as a power-law relationship between the overall nucleation rate and the crystal suspension density, M T (mass of crystals/volume of suspension), in which M T correlates the effect of secondary nucleation on the overall nucleation rate. u is the nucleation kinetic order with respect to the supersaturation and j is the order with respect to the suspension density which characterizes the contribution of secondary nucleation processes to the overall nucleation rate. K N is the nucleation rate constant which depends on the operating conditions (e.g., hydrodynamics, impurity concentrations) and is modelled against temperature with an Arrhenius-type relation, B = K^ M^ S u (2.11) K m = A w exp[-EN/RT] 'N ( 2 . 1 2 ) Whereas the influence of supersaturation., on secondary nucleation is in general different from that on primary - 24 -nucleation, the lack of adequate mechanistic secondary nucleation models does not permit the separation and correlation of primary and secondary nucleation individually. Additionally, experimental nucleation rates are overall rates, and it is difficult to separate the individual contributions of the different types of nucleation. Consequently, nucleation rate equations such as (2.11) have been used to empirically correlate the effect of supersaturation (which influences all nucleation) and suspension density (which influences contact nucleation) on the overall nucleation rate. When the nucleation rate is not affected by the amount of solids in suspension, nucleation is due to primary mechanisms only. The kinetic order j is then effectively zero and the defining kinetic equation reduces to the form given in equation (2.7). When secondary nucleation mechanisms are also operative in the system, the nucleation rate shows a dependence on the crystal suspension density, in which case j takes on non-zero positive values. In many systems j was found to be close to unity indicating the predominant influence of crystal-impeller contact secondary nucleation (e.g., Jones et al., 1986; Youngquist and Randolph, 1972). Crystal-crystal contact nucleation is expected to show a second order dependence on suspension density ( 3 = 2 ) . Equation (2.11) is valid for nucleation rates from - 25 -suspensions undergoing constant energy inputs. Increasing energy input enhances crystal contact and increases contact energy and will therefore influence the rate of secondary nucleation, K N = f(hydrodynamics). In experiments where mechanical energy input was a variable, nucleation rates have been correlated with a power-law function which also includes a dependence on impeller RPM, B = K^ (RPM)h M'J S U (2.13) or K n =• K± (RPM)h (2.14) 2.3.2 Crystal Growth Kinetics Once stable crystal nuclei are produced in a supersaturated solution they begin to grow. The dependence of the growth rate on supersaturation is commonly described by the semiempirical power-law relation, G = K nS g (2.15) u where g is the growth rate kinetic order and Kg is an overall growth rate constant which depends on temperature, hydrodynamics and the concentration of impurities in the crystallizing solution. The effect of temperature on KQ is expressed by an Arrhenius-type relation, - 26 -K g = A g exp[-EG/RT] (2.16) where E„ is the activation energy for growth, (j Since crystal growth can only occur at the surface of a crystal, solute molecules will first have to diffuse from the bulk of the solution to the crystal surface for growth to take place. This diffusion step is then followed by a surface reaction (or particle integration step) that takes place at the crystal surface in which the solute molecules become integrated into the solid crystal structure. The overall rate of growth, G, is the combination of these two processes and is determined by the relative contribution of each. A useful simplified representation of the kinetics of the two processes is given by the two-step crystal growth model (Garside, 1971; Karpinski, 1980; 1985). Diffusion is assumed to proceed under the driving force w - wi and is linear. Particle integration or surface reaction proceeds under the driving force Wj - weq and is assumed to be, in general, non-linear in the concentration driving force. Wi, the solute concentration at the crystal-solution interface, is smaller than the concentration in the bulk solution, w, and larger than the equilibrium concentration, weq (Figure 2.3). At steady state the rate of diffusion must equal the rate of surface reaction which is equal to - 27 -CRYSTAL FACE SURFACE REACTION CONTROL solute concentration in fluid bulk Wj- solute concentration at interface w^ equilibrium solute concentration DIFFUSION CONTROL < on UJ o ~Z. o o Figure 2 . 3 Concentration profile of solute near growing crystal surface - 28 -the overall rate of growth, dM Diffusion k d(w - w ±) = G - j - (2.17) c r 1 d M c Surface reaction k (w. - w o ) = G « -r— -tt— (2.18) r l eo a ci u c where r is the order of the surface reaction kinetics and k^ and kr are kinetic coefficients for diffusion and reaction defined by (2.17) and (2.18) respectively. When r=l, the interfacial concentration, w^ (which is difficult to determine experimentally) is eliminated by combining (2.17) and (2.18), and the growth rate can be expressed in terms of the overall driving force, the supersaturation S (= w - > a-s G = tl/kd I l/kr] S < 2' 1 9> which is a special case of equation (2.15) where g=l and, KG = l/kd + l/kr (2.20) When r=r (r*0), the following general relationship between the growth rate and the supersaturation can be derived, 1 /r p p / x s = ¥ T + rr7F < 2- 2 1> d k ' - 29 -For rapid diffusion, k d is large, K Q « k r, g « r, and the growth rate is controlled by the surface reaction step, G = k S r (2.22) r For rapid reaction, k r is large, K Q « k d, g » 1, and the growth rate is diffusion controlled, G = k dS (2.23) In the general case, however, the growth rate is influenced by both diffusion and reaction and some attempts have been made to mathematically separate the individual contribution of the diffusion step (k^) and the surface reaction step (kr,r) from overall growth rate data using equation (2.21). Given a set of experimental growth rate - supersaturation data, estimates of the three parameters kd, k^ and r can be made by fitting the function in (2.21) to the data using non-linear parameter estimation techniques. The values of the parameters determined this way, however, are influenced more by the character of the experimental error, which is inherent in all experimental data, than by the nature of the actual growth kinetics that produced the data, and in fact when the growth rate is linearly dependent on the supersaturation a meaningful separation of k^ and k r is - 30 -almost impossible. Another approach arbitrarily assumes a fixed value of the surface reaction order r (r*l) and the data is fitted to equation (2.21) using standard linear least squares methods. The estimates of k d and k^ determined this way are less affected by experimental error but will depend on the value of r; k r being particularly sensitive to the choice of r. It has been suggested that by setting r=2 a reference (standard) case of the growth kinetics is created from which "standardized" values of k d and k can be estimated. It is recognized that the r usefulness of such a procedure lies mainly in determining the relative changes in the standardized coefficients with changes in operating variables, rather than in determining absolute values of kd and k^ under given conditions (Karpinski, 1985). Whether or not the two-step crystal growth model is an accurate description of the growth process in a given crystal system, and in view of the fact that little reliable information can be derived about the separate diffusion and reaction steps from the two-step growth kinetics, overall growth rates are usually modelled using overall growth rate equations such as (2.15). Cumulative experimental evidence has shown that in many crystal systems the dependence of the growth rate on supersaturation is closely- approximated by the power-law relation in equation (2.15) and growth rates have been successfully correlated accordingly. This form of - 31 -the growth kinetic equation, now widely accepted, incorporates an overall growth rate constant, K^ which is thought of as a measure of the combined effects of k^ and k^, and an overall growth rate order, g, which, in general, is considered to be between 1 and r. Discrimination between diffusion-controlled growth and reaction-controlled growth can be made by examination of the activation energy of K^ , as well as the growth order g. Diffusion is commonly linear in the supersaturation driving force and has relatively low activation energy (up to 20,000 kJ/kmole). Surface-reaction is commonly non-linear and, since it is considered to be a process of a chemical nature, is expected to have a higher activation energy. Values of g determined experimentally for different crystal systems have often been close to 1 (Helt and Larson, 1977; Budz et al., 1984) and in some cases closer to 2 (Timm and Cooper, 1971; Sikdar and Randolph, 1976); the bulk of the reported values being mostly within the range 1-2, possibly justifying the assumption that the choice of r=2 is a good approximation for the order of the surface reaction kinetics in many systems. Relatively little data is available on the activation energies for growth, however, and, in the few studies where they have been reported, they have generally fallen between the limits expected for diffusion and reaction. - 32 -It should be mentioned, for completion, that in some crystal systems, notably the K2S01+ system, crystal growth rates are not independent of the crystal size, i.e., McCabe's AL law G * G(L) (McCabe, 1929) does not apply. The growth rate kinetic equations presented in this section so far, do not recognize a dependence of the crystal growth rate on crystal size. While the growth rate constant, K G (and k^ and/or kr), is assumed to be influenced by temperature, hydrodynamics, and the concentration of impurities, it is not, in general, considered to be a function of crystal size. In systems where McCabe's AL law is not satisfied, there is an implied dependence of Kg on crystal size and several empirical equations have been proposed to describe it. For correlation of experimental size-dependent growth rate data the following equation is commonly used, G = K Sg(l + aL)C (2.24) o or K_ = K (1 + aL)c (2.25) G g where a and c are empirically determined constants defining the size dependence of the growth rate in a given crystal system, and K is a redefined growth rate constant which depends on the operating conditions. Equation (2.24) is known as the ASL equation (Abegg et al., 1968). - 33 -2.3.3 Relative Kinetics Crystal nucleation and crystal growth are two kinetic processes that proceed simultaneously but not totally independently during the course of a crystallization operation. Since both processes share the supersaturation as a common driving force, there exists an apparent relationship between the nucleation rate and the growth rate. Over the range of operating conditions where the growth rate is given by, G = K GS g (2.15) and the nucleation rate by, B = K BS b (2.7) the supersaturation variable, S, can be eliminated by combining (2.7) and (2.15) to give, B = K.G1 (2.26) b which describes the existing relationship between nucleation and growth that arises because of the common dependence on supersaturation. K^ is the relative nucleation rate constant, - 34 -KR K, = -4-r- (2.27) b Kb/g v 1 G and i is the relative kinetic order of nucleation which is the ratio of the nucleation and growth orders, i = ^ (2.28) Where the nucleation is influenced by the amount of solids in suspension, the nucleation rate is given by, B = K N M;j S u (2.11) and on combination of (2.11) and (2.15) the resulting relationship between nucleation and growth becomes, B = K n M^ G V (2.29) where K is the relative nucleation rate constant, n % K = , (2.30) G and v is the relative nucleation kinetic order, v = - (2.31) g v ' - 35 -Further, it is useful to consider how the crystal size distribution that is being generated in the system is related to the rates of nucleation and growth. For this purpose, it is necessary to introduce the definition of crystal population (or number) density. Thus, if the total number of crystals up to size L per unit volume of suspension is denoted by N = N(L), then a number density of crystals of size L is defined by, dN i n = l = l (number/volume'length) (2.32a) When n is evaluated at L=0, the resulting quantity is the population density of the "zero" sized crystals (or nuclei), „ o 0 dN n = dL L=0 < 2- 3 2 b> The exact specification of the crystal size distribution that develops in a given crystallization process requires knowledge of the process definition and the process constraints as well as of the operative kinetic rates. However, a general relationship exists between nucleation and growth and the characteristic parameter of a crystal size distribution, n°, the nuclei population density. This relationship derives from the definition of the nucleation rate which is given by, - 36 -B = dNi = dN | cPE" L=0 HE I L=0 dL 3t (2.33) and therefore B = n G 0 (2.34) Equation (2.34) and (2.26) (or(2.29)) represent the kinetic constraints that must be satisfied in a crystallizing solution. Combination of (2.34) and (2.26) gives for non-secondary nucleation, and combination of (2.34) and (2.29) gives for general nucleation, Equation (2.35) or (2.36) relates the population density of nuclei to the kinetics of crystallization. In a crystallization operation, the product crystal size is primarily influenced by the relative magnitude of the operative nucleation and growth rates rather than the absolute magnitude of each. In general, at constant suspension density, crystal size is a decreasing function of B/G. Therefore what is ultimately of significance for the evaluation of crystallizer performance is knowledge of the (2.35) B G (2.36) - 37 -relative sensitivity of the nucleation rate to the growth rate as defined by the parameter i (or v). Recognizing that the growth rate is a measure of the supersaturation then, at constant suspension density, an increase in supersaturation reduces crystal size in systems where i is greater than one and increases crystal size when i is less than one. When i is equal to one, crystal size remains constant with changes in supersaturation. The effects of temperature, hydrodynamics and impurity concentration on the crystal size are incorporated in the relative kinetic rate constant K b (or Kn). Clearly, knowledge of the individual kinetics of nucleation and growth provide all the information required to evaluate the relative kinetics. However, because of the difficulty of measuring the supersaturation, many experimental studies have correlated nucleation - growth rate data with relative equations such as (2.26) or (2.29), eliminating the need to measure the supersaturation (Garside and Shah, 1980). In such cases, individual kinetic orders and activation energies for the separate kinetic processes cannot be determined and the effect of temperature on the kinetics can only be "lumped" into the relative rate constant K^ (or K q) which can be fitted to an Arrhenius-type relationship to yield a "relative" activation energy. - 38 -2.4 The Steady-State MSMPR Crystallizer Significant advances have been made in the area of crystallization since the adoption of the population balance approach to crystallizer operation and design. In particular the mixed-suspension, mixed-product-removal crystallizer has been demonstrated to be a useful experimental tool for the determination of the kinetics of crystal nucleation and crystal growth from measurements of steady-state crystal size distributions generated in this type of crystallizer. Using the concept of population balance, in which all particles in the system must be accounted for, Randolph and Larson (1971) developed a comprehensive mathematical model defining the crystallization operation and derived equations describing the crystal size distribution produced in a MSMPR crystallizer, operating at steady-state, in terms of the rates of nucleation and growth that are producing this distribution. This has subsequently provided a framework for the analysis of experimental CSD*s from MSMPR crystallizers to calculate the kinetic rates of nucleation and growth. 2.4.1 The Population Balance For a MSMPR crystallizer of volume V, operating at steady-state under the following constraints, - 39 -- The system is perfectly mixed. - The product withdrawn from the crystallizer is a representative sample of the crystallizer contents no classification at withdrawal. - Crystal nuclei appear with zero size. - There are no crystals in the feed stream. - A constant slurry volume. - Uniform crystal shape factor. - Negligible crystal fracture. and where crystals are born at a rate of B (number/vo1ume• time) and grow at a rate of G (length/time) and where n(L) is the population density of crystals of size L, a number balance can be written in which the number rate of crystal entering a size range Li to L2 must equal the number rate leaving. Thus for an increment in time At the number of crystals entering this size range because of growth is V Gini At and the number of crystals leaving by growth is V G2n2 At The number removal of crystals in this size range by bulk flow is QQn AL At - 40 -where, Q 0 = total exit volume flow AL = L 2 - L I n = average population density in range AL and, ni,n2 = population densities of crystals of sizes Li, L 2 respectively G1,G2 = growth rates of crystals of sizes L 1 ? L 2 respectively. Population balance gives: VGini At = VG 2n 2 At + Q Qn AL At (2.37) Rearranging, and as AL approaches zero, n approaches a point value, n, V d( G n) + n = 0 00, Q 3 E — n U (2.38) If McCabe's AL law (McCabe, 1929) may be assumed to hold, i.e., G * G(L), and defining a mean residence time T = V/Q , then ^ dn , „ Gt _ + n = 0 (2.39) with n° = n(L=0), integration yields n = n° exp[-L/Gx] (2.40) - 41 -Equation (2.40) describes the basic number distribution function of crystals in MSMPR crystallizers in terms of the operative rates of growth, G, and nucleation, B, included here as n° = B/G. It is commonly of more practical interest to look at the mass distribution of crystals rather than the number distribution. This can easily be derived from the fundamental number distribution function, n. Since the volume of a crystal = k yL 3, the total crystal mass per unit volume of suspension can be calculated from, M t = P c k y J q L 3 n ( L ) d L = p ck y L 3 n° exp[-L/Gx] dL or, M x = 6pckvn°(Gx)1+ (2.41) and the cumulative mass fraction up to size L, w , ^ - M(L) _ ^0 l 3 n° exp[-L/Gx] dL n(Li) — —rj — M roc c ! n T J0 n exp[-L/Gt] dL or, W(L) = 1 - exp(- + (L.) + J + 1 ( L _ ) 3 ] (2.42) - 42 -2 Similarly, since the surface area of a crystal = k aL , the total crystal surface area per unit volume of suspension is, At = k a /q L 2 n° exp[-L/Gx] dL or, a t = 2kan°(Gx)3 (2.43) 2.4.2 Crystal Size Distribution (CSD) The size distribution of product crystals from a crystallizer can be defined by two parameters, the mean size, MS, and the coefficient of variation, CV. The mean size is defined as the aperture size of the sieve that retains 50% of the product. The coefficient of variation is a measure of the spread of the distribution and is given by, CV = 1 0° ( a il Mg a 8 ° % (2.44) where a. is and agi+ are the aperture sizes of the sieves that retain 16 and 84% of the product respectively. The CSD generated in an MSMPR crystallizer is described by equation (2.42). This form of distribution has a constant coefficient of variation of 52%. Its mean size is determined by the parameter (Gx) and is given by, MS = 3.67(G x) (2.45) - 43 -2.4.3 The Mass Balance For complete definition and evaluation of the system, the kinetics of crystallization are incorporated into the mass balance solution of the MSMPR crystallizer to determine the performance of this type of crystallizer. While different mass balances can be written for different crystallizing systems (e.g., evaporative, cooling, hydrated solid, etc.), a general mass balance can be written for the solid phase in which the rate of disappearance of solute from the mother liquor must equal the rate of production of crystalline solid, which for the MSMPR crystallizer is Q q M t (mass/time), m ix i - m ox Q = q qM t (2.46) where m.,m = mass flow rates of solvent in the feed inlet l' o stream and product exit stream respectively x^,xQ = mass ratio of solute/solvent in the feed inlet stream and product exit stream respectively A quantity AC can be defined for the crystallizer as AC = (m.x. - m x )/Q (2.47) which can be thought of as the effective solute concentration drop across the crystallizer. For cooling crystallization with no solvent evaporation and a "thin" - 44 -suspension and where density changes with temperature are small, AC is the actual drop of solute concentration across the crystallizer. In general, AC is such that the rate of production of crystals is Q Q A C . The M S M P R mass balance therefore requires that AC = M^. Additionally, the rate of production of solid crystals (Q QAC) must equal the mass deposition rate per unit crystal surface area (Rq) times the total available surface area for solute deposition Using equations (2.5) and (2.15) in (2.48), a relationship is derived for the supersaturation driving force in the crystallizer, s = ( 2 - 4 where Kz = 3kvPcKg/ka. The supersaturation is seen to be inversely related to the crystal surface area per unit suspension volume, Arp. The surface area of crystals available in the crystallizer depends on the kinetic rates of nucleation and growth which determine the crystal size distribution, and is given by, (ATV), Q qAC = R QA TV 'G T (2.48) A T = 2ka(B/G)(Gx) 3 (2.43) - 45 -The rates of nucleation and growth are in turn dependent upon the supersaturation through the kinetic rate equations, A mass balance requires the simultaneous solution of Equations (2.49), (2.43), (2.7) and (2.15). In most crystallization processes, the accumulation of solute as supersaturation is negligible compared to the amount of .solute precipitated, and the exit solute concentration approaches the equilibrium concentration. In such systems the yield is essentially independent of the level of supersaturation in the crystallizer and AC is uniquely determined by the solubility characteristics of the solute and the point of operation relative to the solubility curve. In this case combining Equations (2.49), (2.43), (2.7) and (2.15) leads to the following explicit relationship for S, b (2.7) and G = K QS g (2.15) 1 AC .3g+b (2.50) 3 where K3 = 6k p L L , which determines the level of v c B G - 46 -supersaturation in the crystallizer in terms of the independent parameters AC and x, and temperature, hydrodynamics and impurity concentration which are implicit in K3. The crystal mean size is determined from Equations (2.50), (2.15) and (2.45), as i-1 1 MS = 3.67(5; * ^ (2.51) c v b which summarizes the effects of all major independent variables on the crystal size expected from an MSMPR crystallizer. The effects of residence time ( t ) and crystal suspension density (AC = M T) are explicit in the expression. The effects of temperature, hydrodynamics, and impurity concentration are incorporated in K^. Equations (2.50) and (2.51) provide the relationships required for the evaluation of the performance of the MSMPR crystallizer and represent the mass balance solution of the system derived for nucleation and growth kinetics as described by Equations (2.7) and (2.15) respectively. (Different kinetics will yield a different solution). The requirement AC = M^ is "contained" in Equation (2.48). By substituting for RQ and AT from (2.5) and (2.43) respectively, and using a mean residence time t = V/Q , the following relationship is derived, - 47 -AC = 6p k n (Gx) 2 (2.52) C V The right hand side of this equation is the expression for Mt in an MSMPR crystallizer (Equation (2.41)). 2.5 Previous ffork on Crystallizing Systems 2.5.1 Reported Kinetics Since about the mid-1960s, with the development of the theory of operation of the continuous mixed-suspension, mixed-product-removal crystallizer, to yield quantitative growth and nucleation rates from steady-state crystal size distribution measurements, the MSMPR crystallizer has been extensively used to determine the kinetics of crystallization in numerous crystallizing systems of industrial interest. It has commonly been assumed that the growth and nucleation rates are both expressible as simple power functions of the supersaturation (Equations (2.15) and (2.7) or (2.11)) and therefore that the nucleation rate is expressible as a power function of the growth rate (relative kinetics), B - K ^ 1 (2.26) or - 48 -B = K n MJ G V (2.29) Such relationships have been used when the supersaturation was very low and difficult to measure, to determine the relative nucleation kinetics of the system. The empirical validity of these equations has been verified in many systems and, significantly, the exponent i or v shows little variation between different crystallizing substances, in general, falling between 1 and 2 or 3 with few exceptions. According to Randolph (1984), the earliest reported use of the MSMPR crystallizer to determine crystallization kinetics was by Bransom, Dunning and Millard (1949), who had apparently deduced the exponential form of the steady-state MSMPR distribution prior to its formalization by Randolph and Larson (1971), and used this information to calculate the growth and nucleation rates of cyclonite precipitating from nitric acid solutions. Their data indicate a relative nucleation kinetic order (i) of 2.72. Subsequently, various investigators used the MSMPR crystallizer to study different crystallizing systems. Murray and Larson (1965) investigated the salting out crystallization of ammonium alum from its aqueous solutions using ethanol as a salting out agent. They determined the relative kinetic order i, from steady-state CSD data, to be 2. They also operated the crystallizer under unsteady-state - 49 -conditions to measure the response of the system to step changes in production rate. By solving the transient CSD model, they confirmed the kinetic results obtained. In a later study, Timm and Larson (1968) reported a different result for the same system. They observed a first order dependence of nucleation on growth (i=l). The salting out crystallizations of ammonium sulfate with methanol and sodium chloride with ethanol from their aqueous solutions were also investigated in this study. A relative kinetic order of 4 was determined for ammonium sulfate, and for sodium chloride i was determined to be 9. Experiments on the sodium chloride/H20/Et0H salting out system were subsequently repeated by Liu and Botsaris (1973) who reported a relative kinetic order of 2.4, and Song and Douglas (1975) who reported i = 7.9. The experiments of Liu and Botsaris, however, were conducted in the presence of the lead ion impurity Pb + +, which could influence the kinetics. In another precipitation study, investigating the kinetics of the reaction crystallization of calcium sulfate hemihydrate from phosphoric acid solutions, Amin and Larson (1968) determined a relative kinetic order of 2.8 when reagent grade phosphoric acid was used and 2.6 when plant grade acid was. u§ed. Shor and Larson (1971) determined a relative nucleation kinetic order v of 1.4 for the cooling crystallization of potassium nitrate. In their work, they - 50 -assumed rather than verified a first order dependence of the nucleation rate on the crystal suspension density (j=l). The effect of the ionic impurities Cr + + + and Co + + was also investigated in this study. Another investigation of the cooling crystallization of potassium nitrate was conducted by Juzaszek and Larson (1977). They calculated v = 2.06 and j = 0.5 from their data. Youngquist and Randolph (1972) observed a relative kinetic order v = 1.2 and a first order dependence of nucleation on suspension density (j=l) for ammonium sulfate crystallization. The nucleation rate in this system was found to be also dependent on the impeller RPM which was a variable in this investigation. Randolph, Beckman and Kraljevich (1977) found v = 4.99 and j = 0.14 for the cooling crystallization of potassium chloride. 2.5.2 Effect of Supersaturation Supersaturation is considered to be a fundamental driving force for the kinetics of crystallization. Since a saturated or undersaturated solution cannot crystallize its solute until it is driven to a supersaturated state (McCabe, 1946), it follows that when the supersaturation is zero, both kinetics of growth and nucleation must be zero as implied by equation (2.15) for growth, 51 G = K GS g (2.15) and equation (2.7) or (2.11) for nucleation, b (2.7) B = K n M^ S u ( 2 . 1 1 ) The influence of the supersaturation on the growth rate is described in a simplified manner by the two-step crystal growth model in which S provides the driving force for diffusion and/or surface reaction. The extent to which the overall growth rate is dependent upon S is characterized by the growth rate kinetic order g. The influence of the supersaturation on the nucleation rate is complicated by the phenomenon of metastability. Above a metastable limit of supersaturation nucleation is excessive. Within the metastable region, the dependence of nucleation on the supersaturation is described by the nucleation rate kinetic order b for non-secondary nucleation, or u for nucleation influenced by secondary mechanisms. Garside and Shah (1980) pointed out that b, in general, tends to be higher than u since in systems where secondary nucleation mechanisms are absent, primary nucleation is the dominating mechanism which is highly non-linear in supersaturation and therefore a high value of b may be expected. Secondary nucleation rates are generally less sensitive to supersaturation and so a smaller value of u may be expected. A number of MSMPR kinetic studies reported in the literature have included measurements of the supersaturation driving force. In such studies growth and nucleation rate data had been separately correlated with the supersaturation and the independent effect of the supersaturation on growth and nucleation established through the parameters g and b (or u) respectively. The available data indicate that the effect of the supersaturation on the nucleation rate is, in general, .greater than that on the growth rate (b or u > g), i.e., that i or v is greater than one, but some exceptions to this general observation have been reported. The potassium sulfate crystallizing system in particular, which also exhibits size dependent growth kinetics, shows unusual nucleation behaviour and has been the subject of numerous investigations. Rosen and Hulburt (1971a) studied the crystallization of potassium sulfate from its aqueous solutions in an evaporative vacuum crystallizer at 30°C. A second order dependence on the supersaturation was found for the growth rate (g=2), whereas the nucleation rate was apparently unaffected by the level of supersaturation in the crystallizer (u=0), which gave a relative kinetic order v of zero for this system. The nucleation rate was however - 53 -linearly dependent upon the crystal suspension density (j=l). Randolph and Rajagopal (1970) used a cooling crystallizer to study the potassium sulfate system. They determined the kinetics at 29°C from crystal size distribution measurements over the limited size range 0-50 microns. In this investigation the growth rate was linear in supersaturation (g=l) and the nucleation rate showed a negative dependence on the supersaturation with a power-law exponent u = -1, which therefore gave a negative relative kinetic order v = -1. Nucleation increased with increasing suspension density with an exponent j = 0.4. It has been suggested., however, that negative kinetic orders are probably suspect since it is difficult to envisage kinetic mechanisms giving rise to such data (Garside and Shah, 1980). Potassium sulfate crystallization was also studied by Jones, Budz and Mullin (1986) in a cooling crystallizer. The growth rate was second order (g=2) and the effective nucleation rate was first order with respect to both supersaturation (u=l) and crystal suspension density (j=l). The relative order v was therefore 0.5. Another study in which the relative kinetic order was reported to be less than one was by Sikdar and Randolph (1976). They investigated the kinetics of the cooling crystallization of citric acid monohydrate and found that all kinetic orders were smaller than one in this system. At 20°C the growth - 54 -rate kinetic order g was 0.65 and for nucleation u was 0.543 giving a relative kinetic order v = 0.84. In the same study the magnesium sulfate heptahydrate system was also investigated. The relative order v at 25°C was 1.13 determined from g = 2.29 and u = 2.59. Garside and Jancic (1979) determined v = 1.58 from their data on the potassium alum cooling crystallization system which also exhibits size dependent growth kinetics. The growth rate of a given size correlated with the supersaturation with g = 1.33 and nucleation showed a kinetic order u of 2.1. Nucleation was also linearly dependent on crystal suspension density (j=l) and was influenced by hydrodynamic conditions. Budz, Karpinski and Nuruc (1984) studied the growth rates of sodium thiosulfate pentahydrate and potassium alum crystals in a fluidized bed under conditions of no nucleation. They found the growth rate of the former to be linear in supersaturation (g=l) and g was 1.48 for the latter. 2.5.3 Effect of Residence Time Randolph and Larson (1971) point out that the net effect of a change in crystallizer residence time is a change in the level of supersaturation generated within the crystallizer. Because of the requirement for mass balance, operation with longer residence times at constant suspension density necessitates slower kinetics and therefore a smaller - 55 -supersaturation. The extent to which the supersaturation varies with residence time depends upon the kinetics in the system and has been shown to be (Garside and Shah, 1980), 4 s - x (2 5 3 ) at constant suspension density, as indicated by Equation (2.50). The dependence of the growth rate on the supersaturation combined with this relationship yields an expression describing the dependence of the growth rate on residence time, G « t 1 + 3 (2.54) The mean crystal size produced in a steady-state MSMPR crystallyizer is given by, MS = 3.67(Gx) (2.45) and therefore, i - 1 MS <* t 1 + 3 (2.55) which describes changes in crystal size with changes in residence time. This relationship is contained in Equation (2.51). When i is greater than one, crystal size increases - 56 -with increasing residence time (decreasing supersaturation). When i is less than one, crystal size decreases with increasing residence time. When i is equal to one, no improvement in crystal size can be made with changes in residence time. These effects have been observed experimentally in different systems. For example, in the work of Timm and Cooper (1971) on the cooling crystallization of potassium dichromate from aqueous solutions, the growth rate kinetic order g was 1.7 and the nucleation rate kinetic order b was 0.9 which gave a relative nucleation kinetic order i of 0.53. In this system, crystal size was observed to decrease with increasing residence time. The same effect was observed by Rosen and Hulburt (1971a) in their study of the potassium sulfate system in which the relative kinetic order i was zero. Timm and Larson (1968) found no measurable effect of residence time on the crystal size for the ammonium alum salting out crystallization system in which i was equal to one. In most studies, however, i was greater than one and the crystal size increased with increasing residence time (e.g., Amin and Larson, 1968). 2.5.4 Effect of Crystal Suspension Density In their investigation of the phenomenon of secondary nucleation, Clontz and McCabe (1971) showed that contacts - 57 -between one crystal and another and contacts between a crystal and an inert surface are important contributors to the production of crystal nuclei from a crystallizing solution where secondary nucleation mechanisms are dominant. They found that the number of nuclei produced per unit contact area increased with increasing contact energy and increasing supersaturation. Crystal-crystal contacts gave rise to more nuclei than did crystal-non-crystal contacts. An increased crystal suspension density within a crystallizer will increase the probability of crystal contact. Consequently a dependence of the nucleation rate on suspension density may be expected in systems where contact nucleation is significant. Such a dependence has been observed experimentally in numerous systems and has usually been correlated as a power-law relation between the nucleation rate and the crystal suspension density (Equation (2.11) or (2.29)). The values of j reported in sections 2.5.1 and 2.5.2 reflect some of the available data on the influence of suspension density on the rate of nucleation in different crystal systems. Often j was found to be equal to one indicating the predominance of crystal-equipment contact nucleation. Crystal-crystal contacts are predicted to result in a second order dependence of nucleation on suspension density. However, the range of crystal suspension densities, typically investigated in experimental - 58 -laboratory crystallizers does not accurately simulate conditions found in industrial crystallizers which operate with much higher suspension densities where the relative importance of crystal-crystal contact is increased. Studies on precipitation systems, i.e., salting out or reaction crystallization systems, have not usually included measurements of the crystal suspension density, on the assumption that in such processes secondary nucleation is not significant and therefore suspension density is not a factor influencing the nucleation rate. The effect of crystal suspension density on the crystal size generated in a steady-state MSMPR crystallizer when B * BCMrp) is shown in Equation (2.51). Recognizing that at steady-state AC = MT, then Therefore an increase in MT enhances crystal size when nucleation is independent of M . When B = B(MT) and is given by Equation (2.11) or (2.29), Larson, Timm and Wolff (1968) have shown that the crystal size is then related to the suspension density by, 1 MS M* + 3 (2.56) 1 ~ J MS « Mj + 3 (2.57) - 59 -which predicts that for j<l, crystal size increases at higher suspension densities. For j>l size degradation occurs with increases in suspension density, and for j=l suspension density has no effect on crystal size. 2.5.5 Effect of Hydrodynamics Crystallizer impeller RPM provides a measure of the hydrodynamic conditions prevailing in a given vessel. Changes in impeller RPM can have a significant influence on both growth and nucleation processess. By changing the crystal-solution slip velocity, the boundary layer thickness and therefore the diffusion resistance to the overall growth process is altered. Garside (1984) notes that increasing the relative crystal-solution velocity will cause a diffusion controlled growth rate to increase, rapidly initially and then more slowly as the bulk of the diffusion resistance is eliminated, approaching a constant value corresponding to the surface reaction controlled growth rate. This trend has been observed experimentally by various investigators. For example, Rosen and Hulburt (1971b) found that the growth rate of potassium sulfate seed crystals fluidized by an upward flow of its supersaturated aqueous solution, increased when the solution velocity was increased, up to a limiting velocity of 11 cm/s above which - 60 -the growth rate was apparently unaffected by further increases in solution velocity. Liu, Tsuei and Youngquist (1971) studied the growth of magnesium sulfate heptahydrate crystals from aqueous solutions and observed the same effect. They concluded that when the growth rate ceased to increase with solution velocity, diffusion resistance was negligible. Garside and Jancic (1979), however, reported no effect of impeller RPM on the growth rate of potassium alum crystals and concluded that under the experimental conditions tested, the diffusion resistance to the growth process was not significant. An Influence of agitator RPM on the nucleation rate in mixed suspension crystallizers has also been observed experimentally. Increased RPM increases the energy of crystal contact and is therefore expected to increase the rate of secondary nucleation. By improving the mixing conditions in the system and minimizing local regions of high supersaturation, an increase in agitation rate would also affect the rates of primary nucleation. The dependence of the nucleation rate on impeller RPM observed experimentally has usually been correlated as a power-law relationship such as in Equation (2.13), i.e., B « (RPM)h (2.58) - 61 -The applicability of this relationship has been verified in a number of studies and the values of h reported have varied in different systems. Youngquist and Randolph (1972) found h = 7.84 for ammonium sulfate crystallization. Garside and Jancic (1979) determined a value of h of 1.8 in their study of potassium alum crystallization. Sikdar and Randolph (1976) reported no effect of RPM on the nucleation rates of magnesium sulfate heptahydrate and citric acid monohydrate (h = 0). Bennett, Fiedelman and Randolph (1973) found an effective value of h = 3 for sodium chloride crystallization. 