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The autocausticizing of sodium carbonate with colemanite Sozen, Gulgun 1985

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THE AUTOCAUSTICIZING OF SODIUM CARBONATE WITH COLEMANITE By GULGUN SOZEN B.S c , Middle East Technical U n i v e r s i t y , Turkey, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Chemical Engineering) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1985 © Gulgun Sozen, 1985 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e head o f my department o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date J c A A 2_2_ 19 ?5 DE-6 (3/81) - i i -ABSTRACT Au t o c a u s t i c i z i n g , a new method to regenerate sodium hydroxide from the sodium carbonate, i s intended to replace the conventional Kraft Recovery System which uses calcium hydroxide produced i n a lime k i l n f o r t h i s purpose. I t i s defined as the self-induced expulsion of carbon dioxide bound i n the smelt by using c e r t a i n amphoteric oxides. Thus a u t o c a u s t i c i z i n g can eliminate the need for a lime cycle and hence reduce the K r a f t process c a p i t a l and operating c o s t s . The reactions between sodium carbonate and a number of amphoteric oxides have been reported i n the l i t e r a t u r e . Patents have been issued on the use of titanium dioxide, i r o n oxide and sodium borates f o r t h i s purpose. The sodium borates have the advantage of a high r e a c t i o n rate, but are t o t a l l y soluble and must be c a r r i e d throughout the whole K r a f t c y c l e . In t h i s research colemanite (calcium borate) which Is mined as a cheap mineral i n C a l i f o r n i a and i n Turkey was studied as an a u t o c a u s t i c i z i n g agent. Since i t i s p a r t i a l l y soluble and most l i k e l y can be recycled, i t would eliminate the problems associated with the use of soluble borates. Experiments were performed both isothermally and under constant heating rate c o n d i t i o n s . Isothermal studies were made with T i 0 2 , alumina and colemanite to compare t h e i r performances as a u t o c a u s t i c i z i n g agents at 900°C and 1000°C for various r e a c t i o n times i n an e l e c t r i c furnace. - i i i -The second group of experiments was made using a d i f f e r e n t i a l Chermogravimetric (TG) analyzer. In these experiments mixtures with 20 to 80 weight percent colemanite i n sodium carbonate were heated at a constant heating rate of 10°K/min i n the range of 190-1000°C. The r e s u l t s i n d i c a t e that two re a c t i o n were involved. Above the s t o i c h i o m e t r i c colemanite concentration the colemanite and sodium carbonate had reacted completely by a temperature of about 700°C. Above that temperature the impurities i n the colemanite appeared to catalyze the decomposition of sodium carbonate If the colemanite concentration was less than the s t o i c h i o m e t r i c amount needed. TG data were analyzed for the f i r s t and second reactions between the temperature ranges of 190-700°C and 700-1000°C r e s p e c t i v e l y . K i n e t i c models were developed In terms of the reaction order, a c t i v a t i o n energy and frequency f a c t o r . The f i r s t r e a c t i o n was found to be zero order on sodium carbonate concentration. The r e s u l t s also showed that the a c t i v a t i o n energy and frequency f a c t o r were functions of the colemanite concentration i n the mixtures. As a r e s u l t the rate was a f f e c t e d by the amount of colemanite used. The same was true for the second r e a c t i o n except the re a c t i o n was f i r s t order. The concen-t r a t i o n s predicted f or the isothermal tests by the model were compared with the r e s u l t s of the isothermal study for various colemanite concentrations. Reasonable agreement was found except for the values at lower conversions, which might be due to the Increased importance of the d i f f u s i o n of C O 2 from the mixtures i n the case of Isothermal runs. I t was also found that i t i s possible to obtain conversions as high as 85 percent with 40 percent colemanite i n 20 minutes. Promising r e s u l t s were obtained from the recycle tests as w e l l . - i v -TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i i i LIST OF FIGURES x ACKNOWLEDGEMENTS x i v 1. INTRODUCTION 1 2. LITERATURE REVIEW 3 2.1 Kraft Pulping 3 2.1.1 Problems of Kraft Recovery System . . . . 5 2.1.2 A l t e r n a t i v e s to Conventional K r a f t Pulping 8 2.2 A u t o c a u s t i c i z i n g Processes 9 2.2.1 Decomposition of Sodium Carbonate Without an A u t o c a u s t i c i z i n g Agent 12 2.2.2 A u t o c a u s t i c i z i n g Reactions 12 2.2.3 Agents Proposed for A u t o c a u s t i c i z i n g . . . 14 2.2.3.1 Titanium dioxide 14 2.2.3.2 F e r r i c oxide 19 2.2.3.3 Ilmenite 21 2.2.3.4 S i l i c a t e s , aluminates and phosphates 21 2.2.3.5 Borates 23 2.2.3.6 Colemanite 29 2.3 Study of Reaction K i n e t i c s by Thermogravimetry. . 33 2.3.1 Accuracy of Thermogravimetric Data . . . . 35 2.3.2 The Thermogravimetric (TG) Curve 36 2.3.3 Mathematical Evaluation of Experimental Parameters 38 -v-Page 2.3.4 Comparison of the Accuracy of Mathematical Methods for the Evaluation of the TG Curve 42 2.3.5 T h e o r e t i c a l Considerations for the Evaluation of an Equation for Function f ( a ) 42 2.3.6 Influence of V a r i a t i o n of K i n e t i c Constants on Shape and P o s i t i o n of T h e o r e t i c a l Thermogravimetric Curves 46 3. MODELLING 48 3.1 Development of a Rate Expression 48 3.2 Expressions for F r a c t i o n a l Conversions and Function f(oc) for the Reaction of Sodium Carbonate and Colemanite 52 3.2.1 Expression of the F r a c t i o n a l Conversion of Sodium Carbonate 52 3.2.2 Expression for the F r a c t i o n a l Conversion of Colemanite 54 3.3 Expressions f o r the Decomposition of Sodium Carbonate 58 3.3.1 Development of a Rate Expression . . . . 58 3.4 A n a l y t i c a l Forms of Function f ( a ) and g(ct) . . . 60 4. EXPERIMENTAL STUDIES 62 4.1 Isothermal Experiments 62 4.1.1 System Var i a b l e s 64 4.1.2 Preparation of Samples 65 4.1.3 Experimental Procedure 66 4.1.4 Experimental Data 71 - v i -Page 4.2 Thermogravimetric Analysis 76 4.2.1 Apparatus 76 4.2.2 Preparation of the Samples 79 4.2.3 S e l e c t i o n of Experimental Conditions . . 80 4.2.4 Experimental Procedure and Recording of the Data 82 4.2.5 K i n e t i c Analysis of the TG Data 83 4.3 Recycling Experiments 86 5. ANALYSIS OF A THERMOGRAVIMETRIC DATA 88 5.1 Analysis of the Data for the F i r s t Reaction . . 88 5.2 Analysis of the Data f o r the Second Reaction . . 90 6. RESULTS AND DISCUSSION 91 6.1 Isothermal Experiments 91 6.2 D i f f e r e n t i a l Thermogravimetric Analysis . . . . 101 6.2.1 Model of F i r s t Reaction 121 6.2.2 Model of Second Reaction 139 6.3 Comparison of the Model with the Results of Isothermal Experiments 155 6.4 Recycle of Colemanite 162 7. CONCLUSIONS AND RECOMMENDATIONS 167 NOMENCLATURE 171 REFERENCES 174 APPENDIX I 177 - v i i -Page APPENDIX I I : Sample Ca l c u l a t i o n s and Derivations 181 i - C a l c u l a t i o n of Conversion from the T i t r a t i o n Data Taken i n the Isothermal Runs 182 i i - C a l c u l a t i o n of the Stoichiometric Amount of Colemanite 183 i i i - C a l c u l a t i o n of Frequency Factor, z^, and Rate Constant, k x 185 i v - C a l c u l a t i o n of Frequency Factor, z 2 , and Rate Constant, k 2 187 v - D e r i v a t i o n of a Combined Rate Expression . . . . 189 v i - Na:B Ratios for D i f f e r e n t Colemanite Concentrations 193 APPENDIX I I I : Turkish Colemanite Product S p e c i f i c a t i o n s and T y p i c a l Analysis 194 APPENDIX IV: Standard Deviation Tables for the 1st and 2nd Reactions 197 APPENDIX V: F i t t i n g of the Points on F i g . 56 and 57 . . . 208 - v i i i -LIST OF TABLES Page Table 1: Capital cost structure of a new Kraft pulp m i l l 6 Table 2: Proposed autocausticizing agents 15 Table 3: Composition of ilmenite 22 Table 4: Main constituents of cooking chemical system . . 25 Table 5: Change i n costs by choice of borate-based system 30 Table 6: Consumption and costs of energy 30 Table 7: Thermal c h a r a c t e r i s t i c s of colemanite 32 Table 8: A n a l y t i c a l forms of function f(a) and g(a) for the most probable mechanisms 57 Table 9: A n a l y t i c a l forms of function f(a) and g(a) for the probable mechanisms for the decomposition of Na 2C0 3 61 Table 10: Conditions tested i n the isothermal experiments 67 Table 11: Conversion time data for T i 0 2 72 Table 12: Conversion time data for Alumina 73 Table 13: Conversion time data for Colemanite 74 Table 14: Conversion time data for Colemanite at d i f f e r e n t temperatures 75 Table 15: L i s t of the experiments performed using TG . . 81 Table 16: Standard deviation of B values for 60 percent Colemanite 123 Table 17: Activation energies which gives best f i t s to experimental data for 60 percent Colemanite . . 128 Table 18: K i n e t i c constants for the f i r s t reaction . . . 134 Table 19: K i n e t i c constants for the f i r s t reaction calculated by using equation 6.3, 6.4 and 6.5 138 - i x -Page Table 20: K i n e t i c constants for the second reaction . . . 149 Table 21: K i n e t i c constants for the second reaction calculated by using equation 6.6 and 6.7 . . . 154 Table 22: Rate constants and f r a c t i o n a l conversions for the f i r s t and second reaction 157 Table A l : Na:B mol ratios for various colemanite and sodium carbonate mixtures 193 Table A2: Standard deviation of B values for the f i r s t reaction at 30% colemanite 198 Table A3: Standard deviation of B values for the f i r s t reaction at 40% colemanite 199 Table A4: Standard deviation of B values for the f i r s t reaction at 50% colemanite 200 Table A5: Standard deviation of B values for the second reaction at 30% colemanite 202 Table A6: Standard deviation of B values for the second reaction at 40% colemanite 204 Table A7: Standard deviation of B values for the second reaction at 50% colemanite 206 -x-LIST OF FIGURES Page Figure 1: Schematic Diagram of Kraft Process 4 Figure 2: Comparison of Autocausticizing with Conventional Causticizing . 11 Figure 3: Fraction of the Decomposed Sodium Carbonate as a 17 Function of the Reaction Time with the use of T i 0 2 Figure 4: S i m p l i f i e d Flow Sheet of the DARS Research 20 Plant 26 Figure 5: Autocausticizing Reaction i n A i r with the Use of Borate Figure 6: Areas of Application for Different Kinds of 28 Autocausticizable A l k a l i 37 Figure 7: A Typical TG Curve Figure 8: Theoretical TG Curves Calculated for Different 47 Rate Controlling Processes Figure 9: Theoretical TG Curves Calculated for Various 47 Values of Activation Energy and Frequency Factor 53 62 77 Figure 10: Phase Diagram for the System B 20 3-Na 20»B 20 3 Figure 11: Experimental Set-up for Isothermal Runs Figure 12: The TGS-2 System • « Figure 13: Cutaway Furnace showing position of Sample, 78 Furnace and Thermocouple Figure 14: Results After Subtraction of the Colemanite 85 Curve from the Others Figure 15: Results of the Isothermal Experiments for 10 93 Percent T i 0 2  Figure 16: Results of the Isothermal Experiments for 20 94 Percent T i 0 2  Figure 17: Results of the Isothermal Experiments for 10 95 Percent Alumina Figure 18: Results of the Isothermal Experiments for 20 96 Percent Alumina - x i -Page Figure 19: Results of the Isothermal Experiments for 10, 20 and 30 Percent Alumina 97 Figure 20: Results of the Isothermal Experiments for 40, 50 and 60 Percent Colemanite 99 Figure 21: Results of the Isothermal Experiments for Colemanite 100 Figure 22: TG Data f o r 100 Percent Sodium Carbonate . . . 102 Figure 23: TG Data for 20 Percent Colemanite 103 Figure 24: TG Data for 30 Percent Colemanite 104 Figure 25: TG Data for 40 Percent Colemanite 105 Figure 26: TG Data for 50 Percent Colemanite 106 Figure 27: TG Data for 60 Percent Colemanite 107 Figure 28: TG Data for 70 Percent Colemanite 108 Figure 29: TG Data for 80 Percent Colemanite 109 Figure 30: TG Data for 100 Percent Colemanite 112 Figure 31: TG Results for 100 Percent Boron T r i o x i d e . . . 113 Figure 32: TG Results f o r 100 Percent Calcium Borate . . . 114 Figure 33: Comparison of TG Results f or Colemanite, Boron T r i o x i d e and Calcium Borate 115 Figure 34: Recalculated Data f o r 20 Percent Colemanite . . 116 Figure 35: Recalculated Data for 30 Percent Colemanite . . 117 Figure 36: Recalculated Data f o r 40 Percent Colemanite . . 118 Figure 37: Recalculated Data for 50 Percent Colemanite . . 119 Figure 38: Recalculated Data for 60 Percent Colemanite . . 120 Figure 39: Plot of - l o g g(a) Values for 60 Percent Colemanite 124 Figure 40:- Comparison of - l o g g(a) Values with - l o g p(x) Values for 60 Percent Colemanite 125 - x i i -Page Figure 41: Best F i t t i n g Models to Experimental Data for 60 Percent Colemanite 126 Figure 42: Comparison of the Model P r e d i c t i o n s with the Experimental Results for 30 Percent Colemanite 129 Figure 43: Comparison of the Model Pre d i c t i o n s with the Experimental Results f o r 40 Percent Colemanite 130 Figure 44: Comparison of the Model Pre d i c t i o n s with the Experimental Results for 50 Percent Colemanite 131 Figure 45: Comparison of the Model Pre d i c t i o n s with the Experimental Results for 60 Percent Colemanite 132 Figure 46: E f f e c t of Colemanite Concentration on the A c t i v a t i o n Energy, El 135 Figure 47: E f f e c t of Colemanite Concentration on the Frequency Factor, z^ 136 Figure 48: Comparison of the Results a f t e r the M o d i f i c a t i o n of the Model for 30 Percent Colemanite . . . . 140 Figure 49: Comparison of the Results a f t e r the M o d i f i c a t i o n of the Model for 40 Percent Colemanite . . . . 141 Figure 50: Comparison of the Results a f t e r the M o d i f i c a t i o n of the Model for 50 Percent Colemanite . . . . 142 Figure 51: Comparison of the Results a f t e r the M o d i f i c a t i o n of the Model f o r 60 Percent Colemanite . . . . 143 Figure 52: Comparison of the Model with the Experimental Results for Second Reaction f o r 20 Percent Colemanite 145 Figure 53: Comparison of the Model for the Second Reaction with the Experimental Results for 30 Percent Colemanite 146 Figure 54: Comparison of the Model for the Second Reaction with the Experimental Results for 40 Percent Colemanite 147 Figure 55: Comparison of the Model for the Second Reaction with the Experimental Results for 50 Percent Colemanite 148 Figure 56: E f f e c t of Colemanite Concentration on the A c t i v a t i o n Energy, E 2 151 - x i i i -Page Figure 57: E f f e c t of Colemanite Concentration on the Frequency Factor, z 2 152 Figure 58: Comparison of the Model with the Results of Isothermal Experiments f o r 30 Percent Colemanite 158 Figure 59: Comparison of the Model with the Results of Isothermal Experiments for 40 Percent Colemanite 159 Figure 60: Comparison of the Model with the Results of Isothermal Experiments for 50 Percent Colemanite 160 Figure 61: TG Results f o r the F i r s t Recycle 163 Figure 62: TG Results for the Second Recycle 164 Figure 63: TG Results for the T h i r d Recycle 165 Figure 64: Schematic of Proposed Process 168 - x i v -ACKNOWLEDGEMENTS F i r s t of a l l I wish to express my deepest gratitude to Prof. Kenneth L. Pinder f o r his invaluable supervision, constant encouragement, endless understanding and warm f r i e n d s h i p . Many thanks are due to the members of the department, department's s e c r e t a r i e s ' for t h e i r help and co-operation In every stage of my work, e s p e c i a l l y Marlene Woschee for excel l e n t typing of my t h e s i s . Acknowledgement Is made to the Natural Sciences and Engineering Research Council of Canada and B.C. Science Council for t h e i r f i n a n c i a l support. None of th i s would have been possible without the loving support, encouragement and many valuable suggestions from my husband, Ze k i . -1-1. INTRODUCTION Kraft pulping i s the main pulping method used today. This process uses sodium hydroxide and sodium s u l f i d e as a cooking agent. The former i s converted to sodium carbonate when the a l k a l i n e spent pulping liquors are burned to y i e l d chemicals and heat i n a recovery furnace. Since sodium carbonate i s not s u f f i c i e n t l y a l k a l i n e to pulp wood to an adequate degree i t must consequently be transformed into hydroxide. This process i s c a l l e d c a u s t i c i z a t i o n , and i s conducted with the aid of calcium hydroxide which i s generated i n a lime k i l n . The major disadvantage of the Kraft process i s the cost, complexity and the i n f l e x i b i l i t y of this recovery system. The lime k i l n i s the l a s t major user of f o s s i l f u e l i n a Kraft m i l l and the c a u s t i c i z i n g area i s d i f f i c u l t to maintain In a clean non-polluting state. Autocausticizing i s proposed to replace the conventional c a u s t i c i z i n g and lime k i l n system. This process i s based on the fact that c e r t a i n amphoteric oxides react with sodium carbonate l i b e r a t i n g the a l k a l i bound carbon dioxide from the mixture at high temperatures and forming mixed oxide compounds (smelt) which w i l l give a strong base on di s s o l u t i o n In water. The oxides proposed i n the l i t e r a t u r e as agents for the autocausticizing reaction can be divided into two main groups according to t h e i r behaviour i n the smelt dis s o l v i n g stage. The f i r s t group of compounds consists of chemicals which form a l k a l i n e solutions i n which the amphoteric oxide i s i n a soluble form, so that i t i s carried through the whole cycle of the process, and increase the inorganic load i n the system. In this group of compounds are mainly borates, -2-phosphates, s i l i c a t e s and aluminates (18). The second group of compounds are p r e c i p i t a t e d from the sodium hydroxide solutions during the d i s s o l u t i o n step. Examples of compounds i n this group are titanium dioxide, ilmenite ( F e T i 0 2 ) and i r o n oxide ( F e 2 0 3 ) (18). Titanium dioxide was studied as a c a t a l y s t by K i i s k i l a (20,21). Although i t gave very good c a u s t i c i z i n g e f f i c i e n c y i t didn't appear promising because of the high cost of th i s chemical. A p i l o t plant study was performed using i r o n oxide by A u s t r a l i a n Paper Manufacturers L t d . using a f l u i d i z e d bed reactor, and promising r e s u l t s were reported ( 4 ) . The behaviour of the sodium borates as c a u s t i c i z i n g agents has been studied by J . Janson (8). According to the r e s u l t s of t h i s work, borates seems to be the best agent f o r a u t o c a u s t i c i z i n g r e a c t i o n s . Although sodium borates were studied as an a u t o c a u s t i c i z -ing agent there has been no l i t e r a t u r e a v a i l a b l e on the chemistry and k i n e t i c s of the process which uses calcium borate (colemanite) as an a u t o c a u s t i c i z i n g agent. Colemanite i s a cheap unrefined rock which i s found i n C a l i f o r n i a and Turkey. Since i t i s p a r t i a l l y soluble, i t has c e r t a i n advantages over sodium borates and i t i s expected to be compatible with the other a u t o c a u s t i c i z i n g agents studied p r e v i o u s l y . -3-2. LITERATURE REVIEW 2.1 Kraft Pulping The Kraft process i s the most widely used method of pulping i n North America and i n the world. The following f i g u r e shows this process diagrammatically. The cooking l i q u o r (white l i q u o r ) which c o n s i s t s of sodium hydroxide and sodium s u l f i d e i s sent to a digester where d e l i g n i f i c a t i o n of the wood takes place according to the reactions Na 2S + H 20 NaSH(aq) + NaOH (2.1) NaOH(aq) + NaSH(aq) + HOrg * NaSH(aq) + NaOrg(aq) (2.2) where HOrg stands for the a l k a l i consuming wood components. In the recovery c y c l e , spent cooking chemicals (black l i q u o r ) , a mixture of many sodium-sulfur-carbon compounds are converted to sodium sulphide (Na 2S) and sodium carbonate (Na 2C0 3) i n the recovery furnace following the reactions NaOrg + x0 2 ->• 1/2 Na 2C0 3 + yH 20 + zC0 2 (2.3) and NaSH + NaOrg + x0 2 * Na 2S + yH 20 + zC0 2 (2.4) The product (smelt) i s dissolved i n water to give the so c a l l e d green l i q u o r . The remainder of the cycle i s concerned with converting Na 2C0 3 to sodium hydroxide which w i l l be reused i n the pulping C a O Recovery Boiler E Dissolving Tank $ S laker J 7 weak wash White Liquor Clarifier White Liquor (NaOH+Na2S) Lime Mud Washer Figure 1: Schematic diagram of Kraft Process. -5-process. This c a u s t i c i z a t i o n process uses calcium hydroxide which i s obtained by c a l c i n i n g calcium carbonate i n a lime k i l n v i a the re a c t i o n CaC0 3 -»• CaO + C0 2 (2.5) The f i n a l stage of the recovery takes place i n the slaker where soluble sodium hydroxide i s formed v i a the o v e r a l l r e a c t i o n CaO + H 20 + Na 2C0 3 -»• 2NaOH + CaC0 3 (2.6) The i n s o l u b l e calcium carbonate i s separated from the s o l u t i o n and i s sent back to the lime k i l n . 2 . 1 . 1 Problems of Kraft Recovery System. Although the Kraft process has found worldwide use i n pulping there are some problems e s p e c i a l l y associated with the present recovery system. The K r a f t Recovery Process i s c a p i t a l i n t e n s i v e , and i t i s often d i f f i c u l t to get an adequate return on th i s investment. The c a p i t a l cost structure (18) of a Kraft pulp m i l l i s given i n Table 1. The share of chemical recovery i n the departmental c a p i t a l cost d i s t r i b u t i o n i s about 27.5% and the machinery costs are about 48% of the t o t a l investment (18). I t Is also seen from t h i s table that the lime k i l n and c a u s t i c i z i n g make up 20% of the t o t a l investment of the recovery system. -6-Table 1: C a p i t a l cost structure of a new Kraft pulp m i l l . (18) T o t a l c a p i t a l cost d i s t r i b u t i o n (%) Department c a p i t a l d i s t r i b u t i o n (%) cost C a p i t a l investment cost d i s t r i b u t i o n of recovery (%) Ref. Ehrnrooth (1) Ref. Harris (25) Ref. K i i s k i l a (23) B u i l d i n g 18 Wood preparation 6.2 Recovery furnace 60 Machinery 48 Pulping 16.3 Evaporation 20 Piping 8 Bleaching 11.8 Lime k i l n 16 E l e c t r i f i c a t i o n 9 Drying and b a l i n g 15.6 C a u s t i c i z i n g 4 Instrumentation 4 Chemical recovery 27.5 Project administration 13 E f f l u e n t treatment Power generation 5.8 16.8 T o t a l 100 100 100 -7-The net amount of usable energy obtained from the organic substances i n the black l i q u o r by burning i n the recovery b o i l e r i s low. At present, less than 40% of the f u e l input to the recovery process i s a v a i l a b l e as steam or power outside the recovery process i t s e l f (6). Much of the energy p o t e n t i a l l y a v a i l a b l e i s now used for evaporating water. In a d d i t i o n a s u b s t a n t i a l amount of f u e l , u s u a l l y f o s s i l f u e l s , i s burned i n the lime k i l n . A modern f u e l e f f i c i e n t k i l n requires 8 x 10 6 Btu/Ton of product. As the cost of energy continues to increase, the p o t e n t i a l f o r a s i m p l i f i e d recovery systems i s i n c r e a s i n g . Environmental pressures have also had a major impact on recovery technology. Odors which are the largest s i n g l e environmental problem of the Kraft Recovery Process are inherent i n the process i f s u l f i d e i s used for pulping, due to the very low odor thresholds of the compounds involved. Sulfur dioxide emissions can also be a problem i n some areas. There are some p o t e n t i a l safety problems i n the present Kraft recovery technology. The most pervasive i s the p o t e n t i a l for smelt-water explosions when water comes i n contact with molten smelt. Another p o t e n t i a l hazard involves the c o l l e c t i o n and i n c i n e r a t i o n process for odorous gases, since these are tox i c and can form explosive mixtures with a i r . Another disadvantage of the present recovery system i s Its low c a u s t i c i z i n g e f f i c i e n c y , r e s u l t i n g i n low sodium hydroxide concentrations i n the white l i q u o r . As a r e s u l t of incomplete c a u s t i c i z i n g about 15% of the a l k a l i c i r c u l a t e s as sodium carbonate -8-through the whole pulping and chemical recovery system as a dead load. Since the sodium hydroxide concentration i n the white l i q u o r i s l i m i t e d , because of i t s influence on the c a u s t i c i z i n g e q u i l i b r i u m , i t also influences the t o t a l evaporation demand on a m i l l (13). The status of current Kraft recovery technology might be characterized as "mature" but c e r t a i n l y not stagnant. None of the problems of the present technology are severe enough to render i t obsolete. Rather, they represent opportunities for further improvement. There are two d i r e c t i o n s that evolving K r a f t recovery technology might take, continued improvement of the e x i s t i n g technology and the development of a l t e r n a t i v e processes. 