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UBC Theses and Dissertations

Kinetic studies on the biological leaching of a zinc sulphide concentrate in two stage continuous stirred… Sanmugasunderam, Visvanathakurukal 1981

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KINETIC STUDIES ON THE BIOLOGICAL LEACHING OF A ZINC SULPHIDE CONCENTRATE IN TWO STAGE CONTINUOUS STIRRED TANK REACTORS by VIS VANAT HA KURUKAL ^ SANMUGASUNDERAM B.Sc. ( H o n s . ) , U n i v e r s i t y o f C e y l o n , 1955 P o s t G r a d u a t e D i p l o m a i n C h e m i c a l E n g i n e e r i n g , U n i v e r s i t y C o l l e g e o f Swansea, 1973 M.Sc. ( B i o c h e m . E n g . ) , U n i v e r s i t y o f W a l e s , 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES ( D e p a r t m e n t o f C h e m i c a l E n g i n e e r i n g ) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d HE UNIVERSITY OF BRITISH COLUMBIA © A u g u s t 1981 In present ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the 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 fo r reference and study. I fur ther agree that permission for extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representa t ives . It i s understood that copying or p u b l i c a t i o n of t h i s thes is fo r f i n a n c i a l gain s h a l l not be allowed without my wr i t ten permiss ion. Department of (C^g^A^^TQaJ^. ( \ The Un ivers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date This dissertation is dedicated to my wife, Vi salakshi , to whom special gratitude is expressed for her endless patience, understanding and encouragement. i i i ABSTRACT A novel reactor c o n f i g u r a t i o n was designed and i t s s u i t a b i l i t y tested for small scale leaching of concentrates. The s a l i e n t features of the apparatus were a l e v e l c o n t r o l l e r s u i t a b l e for a g i t a t e d and aerated s l u r r i e s and a seq u e n t i a l timer capable of c o n t r o l l i n g "the automatic operation of the apparatus. Continuous m i c r o b i o l o g i c a l leaching of a zinc sulphide concentrate i n the two stage reactor was conducted i n s t a i g h t through and r e c y c l e modes and steady-states were achieved. K i n e t i c models were developed f o r s t r a i g h t through and r e c y c l e mode operations. The maximum s p e c i f i c growth rate of b a c t e r i a attached to the concentrate was found to be 0.019 h 1 g i v i n g a generation time of about 52.2 hours. The surface area 9 occupied by the attached b a c t e r i a was found to be 0.345 m~/mg or 100 % of the surface area of the residue i n tank at steady s t a t e . The organism T.ferrooxidans used i n t h i s study was shown to e x h i b i t the a b i l i t y to f i x atmospheric nitrogen when ammonium ion concentration i n the medium was depleted. I t was shown that the amount of leaching could gen e r a l l y be p r e d i c t e d by the a p p l i c a t i o n of the sh r i n k i n g core model of Levenspiel (1972). A design procedure based on t h i s model i s given. TABLE OF CONTENTS De'dication '• Abstract Tabl e of Contents • L i s t of Tables L i s t of Figures and Plates ; ••• Acknowledgements Nomenclature 1 . INTRODUCTION 2. THIOBACILLUS FERROQXIDANS .