2.5.6 Effect of Temperature Most experimental kinetic studies have not included temperature as an experimental variable. As a result, relatively little data is available in the literature on the effect of temperature on the kinetics of growth and nucleation. The overall growth process, considered to be the result of the two series steps of diffusion and surface reaction, is expected to be enhanced at higher temperatures, to a greater extent when surface reaction controlled than when diffusion controlled. The temperature dependence of the overall nucleation rate, which can be the result of different nucleation processes operative* in the system, the exact mechanisms of which are not clearly established, is - 62 -less well predicted. Experimental results on the effect of temperature on the growth and nucleation rates have commonly been correlated with an Arrhenius temperature dependence of the kinetic rate constants as, K q = AQ exp[-EG/RT] (2.16) for the growth rate, and Kg = A B exp[-Eg/RT] (2.8) for non-secondary nucleation, or K n = A n exp[-EN/RT] (2.12) for general nucleation, in which the activation energy, E, is a parameter which characterizes the influence of temperature on the kinetic rates when the corresponding kinetic orders are not functions of temperature. In most studies in which the effect of temperature was investigated, the temperature range tested was usually narrow and the data indicated that over such narrow ranges the kinetic orders could be considered essentially constant, permitting the calculation of activation energies. Reported activation energies for the growth rate have shown some variation in magnitude indicating the possible existence of different growth controlling mechanisms in - 63 -different systems. Nucleation rate activation energies have shown a greater variation between systems and in many reported cases the apparent activation energy for the nucleation process was negative. i.e., the nucleation rate decreased with increasing temperature. Sikdar and Randolph (1976) reported a growth rate activation energy E^ , of 29,800 kJ/kmole and a negative activation energy for nucleation E^ of -39,750 kJ/kmole for the crystallization of citric acid monohydrate. Helt and Larson (1977) calculated EQ = 31,000 kJ/kmole and Ejj = - 108,000 kJ/kmole for potassium nitrate. Budz, Karpinski. and Nuruc (1985) studied the growth rate of sodium thiosulfate pentahydrate crystals and determined an activation energy Eq = 12,000 kJ/kmole. From the relatively small magnitude of the activation energy and the linear dependence of the growth rate on the supersaturation, they concluded that the growth process was diffusion controlled. In the same study they observed that the contribution of the diffusion step to the growth of potassium alum crystals increased with increasing temperature. The activation energy for the growth rate of potassium sulfate crystals was reported by Jones, Budz and Mullin (1986) at E^ = 40,400 kJ/kmole. This relatively high value indicated surface reaction controlled growth. The activation energy for nucleation was positive at - 64 -E n = 62,500 kJ/kmole. Amin and Larson (1968) did not calculate activation energies but observed that higher growth rates and lower nucleation rates were operative in the crystallizer at higher temperatures, in the reaction crystallization system of calcium sulfate hemihydrate. The influence of temperature on the crystal size generated in a steady-state MSMPR crystallizer is contained in equation (2.51), i.e. 1 MS « K. 1 + 3 (2.59) b where K, = The specific effect will therefore depend D £5 Lr on the values of the activation energies for growth and nucleation and the value of the relative kinetic order i. It should be mentioned that in almost all crystallizing systems, the solute solubility in the mother liquor is temperature dependent. A change in temperature will therefore alter the equilibrium solubility of the solute in the working liquor as well as influence the crystallization kinetics in the system. The effect of temperature on the kinetics of growth and nucleation, discussed here, is at constant driving force (supersaturation). i.e., when the supersaturation has allowed for the change in solubility with temperature. - 65 -2.5.7 Effect of Soluble Ionic Impurities The process of crystallization is particularly sensitive to the presence of impurities in the crystallizing solution. Trace concentrations of certain impurities can exert a considerable influence on the rate of nucleation and/or the rate of growth and therefore affect the crystal size. Industrially, when a certain impurity is known to have a desirable effect on the crystal product, that impurity is deliberately added to the crystallizing system. The use of trace impurities in this manner is often employed to suppress or promote nucleation and/or promote better crystal growth and/or crystal habit. The specific mechanism by which a given impurity produces a given effect in a given crystal system is not clear. As a result, prediction of impurity effects is difficult and the selection of a particular impurity for a particular effect continues to be a "secret" art. Experimentally, the effect of impurities on the kinetics of crystallization has been investigated in only few studies. Shor and Larson (1971) determined the effect of each of the soluble ionic additives Cr + + + and Co + +, added as Cr(NC>3)3 and C0CI2 respectively, on the cooling crystallization of potassium nitrate from aqueous solutions. The supersaturation was not measured, so only relative kinetics could be determined. The data indicated that the - 66 -growth rate was higher and the nucleation rate was lower when the concentration of the impurity in the crystallizer was increased. This was true for both Cr + + + and Co + +. The resulting crystal size therefore increased with increasing impurity concentration. The relative nucleation kinetic order was determined to be 1.4 for the pure system and was observed to increase to 1.8 and 2.4 in the presence of Co + + and Cr + + + cations respectively. Without supersaturation data, Shor and Larson could not establish the separate effects the impurity might have had on the individual rates of growth and nucleation. They suggested however, that the main effe.ct of the impurity was on nucleation; decreasing the nucleation rate, the resulting apparent increase in the growth rate being mostly due to the increase in the supersaturation necessitated by the mass balance, as a result of the decrease in the nucleation rate. Another study by Liu and Botsaris (1973) investigated the effect of Pb + + ionic impurity, added as PbCl2, on the salting out crystallization of sodium chloride from aqueous solutions by the addition of ethanol. In this study, lower growth rates and higher nucleation rates were observed at higher impurity concentrations, resulting in a smaller crystal size. The relative kinetic order i for the pure system was 2.4 and remained constant for all impurity concentrations. The relative nucleation rate constant K, increased with increasing concentration of the impurity. Again, the lack of supersaturation data in this work did not permit the separate evaluation of the effect of Pb + + ion on the growth and nucleation rate. Liu and Botsaris suggested that the presence of the impurity decreased both, the growth rate and the nucleation rate. The increase in the supersaturation which then resulted, to satisfy the mass balance, increased both rates such that the net effect was an apparent increase in nucleation and decrease in growth rate. 2.5.8 Effect of Salting-Out Agent The.use of an organic solvent as a salting out agent has been employed in the salting out crystallization of various inorganics from their aqueous solutions. Timm and Larson (1968) used methanol for the crystallization of ammonium sulfate and ethanol for ammonium alum and sodium chloride. Murray and Larson (1965) used ethanol in their study of the ammonium alum system. The same alcohol was also used by Liu and Botsaris (1973) and Song and Douglas (1975) for the crystallization of sodium chloride. However, apart from the implied knowledge that the addition of the alcohol caused a reduction in the solubility of the crystallizing substance, and thus produced the supersaturation in the system, these studies did not include any data on the effect of the alcohol concentration on the - 68 -solubility of the crystallizing material which is a major factor in determining the yield of the crystallizer. Budz and co-workers (1986) used acetone for the salting out precipitation of the organic cocarboxylase hydrochloride from its aqueous solution. In this study the solubility of cocarboxylase hydrochloride was determined at 15°C as a function of increasing amounts of acetone in the solution. They found that as the ratio of the volume of added acetone to the volume of the initial solution increased from 0 to 1 there was a sharp decrease in solubility followed by a slower approach to an essentially constant value as the ratio increased above 1. In a basic study by Alfassi and Mosseri (1984), for each of KI03 and K2SOk, the fraction of the salt precipitated from its saturated aqueous solution was measured as a function of increasing amounts of each of the salting out agents, acetone, propylamine and isopropylamine added to the solution. The fraction precipitated was found to increase, rapidly initially and then more slowly as the amount of added agent formed a larger part of the solution. For example, the addition of 0.7 litres of isopropylamine to 1 litre of a saturated aqueous solution of K2SO4 precipitated 95% of the salt. However, to recover 99% of the salt 3 to 4 litres of isopropylamine were required. Alfassi and Mosseri noted that, when the added amount of the organic solvent is large - 69 -enough, the fraction of salt precipitated will start to decrease upon further addition of solvent, and eventually reaching zero for very high ratios of organic solvent/ aqueous solution, since the salt is likely to have a small solubility in the organic solvent itself. In a similar investigation, Kohn and co-workers (1963) studied the precipitation of the neutral sulfates K2S0lt and Na2S0[+ from the aqueous solutions of the corresponding acid sulfates KHSO4 and NaHSOi* by the addition of various organic liquids. They defined a "precipitation ratio" as the fraction of the total potassium or sodium, originally in solution,. precipitated, and a "conversion ratio" as the fraction of the total potassium or sodium, originally in solution, precipitated as the neutral sulfate. They found for an aqueous solution of KHSO^ of initial concentration 245 g/1 at 25°C, treated with increasing amounts of various alcohols (methanol, ethanol, n-propanol, t-butanol, n-butanol, ethylene glycol and 1,4-butanediol), the precipitation and conversion ratios were identical, i.e., all the precipitated solid was the neutral sulfate. For all alcohols tested except ethylene glycol, the ratios, determined as a function of the ratio of the added alcohol volume to the volume of the initial aqueous solution, exhibited an initial rapid rise followed"by a slower approach to a maximum value (« 0.95). For ethylene glycol - 70 -the curve went through a maximum giving a conversion (and precipitation) ratio of about 0.56 at a glycol/aqueous solution volume ratio of 2 above which the conversion ratio started to decrease. With acetone precipitation there was a distinction between the conversion and precipitation ratios; the conversion ratio going through a maximum (« 0.88) at a ratio of acetone/aqueous solution volume of about 2 whereas the precipitation ratio continued to increase with increasing added acetone reaching 0.98 at an acetone/aqueous solution volume ratio of 10. The same trends were observed with NaHS0i+ aqueous solutions using acetone, methanol and n-butanol as precipitants. Again, there was no difference between the precipitation and conversion ratios when the alcohols were used but a difference was observed when the acetone was used; the conversion ratio going through a maximum (» 0.88), in this case, at a ratio of acetone/ aqueous solution volume of about 3 while the precipitation ratio constantly increased. Another early study investigating the possibilities of the crystallization of inorganics from their aqueous solutions with organic precipitants was conducted by Thompson and Molstad (1945) who determined the solubilities of potassium and ammonium nitrates in aqueous isopropanol solvents. They found that solubility decreased with increasing isopropanol concentration in the solvent, and deduced from the data - 71 -that, for example, 1 kg of a saturated aqueous solution of potassium nitrate at 40°C treated with 0.15 kg of isopropanol will precipitate 44% of the salt originally in solution. Half a kilogram of isopropanol added to the same solution increased the salt recovery to 68%. They concluded that since most inorganic salts are relatively insoluble in alcohols, the possibility exists for the commercial crystallization of such salts from their saturated aqueous solutions by the controlled addition of alcohol to the solutions. When the salting out agent is added to a saturated salt solution, the salt solubility is reduced and the amount of the originally dissolved salt in excess of that required for saturation under the new conditions will precipitate. The amount of salt that remains in solution will be the product of the new solubility, as mass solute/mass solvent, and the total mass of solvent. In salting out crystallization, the addition of the salting out agent to the system decreases the solubility and at the same time increases the total mass of solvent available. When the relative reduction in the solubility is greater than the relative increase in the mass of solvent caused by the addition of the salting out agent, the amount of solute that can remain in solution is smaller than the amount of the originally dissolved solute and precipitation of the excess solute takes place. When the - 72 -relative increase in the mass of solvent is greater than the relative decrease in solubility, the amount of solute that can remain in solution is greater than that originally dissolved, in which case the solution, in fact, becomes undersaturated and no precipitation occurs. The rate of decrease of the solubility of inorganic salts in aqueous alcohol solvents with respect to the alcohol content of the solvent is maximum at small alcohol concentrations and approaches zero at large alcohol concentrations. This implies that a relatively small amount of alcohol added to a saturated aqueous solution will precipitate a relatively large amount of the salt, whereas further addition of alcohol to a solution which already contains a high concentration of alcohol will not cause any further precipitation. The fraction of the salt precipitated (yield) can therefore be expected to increase with increasing added amounts of alcohol up to a point of maximum yield and then start to decrease eventually reaching zero. This point can be reached since the solubility of inorganic salts in concentrated alcohols and even in pure alcohols is almost never exactly zero, so that when a large amount of alcohol is added to a saturated solution, there is sufficient total solvent, given the non-zero solubility, to maintain all the originally dissolved solute in solution. The addition of an even larger amount will cause the solution to become undersaturated. - 73 -CHAPTER 3 EXPERIMENTAL SECTION 3.1 Apparatus A schematic representation of the equipment used in this study to investigate the kinetics of the salting out crystallization of sodium sulfate is shown in Figure 3.1. The feed tanks for the main crystallizer feed (25.0% w/w Na2S0i+, 28.5% w/w H2S0i+, 46.5% w/w H 20) and the salting out agent (80% w/w MeOH, 20% w/w H 20) were two 50 litre polypropylene containers kept at a controlled temperature in a large constant temperature water bath which was regulated by a thermostat. During continuous operation, the feed tanks were slightly pressurized with compressed air (1-2 psig) to maintain a constant pressure and to avoid the creation of a vacuum in the tanks as the feed materials were being consumed. The tanks were not open to the atmosphere to prevent potential loss of solvent (particularly methanol) by evaporation which would alter the composition of the salting out agent and/or the main feed. The fluid was pumped from each tank to the crystallizer. The working parts of the pump, in the main acid-feed line, which contacted the fluid were made of Teflon. Each flow was controlled by a valve in the line and monitored with a rotameter; a stainless steel valve and rotameter in the inline filters variable Figure 3.1 Schematic diagram of the equipment - 75 -methanol line, and a Teflon valve and rotameter in the acid line. A Teflon filter (porosity 10-15 microns) in each line removed foreign particles from the feed materials before they were mixed in the crystallizer. The feed materials entered the crystallizer below the surface of the crystal suspension at a point approximately one inch above the stainless steel flat blade turbine impeller which mixed the crystallizer contents. The impeller was 2 3/8" in diameter and was driven by a variable speed motor. The MSMPR crystallizer was a 1.25 litre Plexiglas vessel, 5 inches in diameter, with four wall baffles and a water jacket. Constant temperature water from the constant temperature water bath for the feed tanks was circulated through the crystallizer jacket to maintain isothermal conditions in the crystallizer. The temperature of the crystal suspension was measured with a thermometer accurate to 0.1°C. The mixed suspension continuously overflowed from a sidearm to a collector. The crystallizer had a drain outlet at the bottom, which was plugged on the inside with a cork to eliminate dead space, and a two-piece split cover at the top, which could easily be removed for sampling. Details of the crystallizer are given in Appendix J. 3.2 Extent of Experimental Work The previously described equipment was used to conduct continuous steady-state crystallization experiments in which - 76 -neutral anhydrous sodium sulfate was precipitated from its solution in a 38% w/w sulfuric acid solvent by salting it out with an 80:20 weight % methanol: water solution. The crystal growth and nucleation rates of sodium sulfate in this system were determined from measurements of the steady-state crystal size distribution generated in the MSMPR crystallizer. Experiments were conducted both in the absence and presence of Cr + + + chromium impurity in the crystallizing solution, and at different levels of supersaturation, crystal suspension density, and temperature. The bulk of the experiments was focussed mainly on establishing the kinetic relationships for growth and nucleation that exist for the pure (chromium free) system. A smaller number of experiments were conducted in the presence of the Cr + + + impurity, which was added to the system as chrome alum (KCr(S0i+) 2 "12H20 - contains 10.41% chromium), to determine the effect of the impurity on the kinetic parameters of growth and nucleation. A total of 62 experimental runs were conducted in the absence of the chromium impurity under the following conditions: Temperature at 25, 30, and 35°C Residence time at 40, 50, 60, 80, 100, and 120 seconds and Salting out agent/main feed ratio at 4.25, 3.0, and 1.75 gr/gr - 77 -At each temperature, a change in the level of the supersaturation was brought about by a change in the residence time; supersaturation decreasing with increasing residence time. A change in the ratio of the salting out agent to the main acid-feed caused a change in the crystal suspension density that was generated in the crystallizer; suspension density decreasing with increasing ratio. The working temperature.in the crystallizer was maintained by controlling the feed materials' temperature at 4, 5, and 6°C below the required crystallizer temperature for the respective salting out agent/feed ratios of 4.25, 3.0, and 1.75 gr/gr. The rise in temperature was caused by the heat of dilution of the acid-feed with the methanol solution in the crystallizer. All data collected in the absence of the chromium impurity are divided into 3 datasets classified by temperature. Dataset 1 contains data from experimental runs 1-21 which were conducted at 25°C. Datasets 2 and 3 contain data from run numbers 22-40 and 41-62, which were conducted at 30 and 35°C respectively. Dataset 4 contains the data from the experimental runs 63-77 which were conducted at a constant temperature of 35°C and a constant salting out agent/main feed ratio of 4.25 gr/gr which produced an essentially constant crystal suspension density of about 32 gr/1. The variables in this series of runs were the residence time and the concentration - 78 -of the Cr + + + chromium impurity in the main feed. The residence times used were 40, 60, 80, and 120 seconds. The impurity concentration levels tested were 75, 150, and 300 ppm of chromium in the main acid-feed. The corresponding chromium ion concentrations that existed in the crystallizer after mixing with the salting out agent were therefore 14, 29, and 57 ppm respectively. In order to characterize the reproducibility of the results, selected runs from each dataset were repeated and duplicate data were obtained. The reproducibility was shown to be good. There was more variation in duplicate nucleation rate data than in the growth rate data. This was expected since the method of determination of the kinetic rates from the crystal size distribution (CSD) data inherently produces more variation in the estimated nucleation rate than in the estimated growth rate; the growth rate being related to the inverse of the slope of the best fitting straight line to the CSD data, whereas the nucleation rate is related to the exponential of the intercept of the line which shows greater variation with small changes in the construction of the best line. For example, in duplicate experiments conducted at 35°C, a residence time of 40 seconds, and a crystal suspension density of 32 gr/1, the measured nucleation rate varied from 5.9582 x 10 10 to 4.8185 x 10 1 0 number/hr.litre, whereas the growth rate varied from 2.3546 to 2.4768 mm/hr. At 25°C, - 79 -when the residence time was 50 seconds and the crystal suspension density was 71 gr/1, the nucleation rate varied from 12.427 x 10 1 0 to 11.012 x 10 10 number/hr.litre and the growth rate from 1.7439 to 1.8350 mm/hr. The reproducibility of the supersaturation was very good given that, because of its small magnitude, it is difficult to measure accurately. The supersaturation varied from 0.8636 to 0.8371 gr NaaSOit/kg solvent in duplicate experiments at 25°C with a residence time of 40 seconds and a crystal suspension density of 33.8 gr/1. At 35°C, the measured supersaturation varied from 0.3972 to 0.3444 gr Na2S0i+/kg solvent when the residence time was 120 seconds and the suspension density was 66.8 gr/1. Similarly, measurements of the mean size of the crystal product from identical experiments showed good reproducibility. The mean size varied from 0.1165 to 0.1138 mm in experiments conducted at 30°C with a residence time of 60 seconds and a crystal suspension density of 69 gr/1. The variation was from 0.1088 to 0.1002 mm at 25°C, a residence time of 80 seconds, and a crystal suspension density of 46.7 gr/1. Run numbers 2, 4, 13, 17, 27, 37, 42, 49, 53, 58, 62, 64, 73 and 77 are duplicates of their respective preceding runs. For data analysis, average values of duplicate data were used. - 80 -3.3 Preliminary Procedures 3.3.1 Na2S0lf Solubility in MeOH/HzSO^/HaO Mixtures In order to determine the maximum expected yield of sodium sulfate in the salting out process the solubility of sodium sulfate in the mother liquor must be known. The main crystallizer feed (25.0% w/w Na2S0t+, 28.5% w/w H2SO4, 46.5% w/w H 20) has a composition which represents a 25% solution of sodium sulfate in a 38% w/w sulfuric acid solvent. Upon addition of the salting out agent, which is an 80% w/w aqueous methanol solution, neutral anhydrous sodium sulfate is precipitated and the mother liquor that is produced is a supersaturated solution of sodium sulfate in a mixed solvent containing salting out agent and 38% w/w sulfuric acid. In order to obtain solubility data relevant to the salting out process, the equilibrium solubility of sodium sulfate was determined in mixtures of the two components 80% w/w MeOH and 38% w/w I^SOi*; the H 20 component being fixed in each. The solubility was determined in solvents of different methanol concentrations at 25, 30, and 35°C, and for the range of solvent composition where the saturated solution is in equilibrium with the neutral anhydrous sodium sulfate. This was found to be true when the salting out agent made up at least 60% of the total solvent mass, which is the concentration realized in the crystallizer when the ratio of the salting out agent to the main feed is 1.125 gr/gr. At this ratio, the mother liquor solvent contains 1.125 parts - 81 -by weight of salting out agent and 0.75 parts of 38% w/w H2S0it which makes the mass fraction of salting out agent in the solvent equal to (1.125/(1.125 + 0.75)) 0.6. The procedure involved the preparation of solvents of different alcohol concentration made up of mixtures of the two components 80% w/w MeOH and 38% w/w HaSOi*. Each of two duplicate samples of each solvent was accurately weighed in a glass jar. A known weight of sodium sulfate was added and the jar was sealed with an air tight lid. The contents were placed in a constant temperature shaker and kept for 48 hours to reach an equilibrium state. Equilibrium was assumed.to exist after 48 hours in the jars which left some solid undissolved. The procedure was repeated with a larger weight of sodium sulfate for the jars which contained liquid phase only. This was done, instead of adding more solid to the existing jars, in order to avoid long contact times between the sulfuric acid and methanol which promote the possible reaction between them C H 3 O H + F ^ S O ^ + C H 3HSO IT + H 2 0 ( 3 . 1 ) causing some acid and methanol to be consumed (producing methyl hydrogen sulfate) and therefore altering the composition of the prepared solvent. At equilibrium, samples of the clear saturated solution were withdrawn from each jar and analysed for methanol, acid, and solid content - 82 -(Analytical procedures - Appendix K). The analysis showed that all the methanol and sulfuric acid initially present in the solvent were accounted for in the final saturated solution. i.e., that no measurable reaction had taken place between the methanol and the acid, and that no methanol had escaped from the jars during the 48 hour period. The residual equilibrium solid was filtered, washed with 80% w/w aqueous methanol and left to dry in an oven at 200°C. When dry and cool, it was weighed and dissolved in distilled water, and its acid content was determined by titration with standardized 0.1N NaOH. Since the hydrated forms of sodium sulfate have melting points well below 200°C, the residual solid which contained no acid and did not melt in the oven was assumed to be the neutral anhydrous sodium sulfate. Subsequent analysis of additional equilibrium samples which were allowed time periods longer than 48 hours to reach equilibrium showed that a period of 48 hours was sufficient for an equilibrium state to be attained and that the extent of the acid-methanol reaction producing methyl hydrogen sulfate, or the less likely product methyl sulfate ((CH3)2801+) , was only measurable after time periods much in excess of 48 hours and only at the higher temperature of 35 °C. The solubility data are given in Table 3.1 and plotted on Figure 3.2. The y-coordinate of Figure 3.2 is the solubility defined as the mass of sodium sulfate per unit Table 3.1 Solubility of sodium sulfate in mixed Me0H-H2S0i+-H20 solvents Solvent Composition Solubilil ;y, gr Na2S01+/^ ir solvent Equilibrium Solid gr 80% w/w MeOH gr 38% w/w H 2S0 4 T = 25 ° C T = 30 °C T = 35°C gr solvent gr solvent 0.6 0.7 0.8 0.9 0.4 0.3 0.2 0.1 0.0334 0.0205 0.0130 0.0076 0.0360 0.0227 0.0144 0.0081 0.0401 0.0254 0.0158 0.0087 Na2S01+ NazSO^ Na2SOl+ Na 2S0 4 - 84 --t- O C <0 <D > O CA O) o . in O in 3 o> -cr ® o > cn > -CD o . —) <\J O i f ) OH m o _ 3 O Ld o 0.5 • T • T • T 25 deg. C 30 deg. C 35 deg. C Solution + NaaS04 Solution 0.6 0.7 0.8 0.9 W gr (80% / w MeOH)/gr solvent 1. 0.5 0.4 0.3 0.2 0.1 W gr ( 3 8 / / w H2S04 ) /g r solvent o Figure 3.2 Solubility of sodium sulfate in mixed Me0H-H2S04-H20 solvents - 85 -mass of solvent. The x-coordinate is the solvent composition defined as the mass fraction of the salting out agent in the solvent; the remainder of the solvent being made up of 38% w/w H2S0i+. The solubility is seen to increase as the temperature is increased and decrease as the concentration of methanol in the solvent is increased. The rate of decrease of the solubility with respect to the methanol content of the solvent is maximum at the smallest methanol concentration and decreases as the methanol concentration increases. For example, the solubility of sodium sulfate in a solvent containing 60% w/w of salting out agent; the balance being 38% w/w H2S01+, is 33.4 gr Na2S01+/kg solvent at 25°C. At 35°C the solubility is increased to 40.1 gr/kg solvent in the same solvent. When the mass fraction of the salting out agent in the solvent is increased to 0.7, the solubility is decreased from 40.1 to 25.4 gr/kg solvent. When the mass fraction is increased to 0.9, the solubility decreases to 8.7 gr/kg solvent, at 35°C. Knowledge of the equilibrium solubility of the solute in the mother liquor provides the information required for the evaluation of the crystallizer yield in a Class II crystallization system in which the solute concentration in the crystallizer exit stream approaches the equilibrium concentration. Figure 3.3 plots the concentration of sodium sulfate per unit mass of solvent versus the mass fraction of the salting out agent in the solvent. The bottom curve - 86 -o gr (80 /£ W /w MeOH)/gr solvent Figure 3.3 Concentration of sodium sulfate in the mother liquor solvent as a function of the mass fraction of the salting out agent in the solvent - 87 -represents the equilibrium concentration (solubility) at 25°C. The straight line represents the concentration of sodium sulfate in the feed per unit mass of total incoming solvent. For example, when the ratio of the salting out agent to the main feed is 3.0 gr/gr, the mass fraction of the salting out agent in the mother liquor solvent is (3.0/(3.0 + 0.75)) 0.8 and the concentration of sodium sulfate per unit mass of total solvent at the inlet to the crystallizer is (0.25/(3.0 + 0.75)) 0.0667 gr/gr. When the ratio is 4.25 gr/gr, the mass fraction of the salting out agent in the solvent is (4.25/(4.25 + 0.75)) 0.85 and the inlet concentration of sodium sulfate is (0.25/(4.25 + 0.75)) 0.05 gr/gr of total solvent. Assuming an approach to equilibrium is realized in the crystallizer, then in terms of the parameters a and b, a represents the amount of solid precipitated, a + b represent the amount of solid in the feed, and therefore the quantity a/(a + b) is the fraction of the inlet solid that is precipitated, defined here as the yield. Figure 3.4 shows the yield of sodium sulfate at 25°C as a function of the amount of salting out agent added, again expressed here as the mass fraction of the salting out agent in the mother liquor solvent. The yield is seen to increase initially as the added amount of salting out agent is increased up to a point of maximum yield (80.5%) and then start to decrease upon further addition of salting out - 88 -CO 00 X I + D o CD r -Q r-in o ~1 I I | | | | | | 1 0.5 0.6 0.7 0.8 0.9 1.0 gr (80% W /w MeOH)/gr solvent Figure 3.4 Yield of sodium sulfate as a function of the mass fraction of the salting out agent in the mother liquor solvent - 89 -agent. Maximum yield is obtained when the mass fraction of the salting out agent in the mother liquor solvent is about 0.8, which is the concentration produced when the ratio of the salting out agent to the feed is 3.0 gr/gr. The parameter (a) gives a measure of the density of the crystal suspension and can be thought of as a redefined crystal suspension density per unit mass of solvent (MT is defined per unit volume of suspension). Figure 3.5 shows the change in (a) as the mass fraction of the salting out agent in the mother liquor solvent is increased. (a) is smaller when the mother liquor solvent contains more salting out agent. i.e., the crystal suspension density generated in the crystallizer is smaller when the ratio of the salting out agent to the main feed is higher. 3.3.2 Sieve Analysis The size distribution of the crystal samples withdrawn from the crystallizer during the crystallization experiments was determined by a standard sieve analysis procedure using a sieve shaker. The nest of sieves contained ten 3 inch U.S. standard screens and a bottom pan. The screen aperture sizes were 53, 63, 75, 90, 106, 150, 180, 212, 250, and 300 microns. Prior to experimentation it was desirable to obtain an estimate of the length of time required for "complete" sieving. In order to determine an approximate time period gr (80% / w MeOH)/gr solvent Figure 3.5 Density of the crystal suspension as a function of the mass fraction of the salting out agent in the mother liquor solvent i - 91 -at the end of which sieving was essentially complete, three crystal samples were taken from three preliminary experimental runs and the size distribution of each as given by sieve analysis was determined after 10, 20, 30, 45, 60, and 120 minutes of cumulative sieving time. The data indicated that after a sieving period of 60 minutes, there was no significant change in the crystal size distribution upon further sieving. Accordingly, this sieving period was used for all crystal samples withdrawn from the crystallizer during the main experimental program. Figure 3.6 shows the mean crystal size as a function of the cumulative sieving time for a crystal sample taken at 35°C, a residence time of 60 seconds, and a salting out agent/main feed ratio of 3.0 gr/gr. At 60 minutes, the rate of decrease of the mean size with sieving time is about 0.03 microns/minute. Figures 3.7 and 3.8 show the extent to which the calculated growth rate and the calculated nucleation rate, determined from the size distribution of the same crystal sample, were influenced by the time allowed for sieve analysis. The continued decrease in the mean crystal size with sieving time even after a period of 60 minutes was a possible indication that some crystal breakage might have been taking place during the sieve analysis. Microscopic examination of the sieved crystals showed that some crystals were broken. However, the same was also true for the - 92 -OD CM W c 2 * O <M in o _ Osl CD CM 0 H 1 1 1 T " 40 80 120 SIEVING TIME, minutes 160 Figure 3.6 Crystal mean size versus sieving time - 93 -40 80 120 SIEVING TIME, minutes Figure 3.8 Crystal nucleation rate versus sieving time - 94 -40 80 120 SIEVING TIME, minutes Figure 3.8 Crystal nucleation rate versus sieving time - 95 -unsieved crystals, some of which had apparently been fractured upon contact with the turbine impeller in the crystallizer. The small magnitude of the rate of decrease of the mean crystal size with sieving time (1.5 microns from 60 to 120 minutes) suggested that crystal breakage, if occurring during the sieve analysis, was not taking place to any significant extent. This was confirmed by the microscopic examination of the crystals which revealed that crystal fracture, whether caused by the turbine impeller in the crystallizer or by the sieving procedure, was small. Given the possibility of crystal fracture during sieving, it was considered that the crystal size distribution determined after 60 minutes of sieving time was the best approximation for the true crystal size distribution. 3.3.3 Time Required for Steady-State The method of analysis of the size distribution data of the crystal samples withdrawn from the crystallizer during the crystallization experiments, to yield the kinetic rates of growth and nucleation, is based upon the assumptions of steady-state operation and the existence of MSMPR conditions within the crystallizer. It was therefore necessary to ensure that these assumptions were satisfied during an experiment before samples could be taken for analysis. The former would be satisfied provided sufficient time was allowed for the attainment of a steady flow situation so - 96 -that no parameter of the system was changing with time. In order to obtain an estimate of the length of time (as a multiple of the residence time) that was required to bring about steady-state conditions in the crystallizer, three preliminary test experiments were conducted at different residence times in which the transient CSD was determined at regular time intervals equivalent to one residence time, beginning at one residence time after the setting of the feed flow rates, and for a total time period equivalent to fifteen residence times. The CSD was determined by sieve analysis of the fifteen crystal samples withdrawn from the crystall.izer during each experiment. The results showed that a time period equivalent to about four residence times was sufficient for a steady-state crystal size distribution to exist in the crystallizer. This was indicated by an effectively constant crystal mean size with time after four residence times. During the main experimental program, a minimum of six residence times was allowed for the attainment of a steady-state in each experiment before samples were taken for analysis. 3.3.4 Uniformity of the Crystal Suspension An essential requirement of the experimental crystallizer set-up was that the crystallizer be operated as closely to ideal MSMPR conditions as is practically - 97 -attainable, i.e., a perfectly mixed crystal suspension in the crystallizer and an unclassified continuous removal of the mixed product. It was therefore necessary, prior to the beginning of the main experimental program, to determine the turbine impeller rotational speed which would satisfy these requirements for all experimental conditions tested. The minimum impeller RPM which uniformly suspended the maximum crystal suspension.of about 71 gr/1 that was generated in the crystallizer at 25°C, a residence time of 120 seconds, and a salting out agent/main feed ratio of 1.75 gr/gr, was found to be 600. This determination was made from the data obtained from a preliminary experiment, which was conducted under the conditions that produced the maximum suspension density, and in which impeller RPM was a variable. At each RPM, crystal slurry samples were withdrawn from the crystallizer at three different levels; top, middle, and bottom. The top sample was taken from approximately one inch below the surface of the suspension and the bottom sample was taken one inch from the bottom of the vessel. The density of the crystal suspension and the mean size of the crystal distribution at each level were determined. The suspension density was calculated from the mass of crystals/volume of suspension withdrawn, and the mean size was determined from a sieve analysis of the isolated crystals. Additionally, crystal slurry samples were taken - 98 -from the crystallizer exit stream and analyzed in the same manner. A uniformly distributed crystal suspension was assumed to exist when the data showed that there was no significant difference between the crystal suspension densities and the mean crystal sizes in the exit stream and the top, middle and bottom levels of the crystallizer. It was found that these conditions were satisfied when the impeller RPM was at least 600. At this RPM, analysis of mother liquor samples from the top, middle, and bottom levels, for acid content, showed that good liquid phase mixing was also achieved. Table 3.2 shows the suspension density and mean size data collected at 600 RPM. The data indicate that the assumptions of a perfectly mixed crystal suspension and unclassified product removal are justified. The turbine impeller RPM used during all crystallization experiments was 600. It was assumed that a crystal suspension of smaller density than the maximum would also be perfectly mixed at this RPM. 3.3.5 Shape Factor of NAgSO^ Crystals The calculation of the nucleation rate from the CSD data requires knowledge of the volume shape factor of the precipitated crystals. The volume shape factor, k , relates the volume of a crystal of characteristic size L to the volume of a cubic crystal of the same size. Table 3.2 Crystal suspension density and mean size data at 600 RPM Crystal Crystal Suspension Mean Density Size gr/1 mm Ex: Lt T< 3P Midc H e Bottom 68.06 0.1192 67.47 0.1189 73.91 0.1212 74.16 0.1214 71.53 0.1219 71.41 0.1222 69.21 0.1205 72 .88 0.1184 72 .04 0.1201 70.12 0.1227 74.90 0.1180 67.64 0.1245 73 .01 0.1221 69.39 0.1200 68.37 0.1247 71.45 0.1259 • 69.85 0.1246 71 .08 0.1238 70.46 0.1193 69.38 0.1198 Average 70.90 69.89 71 .37 71 .10 0.1216 0.1215 0.1207 0.1220 - 100 -Volume of crystal = k yL 3 (3.2) Knowledge of k v permits the conversion of the crystal size distribution from a mass basis, as it is determined by sieve analysis, to a number basis which is the form of distribution most useful for the determination of the nucleation and growth rates. The volume shape factor of the sodium sulfate crystals produced in the crystallizer was determined for four different crystal sizes. Analysis of variance of the data showed that k v was not a function of crystal size. The average k v was determined to be 0.1707 for all sizes. The procedure required that a number of crystals from each sieve fraction of average size L retained between two adjacent screens of aperture sizes Lx and L 2, where L = (Lx + L2)/2, be weighed and counted. The volume shape factor of crystals of size L was then calculated from M C k = 3 (3.3) N p L c c where pc is the crystal density (0.002698 gr/mm3), and M c and Nc are the mass and number of the crystals counted respectively. The mass of the crystals was determined with an accuracy of ± 0.2 mg. Nine determinations of kv were made for each crystal size. The data are given in Table 3.3. Table 3.3 Shape factor data for four crystal sizes Crystals produced at Mean S ize = 0.2 75 mm Mean S ize = 0.2 31 mm Mean S ize = 0.196 mm Mean Size = 0.165 mm Crystal Mass (gr) Crystal Count k V Crystal Mass (gr) Crystal Count k V Crystal Mass (gr) Crystal Count k V Crystal Mass (gr) Crystal Count k V T = 30 ° C, t = 120s 0.0035 0.0045 0.0073 0.0085 0.0096 345 522 909 859 959 0.1808 0.1536 0.1431 0.1764 0.1784 0.0043 0.0030 0.0068 0.0149 0.0020 614 569 1460 2320 371 0.2106 0.1585 0.1400 0.1931 0.1621 0.0047 0.0015 0.0090 0.0013 0.0018 1089 527 2398 465 493 0.2125 0.1401 0.1847 0.1376 0.1797 0.0034 0.0016 0.0011 0.0010 0.0026 1162 885 667 560 1165 0.2414 0.1492 0.1361 0.1473 0.1841 T = 35 ° C, t = 60s 0.0023 0.0025 0.0025 0.0031 261 254 235 290 0.1571 0.1754 0.1896 0.1905 0.0024 0.0017 0.0016 0.0022 455 310 351 364 0.1586 0.1649 0.1371 0.1817 0.0020 0.0015 0.0014 0.0019 526 457 405 587 0.1872 0.1616 0.1702 0.1593 0.0015 0.0022 0.0010 0.0018 749 834 442 1120 0.1652 0.2177 0.1867 0.1326 Average 0.1717 0.1674 0.1703 0.1734 - 102 -3.3.6 Mother Liquor Sampling It was expected that, when a crystal slurry sample, withdrawn from the crystallizer, was vacuum filtered To separate the crystals from the mother liquor, some methanol would evaporate from the mother liquor due to the vacuum. Investigation of this potential problem in the laboratory showed that methanol evaporation was in fact taking place during filtration. The amount of methanol that evaporated depended upon the sample temperature, the concentration of methanol in the mother liquor, and the length of time the mother liquor was subjected to vacuum. When the purpose of the filtration was to isolate the solid crystal sample for analysis, the methanol loss from the mother liquor did not present an analytical problem and was essentially irrelevant. However, when it was required to isolate the mother liquor sample for analysis, the methanol loss presented an undesirable source of error. Although the amount of methanol lost during filtration, even under extreme conditions, was not large enough to significantly influence the accuracy of most analyses, it was desirable to try to eliminate this problem especially since the method that was to be used to measure the supersaturation required that no methanol was lost from the isolated mother liquor samples in order for an accurate supersaturation to be determined. In an attempt to solve the problem, pressure filtration of the crystal slurry sample was considered and - 103 -tried. It was found that with pressure filtration, as with vacuum filtration, some methanol was still lost from the mother liquor by flash evaporation upon exit of the mother liquor from the pressure filter. This idea was therefore abandoned. It was finally determined that a mother liquor sample could be separated from the solid crystals without experiencing any loss in methanol if a modified hypodermic syringe, with its top cut off and replaced by a glass filter, were used to draw the mother liquor into the syringe directly from the crystallizer, through the filter. This procedure was therefore used to collect mother liquor samples during all crystallization experiments conducted. 3.3.7 Methanol Loss During Crystallization In order to better characterize the prevailing conditions during crystallization it was considered useful to examine the potential problem of methanol loss from the crystallizer by evaporation due to the relatively high methanol volatility. Since the salting out agent was not a pure but a diluted solution of methanol, which was further diluted upon mixing with the acid-feed in the crystallizer, and given that a short residence time was used, it was not expected that any significant amount of methanol would be lost. To confirm this, a preliminary experimental run was conducted at the highest working temperature considered (35°C), the longest residence time (120 seconds), and the - 104 -largest salting out agent/feed ratio (4.25 gr/gr) which produced the highest concentration of methanol in the crystallizer. At steady-state, mother liquor samples were withdrawn and analyzed for methanol, acid, and solid content. The results showed that there was no measurable loss of methanol from the crystallizer under the prevailing experimental conditions. The same data also showed that the potential reaction between methanol and sulfuric acid producing methyl hydrogen sulfate did not take place to any measurable extent. Since the experimental conditions in this preliminary run were chosen to be most favourable for methanol evaporation and the methanol-acid reaction, it was not expected that these effects would be significant under any other set of experimental conditions. 3.3.8 Crystallization of NaHSOi+'HaO The main acid-feed prepared as 25.0% w/w Na2S01+, 28.5% w/w H2S04, and 46.5% w/w H20, has a composition which allows the crystallization of sodium bisulfate monohydrate if the solution is cooled below the temperature at which it becomes saturated with the dissolved salt. In order to prevent the crystallization of the acid salt in the feed tank, it was necessary to ensure that the feed temperature was above the saturation temperature of the acid-feed solution. Since the minimum feed temperature used was 19°C, it was sufficient to determine that the acid-feed solution remains undersaturated - 105 -when it is cooled down to 19°C. A sample of the acid-feed was prepared and kept at a constant temperature of 19°C in a constant temperature environment for 48 hours. No crystallization had occurred after 48 hours indicating that the temperature of 19°C was greater than the temperature at which the acid-feed solution is saturated. There was, therefore, no danger of crystallization of the acid salt in the main acid-feed tank. 3.3.9 Calibration of Rotameters The two rotameters which were used to measure the volumetric flow rates of the main acid-feed and the salting out agent to the crystallizer were calibrated with the working fluids at 25°C. At each rotameter setting, three determinations of the volumetric flow rate were made by measuring the volume of fluid flowing in a given time. Average values were used to plot the calibration curves. The volumetric flow rate was also determined at selected rotameter settings, at 19 and 31°C, to estimate the change in the flow rate with temperature. The data indicated little change in the volumetric flow rate with temperature over the temperature range considered. The calibration curves determined at 25°C could be used for all feed temperatures with an estimated maximum possible error in the flow rate of ± 1%. The calibration curves are given in Appendix G. - 106 -3.3.10 Densities of the Main Crystallizer Feed and the Salting Out Agent In order to calculate the mass flow rates of the crystallizer feed and the salting out agent to the crystallizer, the densities of the respective fluids at the feed temperature must be known. The density of each fluid was determined as a function of temperature by accurately weighing (± 0.2 mg.) constant temperature samples of accurately known volume (50 ± 0.05 mis). When rounded off to the nearest third decimal place, both densities varied linearly with temperature over the temperature range tested.. The density of the main acid-feed was described by the relationship, Pa = -0.0002 T c + 1.479 (3.4) where T c is the temperature in degrees C, and pa is the acid-feed density in gr/ml, and the density of the methanol solution salting out agent was given by, Pm = -0.0004 Tc + 0.845 (3.5) where pm is the methanol solution density in gr/ml. The density plots are given in Appendix H. - 107 -3.4 Experimental Procedures 3.4.1 Preparation of Feed Materials The main feed to the crystallizer which has the composition 25.0% w/w Na2S0i+, 28.5% w/w H2SC>4 and 46.5% w/w H 20 was prepared accordingly by weighing and mixing the correct amounts of sodium sulfate, concentrated (93.0% w/w) sulfuric acid, and distilled water. Analytical grade sodium sulfate and technical grade sulfuric acid were used. Weighing accuracy was to the nearest .05 kilogram. The minimum weight determined at any time was 7 kilograms (sodium sulfate). The salting out agent was prepared as an 80% w/w aqueous methanol solution using commercial methanol. A minimum of 10 kilograms of methanol was weighed to the nearest .05 kilogram. The weight of the water component was determined to the nearest .5 grams. The feed materials were transferred to their respective feed tanks in the constant temperature water bath. When they had attained the required feed temperature, the system was ready for an experiment. 3.4.2 Continuous Crystallization Experiments To begin an experiment, the feed tanks were slightly pressurized with compressed air to maintain a constant - 108 -pressure of about 2 psig in the tanks during the experiment. The crystallizer drain was plugged on the inside with a cork and the turbine impeller speed was set at 600 RPM. The feed pumps were switched on and the flow in each line was adjusted to the required flow rate. This flow situation was allowed to continue undisturbed for a period of time equivalent to six residence times after which a steady-state was assumed to have been achieved. The mean residence time of the crystal suspension, x, was calculated from x = V/Q0 where V is the crystallizer volume and Q 0 the total exit volumetric flow rate which was non-different from the total inlet volumetric flow rate. At steady-state, two crystal slurry samples were withdrawn from the crystallizer for CSD analysis and two mother liquor samples for supersaturation measurement. 3.4.3 Crystal Sampling and Sample Treatment Samples of the crystal suspension were withdrawn using a 60 mis hypodermic syringe which had a catheter tip of 7 mm inside diameter. The sample withdrawal point was half-way between the surface of the crystal suspension and the bottom of the crystallizer, and withdrawal was quick to prevent classification. The sample was quickly filtered to separate the solid crystals from the mother liquor before any further crystallization could take place. Filtration was carried - 109 -out under vacuum using a glass filter of medium porosity (10-15 microns). When all the mother liquor had passed through the filter the vacuum was shut off and the crystals were sprayed with an 80% w/w aqueous methanol solution from a spray bottle. The slurry was swirled on the filter to suspend the crystals in the wash solvent and the vacuum was then switched on again to remove the wash solvent from the filter. The crystals were washed twice again in the same manner. This washing procedure removed essentially all adhering mother liquor from the crystal surfaces and helped prevent the formation of crystal agglomerates (any agglomerates formed were easily broken up during the sieve analysis). After washing, the filter was disconnected from the vacuum flask and the washed crystals were gently brushed off the filter and collected on a glass dish. The dish was left in an oven for 24 hours to dry the crystals at 200°C. When dry and cool, the crystal sample was analyzed for size distribution using sieve analysis. The sample was sieved for 60 minutes on a sieve shaker in the nest of sieves described in section 3.3.2. The mass of crystals retained on each screen was determined with an accuracy of ± 0.2 mg (crystal size distribution data from all experiments are given in appendix C). The sieved crystals were dissolved in distilled water and the solution was titrated for acid with 0.1N NaOH to determine that the crystals were of the neutral - 110 -sodium sulfate. The acid content of the crystal samples from all experiments never exceeded 0.1% of the total crystal mass. The mass of crystals divided by the volume of the suspension withdrawn, which was measured in the syringe, gave the crystal suspension density MT« The suspension density determined this way was in good agreement with the suspension density calculated from a mass balance. The latter, since it was more accurate, was used for data analysis. 