2 . 1 . 2 Alternatives to Conventional Kraft Pulping. A number of new chemical recovery methods have been patented and published i n recent years. These new methods can be divided, according to t h e i r p r i n c i p a l aims, i n t o two main groups (18); 1. The methods intended to replace the conventional recovery furnace and, as f a r as p o s s i b l e , eliminate the smelt explosion danger. Examples of these methods are wet combustion (18), f l u l d i z e d bed (4), hydropyrolysis (18) and the SCA B i l l e r u d (18) methods. 2. The methods intended to replace the conventional wet c a u s t i c i z i n g and lime reburning system. The drawbacks of wet c a u s t i c i z i n g could be avoided by performing the c a u s t i c i z i n g i n a dry state so that the smelt would be decarbonized by adding an a u x i l i a r y compound to the smelt or by using an unconventional a l k a l i i n pulping. These methods are cal l e d autocausticizing and w i l l be discussed i n th following section. The a i r and water p o l l u t i o n caused by sulfur compounds has led to the development of non-sulfur pulping methods. The most promising non-sulfur pulping method seems to be two-stage soda-oxygen pulping (18). The l a t e s t results on the use of anthraquinone type compounds (18) i n soda pulping suggest new and in t e r e s t i n g p o s s i b i l i t i e s for modifying the conventional a l k a l i n e pulping methods. However the changeover from Kraft pulping to a new pulping system must be motivated not only environmentally but also economically. So most of the present research i s concentrated on finding the autocausticizing agent which w i l l reduce considerably the cost of the process. 2.2 Aatocau8tlcizing Processes Autocausticizing i s a new method to regenerate sodium hydroxid or another strong base from the sodium carbonate and seems to be the most promising a l t e r n a t i v e for the conventional Kraft Recovery System. Autocausticizing i s defined as the self-induced expulsion of the carbon dioxide bound i n the smelt or i n ash formed during the burning of spent l i q u o r , without the use of c a u s t i c i z i n g chemicals such as calcium oxide. This method depends on the fact that c e r t a i n amphoteric oxides react with sodium carbonate, l i b e r a t i n g the a l k a l i bound carbond dioxide from the mixture at high temperatures, and form mixed oxide compounds. The p r i n c i p l e of the autocausticizing method can be i l l u s t r a t e d by the following general reaction -10-a Na 2C0 3 + b M x0 y -> a Na 20 . b M^ O + a C0 2 t (2.7) A u t o c a u s t i c i z i n g processes are divided i n t o two main groups depending on the behaviour of the amphoteric oxide used during the smelt d i s s o l u t i o n step. This step can be represented by the following r e a c t i o n a Na,0 . b M 0 + a H 90 -»• 2a NaOH + b M 0 (2.8) * x y * x y i f the amphoteric oxide i s i n s o l u b l e , i t p r e c i p i t a t e s and can e a s i l y be separated from the white l i q u o r and recycled without entering i n t o the d i g e s t i o n loop as shown i n Figure 2. This i s c a l l e d smelt c a u s t i c i z i n g or the DARS method. If the amphoteric oxide i s soluble, i t c i r c u l a t e s through the whole pulping c y c l e . So i t should not only be a u t o c a u s t i c i z i b l e under reasonable conditions, but also be s u f f i c i e n t l y a l k a l i n e to function as a d e l i g n i f i c a t i o n agent. The research on both types of a u t o c a u s t i c i z i n g methods was s t a r t e d i n 1974 i n F i n l a n d . Since most of the work i s patented, not much i s known about the process. However, during the past two years, p i l o t plant work has been started; one study by J . Janson (9) i n F i n l a n d and the other by an A u s t r a l i a n company under the supervision of G. Covey ( 4 ) . A plant i s to go on stream using a u t o c a u s t i c i z a t i o n i n 1984 at the Kotka M i l l , Finland. Figure 2 shows the comparison of an a u t o c a u s t i c i z i n g method with the K r a f t recovery process. The advantages and disadvantages of a u t o c a u s t i c i z i n g w i l l be discussed i n d e t a i l i n s e c t i o n 2.2.3 for the s p e c i f i c a u t o c a u s t i c i z i n g agents. -11-o o z X o o z Combust ion M X O y Dissolving Separat ion NaOH+M x O y Lime K i l n e Fuel CO o u o Z Kraft Process Autocausticizing Figure 2: Comparison of a u t o c a u s t i c i z i n g with conventional c a u s t i c i z i n g . -12-2.2.1 Decomposition of Sodium Carbonate Without an Autocausticizing  Agent. Sodium carbonate i s thermally unstable above i t s melting point and can be slowly decomposed at low carbon dioxide p a r t i a l pressure even without adding amphoteric oxides (23) , according to the r e a c t i o n Na 2 C0 3 — » Na 2 0 + C 0 2 (2 .9) However, t h i s r e a c t i o n i s hindered by the high p a r t i a l pressures of carbon dioxide i n the recovery furnace. Besides, sodium oxide i s v o l a t i l i z e d from the smelt i f there i s no s t a b i l i z i n g a u x i l i a r y compound present i n the smelt (23) . Thermal decomposition of sodium carbonate by i t s e l f w i l l be studied i n section 6.2 and i l l u s t r a t e d i n Figure (22) . This r e a c t i o n most l i k e l y doesn't take place below 8 5 0 ° C and i t s rate i s very slow even at 1 0 0 0 ° C . 2.2.2 Autocausticizing Reactions. A u t o c a u s t i c i z i n g reactions w i l l be examined i n two p a r t s . 1. Decomposition 2. Hydrolysis The decomposition r e a c t i o n takes place at high temperatures. The optimum temperature for the re a c t i o n i s strongly dependent on the type of agent choosen. This r e a c t i o n i s generally i l l u s t r a t e d as a Na 0C0o + b M 0 + a Na,0 . b K 0 + a CO, t (2.10) l A X y l x y I -13-Th e c a u s t i c i z i n g agent which i s an amphoteric oxide, e i t h e r soluble or i n s o l u b l e , acts i n a two-fold manner i n the decarbonization: ( i ) It accelerates the decomposition of sodium carbonate. ( i i ) I t s t a b i l i z e s the sodium oxide i n the smelt. There are many factors to be analyzed, depending on the choice of the a u t o c a u s t i c i z i n g agent, whether i t i s soluble or Insoluble. If i t i s soluble i t should e i t h e r replace the sodium hydroxide and act as a cooking agent or c i r c u l a t e through the system as a dead load. In t h i s case i t s e f f e c t s on the e f f i c i e n c y of the d e l i g n i f i c a t i o n of the wood during cooking and the properties of the pulp must be considered. For both types of agents the e f f e c t of the following f a c t o r s which e x i s t In the drying and burning zones of Kraft furnace should be analyzed, as w e l l as the rea c t i o n i t s e l f . 1. E f f e c t of presence of s u l f u r on the r e a c t i o n . 2. E f f e c t of carbon dioxide pressure. 3. E f f e c t of the presence of organics. The experiments which were performed by J . Janson (9) and K i i s k i l a (23) showed that the presence of s u l f u r and the organics did not have a s i g n i f i c a n t e f f e c t on the r e a c t i o n . However i t was found that i n the absence of gaseous C0 2, the decarbonization of the smelt can be more e f f e c t i v e . The h y d r o l y s i s step i s more important i n the cases where in s o l u b l e amphoteric oxides are used. The studies on the h y d r o l y s i s of c a u s t i c i z e d smelt showed that the mixed oxides formed as product of the a u t o c a u s t i c i z i n g r e a c t i o n can be e f f e c t i v e l y decomposed to -14-sodium hydroxide at a s u f f i c i e n t l y high d i s s o l v i n g temperature (90°C) with low washing losses (23). The i n s o l u b l e f r a c t i o n of sodium oxide influences the c a u s t i c i z i n g e f f i c i e n c y a f t e r several repeated runs. This was also studied by K i i s k i l a (23) using d i f f e r e n t kinds of a u t o c a u s t i c i z i n g agents. 2.2.3 Agents Proposed for Autocausticizing. The agents which are proposed i n the l i t e r a t u r e f o r a u t o c a u s t i c i z i n g reactions are l i s t e d i n Table 2, i n c l u d i n g the desired r e a c t i o n products. These are divided into two main groups according to t h e i r behaviour i n the smelt d i s s o l v i n g step. The oxides l i s t e d i n group one are chemicals which form io n i z e d a l k a l i n e s o l u t i o n s i n which the amphoteric oxide i s at l e a s t p a r t i a l l y s o l u b l e . The compounds i n the second group are i n s o l u b l e and can be p r e c i p i t a t e d from the sodium hydroxide s o l u t i o n s formed i n the d i s s o l v i n g stage. 2.2.3.1 Titanium Dioxide. Titanium dioxide i s the compound which i s found to be most promising among the group two compounds, according to the l i t e r a t u r e (18). I t i s a stable but very expensive chemical. I t i s p r a c t i c a l l y i n s o l u b l e i n a l k a l i n e solutions and can be e a s i l y separated from the white l i q u o r formed. According to the patent l i t e r a t u r e (19), the process i s based on the formation of sodium metatitanate i n mixtures of sodium carbonate and titanium dioxide and i s represented by the following chemical formulas -15-Table 2: Proposed a u t o c a u s t i c i z i n g agents. Mx°y N a2a Mbx°a+by Group (1) B2°3 Na^B^g, NaB0 2 P2°5 Na 3P0 1 + S i 0 2 N a 2 S i 0 3 A 1 2 0 3 NaA10 2 Group (2) T i 0 2 N a 2 T i 0 3 FeT10 3 2 Na 20:Fe0 3:Ti0 2 F e 2 0 3 NaFe0 2 -16-Na 2C0 3 + T i 0 2 -»• Na 20 . T i 0 2 + C0 2 (2.11) reuse Na 20 . T i 0 2 + H 20 (2,12) The carbon dioxide bound i n the a l k a l i during black l i q u o r combustion i s l i b e r a t e d from the smelt when the mixed oxide i s formed. Because of the weak coordination of the a l k a l i n e oxide with the titanium, the compound decomposes when i t i s dis s o l v e d i n water. Decarbonization of sodium carbonate by titanium dioxide was studied by Er k k i K i i s k i l a (18,20,21). The thermogravimetric curves f o r the mixture of sodium carbonate and titanium dioxide at a molar r a t i o of 1.1:1.0 showed that the decomposition of sodium carbonate caused by titanium dioxide s t a r t s In the s o l i d phase at 500°C (19), but t h i s r e a c t i o n i s very slow u n t i l the melting point of sodium carbonate i s reached. Above 850°C the rate of the reac t i o n between melted sodium carbonate and s o l i d titanium dioxide i s fa s t i f the molar r a t i o of Na 2 0 / T i 0 2 of the re a c t i o n product i s 1.0 (19). The rap i d decomposition of sodium carbonate at 850-950°C i s due to the formation of 4Na 20.5Ti0 2 which reacts further with sodium carbonate to y i e l d Na 2O.TI0 2 at low C0 2 p a r t i a l pressure. According to the f i n a l weight loss of samples at 980°C, 79% of the C0 2 was removed from the mixture f o r a sodium carbonate to titanium dioxide r a t i o of 1.0 (19). Some isothermal experiments were also c a r r i e d out. I t was found that complete decomposition of sodium carbonate i s possible by lengthening the re a c t i o n time, provided that the temperature Is high enough (1100°C) (19) ( F i g . 3). It was also found that the presence of titanium dioxide decreases the sodium losses i n the f l u e gases. V o l a t i l i z a t i o n of the Na 20 becomes s i g n i f i c a n t only above 1100°C (20). 3 0 6 0 9 0 120 T i m e ( m i n ) Figure 3: F r a c t i o n of the Decomposed Sodium Carbonate as a Function of the Reaction Time with the use of T i 0 2 Studies on the hydro l y s i s of the c a u s t i c i z e d smelt were a l s o made and i t was found that the degree of sodium hydroxide formation from bound sodium oxide (Na 20) was dependent on the Na 20/Ti0 2 r a t i o of the t i t a n a t e s i n the smelt. The degree of hy d r o l y s i s decreased with an increase i n the titanium dioxide content of these compounds. The sodium hydroxide formed from Na 2O.Ti0 2 corresponded to 65.8% of the -18-t o t a l sodium, which was the highest recovery; compared to the values for the other t i t a n a t e s such as 4Na 20.5Ti0 2, Na 20.3Ti0 2 (20). So i n a l l cases studied, the hy d r o l y s i s was not complete, and the insolu b l e titanium dioxide residue contained about 0.33 moles of sodium oxide per mole of titanium dioxide (20). For t h i s reason the sodium hydroxide y i e l d i s dependent not only on the degree of sodium carbonate decomposition but also on the Na 20/Ti0 2 r a t i o of the smelt. The e f f e c t of time and temperature on the hy d r o l y s i s of the smelt was studied as well as the e f f e c t of the amount of water used i n the e x t r a c t i o n (20). The rate of hy d r o l y s i s increased when the temperature was rai s e d from 30°C to 60°C, but a further r i s e i n temperature did not improve the e f f i c i e n c y s i g n i f i c a n t l y . Experiments were performed at 90° with the retention time of three hours and i t was found that even a f t e r three hours the i n s o l u b l e residue s t i l l contained i n s o l u b l e Na 20 i n the hydrolyzed compounds (20). This e v i d e n t l y reduces the e f f i c i e n c y of titanium dioxide i n c a u s t i c i z i n g . •Because t h i s undissolved residue i s nearly constant per mole of titanium dioxide, i t causes a constant reduction i n the c a u s t i c i z i n g e f f i c i e n c y when titanium dioxide i s reused. On the whole, i t seems that sodium carbonate can be e f f i c i e n t l y c a u s t i c i z e d by using titanium dioxide. Although i t i s t h e o r e t i c a l l y s u i t a b l e for t h i s purpose, i t i s too expensive to use on a commercial s c a l e . For t h i s reason i n v e s t i g a t i o n s were concentrated on f i n d i n g cheaper chemicals l i k e F e 2 0 3 and i l m e n i t e . -19-2.2.3.2 F e r r i c Oxide. The use of f e r r i c oxide for the c a u s t i c i z a t i o n of sodium carbonate has been studied by K i i s k i l a (21). The chemistry can be represented as follows Na 2C0 3 + F e 2 0 3 2NaFe0 2 + C0 2 t (2.13) 2NaFe0 2 + H 20 -> 2NaOH + F e 2 0 3 4- (2.14) Experiments were performed at 900°C and 1000°C and i t was found that i t i s possible to obtain a c a u s t i c i z i n g e f f i c i e n c y as high as 95 percent. The chemical load i s lower than i n the titanium dioxide case due to the more complete h y d r o l y s i s of sodium f e r r i t e s which r e s u l t s i n more e f f e c t i v e c a u s t i c i z i n g of the smelt to sodium hydroxide. Use of f e r r i c oxide has the disadvantage that the f e r r i c oxide suspended i n the aqueous s o l u t i o n Is not e a s i l y p r e c i p i t a t e d and i s hard to separate. In a d d i t i o n to t h i s , i t s use i n Kraft recovery i s r e s t r i c t e d because of the reduction of f e r r i c oxide and Its reactions with sodium s u l f i d e . However, It could be applied to the soda or soda-oxygen processes which are s u l f u r f r e e . The work on the u t i l i z a t i o n of f e r r i c oxide as an a u t o c a u s t i c i z i n g agent gained importance during 1977 and since then work has been done to commercialize i t . A process which uses a f l u i d i z e d bed type furnace was developed by G. Covey ( 4 ) . This process has been operated since e a r l y 1980 at a p i l o t plant at the Maryvale M i l l of A u s t r a l i a n Paper Manufacturers. The s i m p l i f i e d flow diagram of the process i s shown i n Figure 4. The p i l o t plant operation has been reported to be s u c c e s s f u l (4). -20-NaOH Y -Ul Figure 4: S i m p l i f i e d flow sheet of the DARS research plant ( 4 ) . 1. Digester 2. Batch d i f f u s e r s 3. Live-bottom blow tank 4. Evaporator 5. F l u i d i z e d bed 6. F e r r i c oxide s i l o 7. Main cyclone 8. Venturi scrubber 9. Product cooler 10. Cooler cyclone 11. F e r r i t e leacher 12. F i l t e r -21-2 . 2 . 3 . 3 I l m e n l t e . Ilmenite i s a double oxide which consists of iron (II) oxide and titanium dioxide. Therefore both components can be expected to react with molten sodium carbonate, i f iron (II) oxide i s oxidized to iron ( I I I ) oxide. Table 3 shows the composition of this ore. Laboratory experiments showed that sodium carbonate can be decomposed by adding ilmenite to the smelt. The titanium dioxide part of the ilmenite reacted to sodium titanates while the ferrous iron reacted to sodium f e r r i t e s a f t e r being oxidized to f e r r i c i r o n . The reaction was found to be most e f f e c t i v e at 940°C (22). The ca u s t i c i z i n g e f f i c i e n c y was found to be lower than that for titanium dioxide and f e r r i c oxide. This i s due to the fact that the ilmenite l a t t i c e i s only p a r t i a l l y broken i n the absence of oxygen. The hydrolysis of the smelt was not complete due to the incomplete hydrolysis of sodium titanates (31). In addition to these problems high v o l a t i l i z a t i o n losses of sodium oxide were reported with ilmenite (22). 2 . 2 . 3 . 4 S i l i c a t e s , A l u m i n a t e s and P h o s p h a t e s . These compounds are among those c l a s s i f i e d as the f i r s t group of autocausticizing agents which are soluble i n a l k a l i n e solutions and c i r c u l a t e throughout the process. They must not only be aut o c a u s t i c i -z i b l e but also must be strongly a l k a l i n e In order to function as d e l i g n i f i c a t i o n agents. Among these, phosphates and aluminates were preferred because of thei r high melting point at 1340°C and 1150°C respectively. The reaction products were also s o l i d . This has the -22-Table 3: Composition of ilmenite (17). Composition Titanium ore (Ilmenite) weight % Titanium ore a f t e r 10 times repeated use weight % T i 0 2 52.2% 53.4% F e 2 0 3 46.8% 46.3% A 1 20 3 0.6% 0.2% S i 0 2 0.1% -Others 0.3% 0.1% -23-advantage of easy handling, transport and easier d i s s o l u t i o n i n water compared to the glassy, slowly d i s s o l v i n g smelts. The problem with the phosphates i s that t h e i r a l k a l i n i t y i s not strong enough to match sodium hydroxide. Therefore i t can not be used i n the normal Kraft process but i t i s s u i t a b l e to be used together with other d e l i g n i f y i n g agents such as oxygen. Aluminates are not s u i t a b l e for this r e a c t i o n because sodium aluminates are rather unstable and aluminum hydroxide p r e c i p i t a t e s even i n strongly a l k a l i n e solutions and can cause s c a l i n g (13). Besides, the temperature of the a u t o c a u s t i c i z i n g r e a c t i o n was found to be 1150°C which Is much higher than the one found for a l l other agents. S i l i c a t e s can also act as a decarbonizing agent. However i n the case of s i l i c a , when the compound oxide thus formed i s d i s s o l v e d i n water, the s i l i c a i s p a r t l y d i s s o l v e d i n the form of sodium s i l i c a t e into the s o l u t i o n of c a u s t i c soda, so that when a regenerated white l i q u o r i s used for pulp d i g e s t i o n , s i l i c a t e compounds are deposited on the inner surfaces of the digester and heat exchangers thus causing scale trouble. 2.2.3.5 Borates. Borates are one of the a l t e r n a t i v e s which may be used i n a u t o c a u s t i c i z i n g processes. It has been found that borate compounds f u l f i l l the requirements as regard both the a l k a l i n i t y during cooking and the desired r e a c t i o n during regeneration. Research has been done by the F i n n i s h Pulp and Paper Research I n s t i t u t e i n H e l s i n k i and by J . Janson, and very promising r e s u l t s i n c l u d i n g some p i l o t -24-plant data have been reported on the use of sodium borates. Laboratory experiments were performed using mixtures of monosodium borate and sodium carbonate at a molar r a t i o of Na:B of 2.0. In t h i s case the following reactions can be expected. 2NaB(0H)lt -»• 2NaB0 2 + 4H 20 (2.15) 2NaB02 + Na 2C0 3 -»• Na 4B 20 5 + C0 2 (2.16) In the recovery furnace monosodium borate i s dehydrated to sodium metaborate which reacts with the carbonate with the expulsion of carbon dioxide, to form tetrasodium diborate. On d i s s o l u t i o n i n water the tetrasodium diborate y i e l d s sodium borate which w i l l take the place of sodium hydroxide as a cooking a l k a l i . Table 4 summarizes the d i f f e r e n c e s between the chemical systems i n conventional and borate-based pulping. These laboratory experiments showed that about two hours at 875°C was needed to give an 80 percent removal of C0 2 (10). This i s shown i n Figure 5. The data f i t t e d the k i n e t i c s of a second order r e a c t i o n better than f i r s t and t h i r d order r e a c t i o n . The a c t i v a t i o n energy was found to be 148 kJ/mol and the frequency f a c t o r was found to be -0.304 f o r these s p e c i f i c conditions (10). Seventy percent of the weight loss occurred before l e v e l l i n g o ff at 800-1000°C (10). In the case of the borate reactions . the r a t i o of sodium to boron i s a very important parameter to be considered. The a l k a l i n i t y of borates and thus t h e i r d e l i g n i f y i n g a b i l i t y i n water s o l u t i o n increases with i n c r e a s i n g r a t i o of Na:B. On the other hand t h e i r -25-Table 4: Main constituents of cooking chemical system (9). Chemical system White l i q u o r Black l i q u o r Smelt Green l i q u o r Normal NaOH NaOrg Na 2C0 3 Na 2C0 3 (Na 2S) (NaSH) (Na 2S) (Na 2S) Borate-based Na 2HB0 3 NaOrg N a „ B 2 0 5 Na 2HB0 3 (Na 2S) (NaSH) (Na 2S) (Na 2S) NaH 2B0 3 - 2 6-REMAININC C O , FRACTION OF ORIGINAL 1.2 TIME AT MAX. TEMP., h Figure 5: Au t o c a u s t i c i z i n g r e a c t i o n i n a i r : 2 NaH 2B0 3 + Na 2C0 3 -»• Na 1 +B 20 5 + 2 H 20 + C0 2 (8) -27-a c i d i t y decreases which would r e s u l t In a decrease i n the e f f i c i e n c y of carbon dioxide expulsion from the carbonate. Various Na:B r a t i o s were t r i e d by J . Janson and the optimum r a t i o was reported as 2.0 (10) for the Kraft process. Figure 6 shows the areas of a p p l i c a t i o n f o r d i f f e r e n t r a t i o s of sodium to borate. Experiments have also been made on the pulping c h a r a c t e r i s t i c s of sodium borates. I t was found that one mole of sodium hydroxide can be replaced by one mole of disodium borate without e s s e n t i a l l y changing any other c o n d i t i ons (11). There was very l i t t l e d i f f e r e n c e i n the pulp y i e l d s from hydroxide and borate based pulping, nor were there any di f f e r e n c e s i n pulp p r o p e r t i e s . Black l i q u o r from the borate cooks contained r e l a t i v e l y more inorganic matter and therefore had a correspondingly lower heat value on a dry b a s i s . Thus i t w i l l be necessary to burn a u x i l i a r y f u e l i n the recovery furnace. According to the r e s u l t s of a 9 hour m i l l t r i a l i t was found that the melting point of the smelt was lowered by roughly 50°C. This would be advantageous from the standpoint of smelt d i s s o l u t i o n with a lowered r i s k of explosion. It was also found that the amount of f l y ash was reduced by hal f when the borate-based l i q u o r s were used. Among the disadvantages of using borate-based l i q u o r s are: the probable decrease i n evaporator performance, probable d i f f i c u l t i e s during burning i n the recovery furnace due to the increased v i s c o s i t y of the borate l i q u o r which would cause a larger drop s i z e when sprayed i n t o the furnace, and i n f e r i o r heat economy due to the higher inorganic content of the black l i q u o r . -28-14 pH Slow Fast oxygen d e l i g n i f i c a t i o n oxygen d e l i g n i f i c a t i o n Pine k r a f t B irch k r a f t Figure 6 : Areas of a p p l i c a t i o n f o r d i f f e r e n t kinds of a u t o c a u s t i c i z a b l e a l k a l i ( 9 ) . -29-J . Janson has also performed some c a l c u l a t i o n s to evaluate the economic aspects of using borates i n Kraft pulping. Preliminary c a l c u l a t i o n s were made on the changes i n investment costs and operation costs of a new Kraft m i l l (15) assuming a pulp production of 600 ton/day. Table 5 shows his conclusions. The investment cost w i l l be lower when a u t o c a u s t i c i z i n g i s employed, with the la r g e s t d i f f e r e n c e being i n the lime k i l n c osts. Regarding the operation costs, i t was noted that the make-up chemicals are more expensive i n the borate a l t e r n a t i v e while somewhat les s manpower w i l l be needed and energy w i l l be saved. Table 6 shows the changes i n consumption and cost of energy by a borate-based system. 