• 2.1 Morphology and Physiology 2.2 Chemical Composition 2.3 Mineral-Microbe Interact ions 2.3.1 . Enumeration • • •.• 2.3.2 ' Attachment 2.4 Bacter ia l Leaching 2.4.1 Direct Mechanism 2.4.2 Indi rect Mechanism 2.4.3 Mechanism of Oxidation of Elemental Sul fur and Sul fur Compounds 2.4.4 Mechanism of Oxidation of Ferrous Iron 2.4.5 F ixa t ion of Carbon Dioxide 2.4.6 Tox ic i t y of Metals and UV-Sens i t i v i t y 2.5 Factors Af fect ing Metabolism and Leaching of T. ferrooxidans V 2 . 5 . 3 pH 30 2 . 5 . 4 O x i d a t i o n - R e d u c t i o n P o t e n t i a l (Eh) 3T 2 . 5 . 5 P a r t i c l e S i z e and S u r f a c e A r e a 34 3 . THEORY 38 3.1 B a c t e r i a l K i n e t i c s and M o d e l l i n g 33 3 . 1 . 1 T r a n s f e r P r o c e s s e s 39 3 . 1 . 2 T r a n s f o r m a t i o n P r o c e s s e s 39 3 . 1 . 3 B i o k i n e t i c M o d e l l i n g 40 3 . 2 K i n e t i c s 49 3 . 2 . 1 B a t c h C u l t u r e 4] 3 . 2 . 2 C o n t i n u o u s C u l t u r e 45 3 . 3 K i n e t i c s o f L e a c h i n g 5] 3 . 3 . 1 D e r i v a t i o n o f G o r m e l y ' s Model 5] 3 . 3 . 2 A p p l i c a t i o n o f t h e Model t o a S i n g l e Tank 53 3 . 3 . 3 A p p l i c a t i o n o f G o r m e l y ' s Model t o Two Tanks i n S e r i e s 55 3 . 3 . 4 A p p l i c a t i o n o f t h e Mode l when R e c y c l i n g i s Used 5 6 3 . 3 . 4 . 1 A p p l i c a t i o n o f Model to F i r s t Tank 50 3 . 3 . 4 . 2 A p p l i c a t i o n o f Model t o Second Tank when R e c y c l e i s Used 6 1 3 . 3 . 5 R e v i e w o f G o r m e l y ' s Work 52 4 . EXPERIMENTAL METHODS AND PROCEDURES 6 5 4.1 P r e l i m i n a r y E x p e r i m e n t s 55 4 . 2 D e v e l o p m e n t o f t he A p p a r a t u s 57 4 . 2 . 1 E f f i c i e n t M i x i n g 57 4 . 2 . 2 T r a n s f e r o f S l u r r y be tween R e a c t o r s 57 4 . 2 . 3 R e c y c l e 7] 4 . 2 . 4 S e q u e n t i a l T i m e r 7 ? vi 4.3 Descr ipt ion of the Reactor System 74 4.3.1 St ra ight through Two Stage Operation 74 4.3.2 Two Stage With Recycle to the F i r s t Reactor 8 1 4.4 Operation 32 4.4.1 St ra ight Through Two Stage Operation • 8 2 4.4.2 Recycle 35 4.5 Mater ia ls 37 4.5.1 Organism 37 4.5.2 Substrate 8 8 4 .5 .3 . Culture Medium 33 4.5 .4 . Antifoatn 33 4.6. Procedures 39 4.6.1 Mixing Charac te r i s t i cs of the Reactor . gg 4.6.2 The Concentrate 9] 4.6.2.1 Blending the Concentrate gi 4 .6.2.2 Analys is of the Concentrate g] 4 .6 .2 .3 Determination of the Spec i f i c Surface Area 94 4.6.2.4 Bal l M i l l i n g of the Concentrate 9 4 4.6 .2 .5 Concentrate Fract ionat ion 95 4.6.3 The Organism 95 4.6.3.1 Evaluation of Bacter ia l Growth 98 4.6.4 Leaching Techniques 98 4.6.4.1 Continuous Experiments 98 4.6.4.2 Pulp Density 99 4.6.4.3 Sampling Procedures and Miscellaneous Dai ly Housekeeping Chores }Q] RESULTS AND DISCUSSIONS 103 5.1 Mixing Charac te r i s t i cs of the Reac to r . . . 103 v i i 5.2 Analys is of the Concentrate 107 5.3 Shake Flask Experiments 113 5.4 Continuous Leaching Experiments 120 5 .4 .1 . Introduction 120 5.4 .2 . " S t e r i l e " Run 120 5 .4 .3 . St ra ight Through Mode Runs 125 5 .4 .3 .1 . The F i r s t Reactor 125 5 .4 .3 .2 . The Second Reactor 140 5 .4 .3 .3 . Conclusions from the Stra ight Through Mode Runs 148 5.4.4 Two Stage Continuous Runs in Recycle Mode 151 5 .4 .4 .1 . The F i r s t Reactor 151 5 .4 .4 .2 . The Second Reactor 157 5 .4 .4 .3 . Conclusions from Recycle Runs 161 5.4.5 Wash-out 165 5.4.6 Dissolved Iron Concentration 167 5.4.7 Y ie ld Constants '. 