Crystallization Kinetics of Sodium Sulfate
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CRYSTALLIZATION KINETICS OF SODIUM SULFATE IN A SALTING OUT MSMPR CRYSTALLIZER SYSTEM Na2S0«t/H2S0^/H20/Me0H 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) - ii - 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 g equations of crystal growth (G = KQS ) and crystal nucleation (B = K„Sb) 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^G1) 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). - iii - 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 = KqS0'97) and was statistically non- changing with temperature. The nucleation rate kinetic order b was similarly temperature independent and was determined as 2.1 (B = KgS2*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 Kn = 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 KQ 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 - vi - Page 3.3.1 Na2S0t+ Solubility in Me0H/H2S0i+/H20 Mixtures 80 3.3.2 Sieve Analysis 89 3.3.3 Time Required for Steady-State....... 95 3.3.4 Uniformity of the Crystal Suspension. 96 3.3.5 Shape Factor of Na2S0i+ Crystals 98 3.3.6 Mother Liquor Sampling 102 3.3.7 Methanol Loss During Crystallization. 103 3.3.8 Crystallization of NaHSO^.H20 104 3.3.9 Calibration of Rotameters 3.3.10 Densities of the Main Crystallizer 105 Feed and the Salting Out Agent 106 3.4 Experimental Procedures 107 3.4.1 Preparation of Feed Materials 3.4.2 Continuous Crystallization 107 Experiments 3.4.3 Crystal Sampling and Sample 107 Treatment 108 3.4.4 Measurement of the Supersaturation... 110 3.5 CSD Instability 112 CHAPTER 4 - DATA ANALYSIS AND RESULTS 117 4.1 Determination of the Growth and Nucleation Rates from the Steady-State CSD Data 117 4.2 Results for the Chromium-Free System 121 4.3 Results for the Impure System 142 4.4 Effect of Variables on the CSD 161 CHAPTER 5 - DISCUSSION AND CONCLUSIONS 168 5.1 System Variables 168 5.1.1 Supersaturation 168 5.1.2 Residence Time 171 5.1.3 Alcohol/Feed Ratio 175 5.1.4 Crystal Suspension Density 179 5.1.5 Agitation Rate 182 5.1.6 Temperature 182 5.1.7 Concentration of the Cr+++ Impurity.. 186 5.1.8 Yield 193 5.1.9 Crystal Size Distribution 194 5.2 Relative Kinetics 198 5.3 Check on Data Accuracy 199 5.4 Conclusions 203 5.5 Recommendations for Further Work 206 - vii - Page NOMENCLATURE 208 REFERENCES 213 APPENDICES 216 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 - viii - 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 Summar(Datasey t of1) .result s for run numbers 1-21 122 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 134 - 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.