2.2.3.6 Colemanite (calcium borates). Borate deposits are formed when one or more of the hydrated borates of sodium, calcium and magnesium are c r y s t a l l i z e d by the evaporation and probable cooling of surface water i n a desert b a s i n . Colemanite i s one type of borate deposit which can be represented by the formula 2Ca0.3B 20 3.5H 20. The main colemanite deposits of the world are located i n Southeastern C a l i f o r n i a , Southern Nevada and Turkey. Colemanite has been c r y s t a l l i z e d from aqueous s o l u t i o n as have other forms of c r y s t a l l i n e calcium borate hydrates. Often the p r e c i p i t a t e f i r s t formed i s amorphous and c r y s t a l l i z e s a f t e r standing i n contact with the mother l i q u o r f o r several days (25). Some studies have shown that the c r y s t a l structure of the borate ions of colemanite can be represented as -30-Table 5: Change i n costs by choice of borate-based system (600 t/d) (15). Investment: -30 . 10 6 FIM* (-7.5 . 10 6 USD) Operation: Energy: -23 FIM ptp Chemicals: 14 FIM ptp Labour: -1 FIM ptp T o t a l change: -10 FIM ptp or: -2.5 USD ptp *FIM: F i n i s h money Table 6: Consumption and costs of energy (15). Change i n energy costs by choice of a borate-based system (600 t/d) P r i c e s : O i l : HP steam: LP steam: E l . power: 750 FIM/t = 20 FIM/GJ 24 FIM/GJ 12 FIM/GJ 120 FIM/MWh Change i n consumption/generation ptp (per ton dry pulp): O i l Heat E l . power MJ FIM MJ FIM kWh FIM Consumption Evaporation Combustion C a u s t i c i z i n g Lime reburning Generation HP steam Net change 1400 -2000 -600 -11.3 -600 -11.3 -380 -100 -12 - 8 -480 -5.8 -20 130 3.1 -610 -8.9 -20 -2.4 -2.4 T o t a l change i n energy costs: -22.6 FIM or: - 5.7 USD ptp ptp - 3 1 -These ions have been polymerized by the e l i m i n a t i o n of water between them to form long chains at high temperatures to form colemanite (25). Since colemanite comes from n a t u r a l rocks i t may contain impurities such as s i l i c a t e s , f e r r i c oxides and aluminates. Pure colemanite contains 50.8 percent b o r i c oxide ( B 2 0 3 ) (25). Although i t i s reported to be i n s o l u b l e , i t was found to be soluble to a c e r t a i n degree due to the Impurities i n i t (26). The composition and ph y s i c a l properties of Turkish colemanite determined by the American Borate Company i s shown i n Appendix I I I . An examination of the thermal c h a r a c t e r i s t i c s of colemanite i n d i c a t e s that the thermal changes f a l l i n t o four groups (25). a) i r r e v e r s i b l e endothermic peaks associated with dehydration b) r e v e r s i b l e endothermic peaks associated with polymorphic t r a n s i t i o n s c) r e v e r s i b l e endothermic e f f e c t s associated with melting d) i r r e v e r s i b l e exothermic e f f e c t s associated with s o l i d - s t a t e transformations. -32-Table 7 shows the temperatures associated with each of the thermal changes i n colemanite. Table 7: Thermal c h a r a c t e r i s t i c s of colemanite ( 3 ) . Mineral Ei idothermj .c Peaks Exothermic Peaks Colemanite 1 2 3 4 1 2 320-380 380-400 410 - 710-770 -The idea of using colemanite as an a u t o c a u s t i c i z i n g agent i s very recent and there i s no l i t e r a t u r e a v a i l a b l e on t h i s subject. The r e s u l t s reported by J . Janson on the a u t o c a u s t i c i z i n g e f f e c t of sodium borates i n d i c a t e d that colemanite which i s an i n s o l u b l e borate compound, might act In the same manner. If i t would be possible to use colemanite as an a u t o c a u s t i c i z i n g agent, the disadvantages r e s u l t i n g from the soluble character of the sodium borates such as the increased inorganic load, complexities due to the change of conventional cooking chemical etc. would be eliminated or reduced. Since i t Is only p a r t i a l l y soluble the majority can be recycled without passing throughout the pulping.system. Besides t h i s , colemanite i s a cheap chemical which costs 21 cents/kg, compared to -33-sodium borates at $1.20/kg. This would make a considerable difference from the economic f e a s i b i l i t y point of view of the process i f equal quantities are used. It was for this reason that research on the autocausticizing properties of colemanite was undertaken as the subject of this thesis. 2.3 Study of Reaction Kinetics by Thermogravimetry. Thermogravimetry can be used to study the k i n e t i c s of a chemical reaction and determine the basic k i n e t i c constants such as the rate constant, a c t i v a t i o n energy, order of the reaction and frequency factor. When the k i n e t i c study i s based on the observation of the weight change, two approaches are possible i n p r i n c i p l e , the isothermal and the dynamic heating methods. The isothermal method i s the conventional method for studying the k i n e t i c s of the thermal decomposition of solids and i s based on the determination of the degree of transformation, which i s the f r a c t i o n of material reacted, as a function of time at constant temperature. The dynamic method i s the determination of the degree of transformation as a function of time during a l i n e a r increase of temperature. I d e a l l y , a single thermogram i s equivalent to a very large family of comparable isothermal curves and, as such, constitutes a r i c h source of k i n e t i c data. I t was In 1932 that Skramousky (29) pointed out the advantages of this method. Since the method demands s t r i c t experimental conditions and a high accuracy i n the measurement, development took -34-place only a f t e r 1960 when the equipment reached a s u f f i c i e n t l y high standard (30). Compared with the s t a t i c method, t h i s method has c e r t a i n advantages. I t requires a far smaller number of experimental data because the k i n e t i c values can be determined from a s i n g l e thermogravimetric curve f o r the whole temperature range and one sample s u f f i c e s f o r the whole k i n e t i c a n a l y s i s . This also gives a better i n d i c a t i o n of the state of the sample at any moment with respect to temperature and degree of r e a c t i o n . In the case of isothermal methods the greatest experimental d i f f i c u l t y i s the i n t r o d u c t i o n of the sample i n t o the preheated furnace. Time elapses before the sample a t t a i n s the required temperature, and during t h i s time the re a c t i o n occurs to a c e r t a i n extent. Thus, instead of a correc t value of the weight loss corresponding to the termination of the rea c t i o n , a value i s obtained which i s decreased by an amount corresponding to the reac t i o n which took place before the required temperature was a t t a i n e d . This causes an appreciable amount of error, e s p e c i a l l y i n the case of rapid reactions and can be eliminated with dynamic thermogravimetric methods. However, i n order to obtain dependable r e s u l t s with thermogravimetry i t should be remembered that the measured values such as temperature and the weight change of the sample should be obtained with the maximum pos s i b l e accuracy. The factors e f f e c t i n g the accuracy of obtained k i n e t i c data w i l l be discussed i n the following s e c t i o n . -35-2 . 3 . 1 A c c u r a c y o f T h e r m o g r a v l m e t r l c D a t a . The accuracy of the kinetic data is influenced by the following factors: 1. The accuracy of maintaining under s t r i c t control during the reaction, the linearity of temperature increase, consistency of aerodynamic conditions and composition of the gaseous medium. 2. The accuracy of mathematical evaluation of experimental curves. Maintenance of the predefined conditions can be disturbed by the two important transfer mechanisms which are heat and mass transfer. When the heat transfer rate i s disturbed, non linear temperature Increase occurs (29). Linearity of temperature increase depends on the heat capacity of the furnace, heat inertia of the crucible which depends on i t s weight, heat capacity and thermal conductivity, and most importantly the amount of sample and the heating rate. The amount of sample Influences the enthalpy change during the reaction in the sample and is able to slow down (or speed up) the temperature increase with respect to the original programme (29). Large amounts of sample also cause temperature gradients within the sample and appreciable differences between the temperature of the sample and that of the sample holder. If the heating rate is chosen as small as possible the above stated factors might be removed. The proper heating rate should be chosen not only for this purpose but also considering i t s influence on the temperature range over which the reaction w i l l be accomplished. There is a chance of missing a fast -36-r e a c t i o n or causing an overlapping of the associated weight losses due to two reactions which follow r a p i d l y one a f t e r the other. When the mass transf e r phenomena i s important the most common di s t u r b i n g e f f e c t i s the removal of gaseous re a c t i o n product from the re a c t i o n i n t e r f a c e (29). The f a c t o r s e f f e c t i n g the d i f f u s i o n mechanism could be the shape, s i z e and s i z e d i s t r i b u t i o n of the sample and the consistency of the gaseous environment composition. The amount of sample also has an e f f e c t on the mass t r a n s f e r phenomena, because i f the sample layer becomes too thick the problem of i n t e r n a l d i f f u s i o n a r i s e s . The appropriate experimental conditions may be found by means of semi-empirical tests i n the apparatus intended for k i n e t i c a n a l y s i s . For example, i t i s possible to decide whether a stream of i n e r t gas may influence a reverse reaction or whether the use of vacuum i s necessary (29). There has been a l o t of work done by several authors on the e f f e c t s of a l l these f a c t o r s on the accuracy of the thermogravimetric data (29). The accuracy of the mathematical evaluation of experimental curves w i l l be discussed i n s e c t i o n 2.4.1. 2 . 3 . 2 The T h e r m o g r a v i m e t r i c (TG) C u r v e . As noted e a r l i e r the weight losses or gains due to each decomposition step or reac t i o n i s detected as a function of temperature In thermogravimetric experiments. The record of percent weight losses versus temperature i s c a l l e d a TG curve. A t y p i c a l TG curve i s shown i n Figure 7. FILLED NYLON FILLER T E M P E R A T U R E Figure 7: A t y p i c a l TG curve. -38-In t h i s f i g u r e the dark thick l i n e shows the change i n the weight with temperature. The curve above this i s the d e r i v a t i v e curve which gives a d d i t i o n a l information such as a change i n the mechanism, namely a change of a slope represented by d i f f e r e n t peaks i n the d e r i v a t i v e curve. 2 . 3 . 3 M a t h e m a t i c a l E v a l u a t i o n o f E x p e r i m e n t a l P a r a m e t e r s . Mathematical methods used f o r the evaluation of TG data are more complicated than the isothermal methods because of the continuous Increase of the temperature. One method i s based on the assumption that the thermal decomposition of a s o l i d may be expressed by |f - - k f ( a ) (2.17) where f ( a ) depends on the r e a c t i o n mechanism and k i s the rate constant. The temperature dependence can be expressed by the Arrhenius equation k = Z exp (-E /RT) (2.18) a where E a i s the a c t i v a t i o n energy and Z i s the frequency f a c t o r . Under the conditions of TG a n a l y s i s the temperature of the system Increases l i n e a r l y : dT = q dt (2.19) where q i s the constant rate of heating. The following equation i s obtained by combining equations (2.17), (2.18), (2.19) -39-j^y = | exp (- E a/RT)dT (2.20) Integration of t h i s equation r e s u l t s i n the model of the TG curve (27). The i n t e g r a l of the l e f t hand side can be evaluated when the a n a l y t i c a l form of the function f ( a ) i s known and leads to a new function g(ct). The r i g h t hand side can be integrated i f E i s known (27). Doyle (5) showed that the following form i s obtained by the i n t e g r a t i o n of equation (2.20): ZE g(«) = ~ - P(x) (2.22) The function p ( x ) i s defined by - x - u p ( x ) = T - — du (2.23) r x ' x u where u = E /RT and x = E /RT . This function was tabulated by Doyle a a a J J (5), Akahira (2) and Zsako (31). The main d i f f i c u l t y i n applying eq. (2.22) i s the dependence of P(x) on both temperature and a c t i v a t i o n energy. Doyle (5) has suggested a t r i a l and error curve f i t t i n g method for the determination of a c t i v a t i o n energy. He discussed reactions for which the function f(oc) was known, and thus g(<z) values could be computed from thermogravimetric data. Under such conditions he obtained the -40-approximate value of E a from the slope of the thermogram and c a l c u l a t e d the t h e o r e t i c a l curve by means of eq. (2.22). By modifying the presumed E a value, agreement between the t h e o r e t i c a l and experimental curves can be achieved. The a c t i v a t i o n energy value which ensures the best f i t w i l l be the required one. Zsako (31) has s i m p l i f i e d Doyle's t r i a l and error method. Taking the logarithm of each side of equation (2.22) gets ZE — log g(oc) - log p(x) = log — = B (2.24) where B depends only upon the nature of the compound studied, upon the heating rate, but not upon the temperature. The value of g(ot) for a given temperature can be c a l c u l a t e d from the experimental data i f f ( a ) i s known. S i m i l a r l y p(x) for the same temperature can be found i f the a c t i v a t i o n energy i s known. Constancy of log g(<x) - log p(x) enables the determination of the a c t i v a t i o n energy, consistent with a given function f ( a ) . This procedure i s explained i n more d e t a i l i n s e c t i o n 5.1. The agreement between experimental data and assumed a c t i v a t i o n energy E a can be characterized q u a n t i t a t i v e l y by the standard d e v i a t i o n of i n d i v i d u a l B, values f o r each estimated E from t h e i r i a± a r i t h m e t i c a l mean B. This w i l l be defined as ( B - B ) 2 6 = — (2.25) where r i s the number of experimental data points used for the c a l c u l a t i o n of B. The minimum of 6 i n d i c a t e s the best E value. At a the same time, t h i s 6 . i s a measure of the consistency of the min -41-decoraposition process with the function f(oc). By presuming other k i n e t i c equations and by c a l c u l a t i n g the corresponding &m^n values, the minimum of 6 . values w i l l i n d i c a t e the function f ( a ) , among min those tested which ensures the maximum consistency with experimental data. I f the minimum value, 6 , i s small enough, the v a l i d i t y of a min k i n e t i c equation with the corresponding f ( a ) and the determined E a value as the apparent a c t i v a t i o n energy i s concluded. The best B value can be used for the c a l c u l a t i o n of the frequency f a c t o r , Z, by the following equation l o g Z = B + log Rq - log E (2.26) 3. By knowing the best E a value and Z the rate constant of the r e a c t i o n , k, can be c a l c u l a t e d as a function of temperature. Satava and Skvara (27) brought a fur t h e r s i m p l i f i c a t i o n to the method of Zsako by suggesting a g r a p h i c a l comparison of log g(a) and log p(x). The log g(a) values for various rate processes are p l o t t e d vs. the corresponding T^ values on a transparent paper. The p l o t of - l o g p(x) vs. T^ values Is also prepared. The p l o t of log g(a) i s placed on top of the log p(x) diagram so that the temperature scales coincide and i t i s then s h i f t e d along the ordinate u n t i l one of the log g(a) curves f i t s one of the log p(x) curves. From t h i s log p(x) curve the a c t i v a t i o n energy can be read. The best f i t t i n g log g(a) curve determines the most probable k i n e t i c equation. For t h i s method to be accurate the experimental TG data must f i t for the whole range of a. -42-2 . 3 . 4 C o m p a r i s o n o f t h e A c c u r a c y o f M a t h e m a t i c a l M e t h o d s f o r t h e  E v a l u a t i o n o f t h e TG C u r v e . Each mathematical method i s subject to some inexactness that influences the accuracy of the r e s u l t s to a greater or l e s s e r extent. Doyle's method seems to be very simple because k i n e t i c data may be obtained from a s i n g l e point on the decomposition curve. The necessity to know the value of the rea c t i o n order beforehand appears to be a disadvantage. When the r i g h t value of rea c t i o n order i s assumed the e r r o r from the a p p l i c a t i o n of t h i s method i s around 4% (29). Zsako's method i s almost free from errors i f the r e a l value of the i n t e g r a l p(x) i s used. Since the standard d e v i a t i o n i s a q u a n t i t a t i v e measure of the consistency between experimental data and the presumed k i n e t i c equation, the minimization of the standard d e v i a t i o n ensures the accuracy of the estimations. Although the Satava's method seems simple there i s always a question mark as to whether there i s only one function p(x) which f i t s eq. (2.22) when g(a) i s given. I f the mechanism of the r e a c t i o n i s known, the accuracy of the estimated a c t i v a t i o n energy i s +5% (27). 2 . 3 . 5 T h e o r e t i c a l C o n s i d e r a t i o n s f o r t h e E v a l u a t i o n o f a n E q u a t i o n  f o r F u n c t i o n f ( a ) . The mathematical expressions derived i n se c t i o n 2.3.3 were based on the assumption that the r e a c t i o n can be expressed by the equation # = k ( l - a ) m (2.27) -43-But i n s o l i d state reactions, the concepts of concentration and o r d e r of reaction generally have no s i g n i f i c a n c e . A rate constant cannot be defined i n the same way as for reactions i n gases or s o l u t i o n s . It was reported that a simple rate expression l i k e that from which a l l the derivations quoted are u l t i m a t e l y derived, w i l l not be ap p l i c a b l e to a l l s o l i d state decomposition reactions (1). Coats and Redfern (1) have pointed out that for c e r t a i n exponents (m=0, 0.5, 0.67, 1.0), equation (2.27) corresponds to c e r t a i n k i n e t i c equations, as follows: when m = 0 a = kt (2.28) when m = 0.5 R 2(a) - 1 - ( l - a ) 1 / 2 = kt (2.29) when m = 0.67 R 3(a) = 1 - ( l - a ) 1 / 3 = kt (2.30) when m = 1.0 F,(a) = - In (1 - a) = kt (2.31) Equation (2.28) holds for reactions i n v o l v i n g a high degree of surface adsorption. Equations (2.29) and (2.30) describe reactions proceeding by the movement of an i n t e r f a c e i n two and three dimensions r e s p e c t i v e l y . Equation (2.31) i s the integrated form of the equation for a reaction c o n t r o l l e d by random nu c l e a t i o n . Random nucleation has been studied by Avrami (1) and Erofe'ev (1) and the following equations have been given A 2 ( a ) = ^ / - l n (1-a) = kt (2.32) A 3(a) = 21 -In (1-a) = kt (2.33) -44-On the other hand many s o l i d state reactions are c o n t r o l l e d by d i f f u s i o n a l processes and these reactions cannot be expressed i n the form of equation (2.27). For example, the simplest equation for a d i f f u s i o n - c o n t r o l l e d r e a c t i o n takes the form <x^  = kt which gives — 4~ = (k/2) (l+c+c 2+ ...) (2.34) at For a d i f f u s i o n - c o n t r o l l e d r e a c t i o n i n a s p h e r i c a l p a r t i c l e the equation i s 1 - 2<x/3 - ( l - a ) 2 / 3 = kt (2.35) which gives _ d£ = ( 3 k / 2 ) c 1 / 3 ( l + c 1 / 3 + c 2 / 3 + ...) (2.36) For d i f f u s i o n c o n t r o l l e d reactions the general equation can be w r i t t e n ff - = k f(<x) (2.37) where k i s given by the Arrhenius equation and f ( a ) depends on the form of the d i f f u s i o n mechanism. If the r i s e of temperature i s l i n e a r , T = t Q + qt, then = ( k/q) f ( a ) (2.38) and ( l / f ( a ) ) ( d o / d T ) = (Z/q) exp (-E /RT) (2.39) cL -45-The form of f ( a ) depends on the nature of the r e a c t i o n . For one-dimensional d i f f u s i o n - c o n t r o l l e d reactions i n p l a t e l i k e p a r t i c l e s D L(a) = a 2 (2.40) and f x ( a ) - l/2a (2.41) For two-dimensional d i f f u s i o n - c o n t r o l l e d r e a c t i o n i n a c i r c u l a r d i s c D 2(a) = (1-a) In (1-a) + a (2.42) hence f 2 ( a ) = l / [ - l n (1-a)] (2.43) The equation for a d i f f u s i o n c o n t r o l l e d reaction i n a sphere D 3(a) = [1 - ( 1 - a ) 1 7 3 ] 2 (2.44) which gives f 3 ( a ) = ( 3 / 2 ) [ ( l - a ) ' 1 / 3 - l ] (2.45) The relevant form of f ( a ) should be determined from an i n i t i a l measurement of a versus t for c o n t r o l l e d conditions of T, P and other v a r i a b l e s ( p a r t i c l e s i z e , e t c . ) . Then equation (2.39) can be used to determine values of Z and E a from TG data. -46-2.3.6 Influence of V a r i a t i o n of K i n e t i c Constants on Shape and  P o s i t i o n of Theoretical Thermogravlmetric Curves. In contrast to isothermal decomposition curves, the shape of which depends only on the reaction mechanism, the shape of the TG curve is Influenced by the variations in the values of E a and Z as well as the reaction order. Figure 8 shows how different rate controlling processes affect the shape of the theoretical TG curves. Changes in the frequency factor Z and the activation energy E a induce either a change in the multiplying constant or a change in the [J] term of the right hand side of the eq. 2.21. A decrease in frequency factor shifts the decomposition of substances to the high temperature region as shown in Figure 9. If the value of the activation energy is increased by 10% and the original value of Z Is maintained, the change in the value of the multiplying constant is small but with respect to the change of integral l i m i t s , the value of (/) decreases considerably. This may be compensated for by an increase In the value of the temperature. The compensation w i l l reshift the curves to the region of high temperatures characterising the increase in decomposition temperature due to a higher activation energy (29). This effect is also shown in Figure 9. False determination of directly measured quantities due to errors caused by the experimental arrangement has also an effect on the shape and position of the curves. A theoretical analysis of errors proves that faulty measurements of temperature must distort the value of activation energy while non-linearity of heating rate distorts the value of the reaction order (29). -47-Figure 8: T h e o r e t i c a l TG curves c a l c u l a t e d f o r r characterised by E = 20 kcal/mol, Z = 10 6, q = l°C/n by d i f f e r e n t r a t e -c o n t r o l l i n g processes. (27) 50 100 150 200 Figure 9: T h e o r e t i c a l TG curves ( f r a c t i o n reacted, a, vs T) c a l c u l a t e d for reaction f i t t i n g function R 2 with q = l°/min. (A) E = 20 kcal/mol at various values of Z and (B) Z = 10 9 s - 1 m o l 1 / 2 at various values of E. (27) -48-3. MODELLING In t h i s s ection mathematical expressions which w i l l give f r a c t i o n a l conversions and the rate of the r e a c t i o n as a function of temperature w i l l be developed for the r e a c t i o n between sodium carbonate and colemanite. In a thermogravimetric a n a l y s i s , the r e s i d u a l weight f r a c t i o n versus temperature for a sample heated at a f i x e d rate i s recorded. Since the temperature i s not constant throughout the experiment a new procedure must be developed to i n t e r p r e t the k i n e t i c data from the thermogram. 