167 5.4.8. Nitrogen Fixat ion 169 5.4 .9 . Reduction of Concentration of Surface Area in Feed 173 5.4.10 Shrinking Core Model 176 5.4.11 Economic Considerations of Continuous Leach ing . . . . 179 5.4.11.1 F e a s i b i l i t y 181 5.4.11.2 Design Calcu la t ions 184 6. SUMMARY AND CONCLUSIONS 190 6.1 Recommendations for Future Studies 193 6.1.1 Optimum Number of Tanks 193 6 .1 .2 . Optimum Recycle Ratio 194 7 REFERENCES 195 v i i i APPENDIX 3.1 Der ivat ion of Gormely's Model 206 APPENDIX 3.2 Der ivat ion of Equation 3.42 210 212 APPENDIX 3.3 Recycle Mass Balances , . APPENDIX 3.4 Der ivat ion of Equation 3.53 215 APPENDIX 3.5 Der ivat ion of Equation 3.59 219 APPENDIX 4.1 Results of Runs Made Pr io r to Modi f icat ions to the Apparatus 223 APPENDIX 4.2 Development of a Level Cont ro l le r 225 APPENDIX 4.3 Descr ipt ion of the Sequential Timer 230 APPENDIX 4.4 Procedure for Mixing the Concentrate 233 APPENDIX 4.5 A i r Permeabi l i ty Method for the Determination of Spec i f i c Surface Area 236 APPENDIX 4.6 Experimental Procedure for the Determination of Nitrogen 241 APPENDIX 4.7 Propert ies of S lu r r i es . 243 APPENDIX 5.1. Detai led Experimental Data for Mixing Charac te r i s t i cs Experiment 248 APPENDIX 5.2 Results of the Continuous Stra ight Through Mode Operation 250 APPENDIX 5.3 Calcu la t ion for Steady State Run No.5 254 APPENDIX 5.4 Results of Continuous Recycle Mode Operation 262 APPENDIX 5.5 Ca lcu la t ion for Steady State Run No. 16 266 APPENDIX 5.6 Ca lcu la t ion of Fract ional Extract ion Using Levenspie l 's Shrinking Core Model 2/3 APPENDIX 5.7 App l ica t ion of the Shrinking Core Model to the Second Tank 288 APPENDIX 5.8 Quant i tat ive Method for the Evaluat ion of Mixing E f f i c iency 293 PLATES 299 i x L I S T OF TABLES T a b l e 4.1 V a l v e s A c t u a t e d by t he T i m e r s 75 T a b l e 4 . 2 G e o m e t r i c R a t i o s f o r t he Tank 78 T a b l e 4 . 3 ( M o d i f i e d ) 9k Medium o f S i l v e r m a n and L u n d g r e n 97 T a b l e 5.1 Da ta f o r P u l p D e n s i t y ' o f 10 P e r c e n t 104 T a b l e 5 . 2 Summary o f t h e R e s u l t s o f T r a c e r S t u d y 106 T a b l e 5 . 3 A n a l y t i c a l R e s u l t s o f C o n c e n t r a t e 108 T a b l e 5 . 4 A n a l y s i s o f V a r i a n c e - Z i n c 109 T a b l e 5 . 5 A n a l y s i s o f V a r i a n c e - I r o n 110 T a b l e 5 .6 R e s u l t s o f X - r a y S p e c t r o s c o p i c A n a l y s i s o f C o n c e n t r a t e 112 T a b l e 5 . 8 E f f e c t o f S p e c i f i c S u r f a c e A r e a a t 1.0 P e r c e n t C 0 2 115 T a b l e 5 . 9 Bahco F r a c t i o n s 118 T a b l e 5 . 1 0 Da ta f o r C o n t i n u o u s Run ( S t e r i l e ) a t a D i l u t i o n R a t e o f 0 . 0 1 3 h " 1 122 T a b l e 5.11 Da ta f o r t h e F i r s t Tank 127 T a b l e 5 . 1 2 Summary o f D i l u t i o n R a t e , I n t e r c e p t , S l o p e and t h e i r R e c i p r o c a l s 130 T a b l e 5 . 1 3 Da ta f o r Second Tank 141 T a b l e 5 .14 Da ta f o r Second Tank S t a i g h t Th rough Mode 146 T a b l e 5 . 