3.4.4 Measurement of the Supersaturation Initial attempts to calculate the supersaturation from the expression S = w - w , where w is the concentration eq of sodium sulfate in the mother liquor and w is the eq equilibrium concentration of sodium sulfate in the mother liquor, showed that the supersaturation data were not reproducible when duplicate experiments were conducted. Although each of the two quantities w and w e q could be accurately determined with an estimated maximum error of ± 2%, the combined error relative to the small magnitude of the difference w-weq was significant and caused unacceptable scatter in the data. While this was not totally unexpected, particularly in a salting out system, it was desirable to determine whether or hot, because of the short residence times used in the experiments, the - Ill -supersaturation in the crystallizer was large enough to be accurately measured this way. This was not true and therefore an alternative procedure was used. The procedure for the determination of the supersaturation of the mother liquor utilized the fact that, when a clear supersaturated mother liquor sample is allowed sufficient time to reach saturation or equilibrium conditions, the excess dissolved solute which represents the supersaturation of the solution is precipitated. Each of the two mother liquor samples withdrawn from the crystallizer during an experiment using a 100 mis modified syringe as described in section 3.3.6, was quickly transferred to a pre-weighed glass jar which had an air-tight lid. The jar was weighed again to determine the weight of the mother liquor sample, and the contents were kept in a small constant temperature water bath for 48 hours to reach a state of equilibrium. The temperature in the water bath was controlled to the same temperature that existed in the crystallizer during the experiment which was known to the nearest 0.1°C. At the end of 48 hours the jar contained a saturated solution and a solid residue. The composition of the saturated solution could be calculated from the knowledge of the ratio of the salting out agent to the main feed that was used during the experiment, which determined the alcohol concentration in the mother liquor - 112 -solvent, and the solubility data which determined the solid content of the saturated solution. The solid residue was separated from the saturated solution using a glass filter of medium porosity (10 - 15 microns). The solid retained on the filter was washed with an 80% w/w aqueous methanol solution and left to dry in an oven at 200°C. When dry and cool its weight was determined with an accuracy of ±0.2 mg. The mass of the residue divided by the mass of the solvent part of the saturated solution gave the supersaturation per unit mass of solvent. For each experiment two determinations of the supersaturation were made. The average value was used for data analysis. 3-5 CSD Instability It was observed at the temperatures of 25 and 30°C and at an alcohol/feed ratio of 4.25 gr/gr only, that below a minimum residence time of about 60 seconds, there is a sudden sharp increase in the crystal nucleation rate and as a result a sharp decrease in the mean crystal size as was observed at residence times of 40 and 50 seconds. This finding is consistent with the concept of the metastable region of supersaturations which is located above the normal solubility curve and within which a given state of supersaturation is said to be sustainable with little danger of uncontrolled nucleation (Figure 2.1). The upper boundary of the metastable zone shows the maximum limit of allowable - 113 -supersaturations and forms the metastable or supersolubility curve. When the level of supersaturation is driven beyond the maximum allowable metastable limit S (Figure 2.2b), nisix an explosive increase in crystal nucleation occurs relieving the system of supersaturation in excess of the maximum allowable and reducing the crystal size distribution to mostly fine particles. It is suggested that in the present case, by operating the crystallizer at the short residence times of 40 and 50 seconds, the level of supersaturation momentarily induced in the crystallizer exceeded a maximum limit for the system under the prevailing conditions causing an explosive increase in nucleation thus relieving the system of unsustainable supersaturation and sharply reducing the crystal size. Knowledge of the width of the metastable zone for crystallizing systems is of significant value. It is, however doubtful that in practice the so called metastable or supersolubility curve is a sharply defined line. Rather it is more likely that the change from a metastable to an unstable supersaturated state occurs over a transition zone where a gradual shift from power-law nucleation kinetics to uncontrolled nucleation is effected. With this in mind and noting that experimental measurements of the supersaturation include the inherent - 114 -experimental error, it can be said that for the present system at 25°C and an alcohol/feed ratio of 4.25 gr/gr, a supersaturation of 0.6219 gr Na2S0i+/kg solvent appears to lie within the range of stable supersaturations, while a supersaturation of 0.7512 gr NaaSOit/kg solvent is possibly in excess of the maximum in that range (see dataset 1 - note that higher stable supersaturations could be maintained at other alcohol/feed ratios). Similarly at 30°C and an alcohol/feed ratio of 4.25 gr/gr supersaturations of 0.6313 and 0.6924 gr Na2S0i+/kg solvent appear to lie within and outside the range of stable supersaturations respectively (see dataset 2). Since power-law kinetics no longer hold for uncontrolled nucleation the results obtained under such suspected conditions were not used for the estimation of the power-law kinetic model parameters. Specifically run numbers 1, 2, 3, 4, 22 and 23 were excluded. Nucleation and growth are two parallel simultaneous processes competing to produce the crystal suspension in an MSMPR crystallizer. At a given residence time, when a given suspension density is being produced by more nucleation and less growth, the crystal size is decreased. When the same suspension is being produced by more growth and less nucleation, the crystal size is increased. Also the higher the rate of nucleation operative in an MSMPR crystallizer - 115 -producing the same suspension, the smaller the growth rate at constant residence time; this being a mass balance constraint on the system. The total suspension mass produced in an MSMPR crystallizer, where a crystal growth rate of G and a crystal nucleation rate of B are operative and where the feed materials contain no suspended solids, is given by MT = 6pckvn0(GT)" (3.6) where n° = B/G. Therefore in the present case, when the nucleation rate was increased to excessive levels because the supersaturation driving force was driven beyond a maximum stable nucleation limit, the growth rate correspondingly decreased to satisfy mass balance requirements despite the high supersaturation level (see datasets 1, 2). Figure 3.9 is a log-log plot of the mean crystal size versus residence time for three alcohol/feed ratios. It shows the decrease in the mean crystal size caused by excessive nucleation at 25°C. In contrast to the slow steady increase in crystal size with residence time expected under stable conditions (alcohol/feed = 1.75, 3.0), there is a sudden drop in size with decreasing residence time at the alcohol/feed ratio of 4.25 gr/gr caused by the sharp rise in nucleation at that breakpoint. - 116 -O CD —1 C D " E ^ r -£ o n -•t i. i M C \ J " c o 2 : 7 1 c D i < \n ^ r -o : 0 0 -o C\J " f\l I O 10 T = 25 deg. C Alcohol/feed gr/gr ,n • \ 1 I ™ 1 3 5 10 | I | II I 3 5 103 RESIDENCE TIME, sec. Figure 3.9 Effect of residence time on the crystal mean size - 117 -CHAPTER 4 DATA ANALYSIS AND RESULTS 4.1 Determination of the Growth and Nucleation Rates from the Steady-State CSD Data The crystal size distribution generated in an ideal MSMPR crystallizer operating at steady-state when the feed materials are free of suspended solids, is given in terms of its basic population density function as n = n° exp[-L/GT] (4.1) where n is the population density of crystals of size L, n° is the population density of the nuclei, G is the growth rate, and t is the mean residence time. Taking natural logs, In n = In n° - L/Gx (4.2) Therefore the theoretical CSD from ideal MSMPR crystallizers when plotted as the natural log of the crystal population density versus the crystal size, forms a straight line with a slope of -1/Gx and an intercept equal to In n°. Crystal size distributions from experimental MSMPR crystallizers often closely approximate the theoretical straight line relationship, and by fitting the experimental CSD to the - 118 -theoretical form of the distribution, i.e., by finding the slope and intercept of the least-squares line that best fits the experimental ln n versus L data, the growth rate is calculated from the slope of the line, given the residence time, G = - 1 (slope)(x) (4.3) and the nucleation-rate is calculated from B = n°G (4.4) where n° = exp[intercept] (4.5) This procedure was used here to calculate the growth and nucleation rates from the steady-state crystal size distribution in each experiment. Since the experimental crystal size distribution, as determined by sieve analysis, was defined on a mass basis, it was first necessary to derive population density data from the mass distribution. For each crystal size fraction retained between two adjacent screens of aperture sizes Li and L2, the population density of size L was calculated from y mt n " i (4.6) P c k y L 3 ( L 2 - l o - 119 -where L = (Lx + L2)/2 and y is the mass fraction of crystals retained. Figure 4.1 shows a In n versus crystal size plot for the crystal size distribution that was generated in the crystallizer at 25°C when the residence time was 80 seconds and the crystal suspension density was 34 gr/1 (run number 6). Allowing for experimental inaccuracies, the experimental data points show a good straight line relationship between In n and the crystal size as predicted by theory. Appendix D contains In n versus crystal size plots from all experiments conducted. The calculation of the population density data and the least-squares analysis that was required to determine the growth and nucleation rates in each experiment was performed by the main computer program which was written for this purpose. A copy of the program is given in Appendix E. Appendix F contains the input data to the program which is read on the two logical input units 4 and 5. On unit 4, the program reads for each experiment (one line per experiment) - Feed temperature, °C - Crystallizer temperature, °C - Residence time, seconds - Supersaturation, gr/kg solvent and, - The point of operation on the x-axis of Figure 3.2. - 120 -0.1 0.2 0.3 SIZE (mm) F i g u r e 4 . 1 In n v e r s u s c r y s t a l s i z e (T = 2 5 ° C , x = 80s Mt = 34 g r / 1 ) - 121 -On unit 5 the program reads the mass of crystals (gr) retained on each of the ten sieves and in the pan. The crystal density pc, the volume shape factor kv, and the sieve aperture sizes were supplied as data input to the program. The set of experiments which included the concentration of the chromium impurity as a variable was analysed with a modified version of the main program which also read on unit 4 the concentration of chromium in the feed, in parts per million. 4-2 Results for the Chromium-Free System In the absence of the chromium impurity, growth and nucleation rate data were collected at three temperatures, 25, 30 and 35°C. All data are contained in datasets 1, 2 and 3 which are classified by temperature. Table 4.1 gives the results for dataset 1 at 25°C. Table 4.2 classifies the four major variables in the same set, the growth rate, the nucleation rate, the supersaturation, and the mean crystal size as a function of the residence time and the average suspension density; suspension density being slightly different at different residence times. This format allows for quick observation of the effect of residence time and suspension density on the main variables in the system. The same format is maintained for datasets 2 and 3 in Table 4.4 Table 4.1 Summary of results for run numbers 1-21 (Dataset 1) RUN TEMPERATURE ALCOHOL/ 1 2 3 4 5 6 7 8 9 1 0 1 1 12 13 14 15 16 17 18 19 20 2 1 (deg. C) 25 .0 25 .0 25 .0 25 .0 25 .0 25 . O 25 .0 25 .0 25 .0 25.0 25 .0 25 .0 25.0 25 .0 25 . O 25.0 25 .0 25.0 25.0 25 .0 25 . 0 ACID-FEED RATIO (gr/gr) 2500 2500 2500 2500 2500 2500 2500 2500 0000 0000 0000 OOOO 3.0000 3.0000 3.0000 1.7500 1.7500 1.7500 1.7500 1.7500 1.7500 RESIDENCE SUSPENSION SUPERSATURATION CRYSTAL TIME (Sec.) 40.0 40.0 50.0 50.0 60.0 80.0 1 0 0 . 0 1 2 0 . 0 40.0 50.0 60.0 80.0 80.0 1 0 0 . 0 1 2 0 . 0 NUCLEI NUCLEATION CRYSTAL COEFFICIENT YIELD 50.0 50.0 6 0 . 0 8 0 . 0 100.0 120.0 DENSITY (gr/kg solvent) GROWTH POPULATION RATE MEAN OF OF (gr/i) RATE DENSITY (1/hr.1) SIZE VARIATION Na2S04 (mm/hr) (1/mm.1) (mm) (X) (%) 33 .77 0 . 8636 1 .4187 0 .2187E+12 0 .31026E+12 0 .0614 41 .91 77 . 79 33 . 79 0 .8371 1 .4258 0 .1843E+ 12 0 . 26279E+12 0 .0562 46 . 14 77 .84 33 .87 0 .7512 1 .2104 0 .1791E+12 0 . 21673E+12 0 .0676 43 .03 78 .01 33 .85 0 . 7784 1 .2783 0 .1518E+12 0 .19405E+12 0 .0852 39 . 15 77 .96 33 .98 0 .6219 1 .3348 0 .5348E+11 0 . 7 1387E+11 0 .0954 43 .86 78 .27 34 .07 0 .5185 1 .0357 0 .4619E+1 1 0 .47838E+11 0 .0974 42 .77 78 .48 34 . 15 0. ,4323 0 .8371 0 .4282E+1 1 0 . 35845E+11 0 . 1007 40 .46 78 .65 34 .21 0. .3584 0 . 7500 0 .3247E+11 0 . 24352E+11 0 . 1008 50. .38 78 .80 46 .43 0. ,8930 1 .9824 0 .7235E+11 0 .14342E+12 0 .0958 38, .68 79 . 16 46 .50 O. ,8164 1 . 6989 0 .5306E+11 0 •90143E+11 0 .0987 43, . 14 79 . 28 46. .60 0. 7003 1 .4464 0 .4789E+11 0, ,6927 1 E+ 1 1 0 . 1044 43 , .56 79 .45 46 . 75 0. 5320 1 . 1602 0 .3690E+11 0, .42816E+11 0 . 1088 42 , .70 79 .70 46 . 73 0. 5514 1 . 1568 0, .4103E+11 0, .47466E+1 1 0 . 1002 52 . 07 79 .67 46 , 81 0. 4628 1 .0138 0, , 2577E+1 1 0. ,26128E+11 0 . 1 170 48 . 40 79 .81 46 . 87 0. 3977 0 .8205 0, .3118E+11 0. 25580E+11 0 . 1081 53. .47 79 .90 71 . 08 0. 8145 1 . 7439 0. 7126E+1 1 0. 12427E+12 0 , 1079 39 . 59 78 . 69 71 . 08 0. 8069 1 . 8350 0. 6001E+11 0. 11012E+12 0 . 1084 41 . 26 78 .69 71 . 20 0. 6718 1 . 5888 0. 5186E+11 0. 82393E+1 1 0 , 1084 44. 29 78 . 83 71 . 30 0. 5679 1 .2318 0. 4118E+11 0. 50730E+11 0, , 1 183 41 . 23 78 .93 7 1 . 35 0. 5115 1 . . 1379 0. 2505E+11 0. 28505E+11 0, . 1238 44 . 78 78 . 99 71 . 42 0. 4381 1 , ,0114 0. 2066E+11 0. 20893E+11 0. , 1 199 51 . 54 79 .06 DO CO - 123 -Table 4.2 Summary of results for dataset 1 classified by residence time and average suspension density (T = 25°C) Alcohol/Acid--feed Ratio (gr/gr) Alcohol/Acid--feed Ratio (gr/gr) 4.25 3.0 1.75 4.25 3.0 1.75 Mj - 33.96 " r - 46. .67 Mj - 71.24 Mt - 33.96 Mt - 46. .67 M - 71.24 g/1 g/1 g/1 g/1 g/1 g/1 40s 50s 60s 1003 12Chs 1.4187 1.4258 1.2104 1.2783 1.3348 1.0357 0.8371 0.7500 1.9824 1.6989 1.4464 1.1602 1.1568 1.0138 0.8205 1.7439 1.8350 1.5888 1.2318 1.1379 1.0114 40s 50s 60s 80s 100s 120s 31.026 26.279 21.673 19.405 7.1387 4.7838 3.5845 2.4352 14.342 9.0143 6.9271 4.2816 4.7466 2.6128 2.5580 12.427 11.012 8.2393 5.0730 2.8505 2.0893 Crystal Growth Rate (mm/hr) 10" x Nucleation Rate (number/h-litre) Alcohol/Acid-feed Ratio (gr/gr) 4.25 3.0 1.75 Hp - 33.96 Hj. - 46.67 t^ - 71.24 g/1 g/1 g/1 Alcohol/Acid-feed Ratio (gr/gr) 4.25 3.0 Mj - 33.96 g/1 Supersaturation (gr Na2S0 /^kg solvent) Crystal mean size (mm) 1.75 Hj - 46.67 g/1 Mj - 71.24 g/1 T _ 40s 0. ,8636 0. , 89 30 T „ 40s 0. .0614 0. .0958 0. .8371 0, .0562 T - 50s 0. ,7512 0. ,8164 0. ,8145 T - 50s 0. .0676 0. .0987 0. .1079 0. ,7784 0. .8069 0. .0852 0. ,1084 T - 60s 0. ,6219 0. .7003 0. ,6718 T - 60s 0. .0954 0. ,1044 0. ,1084 T - 80s 0. 5185 0, .5320 0. ,5679 T 80s 0. ,0974 0. 1088 0. 1183 0. .5514 0. 1002 T - 100s 0. 4323 0. ,4628 0. 5115 T - 100s 0. 1007 0. 1170 0. 1238 T - 120s 0. 3584 0. ,3977 0. 4381 T - 120s 0. 1008 0. 1081 0. 1199 - 124 -and Table 4.6 respectively. The complete results for dataset 2 are given in Table 4.3. Table 4.5 contains dataset 3. The experimental data were used to test the validity of the kinetic models G = K GS g (4.7) for the crystal growth rate, and B = K B S b (4-8) for the nucleation rate, where K g = A g exp[-EG/RT] ( 4 . 9 ) and K b = Ab exp[-EB/RT] (4.10) and to determine the values of the kinetic parameters AG' EG a n d g' a n d AB' EB a n d b t h a t b e s t describe the kinetics in this system. Additionally, the nucleation rate equation B = K N ^ s U (4.11) Table 4.3 Summary of results for run numbers 22-40 (Dataset 2) RUN no. TEMPERATURE (cleg. C) ALCOHOL/ ACID-FEED RATIO RESIDENCE TIME (Sec. ) (gr/gr) 22 30 .0 4.2500 40 .0 23 30 .0 4.2500 50 .0 24 30 .0 4.2500 60 .0 25 30 .0 4.2500 80 .0 26 30 .0 4.2500 100 .0 27 30 .0 4.2500 100 .0 28 30 .0 4.2500 120 .0 29 30 .0 3.0000 40 .0 30 30 .0 3.0000 50 .0 31 30. .0 3.0000 60. .0 32 30. .0 3.0000 80. ,0 33 30. 0 3.0000 100. .0 34 30. 0 3.0000 120. 0 35 30. 0 1.7500 50. 0 36 30. 0 1.7500 60. 0 37 30. 0 1.7500 60. 0 38 30. 0 1.7500 80. 0 39 30. 0 1.7500 100. O 40 30. 0 1.7500 120. 0 SUSPENSION DENSITY (gr/1) 32 . 89 33.06 33. 12 33 . 22 33 . 31 33 . 28 33 . 31 45 . 17 45 . 25 45.38 45 . 40 45 . 52 45 . 58 68 . 88 69 .05 69.01 69. 17 69 . 24 69.34 SUPERSATURATION CRYSTAL 0.8895 0.6924 0.6313 0.5121 0.4106 4372 4014 8637 7725 6199 5918 NUCLEI NUCLEATION CRYSTAL COEFFICIENT YIELD O 0 0 0 0 0 0.4632 3880 9010 7148 7566 0.5800 0.5104 0.3956 0. 0. 0. 0. GROWTH POPULATION RATE MEAN OF OF RATE DENSITY (1/hr.l) ' SIZE VARIATION Na2S04 (mm/hr) (1/mm.1) (mm) (%) (%) 1 . 5973 0 .1452E+12 0 . 23191E+12 0 .0769 41 .75 75 .92 1 . 3848 0 .1006E+12 0 . 13928E+12 0 .0930 39 .99 76 .32 1 .6976 0 .1930E+11 0 .32760E+11 0 . 1016 49 .87 76 .44 1 . 1488 0 .2766E+11 0 .31781E+11 0 . 1006 52 .67 76 .68 1 .0775 0 . 1494E+11 0 . 16103E+ 1 1 0 . 1 102 56 . 33 76 .88 1 .0822 0 . 1489E+11 0 .16116E+1 1 0 . 1099 50 . 19 76 .83 0 .9096 0 . 1442E+11 0 .13119E+11 0 . 1 104 50 .55 76 .90 2 . 2824 0 .3958E+11 0 .90345E+11 0 . 1043 46 .73 77 . 16 2 .0111 0 •2721E+11 0 • 54718E+1 1 0 . 1052 46 . 55 77 .30 1 .5858 0 .3107E+11 0 .49266E+11 0 .1112 42 . 19 77 . 53 1 .2181 0 .3162E+1 1 0 .3851 1E+1 1 0 .0980 50 . 19 77 .57 1 .1351 0 . 1712E+1 1 0. .19439E+1 1 0 . 1093 54, ,92 77 . 77 1 .0291 0. . 1 188E+1 1 0 . 12223E+1 1 0 . 1246 52 . 62 77 . 88 2 . 1936 0. -2847E+11 0. ,62451E+1 1 0 . 1 130 47 . 39 76 .41 1 . 9227 0. 2403E+11 0, , 46198E+1 1 0 . 1 165 47 . 06 76 .60 1 . 9225 0. 2486E+11 0. 47793E+11 0 . 1 138 54 . 14 76. .55 1 . 6234 0. 1516E+11 0. 24615E+11 0 . 1287 51 . 40 76. . 73 1 .2913 0. 1591E+11 0. 20542E+11 0. ,1241 58 . 84 76 . £0 1 . 1434 0. 1295E+11 0. 14812E+11 0. 1345 58 . 17 76 , 91 to Ol - 126 -Table 4.4 Summary of results for dataset 2 classified by residence time and average suspension density (T = 30°C) Alcohol/Acid-feed Ratio (gr/gr) Alcohol/Acid-feed Ratio (gr/gr) -4.25 3.0 1.75 4.25 3.0 1.75 Mj - 33.17 g/1 Mt - 45.38 g/1 Mr - 69.12 g/1 Kj - 33.17 g/1 Mj - 45.38 g/1 Mj - 69.12 g/1 T " 40s 1.5973 2.2824 T - 40s 23.191 9.0345 T = 50s 1.3848 '2.0111 2.1936 t = 50s 13.928 5.4718 6.2451 T = 60s 1.6976 1.5858 1.9227 1.9225 T « 60s 3.2760 4.9266 4.6198 4.7793 T •=> 80s 1.1488 1.2181 1.6234 T - 80s 3.1781 3.8511 2.4615 T = 100s 1.0775 1.0822 1.1351 1.2913 T = 100s 1.6103 1.6116 1.9439 2.0542 T -120s 0.9096 1.0291 1.1434 T -120s 1.3119 1.2223 1.4812 Crystal Growth Rate (mm/hr) 10-io x Nucleation Rate (number/h •litre) Alcohol/Acid-feed Ratio ' (gr/gr) Alcohol/Acid-feed Ratio (gr/gr) 4.25 3.0 1.75 4.25 3.0 1.75 Mj - 33.17 g/1 Mt - 45.38 g/1 Mt - 69.12 g/1 Mt - 33.17 g/1 Mt - 45.38 g/1 Mp - 69.12 g/1 T «= 40s 0.8895 0.8637 T " 40s 0.0769 0.1043 T » 50s 0.6924 0.7725 0.9010 T - 50s 0.0930 0.1052 0.1130 T » 60s 0.6313 0.6199 0.7148 0.7566 T • 60s 0.1016 0.1112 0.1165 0.1138 T » 80s 0.5121 0.5918 0.5800 T " 80s 0.1006 0.0980 0.1287 T » 100s 0.4106 0.4372 0.4632 0.5104 T -100s 0.1102 0.1099 0.1093 0.1241 T " 120s 0.4014 0.3880 0.3956 T -120s 0.1104 0.1246 0.1345 Supersaturation (gr Na2SOi,/kg solvent) Crystal Mean Size (mm) Table 4.5 Summary of results for run numbers 41-62 (Dataset 3) RUN no . TEMPERATURE (deg. C) ALCOHOL/ ACID-FEED RATIO RESIDENCE TIME (Sec.) SUSPENSION DENSITY (gr/i) SUPERSATURATION (gr/kg solvent) ( g r / g r ) 4 1 35 .0 4.2500 40 .0 32 .05 0 .8595 42 35 .0 4.2500 40 .0 32 .09 0 .8125 43 35 .0 4.2500 50 .0 32 . 13 0 .7719 44 35 .0 4.2500 60 .0 32 . 27 0 . 6023 45 35 .0 4.2500 80 .0 32 .42 0 .4291 46 35 .0 4.2500 100 .0 32 .41 0 . 4400 47 35 .0 4.2500 120 .0 32 .50 0 .3401 48 35 .0 3.0000 40 .0 43 .82 0, .8956 49 35 .0 3.OOOO 40 .0 43 . 83 0. . 8843 50 35 .0 3.0000 50. .0 43 .89 0. ,8166 51 35 .0 3.0000 60. .0 44 . 06 0. 6225 52 35 .0 3.0000 80. .0 44. . 13 0. 5462 53 35 .0 3.0000 80. 0 44 . 14 0. 5331 54 35 . 0 3.0000 100. 0 44 . 19 0. 4818 55 35 . 0 3.0000 120. 0 44 . 30 0. 3514 56 35 . 0 1.7500 50. 0 66 . 44 0. 8074 57 35 . 0 1.7500 60. 0 66. 53 0. 7105 58 35 . 0 1.7500 60. 0 66. 57 0. 6628 59 35 . 0 1.7500 80. 0 66 . 66 0. 5648 60 35 . 0 , 1.7500 100. 0 66 . 77 0. 4394 61 35 . 0 1.7500 120. 0 66. 81 0. 3972 62 35 . 0 1.7500 120. 0 66 . 85 0. 3444 CRYSTAL GROWTH RATE (mm/hr) 2.3546 2.4768 1.9965 1.9437 1.4539 1.2438 0.9093 2.8383 2.4981 2.1769 1.9385 1 .5481 1.4192 1.3864 1.0875 2.5631 2.1137 2.2401 1.8214 1.4520 1.2252 1.2355 NUCLEI POPULATION DENSITY (1/mm.1 ) 0.2530E+11 0. 1945E+1 1 0.1987E+11 0. 1 1 1 1E+11 0.1090E+11 0.8340E+10 0 NUCLEATION RATE (1/hr.1) CRYSTAL MEAN SIZE (mm) 0.1384E+1 1 0.1653E+1 1 0.2556E+11 0.1942E+11 0. 0. 1517E+1 1 0. 0. 1192E+11 0. 0.1709E+11 0. 0.7513E+10 0. 0.1005E+11 0. O. 1551E+1 1 0. 0.1620E+11 0. 0. 1299E+11 O. 9898E+10 0. 9591E+10 0. 8516E+10 0. 9386E+10 0. .59582E+11 . 48185E+1 1 . 39669E+11 .21600E+11 .15853E+11 .10373E+11 . 12589E+1 1 .46925E+11 .63855E+11 .42287E+ 1 1 .29402E+11 1845 1 E+ 1 1 24257E+11 10416E+11 10932E+11 39747E+11 34243E+11 29096E+ 1 1 18029E+11 13926E+11 10434E+11 11595E+11 0.1236 1334 1453 1461 1553 1535 COEFFICIENT YIELD OF OF VARIATION Na2S04 (%) 0.0945 0.1000 0.1041 O.1104 0.1205 0.1237 0.1195 0.1174 0.1154 1098 1 136 1 191 1 128 1354 1325 1254 51 .90 53.87 50. 36 56. 16 46.99 53.03 47.03 50. 18 47.50 49.47 53. 13 53.22 53. 19 58.29 51.21 55 .84 49.86 51 .74 53 . 82 50.63 64.01 56.63 (%) 74 . 14 74 . 24 74.32 74 . 66 75.00 74 .98 75. 18 75.03 75.05 75. 15 75.44 75.56 75.58 75.65 75.85 73 . 84 73.94 73 . 99 74 .09 74 . 21 74.25 74.31 to <1 - 128 -Table 4.6 Summary of results for dataset 3 classified by residence time and average suspension density (T = 35°C) Alcohol/Acid-feed Ratio (gr/gr) Alcohol/Acid-feed Ratio (gr/gr) 4.25 3.0 1.75 4.25 3.0 1.75 Mj - 32.27 g/1 Mt - 44.05 g/1 Mt - 66.66 g/1 Mj - 32.27 8/1 Mt - 44.05 g/1 Hj - 66.66 g/1 T - 40s 2.3546 2.4768 2.8383 2.4981 t - 40s 5.9582 4.8185 4.6925 6.3855 T - 50s 1.9965 2.1769 2.5631 t - 50s 3.9669 4.2287 3.9747 T - 60s 1.9437 1.9385 2.1137 2.2401 t - 60s 2.1600 2.9402 3.4243 2.9096 T • 80s 1.4539 1.5481 1.4192 1.8214 t - 80s 1.5853 1.8451 2.4257 1.8029 T » 100s 1.2438 1.3864 1.4520 T - 100s 1.0373 1.0416 1.3926 T - 120s 0.9093 1.0875 1.2252 1.2355 t - 120s 1.2589 1.0932 1.0434 1.1595 Crystal Growth Rate (mm/hr) io- 1 0 x Nucleation Rate (number/h' •litre) Alcohol/Acid-feed Ratio (gr/gr) Alcohol/Acid-feed Ratio (gr/gr) 4.25 3.0 1.75 4.25 3.0 1.75 Mt - 32.27 g/1 MT - 44.05 g/1 Mj - 66.66 g/1 Mt - 32.27 g/1 Mt - 44.05 g/1 Hj, - 66.66 g/1 T - 40s 0.8595 0.8125 0.8956 0.8843 t - 40s 0.0945 0.1000 0.1174 0.1154 T « 50s 0.7719 0.8166 0.8074 x - 50s 0.1041 0.1098 0.1254 T - 60s 0.6023 0.6225 0.7105 0.6628 T " 608 0.1104 0.1136 0.1236 0.1334 T - 80s 0.4291 0.5462 0.5331 0.5648 x - 80s 0.1205 0.1191 0.1128 0.1453 T - 100s 0.4400 0.4818 0.4394 T - 100s 0.1237 0.1354 0.1461 T - 120s 0.3401 0.3514 0.3972 0.3444 t - 120s 0.1195 0.1325 0.1553 0.1535 Supersaturation (gr Na2S0i,/kg solvent) Crystal Mean Size (mm) - 129 -which contains a nucleation dependence on the crystal suspension density was tested in parallel with Equation (4.8) to determine if the nucleation rate was influenced by the density of the crystal suspension. The experimental data were also used to estimate the kinetic parameters of the relative kinetic equations B ~ K b G l (4.12) and B = K n MJ g V (4.13) to provide a basis for comparison between the relative kinetic order i (or v) which was estimated independently of the supersaturation data, and the ratio of the nucleation rate kinetic order to the growth rate kinetic order b/g (or u/g) which depends on the estimated values of the individual kinetic orders g and b (or u) which in turn depended on the supersaturation data. At each temperature, the constants of the five kinetic rate equations (4.7), (4.8), (4.11), (4.12) and (4.13) were determined by curve-fitting the experimental data to the linearized (log) form of the equations using linear regression. For example, considering the general power-law function - 130 -Y = ci Xf3 ( 4 > 1 4 ) then, by taking logs the function can be linearized to give log Y = log ci + c2log Xx + c3log X 2 (4.15) from which the constants clt c 2 and c3 can be estimated by simple linear least-squares from experimental data of Y, Xi and X 2. Table 4.7 gives the fitting parameters to the kinetic rate equations with a 95% confidence interval for each parameter at 25°C. Table 4.8 and Table 4.9 give the fit results at 30 and 35°C respectively. Note that the standard deviation is the deviation of the log variable and not of the actual kinetic rate. Similarly, the correlation coefficient is based on the correlation of the log variables. Table 4.10 summarizes the fitted functions at three temperatures. Examination of the confidence intervals of the kinetic orders shows that the kinetic orders remained (statistically) non-changing with temperature. i.e., there was no significant difference in their fitted estimates at different temperatures as determined by statistical testing. Small changes in the magnitude of the fitted estimates with temperature were caused by experimental scatter. The growth rate kinetic order g was the least variable between temperatures changing from 1.0514 to 1.0067 Table 4.7 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 25°C G: mm/hr B: no/hr 1 suspension S: gr/kg solvent T gr/1 suspension Correlation Standard Fitting Parameters Fitted Model Coefficient Deviation ^ r y S t f 1 e. 0 3442 1 nsia log G » 0.3442 L T l G = l 0 g KG - ± 0 ^ 3 0 1 * - ± l ' m i + 1.0514 log S 0.9853 0.0229 log B - 11.855 B • 4 s U ^ - " i S u J - ; o i S l U - ±*0^3838 - ° - 3 6 « * * ° ' 9 6 3 3 0.0771 General _ ... m i + 2.1839 log S Nucleation ° Model B - K log B = 11.593 - >4 Gv log K - i 1 : 5 " - v - 2 - 1 1 8 7 - 0.6336 log M 0.9566 0.0837 n T n ± 0.6786 J ± 0.40fiS v + n A m i T + 2.1187 log G I to I—' I Non-Secondary Nucleation Model K„S K, G b . „ 11.213 l 0 S B " ± 0.1158 log K, 10.539 ± 0.0749 2.0843 ± 0.4194 1.8813 ± 0.5037 log B - 11.213 + 2.0843 log S log B - 10.539 + 1.8813 log G 0.9480 0.9130 0.0879 0 .1126 Table 4.7 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 25°C G: mm/hr B: no/hr 1 suspension S: gr/kg solvent Mt: gr/1 suspension „. _„, - - Correlation Standard Fitting Parameters F l t t e d M o d e l Coefficient Deviation Crystal Growth Model G = K S ® G log Kg . 0.4036 " ± 0.0516 g 1.0067 = ± 0.1875 log G - 0.4036 + 1.0067 log S 0, .9549 0.0398 General Nucleation B = K n MJ SU l 0§ K n • 11.438 ± 0.6298 1 - ~ J ± 0, .2551 .3553 u 2, + .1736 0.3722 log B = 11.438 - 0.2551 log Mj + 2.1736 log S 0, .9656 1 H* 0.0756 W M Model B = Kn M^j, GV log K^ = , 10.936 ± 0.9516 j - " J ± 0. ,4622 ,5819 V _ 2. + ,0204 0.5781 log B = 10.936 - 0.4622 log M t + 2.0204 log G 0. .9121 1 0.1192 Non-Secondary Nucleation B - Kb Sb log % . 10.991 ± 0.1033 b _ 2.1031 ± 0.3752 log B = 10.991 , + 2.1031 log S 0. 9584 0 . 0 7 9 7 Model B = K, G1 b log Kb - 10.185 ' ± 0.1131 i 1.8499 ± 0.5717 log B = 10.185 + 1.8499 log G 0. 8888 0.1280 Table 4.7 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 25°C G: mm/hr B: no/hr 1 suspension S: gr/kg solvent V gr/1 suspension Fitting Parameters Crystal Growth Model KLS log K 0.4635 ± 0.0408 0.9420 ± 0.1425 Fitted Model log G - 0.4635 + 0.9420 log S Correlation Coefficient Standard Deviation 0.9642 0.0374 General Nucleation Nucleation 4 -i „ 10.975 l o g *N = ± 0.6144 log K 10.559 ± 0.7146 - 0.1174 ± 0.3673 - 0.3790 ± 0.4368 1.7619 ± 0.3412 1.7834 ± 0.4154 log B - 10.975 - 0.1174 log Hj, + 1.7619 log S log B - 10.559 - 0.3790 log Mt + 1.7834 log G 0.9475 0.9266 0.0890 0.1047 CO CJ Non-Secondary Nucleation Model K S B •= K,G D log K. log K. 10.781 ± 0.0952 9.9465 b ± 0.1155 1.7608 ± 0.3330' 1.7297 ± 0.4404 log B - 10.781 + 1.7608 log S log B - 9.9465 + 1.7297 log G 0.9457 0.9076 0.0874 0.1130 Table 4.10 Summary of kinetic rate equations as determined by curve-fitting experimental data to the respective kinetic models at three temperatures G: mm/hr B: no/hr 1 suspension S: gr/kg solvent V gr/1 suspension x - 25°C T » 30"C X - 35°C Crystal Growth Model G - 2.2090 s1'0514 G -2.5328S 1 . 0 0 6 7 G - 2.907A S 0' * 9 4 2 0 General Nucleation Model 7 . 1 6 X 1 0 U 3 6 4 3 s 2 . 1 8 3 9 1 1 u - 0 . 6 3 3 6 q Z * 1 1 8 7 B - 3.92 x 10  M^ ' B - 2.74 x 1 0 U Mj- 0' 2 5 5 1 S 2 ' 1 7 3 6 B - 8 . 6 3 x 1 0 1 0 m ^ " 0 ' 4 6 2 2 G 2 - 0 2 0 ^ B - 9.44 x 1010 M ^ " 1 ' 4 S B - 3 . 6 2 x 1 0 l C m t ~ 0 ' 3 7 9 0 G 1 , 7 8 3 1 1 - 0 . 1 7 4 «1.7619 05 Non-Secondary Nucleation Model B - 1.63 x 1011 S 2' 0 8" 3 B - 3.46 x 1010 G 1 ' 8 8 1 3 B - 9 . 8 x 1010 S 2 ' 1 0 3 1 B - 1.53 x 1010 G 1 - 8 4 9 9 B - 6.04 x 1010 S 1 ' 7 6 0 8 B - 8.84 x 109 c1'7297 - 135 -to 0.9420 at. 25, 30 and 35°C respectively. The growth rate constant was a function of temperature increasing (a from 2.2090 at 25°C to 2.9074 at 35°C. The growth kinetics were essentially first order and enhanced by a higher temperature. Figure 4.2 shows the effect of temperature on the growth kinetics. The linear relationship between the log of the growth rate and the log of the supersaturation was verified by the experimental data, allowing for experimental scatter. i.e., the power-law relationship between the growth rate and the supersaturation (Equation (4.7)) was valid for the representation of the growth kinetics in this system. The kinetic parameter j which describes the dependence of the nucleation rate on the crystal suspension density was a non-significant correlation parameter and showed that there was no true relationship between the nucleation rate and the suspension density. j was statistically non-different from zero at 35 and 30°C, and just approached significance at 25°C, with negative point estimates. The apparent negative correlation between the nucleation rate and the suspension density was created by the nature of the experimental error. For example, in a system where the true value for j is zero, experimental data will always show an apparent correlation because of the scatter in the data, i.e., j will take on non-significant non-zero values. In - 136 -• T A T • T 25 deg. C 30 deg. C 35 deg. C T 10"1 2 3 4 5 6 7 8 910' SUPERSATURATION S, gr /kg solvent Figure 4.3 Effect of temperature on the nucleation kinetics - 137 -this system, non-significant negative values for j appeared to minimize the variation in the nucleation rate data. Correlat ion plots of the nucleation rate corrected for the apparent suspension density effect are given in Appendix A. Scatter plots for all fitted kinetic rate equations are given in Appendix B. The lack of evidence of any real correlation between the nucleation rate and the crystal suspension density indicated that the non-secondary nucleation model B = K BS b is a more valid representation of the nucleation kinetics in the system. The nucleation rate kinetic order b showed reasonable variation between temperatures changing from 2.0843 to 2.1031 to 1.7608 at 25, 30 and 35°C respectively. The nucleation rate constant K g was a function of temperature, decreasing with temperature from 1.63 x 10 1 1 at 25°C to 6.04 x 10 1 0 at 35°C. i.e., the nucleation rate was inhibited at higher temperatures. Figure 4.3 shows the effect of temperature on the nucleation kinetics. Again, the linear relationship between the log variables was verified, although there was more scatter in the nucleation rate data than in the growth rate data. The slope of the straight line represents the nucleation order b. At 25 and 30°C, the lines are almost parallel. At 35°C, the straight line has a slope of smaller magnitude reflecting the - 138 -a SUPERSATURATION S, gr /kg solvent Figure 4.3 Effect of temperature on the nucleation kinetics - 139 -apparent decrease in the nucleation order to 1.7608. The change in the magnitude of b at that temperature, however, was statistically non-significant; all three estimates of b being consistent with a constant value for b with temperature. The relative kinetic order i showed less variation between temperatures changing from 1.8813 to 1.8499 to 1.7297 at 25, 30 and 35°C respectively. Since its determination was independent of the supersaturation data, it is probably a more accurate estimate of the true relative kinetic order of the system, compared to the relative kinetic order calculated from the ratio b/g which depended on the supersaturation. The supersaturation data, because of measurement difficulties, possibly contained more significant error than the growth or nucleation rate data, and therefore would have influenced the estimated values of g and b accordingly. The values of the ratio b/g calculated from the estimates of the individual kinetic orders at each temperature were 1.9824, 2.0891 and 1.8692 at 25, 30 and 35°C respectively. These values are slightly deviated from but compare well with the values of i at the corresponding temperatures. Since a high temperature enhanced the growth rate and inhibited the nucleation rate, the relative kinetic constant K b was expectedly a decreasing function of temperature - 140 -changing from 3.46 x 1010 at 25°C to 8.84 x 109 at 35°C. Figure 4.4 shows the effect of temperature on the relative kinetics. A higher temperature shifts the straight line relationship downwards which represents a decrease in K . b Having determined that the nucleation rate in the system was independent of the crystal suspension density and that there was no change in the order of the growth or the nucleation kinetics with temperature, all data were used to estimate the fitting parameters of the kinetic rate equations G = AG exp[-EG/RT] ( 4 > 1 6 ) for the growth kinetics, and B = AB exp[-Eg/RT] S b ( 4 > 1 ? ) for the nucleation kinetics which included the temperature dependence of the rate constants K„ and K , and (j B temperature was used as a second independent variable. This procedure established for each rate equation an average kinetic order over the temperature range considered, and simultaneously determined the temperature dependence of the kinetic rate constant. For this fit, the parameters AG, E g and g, and Ag, Eg and b were determined using the more accurate non-linear parameter estimation - 141 -1 1 I I I ' I I 2 3 4 5 6 7 10° 2 3 GROWTH RATE G, mm/hr I I I ' ' 4 5 6 7 101 Figure 4.3 Effect of temperature on the n u c l e a t i o n kinetics - 142 -techniques. The functions that best fit the experimental data were G = 43962 exp[-24626/RT] s 0 ' 9 7 0 7 (4.18) for the growth rate, and B = 0.064 exp[70870/RT]S2" 1 0 5 5 (4.19) for the nucleation rate, where R is in kJ/kmole.K. The average growth rate kinetic order in the system was 0.9707 and the activation energy for growth was 24626 kJ/kmole. The average order of the nucleation kinetics was 2.1065 and the activation energy for nucleation was negative at -70870 kJ/kmole. Figure 4.5 shows a scatter plot for the fitted growth rate equation (4.18). Most of the experimental growth rate data falls within 15% of the values predicted by the equation. Figure 4.6 shows the scatter plot for the nucleation rate equation (4.19). Because of the greater variation in the nucleation rate, the nucleation rate data is mostly contained within the wider limits of ± 25% of the values predicted by the equation. 4-3 Results for the Impure System The effect of the chromium impurity on the kinetic rates of growth and nucleation was investigated at a - 143 -O PREDICTED GROWTH RATE, mm/hr Figure 4.5 Scatter plot for fitted growth rate equati G = 43962 exp[-24626/RT]S0'9707 - 144 -16.0 10 x PREDICTED NUCLEATION RATE, 1/hrJ Figure 4.6 Scatter plot for fitted nucleation rate equation B = 0.064 exp[70870/RT]S 2 * 1 0 6 5 a - 145 -constant temperature of 35°C and a constant crystal suspension density of about 32 gr/1. The impurity concentration levels tested were 75, 150 and 300 ppm of chromium in the main feed. The results obtained are summarized in Table 4.11. Table 4.12 classifies the data a a function of the residence time and the concentration of the impurity in the feed. In the presence of the impurity the growth rates that were operative in the crystallizer were higher than those measured in the pure sytem and the nucleation rates were lower. The mean size of the crystal product therefore increased. Figure 4.7 shows the effect of the impurity concentration in the feed on the measured growth rate. The rate of increase of the growth rate is maximum as the impurity concentration approaches zero with the effect diminishing as the concentration is increased. Figure 4.8 shows the measured nucleation rate as a function of the impurity concentration. The nucleation rate is seen to decrease as the concentration of the impurity in the feed was increased. Again, maximum effect is realized at low impurity concentration. The increase in the mean crystal size that occurred because of the reduction in the nucleation rate and the enhancement of the growth rate as the impurity concentration was increased is shown in Figure 4.9. Table 4.11 Summary of results for run numbers 63-77 (Dataset 4) RUN Cr ALCOHOL/ no. CONCENTRATION ACID-FEED IN FEED RATIO (ppm) (gr/gr) 63 64 65 66 67 68 69 70 7 1 72 73 74 75 76 77 75 75 75 75 75 . 150.0 150.0 150.0 150.0 300.0 300.0 300.0 300. 0 300.0 300.0 . 2500 . 2 500 . 2500 . 2500 . 2500 . 2500 2500 4.2500 . 2500 . 2500 . 2500 .2500 . 2500 2500 2500 RESIDENCE TIME (Sec. ) 40.0 40.0 60.0 80.0 120.0 40.0 60. 80. 120.0 40.0 40. O 60.0 80.0 120.0 120.0 .0 . 0 SUSPENSION DENSITY (gr/1 ) 32.30 32 . 27 32 . 43 32 . 46 32 .61 32 . 32 32 . 45 32.52 32 . 63 32.32 32 . 35 32.43 32 . 57 32 . 64 32.63 SUPERSATURATION CRYSTAL NUCLEI (gr/kg solvent) GROWTH POPULATION RATE DENSITY (mm/hr) (1/mm.l) 0.5742 0.6103 0.4232 O.3874 0.2169 0.5415 0.4005 0.3121 0.1859 0.5514 0.5 118 0.4161 0.2547 0.1800 0.1905 2.9548 2.9731 2.1272 1.6534 1 . 1108 3.1244 2.2676 1.6973 1.1420 3.3179 3.2851 2.4670 1.7528 1.1909 1.2242 0. 1017E+1 1 0.9903E+10 0.7471E+10 0.6189E+10 6007E+10 7836E+10 5859E+10 5419E+10 5176E+10 5816E+10 0.6088E+10 4333E+10 4722E+ 10 4242E+ 10 3739E+10 NUCLEATION CRYSTAL RATE (1/hr.1) COEFFICIENT YIELD 0.30064E+11 29442E+11 15892E+11 10233E+11 66722E+ 10 24482E+11 13287E+11 0.91974E+ 10 0.59107E+10 0.19295E+ 1 1 0.19999E+ 1 1 0.10690E+11 0.82777E+10 0.50515E+10 0.45769E+10 MEAN OF OF SIZE VARIATION Na2S04 (mm) (%) (%) 0 . 1 163 57 .68 74.71 0 . 1 156 59 .50 74.64 0 .1317 63 .88 75.02 0 . 1366 66 . 65 75 .09 0 .1421 65 . 53 75.43 0 . 1243 71 .21 74.78 0 . 1381 63. .69 75.06 0 . 1462 73 . 62 75.24 0 . 1492 73. . 19 75 . 49 0 . 1384 75 . 48 74.76 0 . 1393 79 . 05 74 . 84 0 . 1471 61 . 69 75.03 0. . 1556 74. 17 75 . 35 0. . 1604 74 . 31 75.50 0. 1692 70. 45 75.^8 05 - 147 -Table 4.12 Summary of results for dataset 4 classified by residence time and Cr r + t concentration (T = 35°C) Concentration of Cr+++ in main feed (pprn) 75 • 150 300 T • 40s 2. .t- as 3. .1244 3. .3179 2. 9731 3. .2851 T - 60s 2. 1272 2. .2676 2. 4670 T = 80s 1 . 6534 1. .6973 1 . 7528 T -- 120s 1 . 1108 1. ,1420 1 . 1909 1 . 2242 Crystal Growth Rate (mm/hr) Concentration of Cr*"4-*" in main feed (ppm) 75 150 300 T - 40s 3, 2. .0064 .9442 2, .4482 1.9295 1.9999 T » 60s 1. ,5892 1. .3287 1.0690 T - 80s 1 . 0233 0 . ,9197 0.8278 T - 120s 0 . 6672 0 . 5911 0.5052 0.4577 10 10 x Nucleation Rate (number/h-litre) Concentration of Cr+"H" in main feed (ppm) 75 150 300 T - 40s 0, 0. .5742 .6103 0.5415 0.5514 0.5118 T » 60s 0 . ,4232 0.4005 0.4161 T « 80s 0 . 3874 0.3121 0.2547 T - 120s 0 . 2169 0.1859 0.1800 0.1905 Supersaturation (gr Na2S01+/kg solvent) Concentration of Cr+++ in main feed (ppm) 75 150 300 T - 40s 0 . 0 . .1163 .1156 0.1243 0.1384 0.1393 T = 60s 0 . 1317 0.1381 0.1471 T - 80s 0 . 1366 0.1462 0.1556 T - 120s 0 . 1421 0.1492 0.1604 0.1692 Crystal mean size (mm) - 148 -O in L. JC o E * E o LJ I— < Qd CO 40 sec. 60 sec. 80 sec. 120 sec. / ^ O g <>i O CO o >- J OtL O o o 0 100 +++ 200 300 400 Cr CONCENTRATION, ppm Figure 4.7 Effect of the Cr + + + concentration in the feed on the operative growth rate (Parameter is residence time) - 149 -IT) p-L. _C -I O CD CO rn~ 40 sec. 60 sec. 80 sec. 120 sec. < Od o I— < in o 3 o CO CO >-OcZ O m \ \ \ \ \ \ o T N \ - A > 0 100 200 300 400 +++ Cr CONCENTRATION, ppm Figure 4.8 Effect of the Cr + + + concentration in the feed on the operative nucleation rate (Parameter is residence time) a - 150 -CD O r-—i o E -N i f ) < LJ in •t—i o CO 1—I o CO >-O 40 sec. 60 sec. 80 sec. 120 sec. / / / / / / / / CD o 0 100 200 300 +++ Cr CONCENTRATION, ppm 400 Figure 4.9 Effect of the Cr + + + concentration in the feed on the mean crystal size (Parameter is residence time) - 151 -In order to determine the effect of the impurity on the kinetic relationships of growth and nucleation, the parameters of the kinetic rate equations G = K S g (4.7) B - K BS b (4.8) and B = K bG x (4.12) were determined at each level of the impurity concentration by curve-fitting the experimental data to the linearized (log) form of the equations using linear regression. Only four data points were available for each fit and therefore the estimated parameters could only be predicted with limited confidence, as indicated by the relatively large confidence intervals of the parameters, in particular the nucleation parameters. The fitting parameters with their 95% confidence intervals, when the impurity concentration in the feed was 75 ppm, are given in Table 4.13. Table 4.14 and Table 4.15 give the fit results for the impurity concentration levels of 150 and 300 ppm respectively. Table 4.16 summarizes the fitted kinetic rate equations in the presence of the impurity. Table 4.13 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C - Cr feed concentration = 75 ppm Fitting Parameters Fitted Model Correlation Standard Coefficient Deviation Crystal Growth G = KGSg log K = 0.6729 ± 0.2736 0.9710 ± 0.6113 log G = 0.6729 + 0.9710 log S 0.9793 0.0446 Crystal Nucleation B = V B = V log 10.735 ± 0.6682 log K = 9.7211 5 b ± 0.2029 b = i = 1.4489 ± 1.4927 1.5275 ± 0.6583 log B = 10.735 + 1.4489 log S log B = 9.7211 + 1.5275 log G 0.9472 0.9901 0.1090 w bo 0.0477 Table 4.14 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C - Cr feed concentration = 150 ppm Correlation Standard Fitting Parameters Fitted Model Coefficient Deviation Crystal G = K S§ log K = °'7316 s = °' 9 4 1 2 lo§ G = °' 7 3 1 6 0 9949 0 0210 Growth b V ± 0 g ^G ± 0.1467 8 ± 0.2907 + 0.9412 log S "-9949 0.0230 r - K ina K- — 10. 678 , _ 1.2964 log B = 10. 678 n Q7,, A C r y s t a l B " KB S l 0 g K B " ± 0.4474 b " ± 0.8867 + t.2964 log S °'9757 °- 0 7 0 1 Nucleation i _ 9.6661 1.3917 log B = 9.6661 N QQno N N,-N B l^G log - ± Q > 1 8 8 1 i - ± Q i 5 7 5 4 + 1.3917 log G 0' 9 9 0 9 °'0431 i Ol w 05 Table 4.15 Fitting parameters (with computed 95% confidence levels) to kinetic rate equations at 35°C - Cr feed concentration = 300 ppm Fitting Parameters Fitted Model Correlation Coefficient Standard Deviation Crystal Growth G - KgS* log K = 0.7592 ± 0.1587 0.9087 ± 0.3013 log G = 0.7592 + 0.9087 log S 0.9941 0.0250 Crystal Nucleation B - V B = V log ^ = log ^ = 10.568 ± 0.5201 9.5712 ± 0.2439 b = i = 1.1851 ± 0.9878 1.3246 ± 0.6976 log B = 10.568 + 1.1851 log S log B = 9.5712 + 1.3246 log G 0.9645 0.9854 0.0820 £ l 0.0530 Table 4.16 Summary of kinetic rate equations as determined by curve-fitting experimental data to the respective kinetic models in the presence of the chromium impurity (T = 35°C) Cr**"*" concentration in feed (ppm) 0 75 150 300 Crystal Growth G = 2.9074 S0'9420 G = 4.7088 s0 , 9 7 1 0 G = 5.3899 s 0 , 9 4 1 2 G = 5. 7443 s 0 ' 9 0 8 7 I I-' Cn Ol B = 6.04 x 1010 S 1' 7 6 0 8 B = 5.43 x 1010 S1'4489 B = 4.76 x 1010 S1 . 2 9 6 4 B = 3 < 70 x 1010 S1 . 1 8511 Crystal Nucleation B = 8.84 x 109 G 1' 7 2 9 7 B = 5.26 x 109 G1'5275 B = 4.64 x 109 G1, 3 9 1 7 B = 3. 