3.1 Development of a Rate Expression In t h i s study colemanite i s used as an a u t o c a u s t i c i z i n g agent, and takes part d i r e c t l y i n the r e a c t i o n . So the following expression can be w r i t t e n to symbolize the r e a c t i o n aA(s) + bB(s) ->• cC(s) + dD(g) (3.1) In general the rate expression for such a s o l i d phase r e a c t i o n can be written as follows dW where m and n are the orders of the r e a c t i o n with respect to compounds A and B r e s p e c t i v e l y . and Wg are the weights of the reacting compounds and k i s the rate constant. -49-In terms of the f r a c t i o n a l conversions WA and Wg can be expressed as WA = WA ( 1 " a A ) ( 3 ' 3 ) o WB = WB ( l - a B ) (3.4) o where a A and ag are the weight f r a c t i o n s of the i n i t i a l compounds reacted. Weight f r a c t i o n s were used instead of mole f r a c t i o n s because the molecular weight of the a c t i v e part of colemanite was not known exa c t l y . The reacted f r a c t i o n of compound B can be expressed i n terms of the reacted f r a c t i o n of compound A as follows W A aA . MW,, o b B C N aB = -MW— ' I • W- <3'5> A B O where MWA and MWg are molecular weights of compounds A and B r e s p e c t i v e l y . By s u b s t i t u t i n g eq. (3.5) into (3.4) MWB WA W B = W B ^ " i M W - w f « A > ( 3 - 6 ) o A B o S u b s t i t u t i o n of eq. (3.3) and (3.6) into eq. (3.2) gives d[W A ( l - a A ) ] MW„ WA u B A , m ,T n,. \m,. D o x n _ N  k lW A WB ( i - a A ) (1 - r — — a A ) (3.7) o o A B -50-t h i s equation can be rewritten as da A , „ m-1 „ n MW W" 1 A B , B A o o / i ~ \ m / i b o N n ( 1 - a A> ~a MW~ W~ aA^ A B o = kiW A "* Wn "dt (3.8) Introducing MWg WA f ( a A ) - d-a^d - i M w - w f V 1 1 <3'8A> A B o the f i n a l form of the equation (3.8) becomes d a A 1 - k l W , m ~ l W, n d t (3.9) f(a.) A B A o o where function f ( a ) depends on the r e a c t i o n mechanism. In eq. (3.9) k j , which i s the rate constant, cannot remain constant under the conditions of thermogravimetric a n a l y s i s and w i l l depend upon temperature. The temperature dependence of k^ can be expressed by the Arrhenius equation k x - Zl exp (-E^RT) (3.10) where E^ i s the a c t i v a t i o n energy and i s the frequency f a c t o r . Under the conditions of thermogravimetric a n a l y s i s , the temperature of the system increases l i n e a r l y , i n other words thermogravimetric a n a l y s i s i s c a r r i e d out with a constant heating rate q, where -51-q = dT/dt (3.11) S u b s t i t u t i n g dt = dT/q and combining eq. (3.10) and eq. (3.11) with eq. (3.9) gives da Z i , E i -1 m-l n 1 = — W A Wn exp (- — ) dt (3.12) f( a . ) q "A "B ^ v RT A' n o o Integration of equation (3.12) r e s u l t s i n the equation of the thermogravimetric curves. To perform t h i s i n t e g r a t i o n the method which was developed by Doyle (5) and described i n the l i t e r a t u r e part of t h i s t h e s i s was used. The following equation i s obtained by the i n t e g r a t i o n of equation (3.12) Z 1 E 1 g ( « A ) (WA m \ n ) p ( x ) , (3.13) Rq o o where p(x) i s defined by equation (2.23). This equation can further be s i m p l i f i e d by introducing the notation k * =-Rq- WA WB n ^ 3 - U > o o and the equation of the thermogravimetric curves can be written as g(a) = k*p(x) (3.15) -52-3 . 2 E x p r e s s i o n s f o r F r a c t i o n a l C o n v e r s i o n s a n d F u n c t i o n f ( a ) f o r  t h e R e a c t i o n o f S o d i u m C a r b o n a t e a n d C o l e m a n i t e . Reaction between sodium carbonate and colemanite i s very complex. There are many fa c t o r s a f f e c t i n g i t and the unknown structure of colemanite which comes n a t u r a l l y from the rocks mixed with i m p u r i t i e s makes the problem more complicated. In order to be able to apply the rate expression derived i n the previous s e c t i o n the s t o i c h i o m e t r i c constants of the reaction should be known. The formula of pure colemanite i s given as 2CaO«3B 20 3»5H 20 and contains 50.8 percent B 2 0 3 . The phase diagram f o r the Na 20-B 20 3 system shown i n F i g . 10 in d i c a t e s that f o r a sodium to boron molar r a t i o greater than 0.995 which i s s a t i s f i e d for a l l the colemanite percentages analyzed i n t h i s study (Appendix I I ) , the r e a c t i o n product would be Na 2OB 20 3 regardless of temperature (7). Hence the proposed form of r e a c t i o n equation i s 3Na 20 3 + [2CaO«3B 20 3«5H 20] 3Na 2OB 20 3 + 3C0 2 t + 2CaO + 5H 20 (3.16) g i v i n g the s t o i c h i o m e t r i c constants a and b i n eq. 3.1 as a = 3 and b - 1. 3 . 2 . 1 E x p r e s s i o n o f t h e F r a c t i o n a l C o n v e r s i o n o f S o d i u m C a r b o n a t e . The following assumptions can be made to s i m p l i f y the mechanism of t h i s r e a c t i o n . 1. There Is no loss of sodium or sodium oxide at elevated temperatures. Hence a l l the weight loss comes from the expulsion of carbon dioxide which i s a re a c t i o n product. -53--54-2. There i s only one r e a c t i o n that takes place within the analyzed temperature range (190-700°C). Since the only source of weight loss i s the evolution of carbon dioxide which i s formed by the decomposition of sodium carbonate the fo l l o w i n g expression can be w r i t t e n W - W s W a = — £ MW (3.17) sn s MW s o CO 2 and subsequently "s - " MW o where W i s the weight at any time during the r e a c t i o n and can be read from TG curve for the corresponding temperature. 3.2.2 Expression for the Fr a c t i o n a l Conversion of Colemanite. S u b s t i t u t i o n of a and b values i n eq. (3.5) gives the f o l l o w i n g expression for <zg which w i l l be denoted as <xc s p e c i f i c a l l y for colemanite MW W 1 c s a = 4 TrrT" 7i~~~ « (3.19) c 3 MW W s s c o -55-However, the colemanite used i n t h i s study was not pure and an independent study which was performed by using the same colemanite stock showed that i t contained 25.24 percent impurity (26). Colemanite i s also very hydroscopic and TG ana l y s i s showed that i t contained 9 percent humidity (see F i g . 30). When the necessary c o r r e c t i o n s have been made equation (3.19) becomes MW W (100 - H ) ^ c s c a c = 3 i " i T (ioo - i ) a s ( 3 * 2 0 ) s c c o where = percent humidity i n colemanite I = percent impurity i n colemanite W s The r a t i o of - — w i l l be d i f f e r e n t f o r each colemanite-Na 2C0 3 c o mixture analyzed. Therefore, t h i s r a t i o must be represented by a general expression which w i l l apply to a l l colemanite percentages. The i n i t i a l weight of colemanite i n a sample can be written as follows Y 100 - H W c * W s <100 - Y > < 100 C> < 3- 2 1> o o c where Y c i s the colemanite percentage i n the samples. Equation (3.21) can also be written i n terms of the weight f r a c t i o n of colemanite and the following equation i s obtained a f t e r making the necessary s i m p l i f i c a t i o n s W X (100 - H ) c c c W ^ = ( i - x ) <3'22> s c o -56-If equation (3.22) i s s u b s t i t u t e d i n equation (3.20) the f i n a l expression for the f r a c t i o n a l conversion of colemanite i s obtained. 1 ^ c ( 1 ~ V °c = 3 MW X (100 - H ) "s (3.23) s c c 3.2.3 Analytical Forms of Function f(oc) and Function g(a) For the  Reaction of Sodium Carbonate and Colemanite. As can be seen from eq. (3.23), a l l the terras are constant i n that expression except a s . Introducing constant N , MW (1 - X ) 1 c c N = J MW~ X (100 - H ) ( 3 ' 2 4 ) s c c eq. (3.20) can be w r i t t e n i n the following form: a - Na " (3.25.) c s ' Then eq. (3.8A) becomes f( a ) = (1-a ) m ( l - N a ) n (3.26) s s and the corresponding forms of the function g(a) can be evaluated by Integrating t h i s f u nction between the l i m i t s of 0 to a. In Table 8 a n a l y t i c a l forms of the function f ( a ) and f u n c t i o n g(a) for the most probable mechanisms f o r the thermal decomposition of s o l i d substances are tabulated. This table also shows the expressions fo r k* which w i l l be used i n the c a l c u l a t i o n of the frequency f a c t o r , Z, and the rate constant, k, corresponding to these proposed ' mechanisms. Table 8: An a l y t i c a l forms of function f(ot) and g(a) for the most probable mechanisms. z,E, mechanism f(a) = ( l - a 8 ) m ( l - N a 8 ) n g(a) = JJ j f l jy k* = *a*~\n m = 0 7 ^ , r l - 3 ( l - a ) 2 / \ Z l E , (Wc J 1 / 3 n = 1/3 f ( < X ) = 8 ( 0 ) " 7 [ ^ 1 -1^ V so m = 0 7^  .1 - / F ^ T . B . E , ( W c J 1 / 2 n - 1/2 f ( < X ) " ( 1" H a-> 7 8 ( < X ) = 2 [ — T " ] " f e 1 - T T ^ ^ i - /(l-«)l/3 , E ) l / 3 n = 2 / 3 f(«) - d - H « 8 ) 2 ^ 3 g(«)-3[ ^ ^ L - ^ i ] - V - w f ™ " J/3 f(a) = ( l - a 8 ) 1 / 3 g(a) = ^ t1 " 3(l-« 8) 2 / 3] W S ( ) ~ 2 / 3 ll T F ( A ) = ^ " " B ) 1 7 2 8<a> = ^ " TT" W s 0 " 1 / 2 m = 0 Z i E , , f(a) = 1 g(a) - a - i - i - W_ 1 n =• 0 s *q s Q -58-3.3 Expressions for the Decomposition of Sodium Carbonate. 3.3.1 Development of a Rate Expression. Besides the colemanite r e a c t i o n , sodium carbonate may decompose d i r e c t l y at high temperatures. The following r e a c t i o n can represent the decarbonization r e a c t i o n of sodium carbonate Na 2C0 3 -»• NaO + C0 2 (3.27) or A(s) + B(s) + C(g) (3.27A) The rate of r e a c t i o n f o r such a reaction can be written as dW - d T - k * w A V ( 3 ' 2 8 ) where v i s the order of the rea c t i o n and k 2 i s the rate constant. In terms of the f r a c t i o n a l conversion can be written as follows WA = WA (1 - a A) (3.29) o S u b s t i t u t i n g equation (3.29) into equation (3.28) gives d[W A ( l - a A ) ] °— t k 2W A V ( l - a A ) V (3.30) o A f t e r making the necessary s i m p l i f i c a t i o n s the following equation i s obtained. -59-da — = k2WA V ~ dt (3.31) / i \ V o d - « A ) Introducing f ( a A ) = ( 1 - « A ) V (3.32) and k 2 = Z 2 exp (- E 2/RT) (3.33) equation (3.31) becomes da J^J - Z 2 exp (- E 2/RT)W A V _ i dt (3.34) Since the thermogravimetric a n a l y s i s i s c a r r i e d out with a constant heating rate, q dt - — (3.35) q S u b s t i t u t i o n of equation (3.35) into the equation (3.34) gives the f i n a l form of the rate equation as such d a * z 2 1 A v-1 W exp (- E 2/RT)dT (3.36) f(« A) 9 A Q I n t e g r a t i o n of equation (3.36) r e s u l t s i n the equation of the thermogravimetric curves which i s given i n equation (3.37) by applying the same procedure described i n s e c t i o n 3.1 Z2E2 V _ L g(oc) = ^ — WA p(x) (3.37) q o -60-3.4 A n a l y t i c a l Forms of Functions f(oc) and g ( a ) . The a n a l y t i c a l forms of function f ( a ) and function g(a) are summarized i n Table 9 i n c l u d i n g the mechanisms for d i f f u s i o n c o n t r o l and random nucleation f o r which the equations were given i n section 2.3.5. -61-Table 9: A n a l y t i c a l forms of function f ( a ) and g(a) for the probable mechanisms for the decomposition of Na2CO mechanism f(oc) = (l-<x A) V „ / „ N - fa d 0 tA m = 0 1 aA m = 1/2 d - a A ) 1 / 3 3/2 [1 - ( l - a A ) 2 / 3 ] m = 2/3 (1 - a A ) 1 / 2 2[1 - / l - o A ] m - 1/3 d - a A ) 2 / 3 3[1 - ( l - a A ) 1 / 3 ] m - 1 d-« A) - l n ( l - o A ) m - 2 d - « A ) 2 aA i-'A One dimensional d i f f u s i o n Dl «A 2 Two dimensional d i f f u s i o n D2 ( l - a A ) l n ( l - a A ) + a A Three dimensional d i f f u s i o n D3 [1 - ( l - o A ) 1 / 3 ] 2 Aurami eq. A2 1/2 [ l n ( l - a A ) ] Aurami eq• A3 1/3 [ l n ( l - a A ) ] 4. EXPERIMENTAL STUDIES The experimental work i n this study consists of two major parts: 1. Experiments performed to determine the most s u i t a b l e agent for the decarbonization of sodium carbonate by evaluating the e f f i c i e n c i e s of a number of proposed a u t o c a u s t i c i z i n g agents. These experiments were performed under isothermal c o n d i t i o n s . 2. Experiments performed to evaluate the k i n e t i c constants of the re a c t i o n of sodium carbonate with the agent chosen from the r e s u l t s of experiments performed i n part one. Reaction mixtures were analyzed i n a thermogravimetric analyzer under the constant heating rate c o n d i t i o n . 4.1 Isothermal Experiments These experiments were based on the measurement of the reacted f r a c t i o n of the sodium carbonate as a function of time at constant temperature and pressure. The experimental set-up used i n these experiments i s shown i n Figure 11. The desired temperature for the reaction was maintained i n an e l e c t r i c furnace (Thermolyne, model F-A1730) which can operate as high as 2000°F (1093°C). The constancy of the temperature i n the r e a c t i o n chamber was maintained by a d i g i t a l temperature c o n t r o l l e r (Sybron/Thermolyne, model LT310X2). The c o n t r o l l e r held the furnace temperature at the desired l e v e l within +5%. -63-Figure 11: Experimental Set-up for Isothermal Runs -64-Th e temperature of the furnace was measured with a Chromel/Alumel thermocouple which was i n s t a l l e d i n a pr o t e c t i v e tube at the back of the furnace. Samples were Introduced i n 10 ml zirconium c r u c i b l e s . Zirconium was used because of the extremely co r r o s i v e nature of high temperature molten c a u s t i c . The c r u c i b l e s stood up w e l l . A f t e r 10 runs of about one hour each only two c r u c i b l e s out of ten had corroded, although most of them had deformed s l i g h t l y . For e f f i c i e n t heating the c r u c i b l e s were placed away from the sides of the furnace and from the tube i n which the thermocouple was i n s e r t e d . They were also placed about 1.5 cm apart to allow the c i r c u l a t i o n of gas around them. Helium was supplied at a rate enough to maintain an i n e r t atmosphere i n the furnace. The aim of t h i s was to prevent the c r u c i b l e s from corroding and to sweep the carbon dioxide from the chamber. 4.1.1 System Variables. The chosen v a r i a b l e s i n t h i s project were temperature, time and composition of the r e a c t i o n mixture. For a wide range of independent v a r i a b l e s , decomposition of sodium carbonate was tested f o r the c a u s t i c i z i n g agents titanium dioxide, alumina and colemanite. Temperature: Temperatures ranging from 800°C to 1100°C were tested, as was suggested by the l i t e r a t u r e . Time: Reaction time was between 5 min. and 80 min. The maximum time was determined by preliminary runs which showed that a f t e r 60 minutes the re a c t i o n proceded very slowly and was almost complete at -65-the end of 80 minutes. Reaction times were chosen according to the nature of the a u t o c a u s t i c i z i n g agent and varied s l i g h t l y . Composition of the reaction mixture: As was proposed i n the l i t e r a t u r e , 10 and 20 weight percent of a u t o c a u s t i c i z i n g agent i n the mixture were tested for titanium dioxide and alumina. Because of the high molecular weight of colemanite i t was necessary to test higher concentrations, i n the range from 10 to 60 weight percent. 4.1.2 Preparation of Samples. In these experiments, as i n a l l the tests made a homogeneous mixture was very important. For t h i s reason s p e c i a l a t t e n t i o n was paid to obtain w e l l mixed samples. The reagents used i n the preparation of samples were anhydrous sodium carbonate which was 99.5% pure and supplied by WEB, titanium dioxide (supplied by Coast Ceramics L t d . ) , alumina, colemanite (supplied by Coast Ceramics Ltd., Nevada colemanite). The p u r i t y of the titanium dioxide and the alumina was greater than 99 percent. Since colemanite comes from an unrefined rock there was no information a v a i l a b l e about i t s p u r i t y and composition. The reagents were weighed on an a n a l y t i c a l balance (Mettler H10T) and placed i n the c r u c i b l e s . Two sets of s i x samples were weighed out, one set at ten percent and one set at twenty percent agent concentration. T o t a l weight of samples was chosen as one gram because i f the thickness of sample layer Is too great the d i f f u s i o n of carbon dioxide could be Impeded r e s u l t i n g i n a considerable decrease i n the re a c t i o n r a t e . A f t e r weighing, the reagents i n each c r u c i b l e were -66-mixed thoroughly with a scoopula to obtain a homogeneous mixture. Then they were s l u r r i e d with d i s t i l l e d water which was just s u f f i c i e n t to wet the mixture. In order to prevent f l a s h i n g o f f the samples from the c r u c i b l e s when they were placed Into the hot furnace they were dried i n an oven at 110°C for approximately one hour. They were then stored u n t i l the furnace test i n a desiccator f i l l e d with s i l i c a g e l . In the case of colemanite, i n a d d i t i o n to the samples prepared at ten and twenty percent colemanite concentrations, samples containing t h i r t y , f o u r t y , f i f t y and s i x t y percent colemanite i n sodium carbonate were prepared as w e l l . The experiments performed under the isothermal conditions are summarized i n Table 10 which shows the type of agent and the conditions used with each sample. Each run was repeated i n order to minimize the e r r o r s . Consistency of the t i t r a t i o n r e s u l t s were checked and found to be accurate to + 1%. 4.1.3 Experimental Procedure. Experimental procedure can be divided into three parts: 1. Reaction of the sample 2. D i s s o l u t i o n of the sample 3. Analysis of products 1. Reaction of sample: Reaction takes place i n the furnace. The furnace was preheated to the desired temperature and kept at t h i s temperature for about one hour to assure a stable operating temperature when the runs were s t a r t e d . Stable temperature was assumed when the temperature c o n t r o l l e r was c y c l i n g frequently. The oven was also -67-Table 10: Conditions tested i n the isothermal experiments.* Run # Agent Agent Temperature Reaction type concentration (°C) time (min) 1 T i 0 2 10 800 5 2 T i 0 2 20 800 5 3 T i 0 2 10 800 15 4 T i 0 2 20 800 15 5 T i 0 2 10 800 25 6 T i 0 2 20 800 25 7 T i 0 2 10 800 35 8 T i 0 2 20 800 35 9 T i 0 2 10 800 50 10 T i 0 2 20 800 50 11 T i 0 2 10 900 5 12 T i 0 2 20 900 5 13 T i 0 2 10 900 15 14 T i 0 2 20 900 15 15 T i 0 2 10 900 25 16 T i 0 2 20 900 25 17 T i 0 2 10 900 35 18 T i 0 2 20 900 35 19 T i 0 2 10 900 50 20 T i 0 2 20 900 50 21 A 1 2 0 3 10 800 10 22 A 1 2 0 3 20 800 10 23 A 1 2 0 3 10 800 20 24 A1 20 3 20 800 20 25 A 1 2 0 3 10 800 30 26 A1 20 3 20 800 30 27 A 1 2 0 3 10 800 40 28 A1 20 3 20 800 40 29 A 1 2 0 3 10 800 50 30 A1 20 3 20 800 50 31 A 1 2 0 3 10 900 10 32 A1 20 3 20 900 10 33 A 1 2 0 3 10 900 20 34 A 1 2 0 3 20 900 20 35 A 1 2 0 3 10 900 30 36 A1 20 3 20 900 30 37 A 1 2 0 3 10 900 40 38 A1 20 3 20 900 40 39 A 1 2 0 3 10 900 50 40 A 1 2 0 3 20 900 50 -68-Table 10: Conditions tested i n the isothermal experiments.* Continued Run # Agent Agent Temperature Reaction type concentration (°C) time (rain) 41 Colemanite 40 800 10 42 Colemanite 40 800 20 43 Colemanite 40 800 30 44 Colemanite 40 800 40 45 Colemanite 40 800 50 46 Colemanite 40 800 60 47 Colemanite 10 900 10 48 Colemanite 20 900 10 49 . Colemanite 30 900 10 50 Colemanite 40 900 10 51 Colemanite 50 900 10 52 Colemanite 60 900 10 53 Colemanite 10 900 20 54 Colemanite 20 900 20 55 Colemanite 30 900 20 56 Colemanite 40 900 20 57 Colemanite 50 900 20 58 Colemanite 60 900 20 59 Colemanite 10 900 30 60 Colemanite 20 900 30 61 Colemanite 30 900 30 62 Colemanite 40 900 30 63 Colemanite 50 900 30 64 Colemanite 60 900 30 65 Colemanite 10 900 40 66 Colemanite 20 900 40 67 Colemanite 30 900 40 68 Colemanite 40 900 40 69 Colemanite 50 900 40 70 Colemanite 60 900 40 71 Colemanite 10 900 50 72 Colemanite 20 900 50 73 Colemanite 30 900 50 74 Colemanite 40 900 50 75 Colemanite 50 900 50 76 Colemanite 60 900 50 * A l l runs i n this table were repeated. -69-flushed with helium for about 15 minutes before the s t a r t of each run and i t flowed continuously throughout the run at a slower rate. At the s t a r t of each run, a l l twelve c r u c i b l e s were placed i n t o the oven. At elapse times of 10, 20, 30, 40, 50 and 80 minutes, two c r u c i b l e s were removed from the oven. One contained 10 and the other contained 20 percent a u t o c a u s t i c i z i n g agent. Samples were immediately placed into the desiccator which contained a s c a r i t e and s i l i c a g e l . The f u n c t i o n of the a s c a r i t e was to prevent carbon dioxide i n the a i r from recombining with sodium oxide to form sodium carbonate. Then the samples were weighed to determine the weight loss due to the r e a c t i o n . This was done as quickly as possible to decrease the chance of the samples rea c t i n g with carbon dioxide of the a i r . Each c r u c i b l e was immediately put back i n t o the desi c c a t o r a f t e r weighing. For the colemanite runs two a u t o c a u s t i c i z i n g agent concentrations would be reacted at the same time u n t i l a l l the samples had been tested. 2. D i s s o l u t i o n of samples: The next step was the removal of products from the c r u c i b l e s . This was done by f i l l i n g the c r u c i b l e s with d i s t i l l e d water, covering them with a watchglass and l e t t i n g them b o i l for about 15 minutes on a hot p l a t e . I t was assumed that the water vapor leaving the c r u c i b l e would prevent carbon dioxide from d i f f u s i n g to the basic s o l u t i o n . The c r u c i b l e s were then scraped out with a scoopula. Since the products were fused at high temperatures, they stuck to the sides of the c r u c i b l e s i n the form of a t h i n f i l m and th i s made t h e i r removal from the c r u c i b l e s very d i f f i c u l t even a f t e r they were b o i l e d . The samples were then dissolved In 100 ml of d i s t i l l e d water at 90°C with vigorous s w i r l i n g . This temperature was -70-reported (20) as the optimum to obtain almost complete d i s s o l u t i o n of the product. The erlenmeyers which contained diss o l v e d samples were placed into a desiccator that was f i l l e d with a s c a r i t e . 3. Analysis of products: The samples were analyzed for sodium carbonate and sodium hydroxide. This was done by two sets of t i t r a t i o n s f o r each sample s o l u t i o n ; one for the determination of t o t a l a l k a l i and the other for the determination of sodium hydroxide alone. Methyl orange was chosen as an i n d i c a t o r rather than phenolphthalein, which i s usual f o r the determination of t o t a l a l k a l i , because at the sodium bicarbonate stage the pH of h a l f - n e u t r a l i z e d sodium carbonate i s about 8.3, but the pH changes comparatively slowly i n the neighbourhood of the equivalence point, consequently the i n d i c a t o r colour-change with phenolphthalein (pH range 8.3-10.0) i s not too sharp. Phenolphthalein was used as an i n d i c a t o r for the determination of sodium hydroxide. The procedure can be summarized as follows. 1. A 25 ml a l i q u o t of sample was taken from each erlenmeyer with a p i p e t t e . Care was taken not to withdraw s o l i d s with the sample because of the p o s s i b i l i t y that s o l i d s could cause errors i n the measurement. It was l a t e r proven that the s o l i d s contributed no a l k a l i to the mixture. Each a l i q u o t was then poured i n t o a separate 125 ml stoppered f l a s k . Two samples were taken from each s o l u t i o n . 2. Five drops of methyl orange were added to each s o l u t i o n of the f i r s t sample and these were t i t r a t e d with 0.998 N sulphuric acid to the end point; colour change of orange to yellow. To obtain s a t i s f a c t o r y r e s u l t s with t h i s i n d i c a t o r , the s o l u t i o n s were kept i n an ice bath before t i t r a t i o n and the loss of carbon dioxide was prevented -71-as far as possible by keeping the t i p of the burette immersed i n the l i q u i d . The volume of s u l f u r i c acid used In t h i s t i t r a t i o n was recorded and used to c a l c u l a t e the t o t a l carbonate. 