1 5 Met Ammonium Ion V a l u e s C a l c u l a t e d on t h e B a s i s o f t h e f o l l o w i n g V a l u e s f o r t h e C o n s t a n t s f , k and v 147 T a b l e 5 .16 Summary o f Two S t a g e C o n t i n u o u s S t r a i g h t Th rough Runs 149 T a b l e 5 .17 Summary o f Z i n c Mass B a l a n c e s 150 T a b l e 5 . 1 8 Summary o f Da ta From F i r s t Tank in. R e c y c l e Mode .". 154 T a b l e 5 .19 I n c r e a s e i n P u l p D e n s i t y i n F i r s t Tank 156 X Table 5.20 Summary of Data from Second Tank in Recycle Mode 158 Table 5.21 Comparison of Experimental and Calculated Values of X, 159 Table 5.22 Values obtained for v, f and k 160 Table 5.23 Summary of Two Stage Continuous Recycle Mode Operation 162 Table 5.24 Summary of Zinc Mass Balance for Recycle Runs 164 Table 5.25 Averaqe Y ie ld Coef f i c ien ts at D i f fe rent D i lu t i on Rates" 170 Table 5.26 Fed-Batch Culture 172 Table 5.27 Reduction of Surface Area Concentration in the Reactors Operating in Stra ight Through Mode 174 Table 5.28 Reduction of Surface Area Concentration in the Reactors Operating with Recycle 175 Table 5.29 Comparison of the Calculated Values of Ext ract ion in Tank 1 with Experimental Values 177 Table 5.30 Extract ion Rates Calculated using the Shrinking Core Model 186 Table 5.31 Summary of Calcu la t ions made on the Basis of the Shrinking Core Model • 189 Table A.4.1 Data from Prel iminary Runs 224 Table A.5.1 Data from Mixing Charac te r i s t i cs Experiment 249 Table A.5.2 Data from Tank One for Continuous Leaching in St ra ight Through Mode (uncorrected) . . . 2hl Table A.5.3 Data from Tank One for Continuous Leaching in Stra ight Through Mode (corrected) 252. Table A.5.4 Data from Tank Two for Continuous Leaching in Stra ight Through Mode 253 Table A.5.5 Data from Tank One for Continuous Leaching in Recycle Mode (uncorrected) 263 Table A.5.6 Data from Tank One for Continuous Leaching in Recycle Mode (corrected) 264 xi Table A.5.7 Data from Tank Two for Continuous Leaching in Recycle Mode .265 Table A.5 .8 Calculated Extract ion for Run Mo. 1 275 Table A.5.9 Calculated Extract ion for Run No. 2 276 Table A.5.10 Calculated Ext ract ion for Run No. 3 277 Table A.5.11 Calculated Extract ion for Run No. 4 278 Table A.5.12 Calculated Extract ion for Run No. 5 279 Table A.5.13 Calculated Extract ion for Run No. 6 280 Table A.5.14 Calculated Ext ract ion for Run No. 7 281 Table A.5.15 Calculated Extract ion for Run No. 8 282 Table A.5.16 Calculated Extract ion for Run No. 9 283 Table A.5.17 Calculated Extract ion for Run No. 10 284 Table A.5.18 Calculated Ext ract ion for Run No. 11 285 Table A.5.19 Calculated Extract ion for Run No. 12 286 Table A.5.20 Calculated Extract ion for Run No. 13 287 Table A. 5.21 Shrinking Core Model Calcu la t ions for Tank 1 291 Table A.5.22 Shrinking Core Model Calcu la t ions for Tank 2 . . . 292 Table A.5.23 Results of Tracer Study 297 xi i LIST OF FIGURES Figure 2.1 Generalized Scheme for the Oxidation of Elemental Sul fur and Produced Compounds by t h i o b a c i l l i 21 Figure 2.2 Scheme for Iron Oxidation 23 Figure 2.3 Eh-pH Diagram of Fe-S-H 2 0 System 32 Figure 2.4 Eh-pH Diagram of Zn-S-H 20 System 35 Figure 3.1 n Vessels in Series 46 Figure 3.2 Recycle Mode Operation Showing Meaning of Recycle R a t i o . . . . 