73 x 109 G1* 321+6 - 156 -The fit statistics considered together with the results in Table 4.9 for the pure system support the following conclusions about the effect of the impurity concentration on the kinetic parameters: - There is no real effect of impurity concentration on the growth rate kinetic order g. - There is evidence of a real increase in the growth rate constant K Q with increasing impurity concentration. - There is no real effect of impurity concentration on the nucleation rate kinetic order b. - There is no real effect of impurity concentration on the nucleation rate constant KD. D - There is no real effect of impurity concentration on the relative kinetic order i. - There is evidence of a real decrease in the relative kinetic constant with increasing impurity concentration. All of the above conclusions may be drawn by simple examination of the confidence intervals of the parameters. However, the trend in the data justifies some explanation. Figure 4.10 shows the effect of the impurity concentration on the growth kinetics. From visual observation of the Plot, and with consideration to the experimental scatter expected in the data, as defined by the scatter of the data - 157 -SUPERSATURATION S, gr /kg solvent Figure 4.10 Effect of the Cr + + + concentration in the feed on the growth kinetics • - 158 -points of the pure system, it can be seen that the slope of the line, which represents the growth rate kinetic order g, is non-changing with impurity concentration and that the data points at the 300 ppm level lie on a distinctly different line than that of the pure system. i.e., a line with a different KQ. These observations are supported by the fit statistics. Figure 4.11 shows the effect of the impurity concentration on the nucleation kinetics. The straight line represents the fitted kinetics for the pure system. The straight lines representing the kinetics at different impurity levels have not been drawn to prevent overcrowding of the figure, however the magnitude of the fitted estimates of both Kg and b showed a decreasing trend with increasing impurity concentration. This trend was not statistically justifiable as "real", and the results indicated that there was no effect of impurity concentration on the nucleation kinetics. Upon visual examination of Figure 4.11 it is easy to see why this might be true. All the data points on the figure, except for three or four outliers at the lower end of the supersaturation scale, are compatible with the straight line relationship of the pure system. It is suggested here that the true nucleation behaviour of the system was indeed independent of the impurity concentration, and that the apparent decrease in K B - 159 -00 r-CD in il co -CM ~ GQ Ld \— < S cm o «—( Z CD O r-I— CD < Ld in _] O z co -CM H o> o —t-• 0 ppm Cr in feed A 75 ppm Cr in feed • 150 ppm Cr in feed V 300 ppm Cr in feed 1 0 " ' T T 4 i — i — r 2 3 5 6 7 8 910° SUPERSATURATION S, g r / k g solvent Figure 4.11 Effect of the Cr + + + concentration in the feed on the nucleation kinetics - 160 -and b with increasing concentration was the result of the four outlying data points which contained significant error in their supersaturation coordinate which was apparently underestimated. Since only four data points were used for the estimation of the kinetic parameters at each level of the impurity concentration, a significant error in only one data point, especially in one of the "end" points, can cause the estimated parameters to deviate considerably from their true values. The assumption that the four outlying data points contained more significant error than the rest of the data finds good support when considering the procedure used for the measurement of the supersaturation. The maximum error introduced by this procedure to the measured values is likely to be a maximum absolute error rather than a maximum relative error. i.e., the accuracy of the procedure when used to measure a true supersaturation S is ± constant. Consequently the relative error in small values of S is greater than in larger values. On a log scale this represents greater variation in the supersaturation data at low supersaturations. The increased scatter at low supersaturations was also a factor influencing the estimated kinetics in the chromium-free system and probably accounted for the small apparent discrepancies between i and b/g. However, in this system, the presence of the chromium - 161 -impurity in the feed reduced the level of supersaturation that was generated in the crystallizer below the minimum encountered in the pure system, which made it even more difficult to measure accurately. Figure 4.12 shows the effect of the impurity concentration on the relative kinetics. Because of the increase in the growth rate constant K Q with increasing concentration of the impurity in the feed, there was an expected decrease in the relative rate constant Kfe as the impurity concentration increased. The small decrease in the slope of the line representing an apparent reduction in the relative kinetic order i with increasing impurity concentration, was non-significant given the extent of scatter expected from the data. In a system where the character of the experimental scatter is described in Figure 4.5 and Figure 4.6, four data points are not sufficient to establish an accurate correlation. 4-4 Effect of Variables on the CSD The kinetics of crystallization determined for this system would indicate that a larger crystal size may be expected at longer residence times, higher crystal suspension densities, and higher temperatures. The presence of the Cr + + + impurity in the crystallizing solution also appears to enhance the crystal size by increasing the growth - 162 -A 0 ppm Cr in feed 75 ppm Cr in 150 ppm Cr in 300 ppm Cr in 10 -i ~ I I I I u | 3 4 5 6 7 10° i — r 2 2 3 4 5 67 10' GROWTH RATE G, m m / h r Figure 4.11 Effect of the Cr+++ concentration in the feed on the relative kinetics - 163 -rate and decreasing the nucleation rate. Figures 4.13, 4.14, 4.15, and 4.16 show the effect of residence time, suspension density, temperature, and impurity concentration respectively, on the straight line In n versus crystal size distribution observed experimentally. A line with a slope of smaller magnitude represents a crystal size distribution with a larger mean size. Higher levels of each variable caused an increase in the mean crystal size. The effect of the crystal suspension density on the straight line is consistent with the determination that the nucleation process in the system was of the non-secondary type (when the nucleation rate is linearly dependent on the suspension density (j=l), a change in the suspension density produces g parallel straight line shifted upwards for higher density or downwards for lower density). In a given crystal system, the change in the orientation (and therefore slope and intercept) of the In n versus crystal size straight line in response to a change in an operating variable is determined by the kinetics of crystallization peculiar to the crystal system. Knowledge of the response of the system to changes in the experimental variables as described in Figures 4.13, 4.14, 4.15, and 4.16 therefore provides an alternative picture of the kinetic behaviour of the system. - 164 -O CRYSTAL SIZE, ( m m ) Figure 4.13 Effect of residence time on the CSD - 165 -O CRYSTAL SIZE, ( m m ) Figure 4.14 Effect of crystal suspension density on the (No evidence of secondary nucleation) I - 166 -O CRYSTAL SIZE, ( m m ) Figure 4.15 Effect of temperature on the CSD i - 167 -O 0.0 0.1 0.2 0.3 0. CRYSTAL SIZE, ( m m ) Figure 4.16 Effect of Cr + + + feed concentration on the CSD - 168 -CHAPTER 5 DISCUSSION AND CONCLUSIONS 5.1 System Variables 5.1.1 Supersaturation The level of supersaturation that exists in an operating crystallizer cannot be arbitrarily fixed. The adjustable parameters, over which control is possible in a crystallization process, include the crystallizer temperature, the mean residence time, the crystal suspension density and the concentration of added impurities in the crystallizing solution. The supersaturation level that is generated as a result of fixed values of these parameters is determined by the kinetics of growth and nucleation peculiar to the specific crystal system. The expression describing the steady-state supersaturation in an MSMPR crystallizer, when the kinetics of nucleation are of the non-secondary type, is given by Equation (2.50) AC 3 g + b S = (5.1) K3T4 from which it is seen that the supersaturation level is more sensitive to changes in the residence time (-u) than to the - 169 -same relative changes in crystal suspension density (AC). This is reflected in the experimental data obtained in this study. For example at 25°C, an increase in the residence time from 40 to 120 seconds caused a decrease in the supersaturation from 0.85 to 0.36 gr Na2S01+/kg solvent, whereas an increase in the suspension density from 34 to 71 gr/1 caused a smaller change in the supersaturation the extent of which is somewhat obscured by experimental error (e.g., from 0.52 to 0.57 gr Na2S04/kg solvent at a residence time of 80 sec). By changing the residence time of the crystal suspension in the crystallizer, significant changes in the level of supersaturation generated in the crystallizer were effected, and the corresponding changes in the growth and nucleation rates were measured. The data relating the growth rate to the supersaturation showed that the growth rate varied with the supersaturation to the power 0.9707, r qc qO • 97 0 7 G K s (5.2) The variation of the growth rate with the supersaturation, at three temperatures, is shown in Figure 4.2. The experimental data was consistent with a power-law relationship between the growth rate and the supersaturation. - 170 -The nucleation rate showed a stronger dependence on the supersaturation, varying with the supersaturation to the power 2.1065, R „ o 2 . 1 0 6 5 B S (5.3) The effect of the supersaturation on the nucleation rate, at three temperatures, is shown in Figure 4.3. the power-law relationship between the nucleation rate and the supersaturation was valid for the given data points. However, the data obtained under conditions of excessive nucleation, which were not included in the curve-fitting procedure, showed that the nucleation rate ceases to follow a power-law relationship with the supersaturation when the supersaturation exceeds an upper metastable nucleation limit for the system. Since the nucleation rate is of higher kinetic order than the growth rate, a decrease in the supersaturation will cause a greater relative decrease in the nucleation rate than in the growth rate, which will reduce the relative rate of nucleation to growth and increase the crystal size. A large crystal size is therefore favoured at long residence times. The kinetic orders of growth (0.9707) and nucleation (2.1065) determined here, compare well with the values of these parameters reported in the literature for different - 171 -crystallizing systems. For example, the growth rate kinetic order of potassium alum crystals was reported to be 1.33 by Garside and Jancic (1979). The nucleation kinetic order in the same system was 2.1. In another investigation of the potassium alum system, Budz and co-workers (1984) reported that the growth rate kinetic order was 1.48. In the same study they also determined that the growth rate of sodium thiosulfate pentahydrate crystals was linear in the supersaturation (g = 1). Sikdar and Randolph (1976) reported that the growth rate kinetic order was 2.29 and the nucleation kinetic order was 2.59 for the magnesium sulfate heptahydrate system. For citric acid monohydrate they found that the kinetic order of the growth rate was 0.65 and the order of the nucleation rate was smaller in magnitude at 0.54. Most of the reported data, however, indicate that the nucleation rate is of higher kinetic order than the growth rate in different crystallizing systems (Garside and Shah, 1980). This was also found to be true in this system. 5.1.2 Residence Time An increase.in the residence time decreased the supersaturation, the growth rate and the nucleation rate, and increased the crystal size. At constant suspension density, the crystal size is a decreasing function of the - 172 -parameter B/G. Since the crystal suspension density in the crystallizer is given by, MT = 6Pckv(B/G)(Gx)4 (5.4) and the mean crystal size from the crystallizer by, MS = 3.67(G x) (5.5) combining Equations (5.4) and (5.5) yields the relationship, M S " (B7§)1/4 (5*6) Thus, when a given crystal suspension is being produced by more nucleation and less growth, B/G is larger and the crystal size is smaller. When the same suspension is being produced by more growth and less nucleation, B/G is smaller and the crystal size is larger. In the present case, the increase in the residence time caused a decrease in the supersaturation driving force which was necessitated by the mass balance. Because the kinetic order with respect to the supersaturation is higher for the nucleation rate (b = 2.1065) than it is for the growth rate (g = 0.9707), the reduction in the supersaturation caused a greater relative decrease in the nucleation rate, and therefore decreased the parameter B/G. The result was an increase in product crystal size. - 173 -An alternative expression which describes the effect of residence time on the crystal size from MSMPR crystallizers is given by Equation (2.51), M i _ 1 1 X T i+3 M s = (5.7) c v b Equations (5.6) and (5.7) are not independent but represent, in fact, the same relationship in terms of different variables. Equation (5.6) shows the effect of the relative parameter B/G on the crystal size. Equation (5.7) expresses the crystal size in terms of the independently controlled parameters, MT and i, and the relative kinetic constants i and K b which in turn determine the relative parameter B/G that exists in the system. Thus, for example, when i is equal to one, the nucleation rate kinetic order is equal to the growth rate kinetic order, and the decrease in supersaturation caused by a longer residence time decreases the nucleation rate and the growth rate to the same relative extent which leaves the ratio B/G unchanged. The result is no change in product crystal size which is the effect predicted by both Equations (5.6) and (5.7). The increase in crystal size with increasing residence time, determined in this study, is consistent with the effect of residence time that was observed by various - 174 -investigators in systems where the relative kinetic order i was greater than one. Amin and Larson (1968) reported crystal size improvement at longer residence times in the reaction crystallization system of calcium sulfate for which the relative kinetic order was 2.8. Timm and Larson (1968) observed the same effect in the salting out crystallization of ammonium sulfate and sodium chloride for which the relative kinetic orders were 4.0 and 9.0 respectively. In contrast, Timm and Cooper (1971) reported size degradation with increasing residence time, in the cooling crystallization of potassium dichromate. However, the relative kinetic order in that system was 0.53. A decrease in crystal size at longer residence times was also observed by Rosen and Hulburt (1971a) for potassium sulfate crystallization in which the relative kinetic order was equal to zero. The relative kinetic order for the system investigated in this study is 2.1065/0.9707 which is equal to 2.17. As predicted by the MSMPR crystallizer model for this value of i longer residence times produced larger crystals. This effect is in agreement with that reported by Amin and Larson (1968) and Timm and Larson (1968). The mean crystal size from MSMPR crystallizers is given by Equation (5.5). Therefore, in order for an increase in residence time to cause an increase in crystal size, the relative decrease in the growth rate should be smaller than - 175 -the relative increase in the residence time which causes the reduction in the growth rate. Randolph and Larson (1971) note that this effect is realized in systems where i is greater than one. The experimental data obtained here showed that this was true for the system investigated. The effect is illustrated in Figure 4.13. The slope of the straight line is given by -1/G-t. A reduction in the magnitude of the slope represents an increase in the parameter (Gt) and therefore a larger crystal size. Finally it should be mentioned that residence times of 40 and 50 seconds, at 25 and 30°C and an alcohol/feed ratio of 4.25 gr/gr, created excessively high supersaturations which were unsustainable under the prevailing conditions, forcing the system to excessive nucleation levels and diminishing the product crystal size. 5.1.3 Alcohol/Feed Ratio The ratios of the salting out agent to the main acid-feed used in this study were 1.75, 3.0 and 4.25 gr/gr. These ratios produced mother liquor concentrations within the range where the solid phase that is in equilibrium with the mother liquor is the neutral anhydrous sodium sulfate. The amount of salting out agent that was added to the feed influenced three parameters in the system; the equilibrium solubility of sodium sulfate in the mother liquor, the fraction of the sodium sulfate in the feed that was - 176 -precipitated, and the density of the crystal suspension generated in the crystallizer. Larger methanol/feed ratios increased the concentration of methanol in the crystallizer and caused a decrease in the equilibrium solubility of sodium sulfate in the mother liquor. The change in sodium sulfate solubility with increasing concentrations of methanol (as 80% w/w methanol) in the mother liquor solvent is shown in Figure 3.2 As the methanol concentration was increased, the solubility continuously decreased; rapidly initially, and then more slowly as the alcohol became a much larger part of the solvent-. This data is consistent with the effect of alcohols on the solubility of inorganic salts observed by various investigators (e.g., Thompson and Molstad, 1945; Kohn et al., 1963). The effect of increasing amounts of added methanol on the fraction of the salt precipitated is shown in Figure 3.4. As the mass fraction of the methanol solution in the mother liquor solvent increases, the precipitated fraction initially increases up to a maximum value and then starts to decrease at high methanol concentrations. The maximum yield is achieved when the methanol solution (the salting out agent) mass fraction in the mother liquor solvent is about 0.8, which is the concentration obtained when the ratio of the methanol solution/acid-feed is 3.0 gr/gr. As the amount of the methanol solution added to the feed is increased up - 177 -to 3.0 gr/gr, the relative reduction in the salt solubility, caused by the addition of the alcohol, is greater than the relative increase in the mass of total available solvent. As a result, the fraction of the salt that remains in solution continuously decreases, and the fraction precipitated continuously increases. As the amount of the added methanol solution increases above 3.0 grams per gram of feed, the relative decrease in the solubility becomes smaller than the relative increase in the mass of solvent and the precipitated fraction starts to decrease. The observation that the yield of a salt, salted out from its solution, goes through a maximum with increasing added amounts of salting out agent has been reported by Kohn and co-workers (1963) for a potassium bisulfate aqueous solution with ethylene glycol as a salting out agent. Alfassi and Mosseri (1984) did not observe the same trend within the range of concentrations of salting out agent tested, but noted that when the added amount of salting out agent is large enough, further addition will cause the yield to start to decrease and eventually reach zero for very large amounts of added agent. In the present study, the yield of sodium sulfate (e.g., at 25°C and 120 sec. residence time) varied from 79.06 to 79.90 to 78.80 when the methanol solution/feed ratio increased from 1.75 to 3.0 to 4.25 gr/gr respectively. - 178 -Different salting out agent/feed ratios also produced different crystal suspension densities in the crystallizer. The effect of increasing alcohol concentration in the crystallizer on the density of the crystal suspension is shown in Figure 3.5. The x-axis is the mass fraction of the salting out agent (80% w/w MeOH) in the mother liquor solvent, which increases with increasing salting out agent/feed ratios.. The suspension density is defined here as gr NaaSO^/kg solvent which provides a measure of the true suspension density defined as gr NaaSO^/l of suspension. As the alcohol solution/feed ratio is increased, increasing the alcohol concentration in the mother liquor solvent, the density of the crystal suspension generated in the crystallizer continuously decreases. This effect is caused by increasing amount of salting out agent. The relative increase in the fraction of salt precipitated (in the range where it is increasing) is smaller than the relative increase in the volume (or mass) of the suspension caused by the addition of the salting out agent, i.e., the precipitated solid is being suspended in a larger relative volume, producing smaller suspension densities. At 25°C, an increase in the methanol solution/acid-feed ratio from 1.75 to 4.25 gr/gr decreased the crystal suspension density from 71 to 34 grams Na 2S0 4 per litre of suspension. Increased residence time caused small increases in the suspension density by reducing the amount of solute accumulated in the - 179 -solution as supersaturation. At 25°C and an alcohol/feed ratio of 1.75, an increase in the residence time from 50 to 120 seconds increased the suspension density from 71.08 to 71.42 gr/1. A change in temperature also affected the crystal suspension density by changing the equilibrium solubility. At an alcohol/feed ratio of 1.75 and a residence time of 120 seconds, the suspension density was 71.42 gr/1 at 25°C and 66.85 gr/1 at 35°C. However, appreciable changes in the crystal suspension density could only be achieved by changing the salting out agent/acid-feed ratio. The kinetic data obtained showed that the concentration of methanol in the crystallizer did not have an independent effect on the kinetics of growth or nucleation, i.e., the kinetic parameters K Q, g, and b were independent of the amount of salting out agent used. However, the results obtained under conditions of excessive nucleation in the crystallizer indicate that the maximum sustainable supersaturation, or the width of the metastable zone for the system is reduced at higher methanol concentrations. 5.1.4 Crystal Suspension Density The data relating the nucleation rate to the crystal suspension density showed that, at a 'constant supersaturation level , an increase in suspension density did not increase the rate of nucleation. The non-dependence of - 180 -the nucleation rate on the amount of solute crystals in suspension suggests that the nucleation mechanisms in the system were predominantly of the non-secondary type. This finding confirms the common assumption that in precipitation crystallization systems, secondary nucleation effects are not usually significant and that primary nucleation is likely to be the dominating mechanism (Garside and Shah, 1980). Based on this assumption, most salting out studies such as that by Song and Douglas (1975) and Murray and Larson (1965) have not included data on the influence of the suspension density on the kinetics of crystallization. However., one study of the reaction crystallization of calcium sulfate conducted by Amin and Larson (1968) reported data on the effect of two different suspension densities on the kinetics in that system. The data indicated that a higher suspension density did not increase the rate of nucleation. Amin and Larson concluded that "the predominant source of nuclei is homogeneous nucleation, and the nuclei generation rate is not dependent on solids present, but only on supersaturation." The effect of the crystal suspension density determined here, i.e., no effect on nucleation, is in agreement with the observations of Amin and Larson. Larson, Timm and Wolff (1968) have shown that when the nucleation rate is not enhanced by an increased crystal suspension density, a larger crystal size will be produced at higher densities. This was seen to be true in this - 181 -system. An increase in crystal suspension density caused an increase in the supersaturation, the growth rate, the nucleation rate and the mean crystal size. The higher suspension density, at constant residence time, caused an increase in the rate of production of crystalline solid which required faster kinetics and therefore the generation of a higher level of supersaturation in the crystallizer. The increased supersaturation caused a greater relative increase in the nucleation rate than in the growth rate because of the larger nucleation kinetic order with respect to the supersaturation. This resulted in an increase in the parameter B/G. The increase in crystal size was due to the fact that, when the nucleation rate is independent of crystal suspension density, the relative increase in suspension density is always greater than the relative increase in the parameter B/G that is caused by the increased density - Equation (5.6). The net effect of crystal suspension density on the crystal size being given by Equation (5.7), i.e., 1 MS - (5.8) Crystal size enhancement consistent with this relationship was observed. - 182 -Figure 4.14 shows the effect of increased suspension density on the product crystal size distribution. A straight line with a slope of smaller magnitude represents distribution with a larger mean size. A line of higher suspension density is always above the line of lower suspension density since the integral ndL increases with increased density. 5.1.5 Agitation Rate The rate of mixing of the crystal suspension was not a variable in this study. The turbine impeller RPM used was 600 and- was maintained at this level for all the experiments. This RPM was found to uniformly suspend a maximum crystal suspension of 71 gr/1 and provide good liquid phase mixing. 5.1.6 Temperature An increase in temperature caused an increase in the growth rate, a reduction in the nucleation rate and therefore an increase in the mean crystal size. The level of supersaturation showed no significant change with increasing temperature. Since the supersaturation remained almost constant as tfc temperature was increased, the increase in the growth rate - 183 -was caused by an increase in the growth rate constant at higher temperatures. The data relating the growth rate constant K^ , to the temperature showed that K varied G G with temperature according to the Arrhenius relationship K q = 43962 exp[-24626/RT] (5.9) in which the activation energy for the growth rate is +24,626 kJ/kmole indicating a positive temperature dependency for Kq. i.e., that K G increased with temperature. Figure 4.2 shows the effect of temperature on the growth kinetics. Similarly the reduction in the nucleation rate, at constant supersaturation, was caused by a decrease in the nucleation rate constant K as the temperature was increased. B K was also an Arrhenius function of temperature which B was determined to be Kg = 0.064 exp[70870/RT] (5.10) in which the activation energy for the nucleation rate is -70,870 kJ/kmole which indicates that Kg is a decreasing function of temperature. Figure 4.3 shows the effect of temperature on the nucleation kinetics. The magnitude of the activation energy for the growth rate suggests that the crystal growth process was probably influenced by both diffusion and surface reaction. At 24,626 kJ/kmole it compares well with the values reported in - 184 -the literature. For example, an activation energy of 12,000 kJ/kmole was reported for the growth rate of sodium thiosulfate pentahydrate crystals by Budz and co-workers (1985). Sikdar and Randolph (1976) reported a growth rate activation energy of 29,800 kJ/kmole for citric acid monohydrate crystals. Jones and co-workers (1986) determined the activation energy for the growth of potassium sulfate crystals to be 40,400 kJ/kmole. The finding that the activation energy for the nucleation rate was negative and larger in magnitude than the growth rate activation energy is also in agreement with most reported data. The activation energy for the nucleation of citric acid monohydrate crystals was -39,750 kJ/kmole as reported by Sikdar and Randolph. Helt and Larson (1977) reported activation energies of 31,000 kJ/kmole for the growth rate and -108,000 kJ/kmole for the nucleation rate of potassium nitrate crystals. Jones and co-workers however found a positive activation energy (62,500 kJ/kmole) for the nucleation of potassium sulfate crystals. The increase in K„ and the decrease in K„ with (j D increasing temperature caused a reduction in the relative rate of nucleation to growth and therefore decreased the relative rate constant K^ (Figure 4.4). The effect of K, on the crystal size is given by Equation (5.7). - 185 -vr i"1 M m T T i +3 MS = 3.67( e^ k K ) (5-7) c v b which predicts an increase in the mean crystal size for a decrease in K, . Because of the reduction in K, , b b crystal size enhancement was observed with increasing temperature. For example, at a constant residence time of 120 seconds, and when the crystal suspension density was within the range 66-72 gr/1, the mean crystal size increased from 120 microns at 25°C to 155 microns at 35°C. The effect of temperature on the size distribution of the crystal product is shown in Figure 4.15. A distribution with a larger average size was obtained at higher temperatures as indicated by the reduction in the magnitude of the slope of the line. A change in temperature also influenced the equilibrium solubility of sodium sulfate in the mother liquor. A higher temperature increased the solubility and therefore caused a small reduction in the crystal suspension density and in the yield of sodium sulfate. e.g., the average crystal suspension density decreased from 46.67 gr/1 at 25°C to 44.05 gr/1 at 35°C, when the alcohol/feed ratio was 3.0 gr/gr. At the same alcohol/feed ratio and a residence time of 120 seconds, the yield decreased from 79.90 to 75.85 when the temperature was increased from 25 to 35°C. - 186 -5.1.7 Concentration of the Cr + + + Impurity The effect of the concentration of the Cr + + + cation in the crystallizer on the kinetics of growth and nucleation was investigated at a constant temperature of 35°C and a constant crystal suspension density of « 32 gr/1, which was produced by an alcohol/feed ratio of 4.25 gr/gr. The concentrations tested were 75, 150 and 300 ppm (mass basis) of chrome ion in the main acid-feed. The corresponding concentrations of the ion in the crystallizer were therefore 14, 29 and 57 ppm respectively. The impurity was added to the feed as chrome alum (KCr(S0i+)2 • 12H20) which contains 10.41%. of chromium. The results from the crystallization experiments conducted in the presence of the Cr + + + impurity showed that as the impurity concentration increased, the steady-state growth rate increased, and the supersaturation and the nucleation rate decreased. The overall result was an increase in the product crystal size. Figures 4.7 and 4.8 show the change in the steady-state kinetic rates of growth and nucleation respectively, with increasing concentration of Cr + + + in the main feed. The rate of change is maximum as the concentration approaches zero with the effect diminishing as the impurity concentration is increased. The increase in the mean crystal size, as a result of the decrease in the parameter B/G, with increasing Cr + + + concentration is shown in Figure 4.9. - 187 -At a residence time of 60 seconds, an increase in the concentration of the impurity in the feed from zero to 75 ppm caused an increase in the growth rate from 1.94 to 2.13 mm/hr, a decrease in the nucleation rate from 2.16 x 1010 to 1.59 x 1010 number/hr.l, and a decrease in the supersaturation from 0.60 to 0.42 gr Na2S0i+/kg solvent. The mean crystal size increased from 110 to 132 microns. When the concentration of the impurity in the feed was 300 ppm, the growth rate was 2.47 mm/hr, the nucleation rate was 1.07 x 1010 number/hr.l, the supersaturation was 0.42 gr NA2S0i+/kg solvent, and the crystal size was 147 microns. The apparent opposite effects that the presence of the Cr+++ impurity had on the rates of growth and nucleation (i.e., an increase in the growth rate and a decrease in the nucleation rate) do not necessarily reflect the true influence of the impurity concentration on these rates. At constant suspension density and constant residence time, a change in an operating variable which affects the kinetics of growth and/or nucleation, forces the kinetics in the system to follow the relationship B - G~3 (5.11) regardless of the independent effect of that variable on the individual rates of growth and nucleation. This requirement arises from the necessity for the mass balance constraint to be satisfied, i.e., - 188 -M t = 6 p c k y ( B / G ) ( G i )4 (5.4) Therefore, at constant M^ , and x, a change in operating conditions which, say, increases both the growth rate and the nucleation rate by increasing the corresponding kinetic rate constants and K D, causes the supersaturation U D level in the system to go down which in turn decreases both rates. The extent to which the growth and the nucleation rate are increased by the change in operating conditions depends upon the effect of the changed variable on these rates. The extent to which the rates are decreased by the decrease in the supersaturation driving force depends upon the magnitude of the kinetic orders g and b. The net change (if any) is a decrease in one rate and an increase in the other, such that Equation (5.4) is again satisfied. This is true for changes in any system variable which affects the kinetics, when operation is such that the crystal suspension density and the residence time are held constant. Therefore in order to evaluate the independent effect of that variable on the individual kinetic rates of growth and nucleation, it is necessary to know the level of supersaturation that exists in the crystallizer. The supersaturation data determined in the presence of the Cr + + + impurity showed that as the impurity concentration increased, there was an increase in the growth rate - 189 -constant, while the nucleation rate constant, K D, VJ D remained essentially unaffected by the level of the impurity concentration in the crystallizer. As a result, the relative kinetic rate constant, K. , decreased with b increasing concentrations of the impurity in the system. The growth rate kinetic order, g, and the nucleation rate kinetic order, b, were independent of the impurity concentration, and, given the experimental scatter in the data, remained essentially constant at the levels determined for the pure system. This information enables one to conclude that the increase, in the operative steady-state growth rate in the presence of the C r + + + impurity was due to a "real" enhancement of the growth kinetic process caused by an increased growth rate constant, whereas the decrease in the nucleation rate was due to the decreased supersaturation. Figure 4.10 shows the effect of the impurity concentration on the growth kinetics. Figure 4.11 shows no real effect of impurity concentration on the nucleation kineti cs, and Figure 4.12 shows the resulting change in the relative kinetics. The increase in the growth rate and the decrease in the nucleation rate observed in this study, in the presence of the C r + + + cation, are in agreement with the effects of the C o + + and C r + + + impurities on the crystallization kinetics of potassium nitrate observed by Shor and Larson (1971). - 190 -However, in the present study, these effects were determined to be mainly due to an increasing growth rate constant with increasing impurity concentration, which is not in agreement with the explanation of these effects offered by Shor and Larson. Without supersaturation data they could not determine the changes in the separate kinetic rate constants, but they proposed that the main effect of the impurity was to inhibit nucleation by decreasing the nucleation rate constant, and that the apparent increase in the growth rate was due to an increased level of supersaturation that must have been generated in the crystallizer in response to the decrease in the nucleation rate. The nucleation process in their system, however, exhibited a dependence on the crystal suspension density, which indicated that secondary nucleation mechanisms were operative in the crystallizer. The nucleation process in the system investigated here showed no dependence on the crystal suspension density and was probably mostly due to primary nucleation mechanisms. Primary and secondary nucleation processes are likely to have quite different mechanisms and might therefore be expected to be influenced to different extents (if at all), and in different manners by the presence of impurities in the crystallizing system. The apparent effect of the Pb++ ion on the kinetics of crystallization of sodium chloride, as reported by Liu and Botasaris (1973), was opposite to the effect of the Cr + + + - 191 -ion determined here. Liu and Botsaris observed lower growth rates and higher nucleation rates as the impurity concentration in the system was increased. However, without supersaturation data, the independent effects of the Pb++ impurity on the separate kinetic parameters of growth and nucleation could not be determined. The relative kinetic order, i, remained constant at all levels of the impurity concentration. The decrease in the growth rate and the increase in the nucleation rate, at constant i, meant that the relative kinetic constant, K^, increased with increasing concentration of the Pb + + impurity. Since K^ is given by, K B K, = —r- (5.12) b „i G this effect could have been achieved by an increase in the nucleation rate constant, Kg, or a decrease in the growth rate constant, KQ, or both. Alternatively, an increase in both K_. and K_ when the relative D (j increase in K n is greater, or a decrease in both D constants when the relative decrease in K^ is greater, could have been responsible for the increase in K^. McCabe (1946) notes that the presence of small concentrations of impurities in a crystallizing system usually inhibits crystallization by reducing the growth rate - 192 -or the nucleation rate or both, but that occasionally increased rates are obtained when impurities are added. The findings reported here support the latter view. Within the range of impurity concentrations considered, the chemical composition and the crystal habit of the precipitated solid continued to be the same as those in the pure system. i.e., the precipitated solid continued to be the neutral anhydrous sodium sulfate with a "thin flat plate" crystal habit. The amount of chromium (if any) co-precipitated with the sodium sulfate was not measured since it was considered that the main variable influencing the kinetics was the chromium concentration in the feed. However, judging from the pale green colour of the crystals, which were white when the system was chromium free, it is probably correct to say that some chromium was incorporated into the crystal structure upon precipitation. The effect of increasing chromium concentration in the feed on the crystal size distribution generated in the crystallizer is shown in Figure 4.16. A straight line with a slope of smaller magnitude, representing a size distribution of a larger mean size, is obtained when the chromium concentration is higher. - 193 -5.1.8 Yield The crystallization system investigated was of the Class II type in which the amount of solute remaining as supersaturation was negligible compared to the amount precipitated or the amount of solute in the feed. Thus, order of magnitude changes in the supersaturation (e.g., caused by changes in the residence time), at a constant alcohol/feed ratio and a constant temperature, left the crystal suspension density and the yield of the crystallizer essentially invariant. Both the yield and the suspension density were practically fixed by fixing the temperature and the ratio of the salting out agent to the main feed used; i.e., by fixing the parameters that determined the equilibrium solubility of the solute in the mother liquor, which represented the approach of the solute concentration in the mother liquor in the crystallizer exit stream. The solids concentration in the main acid-feed was constant at 25.0% w/w Na2S0it • Consequently, the fraction of the solid precipitated depended upon the amount of solid that remained in solution after the addition of the salting out agent, which was determined by the amount of salting out agent used and the equilibrium solubility of the solute in the resulting mixed-solvent, which in turn depended upon the amount of agent used. The optimum ratio of the salting out agent to the main crystallizer feed, for maximum yield of sodium sulfate, was about 3.0 gr/gr. The optimum - 194 -temperature was the lowest temperature considered (25°C) at which the equilibrium solubility of the solute was smallest in a mother liquor of given alcohol concentration. Residence time had no significant effect on the yield of sodium sulfate. However, minor increases in the yield were obtained at longer residence times because of the smaller supersaturations generated under these conditions. For example, at 30°C and an alcohol/feed ratio of 1.75 gr/gr, the yield was increased from 76.41% to 76.91% when the residence time was increased from 50 to 120 seconds. Among all conditions tested, the yield of sodium sulfate, defined here as the fraction of the salt originally in the feed that was precipitated upon addition of the salting out agent, was minimum at a temperature of 35°C, an alcohol/feed ratio of 1.75 gr/gr, and a residence time of 50 seconds (73.84%). A maximum yield of 79.90% was obtained when the temperature in the crystallizer was 25°C, the alcohol/feed ratio was 3.0 gr/gr, and the residence time was 120 seconds. 5.1.9 Crystal Size Distribution The size distribution of product crystals from ideal mixed-suspension, mixed-product-removal crystallizers represents a straight line when plotted as the natural logarithm of the population density of a given crystal size versus the crystal size - Figure 4.1. The size distribution data determined in this study showed good straight line - 195 -behaviour under all conditions tested, indicating that the constraints of the ideal MSMPR operation were closely approximated throughout the experimental program. There was no evidence in the data to support size dependent growth, which produces a distinctly curved size distribution on the In n versus size plot. Thus, the assumption that McCabe's AL law (McCabe, 1929) was valid in the system investigated, has been verified. The neutral anhydrous sodium sulfate crystals produced in the crystallizer were of the "thin flat plate" type (Figure 5.1). The volume shape factor of this crystal habit was determined at k v = 0.1707 and was size independent. The relatively small magnitude of the shape factor reflected the "thinness" of the crystal. Thus, one crystal of a given size occupied about 17% of the volume of a cubic crystal of the same characteristic size. Because of their specific crystal habit, the sodium sulfate crystals were likely to be somewhat more susceptible to breakage in the crystallizer upon collision with the turbine impeller, and during sieve analysis. Microscopic examination of crystal samples, before and after sieve analysis, showed that some degree of crystal breakage had occurred in the crystallizer and possibly a little further breakage during screening. However, the crystal size distribution data showed no significant deviation from the straight line behaviour on the In n versus size plot, - 196 -(x 300) Figure 5.1 Photographs of Na2S01+ plate crystals (x 150) - 197 -indicating that the extent to which crystal breakage had occurred was not significant enough to alter the form of the CSD and therefore had no appreciable influence on the calculated kinetics. The coefficient of variation of the crystal size distribution from ideal MSMPR crystallizers is theoretically constant at 52%. The data obtained here describing the coefficients of variation of the different crystal size distributions showed that the experimental coefficient of variation varied from a minimum of 38.68% to a maximum of 79.05%; the bulk of the data, however, falling within the narrower range 40-60%, which represents the expected variation about the theoretical value. The tendency of the coefficient of variation to be bigger when the average crystal size was larger, provides a possible indication that some crystal fracture was taking place during the sieving procedure and that the larger crystals were being more easily fractured than the smaller crystals. The variation of the mean size of the different crystal size distributions, from all experiments conducted, ranged from 56 to 169 microns. The minimum crystal size of 56 microns was obtained under conditions of excessive nucleation in the crystallizer at 25°C and a residence time of 40 seconds. The maximum size of 169 microns was obtained at 35°C and a residence time of 120 seconds, under conditions when the - 198 -main crystallizer feed contained 300 ppm of the Cr + + + impurity. 5.2 Relative Kinetics Knowledge of the individual kinetics of growth and nucleation provides the required information for the evaluation of the relative kinetics. Thus, since the nucleation rate kinetic order b is 2.1065 and the growth rate kinetic order g is 0.9707, the relative kinetic order i can be calculated using Equation (2.28) from b 2.1065 0 1 = g = 0.9707 = 2 ' 1 7 0 1 < 5- 1 3) Further, since the nucleation rate constant K„ has been D determined as Kg = 0.064 exp[70870/RT] (5.10) and the growth rate constant K„ as Ci Kq = 43962 exp[-24626/RT] (5.9) the relative kinetic constant K b can be calculated using Equation (5.12) from - 199 -b kg 0.064 exp[70870/RT] {43962 exp[-24626/RT]} 2" 1 7 0 1 or, = 5.3736 x 10-12 exp[124310/RT] (5.14) Therefore the relative kinetics in the pure system may be expressed as B = 5.3736 x 10 - 1 2 exp[124310/RT] q 2' 1 7 0 1 (5.15) It should be mentioned that the relative kinetic parameter i, determined at each temperature by curve-fitting the nucleation and growth rate data to the relative kinetic equation, is possibly a more accurate measure of the true relative kinetic order since its determination was independent of the supersaturation data. 5-3 Check on Data Accuracy The theoretical expression for the crystal suspension density generated in an ideal mixed-suspension, - 200 -mixed-product-removal crystallizer, is g i v en in terms of the rates of growth and nucleation that are operative in the crystallizer by, lT = 60cVB/G)(GT) ( 5 . 