3. One percent barium c h l o r i d e s o l u t i o n was added slowly to each f l a s k i n the second set from a burette i n s l i g h t excess, i . e . u n t i l no further p r e c i p i t a t e was produced. This p r e c i p i t a t e d the unreacted sodium carbonate. Then f i v e drops of phenolphthalein was added to each sample and they were t i t r a t e d with 0.998 N s u l f u r i c a c i d to the end point; pink to c l e a r colour change. The barium carbonate p r e c i p i t a t e was not removed since i t i s stable In acid and made the end point easier to see. 4.1.4 Experimental data. The experimental data taken i n t h i s part of the study are summarized i n Tables 11, 12, 13 and 14 f o r titanium dioxide, alumina and colemanite r e s p e c t i v e l y . F r a c t i o n a l conversions of sodium carbonate were c a l c u l a t e d from the t i t r a t i o n r e s u l t s . (See Appendix I I ) . -72-Table 11: Conversion time data for TiO Temp. % Time % (°C) TIO 2 (min.) Conversion 800 10 5 2.0 15 7.3 25 9.3 35 9.6 50 14.1 800 20 5 2.6 15 5.7 25 10.1 35 13.9 50 14.9 900 10 5 13.0 15 18.8 25 20.8 35 25.4 50 32.8 900 20 5 20.3 15 26.9 25 32.6 35 38.5 50 43.6 1000 10 5 29.6 15 33.1 25 27.3 35 33.4 50 34.7 1000 20 5 32.9 15 36.0 25 39.3 35 43.5 50 51.2 -73-Table 12: Conversion time data for alumina Temp. % Time 7 (°C) Alumina (min.) Conversion 800 10 10 1.3 20 1.3 30 2.5 AO 2.8 50 4.7 20 10 1.2 20 2.2 30 3.3 40 4.8 50 5.0 900 10 10 13.1 20 34.8 30 41.4 40 19.9 50 31.3 20 10 16.3 20 23.8 30 17.7 40 25.1 50 34.2 1000 10 5 20.7 15 42.6 25 86.6 30 -35 74.3 20 5 20.4 15 26.8 25 45.3 30 49.5 35 54.8 1000 10 5 20.9 15 27.1 25 23.8 30 25.4 35 28.3 20 5 32.1 10 25.6 20 35.4 30 51.9 35 36.1 -74-Table 13: Conversion time data for colemanite Temp. % Time % CO Colemanite (min.) Conversion 900 10 10 18.5 30 18.8 50 23.9 70 28.3 900 20 10 32.1 20 36.4 30 36.5 40 38.3 50 38.7 900 30 10 39.2 20 46.3 30 48.1 40 50.9 50 51.4 900 40 10 56.5 20 63.0 30 62.1 40 67.3 50 68.5 900 50 10 58.4 20 67.6 30 70.9 40 72.6 50 73.4 900 60 10 69.7 20 73.0 30 79.5 40 71.1 50 84.1 -75-Table 14: Conversion time data for colemanite at d i f f e r e n t temperatures. Agent: Colemanite (40%) Temp. (°C) Time (min.) % Conversion 800 10 34.4 20 46.7 30 48.8 40 53.9 50 56.8 900 10 56.5 20 60.0 30 62.1 40 67.3 50 68.5 -76-4.2 Thermogravimetric Analysis These experiments were only performed for colemanite which was chosen as the best a u t o c a u s t i c i z i n g agent according to the r e s u l t s from the isothermal experiments. The basic measurement i n t h i s method i s the weight change of the sample as a function of a l i n e a r l y i n c r e a s i n g temperature.. This was done i n a Perkin-Elmer thermogravimetric analyzer (model TGS-2) along with the thermal analysis data s t a t i o n (TADS). 4.2.1 Apparatus. The complete TGS-2 system which i s shown i n Figure 12 c o n s i s t s of the following u n i t s : the thermobalance, the e l e c t r o n i c balance c o n t r o l , the temperature c o n t r o l and the heater c o n t r o l u n i t . The analyzer i s the main part of t h i s system. Figure 13 shows the furnace which i s made of a thin-walled alumina mandril wound with a platinum filament which acts as a platinium r e s i s t a n c e thermometer and resi s t a n c e heater. The temperature range for t h i s sytem i s from 300 to 1273 K and heating rates of 0.3 to 160°K/min. can be employed. The sample i s contained i n a platinium pan supported by a platinum s t i r r u p which hangs i n s i d e the furnace on a wire which i s connected to one arm of the microbalance. The sample pans are 5.8 mm ID and 1.8 mm deep and hang about 2 mm above the thermocouple i n s i d e the furnace. The furnace Is surrounded by a pyrex tube and purged with an Inert gas which i s preferably nitrogen. The normal flow rate for the purge gas i s 45 cc/min. -78-antistatic tube F i g . 13: Cutaway Furnace Showing R e l a t i v e P o s i t i o n of Sample, Furnace, B a f f l e and Thermocouple -79-Th e other units i n the system measure the weight by means of the microbalance and c o n t r o l the temperature i n s i d e the furnace adequately. The microbalance measured the weight of the samples within an accuracy of + 1 percent. The temperature c o n t r o l l e r i s the unit which provides for operator c o n t r o l over the temperature with i t s c o n t r o l s , the r e a c t i o n s t a r t i n g temperature, heating rate, stopping temperature etc. are s p e c i f i e d . The heater c o n t r o l provides the controls for c a l i b r a t i n g the furnace so that the sample temperature i s the same as that ind i c a t e d on the programmer readout within a 2 percent accuracy. It also provides the thermocouple c i r c u i t r y f o r monitoring the temperature of the sample environment. The r e s u l t s are recorded on a 5 inch floppy d i s c and analyzed with a software program supplied by the manufacturer. They are a l s o p l o t t e d using a Hewlet-Packard d i g i t a l p l o t t e r . For more s p e c i f i c information on the d e s c r i p t i o n and operation of the TGS-2 and TADS system, the reader should consult the operating manuals for these systems (32). 4.2.2 Preparation of the Samples. Sample preparation f o r these experiments i s very s i m i l a r to the procedure described i n the isothermal experiment s e c t i o n . One gram mixtures of 10, 20, 30, 40, 50, 60, 70, 80 percent colemanite i n sodium carbonate were s l u r r y mixed and dried on watch glasses overnight i n an oven at 110°C. The mixtures were then scraped o f f the watch glasses -80-and ground to a diameter of approximately 0.05 m i l l i m e t r e s , using a glass rod. They were then stored i n v i a l s i n a desiccator which was f i l l e d with s i l i c a g e l to prevent t h e i r hydration. In a d d i t i o n to these colemanite-sodium carbonate mixtures, samples containing 20, 40, 50, and 60 percent calcium borate, which was prepared i n the laboratory by mixing the hot solutions of calcium hydroxide and 20% excess b o r i c a c i d , were prepared i n the same way as stated above. Samples of 100 percent colemanite, 100 percent sodium carbonate and 100 percent calcium borate were also prepared. In each case the reagent was s l u r r i e d with d i s t i l l e d water, dried overnight i n an oven and ground i n the same manner as the mixtures. Table 15 summarizes the experiments performed by using TG. 4.2.3 Selection of Experimental Conditions. Experimental conditions were set by running some preliminary t e s t s on colemanlte-sodium carbonate mixtures as well as by considering some of the t h e o r e t i c a l aspects discussed i n the l i t e r a t u r e part of t h i s thesis which were needed to obtain accurate r e s u l t s . Sample s i z e was between 10 and 30 mill i g r a m s . Use of small samples us u a l l y r e s u l t s i n the best temperature accuracy and r e p e a t a b i l i t y while large sample si z e s often favour better weight change accuracy. For most a p p l i c a t i o n s the range from 5-40 milligrams Is given as optimum for th i s TG system. -81-Table 15: L i s t of the experiments performed using TG.* Sample # Agent type Agent Temp. Heating cone. span Rate (% weight) (°C) 1 Colemanite 10 40-1000 10°C/min. 2 Colemanite 20 40-1000 10°C/min. 3 Colemanite 30 40-1000 10°C/min. 4 Colemanite 40 40-1000 10°C/min. 5 Colemanite 50 40-1000 10°C/min. 6 Colemanite 60 40-1000 10°C/min. 7 Colemanite 70 40-1000 10°C/min. 8 Colemanite 80 40-1000 10°C/min. 9 Colemanite 100 40-1000 10°C/min. 10 Sodium carbonate 100 40-1000 10°C/min. 11 Calcium borate 20 40-1000 10°C/min. 12 Calcium borate 40 40-1000 10°C/min. 13 Calcium borate 50 40-1000 10°C/min. 14 Calcium borate 60 40-1000 10°C/min. 15 Calcium borate 100 40-1000 10°C/min. 16 Boron t r i o x i d e 100 40-1000 10°C/min. * Each run was repeated three times except the run for boron t r i o x i d e . -82-The heating rate was chosen as 10°C/min. i n order to separate any s e r i e s r e a c t i o n . Temperatures of 40°C and 1000°C were set for the minimum and maximum temperatures r e s p e c t i v e l y for this s p e c i f i c r e a c t i o n system. The furnace was purged with nitrogen to remove carbon dioxide whose presence i n the v i c i n i t y of the sample would i n h i b i t further r e a c t i o n . It also supplied a non-oxidative atmosphere f o r the sample holders i n the temperature range of the i n v e s t i g a t i o n . 4.2.4 Experimental Procedure and Recording of the Data. The s i m p l i f i e d procedure can be summarized as: 1. The autobalance and other c o n t r o l units and the computer were switched on with a clean weighing pan i n place and the furnace tube i n p o s i t i o n . Meanwhile the purge gas was s t a r t e d to the furnace. 2. The standard TGS-2 mini-floppy disk was placed into port '0' of the TAD s t a t i o n , while a blank formatted mini-floppy disk was placed in t o port '1'. A f t e r the required information was entered into the TAD s t a t i o n , the TG program was read into the TADS system memory and the system was commanded to proceed to the set-up s e c t i o n of the run. The required parameters and conditions were then entered i n t o the system. These parameters were also entered into the system 7/4 thermal a n a l y s i s c o n t r o l l e r . 3. The weight of the empty pan was displayed on the computer when the read weight button was pressed on the keyboard. The balance was zeroed by using coarse and f i n e zero nobs on the balance c o n t r o l . -83-Then the sample was placed i n the platinum pan. 4. The sample weight was automatically displayed on the computer when the furnace had been set back into p o s i t i o n . 5. The s t a r t button was pressed a f t e r which, the microprocessor proceeded with the heating run and accumulated the data which was also p l o t t e d on the computer d i s p l a y . The data were analyzed and the r e s u l t s were used to study the k i n e t i c s of the reactions involved. 6. When the maximum temperature was reached the unit automatically started c o oling down to the programmed minimum temperature. The t y p i c a l TG curves obtained by using t h i s experimental technique are shown i n Figures 22 to 30 for 100 percent sodium carbonate, 20, 30, 40, 50, 60, 70, and 80 percent colemanite i n sodium carbonate and 100 percent colemanite r e s p e c t i v e l y . 4.2.5 Kinetic Analysis of the TG Data. I t was necessary to r e c a l c u l a t e the weight los s data to eliminate the losses that are evident f o r colemanite when i t i s heated by i t s e l f . This loss would be included i n the curves which show the weight loss f o r mixtures of colemanite and sodium carbonate, i n proportion to the colemanite percentage i n the samples. This r e s u l t s i n higher weight losses than that due to the re a c t i o n . The curves which represent each percentage of colemanite i n sodium carbonate were d i g i t i z e d by using the d i g i t i z e r system which i s connected to the U.B.C. main computer. The curve for 100 percent colemanite was also d i g i t i z e d and a l l data was stored In separate -84-f i l e s . The value of the weight loss at a s p e c i f i c temperature for the 100 percent colemanite was corrected for the weight of colemanite i n the mixture and then subtracted from the value of the weight loss for the mixture at the same temperature. This was done for each point on the curve corresponding to the temperature i n t e r v a l s of 5°C. Plots of these corrected data were also obtained by using the Ace:Graph program which Is a v a i l a b l e i n the U.B.C. computing centre l i b r a r y . These plo t s which are shown i n F i g . 14 showed a weight increase at about 380°C on the curves. Since t h i s was impossible i t was concluded that the loss seen i n the 100 percent colemanite curve at about t h i s temperature should not be included i n the subtraction procedure. This loss might be due to the release of a substance which could be bounded by the presence of sodium carbonate. So the d i g i t i z e d data f o r 100 percent colemanite was corrected excluding the loss from 380-410°C and then the subtruction was repeated. The r e s u l t s were pl o t t e d and smoothly decreasing curves which showed the weight loss due to the r e a c t i o n were obtained for each r e a c t i o n mixture. This f i n a l form of the thermogravimetric data are shown i n Figure 34, 35, 36, 37, and 38 for 20, 30, 40, 50, and 60 percent colemanite mixtures r e s p e c t i v e l y and was used for the evaluation of k i n e t i c constants for t h i s r e a c t i o n system. A> I 400 600 TEMPERATURE ( ° C ) 800 1000 Figure 14: Results a f t e r subtraction of the colemanite curve from the others -86-4.3 Recycling Experiments A s e r i e s of experiments was performed to test the r e c y c l i n g e f f i c i e n c y of colemanite. Tests were made to determine whether there was a decrease i n the conversion of sodium carbonate due to the repeated use of colemanite for several runs. These experiments were done using both the oven and the TGS-2 system. They were performed only f or 40 percent colemanite mixtures and the r e a c t i o n temperature of 900°C. The procedure can be summarized as follows: 1. Five samples, each containing 40 percent colemanite i n sodium carbonate, were prepared i n the same way as used previously and were reacted i n the oven for 80 minutes. They were then d i s s o l v e d as described i n s e c t i o n 4.1.3 and kept i n the desiccator u n t i l c o o l . 2. A f t e r the so l u t i o n s had been cooled, carbon dioxide gas was dispersed through each s o l u t i o n f o r 15 minutes which was found to be s u f f i c i e n t to convert a l l the sodium oxide i n the s o l u t i o n to sodium carbonate. Then the so l u t i o n s were placed i n a vacuum oven and the water was evaporated from the s o l u t i o n s . 3. One of these dri e d samples was then used i n the TG f o r a n a l y s i s and the remainder were placed back into the oven for another run. 4. This procedure was continued, each time keeping one sample for the TG a n a l y s i s a f t e r each run. The TG data are shown i n Figures 61, 62 and 63 for the cases of f i r s t , second and t h i r d recycles r e s p e c t i v e l y . -87-Some a d d i t i o n a l experiments were also performed to determine the boron content and the s o l u b i l i t y of the colemanite. Boron an a l y s i s was made by an acid e x t r a c t i o n method which i s described i n Appendix I. S o l u b i l i t y experiments showed that 60 percent of the colemanite i s ins o l u b l e i n water at 20°C (26). -88-5. ANALYSIS OF THERMOGRAVIMETRIC DATA Thermogravimetric data was analyzed i n two parts; r e a c t i o n between 190-700°C and the re a c t i o n between 700-1000°C. (See Figures 23-29.) The temperature 700°C where the d e r i v a t i v e curve shows a peak which represent a change i n the r e a c t i o n mechanism was chosen as the temperature at which the f i r s t r e a c t i o n stops and the second r e a c t i o n s t a r t s . This point w i l l be discussed In more d e t a i l i n s e c t i o n 6.2. These two reactions were not analyzed as simultaneous reactions f or two main reasons. The d e r i v a t i v e of the weight loss curve showed a sharp break at about 700°C regardless of the colemanite concentration i n the mixtures. The d i g i t a l thermal analyzer (DTA) data also showed a peak which i s due to a new heat e f f e c t . This peak can not be seen above a concentration of colemanite higher than the s t o i c h i o m e t r i c amount needed. In a d d i t i o n , the assumption that these two reactions were taking place simultaneously would have made the a n a l y s i s of the TG data very complex. 5.1 Analysis of the Data for the F i r s t Reaction The method which was developed by Zsako (31) was applied for the analysts of the TG curves which were obtained for the decarbonization r e a c t i o n of sodium carbonate i n the presence of colemanite. A n a l y t i c a l forms of the functions f(oc) and g(a) for the most probable r e a c t i o n mechanisms are tabulated i n Table 8. U t i l i z a t i o n of eq. (3.18) enables the c a l c u l a t i o n of the f r a c t i o n a l conversion of sodium carbonate,a g, throughout the whole temperature range of the -89-r e a c t i o n simply by reading the value of W from the TG curve (e.g. F i g . 34) f o r each corresponding temperature. S u b s t i t u t i o n of these a s values into the equations for g(oc) tabulated i n Table 8 gives the values of function g(a) for each temperature. The following steps were followed to f i n d the k i n e t i c constants of t h i s r e a c t i o n : 1. One of the mechanisms l i s t e d i n Table 8 was presumed. For every temperature s t a r t i n g from 460°K, <xs and the corresponding log g(a) were c a l c u l a t e d at temperature i n t e r v a l s of 10°K. At the same time values were chosen, s t a r t i n g with 1 Kcal/mol and increasing at each step by 1 Kcal/mol, and log p(x) values were evaluated by using the "U.B.C. I n t e g r a l " program f o r the same T values used i n the c a l c u l a t i o n of log g(oc) values. 2. By taking the d i f f e r e n c e s between the log g(cc) and log p(x) values at each temperature, B^ values were found u t i l i z i n g equation (2.24) i n s e c t i o n 2.4. Standard d e v i a t i o n of these B values, 6, were then c a l c u l a t e d by using equation (2.25). 3. This procedure was repeated f o r each mechanism l i s t e d In the table and the minimum of the standard d e v i a t i o n values, 6 . , were min noted f o r each run, corresponding to a s p e c i f i c E^, m and n value. The equation with the smallest 6 . value among these was taken as the best min mechanism that f i t s t h i s p a r t i c u l a r r e a c t i o n and the corresponding value was given as the a c t i v a t i o n energy of the r e a c t i o n . -90-In a d d i t i o n to this comparison which depends on the standard deviations, a double check was made by r e c a l c u l a t i n g the a g values using the chosen m and n values and best value. Calculated values of <xs were then compared with the values of a s obtained from the experimental TG curve. 5.2 Analysis of the Data f o r the Second Reaction The same method which was used for the evaluation of the k i n e t i c model f or the f i r s t r e a c t i o n was followed for the reaction which took place within the temperature range from 700-1000°C. A l l the proposed mechanisms which were l i s t e d i n Table 9 were tested by both evaluating the standard deviations and making the comparison of experimental and t h e o r e t i c a l f r a c t i o n a l conversions of sodium carbonate. The expression which was derived for the f r a c t i o n a l conversion of sodium carbonate eq. (3.18) (see section 3.1.2) applies for this r e a c t i o n too. An important point was the s u b s t i t u t i o n of the r i g h t value f o r the lower l i m i t of the i n t e g r a l i n eq. (2.21), which i s the f r a c t i o n a l conversion of sodium carbonate at the end of the f i r s t r e a c t i o n instead of zero, i n order to f i n d the value of function g(a). -91-6. RESULTS AND DISCUSSION The main aim of t h i s project i s to f i n d the best a u t o c a u s t i c i z i n g agent for the d i r e c t conversion of sodium carbonate to sodium oxide and to study the k i n e t i c s of t h i s r e a c t i o n for the chosen system. The study was performed i n two main parts, as isothermal and as thermogravimetric experiments. 6.1 Isothermal Experiments Percentage conversion of sodium carbonate as a function of time was c a l c u l a t e d f or each of the a u t o c a u s t i c i z i n g agents which were titanium dioxide, alumina and colemanite, by using the t i t r a t i o n data taken i n isothermal experiments (Tables 11, 12, 13, and 14). Conversion c a l c u l a t i o n s were based on the t o t a l t i t r a t e d amount of unreacted and reacted sodium carbonate rather than the i n i t i a l amount of sodium carbonate at the s t a r t of the experiments. The reason f o r t h i s was the d i f f i c u l t y i n recovering the whole sample from the c r u c i b l e s because the r e a c t i o n products fused Into a s o l i d mass when the samples were cooled. It was assumed that the samples were homogeneous so that the sample which was recovered from the c r u c i b l e resembled the whole sample. As such It had the same r a t i o of unreacted to reacted sodium carbonate. Since the samples were prepared by s l u r r y mixing t h i s assumption would be reasonable. A sample c a l c u l a t i o n of conversion i s shown i n Appendix I I . -92-Figures 15 and 16 show the r e s u l t s for 10 and 20 percent titanium dioxide r e s p e c t i v e l y . In both cases higher conversions are obtained at higher temperatures f o r a given time. This i s a t y p i c a l Arrhenius behaviour. I t i s also seen that higher a u t o c a u s t i c i z i n g agent concentration gives higher conversion values. This i n d i c a t e s that r e a c t i o n rate i s proportional to the mass of a u t o c a u s t i c i z i n g agent. It was found that 50 percent conversion can be obtained at 1000°C i n 50 minutes by using titanium dioxide at a concentration of 20 percent. These r e s u l t s are s i m i l a r to those obtained by K i i s k i l a (18). Figures 17 and 18 show the r e s u l t s for alumina. There i s a l o t of s c a t t e r i n t h i s data because of the in t e r f e r e n c e i n the t i t r a t i o n s due to A1(0H) 3 formation ( 9 ) . The e f f e c t of colemanite as an a u t o c a u s t i c i z i n g agent for the d i r e c t reduction of sodium carbonate to sodium oxide i s shown i n Figures 19, 20 and 21. It i s seen that colemanite accelerated the rea c t i o n as well as titanium dioxide d i d . It i s also noticed that the r e a c t i o n i s f a s t e r than the one with titanium dioxide. In the case of colemanite, higher percentages were examined because of the high molecular weight of the colemanite and uncertainty about i t s p u r i t y . For low colemanite concentrations such as 10 and 20 percent the molar r a t i o of the B 2 0 3 , which i s believed to be the e f f e c t i v e part of the colemanite, to the sodium carbonate i s low because of the high molecular weight of the colemanite. Therefore colemanite doesn't seem superior to titanium dioxide when the Figures 15, 16 and 19 are compared for the same agent percentages. % C O N V E R S I O N -C6-- 7 6 -% C O N V E R S I O N -56--96-TEMPERATURE: 900°C 10 20 30 40 50 T I M E (min. ) Figure 19: Results of the isothermal runs for 10, 20 and 30 percent colemanite. -98-In Figure 20 the r e s u l t s of the runs with 40, 50 and 60 percent colemanite i n sodium carbonate are p l o t t e d . These r e s u l t s show that t t i s possible to obtain a conversion as high as 80 percent i n half an hour at 900°C. Since colemanite i s a cheaper material the use of i t i n large amounts would not be too c o s t l y e s p e c i a l l y since i t would most l i k e l y be recycled. Figure 21 shows the e f f e c t of the temperature on the r e a c t i o n . A t y p i c a l Arrhenius e f f e c t i s observed as i s the case for the other a u t o c a u s t i c i z i n g agents studied. Temperatures above 900°C were not studied since the re a c t i o n would be too fast above 900°C. With both agents i t i s noticed that the re a c t i o n rate for a l l runs i s most rapid at f i r s t and then f a l l s o f f with time. This could be explained by the reduction i n reactant concentration with time. In these experiments the major source of error i s the time elapsed before the samples a t t a i n the required temperature a f t e r being introduced into the preheated oven. Reaction occurs to a c e r t a i n extent during t h i s heat up period so that the measured value of the conversion corresponding to a c e r t a i n time i s decreased due to the occurence of the slow re a c t i o n before the desired temperature was a t t a i n e d . This i s a common problem associated with the isothermal method. It i s greatest for the shorter time periods and Is e s p e c i a l l y important for f a s t reactions l i k e the one between colemanite and sodium carbonate. Other errors a r i s e from the experimental procedures such as uncertainty i n the volumes of acid recorded during the t i t r a t i o n s , p r o b a b i l i t y of carbon dioxide absorption by the samples during the TEMPERATURE :900°C 10 20 30 40 50 T I M E (min.) Figure 20: Results of the isothermal runs for 40, 50 and 60 percent colemanite. % C O N V E R S I O N **1 00 c 1 re r o »—• 73 CD CD r-r-1 r r CO O i-r> r r - H zr (i is 0 m 3 " M ma 3 ru 3 ns rtl O rj n O r-1 ft) 3 W H-r r fD 8-CO O " 8--001--101-t r a n s f e r of c r u c i b l e s from oven to desi c c a t o r , the weighing and the d i s s o l u t i o n steps. 