53 Figure 3.3 D is t r i bu t ion of Surface Area and Bacter ia l Concentration during Recycle 59 Figure 3.4 Flow Diagram of a Model showing Complete Mixing with Shor t -C i rcu i t i ng and Dead Space 64 Figure 4.1 Diagramatic Layout of the Intermediate Tank 69 Figure 4.2 Deta i ls of Construct ion of the Gland 70 Figure 4.3 Modi f icat ion for Recycle 73 Figure 4.4 Layout of the Apparatus for St ra ight Through Mode Operation 76 Figure 4.5 Schematic Drawing of Tank 77 Figure 4.6 Geometric Ratios of the Reactor 79 Figure 5.1 Zinc Extract ion Rates of the Bahco Fract ions 116 Figure 5.2 Ef fect of Spec i f i c Surface Area on Zinc Extract ion 117 Figure 5.3 Zinc Extract ion Rate versus P a r t i c l e Diameter , 119 Figure 5.4 P lo t of Met [NH 4 + ] versus [SA] 128 Figure 5.5 Reciprocal Slope versus D i lu t i on Rate 131 Figure 5.6 Reciprocal Intercept versus D i lu t ion Rate 133 Figure 5.7 Net [NHu+] versus Pulp Density 135 Figure 5.8 Uncorrected [Zn] versus [SA] 136 Figure 5.9 Corrected [Zn] versus [SA] 137 x i i i Figure 5.10 Uncorrected [Zn] versus Pulp Density 138 Figure 5.11 Corrected [Zn] versus Pulp Density 139 Figure 5.12 Dif ference in [ z n l versus Dif ference in [SA] 142 Figure 5.13 Dif ference in [Zn] versus Dif ference in Pulp Density 143 Figure 5.14 Net [NH 4 + ] versus [SA] 153 Figure 5.15 Washout of both Reactors at a D i lu t ion Rate of 0.0215 h - 1 166 Figure 5.16 Plot of [Fe] versus [Zn] 168 Figure 5.17 P lo t of Calculated Extract ion versus Experimental Ext ract ion 178 Figure A.4.1 Level Cont ro l le r I ns ta l l a t i on : . . 227 Figure A.4.2 Level Transmitter 229 Figure A.4.3 Diagramatic Representation of the Seven Timers and the Connections to the Relays 231 Figure A.4.4 Schematic C i r c u i t Diagram of One Timer 232 Figure A . 4 . 5 Pa r t i t i on ing of the P lo t 234 Figure A.4.6 Blaine A i r Permeabi l i ty Apparatus 237 Figure A.4.7 Flow Chart for Calcu la tor Program 245-Figure A.5.1 A Typical Residence Time D is t r ibu t ion Curve 294 Figure A.5.2 P lo t of 1 - F(t) Versus t/T 298 xi v ACKNOWLEDGEMENTS It is with great pleasure that I acknowledge my sincere gratitude and thanks to Dr. D.W. Duncan and Dr. R.M.R. Branion for their invaluable guidance, encouragement, support and friendship throughout the course of this research work. I am also grateful to Dr. K.L. Pinder for the inval-uable discussions and guidance given wholeheartedly. I am indebted to B.C. Research for allowing me the use of their faci l i t ies for this study. I wish to thank ihe Chemical Engineering Department Workshop and stores personnel for the technical support provided. I have had fruitful discussions with the staff of Biology at B.C. Research and I am indebted to them for their patience and understanding. Last, but not least, I would like to thank the Word Processing Centre, B.C. Research, for typing the manuscript from the awful scrawl. Financial support for this research program was provided by the National Science and Engineering Research Council of Canada, the University of British Columbia (through its Graduate Fellowship Award) and B.C. Research. XV NOMENCLATURE A = a constant defined by Eq. 3.4 C = defined by Eq. 3.61 C g = concentration of tracer in active volume (see Figure 3.4),g/2. CQ = init ial concentration of tracer,g/£ D = dilution rate ,h - 1 f = surface area occupied unit of bacterial concentration,m2/g F = flow rate, £/h Fpd = feed pulp density, percent (g/100 nu) ki = rate constant of the forward reaction (Eq. 3.31), £/m 2.h k_! = rate constant of the backward reaction (Eq. 3.31) h _ 1 K = ratio of the rate constants of Eq. 3.31 given by k_i/k (Eq. 3.34),m 2 /£ = Michelis-Menten constant,g/£ P = product concentration,g/£ Q = volume of l iquid, £ Q= = volume of 'active' region (see Figure 3.4),.?, a Qh = volume of 'By-pass' (see figure 3,4) i r x = rate of growth of cel ls ,g/£.h s = surface area concentration, m2/£ S = substrate concentration,g/£ [SA] = surface area concentration,m 2/£ t = time, h t = mean residence time, h V = volumetric flow of l iquid, £/h xvi V = volumetric flow in active region (see Figure 3 . 4 ) , £ / h a = volumetric flow in 'by-pass' region,i/h X = concentration of cell mass,q/i y Zn/X = yield constant; zinc production based on concentration of cell mass Y Zn/s = yield constant; zinc production based on surface area con-centration, g/m2 Y X/s = yield constant; concentration of cell mass based on surface area concentration,g/m2 Y X/P = yield of cell growth based on product Y P/S = yield of product based on limiting substrate v X/S = yield of cell growth based on limiting substrate GREEK LETTERS 3 = concentration of cell mass to the second tank from the intermediate tank when recycle is used (Eq. 3 .57) q/i 5 = fraction of solids to recycle 9 = dimensionless residence time v = maximum specific growth rate of bacteria which are attached u = specific growth rate, h - 1 a = concentration of bacteria attached to the surface of mineral g/2, y = recycle ratio defined by Eq. 3 .43 1 1. INTRODUCTION Air pollution problems innerent in smelters, the cost of abating pollution and tne rapidly rising cost of energy emphasize tne necessity for new and pernaps unconventional methods in the mineral processing industry. Microoiologica I leacning could be one of tnose. Considerable effort nas Deen directed towaras developing techniques for Teaching mineral sulphides using oacteria. Bacterial leacning can oe used for ootn low grade ores and concentrates. Arsenic (Enrlicn, 1963), cadmium (Brissette, et a l . 1971), cooalt (De Cuyper, 1964), copper (Bryner and Andersen, 1957), iron (Leathen and Bradley, 1954), lead (Torma and Suoramanian 1974), manganese (Perkins and Novielli, 1974), molybdenum (Bryner and Anderson, 1957), nicKel (Duncan and Trussell, (1964), tin (Duncan, 1967), titanium (Silverman and Munoz, 1972), uranium (Miller et_ al_. 1963), vanadium (Goren, 1967), and zinc (Zimmerly _et aj_. 1958), may be leached oy oacterial oxidation of their associated sulphides. However, oionydrometal1urgical recovery of sulfide-oearing minerals is currently used commercially only for copper (dump ana neap leaching techniques) (Anaerson and Allman, 1968) and uranium ( in-situ leacning) (Matic and Mrost 1964). 2 I n i t i a l l y , laboratory studies on leaching were conducted in a i r l i f t percolators (Bryner ere a l . 