4 ) The steady-state crystal size distribution generated in a crystallization vessel operating as a perfect MSMPR crystallizer yields a perfect straight line on a In n versus size plot, the slope and intercept of which are used to calculate the exact growth rate, G, and the exact nucleation rate, B, such that the right hand side of Equation (5.4) is exactly equal to the crystal suspension density in the crystallizer. Crystal size distributions determined from experimental crystallizers, however, usually show some degree of scatter about the ideal straight line MSMPR size distribution. Factors contributing to the creation of this scatter in the data include the following potential sources of error: (i) In a realistic (experimental) crystallizer, truly MSMPR conditions can often be very closely approached but are probably never exactly satisfied. (ii) The withdrawal of a crystal slurry sample from the crystallizer for size analysis often induces a (small) classifying effect on the crystal size distribution such that the sample withdrawn is - 201 -not necessarily exactly representative of the crystallizer contents, (iii) The treatment of the crystal slurry sample withdrawn might allow for continued crystallization to take place if the separation of the crystals from the mother liquor is not quick enough, or for crystal dissolution to take place during washing of the separated crystals if the crystals are soluble in the wash solvent, (iv) The procedure used to determine the size distribution of the crystal sample withdrawn (especially when sieve analysis is used) can itself cause an originally straight line distribution to deviate from the straight line behaviour by promoting crystal fracture or failing to break up crystal agglomerates or both. In some studies, the best fitting straight line to the experimental CSD data has been calculated with a constraint imposed on the parameters of the line such that the mass balance (Equation (5.4)) is satisfied. In the present study, the best fitting straight line to the CSD data from each experiment, was determined using unconstrained least squares. The construction of the best line therefore depended only on the nature of the scatter in the data. As a result, the growth and nucleation rates, calculated from - 202 -the slope and intercept of the line, were also dependent upon the amount of scatter, and varied according to the construction of the line. The nucleation rate, being related to the exponential of the intercept, was much more sensitive to small changes in the construction of the line (and therefore to the experimental scatter in the CSD data) than was the growth rate which is related to the inverse of the slope. Consequently, the nucleation rate data (Figure 4.6) showed greater (relative) variation than did the growth rate data (Figure 4.5). Since no constraint was imposed on the calculated values of the growth and nucleation rates to force the mass balance to be satisfied, the theoretical suspension density when calculated from the right hand side of Equation (5.4) showed some deviation from the actual (experimental) suspension density in the crystallizer. This deviation provided a useful measure of the effect of experimental sources of error on the accuracy with which the data was collected. Thus, a small difference between the theoretical and experimental suspension densities indicated a near ideal experiment, in which perfect MSMPR operation was closely approximated, and in which the sampling, subsequent sample treatment, and sieving procedures did not significantly alter the form of the crystal size distribution. Conversely, a large difference reflected the extent to which - 203 -ideal experimental conditions and procedures were not realized. In order to provide an overall measure of the degree to which experimental error sources influenced the kinetic data obtained in this study, the deviations of the theoretical suspension density from the experimental suspension density, for all the experiments conducted, are shown on a scatter plot in Figure 5.2. The nature and magnitude of the scatter of the points about the 45° line represents the character of the cumulative experimental error introduced by all combined experimental error sources influencing the CSD. 5.4 Conclusions The data obtained in this study support the following conclusions for the Na2S01+/H2S01+/H20/Me0H salting out crystallizing system. - The growth rate of the precipitated crystals is essentially linear in the supersaturation driving force (g = 0.9707) and is enhanced at higher temperatures. Over the temperature range 25-35°C, the growth rate kinetic order, g, remains constant with temperature. The activation energy for growth is 24626 kJ/kmole. The defining kinetic equation of the growth process can be written as follows: G = 43962 exp[-24626/RT] S 0 " 9 7 0 7 (5.16) - 204 -THEORETICAL SUSPENSION DENSITY, g r / l Figure 5.2 Experimental versus theoretical suspension density - 205 -- The "intermediate" value of the growth rate activation energy indicates that both the diffusional resistance and the surface reaction resistance to the overall growth process are significant. However, the first order dependence of the growth rate on the supersaturation would point to either, (i) A greater but not controlling diffusional resistance. Or, (ii) First order surface reaction kinetics. - The crystal nucleation rate is essentially second order with respect to the supersaturation driving force (b = 2.1065) and is inhibited at higher temperatures. The nucleation rate kinetic order, b, remains constant with temperature over the temperature range 25-35°C. The activation energy for nucleation is negative at -70870 kJ/kmole. The defining kinetic equation of the nucleation process can be written as follows: B = 0.064 exp[70870/RT] S 2' 1 0 6 5 (5 l y ) The rate of nucleation is independent of the amount of solids in suspension (B * B(MT)), indicating that the contribution of secondary nucleation processes to the overall nucleation rate is not significant. The production of crystal nuclei is predominantly due to primary nucleation mechanisms. - 206 -- In order to crystallize the neutral anhydrous sodium sulfate from a solution containing 25.0% w/w Na2S01+, 28.5% w/w H2S0lt and 46.5% w/w H20 by salting out with an 80:20 weight % methanol:water solution, the ratio of the salting out agent to the salt solution must be equal to or greater than 1.125 gr/gr. - Crystals of the neutral anhydrous sodium sulfate have the characteristic "thin flat plate" crystal habit and a volume shape factor kv = 0.1707 which is independent of crystal size. - The addition of the soluble Cr+++ impurity to the crystallizing solution increases the operative growth rate and decreases both the supersaturation and the nucleation rate, resulting in a crystal product of larger size. " The crystal growth rate is independent of crystal size, G * G(L). - Favourable conditions for the production of a large sodium sulfate crystal include a high temperature, a high crystal suspension density and a long residence time. 5 *5 Recommendations for Further Work - It has been shown in this work that by the use of an aqueous solution of methanol as a salting out agent to precipitate sodium sulfate from its solution in a sulfuric - 207 -acid solvent, recoveries in excess of 80% of the sodium sulfate can be achieved. The potential benefits of salting out could be realized and may be investigated for a different crystallizing system. For the present system, the study of the effect of the chromium impurity could be extended to include temperatures other than 35°C. This will permit the calculation of activation energies in the presence of the impurity and will therefore provide better insight into the mechanism by which the impurity influences the kinetics. An energy study of the salting out process, including the unavoidable recovery unit required to separate the mixed solvents, could be made. This will determine the energy efficiency of salting out as it compares to more conventional crystallization processes. In salting out crystallization, local regions of high supersaturation are created at the point of mixing of the crystallizer feed with the salting out agent. These regions will likely influence the overall kinetics in the system, to varying extents depending on the mixing conditions prevailing in the crystallizer. The effect of mixing on the kinetics of crystallization in salting out systems should be studied. - 208 -NOMENCLATUEE A AN a constant in Equation (2.24), 1/mm a i 6 s;:isePr8^ct°f r v e t h a t r e t a i n s i 6 % °f S ^ p J i S c ? ! ™eve t h a t r e t a i n s 84% o f Afi sS??en?)-bln E q U a t i° n (2'8>' d/hP.l)(gr solute/kg Ac Surface area of a crystal, ram2 s o l v e n t E q U a t l o n <2'16)> (mm/hr)(gr/solute/kg (l/hr.l)(gr/l)-J A t . JuspaLsCLynS:aL^raCe a r e a P e r -lume of nucleation rate kinetic order, Equation (2.7) nucleation rate, 1/hr.l constant in Equation (2.24) ci constant in Equation (4.14) ° 2 constant in Equation (4.14) C3 constant in Equation (4.14) coefficient of variation, % solute concentration drop across the crystallizer, activation energy, kJ/kmole e n e r g y f°r QUcleation, Equation (2.8), <G activation energy for growth, kJ/kmole b B c CV AC E EB E - 209 -E N kJ/kmole°n e n 6 r g y f o r n u c Nation, Equation (2.12), g overall growth rate kinetic order G crystal growth rate, mm/hr Gi growth rate of crystals of size Li, mm/hr G 2 growth rate of crystals of size L 2, mm/hr order of nucleation with respect to agitator RPM relative kinetic order, Equation (2.26) j order of nucleation with respect to MT ka surface area shape factor k d kinetic coefficient for diffusion (mm/hr) (gr solute/kg solvent)"1 ; k p S r ^ i ? f*;fficient for surface reaction (mm/hr) • (gr solute/kg solvent)-r ' ' volume shape factor ki constant in Equation (2.6), 1/hr.l k2 constant in Equation (2.6) (i/£"i)(£/2"2i c o n s t a n t' E q u a t i o n Kg nucleation rate constant, Equation (2.7), (1/hr.l) (gr solute/kg solvent)-13 K g E q T t l o ^ t S ? S t ? n t , J 0 ^ S i z e ^ePendent growth, equation (2.24), (mm/hr)(gr solute/kg solvent)16 KG overall growth rate constant (mm/hr) (gr solute/kg solvent)-2 K n relative kinetic constant, Equation (2.29), (l/hr.l)(gr/l)-J(mm/hr)-v KN ^ f j ^ s t a n t , Equation (2.11) /hr•1)(gr/1) J(gr solute/kg solvent)-u - 210 -AL m m M Ki nucleation rate constant, Equation (2.13), (1/hr.l) (RPM) h(gr/l)-J(gr solute/kg solvent)-11 K 2 constant in Equation (2.49), (gr/mm3)(mm/hr) (gr solute/kg solvent) g K 3 constant in Equation (2.50), (gr/mm3Wl/hr. 1) (mm/hr) (gr solute/kg solvent)-(^g+b) } L crystal size, mm size range L 2 - Li, mm ° s s t h e p r o d u o t e i i t r u L a t i r 8uspLs°i fo r S / i " u p t o s l z e L p e r u n l t M c mass of a crystal, gr M c mass of N c crystals, gr M t crystal suspension density, gr/1 crystal mean size, mm population density of crystals of size L (1/mm.l) nuclei population density (1/mm.l) ( l / ^ g l ) P ° P U l a t i 0 n d e n s i t y i n s i ze range AL, population density of crystals of size Lx (1/mm.l) population density of crystals of size L 2 (1/mm.l) S o Z ^ r n U m b S r ° f c r y s t a l s ^ to size L per unit volume of suspension (1/1) N c number of crystals counted total exit volumetric flow rate, 1/hr MS n o n n n i n 2 N Q - 211 -RG RPM S S S r order of surface reaction kinetics R gas constant, kJ/kmole.K g ? / h r d S ? S i t l ° n r a t e P e r M l t surface area, agitator speed, RPM supersaturation, gr solute/kg solvent max upper supersaturation metastable limit (gr solute/kg solvent) min J°wer supersaturation metastable limit (gr solute/kg solvent) t time, hr At time increment, hr T temperature, °K T c temperature, °C nucleation rate kinetic order, Equation (2.11) relative kinetic order, Equation (2.29) volume of crystal suspension, 1 volume of a crystal, mm 3 solute concentration, gr solute/kg solvent 6 q Io?ven? r l U m S ° 1 U t e ^ n t r a t i o n , gr solute/kg gr^ so lute/kg Solvent E t c ^ a l - s o l u t i o n interface, cumulative mass fraction of crystals up to size L u V V V < w w Wj W X . - 212 -Xi independent variable X2 independent variable y mass fraction of crystals retained on the sieve Y dependent variable P a density of crystallizer feed, gr/ml Pm density of salting out agent, gr/ml Pc crystal density, gr/mm3 o supersaturation ratio, w/w ' ' eq t mean residence time of the crystal suspension, hr - 213 -REFERENCES Abegg, C.F., J.D. 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Jancic, A.I.Ch.E.J., Vol. 25, 948 GarSigev.^Vol?d19M;B509S1?98j)d' ^ ^ P ~ Helt'(1977) a n d M'A' L a r S O n ' A.I.Ch.E.J., Vol. 23, 822 J° n e S2002 Ga986) B U d Z' ^ J' W' M U l l l n > ^I-Ch-E.J., Vol. 32 JUZaS(1977^'' ^ M'A' L a r S° n' A-I'Ch.E.J.f Vol. 23, 460 - 214 -Karpinski, P.H., Chem. Eng. Sci., Vol. 35, 2321 (1980). Karpinski, P.H., Chem. Eng. Sci., Vol. 40, 641 (1985). K°hn'259H(1963)yar°n' a n d D' W o l f> J' aPPl- Chem., Vol. 13, LarSO(i984):' A' I' C h' E- ^ P - S e r - No. 240, Vol. 80, 39 Larson,^M.A.,(D.C.)Timm, and P.R. Wolff, A.I.Ch.E.J., Vol. L i U ' S ™ ' T o U e i ) a n d G-R- Youngquist, Chem. Eng. Prog. Symp. Ser., No. 110, Vol. 67, 43 (1971) L ± U ' (i973)?Qd B ° t s a r i s ' A.I.Ch.E.J., Vol. 19, 510 Lobley D G. and K.L. Pinder, Paper presented to 62nd o.i.u. Chemical Conference, June 3-6 (1979). L° b l elAd DTmi' i^?- K , L-v P! n d e r' Proceedings Waste Treatment S m i ° n' V o l < 2' E d i t o rs: Robinson, C.W., M. Moo-Young, and G.J. Farquhar, Pergamon Press Toronto (1981) pp 63-70. 6 ^ress, McCabe, W.L., Ind. Eng. Chem., Vol. 21, 112 (1929). McCabe, W.L., Ind. Eng. Chem., Vol. 38, 18 (1946). M U U i ? K i ^ W A ; v , E n C r 1 ° P e d i a o f Chemical Technology (Kirk-Othmer), Vol. 7, p 243, Wiley, New Y?Jk, 1979. MUrra(19?5?:' a n d M-A- L a r S O n ' A.I.Ch.E.J., vol. 11, 728 Perry^R^^^and^C. H^Chilton^Edito^ ^ R a n d 0a984).- D" A' I- C h- E- ^r., No. 240, Vol. 80, 14 R a n d ° v S : 9 A ; D i 6 5 % ? 0 ) R a J a g O P a 1 ' I n d' ^ d a - . , Randolph, A.D., and M.A. Larson, Theory of Particulate Processes, Academic Press, N e w ^ f c - ^ I S ^ I ? ! . - 215 -S h o r ' ^ : M i i o? n^: A67% s o ? i a 7 c?r- E n s" P r o g- S y m p- S e r--Slkda(i976) .' ' ^  4-D' A. I .Ch. E. J. , Vol. 22, n o S O n g'(W?5). a n < 1 J' M' D o u S l a s . A.I.Ch.E.J., V o l . 21, 924 Thompson^ A.R.^and M.C. Molstad, Ind. Eng. c h e m . , Y o l . 3 7 _ Tlmm'(?968).a,ld M'A- L a r S O n ' Yol. 14, 452 T 1 ° , m - ( i b v i l ^ T'R- C O ° P e r ' A-I-Ch.B.J., Vol. 17, 285 and A.D. Randolph, A.I.Ch.E.J., Vol. 18, - 216 -APPENDICES - 217 -APPENDIX A Correlation Plots of the Nucleation Rate Corrected for Suspension Density at Three Temperatures - 218 -CM SUPERSATURATION S, g r / k g solvent Correlation of the nucleation rate corrected for suspension density with the supersaturation (T = 25°C) B = 7.16 x 1011 M t- 0- 3 6 4 3 S 2- 1 8 3 9 - 219 -•> »—« _ to oo -K) r- — K) <o co-O in-00-\ C M -<0 K> K ) N (O « 2 OO CQ (o-LU m -h-< QL ^ co —i O J— < c CM" o 3 T = 25 deg. C 2 3 4 5 6 7 10° 2 3 GROWTH RATE G, m m / h r I I I I > 11 4 5 6 7 101 Correlation of the nucleation rate corrected for suspensl density with the growth rate (T = 25°C) ion B = 3.92 x 10 11 M — ^ . 6 3 3 6 G2. 1187 - 220 -<M O 10 m <N L. o> oo-CD in \r -oo -T = 3 0 deg. C CM ~ m io CN CD t 00 CD i£r Ld lT)-i I— < r^ on Z oo O I— <t CM -o Z> 1 0 - ' T 2 3 4 5 6 7 SUPERSATURATION S, g r / k g solvent FT 8 910° Correlation of the nucleation rate corrected for suspension density with the supersaturation (T = 30°C) B = 2.74 x 10 1 1 M t " ° . 2 5 5 1 S 2 - 1 7 3 6 - 221 -I II ' ' I 2 3 4 5 6 7 10° 2 3 GROWTH RATE G, m m / h r I I I 1 • • 4 5 6 7 101 Correlation of the nucleation rate corrected for suspension density with the growth rate (T = 30°C) B = 8.63 x lO 1 0 M ^ 0 - ^ 6 2 2 G 2 • 0 2 0 4 - 222 -SUPERSATURATION S, g r / k g solvent Correlation of the nucleation rate corrected for suspension density with the supersaturation (T = 35°C) B = 9.44 x lO 1 0 M t " ° . 1 1 7 4 S 1 - 7 6 1 9 - 223 -N -CO -o o> r - -K> CD -o o LO -\ \ r -L . I I I * I I 2 3 4 5 6 7 10° 2 3 GROWTH RATE G, m m / h r i i i i * i r 4 5 6 7 10' Correlation of the nucleation rate corrected for suspension density with the growth rate (T = 35°C) B = 3.62 x lO 1 0 M t " ° . 3 7 9 0 G 1 - 7 8 3 4 - 224 -APPENDIX B Scatter Plots for Fitted Growth and Nucleation Rate Equations - 225 -1 . 0 2 . 0 3 . 0 PREDICTED GROWTH RATE, m m / h r Scatter plot for fitted growth rate model (T = 25°C) G = 2.2090 S1 • 0 5 11+ - 226 -S1 O 10 \ PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 25°C) B = 7.16 x 10 1 1 M t - 0 - 3 6 4 3 S 2 - 1 8 3 9 - 227 -G1 - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 25°C) B = 3.92 x 10 1 1 M t-°. & 3 3 6 G 2. - 228 -S2 O a cd -to 10 X PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 25°C) B = 1.63 x 10 1 1 s 2 - 0 8 4 * - 229 -G2 - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 25°C) B = 3 . 46 x 10 1 0 G 1 • 8 8 1 3 - 230 -1.0 2 . 0 3 . 0 PREDICTED GROWTH RATE, m m / h r S c a t t e r p l o t for f i t t e d growth r a t e model (T = 3 0 ° C ) I G = 2 . 5 3 2 8 s1 • 0 0 6 7 i 1 - 231 -SI - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 30°C) B = 2.74 x 1 0 1 1 M T - 0 - 2 5 5 1 S 2 - i 7 3 e - 232 -G1 < cm < Ld _J o ID LxJ CL X LxJ O T - to 10 x PREDICTED NUCLEATION RATE, 1 /hr . l S c a t t e r p l o t for f i t t e d n u c l e a t i o n r a t e model (T = 3 0 ° C ) •D - Q C Q , a 1 0 „, - 0 4 6 2 2 c 2 , 0 2 0 4 B = 8 . 6 3 x 10 Mrp • G • - 233 -S2 1 2 . 0 -10 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 30°C) B = 9 . 8 x 1 0 1 0 s 2 - 1 0 3 1 ' - 234 -G2 - K ) 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 30°C) B = 1.53 x lO 1 0 G 1 • 8 4 9 9 - 235 -1 . 0 2 . 0 3 . 0 PREDICTED GROWTH RATE, m m / h r Scatter plot for fitted growth rate model (T = 35°C) G = 2 .9074 S° • 91+20 - 236 -SI - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l S c a t t e r p l o t for f i t t e d n u c l e a t i o n r a t e model (T = 3 5 ° C ) B = 9 .44 x l O 1 0 M T " ° - 1 1 7 1 t S 1 - 7 6 * 9 - 237 -G1 — O L -C oo T = 3 5 deg. C -10 10 x PREDICTED NUCLEATION RATE, 1 /hr . l S c a t t e r p l o t for f i t t e d n u c l e a t i o n r a t e model (T = 3 5 ° C ) D o e o l n 1 0 _ 0 37 9 0 r l 7 8 31( B = 3.62 x 10 My • G • - 238 -S2 - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 35°C) B = 6.04 x lO 1 0 s 1 - 7 6 0'1 - 239 -G2 10 " x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 35°C) B = 8.84 x 109 G 1 • 7 2 9 7 - 240 -1 . 0 2 . 0 3 . 0 PREDICTED GROWTH RATE, m m / h r 4 . 0 Scatter plot for fitted growth rate model (T = 35°C, Cr feed concentration = 300 ppm) G = 4.7088 s ° . 9 7 1 0 - 241 -S2 4 . 0 -10 10 x PREDICTED NUCLEATION RATE, 1 /hr . l S c a t t e r p l o t for f i t t e d n u c l e a t i o n r a t e model (T = 3 5 ° C , Cr feed c o n c e n t r a t i o n = 75 ppm) B = 5.43 x l O ^ S 1 - ^ 8 9 " - 242 -G2 0.0 1.0 2.0 3.0 4.0 10 "x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 35°C, Cr feed concentration = 75 ppm) B = 5.26 x 1 0 9 G 1 ' 5 2 7 5 - 243 -O 1 . 0 2 . 0 3 . 0 PREDICTED GROWTH RATE, m m / h r 4 . 0 S c a t t e r p l o t for f i t t e d growth r a t e model (T = 3 5 ° C , Cr feed c o n c e n t r a t i o n = 150 ppm) G = 5.3899 sO.9412 - 244 -S2 - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 35°C, Cr feed concentration = 300 ppm) B = 4.76 x l O ^ S 1 - 2 9 61* - 245 -G2 —: o Scatter plot for fitted nucleation rate model (T = 35°C, Cr feed concentration = 150 ppm) B = 4.64 x 1 0 9 G 1 - 3 9 1 7 - 246 -O T = 3 5 deg. C 1.0 2.0 3.0 PREDICTED GROWTH RATE, m m / h r Scatter plot for fitted growth rate model (T = 35°C, Cr feed concentration = 300 ppm) G = 5.7443 S ° • 9 0 8 7 - 247 -S2 - 1 0 10 x PREDICTED NUCLEATION RATE, 1 /hr . l Scatter plot for fitted nucleation rate model (T = 35°C, Cr feed concentration = 300 ppm) B = 3.70 x 10 ^ S 1 - 1 8 5 1 - 248 -G2 - 1 0 10 x PREDICTED NUCLEATION RATE, 1 / h r J S c a t t e r p l o t for f i t t e d n u c l e a t i o n r a t e model (T = 3 5 ° C , Cr feed c o n c e n t r a t i o n = 300 ppm) B = 3.73 x 109 q1•3246 - 249 -APPENDIX C D e t a i l e d Run C o n d i t i o n s and CSD Data from Run Numbers 1 - 7 7 RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 3.68 ml/s ( 5.43 gr/s) MeOH solution flow rate = 27.57 ml/s -(23.07 gr/s) Alcohol/Acid-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01099 gr Na2S04/gr ML 0.14835 gr 38°/.w/w H2S04/gr ML 0.84066 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011107 gr Na2S04/gr solvent Equilibrium concentration » 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000864 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY •een Size (mm) Weight I Reta i ned !gr) Wt . % Retained Cumulat ive Wt . % Retained Population Density,n (number/mm 11tre) In n Average Si (mm) 0 . 3000 0 .0 0.0 0. 0 0 . 2500 0 .0 0.0 0. 0 0 . 2 120 0 .0010 0.0603 0. 0603 0. 9432569E+05 1'1 . 45 0, 2310 0 . 1800 0 .0065 0.3916 0. 4519 0. 1191915E+07 13 . 99 0 . 1960 0 . 1500 0 .0157 0.9460 1 , 3978 0. 514 7273E+07 15, , 45 0 . 1650 0 . 1060 0 .0954 5.7480 7 . , 1459 0. 4567893E+08 17 .64 0 . 1280 0 .0900 0 . 1408 8.4835 15, ,6293 0. 4131005E+09 19 .84 0 .0980 0 .0750 0 . 2488 14.9907 30, , 6200 0. 1305112E+10 20 .99 0 .0825 0 . 06 30 0 .28 19 16.9850 47 , 6050 0. 3159486E+ 10 21 .87 0 .0690 0 .0530 0 . 2522 15.1955 62 . 8005 0. 5711012E+10 22 .47 0 .0580 PAN 0 .6174 37.1995 100 .0000 Crystal mean s i ze = 0.0614 mm Coefficient of Variation = 41 .91 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER EXPERIMENTAL CONDITIONS C Crystallizer Temperature * 25.0 Deg. C Suspension Density * 33.79 gr/1 ( 5.43 gr/s) (23.07 gr/s) Feed Temperature 1 21.0 Deg Residence Time = 40.0 s Feed solution flow rate = 3.68 ml/s MeOH solution flow rate = 27.57 ml/s A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01096 gr Na2S04/gr ML 0.14836 gr 38%w/w H2S04/gr ML 0.84068 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011081 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000837 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Welqht Retained Wt.% Retained Cumulative Wt.% Retained Population Density n In n Average Size (number/mm litre) immi (gr) ( ) 0.3000 0. 0 0. 0 0.0 0.2500 0. 0 0. 0 0.0 0.2120 0. 0010 0. 0610 0.0610 0. 9554119E+05 1 1 . 47 0.2310 0.1800 0. 0040 0. 2439 0.3049 0. 7429384E+0S 13. 52 0.1960 0.1500 0, ,02 10 1 , 2807 1.5857 0. 6973607E+07 15 , 76 0.1650 0.1060 0. .0800 4 . 8789 6.4646 •0, ,3879877E+08 17 . 47 0.1280 0.0900 0 .0950 5 .7937 12.2583 0 .2823173E+09 19 .46 0.0980 0.0750 0 . 1835 1 1 .1911 23.4494 0 .9749760E+09 20 .70 0.0825 0.0630 0 .2697 16 . 448 1 39.8975 0 .3061703E+10 21 .84 0.0690 0.0530 0 . 2440 14 .8808 54.7783 0 .5596525E+ 10 22 .45 0.0580 PAN 0 . 74 15 45 .2217 100.0000 W Crystal mean size = 0.0562 mm Coefficient of Variation = 46.14 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.425811 mm/hr Nuclei population density = 0.1843092E+12 number/mm litre Nucleation rate.B = 0.2627900E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 2.94 ml/s ( 4.34 gr/s) MeOH solution flow rate = 22.OS ml/s (18.45 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01088 gr Na2S04/gr ML 0.14837 gr 38%w/w H2S04/gr ML 0.84076 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.010995 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000751 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY -een Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumul at-1 ve Wt.% Retained Population Density,n (number/mm litre) ln n Average S (mm) 0 . 3000 0 .0 0 .0 0. .0 0 . 2500 0 .0 0 .0 0 .0 0 .2120 0 .0022 0 . 1098 0 , 1098 0. 1723432E+06 12 ,06 0. 2310 0 . 1800 0 .0150 0 . 7484 0, .8582 0. 2284363E+07 14 .64 0. 1960 0 . 1500 0 .0250 1 .2474 2, , 1056 0. 680705 1E+07 15, .73 0. 1650 0 . 10S0 0 . 2235 1 1 .1516 13 , 2572 0. 8887642E+08 18 .30 0. 1280 0 . 0900 0 . 2355 1 1 . 7503 25 , 0075 0. 5738330E+09 20 . 17 - 0. 0980 0 .0750 0 . 3055 15 . 2430 40. , 2505 0. 1330915E+10 21 .01 0. 0825 0 .0630 0 .3280 16 . 3656 56 , 6161 0. 3053071E+10 21 .84 0. 0690 0 .0530 0 . 2885 14 . 3948 71 , 0108 0. 5425693E+10 22 .41 0. 0580 PAN 0 .5810 28 .9891 100. ,0000 Crystal mean size = 0.067S mm Coefficient of Variation = 43.03 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER 10 EXPERIMENTAL CONDITIONS Feed Temperature = 21.0 Deg. C Residence Time = 50.0 s Feed solution flow rate = 2.94 ml/s MeOH solution flow rate « 22.06 ml/s A l c o h o l / A c l d - f e e d r a t i o = 4.2500 g r / g r Mother Liquor (ML) Composition : 0.01090 gr Na2S04/gr ML 0.14836 gr 38%w/w H2S04/gr ML 0.84073 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011022 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000778 gr Na2S04/gr solvent Crystallizer Temperature = 25.0 Deg. C Suspension Density = 4S.50 gr/1 ( 4.34 gr/s) (18.45 gr/s) Screen Size (mm) Weight Retained (gr) Wt. % Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0. 0 0.0 0. 0 0 . 2500 0. 0 0.0 0. 0 0 .2 120 0. .0030 0.1555 0. 1555 0. 2439419E+06 12. 40 0. 2310 0 . 1800 0 .0135 0.6997 0. 8551 0.2134032E+07 14 . 57 0. 1960 0 . 1500 0 ,0645 3.3428 4 . , 1980 0. 1822939E+08 16 ,72 0. 1650 0 . 1060 0 .4506 23.3532 27 .5512 0. 1859918E+09 19 .04 0. 1280 0 .0900 0 .3201 16.5898 44 . 1410 0.8096069E+09 20 .51 0. 0980 0 .0750 0 . 3595 18.6318 62 .7728 0.1625667E+10 21 .21 0, ,0825 0 .0630 0 . 2537 13 . 1485 75 .9212 0.2451192E+10 21 .62 0 .0690 0 .0530 0 . 1861 9 .6450 85 . 5662 0.3632868E+10 22 .01 0 .0580 PAN 0 . 2785 14.4338 100 .0000 Crystal mean s 1 ze = 0.0852 mm Coefficient of Variation = • 39 . 15 % M Ui o: CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.278280 mm/hr Nuclei population density = 0.1518030E+12 number/mm litre Nucleation rate.B = 0.1940467E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 2.45 ml/s ( 3.62 gr/s) MeOH solution flow rate = 18.38 ml/s (15.38 gr/s) A1coho!/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01075 gr Na2S04/gr ML 0. 14839 gr 38%w/w H2S04/gr ML 0.84086 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.010866 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000622 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 1i tre) In n Average Size (mm) 0 . 3000 0, .001 1 0.0580 0. 0580 0 . 2500 0 ,0051 0. 2689 0. 3269 0. 1907882E+06 12 . 16 0. 2750 0 .2120 0 ,0147 0. 7750 1 , 1019 0. 1220804E+07 14 . 02 0. 2310 0 . 1800 0 .0624 3 . , 2898 4 , .3916 0. 1007433E+08 16 . 13 0. 1960 0 . 1500 0 . 1608 8 , .4774 12 .8691 0. 4641542E+08 17 ,65 0. 1650 0 . 1060 0 . 5096 26 . 8663 39 . 7354 0. 2148305E+09 19 . 19 0. 1280 0 .0900 0 . 2983 15 .7265 55 .4619 0. 77055S7E+09 20 .46 0. 0980 0 .0750 0 . 2782 14 .6668 70 . 1287 0. 1284854E+10 20 .97 0. 0825 0 .0630 0 . 1987 10 . 4756 80 .6042 0, ,1960733E+10 21 .40 0, 0690 0 . 0530 0 . 1476 7 .7815 88 .3858 0 .2942751E+10 21 .80 0, ,0580 PAN 0 . 2203 1 1 .6143 100 .0001 Crystal mean size = 0.0954 mm Coefficient of Variation = 43.86 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 1.84 ml/s ( 2.71 gr/s) MeOH solution flow rate = 13.79 ml/s ' (11.53 gr/s) Alcohol/Acid-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01065 gr Na2S04/gr ML 0.14840 gr 38°/.w/w H2S04/gr ML 0.84095 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.010762 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000518 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n ln n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0014 0 .0750 0 .0750 0 . 2500 0 .0069 0. . 3697 0 .4447 0. 2630369E+06 12 .48 0 .2750 0 .2120 0 .0188 1 .0073 1 .4521 0. 1591009E+07 14 .28 0 .2310 0 . 1800 0 .0588 3 . , 1506 4 .6027 0, 9673739E+07 16 .08 0 . 1960 0 . 1500 0 . 1769 9 , . 4787 14 .0814 0. 5203438E+08 17 . 77 0 . 1650 0 . 1060 0 .5131 27 , .4929 41 . 5743 0. 2204218E+09 19 .21 0 . 1280 0 . 0900 0 .3018 16 . 17 10 57 .7453 0. 7944330E+09 20 . 49 0 .0980 0 .0750 0 . 2855 15 . 2977 73 .0430 0. 1 343658E+10 21 .02 0 .0825 0 .0630 0 . 1934 10. 3628 83 .4057 0. 1944747E+10 21 .39 0 .0690 0 .0530 0 . 1293 6 , 9282 90 .3338 0. 2626950E+10 21 .69 0 .0580 PAN 0 . 1804 9 , 6662 100 .0000 Crystal mean size = 0.0974 mm Coefficient of Variation = 42.77 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER 7 EXPERIMENTAL CONDITIONS Feed Temperature = 21.0 Deg. C Residence Time = 100.0 s Feed solution flow rate = MeOH solution flow rate = 1 .47 ml/s 11.03 ml/s Crystallizer Temperature = 25.0 Deg. C Suspension Density = 34.15 gr/1 (2.17 gr/s) • ( 9.23 gr/s) Alcohol/Acld-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01056 gr Na2S04/gr ML 0.14842 gr 38%w/w H2S04/gr ML 0.84102 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.010676 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000432 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained (gr) Wt.% Retalned Cumu1 at 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0. 0010 0 .0544 0. 0544 0 . 2500 0, 0076 0 .4138 0. . 4682 0. 2950376E+06 12 , 59 0, .2750 0 .2120 0. 0183 0 . 9964 1 . 4646 0. 1577112E+07 14. 27 0 .2310 0 . 1800 0. 0533 2 .9019 4 . 3665 0. 8929787E+07 16 .00 0 . 1960 0 . 1500 0. 1640 8 .9291 13 .2956 0. 4912502E+08 17 , 71 0 . 1650 0 . 1060 0. 5762 31 .3715 44 ,6671 0. 2520707E+09 19, .35 0 . 1280 0 . 0900 0. 2975 16 . 1975 60 . 8646 0, 7974833E+09 20, . 50 0 .0980 0 .0750 0. 2440 13 . 2847 74 . 1493 0, 1169415E+ 10 20 .88 0 .0825 0 .0630 0. 1791 9 .7512 83 .9005 0, 1833996E+10 21 .33 0 .0690 0 .0530 0. 1252 6 .8166 90 .7171 0, .2590323E+ 10 21 .68 0 .0580 PAN 0. 1705 9 . 2830 100 .0000 t o Ul Oi Crystal mean size = 0.1007 mm Coefficient of Variation = 40.46 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 0.837095 mm/hr Nuclei population density = 0.4282062E+11 number/mm litre Nucleation rate.B = 0.3584494E+11 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 1.23 ml/s ( 1.81 gr/s) MeOH solution flow rate = 9.19 ml/s . ( 7.69 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01049 gr Na2S04/gr ML 0.14843 gr 38%w/w H2S04/gr ML 0.84 108 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.010602 gr Na2S04/gr solvent Equilibrium concentration = 0.010244 gr Na2S04/gr solvent Supersaturation = 0.000358 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY 'een Size (mm) Weight ( Reta i ned gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average S' (mm) 0 . 3000 0. 0010 0 .0717 0, ,0717 0 . 2500 0. 0072 0 .5163 0. .5880 0.3688078E+06 12. 82 0. 2750 0 .2120 0. 0232 1 . 6636 2 .2515 0.2638172E+07 14 , 79 0. 2310 0 . 1800 0. 0970 6 .9554 9 , 2070 0.2144317E+08 16 ,88 0. 1960 0 . 1500 0. 1655 1 1 . 8672 21 .0742 0 . 654 1 245E+08 18, ,00 0. 1650 0 . 1060 0. 3475 24 .9176 45 .9917 0.2005893E+09 19 . 12 0. 1280 0 .0900 0. 1835 13 . 1579 59 , 1496 0 . 6490445E+09 20 . 29 0. 0980 0 .0750 0. 1892 13 . 5666 72 .7162 0.1196476E+10 20 .90 0. 0825 0 .0630 0. 1290 9 .2500 81 .9662 0.1742997E+10 21 .28 0. 0690 0 .0530 0. 0935 6 .7044 88 .6707 0.2552496E+10 21 .66 0. 0580 PAN 0. 1580 1 1 .3294 100 .0001 Crystal mean size = 0.1008 mm Coefficient of Variation = 50.38 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate - 4.97 ml/s ( 7.33 gr/s) MeOH solution flew rate = 26.28 ml/s • (22.00 gr/s) A 1cohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01370 gr Na2S04/gr ML 0.19726 gr 38%w/w H2S04/gr ML 0.78904 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013893 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000893 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0022 0 .2921 0, ,2921 0 . 2500 0 .0025 0 .3320 0 ,6241 0. 3218544E+06 12 , 68 0 .2750 0 .2120 0 .0057 0 .7569 1 , 3810 0. 1629078E+07 14. 30 0 .2310 0 . 1800 0 .0128 1 . 6996 3 ,0806 0. 7111793E+07 15. ,78 0 . 1960 0 . 1500 0 .0422 5 .6035 8 ,6841 0. 4192054E+08 17, , 55 0 . 1650 0 . 1060 0 .2312 30 .6998 39 ,3839 0. 3354227E+09 19 ,63 0 . 1280 0 .0900 0 . 1282 17 .0230 56 . 4068 0, ,1139668E+10 20 .85 0 .0980 0 .0750 0 . 1223 16 . 2395 72 .6464 0, , 194 3841E+10 21 .39 0 .0825 0 .06 30 0 .0737 9 . 7862 82 .4326 0, 2502801E+10 21 .64 0 .0690 0 .0530 0 .0567 7 . 5289 89 .9614 0, ,3890347E+10 22 .08 0 .0580 PAN 0 .0756 10 .0385 99 .9999 Crystal mean size = 0.0958 mm Coefficient of Variation « 38.68 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER 10 EXPERIMENTAL CONDITIONS Crystallizer Temperature = 25.0 Deg. C Suspension Density = 4S.50 gr/1 ( 5.87 gr/s) (17.60 gr/s) Feed Temperature = 20.0 Deg. C Residence Time = 50.0 s Feed solution flow rate = 3.98 ml/s MeOH solution flow rate = 21.02 ml/s A l c o h o l / A c i d - f e e d r a t i o = 3.0000 g r / g r Mother Liquor (ML) Composition : 0.01363 gr Na2S04/gr ML 0.19727 gr 38%w/w H2S04/gr ML 0.78910 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013816 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000816 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION T POPULATION DENSITY Screen Size (mm) Weight ( Retained !gr) Wt . % Retained Cumulat 1ve Wt .% Retained Population Dens1ty,n (number/mm litre) In n Average Size (mm) 0 . 3000 0, 0018 0.3382 0. 3382 0 . 2500 0. 0031 0.5825 0. 9207 0. 5655728E+06 13 . 25 0. 2750 0 .2120 0. .0043 0.8080 1 , 7287 0. 1741577E+07 14. 37 0. 2310 0 . 1800 0, ,0155 2.9124 4 , 641 1 0. 1220417E+08 16, ,32 0. 1960 0 . 1500 0, ,0451 8.4743 13 , 1 154 0. 6348902E+08 17 , 97 0. 1650 0 . 1060 0 , 1628 30.5900 43 .7054 0. 3347082E+09 19 .63 0. 1280 0 .0900 0 .0758 14.2428 57 . 948 1 0. 9549202E+09 20 .68 0. 0980 0 .0750 0 .0746 14.0173 71 . 9654 0 . 1 680277 E4-10 21 . 24 0. 0825 0 . 0630 0 .0487 9.1507 81 .116 1 0 . 2343663E+10 21 .57 0. 0690 0 .0530 0 .0380 7.1402 88 . 2563 0 .3694843E+10 22 .03 0, ,0580 PAN 0 .0625 11.7437 100 .0000 Crystal mean s 1 ze = 0.0987 mm Coefficient of Variation = • 43 . 14 % CO OI CD CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.278280 mm/hr Nuclei population density = 0.1518030E+12 number/mm litre Nucleation rate.B = 0.1940467E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 3.31 ml/s ( 4.89 gr/s) MeOH solution flow rate = 17.52 ml/s (14.66 gr/s) Alcohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01352 gr Na2S04/gr ML 0.19730 gr 38%w/w H2S04/gr ML 0.78919 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013700 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000700 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0.0015 0. . 2234 0. . 2234 0 . 2500 0.0032 0. . 4785 0. ,6999 0. 4637233E+06 13 , .05 0, , 2750 0 .2120 0.0065 0, , 9680 1 . . 6679 0. 2091077E+07 14. ,55 0, , 2310 0 . 1800 0.029 1 4 , . 3336 6 . 0015 0. 1819918E+08 16 , 72 0 . 1960 0 . 1500 0.071 1 10. .5882 16 . 5897 0. 7950123E+08 18 , 19 0 . 1650 0 . 1060 0.2154 32 , 0774 48 , .6671 0. 3517545E+09 19 ,68 0 . 1280 0 .0900 0.0909 13 . 5369 62. . 2040 0. 9095864E+09 20 .63 0 .0980 0 .0750 0.0780 1 1 , 6158 73 , 8198 0. 1395465E+10 21 .06 0 .0825 0 .0630 0.0556 8 . 2800 82 . 0997 0. 2125315E+10 21 .48 0 .0690 0 .0530 0.0442 6 . 5823 88 , 6820 0. 3413634E+ 10 21 .95 0 .0580 PAN 0.0760 1 1 . 3179 100, .0000 Crystal mean size = 0.1044 mm Coefficient of Variation = 43.56 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1 . 4 1 8 7 0 5 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 2.49 ml/s ( 3.67 gr/s) MeOH solution flow rate = 13.14 ml/s • (11.00 gr/s) A1coho1/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition ; 0.01335 gr Na2S04/gr ML 0.19733 gr 38%w/w H2S04/gr ML 0.78932 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013532 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000532 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0013 0 . 2829 0. , 2829 0 . 2500 0 .004 1 0 .8923 1 . 1752 0. 8710263E+06 13, .68 0 .2750 0 .2120 0 .0065 1 .4146 2 . 5898 0. 3065549E+07 14 ,94 0 .2310 0 . 1800 0 .0212 4 .6137 7 . 2035 0. 1943718E+08 16 . 78 0 . 1960 0 . 1500 0 .057 1 12 . 4266 19 . 6300 0. 9360069E+08 18 , 35 0 . 1650 0 . 1060 0 . 1500 32 . 6442 52 . 2742 0. 3591071E+09 19 .70 0 . 1280 0 .0900 0 . 0583 12 . 6877 64 .9619 0. 8552381E+09 20 .57 0 .0980 0 .0750 0 .0520 1 1 . ,3167 76. , 2786 0. 1363848E+ 10 21 .03 0 .0825 0 .0630 0 .0379 8 . , 2481 84 . , 5267 0. 2123860E+10 21 .48 0 .0690 0 .0530 0 .0298 6 . 4853 91 ,0120 0. 3374035E+10 21 .94 0 .0580 PAN 0 .0413 8 . , 9880 100 .0000 Crystal mean size = 0.1088 mm Coefficient of Variation = 42.70 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER 13 Feed Temperature = 20.0 Deg Residence Time = 80.0 s EXPERIMENTAL CONDITIONS C Feed solution flow rate = 2.49 ml/s MeOH solution flow rate = 13.14 ml/s Alcohol/Acld-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01337 gr Na2S04/gr ML 0.19733 gr 38%w/w H2S04/gr ML 0.78930 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013551 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000551 gr Na2S04/gr solvent Crystallizer Temperature = 25,0 Deg. C Suspension Density = 46.73 gr/1 ( 3.67 gr/s) • (11.00 gr/s) Screen Size (mm) Weight Retained (gr) — . m 1 L ILHJ1 1 I Wt.% Retained Cumulative Wt.% Retained Population Density,n (number/mm 1 1 tre) In n Average Size (mm) 0.3000 0.0020 0.0880 0.0880 0.2500 0.0135 0.5937 0.6817 0 .5793699E+06 13 .27 0 . 2750 0.2120 0.0587 2.5816 3.2633 0 .5592529E+07 15 . 54 0 .2310 0.1800 0.1825 8.0262 11.2895 0, .3380142E+08 17 .34 0 . 1960 0. 1500 0.2500 10.9948 22.2843 0. 8278616E+08 18 .23 0 . 1650 0.1060 0.5340 23.4849 45.7692 0. 2582550E+09 19 .37 0 . 1280 0.0900 0.29 15 12.8 200 58.5892 0. 8638372E+09 20, ,58 0 .0980 0.0750 0.3292 14.4780 73.0671 0. 1744205E+10 21 . 28 0 ,0825 0.0630 0.2280 10.0273 83.0944 0. 2581049E+10 21 . 67 0. 0690 0.0530 0.1564 6.8784 89.9727 0. 3577216E+ 10 22. 00 0. 0580 PAN 0.2280 10.0273 100.0000 Crystal mean size = 0.1002 m m Coefficient of Variation = 52 . 07 % CRYSTALLIZATION KINETICS Crystal growth rate.G Nuclei population density = Nucleation rate.B ! 1 . 156766 mm/hr 1 0.4103342 E+11 number/mm 0.4746606E+11 number/hr 1 1 tre 1 1 tre to o> to RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 3 4 . 2 1 gr/1 Feed solution flow rate = 1.99 ml/s ( 2.93 gr/s) MeOH solution flow rate = 10.51 ml/s . ( 8.80 gr/s) A1cohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01328 gr Na2S04/gr ML 0.19734 gr 38%w/w H2S04/gr ML 0.78937 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013463 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000463 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n ln n Average Size (mm) (gr) (number/mm litre) (mm) 0.3000 0.0014 0. 2422 0. . 2422 0.2500 0.0053 0, 9170 1 , , 1592 0. 8962856E+06 13 . , 7 1 0.2750 0.2120 0.0173 2 . 993 1 4 , 1522 0.6494775E+07 15, ,69 0.2310 0.1800 0.0603 10. 4325 14, ,5848 0. 440086 1E+08 17, ,60 0. 1960 0.1500 0.0895 15 , 4844 30, ,0692 0. 1167855E+09 18, ,58 0. 1650 0.1060 0.1522 26. 3322 56, ,4014 0.2900483E+09 19 ,49 0.1280 0.0900 0.054 1 9 . 3599 65 , . 76 12 0.6317404E+09 20 .26 0.0980 0.0750 0.0625 10. 8132 76 , . 5744 0.1304866E+10 20 .99 0.0825 0.0630 0.0450 7 . 7855 84 , 3598 0.2007346E+10 21 .42 0.0690 0.0530 0.0317 5 . 4844 89, , 8443 0.2857034E+10 21 .77 0.0580 PAN 0.0587 10. 1557 100, ,0000 Crystal mean size = 0.1170 mm Coefficient of Variation = 48.40 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 21.0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 1.66 ml/s ( 2.44 gr/s) MeOH solution flow rate = 8.76 ml/s • ( 7.33 gr/s) A1cohol/Acld-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01322 gr Na2S04/gr ML 0.19736 gr 38%w/w H2S04/gr ML 0.78942 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.013398 gr Na2S04/gr solvent Equilibrium concentration = 0.013000 gr Na2S04/gr solvent Supersaturation = 0.000398 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.0/, Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0010 0 .0444 0 .0444 0 . 2500 0 .0152 0 . 6748 0 . 7 192 0. 6603723E+06 13 .40 0 .2750 0 .2 120 0 .0942 4 , 1818 4 .9010 0. 9085404E+07 16 .02 0 . 2310 0 . 1800 0 . 2400 10 . 6544 15 . 5554 0, 4499941E+08 17 .62 0 . 1960 0 . 1500 0 .2915 12 .9406 28 .4960 0. 9771904E+08 18 .40 0 . 1650 0 . 1060 0 .5160 22 . 9069 51 . 4029 0. 2526274E+09 19 .35 0 . 1280 0 .0900 0 . 2685 1 1 . 9196 63 .3224 0. 8054907E+09 20 .51 0 .0980 0 .0750 0 . 2762 12. 2614 75. ,5838 0. 1481441E+10 21 . 12 0 .0825 0 .06 30 0 . 1940 8 . 6123 84 , 196 1 0. 2223240E+10 21 . 52 0 .0690 0 . 0530 0. .14 10 6 . 2594 90, , 4556 0. 3264752E+10 21 ,91 0 .0580 PAN 0. 2 150 9 . 5445 100, 0001 Crystal mean size = 0.1081 mm Coefficient of Variation = 53.47 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER 16 EXPERIMENTAL CONDITIONS C Crystallizer Temperature = 25.0 Deg. C Suspension Density = 71.08 gr/1 ( 9.03 gr/s) (15.81 gr/s) Feed Temperature = 19.0 Deg Residence Time = 50.0 s Feed solution flow rate = 6.12 ml/s MeOH solution flow rate = 18.88 ml/s Alcohol/Acld-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02087 gr Na2S04/gr ML 0.29374 gr 38%w/w H2S04/gr ML 0.68539 gr 80%w/w MeOH/gr ML Exit solute concentration •= 0.021314 gr Na2S04/gr solvent Equilibrium concentration = 0.020500 gr Na2S04/gr solvent Supersaturation = 0.000814 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight I Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 .0010 0 .0342 0, .0342 0 . 2500 0 .0121 0 .4138 0. .4480 0. 6141215E+06 13. 33 0. 2750 0 .2120 0 .0294 1 .0054 1 .4534 0. 3312563E+07 15 , 01 0. 2310 0 , 1800 0 . 1430 4 . 8902 6 , 3436 0. 3132243E+08 17 . 26 0. 1960 0 . 1500 0 . 3395 1 1 .6100 17 .9536 0. 1329550E+09 18 ,71 0, , 1650 0 . 1060 0 . 9905 33 . 8725 51 . 8262 0. 5665119E+09 20 . 15 0, , 1280 0 .0900 0 . 4470 15 . 2862 67 . 1 124 0, 1566563E+10 21 . 17 0 ,0980 0 .0750 0 . 3592 12 . 2837 79 . 3961 0. ,2250718E+ 10 21 .53 0 .0825 0 .0630 0 . 2285 7 .8141 87 .2102 0. ,3059108E+10 21 .84 0 .0690 0 . 0530 0 . 1495 5 . 1 125 92 .3227 0. .4043865E+10 22 . 12 0 .0580 PAN 0 . 2245 7 .6773 100.0000 to o Ui Crystal mean size = 0.1079 mm Coefficient of Variation = 39.59 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.743898 mm/hr Nuclei population density = 0.7125729E+11 number/mm litre Nucleation rate.B = 0.1242654E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 2 1 . 0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = S.12 ml/s ( 9.03 gr/s) MeOH solution flow rate = 18.88 ml/s ' (15.81 gr/s) A1cohol/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02086 gr Na2S04/gr ML 0.29374 gr 38°/.w/w H2S04/gr ML 0.68540 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.021307 gr Na2S04/gr solvent Equilibrium concentration = 0.020500 gr Na2S04/gr solvent Supersaturation = 0.000807 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained Wt (gr) .% Retained Cumulat 1ve Wt . % Retained Population Density,n (number/mm litre) In n Average Size (mm) 0.3000 0 .0033 0.3092 0 . 3092 0.2 500 0 . 0063 0.5902 0 .8994 0. 8760553E+06 13 . 68 0. 2750 0.2120 0 .0177 1.6582 2 . 5576 0. 5464010E+07 15 .51 0. 2310 0.1800 0 .0607 5.6867 8 . 2443 0. 3642752E+08 17 . 4 1 0. 1960 0.1500 0 . 1398 13.0973 21 . 34 16 0. 1500007E+09 18 .83 0, 1650 0.1060 0 . 3296 30.8788 52 , 2204 0. 5164913 E +09 20 .06 0. 1280 0.0900 0 . 1692 15.8516 68 .0720 0. 1624659E+10 21 . 21 0. ,0980 0.0750 0 . 1405 13.1628 81 . 2348 0. 2412030E+10 21 , 60 0. 0825 0.0630 0 .0823 7.7103 88 . 9451 0. 3018770E+10 21 . 83 0. 0690 0.0530 0. .0544 5.0965 94 . 0416 0. 4031584E+10 22, , 12 0. 0580 PAN 0. 0636 5.9584 100. 0000 Crystal mean size = 0.1084 mm Coefficlent : of Variation » 41 . 26 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER a EXPERIMENTAL CONDITIONS Feed Temperature * 2 1 . 0 Deg. C Crystallizer Temperature <= 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 34.21 gr/1 Feed solution flow rate = 5.10 ml/s ( 7.53 gr/s) MeOH solution flow rate = 15.73 ml/s . (13.17 gr/s) Alcohol/Acid-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02073 gr Na2S04/gr ML 0.29378 gr 38%w/w H2S04/gr ML 0.68549 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.021172 gr Na2S04/gr solvent ' Equilibrium concentration = 0.020500 gr Na2S04/gr solvent Supersaturation = 0.000672 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight 1 Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0029 0 . 3625 0, , 3625 0 . 2500 0 .0062 0 . 7750 1 , 1375 0. 1152298E+07 13 , 96 0. 2750 0 . 2 1 20 0 .0170 2 . 1250 3 , 2625 0. 7014060E+07 15 ,76 0, ,2310 0 . 1800 0 .0563 7 .0375 10 ,3000 0, 4515765E+08 17 .63 0 , 1960 0 . 1500 0 . 1024 12 . 8000 23 . 1000 0, 1468481E+09 18 .80 0 . 1650 0 . 1060 0 . 2306 28 . 8250 5 1 . 9250 0. 4829668E+09 20 .00 0 , 1280 0 .0900 0 . 1 104 13 . 8000 65, . 7250 0, 1416815E+10 21 .07 0 .0980 0 .0750 0 .1111 13 .8875 79 , .6125 0, , 2549191E+10 21 .66 0 .0825 0 .0630 0 .0631 7 . 8875 87 ,5000 0, ,3093440E+10 21 .85 0 .0690 0 . 0530 0 .04 1 1 5 . 1375 92, .6375 0, ,4070997E+10 22 . 13 0 .0580 PAN 0 .0589 7 . 3625 100 .0000 Crystal mean size = 0.1084 mm Coefficient of Variation = 44.29 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.418705 mm/hr Nuclei population density = 0.2186889E+12 number/mm litre Nucleation rate.B = 0.3102550E+12 number/hr litre RUN NUMBER 19 Feed Temperature Residence Time = 19.0 Deg 80.0 s EXPERIMENTAL CONDITIONS C Crystallizer Temperature = 25.0 Deg. C Suspension Density = 71.30 gr/1 ( 5.65 gr/s) ( 9.88 gr/s) Feed solution flow rate = 3.83 ml/s MeOH solution flow rate = 11.80 ml/s A1cohol/Acld-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02063 gr Na2S04/gr ML 0.29381 gr 38%w/w H2S04/gr ML 0.68556 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.021068 gr Na2S04/gr solvent Equilibrium concentration = 0.020500 gr Na2S04/gr solvent Supersaturation = 0.000568 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt .% I 3eta1ned Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0024 0 .3115 0 .3115 0 . 2500 0 .0057 0 . 7399 1 .0514 0, 1101523E+07 13, ,91 0 . 2750 0 .2120 0 .0165 2 .14 17 3 . 1931 0. 7078649E+07 15, .77 0 .2310 0 . 1800 0 .0612 7 .9439 1 1 .1371 0, 5104112E+08 17 , 75 0 . 1960 0 . 1500 0 . 1 124 14 . 5898 25 .7269 0, 1676025E+09 18 , 94 0 . 1650 0 . 1060 0 . 263 1 34 .1511 59 ,8780 0. 5729605E+09 20 . 17 0 . 1280 0 .0900 0 .0900 1 1 .6822 71 . 5602 0. 1200970E+10 20, .91 0 .0980 0 .0750 0 .0756 9 .8131 81 . ,3733 0. 1803666E+10 21 , 31 0 .0825 0 .0630 0 .0487 6 .32 14 87 . ,6947 0. 2482488E+10 21 , 63 0 .0690 0 .0530 0 .0348 4 .5171 92 . 2118 0. 3584132E+10 22 , 00 0 .0580 PAN 0 .0600 7 . 7882 99 . , 9999 to o 00 Crystal mean size = 0.1183 mm Coefficient of Variation = 41.23 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.231772 mm/hr Nuclei population density = 0.4118459E+11 number/mm litre Nucleation rate.B = O.5073004E+11 number/hr litre RUN NUMBER 2 1 EXPERIMENTAL CONDITIONS Feed Temperature = 19.0 Deg. C Crystallizer Temperature = 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 71.42 gr/1 Feed solution flow rate = 3.06 ml/s ( 4.52 gr/s) MeOH solution flow rate = 9.44 ml/s ( 7.90 gr/s) A1coho1/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02058 gr Na2S04/gr ML 0.29383 gr 38%w/w H2S04/gr ML 0.68559 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.021011 gr Na2S04/gr solvent Equilibrium concentration = 0.020500 gr Na2S04/gr solvent Supersaturation = 0.000511 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY •een Size Weight Reta1ned Wt. % Retained Cumulat 1ve Wt.% Retained Population Density,n In n Average Size 1 {mm) (gr) (number/mm 11tre) (mm) 1 0 . 3000 0 . 0028 0 .4014 0 . 4014 t o o 0 . 2500 0 .0139 1 .9928 2 . 3943 0.2969036E+07 14 . 90 0 . 2750 CO 0 . 2 1 20 0 . 0364 5 . 2186 7 . 6129 0.1726037E+08 16 . 66 0 . 2310 1 0 . 1800 0 .0719 10 . 3082 17 . 921 1 0.6627962E+08 18. .01 0 . 1960 0 . 1500 0 . 1032 14 . 7957 32 . 7168 0.1700890E+09 18 , 95 0 . 1650 0 . 1060 0 .2101 30 .1219 62 . 8387 0.5057224E+09 20 .04 0 . , 1280 0 .0900 0 .0782 1 1 .2115 74 .0502 0.1153397E+10 20 .87 0 ,0980 0 .0750 0 .0653 9 . 3620 83 .4122 0.1721985E+10 21 .27 0 .0825 0 .0630 0 .0435 6 . 2366 89 .6487 0.2450923E+10 21 .62 0 .0690 0 .0530 0 .0305 4 . 3728 94 .0215 0.3472056E+10 21 .97 0 .0580 PAN 0 .04 17 5 .9785 100 .0000 Crystal mean size = 0.1238 mm Coefficient of Variation = 44.78 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.011396 mm/hr Nuclei population density = 0.2065747E+11 number/mm litre Nucleation rate.B = 0.2089288E+1 1 number/hr litre RUN NUMBER 2 1 EXPERIMENTAL CONDITIONS Feed Temperature = 19.0 Deg. C Crystallizer Temperature = 25.0 Deg. C Residence Time = 120.0 s Suspension Density = 71.42 gr/1 Feed solution flow rate = 2.55 ml/s ( 3.76 gr/s) MeOH solution flow rate = 7.87 ml/s ( 6.59 gr/s) Alcohol/Acld-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02051 gr Na2S04/gr ML 0.29385 gr 38%w/w H2S04/gr ML 0.68564 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.020938 gr Na2S04/gr solvent Equilibrium concentration = 0.020500 gr Na2S04/gr solvent Supersaturation = 0.000438 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 . 026 1 1 .7334 1 . .7334 0 . 2500 0 . 0669 4 .4431 6 . 1765 0.6625781E+07 15 , 7 1 0. 2750 0 .2 120 0 .0910 6 .0437 12 . 2202 0.2000782E+08 16, ,81 0. 2310 0 . 1800 0 . 1418 9 .4176 21 .6378 0.6060898E+08 17 .92 0. 1960 0 . 1500 0 . 1836 12 . 1937 33 ,8315 0.1403068E+09 18 .76 0. , 1650 0 . 1060 0 .3884 25 . 7953 59 , 6268 0.4334861E+09 19 .89 0 , 1280 0 . 0900 0 .19 12 12 . 6984 72 .3252 0.1307584E+10 20 . 99 0 .0980 0 . 0750 0 . 1646 10 .9318 83 . 2570 0.2012592E+10 21 .42 0 .0825 0 .0630 0 . 0989 6 . 5684 89 . 8254 0.2583726E+10 21 .67 0 .0690 0 .0530 0 .0650 4 . 3 169 94 . 1423 0.3430915E+10 21 .96 0 .0580 PAN 0 .0882 5 .8577 100 .0000 Crystal mean size « 0.1199 mm Coefficient of Variation • = 51 .54 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.011396 mm/hr Nuclei population density = 0.2065747E+11 number/mm litre Nucleation rate.B = 0.2089288E+1 1 number/hr litre RUN NUMBER 22 EXPERIMENTAL CONDITIONS Feed Temperature Residence Time = 26.0 Deg. C 40.0 s Crystallizer Temperature = 30.0 Deg. C Suspension Density = 32.89 gr/1 ( 5.42 gr/s) (23.01 gr/s) Feed solution flow rate = 3.67 ml/s MeOH solution flow rate = 27.58 ml/s Alcohol/Acid-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01190 gr Na2S04/gr ML 0.14822 gr 38%w/w H2S04/gr ML 0.83989 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012038 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation = 0.000889 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained (gr) Wt.% Retained Cumu1 at 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 .0 0 .0 0. 0 0 . 2500 0 .0 0 .0 0. 0 0 . 2 120 0 .0026 0 . 1441 0. 1441 0. 2 197107E+06 12 . 30 0. 2310 0 . 1800 0 .0178 0 .9865 1 , 1306 0. 2924152E+07 14 . 89 0. 1960 0 . 1500 0 .0545 3 .0206 4 . 1512 0. 1600744E+08 16 , 59 0, . 1650 0 . 1060 0 . 2757 15 . 2802 19 .4314 0. .1182638E+09 18 .59 0 . 1280 0 .0900 0 .2561 14 . 1939 33 .6252 0. .6731479E+09 20 .33 0 .0980 0 .0750 0 . 3385 18 . 7607 52 .3860 0 ,1590757E+10 21 . 19 0 .0825 0 . 0630 0 . 