6.2 Differential Thermogravimetric Analysis At t h i s stage of the study, a new d i f f e r e n t i a l thermal analyzer was bought by the department. The thermogravimetric method has many advantages over the isothermal method (see se c t i o n 2.3). I t s use can eliminate most of the errors caused by the other experimental procedures and make possible a better understanding of the r e a c t i o n mechanism by g i v i n g information about the sample at any moment. This added information allows the observation of multiple reactions If they occur. Since colemanite gave the highest rates for t h i s r e a c t i o n i t was chosen as the best a u t o c a u s t i c i z i n g agent and further studies are performed on i t by using thermogravimetric techniques. The outputs of the thermogravimetric measurements are shown i n Figures 22 to 30 f o r 0 to 100 percent colemanite concentrations r e s p e c t i v e l y . Sodium carbonate w i l l only begin to d i s s o c i a t e very slowly above 875°C (Figure 22) unless an a u t o c a u s t i c i z i n g agent i s added. From Figures 23 to 29 It i s seen that the re a c t i o n has i t s maximum rate around 640°C f o r a l l cases. There are two common points which can be seen when these curves are examined q u a l i t a t i v e l y . These are the weight losses seen up to 192°C and the i n f l e c t i o n point between 650°C and 700°C, which i s best shown by the d e r i v a t i v e of the weight loss curve. Since the samples were dried at 110°C before use the loss around 190°C would be due to the loss of water of hydration rather than free moisture. The break point between 650-700°C i s most l i k e l y due to SODIUMCARONLY WTi 19.9849 mg SCAN RATEi 10.00 d.g/mln FROMi 641.04 TOi 987.73 WT. X CHANGEi 1.77 98.01X 96. 24X 200 ' 4CX) ' 600 " " 1 800 ' 1000 TEMPERATURE (°C ) F i g u r e 22: Thermogravimetric data for 100 percent sodium carbonate. h-X q LU •z LU U CC LU Cu m co o COLEMANITE 20 - DER IVATIVE WTi 20 . 1700 mg SCAN RATEl 10. 0 0 eUg/m in o LO I I I I I 1 1 I — 200 400 600 800 TEMPERATURE (°C ) Figure 23: Thermogravimetric data for 20 percent colemanite. I 1000 , , , , , , , , — — i — 200 400 600 800 1000 TEMPERATURE (°C ) Figure 24: Thermogravimetric data for 30 percent colemanite. PERCENT WEIGHT -SOI-TEMPERATURE (°C ) Figure 26: Thermogravimetric data for 50 percent colemanite. 2 0 0 4 0 0 600 ' 800 ' 1000 TEMPERATURE (°C ) Figure 27: Thermogravimetric data for 60 percent colemanite. COLM70 WTi 31.5988 mg SCAN RATEi 10.00 d.g/min - DERIVATIVE , | r 1 1 1 1 1 1 200 400 600 800 1000 TEMPERATURE (°C ) Figure 28: Thermogravimetric data for 70 percent colemanite. COLEMANITE80 WTi 2 9 . 3 3 7 2 mg SCAN RATEi 10.00 d . g / m i n i i r i i I 1 I I 200 400 600 800 1000 TEMPERATURE (°C ) Figure 29: Thermogravimetric data for 80 percent colemanite. -110-the end of one reaction which i s followed by another. These two reactions could be series reactions i f the rate of the second reaction i s very small below 700°C. When the Figures 27 to 29 are examined i t i s seen that the curves l e v e l o ff above about 700°C as the percentages of colemanite increases. This indicates that the second phenomena (or reaction) doesn't occur above c e r t a i n concentrations of colemanite. In order to be able to determine the stoichiometric amount of colemanite necessary for the complete conversion of sodium carbonate i t was necessary to know the boron content and the amount of impurity i n the colemanite. Boron analyses were performed as described i n Appendix I. It was found that the colemanite used i n these experiments contains 38 percent B 2 0 3 (26). Since pure colemanite contains 50.83 percent B 20 3, i t was not pure, but contained 25.24% impurities. By u t i l i z i n g the phase diagram shown i n Figure 10 i t was calculated that the stoichiometric amount of colemanite for the reaction i s 63.3% (see Appendix II for c a l c u l a t i o n ) . The r e s u l t s from thermal c a l o r i m e t r i c experiments on this reaction done by others (10) also showed the peaks due to the thermal events noted i n the thermogravimetric curves at the same temperatures. The following explanation of the curves can then be made from the r e s u l t s of the boron analyses. For the low colemanite percentages the reaction continues above 700°C because there i s not enough B 2 0 3 to react with a l l the Na 2C0 3 a v a i l a b l e . The unreacted part of the Na 2C0 3 then decomposes by i t s e l f at higher temperatures. In the case of colemanite concentrations higher than the stoichiometric amount necessary, the second reaction doesn't occur because there i s no - I l l -sod i urn carbonate l e f t unreacted. There i s a good match between the colemanite percentage for which the curves l e v e l o f f and the calculated stoichiometric amount, which i s 63.3 percent, when the errors which are associated with the boron analyses are considered. In Figure 30 the output of a run i n which 100 percent colemanite was used i s shown. The colemanite i s not stable over the studied temperature range and loses a considerable amount of weight during heating. The weight loss which i s seen around 190°C can be explained as water of dehydration. It was d i f f i c u l t to determine what caused the loss around 410°C. The run with the pure B2O3 showed that B2O3 loses weight between 150°C and 400°C ( F i g . 31). It was thought that this loss around 410°C might be due to the loss coming from free B 2 0 3 i n the colemanite. There i s also a weight loss between 650-750°C. The same phenomena i s also seen In the output of 100 percent calcium borate ( F i g . 32). This indicates that the loss at this temperature Is not coming from the impurities i n the colemanite since i t i s seen i n the pure calcium borate case too. F i g . 33 shows the comparison of the curves for these three compounds. Since colemanite loses weight during heating the thermogravimetric data was recalculated by subtracting a proportion of the colemanite curve from the curves of other runs as described i n section 4.2.5. The f i n a l form of the data are presented i n the Figures 34 through 38 for 20, 30, 40, 50 and 60 percent colemanite concentrations r e s p e c t i v e l y . o I  N - * — i 1 1 r 1 1 1 1 1 1— 200 400 600 800 1000 TEMPERATURE (°C ) Figure 30: Thermogravimetric data for 100 percent colemanite. o CO" o CO" BORON TRI OXIDE ONLY DERIVAT IVE V WTi 1 5 . 8 6 8 6 mg SCAN RATEi 1 0 . 0 0 d « g / m i n 200 460 ' 600 T E M P E R A T U R E ( °C ) 8 0 0 1000 Figure 31: TG results for 100 percent boron t r i o x i d e , -711-q oi O q R H — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — 40 160 280 400 520 640 760 880 1000 TEMPERATURE (C) Figure 33: Comparison of TG results for colemanite, boron t r i o x i d e and calcium borate. Figure 34: Recalculated Data for 20 Percent Colemanite. o 81 i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 200 300 400 500 600 700 800 900 1000 TEMPERATURE (C) Figure 35: Recalculated Data for 30 Percent Colemanite. o o UJ -OL P o_ co q sH—I—I—I—I—I—I 1 1 1 1 1 1 1 1 1— 200 300 400 500 600 700 800 900 1000 TEMPERATURE (C) Figure 36: Recalculated Data for 40 Percent Colemanite. o O I S H — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — 200 300 400 500 600 700 800 900 1000 TEMPERATURE (C) Figure 37: Recalculated Data for 50 Percent Colemanite. q d o SH— I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I 200 300 400 500 600 700 800 900 1000 TEMPERATURE (C) Figure 38: Recalculated Data for 60 Percent Colemanite. -121-6.2.1 Model of f i r s t r e a c t i o n . These corrected data were d i g i t i z e d and analyzed to determine a k i n e t i c model which includes the reaction order, a c t i v a t i o n energy and rate constant of the reacti o n . The expressions for the f r a c t i o n a l conversions of the sodium carbonate and colemanite are also shown i n section 3.2.1 and 3.2.2 r e s p e c t i v e l y . In the de r i v a t i o n of these equations the following assumptions were made. - A l l the weight loss comes from the expulsion of carbon dioxide so the losses due to sodium or sodium oxide at elevated temperatures are assumed n e g l i g i b l e . - The e f f e c t of the second reaction i s very small i n the temperature range of 190-700°C so only one reaction i s occurring over t h i s temperature range. - The Arrhenius r e l a t i o n s h i p was assumed for the temperature dependence of the rate constant. The error which w i l l be produced by the f i r s t assumption should be quite small because sodium w i l l most l i k e l y not v o l a t i l i z e below 900°C. It was also reported that the presence of boron decreases the sodium losses at high temperatures (10). The errors caused by the second assumption w i l l be discussed a f t e r the r e s u l t s of the modelling have been shown. The s t a r t i n g point for the f i r s t reaction was taken as 192°C. The temperature at which the f i r s t reaction stops and the second rea c t i o n s t a r t s was calculated as the point where the boron content of the colemanite i s a l l consumed so that there i s no boron to react f u r t h e r . The temperatures which were predicted by the computer program -122-as such were only + 20°C d i f f e r e n t from the temperatures at which the break point on the d e r i v a t i v e curves occurred for a l l colemanite concentrations (see Figure 23 to 29). As i s seen from these figures the temperature at which the d e r i v a t i v e curve shows a break doesn't change with the colemanite concentration. The i t e r a t i v e procedure for the evaluation of the k i n e t i c constants was described i n section 5.1. Table 16 shows the standard deviation of B values for d i f f e r e n t kinds of mechanisms for 60% colemanite, where m and n are the orders of the reactions and Ej^ i s the a c t i v a t i o n energy. The standard deviations for the other colemanite percentages are given i n Appendix IV. As can be seen from t h i s table and the standard deviation r e s u l t s shown i n Appendix IV, the minimum of these standard deviations cannot be chosen e a s i l y . Since those values are a l l very close to each other and are a l l reasonably small, choosing the minimum among them i s not necessarily c o r r e c t . The reason for such r e s u l t s can be c l e a r l y seen from Figure 39. Figure 40 shows that the shape of the curves for log g(a) (concave up) and -log p(x) (concave down) are quite d i f f e r e n t from each other as w e l l . Another approach for choosing the best model i s to recheck the r e s u l t s found from the a p p l i c a t i o n of t h i s method by comparing the f r a c t i o n a l conversions found experimentally with the ones predicted by each proposed model. Figure 41 shows the comparison of the best f i t t i n g models to experimental data for 60 percent colemanite. From th i s figure i t i s seen that the model which best f i t s the data i s zero -123-Table 16: Standard deviation of B values for 60 percent colemanite. Proposed A c t i v a t i o n Standard deviation Mechanism Energy &min (kcal/mol) m = 0 m = 0 7.15 0.21028 m = 0 n = 1/3 7.A5 0.20946 m = 0 n = 1 8.25 0.21979 m = 1/3 n = 0 7.40 0.20930 m = 1/2 n = 0 7.6 0.20937 m=0; n=1 m=1/3; n=1 m=1/2; n=1 m=2/3; n=1 m=1; n=1 m=2; n=1 m=0; n=0 J -Iog(g(o0) — i — i — i — i — i — i — i — i — i — i — i — i — i — r - 1 — i — i — i r 440 500 560 620 680 740 800 860 920 980 TEMPERATURE (K) 1040 Figure 39: Plot of log g(a) values for 60 percent colemanite. q 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I I I 440 500 560 620 680 740 800 860 920 980 1040 TEMPERATURE ( K ) Figure 40: Comparison of log g(ct) values with log p(x) values. -127-order i n both sodium carbonate and colemanite concentrations. That i s , the rate i s s o l e l y a function of the reaction temperature. In order to decide on the a c t i v a t i o n energy of the reaction, standard deviations were found at each colemanite concentration for the values using the above model. It was noticed that the values of a c t i v a t i o n energy which gave the minimum standard deviation for the mechanism of m = 0 n = 0 were d i f f e r e n t for each case. That i s , i t was a function of colemanite concentration. The following table shows the a c t i v a t i o n energies found f o r each colemanite percentages. The comparison of the model predictions with the experimental r e s u l t s are plotted In Figures 42, 43, 44, and 45 for each case using the a c t i v a t i o n energies calculated for each. A reasonably good f i t was found e s p e c i a l l y up to 900°K. At higher temperatures the model predicts lower conversions than those found experimentally. This could be due to a contribution from the second reaction when the temperature becomes high enough for the d i r e c t decomposition of sodium carbonate and both reactions take place simultaneously. Since the e f f e c t of the second reaction was assumed to be n e g l i g i b l e i n the d e r i v a t i o n of the model t h i s high temperature deviation from the model i s not unexpected. This explanation i s substantiated by the r e s u l t s shown i n Figure 45 which shows a perfect f i t even at high temperatures for 60 percent colemanite. Since 60 percent i s approximately the stoichiometric colemanite concentration necessary for the complete conversion of sodium carbonate, the second reaction doesn't occur. So i n t h i s case the second assumption p r e v a i l s . Table 17: Activation energies which give best f i t s to experimental data. % Colemanite Activation Standard deviation Energy o m i n (kcal/mol) 30 5.5 0.18198 40 6.0 0.19007 50 6.4 0.19007 60 7.15 0.21028 00 C M d o CO ^. CO CM oo o o d o d MODEL EXPERIMENTAL / / // / / ^y r n ^ i I I I I yy yy * i i i i i i i i i i 440 504 568 632 696 760 824 888 TEMPERATURE OO Figure 42: Comparison of the Model Predictions with the Experimental Results for 30 Percent Colemanite 952 1016 1080 Figure 43: Comparison of the Model Predictions with the Experimental Results for 40 Percent Colemanite. -131-CM 44-0 5 4 0 6 4 0 7 4 0 8 4 0 9 4 0 1 0 4 0 T E M P E R A T U R E ( K ) Figure 44: Comparison of the Model Predictions with the Experimental Results for 50 Percent Colemanite. - 1 3 2 -1 0 4 0 TEMPERATURE (K) Figure 45: Comparison of the Model Predictions with the Experimental Results for 60 Percent Colemanite. -133-The values of frequency factor, Z j , were calculated by using the equation 2.24 and using the values found for each case for the values of m and. n equal to zero. Equation 3.13 takes the following form for this s p e c i f i c mechanism ZE "" ^  8(a) = £ T Wg p(x) (6.1) o This can also be written i n the logarithm form as ZE ~^ log g(o) - log p(x) = log (— Wg ) = B (6.2) o Sample c a l c u l a t i o n s of Z^ and kj^ values are shown i n Appendix I I . Table 18 shows the parameters calculated for the model at 900°C. As can be seen from t h i s table the rate constant of the reaction i s a function of colemanite concentration as a r e s u l t of both a c t i v a t i o n energy and frequency factor being functions of the colemanite concentration. These r e s u l t s were i n c o n f l i c t with the model which determines the rate as zero order on both reactant concentrations. Colemanite concentration i n d i r e c t l y a f f e c t s the rate constant k^ which i s expected to be constant at constant temperature. This could i n d i c a t e a very complex rate equation for t h i s reaction. The e f f e c t of the colemanite concentration on the a c t i v a t i o n energy, E^, and frequency factor, Z^, i s shown i n Figures 46 and 47 r e s p e c t i v e l y . In both of these figures i t i s seen that there i s a systematic change i n these k i n e t i c constants with the change i n colemanite percentage. This shows that this change doesn't come from the experimental errors and i t Table 18: Kinetic constants for the f i r s t reaction.* Percent Colemanite Activation energy (E 1) cal/mol Frequency factor (Zl) g/min Rate constant ( k l ) g/min 30 5500 16.802 1.587 40 6000 37.180 2.833 50 6400 69.003 4.430 60 7150 180.172 8.383 * Rate constants are calculated at 900°C. -135"-Figure 46: E f f e c t of colemanite concentration on the a c t i v a t i o n energy, E,. o o -m 30 40 50 60 % COLEMANITE Figure 47: E f f e c t of colemanite concentration on the frequency factor, Z^. - 1 3 7 -i s s p e c i f i c for t h i s reaction system. At this point i t i s evident that further studies must be made of this reaction by modifying the model to take into consideration the e f f e c t of the colemanite concentration on the k i n e t i c constants. In order to be able to express the a c t i v a t i o n energy and frequency factor i n terms of the colemanite concentration, the points on Figures 46 and 47 were f i t t e d to an equation by using the OLSF subroutine from the U.B.C. computing centre l i b r a r y . As a r e s u l t i t was found that the a c t i v a t i o n energy changes with colemanite percentage l i n e a r l y according to the following equation E i = 3.75 + 0 .055 Y ( 6 . 3 ) c ' The change i n the frequency f a c t o r , Z^, was found to be exponential and expressed as 0.08Y l l = 1.384 e C ( 6 . 4 ) So the equation of the rate constant for the f i r s t reaction can be w r i t t e n as i n the following form. 0.08Y 3.75 + 0.05 Y k i = 1.384 e C exp ( ^ ^) (6.5) The k i n e t i c constants which are recalculated by using these equations are tabulated i n Table 1 9 . Table 19: Kinetic constant for the f i r s t reaction calculated by using equation 6.3, 6.4 and 6.5. Percent Colemanite Activation energy ( Ex ) cal/mol Frequency factor ( Z X ) g/min Rate constant ( k l ) g/min 30 5400 15.400 1.520 40 5950 35.620 2.773 50 6500 75.010 4.613 60 7050 174.024 8.452 -139-Figures 48 to 51 show the r e s u l t s a f t e r the modification of the model according to the new values of a c t i v a t i o n energy and frequency f a c t o r , calculated from equation 6.3 and 6.4. These figures show s i m i l a r f i t to the ones found by using the a c t i v a t i o n energy values which are found for each case s p e c i f i c a l l y . 6.2.2 Model of Second Reaction. The thermogravimetric data was also analyzed i n the temperature range of ~ 700-1000°C where the second reaction takes place. As was mentioned before t h i s reaction could be the decomposition of sodium carbonate either by i t s e l f or i n the presence of the impurities i n colemanite. The impurities i n colemanite consist of alumina, iron oxide and s i l i c a which are also believed to have an a u t o c a u s t i c i z i n g e f f e c t on the reaction. So these substances might further react with the unreacted part of the sodium carbonate. The method of analysis of th i s reaction was s i m i l a r to that used for the analysis of the f i r s t reaction and described i n section 5.2. The losses due to the v o l a t i l i z a t i o n of sodium at high temperatures were assumed n e g l i g i b l e . The minimum, 6 . , of the standard deviations was searched for min at 0.1 Kcal increments of E a for each mechanism as was done for the anal y s i s of the f i r s t r eaction. The s t a r t i n g temperature of this reaction i s taken as the temperature where the f i r s t reaction stops. It was found that the reaction i s f i r s t order with respect to the sodium carbonate concentration even though some of the other mechanisms Figure 48: Comparison of the Results a f t e r the Modification of the Model for 30 Percent Colemanite. 00 CO • cr CM UJ >° o . ID o i=° 0 _ < oo 01 O LA- 6 o d MODEL EXPER IMENTAL / 4 4 0 5 0 0 ~i—i—i—i—i—i—i—i—i—r 5 6 0 6 2 0 680 7 4 0 8 0 0 T E M P E R A T U R E ( K ) 1—r 8 6 0 n—r 920 9 8 0 Figure 49: Comparison of the Results a f t e r the Modification of the Model for 40 Percent Colemanite. 440 500 560 620 680 740 800 860 920 980 TEMPERATURE (K) Figure 50: Comparison of the Results a f t e r the Modification of the Model for 50 Percent Colemanite. CD CO d TEMPERATURE ( K ) Figure 51: Comparison of the Results a f t e r the Modification of the Model for 60 Percent Colemanite. -144-show minimum standard deviations lower than the minimum value obtained for the f i r s t order case. When the f r a c t i o n a l conversions were plotted, f i r s t order i s the one which gives the best f i t to the experimental data. These r e s u l t s are shown i n Figures 52, 53, 54 and 55 for 20, 30, 40 and 50 percent colemanite percentages r e s p e c t i v e l y . These a l l show extremely good f i t s even at high temperatures. When the f i n a l values for conversions are examined for a l l colemanite percentages i t can be concluded that the substances or impurities i n the colemanite act as agents or possibly c a t a l y s t s for the conversion of sodium carbonate to sodium oxide because there i s a considerable amount of conversion due to the second reaction which cannot be achieved by the self-decomposition of sodium carbonate (see F i g . 22). These r e s u l t s also show that i t i s possible to obtain conversions as high as 60 percent even by using the colemanite i n concentrations as small as 30 percent. This i s an important factor i n the choice of colemanite as the best a u t o c a u s t i c i z i n g agent when the p o s s i b i l i t y of having problems due to the use of colemanite i n large quantities i n the m i l l a p p l i c a t i o n i s considered. Even though the use of colemanite i n stoichiometric amounts (63.35 percent) gives much better r e s u l t s at lower temperatures, the decision on how much colemanite should be used must be found by an economic evaluation. Rate constants for the second reaction were also calculated by using the same technique used i n the f i r s t part. A sample c a l c u l a t i o n of frequency factor and rate constants i s shown i n Appendix I I . The r e s u l t s are tabulated i n Table 20. As i s seen from this table i — i — i — i — i — i — i — i — i — r — i — i — i — i — i — i — i — 960 1000 1040 1080 1120 ' 1160 1200 1240 1280 TEMPERATURE (K) Figure 52: Comparison of the Model with the Experimental Results for Second Reaction for 20 Percent Colemanite. ON T — i — i — i — i — i — i — i — i — r 1040 1080 1120 1160 1200 TEMPERATURE (K) Figure 53: Comparison of the Model for the Second Reaction with the Experimental Results for 30 Percent Colemanite. Figure 54: Comparison of the Model for the Second Reaction with the Experimental Results for 40 Percent Colemanite. Figure 55: i — i — i — i — i — i — i — i — i — r 1040 1080 1120 1160 1200 TEMPERATURE (K) Comparison of the Model for the Second Reaction with the Experimental Results for 50 Percent Colemanite. Table 20: Kinetic constants for the second reaction.* Percent Colemanite Activation energy (E 2) cal/mol Frequency factor ( Z2), (min _ 1 ) Rate constant (min _ 1 ) 20 3900 0.049 9.27 x 1 0 - 3 30 4700 0.174 0.024 40 5800 0.567 0.048 50 13000 64.47 0.244 * Rate constants are calculated at 900°C. -150-the k i n e t i c constants change with the concentration of colemanite. The model assumes that the colemanite, or more c o r r e c t l y , the substances i n i t other than boron act as a true c a t a l y s t so that t h e i r concentration doesn't change throughout the r e a c t i o n . So the changes i n E 2 and Z 2 with the change i n colemanite percentage are unpredictable. An attempt was made to least square f i t the points on Figures 56 and 57 i n order to be able to express the changes i n both a c t i v a t i o n energy, E 2 , and frequency fa c t o r , Z 2, with the change i n colemanite concentration. I t was found that the change i n both k i n e t i c constants with the colemanite percentage ( i n the range of 10-60 percent colemanite) can be described by a t h i r d order polynomial. The goodness of f i t for these equations was very high. The output of the computer program which shows the c o e f f i c i e n t s of this polynomial i s i n Appendix V. As a r e s u l t , the following equations for the a c t i v a t i o n energy and frequency factor can be written E, = - 19999.0013 + 2518.23627 Y - 85.4970639 Y 2 * c c + 0.966638716 Y 3 (6.6) Z, = - 252.342474 + 27.3482681 Y - 0.947228943 Y 2 i c c + 0.0105397707 Y 3 (6.7) c ACTIVATION ENERGY (kcal/mol) 4 6 8 TO 12 I ' i l I — - 1 S T -- 1 5 2 -2 0 3 0 4 0 50 % C O L E M A N I T E Figure 57: E f f e c t of Colemanite Concentration on the Frequency Factor, Z 2--153-The values of the kinetic constants which were calculated using equations 6.6 and 6.7 are tabulated in Table 21 and were used for further calculations. The rate constant for the second reaction can be written as k, - (- 252.34 + 27.348 Y - 0.947 Y 2 + 0.010 Y 3) * * c c c (- 19999 + 2518.23 Y^  - 85.49 Y_2 + 0.966 Y^3) exp [- £== — ](6.8) Recalling that the rate of f i r s t reaction is independent of the reactant concentrations and the rate of the second raction is f i r s t order of the sodium carbonate concentration, the f i n a l forms of the rate expressions can be written as ki (6.9) dti i -1 where kt = ki W 1 1 s o da 2 — - k 2 (1 - a 2) (6.10) where kj^ and k 2 are the rate constants given as functions of the colemanite concentration by eq. (6.5) and eq. (6.8) for the 1st and 2nd reaction respectively. Table 21: Kinetic constants for the second reaction calculated by using equation 6.6 and 6.7.