1954), in Warburg respirometers (Beck 1960) and in stat ionary leacn Dott les (Razzel and T r u s s e l l , 1963). Tnese metnoas dia not f ina favor because in the f i r s t and tne last metnoas supply of oxygen to tne microbes was poor. In tne case of tne WarDurg respirometer tne design was unsuitaole for rout ine studies on •so l id substrates. Duncan et a l . (1964) introduced tne snake f l a s K teennigue whicn has been in vogue since then. Other types of mixers tnat could be used in tne laboratory are a i r spargers, magnetic s t i r r e r s and rec iprocat ing snakers. The las t two methods were reported to give resu l ts comparable to tne snake f lasK technique by Duncan et a l . (1967). Bruynesteyn and Duncan (1971) nave demonstrated tnat a continuous s t i r r e d tank reactor using conventional aeration equipment is eminently sui ted for leacning nign grade materials ana that in th is metnoa tne parameters in f luencing leaching could oe cont ro l led e a s i l y . 3 The objectives of tnis study were to: 1) develop an apparatus suitaole for leacning zinc sulphide concentrate; 2) try and improve the recovery of zinc Dy recycle and/or oy use of two leacn tanKs in series; and 3) study the K ine t i cs of leacning in a two tank continuous s t i r r ed tank reactor (CSTR) system, in order to verify and extend the model proposed by Gormely (1973) to two tank straight through and recycle mode operations. Tne stuoy nas been conducted with Tniobacillus ferrooxidans, tne organism responsiole for microbiological leacning of zinc sulpnide. 4 2. THIOBACILLUS FERROOXIDANS 2.1 iMorpnology and Pnysiology Most bacteria util ize organic compounds to obtain tneir energy. Sucn organisms are classified as neterotropns. A few organisms, c l a s s i f i e d as autotropns nave tne ability to utilize carbon dioxide as tneir sole source of carbon. Tnis capability was f i r s t observed oy WinogradsKy (1887). Cnemosyntnesis is tne use of cnemical bonds as tne source of energy for syntnet ic reactions (i .e. assimilation) as opposed to pnotosyntnesis wnicn is utilization of tne energy of light. Autotropnic bacteria are further subdivided into obligate ano facultative forms. Tne ooligate forms obtain their energy solely from oxidation of inorganic compounds while tne facultative ones nave tne capability of utilizing organic compounds in tne absence of inorganic substances. Tne genus Tniobaci1lus, oelongs to tne family Tniobaci1leae, and derives its name from Greek theion, sulfur and Latin oaci11 us, a small rod. MemDers of tnis genus nave tne unique ability to obtain their energy from tne oxidation of incompletely oxidized sulfur compounds sucn as elemental sulfur, thiosulfate, sulfide, sulfite and polytnionates. The main product of the oxidation is sulfate, nowever sulfur is sometimes formed (Bergey's Manual of Determinative Bacteriology, 8tn edition 1974). 5 Tniobaci]Ii are Gram-negative, roa-snaped cells measuring 0.5 oy 1-3 vm and occur singly, in pairs or in cnains. Tney do not form spores and reproduce normally by transverse or oinary f ission. Altnough tney nave a polar flagellum (whicn is used for mooility), tne fI age 1Ium is generally absent if cultured by sna<ing, prooaoly due to attrition of tnis delicate organ. T. ferrooxidans is ubiquitous in nature; its most common nabitats are acidic mine and ground waters. It was ini t ia l ly isolated from acidic mine water by Colmer ano Hinkle (1947); out Rudolph and Helbronner (1922) in tneir paper entitled "Oxidation of Zinc Sulpnioe oy Microorganisms" described reactions whicn were probaoly due to tne organism. Carpenter and Herndon (1933) were unaoie to demonstrate in showing tnat microbes were responsiole for