2659 14 . 7370 67 . 1230 0 . 2669855E+10 21 .71 0 .0690 0 . 0530 0 . 2010 1 1 . 1401 78 .2630 0 .4077668E+10 22 . 13 0 .0580 PAN 0 . 3922 21 . 7370 100 .0000 t o <1 Crystal mean size = 0.0769 mm Coefficient of Variation = 41.75 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.597252 mm/hr Nuclei population density = 0.1451945E+12 number/mm litre Nucleation rate.B = 0.2319121E+12 number/hr litre RUN NUMBER 28 EXPERIMENTAL CONDITIONS Feed Temperature = 2S.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 120.0 s Suspension Density = 33.31 gr/1 Feed solution flow rate = 2.94 ml/s ( 4.33 gr/s) MeOH solution flow rate = 22.06 ml/s (18.41 gr/s) A1coho1/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01170 gr Na2S04/gr ML 0.14824 gr 38%w/w H2S04/gr ML 0.84005 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011841 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation = 0.000692 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY •een Size Weight Reta1ned Wt. % Retained Cumulat 1ve Wt.% Retained Population Density,n In n Average S-(mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0 0 .0 0. .0 0 . 2500 0 .0015 0 .0708 0. .0708 0. 4885455E+05 10, ,80 0 .2750 0 .2120 0 .0050 0 . 2359 0. .3066 0. 3615193E+06 12 ,80 0 .2310 0 . 1800 0 .0360 1 . 6984 2 . 0050 0. 5060183E+07 15, .44 0 . 1960 0 . 1500 0 . 1300 6 . 1329 8 . 1380 0. 3267026E+08 17 .30 0 . 1650 0 . 1060 0 . 6070 28 . 6362 36 7741 0. 2227860E+09 19 . 22 0 . 1280 0 . 0900 0 . 3485 16 . 44 10 53 .2151 0. 7837676E+09 20 .48 0 .0980 0 .0750 0 . 3405 16 . 0636 69 . 2787 0, 1 369134E+10 21 .04 0 .0825 0 .0630 0 . 2392 1 1 . 2846 80 . 5633 0. 2055011E+10 21 .44 0 .0690 0 .0530 0 . 1645 7 . 7605 88 . 3239 0, ,2855390E+10 21 .77 0 .0580 PAN 0 . 2475 1 1 .6762 100 ,0000 Crystal mean size = 0.0930 mm Coefficient of Variation = 39.99 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 28 EXPERIMENTAL CONDITIONS Feed Temperature = 2S.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 120.0 s Suspension Density = 33.31 gr/1 Feed solution flow rate = 2.45 ml/s ' ( 3.61 gr/s) MeOH solution flow rate = 18.38 ml/s (15.34 gr/s) A l c o h o l / A c l d - f e e d r a t i o = 4.2500 g r / g r Mother Liquor (ML) Composition : 0.01164 gr Na2S04/gr ML 0.14825 gr 38°/.w/w H2S04/gr ML 0.84010 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011780 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation = 0.000631 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY :reen Size (mm) Weight Retained (gr) Wt . % Retained Cumulat 1ve Wt . % Retained Population Density,n (number/mm litre) In n Average SI (mm) 0 . 3000 0 .0063 0.3218 0. 3218 0 . 2 500 0 .0380 1.9409 2 . 2626 0. 1 34207 1E+07 14 . 11 0. 2750 0 .2120 0 . 0667 3.4067 5. 6693 0.5229564E+07 15 . 47 0. 2310 0 . 1800 0 . 1 134 5.7919 11 . 4613 0.1728443E+08 16 . 67 0. 1960 0 . 1500 0 . 1802 9.2037 20. ,6650 0.4910683E+08 17 , 71 0. 1650' 0 . 1060 0 . 4987 25.47 12 46 , . 1362 0.1984800E+09 19 , 1 1 0. 1280 0 . 0900 0 . 2862 14.6177 60 .7539 0.6979635E+09 20 .36 0. 0980 0 .0750 0 .2651 13.5400 74 . 2939 0.1155892E+10 20 .87 0. 0825 0 .0630 0 . 1785 9.1169 83 .4108 0.1662913E+10 21 .23 0. ,0690 0 .0530 0 . 1263 6.4508 89 .8616 0. 2377285E+10 21 .59 0 .0580 PAN 0 . 1985 10.1384 100 .0000 Crystal mean s Ize = 0.1016 mm Coefficient of Variation = ' 49 .87 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 28 EXPERIMENTAL CONDITIONS Feed Temperature = 2S.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 120.0 s Suspension Density = 33.31 gr/1 Feed solution flow rate = 1.84 ml/s ( 2.71 gr/s) MeOH solution flow rate = 13.79 ml/s (11.51 gr/s) Alcohol/Acld-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01153 gr Na2S04/gr ML 0.14827 gr 38%w/w H2S04/gr ML 0.84020 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011661 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation => 0.000512 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY •een Size Weight I Reta1ned Wt.% Retained Cumulat 1ve Wt.% Reta1ned Population Dens1ty,n In n Average Size (mm) (gr) (number/mm litre) (mm) 1 0 . 3000 0 .0025 0 . 1280 0. 1280 to <1 0 . 2500 0 .0115 0 . 5888 0, 7 168 0. 4084426E+06 12 . 92 0. 2750 0 . 2 1 20 0 .034 1 1 . 7460 2 . 4629 0. 2688657E+07 14. 80 0. 2310 1 0 . 1800 0 . 1272 6 .5131 8 . 9759 0, 1949710E+08 16 , 79 0. . 1960 0 . 1500 0 . 2510 12 . 8520 21 . 8280 0, ,6878635E+08 18 . 05 0 ,1650 0 . 1060 0 .4670 23 .9120 45. .7399 0, . 18691 12E+09 19. .05 0 , 1280 0 .0900 0 . 2595 13 . 2873 59 .0272 0 , 6364170E+09 20 . 27 0 .0980 0 .0750 0 . 2425 12 .4168 71 .4440 0 .1063311E+10 20 .78 0 .0825 0 .0630 0 . 1672 8 . 56 12 80 .0052 0 . 1 566422E+10 21 . 17 0 .0690 0 .0530 0 . 1 195 6 . 1 188 86 . 1240 0 .2261971E+10 21 . 54 0 .0580 PAN 0 . 27 10 13 .8761 100 .0001 Crystal mean size = 0.1006 mm Coefficient of Variation = 52.67 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 26 EXPERIMENTAL CONDITIONS Feed Temperature = 26.0 Deg. C Residence Time = 100.0 s Feed solution flow rate = MeOH solution flow rate = 1 .47 ml/s 1 1 .03 ml/s Crystallizer Temperature = 30.0 Deg. C Suspension Density = 33.31 gr/1 ( 2.17 gr/s) ( 9.21 gr/s) Alcohol/Acid-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01143 gr Na2S04/gr ML 0.14829 gr 38%w/w H2S04/gr ML 0.84029 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011559 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation = 0.000411 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight ( Retalned gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Denslty.n (number/mm 11tre) ln n Average Size (mm) 0 . 3000 0. 0048 0 . 2839 0, 2839 0 . 2500 0. 0250 1 . 4784 1 , , 7623 0. 1028205E+07 13. 84 0. 2750 0 .2120 0. 0853 5 .0444 6 . 8066 0. 7788195E+07 15 , 87 0, ,2310 0 . 1800 0. 1895 1 1 . 2064 18 .0130 0. 3363560E+08 17 , .33 0. . 1960 0 . 1500 0. 2069 12 . 2354 30 . 2484 0. 6565918E+08 18 , .00 0 . 1650 0 . 1060 0. 38 10 22 . 531 1 52 . 7794 0. 1765835E+09 18 . 99 0 . 1280 0 .0900 0. 2000 1 1 . 8273 64 .6068 0. 5679900E+09 20 . 16 0 .0980 0 .0750 0. 1805 10 . 6742 75 .2809 0. 9164992E+09 20 . 64 0 .0825 0 . 06 30 0. 1270 7 . 5 104 82 .7913 0. 1377790E+10 21 .04 0 .0690 0 .0530 0. 0955 5 .6476 88 .4388 0. 2093289E+10 21 . 46 0 .0580 PAN 0. 1955 1 1 .5612 100 .0000 to <1 m Crystal mean size = 0.1102 mm Coefficient of Variation = 56.33 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.077503 mm/hr Nuclei population density = 0.1494455E+11 number/mm litre Nucleation rate.B - 0. 1610279E+11 number/hr litre RUN NUMBER 28 EXPERIMENTAL CONDITIONS Feed Temperature = 2S.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 120.0 s Suspension Density = 33.31 gr/1 Feed solution flow rate = 1.47 ml/s ' ( 2.17 gr/s) MeOH solution flow rate = 11.03 ml/s ( 9.21 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition ; 0.01145 gr Na2S04/gr ML 0.14828 gr 38%w/w H2S04/gr ML 0.84026 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011586 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation = 0.000437 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0117 0. 5619 0. , 56 19 0 . 2 500 0 .0450 2 . 1611 2, , 7230 0. 1501938E+07 14 , 22 0. .2750 0 .2120 0 .0973 4 . 6727 7 . 3957 0. 7209418E+07 15 , 79 0 ,2310 0 . 1800 0 . 1532 7 , .3573 14, ,7529 0. 2206723E+08 16, ,91 0 , 1960 0 . 1500 0 . 2322 1 1 .1511 25 , 904 1 0. 5979944E+08 17 , .91 0 . 1650 0 . 1060 0 . 5656 27 , . 1623 53 .0663 0. 2127328E+09 19 , 18 0 . 1280 0 .0900 0 . 2778 13 . 3410 66 , 4074 0. ,6402401E+09 20 , 28 0 .0980 0 .0750 0 . 2356 1 1 . ,3144 77 , 7218 0, 9708009E+09 20 .69 0 .0825 0 .0630 0 . 1643 7 . 8903 85 ,6121 0. .1446493E+ 10 21 .09 0 .0690 0 .0530 0 . 1 129 5 .4219 91 .0340 0 .2008258E+10 21 .42 0 .0580 PAN 0 . 1867 8 ,9661 100 .0000 Crystal mean size = 0.1099 mm Coefficient of Variation = 50.19 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 28 EXPERIMENTAL CONDITIONS Feed Temperature = 2S.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 120.0 s Suspension Density = 33.31 gr/1 Feed solution flow rate = 1.22 ml/s ' (1.81 gr/s) MeOH solution flow rate = 9.19 ml/s ( 7.67 gr/s) Alcohol/Acld-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01142 gr Na2S04/gr ML 0.14829 gr 38%w/w H2S04/gr ML 0.84029 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.011550 gr Na2S04/gr solvent Equilibrium concentration = 0.011149 gr Na2S04/gr solvent Supersaturation = 0.000401 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY •een Size (mm) Weight Retained (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average S( (mm) 0 . 3000 0 .0136 0. . 5753 0. 5753 0 . 2500 0 .0533 2. . 2547 2 , 8300 0. 1568438E+07 14 . 27 0. 2750 0 . 2 1 20 0 . 1 146 4 . 8477 7 , .6777 0. 7486388E+07 15. 83 0. 2310 0 . 1800 0 . 1789 7 . 5677 15. . 2454 0. 2271957E+08 16 . 94 0, 1960 0 . 1500 0 . 2669 1 1 . 2902 26 , 5356 0. 6060157E+08 17. ,92 0. . 1650 0 . 1060 0 . 6350 26 .8613 53 . 3968 0. 2105713E+09 19 . 17 0 . 1280 0 .0900 0 .3 157 13 .3545 66 .7513 0, 6414835E+09 20 .28 0 .0980 0 .0750 0 . 2655 1 1 . 2310 77 .9823 0, .9645386E+09 20 .69 0 .0825 0 .0630 0 . 1858 7 . 8596 85 .8419 0, . 1442198E+10 21 .09 0 .0690 0 .0530 0 .1251 5 . 2919 91 . 1337 0 . 196 1929E+10 21 .40 0 .0580 PAN 0 . 2096 8 . 8663 100 .0001 Crystal mean size = 0.1104 mm Coefficient of Variation = 50.55 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 1 3 9 2 8 12E+12 number/hr litre RUN NUMBER 28 EXPERIMENTAL CONDITIONS Feed Temperature = 2S.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 120.0 s Suspension Density = 33.31 gr/1 Feed solution flow rate = 4.96 ml/s ( 7.32 gr/s) MeOH solution flow rate = 26.29 ml/s (21.95 gr/s) Alcohol/Acld-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01500 gr Na2S04/gr ML 0.19700 gr 38°/,w/w H2S04/gr ML 0.78800 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.015224 gr Na2S04/gr solvent Equilibrium concentration = 0.014360 gr Na2S04/gr solvent Supersaturation = 0.000864 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) ( gr) (number/mm litre) (mm) 0 . 3000 0. 004 1 0. . 1636 0. 1636 0 . 2500 0. 0160 0. . 6383 0. ,8019 0. 6019743E+06 13. .31 0. . 2750 0 .2120 0. 0379 1 . .5119 2 . 3138 0. 3165519E+07 14 , .97 0 .2310 0 . 1800 0. 1645 6 . 5624 8 . 8762 0. 2670998E+08 17 . 10 0 . 1960 0 . 1500 0. 2958 1 1 . . 8004 20 . 6766 0, 8587194E+08 18 . 27 0 . 1650 0 . 1060 0. 7002 27 . 9332 48 , 6098 0. 2968691E+09 19 .51 0 . 1280 0 .0900 0. 3488 13 , .9147 62 . 5245 0. 9061612E+09 20 .62 0 .0980 0 .0750 0. 3236 12. 9094 75 . 4339 0.1503078E+10 21 . 13 0 .0825 0 . 06 30 0. 2124 8 . 4733 83 . 9072 0. .2107908E+10 21 . 47 0 .0690 0 .0530 0. 158 1 6 , 307 1 90 .2143 0. .3170120E+10 21 . 88 0 .0580 PAN 0. 2453 9 . 7858 100 .0001 Crystal mean size = 0.1043 mm Coefficient of Variation = 46.73 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 30 EXPERIMENTAL CONDITIONS Feed Temperature = 25.0 Deg. C Residence Time = 50.0 s Feed solution flow rate = MeOH solution flow rate = 3.97 ml/s 21.03 ml/s Crystallizer Temperature = 30.0 Deg. C Suspension Density = 45.25 gr/1 ( 5.85 gr/s) (17.55 gr/s) Alcohol/Acid-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01491 gr Na2S04/gr ML 0.19702 gr 38%w/w H2S04/gr ML 0.78807 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.015132 gr Na2S04/gr solvent Equilibrium concentration = 0.014360 gr Na2S04/gr solvent Supersaturation = 0.000772 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) 0.3000 0.2500 0.2 120 0.1800 O.1500 0.1060 0.0900 0.0750 0.0630 0.0530 PAN Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n ln n Average Size y \ ! imkflh /r 1 4 +• 1 ( mm I (gr) 0.0039 0.0165 0.0348 0.0649 0.1129 0.3084 0.1547 O.1480 0.0928 0.0641 0.0966 0.3553 1.5033 3.1706 5.9129 10 . 2861 28.0977 14.0944 13.4840 8.4548 5.8400 8.8010 0.3553 1.8586 5.0292 10.9421 2 1 . 2 2 8 1 49.3258 63.4202 76.9042 85.3590 91.1990 100.0000 (number/mm litre) (mm) 0.1420264E+07 14.17 0.2750 0.6649853E+07 15.71 0.2310 0.2410902E+08 17.00 0.1960 O.7498501E+08 18.13 0.1650 0.2991470E+09 19.52 0.1280 O.9194893E+09 20.64 0.0980 0.1572759E+10 21.18 0.0825 0.2107038E+10 21.47 0.0690 0.2940556E+10 21.80 0.0580 t o <1 CD Crystal mean size = 0.1052 mm Coefficient of Variation = 46.55 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.011080 mm/hr Nuclei population density = 0.2720848E+11 number/mm litre Nucleation rate.B = 0.547 1842E+11 number/hr litre RUN NUMBER 31 EXPERIMENTAL CONDITIONS Feed Temperature = 25.0 Deg. C Crystallizer Temperature = 30.0 Deg. C Residence Time = SO.O s Suspension Density = 45.38 gr/1 Feed solution flow rate = 3.31 ml/s ( 4.88 gr/s) MeOH solution flow rate = 17.52 ml/s (14.63 gr/s) A1cohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01476 gr Na2S04/gr ML 0.19705 gr 38%w/w H2S04/gr ML 0.78819 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.014980 gr Na2S04/gr solvent Equilibrium concentration = 0.014360 gr Na2S04/gr solvent Supersaturation = 0.000620 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY -een Size Weight I Reta1ned Wt. % Retained Cumulat 1ve Wt.% Retained Population Density,n 1 n n Average Size I (mm) !gr) (number/mm litre) (mm) j 0 . 3000 0 .0038 0 . 137 1 0. 1371 is: 00 0 . 2 500 0 .0181 0 . 6532 0. 7903 0.6189278E+06 13 . 34 0. 2750 O 0 .2120 0 .0578 2 .0858 2 . 8761 0.4387702E+07 15 . 29 0. 2310 1 0 . 1800 0 . 1667 6 .0157 8 . 89 18 0.2460067E+08 17 .02 0, 1960 0 . 1500 0 .3580 12 .9191 21 . 8108 0.9445822E+08 18 . 36 0, . 1650 0 . 1060 0 . 9030 32 . 5863 54 , 3972 0.3479642E+09 19 .67 0 . 1280 0 .0900 0 . 3735 13 . 4784 67 , 8756 0.8819075E+09 • 20 .60 0 .0980 0 .0750 0 . 3 190 1 1 .5117 79 . 3873 0.1346689E+10 21 .02 0 .0825 0 .0630 0 . 1902 6 . 8637 86 .2509 0.1715580E+10 21 .26 0 .0690 0 .0530 0 .1310 4 .7274 90 .9783 0.2387364E+10 21 .59 0 .0580 PAN 0 .2500 9 .0217 100 .0000 Crystal mean size = 0.1112 mm Coefficient of Variation = 42.19 % CRYSTALLIZATION KINETICS Crystal growth rate,G = 1.585839 mm/hr Nuclei population density = 0.3106594E+11 number/mm litre Nucleation rate.B = O.4926559E+11 number/hr litre RUN NUMBER 32 Feed Temperature = 25.0 Deg Residence Time = 80.0 s EXPERIMENTAL CONDITIONS C Feed solution flow rate = MeOH solution flow rate = 2 .48 ml/s 13.14 ml/s Crystallizer Temperature = 30.0 Deg. C Suspension Density = 45.40 gr/1 ( 3.66 gr/s) (10.97 gr/s) A l c o h o l / A c i d - f e e d r a t i o » 3.0000 g r / g r Mother Liquor (ML) Composition : 0.01473 gr Na2S04/gr ML 0.19705 gr 38°/.w/w H2S04/gr ML 0.78821 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.014952 gr Na2S04/gr solvent Equilibrium concentration = 0.014360 gr Na2S04/gr solvent Supersaturation = 0.000592 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight 1 Reta1ned !gr) Wt.% Retained Cumulat1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 .0063 0 . 2275 0. 2275 0 . 2500 0 .0365 1 .3179 1 . 5454 0. 1249514 E+07 14 . 04 0.2750 0 .2120 0 .0858 3 .0980 4 , 6434 0. 6520539E+07 15. 69 0.2310 0 . 1800 0 . 1477 5 .3331 9. .9765 0. 2182122E+08 16, ,90 0.1960 0 . 1500 0 . 2465 8 .9005 18 .8771 0. 6511195E+08 17 .99 0.1650 0 . 1060 0 . 6685 24 . 1379 43 ,0150 0. 2578904E+09 19 .37 0.1280 0 .0900 0 . 4050 14 . 6236 57 . 6386 0. 9573583E+09 20 .68 0.0980 0 .0750 0 . 3970 14 . 3347 7 1 . 9733 0. 1677855E+10 21 .24 0.0825 0 .0630 0 .2717 9 . 8 104 81 . 7837 0. 2453452E+10 21 .62 0.0690 0 .0530 0 . 1860 6 . 7 160 88 . 4997 0, 3393495E+10 21 .95 0.0580 PAN 0 .3185 1 1 .5003 100 .0000 to 00 Crystal mean size = 0.0980 mm Coefficient of Variation = 50.19 % Crystal growth rate.G Nuclei population density Nucleation rate.B CRYSTALLIZATION KINETICS 1 .218064 mm/hr 0.3161637E+11 number/mm litre 0.3851077E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.99 m 1/s ( 2.93 gr/s) MeOH solution flow rate * 10.51 ml/s ( 8.78 gr/s) A1cohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01461 gr Na2S04/gr ML 0.19708 gr 38%w/w H2S04/gr ML 0.78831 gr 80°/°w/w MeOH/gr ML Exit solute concentration = 0.014823 gr Na2S04/gr solvent Equilibrium concentration = 0.014360 gr Na2S04/gr solvent Supersaturation = 0.000463 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY -een Size (mm) Weight 1 Reta1ned ! gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 1 1tre) 1 n n Average S1 (mm) 0 . 3000 0 .0173 0 ,6021 0. 6021 0 . 2500 0 .0939 3 .2681 3. 8703 0. 3 106193E+07 14. 95 0. 2750 0 . 2 120 0 . 1528 5 ,3181 9 . 1884 0. 1122106E+08 16 . 23 0. 2310 0 . 1800 0 . 2367 8 . 2382 17 , 4266 0. 3379176E+08 17 , 34 0. 1960 0 . 1500 0 . 2985 10 . 3891 27 . ,8157 0. 7619075E+08 18 . 15 0. 1650 0 . 1060 0 . 7046 24 . 5232 52 ,3389 0. 2626580E+09 19 .39 0. 1280 0 .0900 0 . 3650 12 .7036 65 ,0425 0. 8337324E+09 20 .54 0. 0980 0 .0750 0 . 3530 12 .2860 77 .3284 0. 1441626E+ 10 21 .09 0. 0825 0 .0630 0 . 2222 7 .7335 85 .0620 0. 1938858E+10 21 . 39 0. 0690 0 . 0530 0 . 1502 5 . 2276 90 . 2896 0. 2648004E+10 21 .70 0, .0580 PAN 0 . 2790 9 .7104 100 .0000 Crystal mean size = 0.1093 mm Coefficient of Variation = 54.92 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.65 ml/s ( 2.44 gr/s) MeOH solution flow rate = 8.76 ml/s ( 7.32 gr/s) Alcohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01453 gr Na2S04/gr ML 0. 19709 gr 38°/.w/w H2S04/gr ML 0.78837 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.014748 gr Na2S04/gr solvent Equilibrium concentration = 0.014360 gr Na2S04/gr solvent Supersaturation = 0.000388 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight ( Retained Wt. gr) % Retained Cumulative Wt .% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 . 024 1 2 . 2394 2 . 2394 0 . 2500 0. 0506 4 .7017 6 . 941 1 0.4475232E+07 15. 31 0. 2750 0 .2120 0. 0589 5 . 4730 12. 4141 0.1156453E+08 16. 26 0. 2310 0 . 1800 0. 1 109 10 . 3048 22. 7188 0.4232981E+08 17 . 56 0. 1960 0 . 1500 0. 1459 13 . 5570 36 . 2758 0.9956702E+08 18 , 42 0. 1650 0 . 1060 0. 2599 24 . 1498 60. ,4256 0.2590337E+09 19, ,37 0, , 1280 0 .0900 0. 1010 9 . 3849 69 .8104 0.6168184E+09 20 .24 0, .0980 0 .0750 0. 1094 10 . 1654 79 .9758 0.1194531E+10 20 .90 0 .0825 0 .0630 0. 0688 6 .3929 86 . 3687 0.1605064E+10 21 .20 0 .0690 0 .0530 0. 0483 4 . 4880 90 .8567 0.2276660E+10 21 .55 0 .0580 PAN 0. 0984 9 . 1433 100 .0000 Crystal mean size = 0.1246 mm Coefficient of Variation = • 52 .62 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 35 EXPERIMENTAL CONDITIONS Feed Temperature = 24.0 Deg. C Crystallizer Temperature « 30.0 Deg. C Residence Time = 50.0 s Suspension Density = 68.88 gr/1 Feed solution flow rate = 6.12 ml/s ' ( 9.02 gr/s) MeOH solution flow rate = 18.88 ml/s (15.78 gr/s) Alcohol/Acld-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02305 gr Na2S04/gr ML 0.29309 gr 38%w/w H2S04/gr ML 0.68387 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.023591 gr Na2S04/gr solvent Equilibrium concentration = 0.022690 gr Na2S04/gr solvent Supersaturation = 0.000901 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY -een Size Weight I Reta1ned Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n 1 n n Av< srage Size (mm) (gr) (number/mm 11tre) (mm) 0 . 3000 0 . 0296 1.0062 1 , .0062 to 00 0 . 2500 0 .0722 2 .4544 3 . 4606 0.3530275E+07 15 . 08 0. 2750 ^ 0 .2120 0 . 1 159 3.9399 7 . 4005 0.1258064E+08 16. 35 0. 2310 1 0 . 1800 0 .2171 7.3801 14 ,7806 0.4581218E+08 17 , 64 0. 1960 0 . 1500 0 . 3496 11.8843 26 .6649 0 .'1 3 18980E+09 18, ,70 0. 1650 0 . 1060 0 .8519 28.9595 55 .6243 0.4694021E+09 19 ,97 0, , 1280 0 .0900 0 . 3944 13.4072 69 .0315 0. 1331617E+10 21 .01 0 ,0980 0 .0750 0 . 3252 11.0548 80 .0863 0.1963076E+10 21 .40 0 .0825 0 . 0630 0 .2188 7.4379 87 . 5242 0.2822004E+10 21 .76 0 .0690 0 .0530 0 . 1375 4.6742 92 . 1984 0.3583108E+10 22 .00 0 .0580 PAN 0 . 2295 7.8016 100 .0000 Crystal mean size = 0.1130 mm Coefficient of Variation = 47.39 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.193558 mm/hr Nuclei population density •= 0. 2847033E+1 1 number/mm litre Nucleation rate.B = 0.6245131E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 5.10 ml/s ( 7.51 gr/s) MeOH solution flow rate = 15.74 ml/s (13.15 gr/s) A 1 coho1/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02287 gr Na2S04/gr ML 0.29314 gr 38%w/w H2S04/gr ML 0.68399 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.023405 gr Na2S04/gr solvent Equilibrium concentration = 0.022690 gr Na2S04/gr solvent Supersaturation = 0.000715 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen S1ze (mm) Weight Retained Wt (gr) .% Retained Cumu1 at 1ve Wt , % Retained Population Density,h (number/mm 11tre) 1 n n Average Size (mm) 0 . 3000 0 .0192 0.7852 0 . 7852 0 . 2500 0 .0857 3.5047 4 . 2899 0. 5053303E+07 15 .44 0 . 2750 0 .2120 0 . 1 123 4.5925 8 .8824 0. 1470016E+08 16 .50 0 . 2310 0 . 1800 0 . 2032 8.3098 17 . 1922 0. 5 170922E+08 17 .76 0 . 1960 0 . 1500 0 .306 1 12.5179 29 .7101 0. 1392686E+09 18 .75 0 . 1650 0 . 1060 0 . 6874 28. 111 1 57 . ,8212 0. 4567611E+09 19 .94 0 . 1280 0 .0900 0 . 3229 13.2049 71 . 0261 0. 1 314721E+10 21 .00 0 .0980 0 .0750 0 . 3003 12.2807 83. 3068 0. 2186076E+10 21 .51 0 .0825 0 .0630 0 . 1644 6.7231 90. 0299 0. 2557027E+10 21 , 66 0 .0690 0 .0530 0. , 1054 4.3103 94 . 3402 0. 3312235E+10 21 , .92 0 .0580 PAN 0. 1384 5.6598 100. 0001 Crystal mean size =0.1165 mm Coeff1c1ent of Variation = 47, ,06 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 5.10 ml/s ( 7.51 gr/s) MeOH solution flow rate = 15.74 ml/s (13.15 gr/s) A1cohol/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02291 gr Na2S04/gr ML 0.29313 gr 38%w/w H2S04/gr ML 0.68396 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.023447 gr Na2S04/gr solvent Equilibrium concentration = 0.022690 gr Na2S04/gr solvent Supersaturation = 0.000757 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n ln n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0075 0 . 2528 0. 2528 0 . 2500 0 .0845 2 , 8477 3. 1005 0. 4103787E+07 15. 23 0. 2750 0 .2120 0 . 1984 6 .6862 9 . 7867 0.2139032E+08 16. 88 0. 2310 0 . 1800 0 . 2967 9 , 9990 19. 7857 0. 6218643E+08 17 , 95 0. 1960 0 . 1500 0 . 3665 12 ,3513 32 . 1370 0. 1373401E+09 18 , 74 0, 1650 0 . 1060 0 . 6765 22 . 7985 54 , 9355 0. 3702380E+09 19 , 73 0 , 1280 0 .0900 0 . 3550 1 1 .9638 66. ,8992 0. 1190495E+10 20 .90 0 .0980 0 .0750 0 . 3605 12 . 1491 79, ,0483 0. 2161467E+10 21 .49 0 .0825 0 .06 30 0 . 2242 7 .5557 86, ,6040 0, , 2872123E+10 21 .78 0 .0690 0 . 0530 0 .1515 5 . 1057 91 , 7097 0 .3921269E+10 22 .09 0 .0580 PAN 0 . 2460 8 ,2904 100 .0000 Crystal mean size = 0.1138 mm Coefficient of Variation = 54.14 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 38 EXPERIMENTAL CONDITIONS C Crystallizer Temperature = 30.0 Deg. C Suspension Density = 69.17 gr/1 ( 5.63 gr/s) ( 9.86 gr/s) Feed Temperature = 24.0 Ceg Residence Time = 80.0 s Feed solution flow rate = 3.82 ml/s MeOH solution flow rate = 11.80 ml/s A1cohol/Acid-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02274 gr Na2S04/gr ML 0.29318 gr 38%w/w H2S04/gr ML 0.68408 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.023270 gr Na2S04/gr solvent Equilibrium concentration = 0.022690 gr Na2S04/gr solvent Supersaturation = 0.000580 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) 1 n n Average Size (mm) 0 . 3000 0 .0193 1 , ,7780 1 . 7780 0 . 2500 0 .0600 5 . ,5274 7. 3054 0. 7983845E+07 15. 89 0. 2750 0 .2120 0 .0801 7 .3791 14 . 6845 0. 2366142E+08 16. 98 0. 2310 0 . 1800 0 . 1 169 10 .7692 25. 4537 0. 6713133E+08 18 , 02 0. 1960 0 . 1500 0 . 1403 12 .9249 38. 3786 0. 1440502E+09 18, .79 0. 1650 0 . 1060 0 . 2806 25 .8499 64 , 2285 0, 4207588E+09 19 .86 0. , 1280 0 .0900 0 .1151 10 .6034 74 .8319 0. ,1057565E+10 20 .78 0 .0980 0 .0750 0 . 1000 9 .2124 84 .0443 •o ,1642768E+10 21 . 22 0 .0825 0 .0630 0 .0641 5 .9051 89 .9494 0 .2249876E+10 21 .53 0 .0690 0 .0530 0 .0415 3 . 823 1 93 .7725 0 .2943031E+10 21 .80 0 .0580 PAN 0 .0676 6 .2276 100 .0000 CO 00 o Crystal mean size = 0.1287 mm Coefficient of Variation = 51.40 % Crystal growth rate.G Nuclei population density Nucleation rate.B CRYSTALLIZATION KINETICS 1 . 623364 mm/hr 0.1516276E+1 1 number/mm litre 0. 2461468E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.06 ml/s ( 4.51 gr/s) MeOH solution flow rate = 9.44 ml/s ( 7.89 gr/s) A 1cohol/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02267 gr Na2S04/gr ML 0.29320 gr 38%w/w H2S04/gr ML 0.68413 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.023200 gr Na2S04/gr solvent Equilibrium concentration = 0.022690 gr Na2S04/gr solvent Supersaturation = 0.000510 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained Wt (gr) .% Retained Cumulative Wt Retained Population Denslty.n (number/mm 11tre) In n Average Size (mm) 0.3000 0 .0710 2.7283 2 . 7283 0.2 500 0 .1615 6.2058 8 .9341 0. 8971863E+07 16 .01 0.2750 0.2120 0 . 2089 8.0272 16 .9613 0. 2576296E+08 17 .06 0.2310 0.1800 0 . 2782 10.6901 27 .6514 0. 6669866E+08 18 .02 0.1960 0.1500 0 . 2860 10.9899 38 .6413 0. 1225946E+09 18 .62 0.1650 0.1060 0 . 5545 21.3073 59 . 9485 0. 3471337E+09 19. .67 0.1280 0.0900 0 . 2753 10.5787 70. 5272 0. 1056057E+10 20, .78 0.0980 0.0750 0. 2685 10.3174 80. 8446 0. 1841491E+10 21 , 33 0.0825 0.0630 0. 1660 6.3787 87 . 2234 0. 2432526E+10 21 . ,61 • 0.0690 0.0530 0. 1205 4.6303 91 . 8537 0. 3567659E+10 22. 00 0.0580 PAN 0. 2120 8.1463 100. 0000 Crystal mean size = 0.1241 mm Coeff1c1ent of Variation = 58 . 84 % CRYSTALLIZATION KINETICS to 00 00 Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 2.55 ml/s ( 3.76 gr/s) MeOH solution flow rate = 7.87 ml/s ( 6.57 gr/s) Alcohol/Acid-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02256 gr Na2S04/gr ML 0.29323 gr 38%w/w H2S04/gr ML 0.68420 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.023086 gr Na2S04/gr solvent Equilibrium concentration = 0.022690 gr Na2S04/gr solvent Supersaturation = 0.000396 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY •een Size (mm) Weight Retained (gr) Wt . % Retained Cumu!at 1ve Wt .% Retained Population Denslty.n (number/mm 11tre) ln n Average SI (mm) 0 . 3000 0 . 1202 3.1283 3 . 1283 0 . 2500 0 . 3246 8.4478 11 . 5761 0.1223147E+08 16. 32 0.2750 0 . 2 120 0 . 3762 9,7908 21 , 3669 0.3146998E+08 17. 26 0.2310 0 . 1800 0 .421 1 10.9593 32 , 3262 0.6848026E+08 18 . 04 0.1960 0 . 1500 0 . 439 1 11.4278 43 . 7539 0.1276700E+09 18 ,66 0.1650 0 . 1060 0 . 7702 20.0448 63 .7987 0.3270536E+09 19 .61 0.1280 0 . 0900 0 .3813 9.9235 73 , 7222 0.9921290E+09 20 .72 0.0980 0 .0750 0 . 3847 10.0120 83 .7341 0,1789648E+10 21 .31 0.0825 0 . 06 30 0 . 2395 6.233 1 89 .9672 0.2380538E+10 2 1 .59 0.0690 0 . 0530 0 . 1582 4.1172 94 .0844 0.3177040E+10 21 .88 0.0580 PAN 0 . 2273 5.9156 100 .0000 Crystal mean s 1 ze =0.1345 mm Coefficient of Variation = ' 58 . 17 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.67 ml/s ' ( 5.40 gr/s) MeOH solution flow rate = 27.58 ml/s (22.96 gr/s) Alcohol/Acld-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01276 gr Na2S04/gr ML 0.14809 gr 38%w/w H2S04/gr ML O.83915 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012928 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000859 gr Na2S04/gr solvent PRODUCT CRYSTAL .SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average Size (mm) ( ^gr) (number/mm litre) (mm) 0.3000 0. .004 2 0 . 2466 0. 2466 0.2500 0. .0197 1 . 1568 1 . ,4034 0.7741638E+06 13. 56 0.2750 0.2120 0, 0352 2 .0669 3 . ,4703 0.3070841E+07 14. 94 0.2310 0.1800 0, .0917 5 , 3846 8 ,8550 0.1555200E+08 16 , 56 0.1960 0.1500 0. . 1467 8 ,6142 17 .4692 0.4448285E+08 17 . ,61 0.1650 0.1060 0. . 4013 23 . 5643 41 .0335 0. 1777139E+09 19 ,00 0.1280 0.0900 0. . 2202 12 . 9301 53 .9636 0.5975237E+09 20 .21 0.0980 0.0750 0. . 24 12 14 . 1633 68 . 1269 0.1170199E+10 20 .88 0.0825 0.0630 0. 1783 10 . 4698 78 . 5966 0.1848237E+ 10 21 . 34 0.0690 0.0530 0. . 1285 7 . 5455 86 .1421 0.2691263E+10 21 .71 0.0580 PAN 0 . 2360 13 .8579 100 .0000 Crystal mean size = 0.0945 mm Coefficient of Variation = 51.90 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.67 ml/s ' ( 5.40 gr/s) MeOH solution flow rate = 27.58 ml/s (22.96 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01272 gr Na2S04/gr ML 0.14809 gr 38%w/w H2S04/gr ML 0.83919 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012881 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000812 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight i Retained (gr) Wt. % Retained CumulatIve Wt.'/, Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0012 0 .2807 0 . 2807 0 . 2500 0 .0055 1 .2865 1 . 5673 0.8621005E+06 13. 67 0 . 2750 0 .2120 0 .0111 2 . 5965 4 . 1637 0.3862476E+07 15 , 17 0. 2310 0 . 1800 0 .0245 5 .7310 9. 8947 0.1657339E+08 16, ,62 0. , 1960 0 . 1500 0 .0482 1 1 . 2749 21 . 1696 0.5829582E+08 17 .88 0, . 1650 0 . 1060 0 . 1039 24 .3041 45 . 4737 0.1835253E+09 19 ,03 0, , 1280 0 .0900 0 .0542 12 . 6784 58 , 1520 0 . 5866317E+09 20 . 19 0 .0980 0 .0750 0 .0530 12 . 3977 70, ,5497 0.1025619E+10 20 . 75 0 .0825 0 .0630 0 .0357 8 . 3509 78 . , 9006 0.1476055E+10 21 . 1 1 0 .0690 0 .0530 0 .0254 5 .9415 84 .8421 0.2121850E+10 21 .48 0 .0580 PAN 0 .0648 15 . 1579 100 .0000 Co CD Crystal mean size = 0.1000 mm Coefficient of Variation = 53.87 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 43 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Residence Time = 50.O s Feed solution flow rate = 2.93 ml/s MeOH solution flow rate = 22.07 ml/s A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01268 gr Na2S04/gr ML 0.14810 gr 38%w/w H2S04/gr ML 0.83922 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012841 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000772 gr Na2S04/gr solvent Crystallizer Temperature = 35.0 Deg. Suspension Density = 32.13 gr/1 ' ( 4.32 gr/s) (18.37 gr/s) PRODUCT CRYSTAL SIZE DISTRIBUTION POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumu1 at 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0.3000 0 .0010 0.1363 0 . 1368 0.2500 0 . 0089 1.2178 1 .3547 0 .8169539 E+06 13. ,61 0 .2750 0.2 120 0 .0230 3.1472 4 . 5019 0. .4686870E+07 15, ,36 0 .2310 0.1800 0 .0523 7.1565 1 1 . 6585 0, 2071854E+08 16, ,85 0 . 1960 0.1500 0 . 0824 11.2753 22 . 9338 0. 5836203E+08 17 . ,88 0 . 1650 0.1060 0 . 1870 25.5884 48 . 5222 0. 1934348E+09 19 , 08 0 . 1280 0.0900 0 .0980 13.4100 61 . 9321 0. 6211617E+09 20, 25 0 .0980 0.0750 0 .0962 13.1637 75 . 0958 0. 1090179E+10 20, 81 0 .0825 0.0630 0. 06 15 8.4154 83. 5112 0. 1489094E+10 21 . 12 0 .0690 0.0530 0. 0435 5.9524 89 . 4636 0. 2128055E+10 21 . 48 0 .0580 PAN 0. 0770 10.5364 100. 0000 to CD to Crystal mean size 0.104 1 mm Coefficient of Variation = 50.36 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.996469 mm/hr Nuclei population density = 0. 1986973E+11 number/mm litre Nucleation rate.B =. 0. 396693 1E+11 number/hr litre RUN NUMBER 44 EXPERIMENTAL CONDITIONS C Crystallizer Temperature • 35.0 Deg. C Suspension Density = 32.27 gr/1 '( 3.60 gr/s) (15.31 gr/s) Feed Temperature = 31.0 Deg Residence Time = 60.0 s Feed solution flow rate = 2.45 ml/s MeOH solution flow rate = 18.39 ml/s A1coho1/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01251 gr Na2S04/gr ML 0.14812 gr 38%w/w H2S04/gr ML 0.83936 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012671 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000602 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight i Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 .0097 0 . 6309 0. .6309 0 . 2500 0 .0590 3 .8374 4 . , 4683 0. 2585955E+07 14. 77 0. 2750 0 .2120 0 .0974 6 . 3350 10 ,8033 0. 9477104E+07 16 , .06 0. 2310 0 . 1800 0 . 1307 8 .5008 19 ,3041 0. 2472261E+08 17 , 02 0. 1960 0 . 1500 0 . 1549 10 .0748 29 .3789 0. 5238605E+08 17 .77 0, 1650 0 . 1060 0 . 3662 23 .8179 53 . 1968 0. 1808725E+09 19.01 0. . 1280 0 .0900 0 . 2045 13 .3008 66 .4976 0. 6189184E+09 20 .24 0 .0980 0 .07 50 0 .1913 12 .4423 78 .9399 0, .1035140E+10 20 .76 0 .0825 0 .0630 0 . 1 178 7 .6618 86 .6017 0, .1361926E+ 10 21 .03 0 .0690 0 .0530 0 .0763 4 . 9626 9 1 . 5643 0 ,1782295E+10 21 .30 0 .0580 PAN 0 . 1297 8 . 4358 100 .0000 to CD CO Crystal mean size = 0.1104 mm Coefficient of Variation = 56.16 % Crystal growth rate,G Nuclei population density Nucleation rate.B CRYSTALLIZATION KINETICS 1.94369 1 mm/hr 0.1111280E+ 11 number/mm litre 0.2159984E+11 number/hr litre RUN NUMBER 38 EXPERIMENTAL CONDITIONS Crystallizer Temperature = 30.0 Deg. C Suspension Density = 69.17 gr/1 ' ( 2.70 gr/s) (11.48 gr/s) Feed Temperature = 31.0 Deg. C Residence Time = 80.0 s Feed solution flow rate = 1.83 ml/s MeOH solution flow rate = 13.79 ml/s A1coho1/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01234 gr Na2S04/gr ML 0.14815 gr 38%w/w H2S04/gr ML 0.83951 gr 80%w/w MeOH/gr ML Exit' solute concentration = 0.012498 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000429 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight i Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 1 0 . 3000 0 .0059 0 . 6308 0. 6308 to CD 0 . 2500 0 .0274 2 .9295 3. 5604 0. 1 983326 E + 07 14 . 50 0. 2750 0 .2120 0 .0490 5 .2390 8 . 7993 0. 7873853E+07 15 . 88 0. 2310 1 0 . 1800 0 .0980 10 . 4779 19 . 2772 0. 3061395E+08 17 . 24 0. 1960 0 . 1500 0 .1191 12 . 7339 32 , 0111 0. 6651973E+08 18. .01 0. 1650 0 . 1060 0 . 2676 28 .6111 60 , 6222 0. 2182804E+09 19 .20 0. 1280 0 . 0900 0 . 1 172 12 . 5307 73 , 1530 0. 5857902E+09 20 . 19 0. 0980 0 .0750 0 . 105 1 1 1 . 2370 84 .3900 0. ,9392074E+09 20 .66 0. 0825 0 . 0630 0 .0598 6 . 3937 90 . 7837 0. , 1 141784E+10 20 .86 0. 0690 0 .0530 0 .0402 4 .2981 95 .0817 0 .1550798E+10 21 . 16 0. 0580 PAN 0 .0460 4 .9182 99 .9999 Crystal mean size = 0.1205 mm Coefficient of Variation = 46.99 % Crystal growth rate.G Nuclei population density Nucleation rate.B CRYSTALLIZATION KINETICS 1.453914 mm/hr 0.1090334E+11 number/mm litre 0. 1585252E+11 number/hr litre RUN NUMBER 46 Feed Temperature = 31.0 Deg Residence Time = 100.0 s EXPERIMENTAL CONDITIONS C Crystallizer Temperature = 35.0 Deg. C Suspension Density = 32.41 gr/1 ' ( 2.16 gr/s) ( 9.19 gr/s) Feed solution flow rate = 1.47 ml/s MeOH solution flow rate = 11.03 ml/s A 1 coho!/Ac1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01235 gr Na2S04/gr ML 0.14815 gr 38%w/w H2S04/gr ML 0.83950 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012509 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000440 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumu1 at 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0.3000 0 . 0205 0. 9846 0 . 9846 0.2500 0 .0772 3.7078 4 .6924 0 .2509483E+07 14 .74 0 .2750 0.2120 0 . 1649 7.9199 12 .6123 0 , 1 189967 E+08 16 . 29 0 .2310 0.1800 0 . 2322 11.1522 23 .7645 0. .3257461E+08 17 .30 0 . 1960 0.1500 0 . 2748 13.1982 36 .9627 0. , 6892538E+08 18 .05 0 . 1650 0.1060 0 .4902 23.5436 60, 5063 0. 1795666E+09 19, .01 0 . 1280 0.0900 0. . 2284 10.9697 71 . 4760 0. 5126656E+09 20, .06 0 .0980 0.0750 0. 2005 9.6297 81 . 1057 0. 8046303E+09 20, .51 0 .0825 0.0630 0. 1315 6.3157 87 . 4214 0. 1127540E+10 20. 84 0 .0690 0.0530 0. 0853 4.0968 91 . 5182 0. 1477754E+ 10 21 . 1 1 0 .0580 PAN 0. 1766 8.4818 100. 0001 to CD Ul Crystal mean size = 0.1237 mm Coefficient of Variation = 53.03 % Crystal growth rate.G Nuclei population density Nucleation rate.B CRYSTALLIZATION KINETICS 1.243789 mm/hr 0.8339624E+10 number/mm litre 0.1037273E+1 1 number/hr litre RUN NUMBER 61 EXPERIMENTAL CONDITIONS Feed Temperature = 29.0 Deg. C Residence Time = 120.0 s Feed solution flow rate * MeOH solution flow rate = 1.22 ml/s 9. 19 ml/s Crystallizer Temperature = 35.0 Deg. C Suspension Density = 66.81 gr/1 ' ( 1.80 gr/s) ( 7.65 gr/s) A1coho1/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : 0.01226 gr Na2S04/gr ML 0.14816 gr 38%w/w H2S04/gr ML 0.83958 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012409 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000340 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained (gr) Wt . % Retained Cumulative Wt.% Reta1ned Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0. ,0088 0.4653 0.4653 0 . 2500 0 .0344 1.8188 2.2840 0.1234239E+07 14. 03 0. 2750 0 .2120 0 . 0726 3.8384 6.1225 0.5782629E+07 15 . 57 0. 2310 0 . 1800 0 .2027 10.7169 16.8394 0.3138662E+08 17 . 26 0. 1960 0 . 1500 0 . 298 1 15.7608 32.6002 0.8252744E+08 18 , 23 0. 1650 0 . 1060 0 . 4930 26.0654 58.6656 0.1993302E+09 19 . 1 1 0. 1280 0 . 0900 0 .2145 11.3408 70.0064 0.5314217E+09 20 .09 0 .0980 0 .0750 0 . 1972 10.4262 80.4326 0.8735002E+09 20 . 59 0 .0825 0 .0630 0 .1401 7.4072 87.8398 0.1325923E+10 21 .01 0 .0690 0 . 0530 0 .0937 4.9540 92.7938 0.1791704E+10 21 .31 0 .0580 PAN 0 . 1363 7.2063 100.0001 Crystal mean s 1 ze = 0.1195 mm Coefficient of Variation = ° 47 .03 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.225221 mm/hr Nuclei population density = 0.8516186E+10 number/mm litre Nucleation rate.B = 0.1043420E+11 number/hr litre CO CO <35 RUN NUMBER 48 EXPERIMENTAL CONDITIONS Feed Temperature Residence Time = 30.0 Deg. C 40.0 s Crystallizer Temperature = 35.0 Deg. C Suspension Density = 43.82 gr/1 ' ( 7.30 gr/s) (21.90 gr/s) Feed solution flow rate = 4.96 ml/s MeOH solution flow rate = 26.29 ml/s Alcohol/Acid-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01637 gr Na2S04/gr ML 0.19673 gr 38%w/w H2S04/gr ML 0.78690 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.016646 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation = 0.000896 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight i Reta i ned (gr) Wt. % Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0069 0 . 5886 0. 5886 0 . 2500 0 .0269 2 . 2946 2 . 8832 0.2099799E+07 14 . 56 0. 2750 0 . 2 120 0 .0713 6 .0821 8 . 9653 0.1235559E+08 16. 33 0. 2310 0 . 1800 0 .1216 10 . 3728 19 , 3381 0.4096464E+08 17 . ,53 0. 1960 0 . 1500 0 . 1572 13 . 4096 32. . 7476 0.9468333E+08 18 ,37 0. . 1650 0 . 1060 0 . 291 1 24 . 8316 57 . 5792: 0.2560669E+09 19 , 36 0 , 1280 0 .0900 0 . 1447 12 . 3433 69 .9224 0.7799473E+09 20 .47 0 ,0980 0 .0750 0 . 1333 1 1 .3708 81 .2933 0.1284610E+10 20 .97 0 .0825 0 .0630 0 .0871 7 .4299 88 . 7231 0.1793425E+ 10 21 .31 0 .0690 0 .0530 0 .0554 4 . 7258 93 .4489 0.2304737E+10 21 .56 0 .0580 PAN 0 .0768 6 .5512 100 .0001 to CD <1 Crystal mean size = 0.1174 mm Coefficient of Variation = 50.18 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.838276 mm/hr Nuclei population density = 0,1653302E+11 number/mm litre Nucleation rate.B = 0.4692527E+11 number/hr litre RUN NUMBER 49 EXPERIMENTAL CONDITIONS Feed Temperature = 30.0 Deg. C Residence Time = 40.0 s Feed solution flow rate = 4.96 ml/s MeOH solution flow rate = 26.29 ml/s A1 cohol/Ac1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01636 gr Na2S04/gr ML 0.19673 gr 38%w/w H2S04/gr ML 0.78691 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.016634 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation = 0.000884 gr Na2S04/gr solvent Crystallizer Temperature = 35.0 Deg. Suspension Density = 43.83 gr/1 ( 7.30 gr/s) (21.90 gr/s) PRODUCT CRYSTAL SIZE DISTRIBUTION POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Reta1ned Cumulat 1ve Wt.% Retained Population Denslty.n (number/mm litre) 1 n n Average Size (mm) 0.3000 0 .0025 0 .0852 0 .0852 0.2 500 0 .0278 0 . 9478 1 .0330 0 .8674923E+06 13.67 0 . 2750 0.2120 0 .0637 2 .1717 3 .2047 0 .4412737E+07 15 . 30 0 .2310 0.1800 0 .3012 10 .2687 13 . 4734 0, ,4056258E+08 17.52 0 . 1960 0.1500 0 .4836 16 .4871 29 ,9605 0, ,1164400E+09 18.57 0 . 1650 0.1060 0 . 7677 26 . 1728 56 . 1333 0. 2699587E+09 19.41 0 . 1280 0.0900 0 . 3365 1 1 .4721 67 . 6054 0. 7250647E+09 20.40 0 .0980 0.0750 0. 3034 10. . 3437 77 . 9490 0. 1168830E+10 20.88 0 .0825 0.0630 0. 2155 7. .3469 85. 2959 0. 1773810E+10 21 . 30 0 .0690 0.0530 0. 1593 5. 4309 90. 7269 0. 2649247E+10 21 .70 0 .0580 PAN 0. 2720 9 . 2732 100. 0000 to CD 00 Crystal mean size = 0.1154 Coefficient of Variation = 47.50 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.498085 mm/hr Nuclei population density = 0.2556156E+11 number/mm litre Nucleation rate.B = 0.6385494E+11 number/hr litre RUN NUMBER 50 EXPERIMENTAL CONDITIONS Crystallizer Temperature * 35.0 Deg. C Suspension Density = 43.89 gr/1 ( 5,84 gr/s) (17.52 gr/s) Feed Temperature = 30.0 Deg. C Residence Time = 50.0 s Feed solution flow rate = 3.97 ml/s MeOH solution flow rate = 21.03 ml/s A1cohol/Ac1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01S30 gr Na2S04/gr ML 0.19G74 gr 38%w/w H2S04/gr ML 0.78696 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.016567 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation = 0.000817 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) We 1ght Retained Wt (gr) .% Retained Cumulative Wt.% Re 3ta 1 ned Population Density,n (number/mm 11tre) In n Average Size (mm) 0.3000 0 .0045 0.3135 0 .3135 0.2500 0 . 0305 2.1250 2 . 4385 0. 1947631E+07 14 .48 0 .2750 0.2120 0 .0709 4.9397 7 . 3783 0. 1005082E+08 16 . 12 0 .2310 0.1800 0 . 1 140 7.9426 15 .3209 0. 3141680E+08 17 .26 0 . 1960 0.1500 0 . 1647 11.4750 26, ,7958 0. 8115133E+08 18 .21 0 . 1650 0.1060 0 . 3756 26.1688 52. 9646 0. 2702825E+09 19, ,41 0 . 1280 0.0900 0. . 2004 13.9623 66 . 9268 0. 8836406E+09 20, ,60 0 .0980 0.0750 0. 1872 13.0426 79. 9694 0. 1475801E+10 21 , 1 1 0 .0825 0.0630 0. 1113 7.7545 87 . 7239 0. 1874742E+ 10 21 . 35 0 ,0690 0.0530 0. 0686 4.7795 92 . 5034 0. 2334624E+ 10 21 . 57 0, ,0580 PAN 0 . 1076 7.4967 100. 0001 Crystal mean size = 0.1098 mm CoeffIclent of Variation = 49 . 47 % CRYSTALLIZATION KINETICS to CO CD Crystal growth rate.G = 2.176948 mm/hr Nuclei population density = 0.1942486E+11 number/mm litre Nucleation rate.B = 0.4228690E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.30 ml/s ( 4.87 gr/s) MeOH solution flow rate = 17.53 ml/s (14.60 gr/s) A1coho1/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01611 gr Na2S04/gr ML 0.19678 gr 38%w/w H2S04/gr ML 0.78711 gr 80%w/w MeOH/gr ML Exit solute concentration - 0.016372 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent SupersaturatIon = 0.000622 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt .% Reta1ned Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 .0045 0 . 4439 0 .4439 0 . 2 500 0 .0327 3 . 2258 3 .6697 0. 2968022E+07 14 .90 0 . 2750 0 . 2 1 20 0 . 0646 6 . 3727 10 ,0424 0. 1301666E+08 16 .38 0 . 2310 0 . 1800 0 .092 1 9 .0855 19 . 1279 0. 3607690E+08 17 . 40 0 . 1960 0 . 1500 0 . 1 170 1 1 . 54 19 30. , 6698 0. 8194088 E+08 18 . 22 0 . 1650 0 . 1060 0. 2503 24 .6917 55 . 3615 0. 2560151E+09 19 . 36 0 . 1280 0 .0900 0 . 1302 12 . 8440 68 . 2056 0. 8160215E+09 20 .52 0 .0980 0 .0750 0. 1208 1 1 .9167 80. 1223 0. 1353636E+10 21 .03 0 .0825 0. .0630 0. 0734 7 . 2408 87 . 363 1 0. 1757337E+10 21 . 29 0 .0690 0. 0530 0. 0480 4 . 735 1 92 . 0982 0. 2321916E+10 21 , .57 0 .0580 PAN 0. 0801 7 .9017 100. 0000 Crystal mean size = 0.1136 mm Coefficient of Variation = 53.13 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 2.48 ml/s ( 3.65 gr/s) MeOH solution flow rate = 13.15 ml/s (10.95 gr/s) Alcohol/Acid-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01603 gr Na2S04/gr ML 0.19679 gr 38%w/w H2S04/gr ML 0.787 17 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.016296 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation 1 0.000546 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n ln n Average Size (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0096 1 .0835 1 .0835 0 . 2500 0 .0486 5. .4853 6 .5688 0. 5054637E+07 15, ,44 0, , 2750 0 .2120 0 .0582 6. , 5688 13 . 1377 0. 1343768E+08 16, ,41 0 .2310 0 . 1800 0 .0753 8 , .4989 21 .6366 0. 3379858E+08 17, , 34 0 . 1960 0 . 1500 0 . 1038 1 1 . .7156 33 .3521 0. 8330027E+08 18 ,24 0 . 1650 0 . 1060 0 . 2268 25 . 5982 58 . 9503 0. 2658164 E+09 19 , 40 0 . 1280 0 . 0900 0 . 1 108 12. . 5056 71 . 4560 0. 7957279E+09 20 .49 0 .0980 0 .0750 0 .0997 1 1 , 2528 82 . 7088 0, 1280159E+10 20 .97 0 .0825 0 . 0630 0 .059 1 6 , . 6704 89 . 3792 0, 1621362E+ 10 21 .21 0 .0690 0 .0530 0 .0376 4 , 2438 93 .6230 0. 2084142E+10 21 .46 0 .0580 PAN 0 .0565 6 . 3770 100 .0000 Crystal mean size = 0.1191 mm Coefficient of Variation = 53.22 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 53 EXPERIMENTAL CONDITIONS Feed Temperature Residence Time = 30.0 Deg. C 80.0 s Crystallizer Temperature = 35.0 Deg. C Suspension Density = 44.14 gr/1 ( 3.65 gr/s) (10.95 gr/s) Feed solution flow rate = 2.48 ml/s MeOH solution flow rate = 13.15 ml/s A 1cohol/AcId-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01602 gr Na2S04/gr ML 0.19680 gr 38°/.w/w H2S04/gr ML 0.78718 gr 80°/w/w MeOH/gr ML Exit solute concentration = 0.016283 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation = 0.000533 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained Wt (gr) .'/• Retained Cumulative Wt .% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0.3000 0 .007 5 0.2587 0 . 2587 0.2 500 0 .0855 2.9497 3 .2084 0. 27 18807E+07 14 .82 0 .2750 0.2120 0 . 1542 5.3198 8 . 5283 0. 1088540E+08 16 .20 0 .2310 0.1800 0 .3112 10.7362 19 .2645 0. 4270726E+08 17 .57 0 . 1960 0.1500 0 . 3375 11.6436 30 . 9080 0. 8280971E+08 18, ,23 0 . 1650 0.1060 0 .6820 23.5286 54 . 4366 0. 2443891E+09 19. 31 0 . 1280 0.0900 0. 3525 12.16 11 66 , 5977 0. 7740027E+09 20. 47 0 .0980 0.0750 0. 3777 13.0304 79 . 628 1 0. 1482772E+10 21 . 12 0 .0825 0.0630 0. 2265 7.8141 87 . 4422 0. 1899852E+10 2 1 . 37 0 .0690 0.0530 0. 1525 5.2612 92 . 7034 0. 2584449E+10 21 . 67 0 ,0580 PAN 0. 2115 7.2966 100. 0000 Crystal mean size = 0.1128 mm Coeff1c1ent of Variation = 53. 19 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.419183 mm/hr Nuclei population density = 0.170922 3E+11 number/mm litre Nucleation rate.B = 0.2425699E+11 number/hr litre CO O to RUN NUMBER 46 Feed Temperature = 31.0 Deg Residence Time = 100.0 s EXPERIMENTAL CONDITIONS C Feed solution flow rate MeOH solution flow rate 1 .98 ml/s 10.52 ml/s Crystallizer Temperature = 35.0 Deg. C Suspension Density = 32.41 gr/1 ( 2.92 gr/s) ( 8.76 gr/s) Alcohol/Acid-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01597 gr Na2S04/gr ML 0.19681 gr 38%w/w H2S04/gr ML 0.78722 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.016232 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation = 0.000482 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt .% Reta1ned Cumu1 at 1ve Wt.% Retained Population Denslty.n (number/mm litre) In n Average Size (mm) 0 . 3000 0 . 0253 4 . 3064 4 . 3064 0 . 2500 0 .0504 8 . 5787 12 .8851 0. .7915256E+07 15 . 88 0 .2750 0 .2120 0 .0473 8 .051 1 20 . 9362 0. .1649085E+08 16. ,62 0 .2310 0 . 1800 0 .0623 10 . 6043 31 . 5404 0. 4222525E+08 17 , 56 0 . 1960 0 . 1500 0 .0700 1 1 .9149 43 . 4553 0. 8482573E+08 18 , 26 0 . 1650 0 . 1060 0 . 1264 21 .5149 64 . 9702 0. 2237003E+09 19. 23 0 . 1280 0 .0900 0 . 0565 9 .6 170 74 . 5872 0. 6127081E+09 20, 23 0 .0980 0 .0750 0 .0561 9 . 5489 84 . 1362 0. 1087 708E+10 20. 81 0 .0825 0. 0630 0. 0305 5 .1915 89. 3276 0. 1263495E+10 20. 96 0 .0690 0. 0530 0. 0212 3 . 6085 92 . 9361 0. 1774418E+ 10 21 . 30 0 .0580 PAN 0. 04 15 7 .0638 100. 0000 CO O 00 Crystal mean size = 0.1354 Crystal growth rate.G Nuclei population density Nucleation rate.B Coefficient of Variation = 58.29 % CRYSTALLIZATION KINETICS 1 . 3864 15 mm/hr 0.7512642E+10 number/mm litre 0.1041563E+11 number/hr litre RUN NUMBER 55 EXPERIMENTAL CONDITIONS Crystal H z e r Temperature = 35.0 Deg. C Suspension Density = 44.30 gr/1 '( 2.43 gr/s) ( 7.30 gr/s) Feed Temperature = 30.0 Deg. C Residence Time = 120.0 s Feed solution flow rate = 1.65 ml/s MeOH solution flow rate = 8.76 ml/s A1cohol/Ac 1d-feed ratio = 3.0000 gr/gr Mother Liquor (ML) Composition : 0.01585 gr Na2S04/gr ML 0.19683 gr 38%w/w H2S04/gr ML 0.78732 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.016101 gr Na2S04/gr solvent Equilibrium concentration = 0.015750 gr Na2S04/gr solvent Supersaturation = 0.000351 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulative Wt . % Reta1ned Population Density.n (number/mm 11tre) In n Average Size (mm) 0.3000 0 .0030 0.1123 0 .1123 0.2500 0 . 1295 4.8455 4 .9577 0. 4482288E+07 15 . 32 0 .2750 0.2120 0 .2582 9.6610 14 .6187 0. 