* Percent Colemanite Activation energy (E 2) cal/mol Frequency factor ( Z 2 ) (min _ 1 ) Rate constant ( k 2 ) (min _ 1 ) 20 3900 0.052 9.75 x 1 0 - 3 30 4699 0.182 0.024 40 5800 0.588 0.048 50 13000 64.51 0.244 * Rate constants are calculated at 900°C. -155-6.3 Comparison of the Model with the Results of Isothermal  Experiments. The reaction model i n i t s f i n a l form was used to calculate the f i n a l conversions at 900°C for d i f f e r e n t reaction times and the re s u l t s were compared with the r e s u l t s of the isothermal experiments for each colemanite concentration. As was stated before the f i r s t and second reactions are d i f f e r e n t i n nature. The previous r e s u l t s showed that the f i r s t reaction stops when the active part of the colemanite i s f i n i s h e d , because colemanite acts as a reactant rather than a c a t a l y s t . So u n t i l t h i s point i s reached both reactions take place at the same time and then the second reaction continues u n t i l the amount of sodium carbonate a v a i l a b l e i s a l l consumed. A possible reason why the f i r s t and the second reactions take place at the same time even though the second reaction doesn't seem to s t a r t before the f i r s t reaction f i n i s h e s or a c e r t a i n temperature i s reached during the thermogravimetric experiments Is that the second reaction might not s t a r t before the temperature at which the mixture i s a l l melted. In fac t the DTA work on the same reaction showed a physical change which could be melting around the temperature where the second reaction started (26). When the samples were placed into the furnace at 900°C both reactions could take place simultaneously because the temperature i s high enough for melting to occur and for the second reaction to take place at an appreciable r a t e . Thus at the beginning of the reaction the o v e r a l l rate of the reaction i s expressed as -156-da dt = k i + k 2 (1-a) (6.11) or k i + k 2 - k 2 a da The time at which the f i r s t reaction ceased can be calculated from the integrated form of eq. (6.9) by knowing the conversion value at the end of the f i r s t reaction from the Figures 24 to 26 for each colemanite percentage. These times are found to be ti = 17.05 min for 30% colemanite t i = 15.083 min for 40% colemanite t^ = 12.693 min for 50% colemanite For times longer than these the following equation which i s the integrated form of the equation (6.10) i s used to f i n d the conversions. The following table shows the rate constants as well as the f r a c t i o n a l conversions. These r e s u l t s are compared with the r e s u l t s of the isothermal experiments i n Figures 58, 59 and 60 for the 30, 40 and 50 percent colemanite cases r e s p e c t i v e l y . These figures show that this model predicts the conversion values very well s p e c i a l l y i n the f i r s t 10 a 2 = 1 - [(1-a') exp ( - k 2 ( t 2 - t 1 ) ) ] (6.12) T a b l e 22: Rate c o n s t a n t s and f r a c t i o n a l c o n v e r s i o n s f o r the 1st and 2nd r e a c t i o n . P e rcent Colemanite g/min k 2 i (min _ 1 ) t (min) a' a 2 10 0. 351 0 .351 20 0. 552 0 .582 30 1 520 0 .024 30 0. 552 0 672 40 0. 552 0 743 50 0. 552 0 798 10 0. 596 0 596 20 0. 804 0 846 40 2 773 0 048 30 0. 804 0 905 40 0. 804 0 942 50 0. 804 0 964 5 0. 841 0. 841 10 1. 0 1. 0 50 4 613 0 244 20 1. 0 1. 0 30 1. 0 1 0 40 1. 0 1. 0 TEMPERATURE : 9 0 0 ° C Z o CO C£ LU > z o o o o, 00 o CD o CN • ISOTHERMAL * MODEL •09 I T " 5 0 T IME (m in . ) Figure 58: Comparison of the Model with the Results of Isothermal Experiments for 30 Percent Colemanite. TEMPERATURE : 900 C o o Z O o. — CO to U l > o, Z co O u o CM ISOTHERMAL MODEL — i 1 1 1 r 10 20 30 40 50 T IME (m in . ) Figure 59: Comparison of the Model with the Results of Isothermal Experiments for 40 Percent Colemanite. T E M P E R A T U R E : 900 °C — , 1 1 1 r 10 20 30 40 50 TIME ( m i n . ) Figure 60: Comparison of the Model with the Results of Isothermal Experiments for 50 Percent Colemanite. -161-minutes of the reaction. For longer times the model predicts higher conversions than the ones obtained experimentally. This could r e s u l t from the errors due to the. poor experimental technique used i n the isothermal experiments. As was mentioned previously, at high temperatures, samples are fused into a s o l i d mass which made the recovery of the reaction product from the c r u c i b l e s very d i f f i c u l t . This was even more d i f f i c u l t for the samples which were kept i n the oven for a long time. During the d i s s o l u t i o n of the samples some s p i t t i n g occured and also a part of the product was l e f t i n the c r u c i b l e s . These losses might cause lower conversion values than the model p r e d i c t i o n . The isothermal r e s u l t s may also include some t i t r a t i o n e r r o r s . For the 50 percent colemanite case the p r e d i c t i o n of the model doesn't seem as good as the ones for 30 and 40 percent colemanite cases even i n the f i r s t ten minutes of the r e a c t i o n . This can be explained as before, e s p e c i a l l y since as the colemanite concentration increases the s o l i d mass becomes more d i f f i c u l t to dissol v e from the c r u c i b l e s . In fact the two sets of r e s u l t s were obtained i n two t o t a l l y d i f f e r e n t ways. Therefore, some differ e n c e between them would be expected. The k i n e t i c constants were obtained by using a very small amount of sample. For larger amounts of sample the k i n e t i c s of the l i b e r a t i o n of carbon dioxide might be d i f f e r e n t ; the d i f f u s i o n of the carbon dioxide through the sample thickness might become more important as w e l l . The conditions inside the furnaces were not the same i n both cases e i t h e r . I f there was any carbon dioxide pressure b u i l t up i n the big oven this would retard the l i b e r a t i o n of carbon dioxide considerably. From these r e s u l t s i t seems that i t i s -162-possible to obtain complete conversion of sodium carbonate i n ten minutes at 900°C. This makes colemanite superior to the titanium dioxide and also brings some advantages from the heat economy and operation point of view. The k i n e t i c constants reported i n th i s chapter are s p e c i f i c for thi s study. Since they are dependent on factors such as sample size and conditions inside the furnace these values can not be applied d i r e c t l y to plant scale operations. In a sprayed sample the p a r t i c l e s would have a large area, and should have k i n e t i c s closer to that of the small TG samples. However i n a molten mass at the bottom of the furnace the isothermal r e s u l t s may hold. The true answer w i l l be most l i k e l y between the two obtained here. 6.A Recycle of Colemanite The r e c y c l a b i l i t y of the colemanite was also studied i n t h i s p r o j e c t . The re s u l t s obtained from the thermogravimetric analysis of recycled colemanite and sodium carbonate mixtures are shown i n Figures 61, 62 and 63 for the f i r s t , second and t h i r d recycle of the colemanite r e s p e c t i v e l y . When these figures are compared with the Figure 25 which shows the weight loss f o r AO percent colemanite i t i s seen that the shape of the curves are the same. This means that the mechanism of the reac t i o n stays the same when the colemanite i s reused. It i s also seen that the weight changes are about the same i n both cases. The weight changes are also the same for the f i r s t , second and t h i r d recycle t e s t s . This i s a promising r e s u l t for the use of colemanite i n the pulping process. Quantitative values for the conversions of sodium o OH COLEMANITE CARBONATED RECYCLE - DERIVATIVE WTi 2 7 . 6 7 8 8 mg SCAN RATEi 1 0 . 0 0 d a g / m l n H -X o LU U J u oc L U CL FROMI 192. 12 TOi 9 8 7 . 7 2 WT. X CHANGEi 2 1 . 7 ON w I o 1000 I I I I I I I 200 400 600 800 TEMPERATURE (°C ) Figure 61: TG Results for the F i r s t Recycle. COLEMANITE CARBONATED RECYCLE WTi 1 9 . 2 3 5 8 mg SCAN RATEi 1 0 . 0 0 d « g / m i n _T I T i I 1 i i r~~ 200 400 600 800 1000 T E M P E R A T U R E ( ° C ) Figure 62: TG Results for the Second Recycle. C O L E M A N I T E C A R B O N A T E D R E C Y C L E WT. 19 .3431 mg SCAN RATE. 1 0 . 0 0 d e g / m i n - DER IVATIVE _ l I T I I I I I l ~ 200 400 600 8 0 0 1000 T E M P E R A T U R E (°C ) Figure 63: TG Results for the Third Recycle. -166-carbonate when the recycled colemanite i s used can not be found from this data because the analysis of these curves can not be made without knowing the losses of colemanite when i t i s reused. Besides t h i s , three recycle tests are not enough to make a d e f i n i t i v e statement on the r e c y c l i b i l i t y of colemanite. From the process point of view, i f colemanite can be reused, i t would be p a r t i a l l y separated from the sodium hydroxide and recycled back to the furnace without going through the whole cycle because of the p a r t i a l s o l u b i l i t y of colemanite. The work done by K.L. Pinder (26) on the s o l u b i l i t y of colemanite showed that only AO percent of the colemanite Is soluble at 20°C. Therefore the soluble borate would go throughout the pulping cycle and would a s s i s t pulping as i t does i n the case of sodium borates (11). The make—up should be only that colemanite which i s l o s t during pulp washing etc. Colemanite seems to be the best a u t o c a u s t i c i z i n g agent from t h i s point of view as w e l l . -167-7. CONCLUSIONS AND RECOMMENDATIONS The r e s u l t s of this study show that colemanite i s a good agent f o r the a u t o c a u s t i c i z a t i o n of black l i q u o r . It seems superior to the other amphoteric oxides studied before from the following points of view. 1. It gives quite high conversions at temperatures found i n Kraft furnaces. I t was found that for Na:B molar r a t i o of 1.15 the r e a c t i o n goes to completion at 700°C. Thus i s won't be necessary to go to temperatures as high as 1000°C as i s the case with titanium dioxide. This could r e s u l t i n a considerable saving of energy. 2. Colemanite Is p a r t i a l l y soluble and about 60 percent of i t i s s e t t l e d out (26) and returned d i r e c t l y to the furnace. Thus there i s less t o t a l hold-up and not as large a dead load on the evaporators. This i s the main difference between colemanite and sodium borate which i s completely soluble and c a r r i e d through the whole process. In Figure 64 i s shown the process proposed from t h i s research for the a u t o c a u s t i c i z i n g of Kraft l i q u o r with colemanite. When t h i s f i g u r e i s compared with Figure 1 i t can be seen that there i s a considerable saving i n c a p i t a l equipment i n the new process. E l i m i n a t i o n of the lime k i l n brings savings i n both energy and c a p i t a l investments. In addition to these advantages colemanite i s very cheap compared to other agents. However i t s actual performance can only be determined by p i l o t plant scale t e s t s . PULPING EVAPORATING RECOVERY FURNACE r DISSOLVING f . SETTLER Figure 64: Schematic of Proposed Proc ess -169-Experimental r e s u l t s showed that there are two d i f f e r e n t main reactions i n the temperature range from 190-1000°C. The f i r s t r e action i s between colemanite and sodium carbonate i n the temperature range of 192 and 700°C. This reaction goes p r a c t i c a l l y to completion at 700°C. Then the unreacted part of the sodium carbonate i s catalyzed by the substances other than boron which are present i n the colemanite at temperatures between 700 and 1000°C. The f i r s t reaction was found to be zero order i n sodium carbonate and a complex function of the colemanite concentration. Thus the reaction depends only on the temperature and the colemanite concentration. The second reaction was found to be f i r s t order on the sodium carbonate concentration and a complex function of the impurities i n colemanite. The derived model gave very good f i t s to the experimental data taken i n t h i s study. Further studies w i l l be needed to determine whether modifications must be made to the models. The comparison of the r e s u l t s of isothermal experiments and the r e s u l t s of TG analysis agreed reasonably well except for the diffe r e n c e i n conversions at high temperatures for the longer runs. This may be the r e s u l t of increased importance of d i f f u s i o n i n the bulk isothermal t e s t s . Colemanite can be reused several times without l o s i n g i t s a c t i v i t y as an a u t o c a u s t i c i z i n g agent. So i t i s most l i k e l y r e c y c l a b l e . Although the r e s u l t s of this study are very promising i t i s d i f f i c u l t to say from such small scale tests whether t h i s process could s a t i s f a c t o r i l y replace the conventional Kraft Recovery Process. -170-Further research i s recommended i n order to answer the following questions. 1. Since t h i s method w i l l be u t i l i z e d i n Kraft m i l l s , what would be the e f f e c t of sodium s u l f i d e (Na 2S) on this reaction? 2. Does the use of this process have any e f f e c t on the pulp y i e l d and paper quality? 3. Does colemanite cause any s c a l i n g problem as i t i s carried throughout the process? Although the TGA i s a very e f f e c t i v e technique for measuring the k i n e t i c s of such reactions and for d i s t i n g u i s h i n g between mechanisms a p i l o t plant study or a small m i l l t r i a l i s necessary to answer a l l these questions p r i o r to i n d u s t r i a l scale operations. Such tests would not be subject to such large errors caused by the carbonate losses during the d i s s o l u t i o n of the product. The e f f i c i e n c y of the recycle step w i l l also be better tested. -171-NOMENCLATURE A 2 Avrami and Erofev equation for random nucleation A 3 Avrami and Erofev equation for random nucleation difference of the logarithms of g(oc) and p(x) for a s p e c i f i c temperature B a r i t h m e t i c a l mean of B^ values C percent conversion of sodium carbonate to sodium oxide function g(a) for one-dimensional d i f f u s i o n c o n t r o l l e d reaction T>2 function g(a) for two-dimensional d i f f u s i o n c o n t r o l l e d reaction D 3 function g(a) for a d i f f u s i o n c o n t r o l l e d reaction i n sphere E a c t i v a t i o n energy of the reaction (cal/mol) E± a c t i v a t i o n energy of the f i r s t reaction (cal/mol) E 2 a c t i v a t i o n energy of the second reaction (cal/mol) f(a) function which shows the dependence of the rate of reaction on the reaction mechanism f^(a) function f ( a ) for one-dimensional d i f f u s i o n c o n t r o l l e d reaction f 2 ( a ) function f ( a ) for two-dimensional d i f f u s i o n c o n t r o l l e d reaction f 3 ( a ) function f ( a ) for a d i f f u s i o n c o n t r o l l e d reaction i n sphere g(<x) a function which i s obtained a f t e r the in t e g r a t i o n of f ( a ) H c percentage of humidity i n colemanite I percentage of impurity i n colemanite k reaction rate constant [unit depends on mechanism] k± rate constant of the f i r s t reaction (g/min) k l constant defined i n equation 6.9 (min - 1) -172-k 2 rate constant of the second reaction (min - 1) k r combined rate constant (min - 1) k* modified rate constant defined i n equation (3.14) [unit depends on mechanism] m order of the f i r s t reaction on sodium carbonate M molarity of the s u l f u r i c a c i d MWc molecular weight of colemanite (g/g-mole) MW£Q 2 molecular weight of carbon dioxide (g/g-mole) MWg molecular weight of sodium carbonate (g/g-mole) n order of the f i r s t reaction on colemanite N constant defined i n equation (3.24) p(x) function which shows the dependence of the rate of the reaction on temperature and the a c t i v a t i o n energy q heating rate (°K/min) r number of experimental data points R the gas constant (cal/mol-°K) R^ rate of the f i r s t reaction (min - 1) R 2 rate of the second reaction ( m in - 1) t time (min) t^ time at which the f i r s t reaction ceased (min) t 2 i n t e g r a t i o n time l i m i t for the second reaction (min) T temperature (°K) volume of the acid to t i t r a t e t o t a l carbonate (ml) V 2 volume of the acid to t i t r a t e sodium hydroxide (ml) W weight of the sample at any moment of the reaction (g) weight of the compound A (g) WR weight of the compound B (g) -173-W I n i t i a l weight of the compound A (g) A o Wg i n i t i a l weight of the compound B (g) o W i n i t i a l weight of colemanite (g) o W i n i t i a l weight of sodium carbonate (g) s o X c weight f r a c t i o n of colemanite Y c percentage of colemanite Z frequency factor [unit depends on reaction mechanism] Z 1 frequency factor for the f i r s t reaction (g/min) Z 2 frequency factor for the second reaction ( m i n - 1) a weight f r a c t i o n converted weight f r a c t i o n of compound A converted <xB weight f r a c t i o n of compound B converted a c weight f r a c t i o n of colemanite converted ct g weight f r a c t i o n of sodium carbonate converted rj^ f r a c t i o n a l conversion at the end of time t^ <x2 f r a c t i o n a l conversion at the end of time t 2 a' weight f r a c t i o n converted from the combination of f i r s t and second reaction 6 standard deviation of B^ values Omin minimum of the standard deviation, 6 v order of the second reaction on sodium carbonate -174-REFERENCES 1. Achar, B.N.N.•, Brindley, G.W., Sharp, J.H., Proceedings of the International Clay Conference, Jerusalem, I s r a e l (1966) _1, 67-73. 2. Achar, B.N.N., Brindley, G.W., Sharp, J.H., Numerical Data for Some Commonly Used Sol i d State Reaction Equations, Journal of American Ceramic Society, 49_, 379-382 (1966). 3. Berg, L.G., "Thermografiya" [Thermal A n a l y s i s ] , p. 473-5, Moscow, (1944). 4. Covey, G.H., "Development of the Direct A l k a l i Recovery System and P o t e n t i a l Applications", Journal of Pulp and Paper, 83, 92-6, (1982). 5. Doyle, CD., "Kinetic Analysis of Thermogravimetric Data", Journal of Applied Polymer Science, 5, 285-292, (1961). 6. Grace, M.T., "Improved Energy E f f i c i e n c y , Safety L i k e l y i n Future Recovery Systems", Pulp and Paper, 2, 90, (1981). 7. H a l l , F.P., Insley, H., "Phase Diagrams for Ceramists", The Journal of American Ceramic Society, 33^, 21, (1947). 8. Janson, J . , U.S. Patent 4,116,759 (1978). 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K i i s k i l a , E., "Comparison of Various C a u s t i c i z i n g Chemicals", Paperi ja Puu, 61_, 639-50, (1979). 23. K i i s k i l a , E., "Recovery of Sodium Hydroxide from A l k a l i n e Pulping Liquors by C a u s t i c i z i n g Molten Sodium Carbonate with Amphoteric Oxides", Paperi ja Puu, 62_, 339-50, (1980). 24. Kojo, M., " P r o f i t a b i l i t y of Re c a u s t i c i z i n g " , Paperi ja Puu, 61_, 581-3, (1979). 25. Othmer, Kirk, "Encylopedia of Chemical Technology", 2nd e d i t i o n , John Wiley & Sons, Inc., New York, (1964) 3^, 602-680. 26. Pinder, K.L., Personal communication on the DTA analysis of colemanite and sodium carbonate mixtures and boron a n a l y s i s . 27. Satava, V., Skvara, F., "Mechanism and K i n e t i c s of the Decomposition of Solids by a Thermogravimetric Method", Journal of American Ceramic Society, 52_ [11], 591-5, (1969). 28. Sestak, J . , Satava, V, Rihak, V., "Algorithm for Evaluating K i n e t i c Data from Non-Isothermal Thermogravimetric Curve", S i l i k a t y , 11_ [4], 315-24, (1967). 29. Sestak, J . , "Errors of K i n e t i c Data Obtained from Thermogravimetric Curves at Increasing Temperatures", Talanta, 13, 567-79, (1966). -176-30. Wendlandt, W.W., "Thermal Methods of Analysis", 2nd e d i t i o n , England, (1966) p. 29-40. 31. Zsako, J . , "Kinetic Analysis of Thermogravimetric Data", The Journal of Physical Chemistry, 72_ [7], 2406-11, (1968). 32. The manuals of Perkin-Elmer Thermogravimetric Analysis System. -177-APPENDIX I : GENERAL PROCEDURE FOR DETERMINATION OF ACID SOLUBLE BORON -178-A. SCOPE OF PROCEDURE This procedure can be used to determine boron at le v e l s of 0.05 to 5% i n boron-containing substances such as boron minerals (except tourmaline and elemental boron), s o i l s and organic substances impregnated with borates. B. REAGENTS 1. Standard 0.1 N sodium hydroxide. 2. Concentrated hydrochloric a c i d . 3. 1 _N sodium hydroxide. C. SOLUTION OF SAMPLE FOR ANALYSIS 1. Weigh 5 grams and record weight to nearest 1 mg. Transfer to a 250-ml wide-mouthed erlenmeyer f l a s k and heat the contents under r e f l u x for two hours with 3 ml of cone, hydrochloric acid and 150 ml of water. 2. Cool the s o l u t i o n , f i l t e r and wash the residue. 3. The f i l t r a t e i s used for the barium carbonate procedure, which follows. D. BARIUM CARBONATE PROCEDURE FOR DETERMINING B 2 0 3 1. OUTLINE OF METHOD The "Barium Carbonate Method" i s a procedure used to remove heavy metals from solutions of crude borates, such as Rasorite, colemanite or u l e x i t e , which would normally i n t e r f e r with the determination of B 2 0 3 by t i t r a t i o n . The heavy metals, iron, alumina, soluble s i l i c a and manganese are removed by the addition of barium carbonate to boric -179-a c l d . The r e s u l t i n g s o l u t i o n acts l i k e a buffer with the proper hydrogen-ion concentration to p r e c i p i t a t e the metals as hydroxides. Insoluble barium compounds are also formed of the a c i d i c compounds present, such as s i l i c a . Barium borate i t s e l f i s quite soluble. This method i s useful i n precepitating almost a l l heavy metals except ferrous i r o n which must f i r s t be oxidized to the f e r r i c state by the addition of bromine water. It i s necessary to remove the excess bromine by b o i l i n g , as i t would otherwise decolorize the methyl-red i n d i c a t o r . 2. PROCEDURE a. Neutralize the f i l t r a t e with IN NaOH to the methyl red end point. Make s l i g h t l y acid to methyl red with HC1. b. Add a few drops of bromine water and b o i l to remove the excess. c. Add to this s o l u t i o n about two g of barium carbonate powder and b o i l for 2-3 minutes. Add more barium carbonate u n t i l there i s a s l i g h t excess i n the bottom of the beaker. d. Allow the so l u t i o n to stand at room temperature for two hours. e. F i l t e r the s o l u t i o n and wash with hot water. If a strong colour p e r s i s t s which would i n t e r f e r with the perception of the endpoint, add a small amount of activated charcoal, bring to a b o i l and f i l t e r again. f. A c i d i f y the f i l t r a t e with HC1 and b o i l to remove carbon dioxide. -180-g. Neutralize the f i l t r a t e with 0.1 _N NaOH using methyl red as an i n d i c a t o r . h. Add three heaping teaspoonsful of mannitol and seven drops of 1% phenolphthalein i n d i c a t o r s o l u t i o n . i . T i t r a t e with standard 0.1 N_ sodium hydroxide s o l u t i o n . The color of the so l u t i o n i n the presence of borate w i l l change from red to yellow and then to pink at the phenolphthalein end point as sodium hydroxide i s added. j . C a l c u l a t i o n : „ (Volume of NaOH) x (Normality of NaOH) x 1.082 (Sample Weight) -181-APPENDIX I I : SAMPLE CALCULATIONS AND DERIVATIONS -182-i . - C a l c u l a t i o n of conversion from the t i t r a t i o n data taken i n the isothermal runs. Define percent conversion as: moles of reacted Na 2C0 3 ^ moles of reacted Na 2C0 3 + moles of unreacted Na 2C0 3 x 1 - ^ The reactions are Na 2C0 3 -»• Na 20 + C0 2 Na 20 + H 20 + 2NaOH Let V^: volume of acid to t i t r a t e NaOH and unreacted sodium carbonate Let V 2: volume of acid to t i t r a t e sodium hydroxide Let molarity of ac i d : M Therefore moles of NaOH = M«V 2»2 moles of unreacted Na 2C0 3 = (V^-V 2) • M 1/2 (M»V 2*2) Then percent conversion = 1 / 2 ( M v 2 . 