1983963E+08 16 .80 0 .2310 0.1800 0 . 4200 15.7151 30 , 3338 0. 6273781E+08 17 .95 0 . 1960 0.1500 0 . 3340 12.4972 42 . 83 10 0. 8920141E+08 18 ,31 0 . 1650 0.1060 0 . 5272 19.7261 62 . 557 1 0. 2056320E+09 19, , 14 0 . 1280 0.0900 0 . 2560 9.5787 72 . 1358 0. 6118441E+09 20. , 23 0 .0980 0.0750 0 , 2847 10.6526 82 . 7883 0. 1216557E+10 20, 92 0 .0825 0.0630 0. 1765 6.6041 89 . 3924 0. 1611439E+10 21 . 20 0 .0690 0.0530 0. 1 150 4.3029 93 . 6953 0. 2121358E+10 21 . 48 0 .0580 PAN 0. 1685 6.3047 100. 0000 Crystal mean s Ize = 0.1325 mm Coef f Icient of Variation = 51 . 21 % CRYSTALLIZATION KINETICS CO O Crystal growth rate.G Nuclei population density Nucleation rate.B 1.087498 mm/hr 0.1005199E+11 number/mm litre 0.1093152E+11 number/hr litre RUN NUMBER 56 EXPERIMENTAL CONDITIONS Crystallizer Temperature = 35.0 Deg. C Suspension Density = 66.44 gr/1 ( 9.00 gr/s) (15.75 gr/s) Feed Temperature = 29.0 Deg. C Residence Time = 50.0 s Feed solution flow rate = 6.11 ml/s MeOH solution flow rate = 18.89 m1/s A 1cohol/Acld-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02549 gr Na2S04/gr ML 0.29235 gr 38%w/w H2S04/gr ML 0.68216 gr 80%w/w MeOH/gr ML Exit solute concentration =* 0.026157 gr Na2S04/gr solvent Equilibrium concentration = 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000807 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0.3000 0 .0543 2 . 3487 2 . 3487 0.2500 0 .1214 5 . 251 1 7 . 5998 0. 7284897E+07 15 .80 0 .2750 0.2 1 20 0 . 1826 7 . 8983 15 . 498 1 0. 2432499E+08 17 .01 0 .2310 0.1800 0 .2551 1 1 .0342 26 . 5323 0. 6606402E+08 18 .01 0 . 1960 0.1500 0 . 2809 12 . 1502 38 .6825 0. 1300624E+09 18 .68 0 . 1650 0.1060 0. ,5182 22 .4 145 61 ,0970 0. 3504184E+09 19. .67 0 . 1280 0.0900 0. 2485 10 .7487 71 , 8457 0. 1029679E+10 20, 75 0 .0980 0.0750 0. 2146 9 . 2824 81 . 1281 0. 1589825E+ 10 21 , 19 0 .0825 0.0630 0. 1577 6 ,8212 87 . 9493 0. 2496178E+10 21 , 64 0 .0690 0.0530 0. 0958 4 . , 1438 92. 093 1 0. 3063769E+10 21 . 84 0 .0580 PAN 0. 1828 7 . 9069 100. 0000 CO 0 01 Crystal mean size = 0.1254 "m Coefficient of Variation = 55.84 % CRYSTALLIZATION KINETICS Crystal growth rate.G « 2.563105 mm/hr Nuclei population density = 0.1550742E+11 number/mm litre Nucleation rate.B = 0.3974714E+11 number/hr litre RUN NUMBER 57 EXPERIMENTAL CONDITIONS Feed Temperature = 29.0 Deg. C Residence Time = GO.O s Feed solution flow rate = 5.09 ml/s MeOH solution flow rate = 15.74 ml/s A1coho1/AcId-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : Crystallizer Temperature = 35.0 Deg. C Suspension Density = G6.53 gr/1 ( 7.50 gr/s) (13.12 gr/s) 0.02540 gr Na2S04/gr ML 0.29238 gr 38%w/w H2S04/gr ML 0.68222 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.026060 gr Na2S04/gr solvent Equilibrium concentration = 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000710 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulative Wt.% Reta1ned Population Density,n (number/mm litre) In n Average Size (mm) 0.3000 0 .0345 1.1270 1.1270 0.2500 0 . 1740 5.6842 6.8113 0. 7896140E+07 15 . 88 0 . 2750 0.2120 0 . 2007 6.556b 13.3678 0. 2021902E+08 16 .82 0 .2310 0.1800 0 . 2850 9.3104 22.678 1 0. 5581622E+08 17 .84 0 . 1960 0.1500 0 . 3745 12.2342 34.9123 0. 1311332E+09 18 .69 0 . 1650 0.1060 0 . 8430 27.5391 62.4514 0. 4311002E+09 19 . 88 0 . 1280 0.0900 0 . 3883 12.6850 75.1364 0. 1216757E+ 10 20 ,92 0 .0980 0.0750 0. 3372 11.0157 86.1521 0. 1889158E+10 21 . 36 0 .0825 0.0630 0. 1793 5.8574 92.0094 0. 2146274E+ 10 21 , 49 0 .0690 0.0530 0. 1 121 3.6621 95.6715 0. 2711173E+10 21 . 72 0 .0580 PAN 0. 1325 4.3285 100.0000 Crystal mean s ize = 0.1236 mm CoeffIclent of Variation = 49. 86 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.113697 mm/hr Nuclei population density = O.1620038E+11 number/mm litre Nucleation rate.B = 0.3424270E+11 number/hr litre CO O cn RUN NUMBER 58 EXPERIMENTAL CONDITIONS C Crystallizer Temperature = 35.0 Deg. C Suspension Density = 66.57 gr/1 ( 7.50 gr/s) (13.12 gr/s) Feed Temperature = 29.0 Deg Residence Time = 60.0 s Feed solution flow rate = 5.09 ml/s MeOH solution flow rate = 15.74 ml/s A1cohol/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02535 gr Na2S04/gr ML 0.29239 gr 38%w/w H2S04/gr ML 0.68225 gr 80%w/w MeOH/gr ML Exit solute concentration « 0.026013 gr Na2S04/gr solvent Equilibrium concentration = 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000663 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt .% Reta1ned Cumulat 1ve Wt.% Retained Population Density,n (number/mm 1 1 tre) In n Average Size (mm) 0.3000 0 . 027 1 2 . 1367 2 . 1367 0.2 500 0 .0796 6 . 276 1 8 .4129 0 .8723978E+07 15 .98 0 . 2750 0.2120 0 . 1085 8 . 5548 16 . 9676 0. 2639850E+08 17 .09 0 . 2310 0.1800 0 . 1435 1 1 .3144 28 . 2820 0. 6787400E+08 18 .03 0 . 1960 0.1500 0 .1741 13 . 727 1 42. 0090 0. 1472297E+09 18 .81 0 . 1650 0.1060 0 . 2927 23 .0782 65 . 0872 0. 3615009E+09 19, .71 0 . 1280 0.0900 0 . 1357 10 . 6994 75 . 7866 0. 1026958E+10 20. ,75 0 .0980 0.0750 0. .1213 9 . 5640 85 . 3506 0. 1641262E+10 21 . ,22 0 .0825 0.0630 0, 0696 5 .4877 90. 8383 0. 2012103E+10 21 . 42 0 .0690 0.0530 0. 0451 3 .5559 94 . 3942 0. 2634294E+10 21 . 69 0 .0580 PAN 0. 07 1 1 5 . 6059 100. 0001 CO O <1 Crystal mean size 0.1334 mm Coefficient of Variation « 51.74 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.240132 mm/hr Nuclei population density = 0.1298860E+11 number/mm litre Nucleation rate.B = 0.2909619E+11 number/hr litre RUN NUMBER 59 EXPERIMENTAL CONDITIONS Feed Temperature = 29.0 Deg. C Residence Time = 80.0 s Feed solution flow rate = 3.82 ml/s MeOH solution flow rate = 11.81 ml/s A1coho1/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : Crystallizer Temperature = 35.0 Deg. C Suspension Density = 66.66 gr/1 " ( 5.62 gr/s) ( 9.84 gr/s) 0.02526 gr Na2S04/gr ML 0.29242 gr 38%w/w H2S04/gr ML 0.68232 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.025915 gr Na2S04/gr solvent Equilibrium concentration = 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000565 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained (gr) Wt .% Retained Cumulative Wt.% Retained Population Density,n (number/mm 11tre) ln n Average Size (mm) 0.3000 0.032 1 2,9246 2.9246 0.2 500 0.1019 9.2839 12.2085 0. 1292196E+08 16 . 37 0.2750 0.2 120 0. 1263 11.5069 23.7154 0.3555538E+08 17 .39 0. 2310 0.1800 0. 1420 12.9373 36.6527 0.7771283E+08 18 . 17 0.1960 0.1500 0.1273 11.5981 48.2508 0. 1245599E+09 18 .64 0.1650 0.1060 0.2117 19.2876 67.5384 0.3025244E+09 19 . 53 0.1280 0.0900 0.1087 9.9034 77.44 18 0.9518200E+09 20. ,67 0.0980 0.0750 0.098 1 8.9377 86.3795 0.1535814E+10 21 , 15 0.0825 0.0630 0.0605 5.5 120 91.8915 0.2023713E+ 10 21 . 43 0.0690 0.0530 0.0359 3.2708 95.1623 0.2426244E+ 10 21 . 61 0.0580 PAN 0.0531 4.8378 100.0001 Crystal mean S' Ize = 0.1453 m m Coefflc lent of Variation = 53. 82 t CRYSTALLIZATION KINETICS Crystal growth rate.G = Nuclei population density = Nucleation rate.B = 1 .821439 mm/hr = 0.9898263E+10 number/mm = 0.1802908E+11 number/hr 1 1 tre 1 1 tre CO O 00 RUN NUMBER SO EXPERIMENTAL CONDITIONS Crystallizer Temperature = 35.0 Deg. C Suspension Density = 66.77 gr/1 ( 4.50 gr/s) ( 7.87 gr/s) Feed Temperature = 29.0 Deg. C Residence Time = 100.0 s Feed solution flow rate = 3.05 m1/s MeOH solution flow rate = 9.45 ml/s A1cohol/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02514 gr Na2S04/gr ML 0.29246 gr 38%w/w H2S04/gr ML 0.68240 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.025789 gr Na2S04/gr solvent Equilibrium concentration = 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000439 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained Wt (gr) .% Retail ned Cumulative Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0.3000 0.0454 3.9682 3.9682 0.2500 0.0864 7.55 18 11.5200 0. 1052889E+08 16 . 17 0 . 2750 0.2120 0.1206 10.5411 22.0610 0. 3262602E+08 17 .30 0 .2310 0.1800 0.1494 13.0583 35.1193 0. 7857232E+08 18 . 18 0 . 1960 0.1500 0.1502 13.1282 48.2476 0. 1412324E+09 18 .77 0 . 1650 0.1060 0.2518 22.0086 70.2562 0. 3457879E+09 19 .66 0 . 1280 0.0900 0.1122 9.8069 80.0630 0. 9441329E+09 • 20 .67 0 .0980 0.0750 0.0964 8.4259 88.4888 0. 1450311E+10 21 . 10 0 .0825 0.0630 0.0528 4.6150 93.1038 0. 1697236E+10 21 . 25 0 .0690 0.0530 0.0326 2.8494 95.9532 0. 2117252E+10 21 . 47 0 .0580 PAN 0.0463 4.0469 100.0001 Crystal mean size = 0.1461 mm Coefficient of Variation = 50. 63 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.451990 mm/hr Nuclei population density = O . 959 1 235E+10 number/mm H t r e Nucleation rate.B = 0.1392638E+11 number/hr litre CO O CD RUN NUMBER 61 EXPERIMENTAL CONDITIONS Feed Temperature = 29.0 Deg. C Residence Time = 120.0 s Feed solution flow rate = MeOH solution flow rate = 2.54 ml/s 7.87 m1/s Crystallizer Temperature = 35.0 Deg. C Suspension Density = 66.81 gr/1 ( 3.75 gr/s) ( 6.56 gr/s) A1cohol/Actd-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02510 gr Na2S04/gr ML 0.29247 gr 38°/.w/w H2S04/gr ML 0.68243 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.025747 gr Na2S04/gr solvent Equilibrium concentration =• 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000397 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt .% Reta1ned Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 . 3744 12 . 3806 12 . 3806 0 . 2500 0 . 2980 9 .8542 22 . 2347 'o. , 1374674E+08 16 .44 0 .2750 0 .2 120 0 . 2870 9 . 4904 31 . 7252 0. 2939093E+08 17 .20 0 .2310 0 . 1800 0 . 2925 9 . 6723 41 . 3975 0, 5823170E+08 17 .88 0 . 1960 0 . 1500 0 . 3205 10 . 5982 51 .9957 0. 1140793E+09 18 . 55 0 . 1650 0 . 1060 0 .5715 18 . 8982 70. 8939 0, 2970880E+09 19 .51 0 . 1280 0 .0900 0 . 2495 8 . 2504 79 . 1443 0. 7947405E+09 20 .49 0 .0980 0 .0750 0 ,2412 7 .9759 87 . 1202 0. 1373650E+10 21 .04 0 .0825 0 .0630 0. 1365 4 .5137 9 1 . 6339 0. 1660947E+ 10 21 , 23 0 .0690 0. 0530 0. 0935 3 .0918 94 . 7258 0. 2298694E+10 21 , 56 0 .0580 PAN 0. 1595 5 . 2743 100. 0000 I 03 h-4 O I Crystal mean size = 0.1553 Coefficient of Variation = 64.01 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.225221 mm/hr Nuclei population density = 0.8516186E+10 number/mm litre Nucleation rate.B = 0.1043420E+11 number/hr litre RUN NUMBER 62 Feed Tempera-tune = 29.0 Deg Residence Time = 120.0 s EXPERIMENTAL CONDITIONS C Crystallizer Temperature =• 35.0 Deg. C Suspension Density = 66.85 gr/1 ( 3.75 gr/s) ( 6.56 gr/s) Feed solution flow rate = 2.54 ml/s MeOH solution flow rate = 7.87 ml/s A1cohol/Ac 1d-feed ratio = 1.7500 gr/gr Mother Liquor (ML) Composition : 0.02505 gr Na2S04/gr ML 0.29248 gr 38%w/w H2S04/gr ML 0.68246 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.025694 gr Na2S04/gr solvent Equilibrium concentration = 0.025350 gr Na2S04/gr solvent Supersaturation = 0.000344 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY :reen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulative Wt .% Retained Population Density,n (number/mm 11tre) in n Average S (mm) 0.3000 0 . 1700 4 . 2592 4 . 2592 0.2500 0 . 4605 1 1 , 5373 15 . 7965 0. 1610619E+08 16 .59 0 .2750 0.2120 0 . 501 1 12 . 5545 28 .3510 0. 3890766E+08 17 .48 0 . 2310 0.1800 0 . 4830 12. 1010 40 .4520 0. 7290546E+08 18 . 10 0 . 1960 0.1500 0. 4285 10. 7356 51 . 1876 0. 1156403E+09 18 .57 0 . 1650 0.1060 0. 6266 15 . 6988 66 ,8863 0. 2469670E+09 19 .32 0 . 1280 0.0900 0. 3220 8 . 0674 74 , 9537 0. 7776602E+09 20 .47 0 .0980 0.0750 0. 3712 9 . 3000 84 . 2537 0. 1602826E+10 21 , 20 0 .0825 0.0630 0. 2365 5. 9252 90. 1789 0. 2181894E+10 21 , 50 0 ,0690 0.0530 0. 1570 3 . 9335 94 . 1 124 0. 2926501E+ 10 21 . 80 0, ,0580 PAN 0. 2350 5 . 8877 100. 0000 Crystal mean size = 0 . 1535 mm Coefficient of Variation = 56. 63 % CRYSTALLIZATION KINETICS Crystal growth rate,G • 1.235468 mm/hr Nuclei population density = 0.9385509E+10 number/mm litre Nucleation rate.B = 0.1159549E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.67 ml/s ( 5.40 gr/s) MeOH solution flow rate = 27.58 ml/s (22.96 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Cr concentration In feed = 75.0 ppm Mother Liquor (ML) Composition : 0.01249 gr Na2S04/gr ML 0.14813 gr 38%w/w H2S04/gr ML 0.83939 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012643 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000574 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n ln n Average S1 (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 .0514 3 . 1588 3 . 1588 0 . 2500 0 .0645 3 . 9639 7 . 1227 0, 2673192E+07 14 ,80 0 . 2750 0 .2120 0 .0918 5 . 64 16 12 .7643 0. 8446189E+07 15 .95 0 . 2310 0 . 1800 0 .1515 9 .3105 22 .0748 0. 2709773E+08 17 . 1 1 0 . 1960 0 . 1500 0 . 1842 1 1 . . 3201 33 . 3948 0. 5890546E+08 17 , 89 0 . 1650 0 . 1060 0 . 3705 22 . 7692 56 . 1640 0. 1730390E+09 18 .97 0 . 1280 0 . 0900 0 . 1725 10. 601 1 66 . 7651 0, 4936630E+09 20 .02 0 .0980 0 . 0750 0 .1721 10. 5765 77 . 34 16 0, 8805752E+09 20.60 0 .0825 0 . 0630 0 . 1289 7 , 9216 85 , .2631 0. .1409168E+10 21 .07 0 .0690 0 . 0530 0 .0816 5 . 0148 90. . 2779 0, 1802381E+10 21 .31 0 .0580 PAN 0 . 1582 9 . 7222 100. .0001 Crystal mean size = 0.1163 mm Coefficient of Variation = 57.68 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.67 ml/s ( 5.40 gr/s) MeOH solution flow rate = 27.58 ml/s (22.96 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Cr concentration In feed = 75.0 ppm Mother Liquor (ML) Composition : 0.01252 gr Na2S04/gr ML 0.14812 gr 38%w/w H2S04/gr ML 0.83936 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012679 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000610 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt .% Retained Cumulat 1ve Wt . % Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0762 4 .2864 4 . 2864 0 . 2500 0 .0853 4 . 7983 9 .0848 0. 3232820E+07 14 .99 0 .2750 0 . 2 120 0 .0910 5 . 1 190 14 . 2038 0. 7656347E+07 15 . 85 0 .2310 0 . 1800 0 . 1495 8 .4097 22 .6135 0. 2445251E+08 17 .01 0 . 1960 0 . 1500 0 . 198 1 1 1 . 1436 33 . 757 1 0. 5793110E+08 17 . 87 0 . 1650 0 . 1060 0 . 3896 21 . 9 160 55 .6731 0. 1663936E+09 18 .93 0 . 1280 0 .0900 0 . 1985 1 1 . 166 1 66 . 8392 0. 5194739E+09 20 .07 0 .0980 0 .0750 0 .2075 1 1 .6724 78 , 5116 0. 9708800E+09 20, ,69 0 .0825 0 .0630 0 . 1282 7 .2116 85 , 7231 0. 1281621E+10 20 ,97 0 .0690 0 ,0530 0, .0905 5 . 0909 90. 8140 0. 1827961E+10 21 . ,33 0 .0580 PAN 0, 1633 9 . 1860 100. 0000 Crystal mean s 1ze = 0. 1 156 mm Coeff1c1ent of Variation = 59, .50 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 2.45 ml/s ( 3.60 gr/s) MeOH solution flow rate = 18.39 ml/s (15.31 gr/s) Alcohol/Acid-feed ratio = 4.2500 gr/gr Cr concentration In feed = 75.0 ppm Mother Liquor (ML) Composition : 0.01234 gr Na2S04/gr ML 0.14815 gr 38%w/w H2S04/gr ML 0.83951 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012492 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000423 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY reen Size (mm) Weight 1 Reta1ned !gr) Wt.% Reta1ned Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average S (mm) 0 . 3000 0 . 1682 8 . 4646 8 . 4646 0 . 2 500 0 .1165 5 . 8628 14 . 3274 0. 3969810E+07 15 . 19 0 . 2750 0 .2120 0. 1454 7 .3172 21 .6446 0. 1099906E+08 16. .21 0 .2310 0 . 1800 0. 1879 9 .4560 31 . 1006 0. 2763250E+08 17 , 13 0 . 1960 0 . 1500 0. 2291 1 1 . 5294 42 .6300 0. 6023707E+08 17 , 91 0 . 1650 0 . 1060 0. 3885 19 . 55 1 1 62 .18 11 0. 1491831E+09 18 , 82 0 . 1280 0 . 0900 0 . 1925 9 . 6875 71 . 8686 0. 4529446E+09 19. 93 0 .0980 0 .0750 0. 1965 9 . 8888 81 . 7574 0. 8266493E+09 20. , 53 0 .0825 0 . 0630 0. 1325 6 . 6680 88 . 4254 0. 1190964E+10 20. .90 0 .0690 0 .0530 0. 09 15 4 .6047 93 .0301 0. 1661691E+10 21 .23 0 .0580 PAN 0. 1385 6 .9700 100 .0001 Crystal mean size = 0.1317 mm Coefficient of Variation = 63.88 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 1 3 9 2 8 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 3 2 . 6 3 gr/1 Feed solution flow rate = 1.83 ml/s ( 2.70 gr/s) MeOH solution flow rate = 13.79 ml/s (11.48 gr/s) A 1coho1/Ac 1d-feed ratio = 4.2500 gr/gr Cr concentration In feed = 75.0 ppm Mother Liquor (ML) Composition : 0.01230 gr Na2S04/gr ML 0.14815 gr 38%w/w H2S04/gr ML 0.83954 gr 80°/.w/w MeOH/gr ML Exit solute concentration = 0.012456 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000387 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY -een Size Weight Reta1ned Wt. % Retained Cumulat 1ve Wt.% Retained Population Density,n In n Average S' (mm) (gr) (number/mm litre) (mm) 0 .3000 0 . 1983 10 . 1938 10. 1938 0 . 2500 0 . 1255 6 .4515 16. 6453 0. 4372550E+07 15 . 29 0. 2750 0 ,2 120 0 . 1390 7 . 1454 23. 7907 0. 1075112E+08 16. 19 0. 2310 0 . 1800 0 . 1868 9 .6026 33 , 3933 0. 2808779E+08 17 . 15 0. 1960 0 , 1500 0 .2181 1 1 .2117 44 , .6050 0. 5863298E+08 17 , 89 0. 1650 0 . 1060 0 . 3890 19 .9969 64 , 6019 0, 1527305E+09 18 . 84 0. 1280 0 . 0900 0 . 1840 9 . 4587 74 . 0606 0. 4426696E+09 19. ,91 0. 0980 0 . 0750 0 .169 1 8 . 6928 82 . 7533 0, ,7273603E+09 20 , 40 0. 0825 0 . 0630 0 . 1020 5 . 2434 87 , 9967 0, .9374121E+09 20 ,66 0. 0690 0 . 0530 0 .0808 4 . 1536 92, , 1503 0 ,1500335E+10 21 . 13 0. 0580 PAN 0 . 1527 7 .8497 100, .0000 Crystal mean size = 0.1366 mm Coefficient of Variation = 66.65 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.22 ml/s ( 1.80 gr/s) MeOH solution flow rate = 9.19 ml/s ( 7.65 gr/s) A 1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Cr concentration In feed = 75.0 ppm Mother Liquor (ML) Composition : 0.01214 gr Na2S04/gr ML 0.14818 gr 38°/,w/w H2S04/gr ML 0.83968 gr 80°/.w/w MeOH/gr ML Exit solute concentration = 0.012286 gr Na2S04/gr solvent Equilibrium concentrat1 on = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000217 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY -een Size (mm) Weight Retained Wt (gr) ,% Retained Cumulat 1ve Wt . % Retained Population Density,n (number/mm 11tre) l'n n Average S' (mm) 0 . 3000 0 .2187 11.1633 1 1 . 1633 0 . 2500 0 .1310 6.6867 17 .8500 0. 4552604E+07 15 , .33 0 . 2750 0 .2120 0 . 1295 6.6102 24 .4602 0. 9990930E+07 16 . 12 0 .2310 0 . 1800 0 . 1857 9.4788 33 ,939 1 0. 2785162 E+08 17 , . 14 0 . 1960 0 . 1500 0 . 2434 12.4241 46 .3631 0. 6526862E+08 17 . ,99 0 . 1650 0 . 1060 0 .4256 21.7243 68 .0874 0. 1666769E+09 18 , 93 0 . 1280 0 .0900 0 . 1745 8.9072 76 , 9946 0. 4187500E+09 19 ,85 0 .0980 0 .0750 0 . 1698 8.6673 85 .6618 0. 7285202E+09 20. ,41 0 .0825 0 . 0630 0 . 1015 5.18 10 90 . 8428 0. 9304520E+09 20 ,65 0 .0690 0 . 0530 0 .0742 3.7875 94 . 6302 0. 1374290E+10 21 .04 0 .0580 PAN 0 . 1052 5.3698 100 .0000 Crystal mean size = 0.1421 mm Coeff1c1en1 : of Variation » 65 .53 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 68 Feed Temperature Residence Time = 31.0 Deg 40.0 s EXPERIMENTAL CONDITIONS C Feed solution flow rate = 3.67 ml/s MeOH solution flow rate = 27.58 ml/s Alcohol/Acid-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : Crystallizer Temperature = 35.0 Deg. C Suspension Density = 32.32 gr/1 ( 5.40 gr/s) (22.96 gr/s) Cr concentration in feed = 150.0 ppm 0.01245 gr Na2S04/gr ML 0.14813 gr 38%w/w H2S04/gr ML 0.83941 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012610 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000541 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Reta1ned Cumulat 1ve Wt.% Retained Population Denslty.n (number/mm 11tre) 1 n n Average Size (mm) 0.3000 0 . 1466 9 .0768 9 .0768 0.2500 0 .0990 6 . 1297 15 . 2065 0. 4137392E+07 15 , 24 0 . 2750 0.2 120 0 .0976 6 .0430 21 . 2495 0. 9055010E+07 16, .02 0 .2310 0.1800 0 . 1325 8 . 2038 29 . 4533 0. 2389776E+08 16 , 99 0 . 1960 0.1500 0 . 1620 10 . 0303 39 . 4836 0. 5223982E+08 17 . 77 0 . 1650 0.1060 0 .3173 19 .6459 59 . 1295 0. 1494331E+09 18. 82 0 . 1280 0.0900 0 . 1565 9 .6898 68. .8193 0. 4516237E+09 19 , 93 0 .0980 0.0750 0 . 1698 10 .5133 79. .3326 0. 8760812E+09 20, 59 0 .0825 0.0630 0. , 1069 6 .6188 85. 9514 0. 1178442E+10 20. 89 0 .0690 0.0530 0. 0779 4 .8232 90. 7746 0. 1735061E+10 21 . 27 0 .0580 PAN 0. 1490 9. . 2254 100. 0000 I 00 I—1 <1 I Crystal mean size = 0.1243 mm Coefficient of Variation = 71.21 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 3.124395 mm/hr Nuclei population density = 0.7835787E+10 number/mm litre Nucleation rate.B = O.2448210E+11 number/hr litre RUN NUMBER 69 EXPERIMENTAL CONDITIONS C Feed Temperature = 31.0 Deg Residence Time = 60.0 s Feed solution flow rate = 2.45 m1/s MeOH solution flow rate = 18.39 ml/s Al cohol/Ac 1d-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : Crystallizer Temperature » 35.0 Deg. C Suspension Density = 32.45 gr/1 ( 3.60 gr/s) (15.31 gr/s) Cr concentration In feed = 150.0 ppm 0.01232 gr Na2S04/gr ML 0.14815 gr 38%w/w H2S04/gr ML 0.83953 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012469 gr Na2S04/gr solvent Equilibrium concentration • 0.012069 gr Na2S04/gr solvent Supersaturation - 0.000400 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt . % Reta1ned Cumulat 1ve Wt .% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 . 1224 1 .2598 7 . 2598 0 . 2500 0 . 1345 7 .9775 15 . 2373 0 .5404937E+07 15 .50 0 .2750 0 .2120 0 . 1479 8 .7723 24 .0095 0 .1319424E+08 16, .40 0 .2310 0 . 1800 0 . 1618 9 .5967 33 .6062 0, ,2806058E+08 17 , 15 0 . 1960 0 . 1500 0 . 1947 1 1 . 5480 45, , 1542 0. 6037110E+08 17. 92 0 . 1650 0 . 1060 0 .3216 19 .0747 64 . 2290 0. 1456362E+09 18. 80 0 . 1280 0 .0900 0 . 1423 8 . 4401 72 , 669 1 0. 3948611E+09 19. 79 0 .0980 0 ,0750 0 , 1493 8 .8553 81 , 5243 0. 7407017E+09 20. 42 0 .0825 0. .0630 0. . 1012 6 .0024 87 . 5267 0. 1072724E+10 20. 79 0 .0690 0. 0530 0, 0742 4 .4010 91 . 9276 0. 1589124E+10 21 . 19 0 .0580 PAN 0. 1361 8 .0724 100. 0000 I CO I—1 00 I Crystal mean size = 0.1381 mm Coefficient of Variation = 63.69 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 2.267566 mm/hr Nuclei population density = 0.5859426E+10 number/mm litre Nucleation rate.B = 0.1328663E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.83 ml/s ( 2.70 gr/s) MeOH solution flow rate = 13.79 ml/s (11.48 gr/s) Alcohol/Acld-feed ratio = 4.2500 gr/gr Cr concentration 1n feed = 150.0 ppm Mother Liquor (ML) Composition : 0.01223 gr Na2S04/gr ML 0.14817 gr 38%w/w H2S04/gr ML 0.8396 1 gr 80*/.w/w MeOH/gr ML Exit solute concentrat1 on = 0.012381 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000312 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.'/. Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 .3000 0 . 2463 14 . 2683 14 . 2683 0 . 2500 0 . 1283 7 . 4325 21 . 7009 0, ,5047581E+07 15, ,43 0.2750 0 .2120 0 . 1295 7 .5020 29 .2029 . 0. .1131030E+08 16 , 24 0 .2310 0 . 1800 0 . 1551 8 .9851 38 . 1879 0, ,2633408E+08 17, 09 0 . 1960 0 . 1500 0 .1801 10 .4333 48 . ,6213 0. 5467208E+08 17, 82 0 . 1650 0 . 1060 0 . 3067 17 .7674 66. ,3886 0, 1359740E+09 18 , 73 0 . 1280 0 .0900 0 . 1450 8 .4000 74 . ,7886 0. 3939087E+09 19 , 79 0 .0980 0 .0750 0 . 1408 8 . 1567 82 , 9452 0. 6838712E+09 20. 34 0 .0825 0 , 0630 0 .0881 5 . 1037 88 . 0489 0. 9142646E+09 20. 63 0 .0690 0, .0530 0 .0702 4 .0667 92 . 1 156 0. 1471905E+10 21 . 1 1 0 .0580 PAN 0. . 1361 7 . 8844 100. 0000 Crystal mean size = 0.1462 mm Coefficient of Variation « 73.62 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1 . 3 8 4 8 3 1 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.22 ml/s ( 1.80 gr/s) MeOH solution flow rate = 9.19 ml/s ( 7.65 gr/s) Alcohol/Acid-feed ratio = 4.2500 gr/gr Cr concentration 1n feed • 150.0 ppm Mother Liquor (ML) Composition : 0.01211 gr Na2S04/gr ML 0.14818 gr 38%w/w H2S04/gr ML 0.83971 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012255 gr Na2S04/gr solvent Equilibrium concentration » 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000186 gr Na2S04/gr' solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY reen Size (mm) Weight Reta1ned (gr) Wt .% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average S (mm) 0 .3000 0 . 2783 15 .3613 15 .3613 0 . 2 500 0 .1318 7 . 2749 22 .6362 0. 4957142E+07 15. .42 0.2750 0 .2 120 0 .1361 7 .5123 30 . 1485 0. 1 136375E+08 16 ,25 0.2310 0 . 1800 0 . 1634 9 .0192 39 . 1677 0. 2652270E+08 17. ,09 0.1960 0 . 1500 0 . 1910 10 .5426 49 .7103 0. 5542994E+08 17 . 83 0.1650 0 . 1060 0 . 3445 19 .0153 68 .7256 0. 1460126E+09 18. .80 0.1280 0 .0900 0 . 1505 8 .3071 77, .0327 0. 3908618E+09 19, 78 0.0980 0 .0750 0 . 1438 7 .9373 84 , 9700 0. 6677135E+09 20. 32 0.0825 0. .0630 0 ,0888 4 .9015 89. 8714 0. 8809846E+09 20. 60 0.0690 0.0530 0. ,0660 3 .6430 93. 5144 0. 1322956E+10 21 .00 0.0580 PAN 0. 1 175 6 .4856 100. 0001 Crystal mean size = 0.1492 mm Coefficient of Variation = 73.19 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 3.67 ml/s ( 5.40 gr/s) MeOH solution flow rate = 27.58 ml/s (22.96 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Cr concentration 1n feed = 300.0 ppm Mother Liquor (ML) Composition : 0.01246 gr Na2S04/gr ML 0.14813 gr 38%w/w H2S04/gr ML 0.83941 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012620 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000551 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 .2123 13 . 3279 13 . 3279 0 , 2500 0 . 1084 6 .8052 20 .133 1 0 ,4592159E+07 15 .34 0.2750 0 .2120 0 . 1 107 6 . 9496 27 . 0827 0. . 1041078E+08 16 . 16 0.2310 0 . 1800 0 . 1335 8 . 38 10 35 . 4637 0, 2440725E+08 17 .01 0.1960 0 . 1500 0 . 1590 9 . 98 18 45 .4455 0, 5197328E+08 17 , 77 0.1650 0 . 1060 0 .3070 19 .2730 64 .7185 0, 1465586E+09 18 ,80 0.1280 0 .0900 0 . 1360 8 . 5379 73 . 2564 0. 3978301E+09 19, ,80 0.0980 0 .0750 0 . 1375 8 .6321 81 . 8885 0. 7191270E+09 20, ,39 0.0825 0 .0630 0. .0895 5 .6187 87 . 5071 0. 1000115E+10 20, .72 0.0690 0. 0530 0. 0600 3 . 7667 91 . 2738 ' 0. 1354643E+10 21 . 03 0.0580 PAN 0. 1390 8 .7262 100. 0001 Crystal mean size = 0.1384 mm Coefficient of Variation » 75.48 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1 . 3 8 4 8 3 1 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 73 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Residence Time = 40.0 s Feed solution flow rate = 3.67 ml/s MeOH solution flow rate = 27.58 ml/s A1cohol/AcId-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : Crystallizer Temperature = 35.0 Deg. C Suspension Density « 32.35 gr/1 ( 5.40 gr/s) (22.96 gr/s) Cr concentration 1n feed 300.0 ppm 0.01242 gr Na2S04/gr ML 0.14814 gr 38%w/w H2S04/gr ML 0.83944 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012581 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000512 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retalned (gr) Wt.% Retalned Cumu!at 1ve Wt.% Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 . 2 104 14 .4189 14 .4189 0 . 2500 0 . 1010 6 .9216 21 .3405 0 .4675656E+07 15 .36 0 .2750 0 .2 120 0 . 1023 7 .0107 28 .3512 0, .1051344E+08 16 . 17 0.2310 0 . 1800 0 . 1246 8 .5389 36 .8901 0. .2489370E+08 17. .03 0 . 19S0 0 . 1500 0 . 1358 9 . 3065 46 , 1966 0. 4850835E+08 17 , .70 0 . 1650 0 . 1060 0 . 2540 17 . 406.8 63 ,6034 0. 1325074 E+09 18 . ,70 0 . 1280 0 . 0900 0 . 1 150 7 .8810 71 . 4845 0. 3676127E+09 19 , 72 0 .0980 0 . 0750 0. 1321 9 .0529 80. 5374 0. 7549873E+09 20, ,44 0 .0825 0. .0630 0. 0855 5 .8594 86. 3968 0. 1044064E+10 20, ,77 0 .0690 0. 0530 0. 0650 4 .4545 90. 8513 0. 1603690E+10 21 . 20 0 .0580 PAN 0. 1335 9. , 1489 100.0001 CO to to Crystal mean size = 0.1393 mm Coefficient of Variation =• 79.05 % Crystal growth rate.G Nuclei population density Nucleation rate.B CRYSTALLIZATION KINETICS 3.285091 mm/hr O. 6087913E+10 number/mm litre 0.1999935E+11 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 2.45 ml/s ( 3.60 gr/s) MeOH solution flow rate = 18.39 ml/s (15.31 gr/s) A1cohol/Ac 1d-feed ratio = 4.2500 gr/gr Cr concentration In feed • 300.0 ppm Mother Liquor (ML) Composition : 0.01233 gr Na2S04/gr ML 0.14815 gr 38%w/w H2S04/gr ML 0.83952 gr 80°/.w/w MeOH/gr ML Exit solute concentration « 0.012485 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000416 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Retained Wt (gr) Reta1ned Cumulat 1ve Wt . % Retained Population Density,n (number/mm litre) In n Average Size (mm) 0 . 3000 0 .0728 4 . 6420 4 .6420 0 . 2500 0 .1781 1 1 .3563 15 .9982 0. 7690959E+07 15 .86 0.2750 0 . 2 1 20 0 . 1767 1 1 . 2670 27 .2652 0. 1693950E+08 16 .65 0.2310 0 . 1800 0 . 1549 9 .8770 37 . 1422 0. 2886808E+08 17 . 18 0.1960 0 . 1 500 0 . 1838 1 1 .7197 48 .8619 0. 6124309E+08 17 ,93 0.1650 0 . 1060 0 .27 17 17 . 3245 66 , 1864 0. 1322183E+09 18. ,70 0.1280 0 .0900 0 .1111 7 .084 1 73. , 2705 0. 3312847E+09 19, ,62 0.0980 0 .0750 0 .1215 7 .7473 81 , .0178 0. 6477512E+09 20, ,29 0.0825 0. .0630 0. ,0830 5 .2924 86 . 3102 0 . 9454400E+09 20, ,67 0.0690 0. 0530 0, ,0662 4 . 221 1 90. 53 13 0 . 1 523564E +10 21 , 14 0.0580 PAN 0. 1485 9 .4689 100. 0002 Crystal mean size » 0.147 1 mm CoeffIclent of Variation = 61 . 69 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.83 ml/s ( 2.70 gr/s) MeOH solution flow rate = 13.79 ml/s (11.48 gr/s) Alcohol/Acid-feed ratio = 4.2500 gr/gr Cr concentration 1n feed « 300.0 ppm Mother Liquor (ML) Composition : 0.01217 gr Na2S04/gr ML 0.14817 gr 38%w/w H2S04/gr ML 0.83965 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012323 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000255 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size Weight Retained Wt.% Retained Cumulative Wt.% Retained Population Density,n In n Average S1 (mm) (gr) (number/mm litre) (mm) 0 . 3000 0 . 267 1 16 .5152 16 .5152 0 . 2500 0 . 1465 9 .0583 25 . 5735 0, ,6 161085E+07 15 .63 0. 2750 0 .2120 0 .1315 8 . 1308 33 .7044 0, 1227702E+08 16 .32 0. 2310 0 . 1800 0 . 1378 8 .5204 42 , 2247 0. 2501029E+08 17. ,03 0. 1960 0 . 1 500 0 . 1559 9 . 6395 51 . 8643 0. 5058955E+08 17 . 74 0. 1650 0 . 1060 0 . 2533 15 .6619 67 , 5262 0. 1200439E+09 18 , .60 0. 1280 0 .0900 0 . 1 197 7 .4012 74 ,9274 0, 3476040E+09 19 .67 0. 0980 0 .0750 0 . 1255 7 .7599 82 .6873 0, 6515965E+09 20 .29 0. 0825 0 .0630 0 .0822 5, ,0826 87 , 7698 0. 91 18651E+09 20.63 0, 0690 0 . 0530 0 .0660 4 . ,0809 91 , 8507 0. 1479276E+10 21 , 1 1 0, 0580 PAN 0 ,1318 8 , 1494 100, ,0001 Crystal mean size = 0.1556 mm Coefficient of Variation = 74.17 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1 . 3 8 4 8 3 1 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 1 2 E + 1 2 number/hr litre RUN NUMBER 76 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Residence Time = 120.0 s Feed solution flow rate = 1.22 ml/s MeOH solution flow rate = 9.19 ml/s Alcohol/Acld-feed ratio = 4.2500 gr/gr Mother Liquor (ML) Composition : Crystallizer Temperature « 35.0 Deg. C Suspension Density = 32.64 gr/1 ' ( 1.80 gr/s) ( 7.65 gr/s) Cr concentration 1n feed « 300.0 ppm 0.01210 gr Na2S04/gr ML 0.14818 gr 38°/»w/w H2S04/gr ML 0.83971 gr 80%w/w MeOH/gr ML Exit solute concentration = 0.012249 gr Na2S04/gr solvent Equilibrium concentration • 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000180 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY Screen Size (mm) Weight Reta1ned (gr) Wt.0/. Reta1ned Cumulat 1ve Wt.% Retained Population Density,n (number/mm 11tre) In n Average Size (mm) 0 . 3000 0 . 3698 18 .4891 18 .4891 0 . 2500 0 . 1723 8 . 6 146 27 . 1037 0. 5870888E+07 15 .59 0. 2750 0 . 2 120 0 . 1620 8 .0996 35 .2033 0. 1225409E+08 16 .32 0.2310 0 . 1800 0 . 1739 8 . 6946 43 .8978 0. 2557219E+08 17, ,06 0.1960 0 . 1500 0 . 1904 9 .5195 53. ,4174 0. 5005882E+08 17 , 73 0.1650 0 . 1060 0 . 336 1 16 . 8042 70, ,2215 0. 1290542E+09 18 , 68 0.1280 0 .0900 0 . 1505 7 . 5246 77 . ,7462 0. 3540997E+09 19. 69 0.0980 0 .0750 0 .14 10 7 . 0497 84 . 7958 0. 5931336E+09 20. 20 0.0825 0 . 0630 0 . 0902 4 . 5098 89. 3056 0. 8107080E+09 20.51 0.0690 0. .0530 0. .0681 3 . 4048 92 . 7104 0. 1236663E+10 20.94 0.0580 PAN 0. 1458 7 . 2896 100. 0001 CO (S3 OI Crystal mean size = 0.1604 mm Coefficient of Variation = 74.31 % CRYSTALLIZATION KINETICS Crystal growth rate.G = 1.190928 mm/hr Nuclei population density = 0.4241628E+10 number/mm litre Nucleation rate.B = 0.5051474E+10 number/hr litre RUN NUMBER 7 1 EXPERIMENTAL CONDITIONS Feed Temperature = 31.0 Deg. C Crystallizer Temperature = 35.0 Deg. C Residence Time = 120.0 s Suspension Density = 32.63 gr/1 Feed solution flow rate = 1.22 ml/s ( 1.80 gr/s) MeOH solution flow rate = 9.19 ml/s ( 7.65 gr/s) Alcohol/Ac1d-feed ratio •= 4.2500 gr/gr Cr concentration In feed • 300.0 ppm Mother Liquor (ML) Composition : 0.01211 gr Na2S04/gr ML 0.14818 gr 38%w/w H2S04/gr ML 0.83971 gr 80°/.w/w MeOH/gr ML Exit solute concentration = 0.012259 gr Na2S04/gr solvent Equilibrium concentration = 0.012069 gr Na2S04/gr solvent Supersaturation = 0.000191 gr Na2S04/gr solvent PRODUCT CRYSTAL SIZE DISTRIBUTION - POPULATION DENSITY reen Size (mm) Weight Reta1ned (gr) Wt.% Retained Cumulat 1ve Wt.% Retained Population Denslty.n (number/mm 11tre) In n Average S (mm) 0 . 3000 0 . 3798 20.7916 20 . 7916 0 . 2500 0 . 1795 9.8265 30 .6181 0 ,6694942E+07 15 . 72 0 .2750 0 .2120 0 .14 11 7.7243 38 . 3424 0 ,1168307E+08 16 .27 0 . 2310 0 . 1800 0 . 1528 8.3648 46 . 7072 0, ,2459549E+08 17 .02 0 . 1960 0 . 1500 0 . 1729 9.4652 56 . 1724 0, 4975909E+08 17 .72 0 . 1650 0 . 1060 0 . 2894 15.8428 72 ,0152 0, 1216371E+09 18, ,62 0 . 1280 0 .0900 0 . 1425 7.8010 79. ,8162 0. 3670016E+09 19, .72 0 .0980 0 .0750 0 . 1300 7.1167 86 , 9328 0. 5986058E+09 20, .21 0 .0825 0 .0630 0 .0778 4.2591 91 , 1919 0. 7654223E+09 20. .46 0 .0690 0 .0530 0 ,0504 2.7591 93. 95 10 0. 1001841E+10 20. 73 0.0580 PAN 0 . 1 105 6.0492 100. 0001 Crystal mean size = 0.1692 mm Coefficient of Variation = 70.45 % CRYSTALLIZATION KINETICS Crystal growth rate.G •= 1.384831 mm/hr Nuclei population density = 0.1005763E+12 number/mm litre Nucleation rate.B = 0. 13928 12E+12 number/hr litre - 327 -APPENDIX D Loge Population Density Versus Crystal Size Plots for Run Numbers 1-77 - 328 -o tp-* (M . CNJ OO _ O RUN no. 1 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 25 .0 deg. C 40 .0 sec. 3 3 . 7 g r / 1 0 .863 g r / k g I ~1 I I I 1 1 0.0 0.1 0.2 0.3 SIZE (mm) 0 . 4 CD CM CM <M C D _ O O o. RUN no. 2 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 2 5 . 0 deg. C 4 0 . 0 sec. 3 3 . 7 g r / 1 0 . 8 3 7 g r / k g "i—r T 1— 0-0 o.l 0.2 0.3 SIZE (mm) 0 .4 CD . <M CNJ . CNJ O •sr. o o _l RUN no. 3 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 25 .0 deg. C 50.0 sec. 33 .8 g r / 1 0.751 g r / k g 0.0 0.1 0.2 0.3 SIZE ( m m ) 0 . 4 CD CNJ CM CNI O O . 0 . 0 RUN no. 1 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 25 .0 deg. C 5 0 . 0 sec. 3 3 . 8 g r / 1 0 .776 g r / k g SIZE (mm) "i—i—i 1—i 0 . 2 0 . 3 0 . 4 ) - 329 -CD CM <M _ CM CD _ O o o _ RUN no. 5 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION C 2S.0 6 0 . 0 3 3 . 9 g r / 1 0 .621 g r / k g 0-0 0.1 0.2 0.3 SIZE ( m m ) 0 . 4 CD CM CM CM OO _ O \r _ o o _ r 0 .0 RUN no. 6 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 2 5 . 0 deg. C 80 .0 sec. 34 .0 g r / 1 0 .51B g r / k g ~i r 0 . 2 0 . 1 0 . 3 SIZE ( m m ) 0 . 4 CD CM CM . CM RUN no. 7 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 2 5 . 0 deg. C 100.0 sec. 34 .1 g r / 1 0 .432 g r / k g 0 . 0 r o. 0.1 0.2 0.3 0.4 SIZE (mm) 0 . 4 CD _. CM CM c\j CD CD . TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 2 5 . 0 deg. C 120.0 sec. 3 4 . 2 g r / l 0 . 3 5 6 g r / k g 0 . 0 0. ~ — i — i — r 0 . 2 0 . 3 0 . 4 SIZE (mm) - 330 -RUN no. 9 TEMPERATURE RESIDENCE TIME SUSPENSION DENsrrr SUPERSATURATION 25 .0 de^. C 4 0 . 0 sec. 4 6 . 4 g r / 1 0 .893 g r / k g 0 . 0 r o. 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD CM OJ _ C\J o o o. RUN no. 10 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 25.0 deg. C 50 .0 m c . 46 .5 g r / 1 0 .816 g r / k g 0.0 0 . 1 0 . 2 0 .3 SIZE ( m m ) 0 . 4 1 r o.o RUN no. 1 ] TEMPERATIRE - 25 .0 (teg. C RESIDENCE TIME - 60 .0 sec. SUSPENSION DENSITY . 4 6 . 6 g r / 1 SUPERSATURATION . 0 .700 g r / k g I 0. 1 0.2 0.3 SIZE (mm) 0.4 CD C\J CM r\j CD \r _ o o _ TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 25 .0 deg. C 80.0 sec. 46 .7 g r / 1 0 .532 g r / k g 0-0 0.1 0.2 0.3 SIZE (mm) 0.4 - 331 -RUN no. 13 TEMPERATURE - 2 5 . 0 deg. C RESIDENCE TIME - 8 0 . 0 sec. SUSPENSION DENSITY - 4 6 . 7 g r / 1 SUPERSATURATION = 0 . 5 5 1 g r / k g 0.0 0.1 0.2 0.3 SIZE ( m m ) 0 . 4 CD __ CM C\J. CM CD _ O sr. o o _ RUN no. 14 TEMPERATURE RESIOENCE TIME SUSPENSION DENSITY SUPERSATURATION 25 .0 deg. C 100 .0 sec. 4 6 . 6 g r / 1 0 .462 g r / k g 0.0 0 .1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 15 TEMPERATURE - 2 5 . 0 deg. C RESIDENCE TIME - 120.0 sec. SUSPENSION DENSITY . 4 6 . 8 g r / 1 SUPERSATURATION « 0 . 3 9 7 g r / k g ~ i—i—i—i—i—r~ 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 SIZE ( m m ) CD CNJ CM _ CM O O . 0 . 0 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 25 .0 deg. C 5 0 . 0 sec. 71 .0 g x / l 0 . 8 1 4 g r / k g r o. —i—r 0 . 3 0.1 0.2 0.4 SIZE ( m m ) - 332 -RUN no. 17 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 2 5 . 0 deg. C 5 0 . 0 sec. 7 1 . 0 g r / 1 0 . 6 0 6 g r / k g 1 1 1 1 1 0.0 0 .1 0 . 2 0 .3 0 . 4 SIZE ( m m ) CO CM CM . CM O o o. RUN no. 18 TEMPERATURE - 2 5 . 0 deg. C RESIDENCE TIME - SO.O sec. SUSPENSION DENSITY - 7 1 . 2 g r / 1 SUPERSATURATION = 0 . 6 7 1 g r / k g 0 .0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 0.0 RUN no. 19 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 2 5 . 0 deg. C 8 0 . 0 sec. 7 1 . 3 g r / 1 0 . 5 6 7 g r / k g ~i—r o.i ^ i i i — 0 . 2 0 . 3 0 . 4 SIZE (mm) CD CM r\j CM o CD . RUN no. 20 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION - 2 5 . 0 deg. C - 100 .0 sec. - 7 1 . 3 g r / 1 - 0 . 5 1 1 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 - 333 -RUN no. 21 TEMPERATURE - 2S.0 deg. C RESIDENCE TIME - 120.0 sec. SUSPENSION DENSITY - 7 1 A g r / 1 SUPERSATURATION = 0 . 4 3 8 g r / k g 1 — T 0.0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . CM O RUN no. 22 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 dug. C 40 .0 soc. 3 2 . 6 g r / 1 0 . 8 8 9 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 23 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 5 0 . 0 sec. 3 3 . 0 g r / 1 0 . 6 9 2 g r / k g -1 1 1 0 . 2 0 . 3 0.0 0.1 0. 0.4 SIZE (mm) CD . CM CM . CM RUN no. 24 TEMPERATURE - 30 .0 deg. C RESIDENCE TIME - 60 .0 sec. SUSPENSION DENSITY - 33 .1 g t / l SUPERSATURATION » 0 .631 g r / k g 1 I I I 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 SIZE (mm) - 334 -RUN no. 25 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION deg. C 3 0 . 0 8 0 . 0 3 3 . 2 g r / 1 0 . 5 1 2 g r / k g • i ^ i i i—i—r—r— 0 - 0 0 . 1 0 . 2 0 . 3 0 . 4 SIZE ( m m ) CD (N CM _ <M O o o _ 0.0 RUN no. 26 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 100.0 sec. 3 3 . 3 g r / 1 0 . 4 1 0 g r / k g I 0 . 2 0 . 1 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 27 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 100.0 sec. 3 3 . 2 g r / 1 0 . 4 3 7 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 CO CM CM . CM O o o _ 0.0 RUN no. 28 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 120.0 sec. 3 3 . 3 g r / 1 0 .401 g r / k g r 0. 1 0.2 0.3 SIZE (mm) 0.4 - 335 -RUN no. 29 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 30 .0 deg. C 4 0 . 0 sec. 45 .1 g r / 1 0 . 6 6 3 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD CM OJ. CM CD _ O \r. o O . RUN no. 30 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 30 .0 deg. C 5 0 . 0 sec. 4 5 . 2 g r / 1 0 . 7 7 2 g r / k g 0 .0 0 .1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 31 TEMPERATURE RESIDENCE TIME SUSPENSION DENSrTY SUPERSATURATION 30.0 deg. C 60.0 sec. 45 .3 g r / 1 0 . 6 1 9 g r / k g H 1 1 1 1 1— 0 . 0 0 . 1 0 . 2 0 . 3 SIZE (mm) 0.4 CD CM CM . CM O CD _ RUN no. 32 TEMPERATURE - 30 .0 deg. C RESIOENCE TIME _ 6 0 . 0 sec. SUSPENSION DENSITY - 4 5 . 4 g r / 1 SUPERSATURATION - 0 .591 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 - 336 -RUN no. 33 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION deg. C 3 0 . 0 100.0 4 5 . 5 g r / l 0 . 4 6 3 g r / k g ' I n I 1 1 1 1 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . CM CO _ O O O . RUN no. 34 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 120.0 sec. 4 5 . 5 g r / 1 0 . 3 8 8 g r / k g 0.0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 35 TEMPERATURE - 3 0 . 0 RESIDENCE TIME - 5 0 . 0 SUSPENSION DENSITY - 6 8 . 6 SUPERSATURATION - 0 . 9 0 1 deg. C sec. g r / 1 g r / k g 1 1 1 1 1— 0.0 0.1 0.2 0.3 SIZE (mm) 0.3 CD . CM CM _ CM O sr. o o _ RUN no. 36 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 6 0 . 0 sec. 6 9 . 0 g r / 1 0 . 7 1 4 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 - 337 -CD . CM CM . CM O XT . O o _ . 0 . 0 RUN no. 37 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 60 .0 sec. 63 .0 g r / 1 0 .756 g r / k g I 0.2 0 . 1  0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . CM CD _ O O o. RUN no. 38 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 30 .0 deg . C 80.0 96C. 6 9 . 1 g r / 1 0 . 5 8 0 g r / k g 0 .0 0 .1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 39 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 30 .0 deg. C 100.0 sec. 6 9 . 2 g r / 1 0 .510 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 CD . CM C\J . CM O \r. o CD _ RUN no. 40 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 0 . 0 deg. C 120 .0 sec. 6 9 . 3 g r / 1 0 . 3 9 5 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0.4 I - 338 -CD . CM CM . C\J O O O . RUN no. <11 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 5 . 0 deg. C 4 0 . 0 sec. 3 2 . 0 o r / I 0 . 8 5 9 g r / k g ~T 1 1 1 1 1— 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CNJ CM . CM 00 _ O O o. 0 .0 RUN no. 42 TEMPERATURE - 3 5 . 0 deg. C RESOENCE TIME - 4 0 . 0 sec. SUSPENSION DENSITY - 3 2 . 0 g r / 1 SUPERSATURATION = 0 . 8 1 2 g r / k g ~i r 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . Osl CH o CD 0 . 0 RUN no. 43 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 5 . 0 5 0 . 0 3 2 . 1 deg. C sec. g r / l 0 . 7 7 1 g r / k g r o. 1 0.2 0.3 SIZE (mm) 0 . 4 CD . CM CM . CM O RUN no. 44 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 5 . 0 deg. C 6 0 . 0 sec. 3 2 . 2 g r / 1 0 . 6 0 2 g r / k g 0 . 0 r 0 . 1 0 . 2 0 . 3 SIZE ( m m ) -0 . 4 I - 339 -CD . r\j <M . (M o M" . o o. RUN no. 45 TEMPERATURE - 35 .0 deg. C RESIDENCE TIME - 80 .0 sec. SUSPENSION DENSITY - 3 2 . 4 g r / 1 SUPERSATURATION = 0 . 4 2 9 g r / k g ~ I I 1 1 1 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . CM O O O . RUN no. 46 TEMPERATURE RESIDENCE: TIME SUSPENSION DENSITY SUPERSATURATION 35 .0 deg. C 100.0 sec. 3 2 . 4 g r / 1 0 .440 g r / k g 0 .0 0 . 1 0 . 2 SIZE ( m m ) ~ r 0 . 3 0 . 4 CD . CM CM . OM O XT . O CD . RUN no. 4? TEMPERATURE - 35 .0 deg. C RESIDENCE TIME • 120.0 sec. SUSPENSION DENSITY » 32.5 g r / 1 SUPERSATURATION «. 0 .340 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 CD . CM CM . CM o CD _ RUN no. ' TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 35 .0 deg. C 4 0 . 0 sec. 4 3 . 6 g r / 1 0 . 6 9 5 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0.4 - 340 -CD (M CM _ (M CO . O O o. RUN no. 49 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION ~~l 1 0.0 0.1 3 5 . 0 deg. C 4 0 . 0 sec. 4 3 . 8 g r / 1 0 . 8 8 1 g r / k g ~i 1—i—i—f 0 . 2 0 . 3 0 . 4 SIZE ( m m ) CD CM CM . CM C ^ CD . c ~ o \f. o o. 0 .0 RUN no. 50 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 5 . 0 deg. C 5 0 . 0 sec. 4 3 . 8 g r / 1 0 . 8 1 6 g r / k g T 0. 1 0.2 0 .3 SIZE ( m m ) 0 . 4 CD . CM CM . CM deg. C RUN no. 51 TEMPERATURE - 3 5 . 0 RESIDENCE TIME - 6 0 . 0 SUSPENSION DENSITY - 4 4 . 0 g r / 1 SUPERSATURATION « 0 . 6 2 2 g r / k g O \f . 1 I I 1 1 1 o . o 0 . 1 0 . 2 0 . 3 SIZE (mm) I 0 . 4 CD . CM CM . CM o •sr. RUN no. 52 TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 3 5 . 0 deg. C 8 0 . 0 sec. 4 4 . 1 g r / 1 0 . 5 « g r / k g 0.1 0.2 0.3 0.4 SIZE (mm) - 341 -CD _ _ CM CM * O o o. 0 .0 RUN no. 53 TEMPERATURE - 3 5 . 0 deg . C RESIDENCE TIME - 8 0 . 0 soc. SUSPENSION DENSITY - 44 .1 gr / I SUPERSATURATION = 0 . 5 3 3 g r / k g 0.1 r 0 . 2 l 0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . CM CD _ O O o . RUN no. 54 TEMPERATURE - 3S.0 deg. C RESIDENCE TIME » 100.0 sec. SUSPENSION DENSITY « 44 .1 g r / 1 SUPERSATURATION = 0 .481 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 0 . 0 RUN no. 55 TEMPERATURE - 3 5 . 0 deg. C RESIDENCE TIME - 120.0 sec. SUSPENSION DENSITY - 4 4 . 3 g r / 1 SUPERSATURATION - 0 . 3 5 1 g r / k g I I I I 0 . 2 0 . 3 0.1 0. 0.4 SIZE (mm) CD , CM CM . CM O o o _ 0.0 TEMPERATURE RESIDENCE TIME SUSPENSON DENSITY SUPERSATURATION 3 5 . 0 deg. C 5 0 . 0 sec. 6 6 . 4 g r / 1 0 .807 g r / k g o.; —l 1 1— 0 . 2 0 . 3 I 0 . 4 SIZE (mm) - 342 -RUN no. 57 TEMPERATURE - 35 .0 deg. C RESIDENCE TIME " 6 0 . 0 sec. SUSPENSION DENSITY - 6 6 . 5 g r / 1 SUPERSATURATION = 0 .710 g r / k g ~ I I I I I 0.0 0.1 0.2 0.3 SIZE ( m m ) 0 . 4 CD . C\J CM . CM CO _ O O O . 0.0 RUN no. 56 TEMPERATURE RESIOENCE TIME SUSPENSION DENSITY SUPERSATURATION I 0.1 0 . 2 0 . 3 SIZE ( m m ) 35.0 deg. C 6 0 . 0 sec. 6 6 . 5 g r / 1 0 . 6 6 2 g r / k g 0 . 4 RUN no. 59 TEMPERATURE - 35.0 deg. C RESIDENCE TIME - 00 .0 sec. SUSPENSION DENSITY - 6 6 . 6 g r / 1 SUPERSATURATION « 0 .564 g r / k g 0.4 ~ 1 1 1 1 -0 . 2 0 . 3 0 . 4 SIZE (mm) CD . CM CM . CM CD XT . O CD . TEMPERATURE RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 35 .0 deg. C 100.0 sec. 6 6 . 7 g r / 1 0 .439 g r / k g 0.0 0.1 0.2 0.3 SIZE (mm) 0.4 - 343 -RUN no. 61 TEMPERATURE - 3 5 . 0 deg. C RESIDENCE TIME - 120.0 sec. SUSPENSION DENSITY - 6 6 . 6 g r / 1 SUPERSATURATION = 0 . 3 9 7 g r / k g 0 . 0 0 . 1 0 . 2 SIZE ( m m ) i 0 . 3 0 . 4 CD . CM CM . CM O O O . RUN no. 62 TEMPERATURE « 35 .0 deg. C RESIDENCE TIME - 120.0 sec. SUSPENSION DENSITY - 6 6 . 6 g r / 1 SUPERSATURATION = 0.3<W g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 - 344 -CD . CNJ CNJ . CNI CO _ O xr. o o. RUN no. 63 Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION ppm TS 40.0 32 .3 or/1 0 .574 gr/kg ~l I 1 1 1 1 1-0.0 0.1 0.2 0.3 0.4 SIZE ( m m ) CD CNJ CNJ . CNJ O NT . o O . RUN no. 64 Cr CONCENTRATION RESIOENCE TIME SUSPENSION DENSITY SUPERSATURATION 75 ppm 40 . 0 sec . 32 .2 gr/1 0 . 610 g r / k g — i r 0 . 2 0 . 0 0 . 1 .  0 . 3 SIZE ( m m ) 0 . 4 RUN no. 65 Cr CONCENTRATION RESIDENCE TIME SUSPENSION OENSITY SUPERSATURATION 75 ppm 60 .0 sec. 32 . 4 gr/1 0 .423 g r / k g 0.0 0.1 0.2 0.3 SIZE ( m m ) 0 . 4 CD . CNI CNI . CNJ RUN no. 66 Cr CONCENTRATION RESIOENCE TIME SUSPENSION DENSITY SUPERSATURATION 75 ppm 80 .0 sec. 32 .4 gr/1 0 .387 g r / k g — i — i — i — r 0 . 0 0 . 1 0 . 2 —1 1 0 . 3 0 . 4 SIZE ( m m ) - 345 -RUN no. 67 Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 75 ppm 120.0 sec. 3 2 . 6 gr/1 0 . 216 g r / k g o.o 0.1 0.2 0.3 SIZE ( m m ) 0 . 4 CD . CM CM . CM 00 _ O o o. RUN no. 68 Cr CONCENTRATION - 150 RESIDENCE TIME - 40 .0 SUSPENSION DENSITY - 32 . 3 SUPERSATURATION = 0.541 gr/1 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 69 Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION ISO ppm 60 .0 sec. 32.4 gr/i 0 .400 gr/kg v . ~1—I—I—I— 0.0 0.1 0.2 0 . 3 1 0.4 SIZE ( m m ) CD CM CM CM \r _ RUN no. 70 Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 150 ppm 80 .0 sec . 32 .5 gr/1 0 . 312 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 - 346 -RUN no. 71 Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 150 ppm 120.0 sec . 3 2 . 6 gr /1 0 . 1 85 g r / k g 0 . 0 0.1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD CM CM , CM O o o _ 0 . 0 RUN no. 72 Cr CONCENTRATION - 300 RESIDENCE TIME - <0.0 SUSPENSION DENSITY - 3 2 . 3 SUPERSATURATION = 0.551 g r / k g ppm sec . 9-/1 1—r 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 RUN no. 73 Cr CONCENTRATION RESIDENCE TIME SUSPENSION OENSITY SUPERSATURATION M0 40 .0 32 .3 0 .511 ppm sec . gr /1 g r / k g ~1 1 1 1 1 1 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD CM CM CM \r _ Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 300 ppm 60 .0 sec . 32 . 4 gr/1 0 .416 g r / k g 0 . 0 0 . 1 0 . 2 0.3 SIZE ( m m ) i — f 0 . 3 0 . 4 - 347 -CD . CM r\i. CM CO _ o o o. RUN no. 75 Cr CONCENTRATION » 300 ppm RESIDENCE TIME - 8 0 . 0 sec . SUSPENSION DENSITY - 3 2 . 5 gr/1 SUPERSATURATION = 0 . 2 5 4 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CM ( M . CM O \T . O O . RUN no. 76 Cr CONCENTRATION RES10ENCE TIME SUSPENSION DENSITY SUPERSATURATION 300 ppm 120.0 sec. 32 .6 gr/1 0 . 160 g r / k g 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 CD . CM CM . CM O xr. RUN no. 77 Cr CONCENTRATION RESIDENCE TIME SUSPENSION DENSITY SUPERSATURATION 300 ppm 120.0 sec. 32 .6 gr/1 0 . 190 g r / k g —I 1 1 1 1 1 0 . 0 0 . 1 0 . 2 0 . 3 SIZE ( m m ) 0 . 4 - 348 -APPENDIX E Computer Program C PROGRAM TO CALCULATE GROWTH AND NUCLEATION RATES OF Na2S04 C SALTING OUT CRYSTALLIZATION FROM SCREEN ANALYSIS DATA. C C TO OPTIONALLY PLOT CALCULATED RESULTS. C R EAL * 4 MT,MTTH,MS,MSTH,KV,NO,LAV.LNN EXTERNAL FUN 1 ,FUN2,FUN3 DIMENSION TEMP ( 10O),TI ME(10O),MT(10O),COMP1(100),C0MP2(100) DIMENSION TFEED(100),PARM(100),QACID(100),QME0H(100) DIMENSION WACID(100),WME0H(100),DENA(100),DENM(100),QT0TAL(100) DIMENSION C0MP3(100),CV(100),MS(100),MSTH(100),MTTH(100) DIMENSION CEXIT(100),CEQ(100),SS(100),CSS(100),G(100),N0(100) DIMENSION B(100),YS(100),R(100),WR(100,11),WPC(11),CUMWPC(11) DIMENSION SIZE(11),TSIZE(11),TFRAC(11),LAV(9),LNN(9),P0P(9) DIMENSION X(9,2),XX( 1 ,2),SY(1),CB(2),SB(2),FX(1),RAT(100) DIMENSION XXX(50),YYY(50),XKK(20),YKK(20),YIELD(100) DIMENSION XSHIFT(2),YSHIFT(2),XL(2),YL(2),XMIN(2),YMIN(2) DIMENSION DX(2),DY(2),SSIZE1(2),SSIZE2(2),SSIZE3(2) DIMENSION XT EXT(2).YTEXT(2) ,ITEXT(2),LIB2(3),LIB3(3).R00T( 1) C DATA RHOC.KV/O.002698,0.1707/ DATA SIZE/0.3,.25,.212,.18,.15,.106,.09,.075,.063,.053,0.0/ DATA XX(1,1),IP.LU/-1.0,1,6/ DATA XSHIFT/2.25,2.25/ DATA YSHIFT/4. 1,4.1/ DATA XL/8.0,8.0/ DATA YL/8.0,8.0/ DATA XMIN/O.0,0.0/ DATA YMIN/10.0,0.0/ DATA DX/0.05,0.05/ DATA DY/2.0,0.125/ DATA SSIZE1/0.23,0.2/ DATA SSIZE2/0.3.0.25/ DATA SSIZE 3/0 16,0. 16/ DATA SCALE/0.625/ DATA DF,IDF/0.004.5/ DATA NSYM1.NSYM2/15,15/ DATA ITEXT/1,1/ DATA XTEXT/2.0,2.0/ DATA YTEXT/6.0,6.0/ DATA I PLOT/ 1 / DATA LIB2/4HSANS,4HERIF,4H.2 / DATA LIB3/4HSANS.4HERIF,4H.1 / DATA NRUNIN.NRUN/1,62/ C DO 10 1=1.NRUN RE AD(4, 11) TFEED(I),TEMP(I),TIME(I),CSS(I),YS(I) READ(5,12) (Wk( I ,J),d=1,11) 11 FORMAT(2X,F4.1,2X,F4.1,2X,F5.1,2X,F6.4,2X,F4.2) 12 FORMAT( 1 1( 1X , F6.4)) 10 CONTINUE C DO 14 J= 1 .2 xshift(j)=xshift(j)/scale YSHIFT(J)=YSHIFT(j)/SCALE xtext(j)=xtext(j)+xshift(j) YTEXT(d)=YTEXT(J)+YSHIFT(U) 14 CONTINUE C DO 20 I =NRUNI N , NRUN W CO SS(I)=CSS(I)/1000.0 CEQ(I)=CSTAR(TEMP(I),YS(I ) ) C E X I T (I)=CEQ(I)+SS(I) RAT(I)=0.75*YS(I)/(1.0-YS(I)) YIELD(I)=100.0*(1.0-3.0*CEXIT(I)/(1.0-YS(I))) COMP1(I )=CEXIT(I)/(1 .0+CEXIT(I)) COMP3(I) = ( 1 .0-C0MP1(I))»YS(I) C0MP2(I) = 1 .0-C0MP1(I)-C0MP3(I) OTOTALfI)=1250.0/TI ME(I) DENA(I)=RH0A(TFEED(I)) DENM(I)=RHOM(TFEED(I)) PARM(I)=DENM(I)/(RAT(I)*DENA(I)) OMEOHfI)=OTOTAL(I)/(1.0+PARM(I)) OAC10(I )=QTOTAL(I)-QMEOH(I) WMEOH(I)=OMEOH(I)*DENM(I ) WACID( I )=QACID(X)*DENA(I ) MT(I)=(((1.0-YS(I))/3.0-CEXIT(I))*(O.75*WACID(I)+WMEOH(I))* S1000,0)/QTOTAL(I ) 20 CONTINUE DO 30 I=NRUNIN,NRUN I I =0 TW=0.0 DO 40 J=1 . 1 1 TW=TW+WR(I,J) IF(WR(I,J).EO.0.0) 11=11+1 40 CONTINUE WPC(1)=WR(I,1)*100.0/TW CUMWPC(1)=WPC(1) I IM=I I - 1 IF(IIM.LT.0) I IM = 0 DO 50 J=2,11 JM=J-1 WPC(ul) =WR( I , J) « 100. O/TW CUMWPC(J)=CUMWPC(J-1)+WPC(J) IF(JM.LE.IIM.OR.J.EO.11) GO TO 50 LAV(J-1-IIM)=(SIZE(J-1)+SIZE(U))/2.0 POP(J-1~IIM)=WPC(J)*0.01*MT(I)/(RHOC *KV*(LAV(J-1-IIM)«*3)* $(SIZE(0-1 )-SIZE(J))) LNN(J- 1-IIM)=ALOG(POP(J-1-I IM) ) 50 CONTINUE ID-9-IIM DO 60 d= 1 ,ID X(J, 1 )=1 .0 X(J,2)=LAV(J) 60 CONTINUE CALL REGRES(X,LNN.9, ID,2,XX, 1,SY, 1.CB.SB.FX. 1,F.R(I),D1,D2.IP,LU) NO(I) = EXP(CB( 1)) G ( I ) = -3600 . 0/ ( CB ( 2 ) *T I ME ( I ) ) B(I)=N0(I)*G(I ) MSTH(I)=3.67*G(I)*TIME(I)/3600.0 MTTH(I)=6,0*RH0C»KV*N0(I)*(G(I)*TIME(I)/3600.0)«*4 I D 1 = 1 1 - 11 DO 70 J=1,ID1 TFRAC(U)=CUMWPC(12-J)/100.0 TSIZE(U)=SIZE(12-J) 70 CONTINUE CALL SPLN(TSIZE,TFRAC,ID 1 ) CALL BISECT(FUN1.0.0,0.6,1,ROOT,0.05,0.0001.NR) IF(NR.EO.0) GO TO 1111 CO cn o MS(I)= ROOT( 1 ) CALL BISECT(FUN2,0.0,0.6,1,ROOT,O.05,O.0001, NR ) IF(NR.EO.0) GO TO 1111 ROOT 1=R00T( 1 ) CALL BI SECT(FUN3,0.0,0.6, 1 ,ROOT,O.05,O.0001 ,NR) IF(NR.EO.0) GO TO 1111 ROOT2=ROOT( 1 ) CV( I ) = ( R00T1-R00T2)* 100 . 0/( 2 . 0*MS ( I ) ) 'RUN NUMBER ',13/) Deg. C',10X, Deg. C') ' s ' , 1GX, 'Suspens1 on ,F5.2,' ml/s',5X,'(' . F5.2, ml/s',5X,'(', ,F6.4, ' gr/gr'/) C c WRIT E(6,600) I GOO FORMAT(1H1//7X, WRIT E(6.601 ) 601 FORMAT(50X,'EXPERIMENTAL CONDITIONS'/1H+,49X,23(1H_)/) WRIT E(6,602) TFEED(I),TEMP(I) 602 FORMAT(22X,'Feed Temperature = ',F4. 1 , $'Crysta11 1zer Temperature = ' ,F4. 1 , WRIT E(6.902) TI ME(I ) ,MT(I 1 902 FORMAT(22X,'Res 1dence Time = ' ,F5. 1 , '$'Dens 1ty = '.F6.2,' gr/1'/) WRIT E(6,903) QAC10(I),WACID(I) 903 F0RMAT(22X,'Feed solution flow rate = $ F 5.2, ' gr/s)' ) WRIT E(6,904) OMEOH(I),WMEOH(I) 904 FORMAT(22X.'MeOH solution flow rate = $F5.2,' gr/s)'/) WRIT E(6,400) RAT(I) 400 F0RMAT(22X. 'A 1coho1/Ac 1d-feed ratio WRITE(6,603 ) 603 F0RMAT(22X,'Mother Liquor (ML) Composition : WRIT E(6,604) CCMP1(I) 604 F0RMAT(41X,F7.5,2X,'gr Na2S04/gr ML') WRITE(6,605) C0MP2(I) 605 F0RMAT(41X.F7.5,2X,'gr 38%w/w H2S04/gr ML') WRITE(6.606) C0MP3(I) 606 F0RMAT(41X,F7.5,2X,'gr 80%w/w MeOH/gr ML'/) WRIT E(6,607) CEXIT(I) 607 FORMAT(22X,'Exit solute concentration $' gr Na2S04/gr solvent') WRITE(6,608) CEQ(I) 608 FORMAT(22X, 'Equ11 1br1um concentration $' gr Na2S04/gr solvent') WRITE(6,609) SS(I ) 609 F0RMAT(22X.'Supersaturation $' gr Na2S04/gr solvent'/) WRITE(6,6 1 1 ) 611 F0RMAT(36X,'PRODUCT CRYSTAL SIZE DISTRIBUTION - ', $'POPULATION DENSITY'/1H+,35X,54( 1 ) / ) WRITE(6,612) 612 FORMAT(7X,'Screen Size Weight Retained Wt.% Retained' $'Cumu1 at 1ve Wt.% Retained Population Density,n $'Average Size') WR I T E ( 6 , 6 1 3 ) 613 FORMAT(11X.'(mm)'.11X,'(gr)' DO 6 14 0=1,11 JM=J-1 IF(JM.LE.IIM) GO TO 620 IF(d.EO.11) GO TO 630 WRITE(6,615) SIZE(J),WR( I.J) ,WPC(J),CUMWPC(0) ,POP(J-1 - I IM) , $ LNN(J-1-IIM).LAV(J-I-IIM) CO U1 .F8.6, .F8.6, ,F8.G. 1 n n .50X,'(number/mm 11tre)',13X,'(mm)'/) 6 1 5 FORMAT( 10X , FS . 4,8X,F7 . 4 , 8X , F8 .4, 12X, F8 .4, 14X, E 14 . 7 , 5X , F5 . 2 , 4X SF6.4/) GO TO 614 620 WRITE(6,616) SIZE(J),WR(I,J),WPC(J).CUMWPC(J) 6 16 FORMAT(1 OX,F6.4,8X,F7.4,8X,F8.4, 12X,F8.4/) GO TO 6 14 630 WRIT £(6,6 1 7 ) WR ( I , J),WPC(J) ,CUMWPC(J) 6 17 FORMAT(11X,'PAN',10X,F7.4,8X,F8.4,12X,F8.4//) 614 CONTINUE WRITE(6,401) MS(I),CV(I) 401 FORMAT(22X,'Crystal mean size = ',F6.4, ' mm',22X,'Coeff1cient $'of Variation = ',F5.2,' '/.'/) WR I T E ( 6 , 6 1 8 ) 618 F0RMAT(50X, 'CRYSTALLIZATION KI NET ICS'/1H+,49X,24(1H_)/) WRITE(6,619 ) G(I) 619 F0RMAT(22X,'Crystal growth rate.G = '.F8.6,' mm/hr') WRITE(6,621) N0(I) 621 FORMAT(22X,'Nucle1 population density = '.E14.7,' number/mm ', $'1i tre' ) WRITE(6.622) B(I) 6 2 2 FORMAT(22X,'Nuc1 eation rate.B = '.E14.7,' number/hr ', $'11tre ' ) C C c IF(IPLOT.EO.0) GO TO 30 C C XK1= LAV(ID) YK1=C8(1)+CB(2)»XK1 XK2 = LAV( 1 ) YK2 =CB( 1 )+CB(2)*XK2 C XKK(1)=XK1 DXKK=XK1/9.0 DO 65 J=1 , 10 YKK(J)=CB( 1 )+C8(2)* XKK(J) IF(J.EO.10) GO TO 65 XKK(J+1)=XKK(J)-DXKK 65 CONTINUE C DXXX=(TSIZE(ID1 )-TSIZE( 1 ) )/4 9.0 XXX( 1 ) = T SIZ E( 1 ) DO 80 0=1,50 YYY(J) = FSPLN(XXX(J) ) IF(J.EO.50) GO TO 80 XXX(J+1 )=XXX(J)+DXXX 80 CONTINUE C C XK1 = (XK1-XMIN( 1 ))/DX( 1)+XSHIFT( 1 ) XK2=(XK2-XMIN(1))/DX(1)+XSHIFT(1) YK1=(YK1-YMIN(1))/DY(1)+YSHIFT(1) YK2-(YK2-YMIN(1))/DY(1)+YSHIFT(1) C DO 90 J=1,ID LAV(J)=(LAV(J)-XMIN(1))/DX(1)+XSHIFT(1) LNN(J)=(LNN(J)-YMIN(1))/DY(1)+YSHIFT(1) 90 CONTINUE C I CO Ul CO I 0 0 9 5 J= 1 . 1 0 X K K ( J ) = ( X K K ( J ) - X M I N ( 1 ) ) / D X ( 1 ) + X S H I F T ( 1 ) V K K ( d ) = ( Y K K ( J ) - Y M I N ( 1 ) ) / 0 Y ( 1 ) + Y S H I F T ( 1 ) 9 5 C O N T I N U E DO 1 0 0 d=1 . ID 1 T S I Z E ( J ) = ( T S I Z E ( J ) - X M I N ( 2 ) ) / D X ( 2 ) + X S H I F T ( 2 ) T F R A C ( J ) = ( T F R A C ( J ) - Y M I N ( 2 ) ) / D Y ( 2 ) + Y S H I F T ( 2 ) 1 0 0 C O N T I N U E 0 0 1 1 0 J = 1 . 5 0 X X X ( J ) = ( X X X ( J ) - X M I N ( 2 ) ) / D X ( 2 ) + X S H I F T ( 2 ) Y Y Y ( J ) = ( Y Y Y ( J ) - Y M I N ( 2 ) ) / D Y ( 2 ) + Y S H I F T ( 2 ) 1 1 0 C O N T I N U E C A L L P L C T R L ( ' S C A L E ' . S C A L E ) C A L L D A S H L N ( 0 . 2 , 0 . 0 8 . 0 . 2 , 0 . 0 8 ) DO 1 5 0 I L = 1 , I P LOT C A L L A X C T R H ' X O R I ' . X S H I FT (. I L ) ) C A L L A X C T R L ( ' Y O R I ' , Y S H I F T ( I L ) ) C A L L A X P L O T ( ' ; ' . 0 . 0 , X L ( I L ) , X M I N ( I L ) , D X ( I L ) ) C A L L A X P L O T ( ' ; ' , 9 0 . O . Y L ( I L ) , Y M I N ( I L ) , D Y ( I L ) ) P Y 1 = Y L ( I L ) + Y S H I F T ( I L ) P X 1 = X L ( I L ) + X S H I F T ( I L ) C A L L P L O T ( X S H I F T ( I L ) , P Y 1 , 3 ) C A L L P L O T ( P X 1 , P Y 1 , 2 ) C A L L P L 0 T ( P X 1 . Y S H I F T ( I L ) , 2 ) X F 1 = X S H I F T ( I L J - D F Y F 1 = Y S H I F T ( I L ) - D F X F 2 = X F 1 Y F 2 = P Y 1 + DF X F 3 = P X 1 + D F Y F 3 = Y F 2 X F 4 = X F 3 Y F 4 = Y F 1 0 0 1 2 0 J = 1 , I D F C A L L P L O T ( X F 1 , Y F 1 , 3 ) C A L L P L 0 T ( X F 2 . Y F 2 , 2 ) C A L L P L O T ( X F 3 . Y F 3 , 2 ) C A L L P L O T ( X F 4 , Y F 4 , 2 ) C A L L P L O T ( X F 1 , YF 1 , 2 ) I F ( J . E O . I D F ) GO TO 1 2 0 X F 1 = X F 1 - D F Y F 1 = Y F 1 - O F X F 2 =X F1 Y F 2 = Y F 2 + D F X F 3 = X F 3 + D F Y F 3 = Y F 2 X F4 =XF 3 Y F 4 = Y F1 1 2 0 C O N T I N U E I F ( I T E X T ( I L ) . E O . O ) GO TO 126 C A L L P A L P H A ( L I 8 3 . 0 . 5 5 0 0 ) T S Z 1 = P S M L E N ( ' T T T T T S U P E R S A T U R A T I O N ' , 2 2 , S S I Z E 3 ( I L ) ) T S Z 2 = P S M L E N ( ' = ' , 3 , S S I Z E 3 ( I L ) ) T S Z 3 = P S M L E N ( ' 1 0 0 0 . 0 ' . 7 , S S I Z E 3 ( I L ) ) T S Z 4 = P S M L E N ( ' d e g . C ' , 6 , S S I Z E 3 ( I L ) ) T S Z 5 = P S M L E N ( ' R U N n o . 1 0 ' , 1 0 , S S I Z E 3 ( I L ) ) T S Z 6 = P S M L E N ( ' R U N n o . ' , 8 , S S I Z E 3 ( I L ) ) X T T 1 = X T E X T ( I L ) + T S Z 1 X T T 2 = X T T 1 + T S Z 2 X T T 3 = X T T 2 + T S Z 3 X T T 4 = ( T S Z 1 + T S Z 2 + T S Z 3 + T S Z 4 - T S Z 5 ) / 2 . O + X T E X T ( I L ) X T T 5 = X T T 4 + T S Z 6 C A L L P S Y M ( X T E X T ( I L ) , Y T E X T ( I L ) , S S I Z E 3 ( I L ) , $ ' S U P E R S A T U R A T I O N ' , 0 . 0 , 1 6 , 5 5 0 0 ) C A L L P S Y M ( X T T 1 , Y T E X T ( I L ) , S S I Z E 3 ( I L ) , ' = ' , 0 . 0 , 2 , 8 . 5 0 0 ) C A L L N U M B E R ( X T T 2 , Y T E X T ( I L ) , S S I Z E 3 ( I L ) , C S S ( I ) , 0 . 0 , 3 ) C A L L P S Y M ( X T T 3 . Y T E X T ( I L ) , S S I Z E 3 ( I L ) , ' g r / k g ' , 0 . 0 , 5 , 5 5 0 0 ) Y T T = Y T E X T ( I L ) + 2 , 0 * S S I Z E 3 ( I L ) C A L L P S Y M ( X T E X T ( I L ) , Y T T , S S I Z E 3 ( I L ) , ' S U S P E N S I O N D E N S I T Y ' , $ 0 . 0 , 1 8 , 8 . 5 0 0 ) C A L L P S Y M ( X T T 1 , Y T T , S S I Z E 3 ( I L ) , ' = ' , 0 . 0 , 2 , 5 5 0 0 ) C A L L N U M B E R ( X T T 2 , Y T T , S S I Z E 3 ( I L ) , M T ( I ) , 0 . 0 , 1 ) C A L L P S Y M C X T T 3 , Y T T , S S I Z E 3 ( I L ) , ' g r / 1 ' . 0 . 0 , 4 , 5 5 0 0 ) Y T T = Y T T + 2 . 0 * S S I Z E 3 ( I L ) C A L L P S Y M ( X T E X T ( I L ) , Y T T , S S I Z E 3 ( I L ) , ' R E S I D E N C E T I M E ' , $ 0 . 0 , 1 4 , 8 . 5 0 0 ) C A L L P S Y M ( X T T 1 , Y T T , S S I Z E 3 ( I L ) , ' = ' , 0 . 0 , 2 , 5 5 0 0 ) C A L L N U M B E R ( X T T 2 , Y T T , S S I Z E 3 ( I L ) , T I M E ( I ) , 0 . 0 , 1 ) C A L L P S Y M ( X T T 3 , Y T T , S S I Z E 3 ( I L ) , ' s e c . ' , 0 . 0 , 4 , 5 5 0 0 ) Y T T = Y T T + 2 . 0 * S S I Z E 3 ( I L ) C A L L P S Y M ( X T E X T ( I L ) , Y T T , S S I Z E 3 ( I L ) , ' T E M P E R A T U R E ' , 0 . , 1 1 , & 5 0 0 C A L L P S Y M ( X T T 1 , Y T T , S S I Z E 3 ( I L ) , ' = ' , 0 . 0 , 2 , & 5 0 0 ) C A L L N U M B E R ( X T T 2 , Y T T , S S I Z E 3 ( I L ) , T E M P ( I ) , 0 . 0 , 1 ) C A L L P S Y M ( X T T 3 , Y T T , S S I Z E 3 ( I L ) , ' d e g . C ' , 0 . 0 , 6 , 5 5 0 0 ) Y T T = Y T T + 2 . 0 * S S I Z E 3 ( I L ) C A L L P S Y M ( X T T 4 , Y T T , S S I Z E 3 ( I L ) , ' R U N n o . ' , 0 . 0 , 8 , 5 5 0 0 ) F I = F L O A T ( I ) C A L L N U M B E R ( X T T 5 , Y T T , S S I Z E 3 ( I L ) , F I , 0 . 0 . - 1 ) C A L L P A L P H A ( ' S T A N D A R D ' , 0 , 5 5 0 0 ) ,C 1 2 6 I F ( I L . E O . 2 ) GO TO 1 5 0 C C A L L P L O T ( X K 1 , Y K 1 , 3 ) C A L L P L O T ( X K 2 , Y K 2 , 2 ) C DO 125 0 = 1 , 10 J C = J / 2 J C 2 = 2 * J C I F ( J C 2 . E Q . J ) C A L L P L O T ( X K K ( d ) , Y K K ( U ) , 2 ) I F ( J C 2 . N E . J ) C A L L P L O T ( X K K ( J ) , Y K K ( J ) , 3 ) 1 25 C O N T I N U E C D S S I Z = S S I Z E 1 ( 1 ) / F L O A T ( N S Y M 1 ) DO 1 3 0 J = 1 , ID S Z = 0 , 0 DO 1 4 0 K = 1 , N S Y M 1 S Z = S Z + D S S I Z C A L L S Y M B 0 L ( L A V ( J ) , L N N ( J ) , S Z , 5 , 0 . 0 , - 1 ) 1 4 0 C O N T I N U E 1 3 0 C O N T I N U E C C A L L PA L P H A ( L I B 2 , O , 5 5 0 0 ) S L E N 1 = P S M L E N ( ' S I Z E ( m m ) ' , 9 , S S I Z E 2 ( 1 ) ) X L E N = ( X L ( 1 ) - S L E N 1 ) / 2 . O + X S H I F T ( 1 ) I CO cn i Y L E N = Y S H I F T ( 1 ) - 1 . 0 - 1 . 2 * S S I Z E 2 ( 1 ) C A L L P S Y M ( X L E N , Y L E N , S S I Z E 2 ( 1 ) , ' S I Z E (mm) ' , 0 . 0 , 9 , 8 . 5 0 0 ) S L E N 2 = P S M L E N ( ' l n n ' , 4 . S S I Z E 2 ( 1 ) ) X L E N = X S H I F T ( 1 ) - O . 8 5 - 0 . 2 * S S I Z E 2 ( 1 ) Y L E N = ( Y L ( 1 ) - S L E N 2 ) / 2 . 0 + Y S H I F T ( 1 ) C A L L P S Y M ( X L E N , Y L E N , S S I Z E 2 ( 1 ) , ' I n n ' , 9 0 . 0 , 4 , 8 . 500 ) C A L L P A L P H A ( ' S T A N D A R D ' , 0 , & 5 0 0 ) I F ( I P L O T . E O . 1 ) GO TO 4 0 4 C A L L P L 0 T ( 3 0 . 0 . 0 . 0 , - 3 ) 1 5 0 C O N T I N U E D S S I Z = S S I Z E 1 ( 2 ) / F L 0 A T ( N S Y M 2 ) DO 1 6 0 0 = 1 , 1 0 1 S Z = 0 . 0 DO 1 7 0 K = 1 , N S Y M 2 S Z = S Z + D S S I Z C A L L S Y M B O L ( T S I Z E ( J ) . T F R A C ( d ) , S Z , 5 , 0 . 0 , - 1 ) 1 7 0 C O N T I N U E 1 6 0 C O N T I N U E C A L L P L O T ( X X X ( 1 ) , Y Y Y ( 1 ) , 3 ) DO 161 J = 2 , 5 0 C A L L P L O T ( X X X ( J ) , Y Y Y ( J ) , 4 ) 161 C O N T I N U E C A L L P A L P H A ( L I B 2 , 0 , 8 . 5 0 0 ) S L E N 1 = P S M L E N ( ' S C R E E N S I Z E ( m m ) ' , 1 6 . S S I Z E 2 ( 2 ) ) X L E N = ( X L ( 2 ) - S L E N 1 ) / 2 . 0 + X S H I F T ( 2 ) Y L E N = Y S H I F T ( 2 ) - 1 . 0 - 1 . 2 * S S I Z E 2 ( 2 ) C A L L P S Y M ( X L E N , Y L E N , S S I Z E 2 ( 2 ) , ' S C R E E N S I Z E ( mm ) ' , O . 0 , 1 6 , 8 . 5 0 0 ) S L E N 2 = P S M L E N ( ' C U M U L A T I V E W t . F R A C T I O N R E T A I N E D ' , 3 2 , S S I Z E 2 ( 2 ) ) X L E N = X S H I F T ( 2 ) - 0 . 8 5 - 0 . 2 » S S I Z E 2 ( 2 ) Y L E N = ( Y L ( 2 ) - S L E N 2 ) / 2 . 0 + Y S H I F T ( 2 ) C A L L P S Y M ( X L E N , Y L E N , S S I Z E 2 ( 2 ) , $ ' CUMUL A T I VE W t . F R A C T I O N R E T A I NED ' , 9 0 . 0 , 3 2 , 8 . 500 ) C A L L P A L P H A ( ' S T A N D A R D ' , 0 , 8 . 5 0 0 ) 4 0 4 I F ( I . N E . N R U N ) C A L L P L O T ( 3 0 . 0 . O . O , - 3 ) I F ( I . E O . N R U N ) C A L L P L O T N D 3 0 C O N T I N U E WRIT E ( 6 . 7 0 0 ) N R U N I N . N R U N 7 0 0 F 0 R M A T ( 1 H 1 / 4 0 X , ' S U M M A R Y OF R E S U L T S FOR RUN N U M B E R S ' , 1 3 , $ ' - ' , 1 3 / 1 H + . 3 9 X , 4 4 ( 1 H _ ) / ) WRIT E ( 6 . 7 0 1 ) 7 0 1 F 0 R M A T ( 5 X . ' R U N T E M P E R A T U R E A L C O H O L / R E S I D E N C E S U S P E N S I O N ' , $ ' S U P E R S A T U R A T I O N C R Y S T A L N U C L E I N U C L E A T I O N C R Y S T A L ' , $ ' C O E F F I C I E N T Y I E L D ' ) WR IT E ( 6 , 7 0 2 ) 7 0 2 F 0 R M A T ( 5 X . ' n o . ( d e g . C ) A C I D - F E E D T I M E D E N S I T Y $ ' ( g r / k g s o l v e n t ) GROWTH P O P U L A T I O N R A T E M E A N ' , 6 X , ' OF ' , $8X,'OF') W R I T E ( 6 , 7 0 3 ) 7 0 3 F 0 R M A T ( 2 1 X , ' R A T I O ( S e c . ) ( g r / 1 ) ' , 2 0 X , ' R A T E D E N S I T Y ' $ ' ( 1 / h r . l ) S I Z E V A R I A T I O N N a 2 S 0 4 ' ) W R I T E ( 6 , 7 7 7 ) 7 7 7 F 0 R M A T ( 2 1 X , ' ( g r / g r ) ' , 4 0 X . ' ( m m / h r ) ( 1 / m m . 1 ) ' , 1 5 X , ' ( m m ) $ ' ( % ) ( % ) ' / ) DO 8 0 0 I = N R U N I N , N R U N W R I T E ( 6 , 7 7 8 ) I , T E M P ( I ) , R A T ( 1 ) , T I M E ( I ) , M T ( I ) , C S S ( I ) , G ( I ) , N O ( I ) , SBC I ) , M S ( I ) , C V ( I ) , Y I E L O f I ) 7 78 F O R M A T ( 4 X , I 3 , 5 X , F 4 . 1 , S X , F S . 4 , 5 X , F 5 . 1 , 5 X , F S . 2 , 7 X , F 6 . 4 , 6 X , F 6 . 4 , 1 X , $ E 1 f . 4 , E 1 2 . 5 , 1 X , F S . 4 , 4 X , F 5 . 2 , 4 X , F 5 . 2 ) 8 0 0 C O N T I N U E C WRIT E ( 6 , 7 0 5 ) N R U N I N , N R U N 7 0 5 F O R M A T ! 1 H 1 / 2 3 X , ' C O M P A R I S O N OF T H E O R E T I C A L AND E X P E R I M E N T A L ' , $ ' P A R A M E T E R S FOR RUN N U M B E R S ' , 1 3 , ' - ' , I 3 / 1 H + . 2 2 X , 7 9 ( 1 H _ ) / ) WRIT E ( 6 , 7 0 6 ) 7 0 6 F O R M A T ( 6 X , ' R U N n o . R e s i d e n c e T i m e C r y s t a l S u s p e n s i o n ' , $ ' D e n s i t y C r y s t a l M e a n S i z e C o e f f i c i e n t o f V a r i a t i o n ' ) W R I T E ( 6 , 7 0 7 ) 7 0 7 F O R M A T ( 1 9 X , ' ( S e c . ) ' , 2 5 X , ' ( g r / 1 ) ' , 2 3 X , ' ( m m ) ' , 2 5 X , ' ( % ) ' / ) WRIT E ( 6 , 7 0 8 ) 7 0 8 F O R M A T ( 4 1 X , ' T h e o r e t 1 c a l E x p e r 1 m e n t a 1 ' . 5 X , ' T h e o r e t 1 c a 1 ' , $ ' E x p e r i m e n t a l ' , 4 X . ' T h e o r e t 1 c a l E x p e r i m e n t a l ' / 1 H + , 4 0 X , 1 1 ( 1 H _ ) , $1X,12(1H_),5X,11(1H_),1X,12(1H_),4X.11(1H_),1X,12(1H_)/) DO 9 0 0 I = N R U N I N , N R U N W R I T E ( 6 , 7 0 9 ) I , T I M E ( I ) , M T T H ( I ) , M T ( I ) , M S T H ( I ) , M S ( I ) , C V ( I ) 7 0 9 F O R M A T ( 8 X , 1 3 , 8 X , F 5 . 1 , 1 9 X , F 6 . 2 , 7 X , F 6 . 2 , 1 0 X , F 6 . 4 , 7 X , F 6 . 4 , 1 0 X , ' 5 2 . 0 0 ' $,7X,F6.2) 9 0 0 C O N T I N U E C S T O P C 5 0 0 W R I T E ( 6 , 5 0 1 ) 5 0 1 F 0 R M A T ( / / / / / 2 0 X , ' P L O T T I N G P R O B L E M S ! ! ! ' / / / / / ) S T O P • | 1 1 1 1 WR IT E ( 6 , 1 1 1 2 ) 1 1 1 2 F O R M A T ( / / / / / 2 0 X , ' ! ! ROOT F I N O I N G P R O B L E M S ! ! ' / / / / / ) W S T O P U1 END C i C c I F U N C T I O N C S T A R ( T . X ) C C E Q U I L I B R I U M S O L U B I L I T Y F U N C T I O N C C T : T E M P E R A T U R E I N D E G R E E S C C X : S O L V E N T C O M P O S I T I O N AS g r 80%w/w M e O H / g r S O L V E N T C D I M E N S I O N X X ( 4 ) . Y 1 ( 4 ) , Y 2 ( 4 ) , Y 3 ( 4 ) D A T A X X / O . 6 , O . 7 , O . 8 , 0 . 9 / D A T A Y 1 / 0 . 0 4 0 1 , 0 . 0 2 5 3 5 , 0 . 0 1 5 7 5 , 0 . 0 0 8 7 / D A T A Y 2 / 0 . 0 3 5 9 8 , 0 . 0 2 2 6 9 , 0 . 0 1 4 3 6 , 0 . 0 0 8 0 9 / D A T A Y 3 / 0 . 0 3 3 4 , O . 0 2 0 5 , O . 0 1 3 , O . 0 0 7 6 / D A T A D I N F O / - 1 . 0 / C I F ( T . E O . 3 5 . O . O R . T . E O . 3 0 . 0 . O R . T . E O . 2 5 . 0 ) GO TO 10 GO TO 13 10 I F ( X . L T . 0 . 5 9 . 0 R . X . G T . 0 . 9 ) GO TO 11 I F ( T . E O . D I N F O ) GO TO 12 I F ( T . E O . 3 5 . 0 ) C A L L S P L N ( X X , Y 1 , 4 ) I F ( T . E Q . 3 0 . 0 ) C A L L S P L N ( X X . Y 2 , 4 ) I F ( T . E O . 2 5 . O ) C A L L S P L N ( X X , Y 3 , 4 ) 12 C S T A R = F S P L N ( X ) D I N F O = T R E T U R N 13 WRIT E ( 6 , 1 4 ) T 14 F O R M A T ( / / / / / 1 0 X , ' ! ! W A R N I N G - E Q U I L I B R I U M DATA I S U N D E F I N E D ' , $ ' FOR T = ' , E 1 5 . 8 , ' D e g . C ' / / / / / ) S T O P 1 1 W R I T E ( 6 , 1 5 ) X 15 F 0 R M A T ( / / / / / 1 O X , ' 1 ' W A R N I N G - E Q U I L I B R I U M DATA I S U N D E F I N E D $ ' FOR X = ' . E l 5 . 8 / / / / / ) S T O P END C S U B R O U T I N E S P L N ( X , Y , N ) C C C U B I C S P L I N E I N T E R P O L A T I N G R O U T I N E C C O M M O N / A B C 1 / X X ( 101 ) . Y Y ( 10 1 ) , NN , Q ( 1 0 0 ) , R ( 1 01 ) . S ( 1 0 0 ) D I M E N S I O N H ( 1 0 0 ) , A ( 1 0 1 ) , B ( 1 0 1 ) , C ( 1 0 1 ) , D ( 1 0 1 ) , T ( 1 0 0 , 5 ) D I M E N S I O N X ( N } , Y ( N ) C NN = N DO 5 0 I = 1 , N X X ( I ) = X ( I ) Y Y ( I ) = Y ( I ) 5 0 C O N T I N U E N M = N - 1 M = 3 DO 10 I = 1 ,NM T ( I , 1 ) = ( Y ( I - * - 1 ) - Y ( I ) ) / ( X ( I + 1 ) - X ( I ) ) 10 C O N T I N U E DO 1 1 J = 2 , M DO 12 I = J , N M I S = I + 1 - J T ( I , J ) = ( T ( I , d - 1 ) - T ( I - 1 , J - 1 ) ) / ( X ( I + 1 ) - X ( I S ) ) 12 C O N T I N U E 11 C O N T I N U E A 4 = T ( M , M ) B4 = T ( N M , M ) DO 2 0 I = 1 , N M H ( I ) = X ( 1 + 1 ) - X (. I ) 2 0 C O N T I N U E 8 ( 1 ) = - H ( 1 ) C ( 1 )=H( 1 ) D( 1 ) = 3 . 0 * H ( 1 ) » H ( 1 ) * A 4 DO 3 0 1 = 2 . N M I P = I + 1 I M = I - 1 A ( I ) = H ( I M ) B ( I ) = 2 . 0 * ( H ( I M ) + H ( I ) ) C ( I ) = H ( I ) D ( I ) = 3 . 0 M ( Y ( I P ) - Y ( I ) ) / H ( I ) - ( Y ( I ) - Y ( I M ) ) / H ( I M ) ) 3 0 C O N T I N U E A(N)=H(NM) B ( N ) = - H ( N M ) C(N)=0.0 D ( N ) = - 3 . 0 * H ( N M ) * H ( N M ) * B 4 I 03 OI <1 I C A L L T D M A ( A , B , C , O . R . N ) C DO 4 0 I = 1 . N M I P = I + 1 Q ( I ) = ( Y ( I P ) - Y ( I ) ) / H ( I ) - H ( I ) « ( 2 . 0 * R ( I ) + R ( I P ) ) / 3 . 0 S ( I ) = ( R ( I P ) - R ( I ) ) / ( 3 . 0 * H ( I ) ) 4 0 C O N T I N U E C R E T U R N ENO C C C S U B R O U T I N E T D M A ( A , B , C , D , X , N ) D I M E N S I O N A ( N ) , 8 ( N ) , C ( N ) , D ( N ) , X ( N ) , P ( 1 0 1 ) , 0 ( 1 0 1 ) NM=N-1 P ( 1 ) = - C ( 1 ) / B ( 1 ) Q ( 1 ) = D ( 1 ) / B ( 1 ) DO 10 1 = 2 , N IM=I - 1 D E N = A ( I ) * P ( I M ) + B ( I ) P ( I ) = - C ( I ) / D E N Q ( I ) = ( D ( I ) - A ( I ) * Q ( I M ) ) / D E N 10 C O N T I N U E X(N)=0(N) DO 2 0 I I = 1 , N M I= N - 11 X ( I ) = P ( I ) » X ( 1 + 1 )+Q ( I ) 2 0 C O N T I N U E R E T U R N ENO C C C F U N C T I O N F S P L N ( Z ) *C C C U B I C S P L I N E I N T E R P O L A T I N G F U N C T I O N C C O M M O N / A B C 1 / X ( 1 0 1 ) , Y ( 1 0 1 ) . N , Q ( 1 0 0 ) , R ( 1 0 1 ) , S ( 1 0 0 ) NM=N-1 1=1 I F ( Z . LT . X ( 1 ) ) GO TO 3 0 I F ( Z . G E . X ( N M ) ) GO TO 2 0 U = NM 10 K = ( I + J ) / 2 I F ( Z . L T . X ( K ) ) J = K I F ( Z . G E . X ( K ) ) I =K I F ( J . E Q . 1 + 1 ) GO TO 3 0 GO TO 10 2 0 I=NM 3 0 D X = Z - X ( I ) F S P L N = Y ( I ) + D X * ( 0 ( I ) + D X * ( R ( I ) + D X * S ( I ) ) ) R E T U R N END C C S U B R O U T I N E R E G R E S ( X , Y , M D , M , N , X X , L D , S Y , L , B , S B , F X , N M 1 , F , R , D M S R E G , $ D M S R E S , I PR I N T , L U N I T ) C C P E R F O R M S M U L T I P L E L I N E A R R E G R E S S I O N OF Y ON X 1 , 1 = 1 , 2 . . .NM1 CO Vi 00 MD M N XX ( N M 1 = N - 1 ) WHERE , X : I S A R E A L M TWO D I M E N S I O N A L ARRAY- , D I M E N S I O N E D X (MD , N ) ON E N T R Y X MUST C O N T A I N THE O B S E R V E D V A L U E S OF THE I N D E P E N D E N T V A R I A B L E S C O L U M N W I S E , I N COLUMNS 2 TO N . COLUMN 1 OF X MUST A L W A Y S C O N T A I N M 1 ' s . Y : I S A R E A L M ONE D I M E N S I O N A L A R R A Y , D I MENS I O N E D Y ( M ) . ON ENTRY Y MUST C O N T A I N THE C O R R E S P O N D I N G O B S E R V E D V A L U E S OF THE D E P E N D E N T V A R I A B L E . I S THE F I R S T D I M E N S I O N OF A R R A Y X I S THE NO . OF ROWS I N THE M A T R I X C O N T A I N E D I N X = NO . OF O B S E R V A T I O N S I S THE NO . OF COLUMNS I N THE M A T R I X C O N T A I N E D I N X = NO . OF I N D E P E N D E N T V A R I A B L E S + 1 I S A R E A L M TWO D I M E N S I O N A L A R R A Y , D I MENS I O N E D X X ( L D . N ) . ON E N T R Y XX W I L L C O N T A I N , I N C O L U M N S 2 TO N (AND FOR L ROWS) THE L E V E L S OF THE I N D E P E N D E N T V A R I A B L E S X 1 , I = 1 , 2 . . . N M 1 , A T WHICH THE S T A N D A R D ERROR OF Y I S TO BE C A L C U L A T E D . COLUMN 1 OF XX W I L L C O N T A I N L 1 ' s . THE S T A N D A R D ERROR I S C A L C U L A T E D FOR "THE A V E R A G E OF A L L Y ' s " AT THAT P O I N T . I F THE S T A N D A R D ERROR OF Y I S NOT R E O U I R E D , X X ( 1 , 1 ) MUST BE N E G A T I V E . T H E R E M A I N D E R OF XX NEED NOT BE I N I T I A L I Z E D . I S THE F I R S T D I M E N S I O N OF A R R A Y XX I S A R E A L M ONE D I M E N S I O N A L A R R A Y . D I M E N S I O N E D S Y ( L ) . ON E X I T SY W I L L C O N T A I N THE C A L C U L A T E D S T A N D A R D E R R O R S OF Y . I S THE NO . OF ROWS I N THE M A T R I X C O N T A I N E D I N XX = NO . OF P O I N T S AT W H I C H THE S T A N D A R D ERROR OF Y I S TO BE C A L C U L A T E D I S A R E A L M ONE D I M E N S I O N A L A R R A Y , D I MENS IONED B ( N ) . ON E X I T B W I L L C O N T A I N THE E S T I M A T E D R E G R E S S I O N C O E F F ' s . I S A R E A L M ONE D I M E N S I O N A L A R R A Y , D I MENS I O N E D S B ( N ) . ON E X I T SB W I L L C O N T A I N THE S T A N D A R D ERROR OF THE R E G R E S S I O N C O E F F I C I E N T S . I S A R E A L M ONE D I M E N S I O N A L A R R A Y , D I MENS I O N E D F X ( N M 1 ) . ON E X I T FX W I L L C O N T A I N THE P A R T I A L F - V A L U E S FOR THE I N D E P E N D E N T V A R I A B L E S . F - V A L U E FOR R E G R E S S I O N . C O R R E L A T I O N C O E F F I C I E N T . R E G R E S S I O N MEAN S Q U A R E . R E S I O U A L MEAN S Q U A R E . P R I N T C O N T R O L V A R I A B L E , =0 NO P R I N T I N G I S D O N E . =1 ANOVA T A B L E AND E S T I M A T E D R E G R E S S I O N C O E F F I C I E N T S AND T H E I R S T A N D A R D E R R O R S A R E P R I N T E D ON L O G I C A L OUTPUT U N I T L U N I T . =2 THE A B O V E + P A R T I A L F - V A L U E S OF THE I N D E P E N D E N T V A R I A B L E S A R E P R I N T E D . =3 S T A N D A R D E R R O R S OF Y ARE A L S O P R I N T E D I F C A L C U L A T E D . L U N I T : I S A N I N T E G E R S P E C I F Y I N G THE L O G I C A L MTS OUTPUT U N I T LD SY B SB FX F R D M S R E G D M S R E S I PR I NT WHERE R E G R E S I S TO D I R E C T I T S O U T P U T . R E S T R I C T I O N S : NO . NO . OF I N D E P E N D E N T V A R I A B L E S OF D A T A P O I N T S . L E . 2 0 0 . LE . CO Ui to D I M E N S I O N X ( M D , N ) , Y (M ) , X X ( L D , N ) , B ( N ) , S B ( N ) , F X ( N M 1 ) , S Y ( L ) D I M E N S I O N X T ( 2 0 , 2 0 0 ) , X T X ( 2 0 , 2 0 ) , X T Y ( 2 0 ) , X T X I N V ( 2 0 , 2 0 ) D I M E N S I O N I P ( 5 0 ) , S P X Y ( 1 9 ) , Y Y ( 2 0 ) , P Y ( 2 0 ) C I F ( N . G T . 2 0 ) GO TO 101 I F ( M . G T . 2 0 0 ) GO TO 101 C A L L G T R A N ( X , X T , M , N , M D , 2 0 ) C A L L G M U L T ( X T , X , X T X . N , M , N , 2 0 , M D , 2 0 ) C A L L G M A T V ( X T , Y , X T Y , N , M , 2 0 ) C A L L F I N V ( N , 2 0 , X T X , I P , 2 0 , X T X I N V , D E T , d E X P , C O N D ) I F ( C 0 N D . E Q . O . O ) GO TO 1 0 0 C A L L G M A T V ( X T X I N V , X T Y , B , N , N , 2 0 ) SY 2 = G V V ( Y , Y , M ) S S T 0 T = S Y 2 - X T Y ( 1 )* XT Y ( 1 ) / M DO 10 1 = 1 , N M 1 S P X Y ( I ) = X T Y ( I + 1 ) - X T Y ( 1 ) » X T X ( 1 , 1 + 1 ) / M 10 C O N T I N U E S S R E G = 0 . 0 DO 2 0 1 = 1 . N M 1 S S R E G = S S R E G + B ( I + 1 ) * S P X Y ( I ) 2 0 C O N T I N U E S S R E S = S S T O T - S S R E G I D F R E G = N - 1 I D F T 0 T = M - 1 I D F R E S = I O F T O T - I D F R E G D M S R E G = S S R E G / I D F R E G D M S R E S = S S R E S / I O F R E S F = D M S R E G / D M S R E S R S Q = S S R E G / S S T O T R = S Q R T ( R S Q ) DO 3 0 1 = 1 , N M 1 F X ( I ) = B ( I + 1 ) + 8 ( I + 1 ) / ( D M S R E S * X T X I N V ( 1 + 1 . 1 + 1 ) ) 3 0 C O N T I N U E DO 4 0 I = 1 , N S B ( I ) = S Q R T ( D M S R E S * X T X I N V ( 1 , 1 ) ) 4 0 C O N T I N U E I F ( X X ( 1 , 1 ) . L T . 0 . 0 ) GO TO 7 0 DO 5 0 I = 1 , L DO SO J = 1 , N Y Y ( J ) = X X ( I , d ) 6 0 C O N T I N U E C A L L G V M A T ( Y Y , X T X I N V , P Y , N , N , 2 0 ) ST 1 = G V V ( P Y , Y Y , N ) S T 2 = S T 1 * D M S R E S S Y ( I ) = S Q R T ( S T 2 ) 5 0 C O N T I N U E 7 0 I F ( I PR I N T . E Q . 0 ) R E T U R N C W R I T E ( L U N I T , 5 0 0 ) N M 1 . M 5 0 0 F O R M A T ( 1 H 1 , 1 X , ' N O . OF I N D E P E N D E N T V A R I A B L E S ' . I 2 / 2 X , $ ' N O . OF O B S E R V A T I O N S ' , 9 X , I 3 / ) W R I T E ( L U N I T , 5 0 1 ) 5 0 1 F O R M A T ( 3 2 X , ' A N O V A T a b l e F o r T h e R e g r e s s i o n M o d e l - ) W R I T E ( L U N I T , 5 0 2 ) 5 0 2 F O R M A T ( 1 H + , 3 1 X , 3 6 ( 1 H _ ) / / ) W R I T E ( L U N I T , 5 0 3 ) 5 0 3 F O R M A T ( 1X , ' S O U R C E OF V A R I AT I O N ' , 5 X , ' D E G R E E S OF F R E E D O M ' , 5 X , $ ' S U M OF S Q U A R E S ' , 7 X , ' M E A N S Q U A R E ' , 1 1 X , ' F - V A L U E ' / / ) W R I T E ( L U N I T , 5 0 4 ) I D F R E G , S S R E G , D M S R E G , F 5 0 4 F O R M A T ( 5 X , ' R E G R E S S I O N ' , 1 7 X , I 3 , 1 2 X , E 1 5 . 8 , 5 X , E 1 5 . 8 , 5 X , E 1 5 . 8 / ) WRIT E ( L U N I T , 5 0 5 ) I D F R E S , S S R E S . D M S R E S 5 0 5 F O R M A T ( 5 X , ' R E S I D U A L ' , 1 9 X , I 3 , 1 2 X , E 1 5 . 8 , 5 X , E 1 5 . 8 / ) W R I T E ( L U N I T , 5 0 6 ) I D F T O T . S S T O T 5 0 6 F O R M A T ( 5 X , ' T O T A L ' , 2 2 X , 1 3 , 1 2 X , E 1 5 . 8 ) W R I T E ( L U N I T , 5 0 7 ) R 5 0 7 F 0 R M A T ( / / / 1 X , ' C O R R E L A T I O N C O E F F I C I E N T , R = ' . E 1 5 . 8 ) W R I T E ( L U N I T , 5 0 8 ) 5 0 8 F 0 R M A T ( / / 2 5 X , ' E S T I M A T E D R E G R E S S I O N C O E F F I C I E N T S AND S T A N D A R D ' , $ ' E R R O R S ' ) W R I T E ( L U N I T , 5 0 9 ) 5 0 9 F O R M A T f 1 H + . 2 4 X , 5 3 ( 1 H _ ) / / ) W R I T E ( L U N I T , 5 1 0 ) 5 1 0 F O R M A T ( 1 0 X . ' R E G R E S S I O N C O E F F I C I E N T ' , 1 0 X , ' S T A N D A R D E R R O R ' / ) DO 8 0 I = 1 , N W R I T E ( L U N I T , 5 1 1 ) 8 ( I ) , S B ( I ) 5 1 1 F O R M A T ! 1 3 X . E 1 5 . 8 , 1 3 X . E 1 5 . 8 ) 8 0 C O N T I N U E I F ( I PR I N T . E O . 1 ) R E T U R N W R I T E f L U N I T , 5 1 2 ) 5 1 2 F O R M A T ( / / 3 0 X , ' P A R T I A L F - V A L U E S FOR I N D I V I D U A L V A R I A B L E S X ' ) W R I T E ( L U N I T , 5 1 3 ) 5 1 3 F O R M A T ( 1 H + , 2 9 X , 4 3 ( 1 H _ ) / / ) W R I T E ( L U N I T , 5 1 4 ) 5 14 F O R M A T ( 1 0 X , ' V A R I A B L E ' , 2 0 X , ' F - V A L U E ' / ) DO 9 0 I = 1 , N M 1 W R I T E ( L U N I T , 5 1 5 ) I , F X ( I ) 5 1 5 F O R M A T ( 1 3 X , ' X ' , 1 2 , 1 7 X , E 1 5 . 8 ) 9 0 C O N T I N U E I F ( I P R I N T . E O . 2 ) R E T U R N I F ( X X ( 1 , 1 ) . L T . 0 . 0 ) R E T U R N W R I T E ( L U N I T , 5 1 6 ) 5 1 6 F O R M A T ( / / 1 7 X , ' E S T I M A T E D S T A N D A R D ERROR OF Y AS G I V E N I N XX ' , $ ' ( S A M E ORDER AS I N P U T D A T A ) ' ) W R I T E ( L U N I T , 5 1 7 ) ' 5 1 7 F O R M A T ( 1H+, 1 6 X , 7 1 ( 1 H _ ) / / ) WRI TE ( L U N I T , 5 1 8 ) ( SY ( I ) , I = 1 , L ) 5 18 F O R M A T f 5 ( 2 X . E 1 5 . 8 ) / ) R E T U R N 101 W R I T E ( S . 1 0 2 ) 102 F O R M A T ( / / / / 5 X . ' R E G R E S : ! !WARN I N G - I N P U T A R G U M E N T S V I O L A T E ' , $ ' R E S T R I C T I O N S ' / / / / ) S T O P 1 0 0 W R I T E ( 6 , 1 0 3 ) 103 F 0 R M A T ( / / / / 5 X , ' R E G R E S : ! ! W A R N I N G - M A T R I X I N V E R S I O N F A I L E D ' / / / / ) S T O P END C C S U B R O U T I N E B I S E C T ( F , X I , X F , N R O O T , R , D X I . T O L . N R ) C C ROOT F I N D I N G R O U T I N E C C * * * U S E S I N C R E M E N T A L S E A R C H TO B R A C K E T NR ROOTS OF THE C - « * F U N C T I O N F ( X ) I N I N T E R V A L ( X I , X F ) U S I N G I N I T I A L C * * * I N C R E M E N T O X I . C * * * B I S E C T I O N METHOD I S A P P L I E D TO C O N V E R G E ON E A C H ROOT . C * * * THE ROOTS A R E R E T U R N E D I N THE A R R A Y R ( N R O O T ) . C * * * TOL I S THE ERROR T O L E R A N C E ON F ( X ) : F ( X ) . L E . TOL C * - « NROOT = NO . OF ROOTS SOUGHT C * * * NR = NO . OF ROOTS FOUND C » * * METHOD A V O I D S D I S C O N T I N U I T I E S C D I M E N S I O N R ( N R O O T ) NR =0 X = X I 4 0 0 DX =DXI 1 0 0 X 2 = 0 . 0 E 2 = 0 . 0 2 0 0 I F ( X . G T . X F ) R E T U R N E - F ( X ) E 1 = E2 E2 = E X 1 =X2 X 2 = X I F ( A B S ( E ) . L T . T O L ) GO TO 9 0 0 I F ( E 1 * E 2 . LT . 0 . 0 . AND .DX . EQ . D X I )' GO TO 5 0 0 I F ( E 1 * E 2 . L T . O . 0 . A N D . D X . N E . D X I ) GO TO 6 0 0 X=X+DX GO TO 2 0 0 5 0 0 D Y I = A B S ( E 2 - E 1 ) X = X - D X D X = D X / 1 0 . 0 GO TO 1 0 0 600 DY2 =A8S{E2-E1) I F ( D Y 2 . L T . D Y 1 ) GO TO 7 0 0 X = X 2 GO TO 4 0 0 7 0 0 I C O U N T = 0 7 4 0 I F ( I C O U N T . G E . 1 0 0 ) GO TO 8 0 0 X = ( X 1 + X 2 ) / 2 . 0 E = F ( X ) I C O U N T = I C O U N T + 1 I F ( A B S ( E ) . L T . T O L ) GO TO 9 0 0 I F ( E 1 » E . L T . 0 . 0 ) GO TO 7 5 0 X 1 =X E 1 =E GO TO 7 4 0 7 5 0 X 2 =X E 2 = E GO TO 7 4 0 8 0 0 X = X 2 GO TO 4 0 0 9 0 0 NR =NR+1 R C N R ) = X I F ( N R . E O . N R O O T ) R E T U R N X = X + DX GO TO 4 0 0 END C F U N C T I O N F U N 1 ( X ) F U N 1 = F S P L N ( X ) - 0 . 5 R E T U R N END C F U N C T I O N F U N 2 f X ) F U N 2 = F S P L N ( X ) - 0 . 1 6 R E T U R N END C F U N C T I O N F U N 3 ( X ) CO M F U N 3 = F S P L N ( X ) - 0 . 8 4 R E T U R N END C C F U N C T I O N R H O M ( X ) C C D E N S I T Y F U N C T I O N OF 80%w/w MeOH S O L U T I O N C X : T E M P E R A T U R E I N D E G . C C R H 0 M = - 0 . 0 0 0 4 * X + 0 . 8 4 5 R E T U R N ENO C C F U N C T I O N R H O A ( X ) C C D E N S I T Y F U N C T I O N OF A C I D F E E D S O L U T I O N C X : T E M P E R A T U R E I N D E G . C C R HO A = - O . 0 0 0 2 * X + 1 . 4 7 9 R E T U R N END CO Gi CO - 364 -APPENDIX F Input Data to Computer Prog Listing of data file read by computer program on logical input unit 4 1 2 1 .0 25 .0 40, .0 0. 8636 0, 85 2 21 .0 25 .0 40 .0 0. 837 1 0. 85 3 2 1 .0 25 .0 50 .0 0. 7512 0, 85 4 21 .0 25 .0 50 ,0 0. 7784 0. 85 5 2 1 .0 25 .0 60 .0 0 . 62 19 0. , 85 6 21 .0 25 .0 80 .0 0. 5 185 0. .85 7 21 .0 25 .0 100 .0 0 .4323 0, ,85 8 2 1 .0 25 .0 120 .0 0, . 3584 0. . 85 9 20 .0 25 .0 40 .0 0, . 8930 0 , 80 10 20 . 0 25 .0 50 .0 0 . 8 164 0 . 80 1 1 20 .0 25 .0 60 .0 0 . 7003 0 .80 12 20 .0 25 .0 80 .0 0 .5320 0 .80 13 20 . 0 25 .0 80 .0 0 .5514 0 . 80 14 20 .0 25 .0 100 .0 0 . 4628 0 . 80 15 20 . 0 25 .0 120 .0 0 . 3977 0 .80 16 19 .0 25 .0 50 .0 0 . 8 145 0 .70 1 7 19 . 0 25 .0 50 .0 0 . 8069 0 . 70 18 19 .0 25 .0 60 .0 0 .6718 0 . 70 19 19 .0 25 .0 80 .0 0 . 5679 0 . 70 20 19 .0 25 .O 100 . 0 0 .5115 0 . 70 2 1 19 .0 25 .0 120 .0 0, . 438 1 0 . 70 22 26 .0 30 .0 40 .0 0. . 8895 0 . 85 23 26 .0 30 .0 50 .0 0, .6924 0 .85 24 26 .0 30 .0 60 .0 0. ,6313 0, .85 25 26 .0 ' 30 .0 • 80 .0 0, ,5121 0. .85 26 26 .0 30 .0 100 .0 0. ,4 106 0, , 85 27 26 .0 30 .0 100 .0 0. 4372 0, , 85 28 26 .0 30 .0 120 .0 0. 4014 0, ,85 29 25 .0 30 .0 40 ,0 0. 8637 0, . 80 30 25 .0 30 .0 50, .0 0. 7725 0. .80 3 1 25 . 0 30 .0 60 ,0 0. 6 199 0, 80 32 25 . 0 30 .0 80, ,0 0. 5918 0. 80 33 25 . 0 30. .0 100, ,0 0. 4632 0. 80 34 25 . 0 30, .0 120, 0 0. 3880 0. 80 35 24 . 0 30, ,0 50. 0 0. 9010 0. 70 36 24 . 0 30, 0 60. 0 0. 7148 0. 70 37 24 . 0 30, ,0 60. 0 0. 7566 0. 70 38 24 . 0 30 , 0 80. 0 0. 5800 0. 70 39 24 . 0 30. 0 100. 0 0. 5 104 0. 70 40 24 . 0 30. 0 120. 0 0. 3956 0. 70 4 1 31 . 0 35 . 0 40. 0 0. 8595 0. 85 42 31 . 0 35 . 0 40. 0 0. 8125 0. 85 43 3 1 . 0 35 . 0 50. 0 0. 77 19 0. 85 44 3 1 . 0 35 . 0 60. 0 0. 6023 0. 85 45 3 1 . 0 35 . 0 80. 0 0. 429 1 0. 85 46 3 1 . 0 35 . 0 100. 0 0. 4400 0. 85 47 3 1 . 0 35 . 0 120. 0 0. 3401 0. 85 48 30. 0 35 . 0 40. 0 0. 8956 0. 80 49 30. 0 35 . 0 40. 0 0. 8843 0. 80 50 30. 0 35 .0 50. 0 0. 8 166 0. 80 51 30. 0 35 . 0 60. 0 0. 6225 0. 80 52 30. 0 35 .0 80. 0 0. 5462 0. 80 53 30 .0 35 .0 80. 0 0. 5331 0. 80 54 30 . 0 35 .0 100. 0 0. 4818 0. 80 55 30 .0 35 .0 120. 0 0. 3514 0. 80 56 29 .0 35 . 0 50. .0 0. 8074 0. 70 57 29 .0 35 .0 60. .0 0. 7 105 0. 70 58 29 . 0 35 .0 60 .0 0. .6628 0. ,70 59 29 .0 35 .0 80 .0 0. .5648 0. . 70 60 29 .0 35 .0 100 .0 0. , 4394 0. . 70 61 29 .0 35 .0 120. .0 0. . 3972 0, , 70 62 29 .0 35 .0 120 .0 0 . 3444 0 . 70 63 31 .0 35 .0 40 .0 0 , 5742 0 ,85 75 . 0 64 31 .0 35 .0 40 .0 0 . 6 103 0 .85 75 , . 0 65 3 1 .0 35 .0 60 .0 0 . 4232 0 .85 75 , 0 66 3 1 .0 35 .0 80 .0 0 . 3874 0 .85 75, .0 67 3 1 .0 35 .0 120 .0 0 .2169 0 . 85 75 ,0 68 31 .0 35 .0 40 .0 0. ,5415 0 .85 150 .0 69 3 1 .0 35 .0 60 .0 0 . 4005 0 .85 150 ,0 70 31 .0 35 .0 80 .0 0 .3121 0 .85 150 .0 7 1 31 .0 35 .0 120 .0 0 . 1859 0 .85 150 .0 72 31 .0 , 35 .0 40 .0 0 . 55 14 0 . 85 300. .0 73 3 1 .0 ' 35 .0 40 .0 0 .5118 0 .85 300 .0 74 3 1 .0 35 . 0 60 .0 0 .4161 0 . 85 300 .0 75 3 1 .0 35 .0 80 .0 0 . 2547 0 . 85 300. .0 76 3 1 .0 35 .0 120 .0 0 . 1800 0 . 85 300 .0 77 3 1 .0 35 .0 120 .0 0 . 1905 0 . 85 300 .0 I CO 05 O I L1st i ng of data file read by computer program on logical input unit 5 1 0. 0000 0. 0000 0. 0010 0 . 0065 0. 0157 0. 0954 0. 1408 0. 2488 0. 2819 0. 2522 0. 6174 2 0 .0000 0. 0000 0. 0010 0. 0040 0. 0210 0. 0800 0. 0950 0. 1835 0. 2697 0. 2440 0. 7415 3 0 0000 0, 0000 0. 0022 0 . 0150 0. 0250 0. 2235 0. 2355 0. 3055 0. 3280 0. 2885 0. 58 10 4 0 .0000 0. .0000 0. 0030 0. 0135 0. 0645 0. 4506 0. 3201 0. 3595 0. 2537 0. 1861 0. 2785 5 0 . 001 1 0 .005 1 0. 0147 0. 0624 0. 1608 0. 5096 0. 2983 0. 2782 0. 1987 0. 1476 0. 2203 6 0 .0014 0 .0069 0. 0188 0. 0588 0. 1769 0. 5131 0. 3018 0. 2855 0. 1934 0. 1293 0. 1804 7 0 .0010 0 .0076 0. .0183 0. 0533 0. 1640 0. 5762 0. 2975 0. 2440 0. 1791 0. 1252 0. 1705 8 0 .0010 0 .007 2 0. .0232 0. 0970 0. 1655 0. 3475 0. 1835 0. 1892 0. 1290 0. 0935 0. 1580 9 0 . 0022 0 .0025 0 .0057 0 .0128 0. .0422 0. 2312 0. 1282 0. 1223 0. 0737 0. 0567 0. 0756 10 0 .0018 0 .003 1 0 .004 3 0 .0155 0. .0451 0. 1628 0. 0758 0. 0746 0. 0487 0. 0380 0. 0625 1 1 0 .0015 0 . 0032 0 .0065 0 .0291 0. .07 1 1 0. ,2154 0. 0909 0. .0780 0. 0556 0. 0442 0. 0760 12 0 .0013 0 .004 1 0 . 0065 0 .0212 0 .057 1 0. . 1500 0. 0583 0. ,0520 0. 0379 0. 0298 0. 0413 13 0 .0020 0 .0135 0 .0587 0 . 1825 0 . 2500 0, ,5340 0. 2915 0. 3292 0. 2280 0. 1564 0. 2280 14 0 .0014 0 .0053 0 .0173 0 .0603 0 .0895 0. , 1522 0. 054 1 0. .0625 0. 0450 0. 0317 0. 0587 15 0 .0010 0 .0152 0 .0942 0 . 2400 0 .2915 0. ,5160 0. 2685 0. , 2762 0. 1940 0. 1410 0. 2150 16 0 .0010 0 .0121 0 , 0294 0 . 1430 0 . 3395 0 .9905 0. ,4470 0. , 3592 0. 2285 0. , 1495 0. 2245 17 0 . 003 3 0 . 0063 0 .0177 0 .0607 0 . 1398 0. . 3296 0, 1692 0, , 1405 0. .0823 0. ,0544 0. 0636 18 0 . 0029 0 .0062 0 .0170 0 . 0563 0 . 1024 0. . 2306 0. 1 104 0, ,1111 0, 0631 0. ,041 1 0. 0589 19 0 . 0024 0 .0057 0 .0165 0 .0612 0 . 1 124 0. . 2631 0, ,0900 0, ,0756 0, 0487 0. ,0348 0. 0600 20 0 . 0028 0 .0139 0 .0364 0 . 07 19 0 . 1032 0. .2101 0. 0782 0, .0653 0, 0435 0. ,0305 0. 0417 2 1 0 .0261 0 .0669 0 .0910 0 .1418 0 . 1836 0. . 3884 0. 1912 0, . 1646 0. 0989 0. ,0650 0. 0882 22 0 .0000 0 .0000 0 ,0026 0 .0178 0 .0545 0. , 2757 0. 256 1 0. .3385 0, ,2659 0. ,2010 0. 3922 23 0 .0000 0 .0015 0 .0050 0 .0360 0 . 1300 0. .6070 0. 3485 0. . 3405 0. ,2392 0. , 1645 0. 2475 24 0 .0063, 0 .0380 0 .0667 0 . 1 134 0 . 1802 0. . 4987 0. 2862 0. . 2651 0. , 1785 0. , 1263 0. 1985 25 0 .0025 0 .0115 0 .034 1 0 . 1272 0 .2510 0. .4670 0. 2595 0 . 2425 0, . 1672 0. . 1 195 0. ,2710 26 0 .0048 0 .0250 0 .0853 0 . 1895 0 . 2069 0. . 3810 0. 2000 0. . 1805 0. , 1270 0. .0955 0. 1955 27 0 .0117 0 . 0450 0. .0973 0. . 1532 0. . 2322 0 . 5656 0. 2778 0. . 2356 0. . 1643 0, . 1 129 0. , 1867 28 0 .0136 0 .0533 0 . 1 146 0 . 1789 0 . 2669 0 , 6350 0. 3157 0, . 2655 0, . 1858 0 .1251 0. , 2096 29 0 .004 1 0 .0160 0 .0379 0 . 1645 0 . 2958 0 . 7002 0, 3488 0, , 3236 0, .2124 0 , 158 1 0. . 2453 30 0 .0039 0 .0165 0. .0348 0. .0649 0 . 1 129 0 . 3084 0. 1547 0, . 1480 0, ,0928 0 .0641 ti. ,0966 3 1 0 . 0038 0 .018 1 0. .0578 0. . 1667 0. . 3580 0. , 9030 0, , 3735 0, , 3 190 0, . 1902 0 .1310 0. , 2500 32 0 . 006 3 0 .0365 0. .0858 0 . 1477 0 . 2465 0 . 6685 0, 4050 0 , 3970 0. .2717 0 . 1860 0, ,3185 33 0 .0173 0. . 0939 0. . 1528 0. . 2367 0 . 2985 0 . 7046 0. , 3650 0 . 3530 0 . 2222 0 . 1502 0 . 2790 34 0 .0241 0 , 0506 0. .0589 0. . 1 109 0 . 1459 0, , 2599 0. 1010 0 , 1094 0, .0688 0 .0483 0, .0984 35 0 .0296 0. .0722 0. . 1 159 0. .2171 0 . 3496 0. .8519 0. , 3944 0 . 3252 0 .2188 0 . 1375 0 .2295 36 0 .0192 0 .0857 0. 1123 0 . 2032 0 . 3061 0. . 6874 0. . 3229 0 . 3003 0 . 1644 0 . 1054 0 . 1384 37 0. .0075 0. .0845 0. 1984 0. 2967 0, . 3665 0. ,6765 0. ,3550 0, . 3605 0 , 2242 0 .1515 0 .2460 38 0. 0193 0. .0600 0. 0801 0. . 1 169 0 . 1403 o. . 2806 0. ,1151 0 . 1000 0 .064 1 0 .0415 0 .0676 39 0. 0710 0. .1615 0. . 2089 0. . 2782 0. . 2860 0, ,5545 0, ,2753 0 . 2685 0 . 1660 0 . 1205 0 .2120 40 0. 1202 0. . 3246 0. 3762 0. 42 11 0. .4391 0. . 7702 0. 38 13 0 . 3847 0 . 2395 0 . 1582 0 . 2273 4 1 0 . 0042 0. 0197 0. 0352 0. .0917 0. . 1467 0. ,4013 0, , 2202 0 .2412 0 . 1783 0 . 1285 0 . 2360 42 0. 0012 0. 0055 0. 0111 0. 0245 0. .0482 0, , 1039 0, ,0542 0 .0530 '0 .0357 0 .0254 0 .0648 43 0 . 0010 0, 0089 0. 0230 0. 0523 0. .0824 0. . 1870 0, ,0980 0 .0962 0 .0615 0 .0435 0 .0770 44 0. 0097 0. 0590 0. 0974 0. 1307 0. . 1549 0. . 3662 0, ,2045 0 .1913 0 . 1 178 0 .0763 0 . 1297 45 0 . 0059 0 . 0274 0. 0490 0. 0980 0. .1191 0. . 2676 0, 1 172 0 .1051 0 .0598 0 .0402 0 .0460 46 0. 0205 0. 0772 0. 1649 0. 2322 0. 2748 0. 4902 0. 2284 0. 2005 0. 1315 0. ,0853 0. 1766 47 0. 0088 0. 0344 0. 0726 0. 2027 0. 2981 0. 4930 0. 2145 0. 1972 0. 1401 0, .0937 0. 1363 48 0. 0069 0. 0269 0. 07 13 0. 1216 0. 1572 0. 291 1 0. 1447 0. 1333 0. 0871 0, .0554 0. 0768 49 0. 002 5 0. 0278 0. 0637 0. 3012 0. 4836 0. 7677 0. 3365 0. 3034 0. 2155 0. . 1593 0. 2720 50 0 . 0045 0. 0305 0. 0709 0. 1 140 0. 1647 0. 3756 0. 2004 0. 1872 0. 1113 0. .0686 0. 1076 5 1 0. 0045 0. 0327 0. 0646 0. 0921 0. 1 170 0. 2503 0. 1302 0. 1208 0. 0734 0. ,0480 0. 0801 52 0. .0096 0 . 0486 0. 0582 0. 0753 0. 1038 0. 2268 0. 1 108 0. 0997 0. 0591 0. ,0376 0. 0565 53 0 007 5 0. 0855 0. 1542 0. 3112 0. 3375 0. .6820 0. 3525 0. 3777 0. 2265 0, 1525 0. 2115 54 0 .0253 0. 0504 0. 0473 0. 0623 0. 0700 0. 1264 0. 0565 0. 056 1 0. 0305 0. .02 12 0. 04 15 55 0 . 0030 0. 1295 0. 2582 0. 4 200 0. 3340 0. 5272 0. 2560 0. 2847 0. 1765 0. 1 150 0. 1685 56 0 . 0543 0 1214 0. . 1826 0. 2551 0. 2809 0. 5 182 0. 2485 0. 2 146 0. 1577 0. ,0958 0. 1828 57 0 . 0345 0 . 1740 0 . 2007 0. 2850 0. 3745 0. . 8430 0. 3883 0. . 3372 0. 1793 0. 1121 0. 1325 58 0 . 027 1 0 .0796 0. . 1085 0. . 1435 0. 174 1 0. . 2927 0. 1357 0. .1213 0. 0696 0. 0451 0. 071 1 59 0 .032 1 0 . 1019 0 . 1263 0 . 1420 0. 1273 0. .2117 0. . 1087 0. .0981 0. .0605 0. ,0359 0. 0531 60 0 .0454 0 .0864 0 . 1206 0. . 1494 0. 1502 0 .2518 0. 1 122 0. .0964 0. 0528 0, 0326 0. 0463 6 1 0 . 3744 0 , 2980 0 . 2870 0 . 2925 0. 3205 0. .5715 0. .2495 0. .2412 0. . 1365 0. ,0935 0. 1595 62 0 . 1700 0 . 4605 0 . 501 1 0 . 4830 0. 4285 0 .6266 0. . 3220 0. .3712 0. 2365 0. , 1570 0. 2350 63 0 .0514 0 .0645 0 .0918 0 .1515 0. 1842 0 . 3705 0, 1725 0, .1721 0. . 1289 0. ,0816 0. 1582 64 0 . 0762 0 .0853 0 .0910 0 . 1495 0. . 1981 0 . 3896 0. , 1985 0. . 2075 0. . 1282 0. .0905 0. 1633 65 0 . 1682 0. .1165 0 . 1454 0 . 1879 0. 2291 0 . 3885 0. . 1925 0. . 1965 0. . 1325 0. .0915 0. 1385 66 0 . 1983 0. . 1255 0. . 1390 0. , 1868 0. 2181 0 .3890 0. . 1840 0 .1691 0. . 1020 0, ,0808 0. 1527 67 0 .2 187 0. .1310 0 . 1295 0. . 1857 0. 2434 0 .4256 0. . 1745 0. . 1698 0, ,1015 0, ,0742 0. 1052 68 0. . 1466 0. .0990 0. .0976 0. . 1325 0. 1620 0 ,3173 0. . 1565 0. . 1698 0. . 1069 0. ,0779 0. 1490 69 0. . 1224 0. 1345 0 , 1479 0. .1618 0. 1947 0 .3216 0. . 1423 0 . 1493 0. , 1012 0. ,0742 0. 1361 70 0. . 2463 0, . 1283 0. . 1295 0. .1551 0. 1801 0 .3067 0. . 1450 0. . 1408 0. .0881 0. ,0702 0. 1361 7 1 0 . 2783 0 .1318 0 .1361 0 . 1634 0. 1910 0 . 3445 0 . 1505 0 . 1438 0 .0888 0 .0660 0. . 1 175 72 0. 2123' 0. 1084 0. . 1 107 0 . 1335 0. 1590 0 . 3070 0. . 1360 0 . 1375 0 .0895 0 ,0600 0, . 1390 73 0. . 2 104 0. . 1010 0 . 1023 0. . 1246 0. 1358 0 .2540 0. . 1 150 0 .1321 0 ,0855 0 .0650 0, , 1335 74 0 .0728 0. .1781 0. . 1767 0. . 1549 0. 1838 0 .2717 0. .1111 0 .1215 0 .0830 0 .0662 0, . 1485 75 0. . 267 1 0. . 1465 0. .1315 0. . 1378 0. 1559 0 .2533 0. . 1 197 0 . 1255 0 .0822 0 .0660 0, .1318 76 0. . 3698 0. 1723 0. . 1620 0. . 1739 0. 1904 0 . 3361 0. . 1505 0 .14 10 0 .0902 0 .0681 0, . 1458 77 0. 3798 0. 1795 0. .14 11 0. . 1528 0. 1729 0 . 2894 0. . 1425 0 . 1300 0 .0778 0 .0504 0 . 1 105 - 369 -APPENDIX G Rotameter Calibration Curves j i - 370 -ROTAMETER SCALE READING Calibration curve of acid line flowmeter at 25°C - 371 -o ROTAMETER SCALE READING Calibration curve of methanol line flowmeter at 25°C - 372 -APPENDIX H Densities of Crystallizer Feed and Salting Out Agent - 373 -CO TEMPERATURE (deg. C) Density of crystallizer feed versus temperature - 374 -OO CO TEMPERATURE (deg. C) Density of salting out agent versus temperature - 375 -APPENDIX J Details of the Crystallizer I i! 5 - 376 -H CryacalLls^r wall - 377 -APPENDIX K Analytical Procedures - 378 -Determination of H2SO4 Content of Saturated Solution A sample of the saturated solution containing 2-2.5 grams H2SO4 was weighed and diluted to 500 mis with distilled water in a volumetric flask. A 50 mis sample of the diluted solution was withdrawn and titrated with standardized 0.1N NaOH using phenolphthalein as indicator. Then, acid present in original sample was calculated from (volume of 0.1N NaOH in litres)(0.1)(0.5)(98.08)(10) gr The average of three determinations was used to calculate the H2SO4 content of the saturated solution. Determination of Na2S04 Content of Saturated Solution A sample of the saturated solution containing about 1 gram Na2S04 was weighed and its acid component was neutralized with IN NaOH initially, switching to 0.IN NaOH as the end point was approached. The sulfate resulting from the neutralization of the sulfuric acid was calculated from the acid content of the solution. The water and methanol were evaporated and the residue dried in an oven at 200°C. The residue weight was determined after cooling to room temperature and the weight of Na2S04 in the sample was calculated from Residue weight - Na2S04 from neutralization The average of two determinations was used to calculate the Na2S04 content of the saturated solution. - 379 -Determination of MeOH Content of Saturated Solution Methanol determination was based upon its oxidation reaction with acidified potassium dichromate to carbon dioxide and water K 2Cr 20 7 + CH3OH + ^ S O ^ > C02 + 6H20 + K2SC\ + C r ^ S O ^ Excess dichromate was determined by titration with ferrous ion K2Cr207 + 6FeS0^ + 7H2S(\ + K2S04 + C r ^ S O ^ g + 3Fe2(S04)3 + 7H20 using Ferroin reagent (o-phenanthroline) as indicator which goes through a number of colour changes and then turns sharply to red at the end point. Thus, to determine the amount of methanol in the saturated solution a sample of the solution containing about 1 gram of methanol was quickly weighed and diluted to 500 mis with distilled water in a volumetric flask. A 10 mis sample of the diluted solution was withdrawn and carefully added to 10 mis of 0.5N (M/12) K2Cr207 and 25 mis of concentrated sulfuric acid (95.5 - 96.5% w/w) in a 250 mis Erlenmeyer flask. The flask was sealed and allowed to stand for ten mintues after which methanol oxidation was complete. It was then treated with about 100 mis of cold water and allowed to cool to room temperature. The cool contents were titrated for excess dichromate with 0.1N ferrous ammonium sulfate ( FeSO^ • (NHl, ) 2SO4 • 6H2 0) and the titration was repeated for a - 380 -blank. i.e., where 10 mis of water was substituted for the sample containing methanol. Then, if a and b were the volumes of 0.1N ferrous ammonium sulfate required for the original and blank titrations respectively, the weight of methanol in the saturated solution sample was calculated from ((b - a)/b) (26.67) (50) mg Note that 10 mis of 0.5N K 2Cr 20 7 can oxidise a maximum of 26.67 mg of methanol. Reagents 0.5N K2Cr2O7 was prepared by dissolving 24.518 grams of cool dry K 2Cr 20 7 in distilled water and diluting to 1000 mis in a volumetric flask. 0.1N ferrous ammonium sulfate was prepared by dissolving 45 to 50 grams of FeSO^ • (NH4 ) ^ O,, • 6H 20 and 10 grams of (NH1+)2S04 in distilled water, adding 10 mis of concentrated sulfuric acid, and diluting to 1000 mis in a volumetric flask. 

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