2 ) + ( V l-V 2)M X 1 0 0 MV2 C = MV2 + MV, - MV2 X 1 0 0 V2 C = — x 100 v l -183-i i - C a l c u l a t i o n of the stoichiometric amount of colemanite for the d i r e c t reduction of sodium carbonate. Data for this c a l c u l a t i o n : Formula of colemanite: 2Ca03B 20 3»5H 20 MW of B 20 3: 69.6 g/g mole MW of Na 20: 62 g/g mole MW of Na 2C0 3: 106 g/g mole MW of colemanite: 410.8 g/g mole MW of Na 20 B 2 0 3 : 131.6 g/g mole From the phase diagram shown i n Figure 10 i t i s seen that the compound which w i l l form as a reaction product would be Na 20 B 2 0 3 for Na:B r a t i o of greater than 0.999. The percentage of Na 20 and B 2 0 3 i n th i s compound can be calculated as follows: % Na 20: Y3TT X 1 0 0 = 4 7 , 1 % B 2 0 3 : 1 3 1 6 x 100 = 52.9. Then what would be the percentage of colemanite i n the mixture of colemanite and sodium carbonate i n order to have Na 20 B 2 0 3 as the product? -184-Basis: 100 gr Na 20 B 2 0 3 which w i l l form as a reaction product. weight of sodium carbonate needed: x 1^6 = 80.53 g 1 52.9 weight of pure colemanite needed: x x 410.8 = 104.08 g Since the colemanite which i s used i n th i s study was not pure and contained 38% B 2 0 3 rather than 50.83% B 2 0 3 actual needed amount of colemanite: 104.08 x 5 ° ' 8 3 = 139.22 g. So the t o t a l weight of the mixture should be: 80.53 + 139.22 = 219.75 g. Then weight % of Na 2C0 3: 36.65 weight % of colemanite: 63.35 -185-i i i - Ca l c u l a t i o n of frequency factor, Z^, and rate constant, k^, for the f i r s t reaction. S t a r t i n g with the equation (3.13) / \ T T m—i T T n M v g ( a ) = — W s Wc p(x) o o Since the reaction i s zero order on both sodium carbonate and colemanite concentration the values of m and n are zero. Then the equation becomes Z 1 E 1 _! g ( a ) = W g p ( x ) o Taking the logarithms of both sides Z l E l log g(oc) = log — log Wg + log p(x) o rearranging log g(a) - log p(x) = log — — = B s therefore log Z]+ log E i - log RqWg = B E l So log Zi = B - log RqWs o Z\ = l o g " 1 [B - log RqWs -186-Rate constant can be calculated from the Arrhenius equation (6.3) k i = Z\ exp (- — ) where T i s the temperature. Sample c a l c u l a t i o n f o r 60 percent colemanite: Data for t h i s c a l c u l a t i o n : R = 1.987 x 1 0 - 3 kcal/mol-°K W = 98.56 g s o q = 10 °K/min Y = 60 c Ei = 7.15 kcal/mol B = 2.8392 (from figure 45) 7 15 log Z\ = 2.8392 - log (1.987 x 10~ 3)(10)(98.56) Z1 = 180.172 g/min k i = 180.172 exp [ • ] (1.987 x 1 0 _ 3 ) ( T ) at T = 1173°K (900°C) k^ = 8.383 g/min -187-i v - Ca l c u l a t i o n of frequency f a c t o r , Z 2, and rate constant, k 2, for the 2nd reaction. S t a r t i n g with the following equation Z 2 E 2 V _ X 8 ( A ) = " R T W S P ( X ) o Since the reaction i s f i r s t order on the sodium carbonate concentration v = 1 therefore; Z 2 E 2 G ( A ) = " I T P ( X ) Taking the logrithms of both sides Z 2 E 2 log g(a) = log + log p(x) rearranging Z 2 E 2 log g(a) - log p(x) = log -g^— = B therefore E 2 log Z 2 = B - log g-j--1 - E 2 Z 2 = log [B - log ^ ] E 2 and k 2 = Z 2 exp (- — ) -188- • Sample c a l c u l a t i o n for 30 percent colemanite: Data for this c a l c u l a t i o n : R = 1.987 cal/mol °K q = 10 °K/min E 2 = 4700 cal/mol B = 1.6134 (From figure 53) Z 2 = l o g " 1 [B - log |^ -] l , 4700 Z 2 = log (1.6134 - log ( 1 > 9 8 7 ) ( 1 Q ) ) Z 2 = 0.1736 m i n - 1 ~ ,-,.», , 4700 k 2 = 0.1736 exp (- ( 1 . 9 8 7 ) ( T ) ) at T = 900°C (1173 °K) rs , 4700 k 2 = 0.1736 exp (- ( 1 . 9 8 7 ) ( 1 1 7 3 ) ) k 2 = 0.02311 min" 1 -189-v - Derivation of a combined rate expression. The rate expression for the 1st reaction i s | f - R X - l e i (1) where The rate expression for the 2nd reaction i s = R 2 = k 2 ( l - a ) (2) When these two reactions take place at the same time the o v e r a l l rate of the reaction would be |2- = k[ + k 2 ( l - a ) ( 3 ) rearranging i t 42 = dt (4) t k i + k 2 - k 2 a t 1 et k i + k 2 = k^ r 0 -190-Integratlon of this equation gives the following so l u t i o n 1 , , v «' t, K 2 R 0 0 In (k r-k 2a') - In k r = - k 2 t ! k -k 2a' In = - k 2 t i r k - k 2 a ' — ^ = exp ( - k 2 t i ) r k r ~ k 2 a ' = k r exp (-k 2t!) k -k exp ( - k 2 t i ) a ' = - I - ^ (6) Since the 1st reaction stops when the boron oxide content of the colemanite f i n i s h e s there would be a s p e c i f i c time for each colemanite percentage at which the f i r s t reaction stops. This time can be calculated from the int e g r a t i o n of equation 1 which w i l l r e s u l t i n a^ = k ^ t i by knowing the f i n a l conversions at the end of the 1st reaction from the f r a c t i o n a l conversions vs temperature p l o t s . After the time t^ i s reached only the 2nd reaction takes place so the rate of the reaction i s expressed as eq. 2. When eq. 2 i s integrated a 9 , t 9 cc i cc2 12 In (1-a) I , = k t I a' 2 t1 -191-l - a 2 - In — = k 2 ( t 2 " t i ) 1-a' ( 1 - B 2 ) = exp (- k 2 ( t 2 - t x ) ) (1 - a ' ) ( l - a 2 ) = (1-a') exp ( - k 2 ( t 2 ~ t 1 ) ) a 2 = 1 - [(1-a') exp (- k 2 ( t 2 - t 1 ) ) ] (8) where a 2 w i l l be the f i n a l conversion at the end of the time t 2 . -192-Sample c a l c u l a t i o n for 30 percent colemanite: Ws - 99.6 g o From Figure 42 al = 0.26 From Table 22 k x = 1.520 g/min k 2 = 0.024 m i n - 1 k' = (k ) (We r 1 1 1 S o therefore \al = (1.520) (99.6) -1 k x = 0.01525 min 0.26 ,., ^ " 0T0T525 " 1 7 ' 0 5 k = ki + k 2 = 0.03949 r 0.03949 - 0.03949 exp [ ( - 0.024) (17.05)] 0.024 a' = 0.552 For t 2 = 30 min. a 2 = 1 - [(1-0.552) exp [- (0.024) (30-17.05)]] a 2 = 0.672 Table A l : Na:B ratios for dif f e r e n t colemanite concentrations. % colemanite Na:B for Na 2C0 3 + colemanite Na:B for Na 2C0 3 + calcium borate 30 4.04 5.16 40 2.59 3.35 50 1.73 2.24 60 1.15 1.5 -194-APPENDIX III: TURKISH COLEMANITE PRODUCT SPECIFICATIONS AND TYPICAL ANALYSIS -195-Chemical Analysis Contract S p e c i f i c a t i o n s Max. Min. Typ i c a l Analysis B 2°3 40.0 38.0 39.50 Na 20 0.5 0.15 CaO 27.5 24.5 27.00 F e 2 0 3 0.3 0.09 S i 0 2 7.0 5.14 A1 20 3 1.0 0.38 SrO 1.5 0.95 MgO 3.0 1.95 SO 3 0.8 0.74 LOI (1600°F for 30 min) 26.5 24.30 H 20 (60°C for 2 hrs.) 2.0 0.80 * Analysis done by the American Borate Company -196-Physical Analysis U.S. Screen Size Cumulative Weight Percent Retained Mesh Max. Min. + 60 .05 + 70 .25 +100 3.25 +140 9.25 +200 20.00 -200 80. Other Physical Data S p e c i f i c Gravity 2.4 R e a c t i v i t y with Steel None Angle of Repose-Settled 25° Bulk Density ( l b s . / c u . f t . ) Tap Pour 90 70 Hardness (Mohs Scale) Colemanite C a l c i t e 4.5 3.0 * Analysis done by the American Borate Company -197-APPENDIX IV: STANDARD DEVIATION TABLES FOR THE FIRST AND SECOND REACTIONS T i i b l e A 2 S t a n d a r d d e v i a t i o n o f t h e B ( a s d e f i n e d b y E q u a t i o n 2 . 2 4 ) v a l u e s ( S T D ) f o r v a r i o u s r e a c t i o n m e c h a n i s m s a n d a c t i v a t i o n e n e r g i e s ( E ) f o r t h e f i r s t r e a c t i o n a t 3 0 % b y w e i g h t c o l e m a n i t e E/CAL. \ IMOL J N = 1 / 3 M = 0 N= 1/2 M = 0 N = 2 / 3 M = 0 N= 1 M = 0 N = 0 M= 1/3 N = 0 M= 1 / 2 N = 0 M = 0 5 0 0 0 B STD 1 O . " 1 6 5 0 . 1 9 17 6 1 O -17 7 9 1 9 6 4 1 1 0 . 4 9 0 3 . 2 0 2 2 6 1 0 5 1 6 2 2 1 7 8 1 1 0 . 4 4 7 4 . 1 8 6 5 1 1 0 . 4 4 9 8 . 1 8 6 9 6 1 0 . 4 4 2 7 . 1 8 5 7 0 5 2 0 0 B STD 1 0 . 5 5 9 0 . 1 8 8 12 1 0 . 5 7 1 0 . 1 9 2 0 8 1 0 . 5 8 3 5 . 1 9 7 2 8 1 0 6 0 9 4 2 1 1 6 7 1 0 . 5 4 0 6 . 1 8 3 9 9 1 0 . 5 4 3 0 . 1 8 4 3 0 1 0 5 3 5 8 1 8 3 4 6 5 - 1 0 0 B STD 1 0 6 5 1 1 1 8 5 - 1 0 1 0 . 6 6 3 2 1 8 8 G 3 1 0 . 6 7 5 6 1 9 3 12 1 0 7 0 1 5 2 0 6 2 3 1 0 . 6 3 2 7 . 1 8 2 4 6 1 0 . 6 3 5 1 1 8 2 6 3 1 0 6 2 7 9 1 8 2 2 2 5 GOO B STO 1 0 7 4 2 3 1 8 3 7 4 1 O 7 54-1 1 8 6 2 1 1 0 7 6 6 8 1 8 9 9 5 1 0 7 9 2 7 2 0 1 6 4 1 0 . 7 2 3 9 . 1 8 2 0 3 1 0 . 7 2 6 3 1 8 2 0 5 1 0 7 1 9 2 18 2 0 9 5 B 0 0 B STD 1 0 8 3 2 6 1 8 3 0 4 1 0 8 4 4 7 1 8 4 7 1 1 0 8 5 7 1 1 8 7 6 6 1 0 8 8 3 0 1 9 7 8 6 1 0 . 8 1 4 2 1 8 2 5 6 1 0 8 1 6 6 1 8 2 4 3 1 0 8 0 9 4 1 8 2 9 0 5 5 0 0 B STD 1 0 6 9 G 8 1 8 4 4 0 1 0 7 0 8 9 1 8 7 2 6 1 0 7 2 14 1 9 1 3 8 1 0 7 4 7 2 2 0 3 7 9 1 0 6 7 8 5 1 8 2 0 8 0 6 8 0 9 1 8 2 17 1 0 6 7 3 7 1 8 1 9 8 5 7 0 0 B STD 1 0 7 8 7 6 1 8 3 2 2 1 0 7 9 9 6 1 8 5 3 0 1 0 8 12 1 1 8 8 6 5 1 . 0 8 3 8 0 1 9 9 6 1 1 0 7 6 9 2 1 8 2 12 1 0 7 7 1 6 1 8 2 0 7 1 0 7 6 4 4 1 8 2 3 2 T a b l e A 3 S t a n d a r d d e v i a t i o n o f t h e B ( a s d e f i n e d b y E q u a t i o n 2 . 2 4 ) v a l u e s ( S T D ) f o r v a r i o u s r e a c t i o n m e c h a n i s m s a n d a c t i v a t i o n e n e r g i e s ( E ) f o r t h e f i r s t r e a c t i o n a t 4 0 % b y w e i g h t c o l e m a n i t e E [ C A L \ I M O L ; N= 1/3 M = 0 N= 1/2 M = 0 N = 2 / 3 M = 0 N= 1 M = 0 N = 0 M= 1/3 M > 0 M= 1 / 2 N = 0 M = 0 B 1 . 6 1 6 2 1 . 6 2 7 6 1 . 6 3 9 3 1 . 6 6 3 8 1 . 6 0 1 5 1 . 6 0 5 1 1 . 5 9 4 4 5000 S T D 0 . 2 0 9 9 7 o . 2 1 5 4 0 0 . 2 2 1 9 8 0 2 3 8 8 9 0 . 2 0 4 0 7 0 . 2 0 5 1 4 0 . 2 0 2 1 4 B 2 . 0 7 3 5 2 . 0 8 4 9 2 . 0 9 6 6 2 12 11 2 . 0 5 8 8 2 . 0 6 2 4 2 . 0 5 16 SOOO S T O 0 . 1 9 1 5 4 0 . 1 9 3 8 7 0 . 1 9 7 4 6 0 2 0 8 9 6 0 . 1 8 9 9 9 0 . 1 9 0 0 5 0 1 9 0 0 7 B 2 5 1 1 5 2 5 2 2 9 2 . 5 3 4 6 2 5 5 9 1 2 . 4 9 6 8 2 5 0 0 4 2 4 8 9 6 7000 S T D 0 . 1 9 7 0 6 0 . 1 9 5 7 7 0 . 1 9 5 6 2 0 1 9 9 6 1 0 . 2 0 0 1 9 0 1 9 9 2 3 0 2 0 2 2 8 B 2 1 6 2 4 2 . 1 7 3 8 2 . 1 8 5 5 2 2 1 0 0 2 1 4 7 7 2 1 5 13 2 1 4 0 6 6200 S T D 0 1 9 0 6 7 0 1 9 2 2 7 0 . 1 9 5 1 3 0 2 0 5 2 6 0 1 9 0 0 8 0 1 8 9 9 2 0 1 9 0 5 9 B 1 9 8 3 8 1 9 9 5 2 2 0 0 6 9 2 0 3 14 1 9 6 9 1 1 9 7 2 7 1 9 6 2 0 5 8 0 0 S T D 0 1 9 3 3 5 0 1 9 6 3 7 0 2 0 0 6 5 0 2 1 3 4 4 0 1 9 0 8 4 0 1 9 1 1 2 0 1 9 0 5 0 B 2 0 2 8 8 2 0 4 0 2 2 0 5 1 9 2 0 7 6 4 2 0 1 4 1 2 0 1 7 7 2 0 0 6 9 5 9 0 0 S T O 0 1 9 2 3 9 0 1 9 5 0 7 0 1 9 9 0 1 0 . 2 1 1 1 8 0 1 9 0 3 5 0 1 9 0 5 3 0 . . 1 9 0 2 2 B 2 1 1 8 1 2 1 2 9 5 2 14 12 2 . 1 6 5 7 2 1 0 3 4 2 1 0 7 0 2 . 0 9 6 2 6 100 S T D 0 1 9 0 9 4 0 1 9 2 9 0 0 1 9 6 14 0 . 2 0 6 9 6 0 1 8 9 8 6 0 . 1 8 9 8 2 0 . 1 9 0 1 6 T a b l e A-1 S t a n d a r d d e v i a t i o n o f t h e B ( a s d e f i n e d b y E q u a t i o n 2 . 2 4 ) v a l u e s ( S T D ) f o r v a r i o u s r e a c t i o n m e c h a n i s m s a n d a c t i v a t i o n e n e r g i e s ( E ) f o r t h e f i r s t r e a c t i o n a t 5 0 % b y w e i g h t c o l e m a n i t e ifCAL ^ V M O L ; N = 1/3 M = 0 11= 1/2 M = 0 N = 2 / 3 M = 0 N= 1 M = 0 N = 0 M= 1 / 3 N = 0 M= 1/2 N = 0 M = 0 B 1 . 7 4 7 8 1 . 7 5 9 7 1 . 7 7 19 1 7 9 7 5 1 . 7 3 6 9 1 . 7 4 2 8 1 7 2 5 2 5 0 0 0 S T D 0 . 2 2 4 3 3 0 . 2 3 1 2 1 0 . 2 3 9 3 1 0 2 5 9 5 1 0 . 2 1 8 4 0 0 . 2 2 0 9 8 0 2 1 3 8 3 B 2 . 2 0 1 2 2 . 2 t 3 0 2 . 2 2 5 2 2 2 5 0 9 2 . 1 9 0 2 2 . 1 9 6 1 2 1 7 8 6 6 0 0 0 S T D O . 1 9 6 4 8 0 . 2 0 0 4 9 0 . 2 0 5 9 1 0 2 2 1 4 7 O . 1 9 3 5 3 0 . 1 9 4 5 9 0 1 9 2 0 8 B 2 . 6 3 5 3 2 . 6 4 7 2 2 . 6 5 9 4 2 6 8 5 0 2 . 6 2 4 4 2 . 6 3 0 3 2 6 1 2 7 7 000 S T D 0 . 1 9 1 8 5 0 . 1 9 2 0 1 0 . 1 9 3 5 7 0 2 0 1 7 9 0 1 9 2 6 8 0 . 1 9 1 8 8 0 1 9 4 8 8 B 3 0 5 5 0 3 0 G 6 H 3 0 7 9 1 3 1 0 4 7 3 0 4 4 0 3 0 4 9 9 3 0 3 2 4 8 0 0 0 S T D 0 2 1 1 5 9 0 2 0 8 1 1 0 . 2 0 5 7 3 0 2 0 5 4 2 0 2 15 7 4 0 2 1 3 3 6 0 2 2 0 8 9 B 2 2 8 9 4 2 3 0 1 2 2 3 1 3 4 2 3 3 9 0 2 2 7 8 4 2 2 8 4 3 2 2 6 6 8 6 2 0 0 S T D O 1 9 3 5 1 0 1 9 6 8 0 0 2 0 1 5 2 0 2 1 5 8 1 0 1 9 1 2 9 0 19 1 9 8 0 1 9 0 5 7 B 2 3 7 6 8 2 3 8 8 7 2 4 0 0 9 2 4 2 6 5 2 3 6 5 9 2 3 7 18 2 3 5 4 3 6 4 0 0 S T D 0 1 9 1 5 3 0 1 9 4 0 7 0 1 9 8 0 5 0 2 1 0 9 8 0 1 9 0 0 6 0 1 9 0 3 8 0 1 9 0 0 7 B 2 4 6 3 6 2 4 7 5 5 2 4 8 7 7 2 . 5 1 3 3 2 4 5 2 6 2 4 5 8 5 2 . 4 4 1 0 6 6 0 0 S T D 0 1 9 0 6 3 0 1 9 2 3 9 0 1 9 5 5 8 0 . 2 0 7 0 3 0 1 8 9 9 3 0 1 8 9 8 7 0 . 1 9 0 6 9 T a b l e A 4 . C o n t i n u e f C A L ) \ M O L ; N= 1 / 3 M = 0 N= 1/2 M = 0 N = 2 / 3 M = 0 N = 1 M = 0 |M=0 M= 1 / 3 N = 0 M= 1 / 2 N - 0 M = 0 B 2 . 5 4 9 8 2 . 5 6 16 2 . 5 7 3 8 2 5 9 9 5 2 . 5 3 8 8 2 . 5 4 4 7 2 5 2 7 2 6 8 0 0 S T D 0 . 1 9 0 7 8 0 . 19 1 7 3 0 . 1 9 4 12 0 2 0 3 9 8 0 . 1 9 0 8 4 0 . 1 9 0 4 1 0 1 9 2 3 3 B 2 . 3 3 3 2 2 . 3 4 5 1 2 . 3 5 7 3 2 3 8 2 9 2 . 3 2 2 3 2 . 3 2 8 2 2 3 1 0 7 6 3 0 0 S T D 0 . 1 9 2 4 0 0 . 1 9 5 3 2 0 1 9 9 6 8 0 2 1 3 3 2 0 . 1 9 0 5 4 0 . 1 9 1 0 5 0 1 9 0 1 9 B 2 . 4 2 0 3 2 . 4 3 2 2 2 4 4 4 4 2 4 7 0 0 2 . 4 0 9 4 2 . 4 1 5 3 2 3 9 7 8 6 5 0 0 S T D O 1 9 1 0 4 0 1 9 3 19 0 1 9 6 7 8 0 2 0 8 9 8 0 1 8 9 9 4 0 1 9 0 0 8 O 1 9 0 3 3 I ' a b l e A 5 S t a n d a r d d e v i a t i o n o f t h e B ( a s d e f i n e d b y E q u a t i o n 2 . 2 4 ) v a l u e s ( S T D ) f o r v a r i o u s r e a c t i o n m e c h a n i s m s a n d a c t i v a t i o n e n e r g i e s ( E ) f o r t h e s e c o n d r e a c t i o n a t 3 0 % b y w e i g h t c o l e m a n i t e UIOL 1 M = 0 M = 1 / 3 M = 1 / 2 M = 2 / 3 . M= 1 M = 2 D 1 D 2 D 3 A 2 A 3 2 0 0 0 3 0 0 0 4 0 0 O 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 B S T D B S T D B S T D B S T D B S T D B S T D B S T D 0 . 3 7 8 7 0 . 4 1 9 1 0 . 4 3 9 9 0 . 4 6 1 1 0 . 5 0 4 7 0 . 6 4 5 4 0 . 0 2 2 8 1 9 8 8 - . 7 6 6 6 0 . 6 1 9 6 0 . 6 5 7 9 0 0 2 5 2 8 0 . 0 3 2 5 4 0 . 0 3 6 9 4 0 . 0 4 1 7 6 0 . 0 5 2 4 3 0 . 0 9 1 , 1 3 0 . 1 1 7 1 3 0 . 1 3 6 0 7 0 . 1 5 8 1 2 0 . 0 1 9 9 5 0 . 0 3 8 6 8 0 . 8 4 1 6 0 . 8 8 2 0 0 . 9 0 2 B 0 . 9 2 4 0 0 . 9 6 7 6 1 . 1 0 8 3 0 . 4 8 5 7 0 . 2 6 4 0 - . 3 0 3 7 1 . 0 8 2 5 1 . 1 2 0 8 0 . 0 2 0 8 7 0 . 0 2 2 0 2 0 . 0 2 4 3 8 0 . 0 2 7 7 4 0 . 0 3 6 6 8 0 . 0 7 3 7 0 0 . 1 0 0 2 9 0 . 1 1 8 9 1 0 . 1 4 0 7 1 0 . 0 3 6 3 8 0 . 0 5 6 5 5 1 . 2 3 5 7 1 . 2 7 6 2 1 . 2 9 7 0 1 . 3 1 8 2 1 . 3 6 1 8 1 . 5 0 2 5 0 . 8 7 9 9 0 . 6 5 8 2 0 . 0 9 0 5 1 . 4 7 6 7 1 . 5 1 5 0 0 0 2 9 3 7 0 . 0 2 3 6 0 0 . 0 2 1 8 7 0 . 0 2 1 4 1 0 . 0 2 4 9 4 0 . 0 5 7 4 6 0 . 0 8 4 7 1 0 . 1 0 2 8 2 0 . 1 2 4 2 6 0 . 0 5 3 2 0 0 . 0 7 3 0 1 1 . 5 9 0 6 1 . 6 3 1 0 1 . 6 5 1 8 1 . 6 7 3 0 1 . 7 1 6 7 1 . 8 5 7 4 1 . 2 3 4 8 1 . 0 1 3 1 0 . 4 4 5 4 1 . 8 3 1 6 1 . 8 G 9 9 0 . 0 4 3 0 6 0 . 0 3 4 6 7 0 . 0 3 0 6 6 0 . 0 2 7 0 2 0 . 0 2 2 1 9 0 . 0 4 2 4 2 0 . 0 7 0 2 5 0 . 0 8 7 5 4 0 . 1 0 8 4 4 0 . 0 6 9 8 3 0 . 0 9 0 6 6 1 . 9 1 9 9 1 . 9 6 0 3 1 . 9 8 1 1 2 . 0 0 2 4 2 . 0 4 6 0 2 . 1 8 6 7 1 . 5 6 4 1 1 . 3 4 2 4 0 . 7 7 4 7 2 . 1 6 0 9 2 . 1 9 9 2 0 . 0 5 8 2 1 0 . 0 4 8 9 4 0 . 0 4 4 2 0 0 . 0 3 9 4 5 0 . 0 3 0 4 0 0 . 0 2 9 7 3 0 . 0 5 7 4 0 0 . 0 7 3 2 7 0 . 0 9 3 3 0 0 . 0 8 6 2 9 0 . 1 0 7 2 5 2 . 2 3 1 2 2 . 2 7 1 6 2 . 2 9 2 4 2 . 3 1 3 6 2 . 3 5 7 2 2 . 4 9 7 9 1 . 8 7 5 3 1 . 6 5 3 6 1 . 0 8 5 9 2 . 4 7 2 1 2 . 5 1 0 4 0 . 0 7 3 8 9 0 . 0 6 4 2 6 0 . 0 5 9 2 4 0 . 0 5 4 1 0 0 . 0 4 3 6 3 0 . 0 2 2 9 8 0 . 0 4 7 1 6 0 . 0 6 0 3 8 0 . 0 7 8 9 5 0 . 1 0 2 6 8 0 . 1 2 3 7 1 2 . 5 2 8 7 2 . 5 6 9 1 2 . 5 8 9 9 2 . 6 1 1 1 2 . 6 5 4 8 2 . 7 9 5 5 2 . 1 7 2 9 1 . 9 5 1 2 1 . 3 8 3 5 2 7 6 9 7 2 . 8 0 5 0 0 . 0 8 9 6 8 0 . 0 7 9 8 7 0 . 0 7 4 7 1 0 . 0 6 9 3 9 0 . 0 5 8 3 5 0 . 0 2 6 5 3 0 . 0 4 1 0 5 0 . 0 4 9 6 2 0 . 0 6 5 6 0 0 . 1 1 0 9 4 0 . 1 4 0 0 3 T a b l e A 5 . C o n t i n u e : ( C A L \ \ M L J L J 9 0 0 0 4 8 0 0 5 2 0 0 • 1 6 0 0 - 1 7 0 0 4 9 0 0 B S T D B S T D B S T D B S T O B S T D B S T D M = 0 M = 1 / 3 M = 1 / 2 M = 2 / 3 M= 1 M = 2 D 1 D 2 D 3 A 2 A3 2 . 8 1 5 E 2 . 8 5 6 2 2 . 8 7 7 0 2 . 8 9 8 2 2 . 9 4 1 9 3 . 0 8 2 5 2 . 4 6 0 0 2 . 2 3 8 3 1 . 6 7 0 6 3 . 0 5 6 7 3 . 0 9 5 0 0 . 1 0 5 5 1 0 . 0 9 5 5 9 0 . 0 9 0 3 6 0 . 0 8 4 9 5 0 . 0 7 3 6 2 0 . 0 3 7 5 1 0 . 0 4 1 0 2 0 . 0 4 2 6 6 0 . 0 5 4 0 6 0 . 1 3 5 0 7 0 . 1 5 6 2 1 1 . 5 2 2 1 1 . 5 6 2 5 1 . 5 8 3 3 1 . 6 0 4 5 1 . 6 4 8 1 1 . 7 8 8 8 1 . 1 6 6 3 0 . 9 4 4 6 0 . 3 7 6 8 1 . 7 6 3 0 1 . 8 0 1 3 0 0 4 0 1 3 0 . 0 3 2 0 6 0 . 0 2 8 3 3 0 . 0 2 5 1 1 0 . 0 2 1 7 5 0 . 0 4 5 3 4 O . 0 7 3 0 8 0 . 0 9 0 5 7 0 . 1 1 1 6 0 0 . 0 6 6 4 9 0 0 8 7 2 8 1 . 6 5 8 3 1 . 6 9 8 7 1 . 7 1 9 5 1 . 7 4 0 7 1 . 7 B 4 4 1 . 9 2 5 0 1 . 3 0 2 5 . 0 8 0 8 0 . 5 1 3 1 1 . 8 9 9 2 1 . 9 3 7 5 O 0 - 1 5 9 9 0 . 0 3 7 3 5 0 . 0 3 3 1 2 0 . 0 2 9 1 4 0 . 0 2 3 0 7 O . 0 0 9 6 2 O O G 7 5 I O . O B 4 5 9 O t 0 5 3 5 0 . 0 7 3 1 2 0 . 0 9 3 9 8 1 . 4 5 2 3 1 . 4 9 2 7 1 . 5 1 3 5 1 . 5 3 4 8 1 . 5 7 8 4 1 . 7 1 9 1 1 . . 0 9 6 5 0 . 8 7 4 8 0 . 3 0 7 1 1 . 6 9 3 3 1 . 7 3 1 6 0 . 0 3 7 2 6 0 . 0 2 9 5 8 0 . 0 2 6 2 0 0 . 0 2 3 5 1 0 . 0 2 1 8 1 0 . 0 4 8 3 0 0 . 0 7 5 9 2 0 . 0 9 3 6 0 0 . 1 1 4 7 4 0 . 0 6 3 1 5 O . 0 8 3 9 1 1 . 4 8 7 3 1 . 5 2 7 7 1 . 5 4 8 5 1 . 5 6 9 8 1 . 6 1 3 4 1 . 7 5 4 1 1 3 1 5 0 . 9 0 9 8 0 . 3 4 2 1 1 . 7 2 8 3 1 . 7 6 G 6 0 . 0 3 8 7 2 0 . 0 3 0 8 2 0 . 0 2 7 2 6 0 . 0 2 4 2 8 0 . 0 2 1 7 0 0 . 0 4 6 7 7 0 . 0 7 4 4 5 0 . 0 9 2 0 4 0 . 1 1 3 1 2 0 . 0 6 4 8 6 0 . 0 8 5 6 4 1 . 5 5 6 5 1 . 5 9 6 9 1 . 6 1 7 7 1 . 6 3 8 9 1 . 6 8 2 6 1 . 8 2 3 2 1 . 2 0 0 7 0 . 9 7 9 0 0 . 4 1 1 3 1 . 7 9 7 4 1 . 8 3 5 7 O . 0 4 1 6 5 0 . 0 3 3 4 1 0 . 0 2 9 5 3 O . 0 2 6 0 8 0 . 0 2 1 9 2 O . 0 4 3 8 2 0 . 0 7 1 6 0 0 . 0 8 8 9 9 0 . 1 0 9 9 5 0 . 0 6 8 2 3 0 . 0 8 9 0 5 I o CO I T a b l e A G S t a n d a r d d e v i a t i o n o f t h e B ( a s d e f i n e d b y E q u a t i o n 2 . 2 4 ) v a l u e s ( S T D ) f o r v a r i o u s r e a c t i o n m e c h a n i s m s a n d a c t i v a t i o n e n e r g i e s ( E ) f o r t h e s e c o n d r e a c t i o n a t 4 0 % b y w e i g h t c o l e m a n i t e E( C A L "\ VMOL J M = 0 M = 1 / 3 M = l / 2 M = 2 / 3 M= 1 M-2 D 1 D 2 0 3 A 2 A 3 3 0 0 0 4 000 5000 G 0 0 0 7 0 0 0 8 0 0 0 9 0 0 0 B S T D B S T D B S T D B S T D B S T D 8 S T D B S T D 0 . 9 9 8 5 1 . 0 5 9 5 1 . 0 9 1 5 1 . 1 2 4 6 1 . 1 9 3 9 1 . 4 2 7 2 0 . 7 7 7 4 0 . 5 9 4 8 0 . 0 7 5 4 1 . 2 0 6 8 1 . 2 1 1 1 0 . 0 1 5 4 4 0 . 0 1 4 4 1 0 . 0 1 9 8 2 0 . 0 2 7 3 8 0 . 0 4 5 9 0 0 . 1 1 8 2 6 0 . 0 7 8 4 3 0 . 1 0 6 3 4 0 . 1 4 2 4 3 0 . 0 2 4 0 8 0 . 0 4 G 1 7 1 . 3 9 6 6 1 . 4 5 7 6 1 . 4 8 9 6 1 . 5 2 2 7 1 . 5 9 2 0 1 . 8 2 5 3 1 . 1 7 5 5 0 . 9 9 2 8 0 . 4 7 3 4 1 . 6 0 4 8 1 . 6 0 9 1 0 . 0 2 7 8 1 0 . 0 1 5 6 3 0 . 0 1 2 4 1 0 . 0 1 4 7 3 0 . 0 3 0 5 1 0 . 1 0 2 1 9 0 . 0 6 3 3 8 0 . 0 9 0 7 5 0 . 1 2 G 5 5 0 . 0 3 9 9 3 0 . 0 6 2 2 G 1 . 7 5 5 3 1 . 8 1 G 2 1 . 8 4 8 3 1 . 8 8 1 4 1 . 9 5 0 7 2 . 1 8 4 0 1 . 5 3 4 1 1 . 3 5 1 5 0 . 8 3 2 1 1 . 9 6 3 5 1 . 9 6 7 8 0 . 0 4 2 3 5 0 . 0 2 7 8 7 0 . 0 2 0 4 3 0 . 0 1 3 9 1 0 . 0 1 6 7 3 O . O B G 4 8 0 . 0 4 9 2 3 0 . 0 7 5 6 6 0 . 1 1 1 0 6 0 . 0 5 5 5 4 0 . 0 7 7 9 8 2 . 0 8 8 3 2 . 1 4 9 3 2 . 1 8 1 3 2 . 2 1 4 4 2 . 2 8 3 7 2 . 5 1 7 0 1 . 8 6 7 2 1 . 6 8 4 5 1 . 1 6 5 1 2 . 2 9 G 5 2 . 3 0 0 8 0 . 0 5 7 2 5 0 . 0 4 2 2 4 0 . 0 3 4 0 7 0 . 0 2 5 6 1 0 . 0 1 1 2 6 0 . 0 7 1 1 2 0 . 0 3 6 7 3 0 . 0 6 1 2 4 0 . 0 9 6 0 0 0 . 0 7 0 9 3 0 . 0 9 3 4 2 2 . 4 0 3 2 2 . 4 6 4 2 2 . 4 9 6 2 2 . 5 2 9 3 2 . 5 9 8 6 2 . 8 3 1 9 2 . 1 B 2 1 1 . 9 9 9 4 1 . 4 8 0 0 2 . 6 1 1 5 2 . 6 1 5 7 0 . 0 7 2 2 8 0 . 0 5 7 0 7 0 . 0 4 8 6 9 0 . 0 3 9 8 3 0 . 0 2 1 1 3 0 . 0 5 5 9 1 0 . 0 2 7 4 7 0 . 0 4 7 5 7 0 . 0 8 1 1 7 0 . 0 8 6 2 2 0 . 1 0 8 7 4 2 . 7 0 4 4 2 . 7 6 5 4 2 . 7 9 7 4 2 . 8 3 0 5 2 . 8 9 9 8 3 . 1 3 3 1 2 . 4 8 3 3 2 . 3 0 0 6 1 . 7 8 1 2 2 . 9 1 2 6 2 . 9 I G 9 0 . 0 8 7 3 0 0 . 0 7 1 9 9 0 . 0 6 3 5 4 0 . 0 5 4 5 5 0 . 0 3 5 0 7 0 . 0 4 0 9 6 0 . 0 2 5 1 6 0 . 0 3 5 4 5 0 . 0 6 6 7 4 0 . 1 0 1 4 0 0 . 1 2 3 9 4 2 . 9 9 5 1 3 . 0 5 6 1 3 . 0 8 8 1 3 . 1 2 1 2 3 . 1 9 0 5 3 . 4 2 3 8 2 . 7 7 4 0 2 . 5 9 1 3 2 . 0 7 1 9 3 . 2 0 3 3 3 . 2 0 7 6 0 . 1 0 2 2 4 0 . 0 8 6 8 8 0 . 0 7 B 3 9 0 . 0 6 9 3 5 0 . 0 4 9 6 2 0 . 0 2 6 3 6 0 . 0 3 1 0 1 0 . 0 2 6 5 8 0 . 0 5 2 7 7 0 . 1 1 6 4 8 0 . 1 3 9 0 3 T a b l e A G . C o n t i n u e E f C A L A VMOI. 1 M = 0 M= 1 / 3 M= 1/2 M = 2 / 3 M= 1 M = 2 D 1 0 2 D 3 A 2 A 3 sn oo B S T D 2 . 0 2 3 4 0 . 0 5 4 2 7 2 . 0 8 4 3 0 . 0 3 9 3 2 2 . 1 1 6 4 0 . 0 3 1 2 3 2 . 1 4 9 4 0 . 0 2 2 9 4 2 . 2 1 8 8 0 . 0 1 0 9 3 2 . 4 5 2 1 0 . 0 7 4 17 0 1 . 8 0 2 2 0 3 9 0 6 0 1 . 6 1 9 6 0 6 4 0 8 0 . 1 0 0 2 0 9 8 9 9 2 . 2 3 16 O . O S 7 8 7 2 . 2 3 5 9 0 . 0 9 0 3 5 5 6 0 0 B S T D 1 . 9 5 7 6 0 . 0 5 1 2 5 2 . 0 1 8 6 0 . 0 3 6 3 9 2 . 0 5 0 6 0 . 0 2 8 4 0 2 . 0 8 3 7 0 . 0 2 0 3 5 2 . 1 5 3 0 0 . 0 1 1 4 7 2 . 3 8 6 3 0 . 0 7 7 2 7 0 . 7 3 6 5 0 4 1 5 1 0 . 5 5 3 8 0 6 6 9 7 0 . 0 3 4 4 1 0 2 0 2 2 . 1 6 5 8 O . O G 4 7 7 2 . 1 7 0 1 0 . 0 8 7 2 4 5 9 0 0 8 S T D 2 . 0 5 5 9 0 . 0 5 5 8 2 2 . 1 1 6 9 0 . 0 4 0 8 3 2 . 1 4 8 9 0 . 0 3 2 7 0 2 . 1 8 2 0 0 . 0 2 4 3 1 2 . 2 5 13 0 . 0 1 1 0 0 2 . 4 8 4 6 0 . 0 7 2 5 9 0 . 8 3 4 8 0 3 7 8 5 0 . 6 5 2 1 0 6 2 6 1 0 . 1 3 2 7 0 9 7 4 4 2 . 2 6 4 1 0 . 0 6 9 4 5 2 . 2 6 8 4 O . 0 9 1 9 4 5 7 0 0 B S T D 1 . 9 9 0 6 0 . 0 5 2 7 9 2 . 0 5 15 0 . 0 3 7 8 8 2 . 0 8 3 6 0 . 0 2 9 8 3 2 . 1 1 6 7 0 . 0 2 1 6 4 2 . 1 8 6 0 0 . 0 1 1 0 7 2 . 4 1 9 3 0 . 0 7 5 6 9 0 . 7 6 9 4 0 4 0 2 4 0 . 5 8 6 8 0 6 5 4 8 0 . 0 6 7 4 1 0 0 4 7 2 . 1 3 8 8 0 . 0 6 6 3 5 2 . 2 0 3 1 0 0 8 8 8 2 T a b l e A 7 S t a n d a r d d e v i a t i o n o f t h e Q ( a s d e f i n e d b y E q u a t i o n 2 . 2 4 ) v a l u e s ( S T D ) f o r v a r i o u s r e a c t i o n m e c h a n i s m s a n d a c t i v a t i o n e n e r g i e s ( E ) f o r t h e s e c o n d r e a c t i o n a t 5 0 % b y w e i g h t c o l e m a n i t e M = 0 M = 1 / 3 M = 1 / 2 M = 2 / 3 M=1 M = 2 D1 D 2 D 3 A 2 A 3 B S T D B S T D B S T D B S T D B S T D B S T D B S T D 2 . 2 2 8 8 2 . 3 3 9 7 2 . 4 0 3 1 2 . 4 7 2 G 2 . 6 3 2 1 3 . 2 7 2 2 2 . 1 5 4 6 2 . 0 6 0 0 1 . 6 8 8 0 2 . 4 6 7 5 2 . 4 1 2 6 0 . 0 5 9 B 1 0 . 0 3 0 3 0 0 . 0 1 4 8 5 0 . 0 2 5 6 7 0 . 0 9 6 1 2 0 . 4 7 4 5 6 0 . 0 3 3 9 5 0 . 0 6 7 7 1 0 . 1 6 5 9 1 0 . 0 2 0 2 3 0 . 0 5 0 2 4 2 . 5 4 2 9 2 . 6 5 3 8 2 . 7 1 7 2 2 . 7 8 6 8 2 . 9 4 6 3 3 . 5 8 6 3 2 . 4 6 8 8 2 . 3 7 4 2 2 . 0 0 2 2 2 . 7 8 1 7 2 . 7 2 6 8 0 . 0 7 2 6 1 0 . 0 4 2 1 2 0 . 0 2 2 5 0 0 . 0 1 5 7 5 0 . 0 8 3 5 7 0 . 4 6 2 4 9 0 . 0 3 4 5 0 0 . 0 5 6 6 1 0 . 1 5 2 8 2 0 . 0 3 0 9 4 0 . 0 6 3 3 0 2 . 8 4 3 4 2 . 9 5 4 3 3 . 0 1 7 7 3 . O 0 7 2 3 . 2 4 6 8 3 . 8 8 6 8 2 . 7 6 9 3 2 . 6 7 4 6 2 . 3 0 2 7 3 . 0 8 2 1 3 . 0 2 7 3 0 . 0 8 5 3 9 0 . 0 5 4 1 5 0 . 0 3 3 6 9 0 . 0 1 3 7 7 0 . 0 7 1 4 B 0 . 4 5 0 6 7 0 . 0 3 9 6 7 0 . 0 4 6 7 9 0 . 1 3 9 9 3 0 . 0 4 2 9 8 0 . 0 7 6 2 8 3 . 1 3 3 3 3 . 2 4 4 2 3 . 3 0 7 6 3 . 3 7 7 2 3 . 5 3 6 7 4 . 1 7 6 7 3 . 0 5 9 2 2 . 9 6 4 6 2 . 5 9 2 6 3 . 3 7 2 1 3 . 3 1 7 2 0 . 0 9 8 1 5 0 . 0 6 6 9 7 0 . 0 4 5 7 9 0 . 0 2 1 6 7 0 . 0 5 9 8 8 0 . 4 3 9 0 1 0 . 0 4 7 8 5 0 . 0 3 8 9 4 0 . 1 2 7 1 7 0 . 0 5 5 4 1 0 . 0 8 9 1 9 3 4 1 4 8 3 5 2 5 7 3 . 5 8 9 1 3 . 6 5 8 6 3 . 8 1 8 2 4 . 4 5 8 2 3 . 3 4 0 7 3 . 2 4 6 0 2 . 8 7 4 1 3 . 6 5 3 6 3 . 5 9 8 7 0 . 1 1 0 9 6 0 0 7 9 6 3 0 . 0 5 8 2 7 0 . 0 3 2 9 6 0 . 0 4 8 9 9 0 . 4 2 7 4 3 0 . 0 5 7 0 3 0 . 0 3 4 4 0 0 . 1 1 4 4 8 0 . 0 6 8 0 3 0 . 1 0 2 1 2 3 . 6 8 9 3 3 . 8 0 0 2 0 . 1 2 3 7 6 0 . 0 9 2 3 5 3 . 8 6 3 6 3 . 9 3 3 1 4 . 0 9 2 7 4 . 7 3 2 7 3 . 6 1 5 2 3 . 5 2 0 5 3 . 1 4 8 6 3 . 9 2 8 1 3 . 8 7 3 2 0 . 0 7 0 8 9 0 . 0 4 5 1 3 0 . 0 3 9 3 6 0 . 4 1 5 9 4 0 . 0 6 8 7 9 0 . 0 3 4 4 7 0 . 1 0 1 8 9 0 . 0 8 0 7 1 0 . 1 1 5 0 1 3 . 9 5 7 9 4 . 0 6 8 9 4 . 1 3 2 3 4 . 2 0 1 8 4 . 3 6 1 3 5 . 0 0 1 4 3 . 8 8 3 8 3 . 7 8 9 2 3 . 4 1 7 2 4 . 1 9 6 7 . 1 . 1 4 1 0 O . 1 3 G 4 G 0 . 1 0 4 9 9 0 . 0 8 3 4 9 0 . 0 5 7 5 2 0 . 0 3 2 3 1 0 . 4 0 4 6 9 O . 0 8 0 2 4 0 . 0 3 9 0 8 0 . 0 8 9 5 8 0 . 0 9 3 3 4 0 . 1 2 7 7 7 - 2 0 7 -c C 01 CO „ CO r~ CO rr in r^ n m LI CM O 6 r- O CO O 01 ro — Ol < O o n CM LP m D in CO r~ 01 ro rj LD in Cl LO rr rr C O C O ro ro rr rr - .. - • 3 ^ rr o O o o O O O IT- O r- LD r- CN o LD CM LO LD O c O LO in ro OJ in CO in rr CO LD ro < rv CO r- — — CO O CO ro rr CO o r~ — 01 ro ID O O rr O rr O — — rr rr rr rr T rr r r o O O o O o O o rr i n CM in CN 01 in rr CO r» — to O rr LD Ol Ol CO r- rr in O G CO r- — in Ol n CM 01 i n CO O CD <£> r~- 01 LD — in r- r- LD h- LO r- r* O O O O o O O n ro rr n CO CO ro O O O O o O 6 O CC IT. ro CM CO CM „ in CO CO in O 01 CN ro m CO CO Cl in m O o LD 01 01 ID G IX) LD — CD LD LO O 00 O in CM m r^ r~ O — n LO in LD — O rr o rr O rr O o O o O O O T rr rr rr r r rr 0 o O o O O 6 o — C CO CO in _ O O ~- r— — r~ O CM CD n in r~ -- 01 CO rM G rr fM O -r LO LD 01 01 CM O r^ - ro — O) - rr O LD — ai O ca — Cl — 01 o —- — O o o O rr rr rr rr rr rr o o o O o o 6 — rr LP CM ro rr LP p~ _ 01 LD CM rr CM in — rr in O LD n CO m — ro ti . w n CN CM CC — — — --in CO 01 CM CN oi in CO r~ D 01 CM 01 CM 01 CM 01 n ro ro CO CO CO o m in in in in in in O O O O O o O ro LO CM ro in n LP LD o 01 CM CM in "~ in ro rr CO O in r- CM LD CO rr •— CO 11 CN 01 CO - rr CO r» 01 r- Ol Cl 01 in O) <s CM CC n n <S> CM m CM in CN LD CM O O O O o o o — in rr rr rr rr O O O o C o 6 n e> _ O CM CO in CO CM ,_ ro r- LO CO \ LT — LO LO O CM in CO LD Cl CO ro CN o CN CM CO m i~ CM r-- CO CO 01 il rr r- CO 01 01 m r~ rr LD rr LO rr r-O o O O O o rr T rr rr rr rr rr O O O O o c O CM O 01 i n LO n - n CM LD r- CO rr _ r--\ — in — rr CO LO CO LO Cl 01 CM rr *~ cn LD i n CO -~ rr CO rr CO LD rr CM r^ -u n Cl L9 O Ol CM rr Ol CO Cl ro Cl rr Ol 2» O — o O o O rr T rr rr rr rr rr O O O O O o O n Ul CM 01 Cl C D in CNI o T T r- O " \ CN r~ CM ro Cl rr — O CM LD T co O *- D r~ 01 O CM CO O CO in o LD in Ol II n *~ in C O CO n CJ CM ro - ro — - — — — — • * T J -77 — T o O o o o o o C) in O) cn CO c in CO CC rv o — CN CO LO Li tn Cl in 01 ~- m 11 CN CO CC — C) rr r— — LO U 3 Ol r- -T O CN T rr LD r - r- CN in — — — rr CM in — »- — »— — r; TT rr rr — rr o o O o o o O Q O a Q Q o G CO i— CO v~ CO r— ca t— CO 1 — CO t— CO L O l / l LO LO i/l in IS) _J o O o o O O O < g o O o o C O O o O o CN r~ cn rr in n Oi a " -208-APPENDIX V : F ITTING OF THE POINTS ON F I G . 56 AND 57 -209-X POWER C O E F F I C I E N T 0 - 1 9 9 9 9 . 0 0 1 3 1 2 5 1 S . 2 3 6 2 7 2 - 8 5 . 4 9 7 0 6 3 9 3 . 9 6 6 6 3 8 7 i 6 ' PERCENTAGE GOODNESS OF F I T = 100 X POWER C O E F F I C I E N T 0 - 2 5 2 . 3 4 2 4 7 4 1 2 7 . 3 4 8 2 6 8 1 2 - . 9 4 7 2 2 8 9 4 3 3 . 0 1 0 5 3 9 7 7 0 7 PERCENTAGE GOODNESS OF F I T = 1 0 0 X POWER C O E F F I C I E N T 0 . 2 2 9 3 7 0 3 9 6 1 - . 0 2 4 9 9 3 2 3 2 9 2 8 . 8 3 0 2 1 7 4 2 E - 0 4 3 - 9 . 3 0 3 0 6 4 2 2 E - 0 6 PERCENTAGE GOODNESS OF F I T = 100 

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