tne acid sulfate content of mine waters. Tne species T. tniooxiQans ano T. ferrooxipans are usually considered to oe ooligate chemolitnotropns, using energy derived from tne oxidation of inorganic compounds. T. tniooxiaans are strictly aerobic and oxidize elemental sulfur, thiosulfate and nydrogen sulpnioe. Tney utilize caroon dioxide from tne atmosphere as a source of caroon. T. ferrooxi dans are similar to T. tniooxidans except that they are able to utilize the energy of the oxidation of ferrous iron and sulpniae minerals. Tnis exceptional aoiIity is exploited commercially. Leathen e_t aj_ (1956) assigned tne name FerroDaci1lus ferrooxidans to an organism, wnich tney isolated from acidic mine waters, since tney tnougnt it oxidised iron, out not sulfur. Similarly, Kinsel (1960^  assigned tne name F_. sulpnooxidans to a microorganism wnicn sne reported utilized iron ana elemental sulfur out not tniosulfate. Subsequently, (cased on nutritional and taxonomic studies) Unz and Lundgren (1961), Ivanov and LyaliKova (1962) Beck and Snafia (1964), Hutchinson _et a_l_ (1966, 1969), Margalitn et aj_ (1966), Silver and Lundgren (1968), Silver (1970), Kelly and Touvinen (1972), and Bounds and Colmer (1972), nave all inaicated tnat tnere are no major differences oetween F_. sulpnooxiaans, F_. ferrooxiaans and ferrooxidans, and tnat they should all oe regaroea as T. ferrooxiaans. Recently, Silver and Torma (1974) demonstrated tnat T. ferrooxi dans adapted to, and grown on different substrates showed botn qualitative and quantitative differences in their aoility to oxidize various sulpniae minerals and in tneir aoility to fix C0 9. 7 Tnere is evidence in tne literature tnat many of tne cultures of _T. ferroxidans are not pure cultures. For example Harrison _e_t a "I (1980) isolated an acidophilic heterotropn, and a strict autotropn from several presumaDly pure cultures of T_. ferrooxidans. By means of deoxyribonucleic acid (DNA) homology tney demonstrated that the acidopnillic neterotropns were of a different genotype from T. ferrooxidans. This observation may explain in part Guay et al 's (1975, 1976) finding tnat T. ferroxidans grown on different substrates nad a different DNA composition. T. ferrooxidans has oeen claimed to grow on organic compounds (Snafia and Wilkinson (1969) and Taoita and Lundgren (1970)). Tuovinen and Kelly (1972) and Lundgren et aj_ (1972) nave reported tnat such growth resulted in alterations of tne morpnology and pnysiology of tne organisms. T. ferrooxidans, adapted to grow on organic compounds, lose their aDility to assimilate CO2 and to oxidize ferrous iron. Guay ano Silver (1975) nave proposed tnat tne neterotropnic oacteria derived from T. ferrooxidans oy such adaptation be assigned to a new species, T. acidopnilus, wnicn grows on sulfur compounds out not on ferrous iron. 8 2.2 Cnemical Composition and Structure of T. ferrooxidans Lundgren e_t aj_ (1962, 1964) reported tne cell composition of T. ferrooxidans to De 44 percent protein, 26 percent l ip id, 15 percent carbonydrate, and 10 percent asn. At least two B-vitamins, thiamin and riboflavin, are present. Tne protein is said to consist of 18 amino acids. The elemental analysis of tne dried organism snowed it to contain 47.5 percent caroon, 14.88 percent nitrogen and 7.59 percent nydrogen (Tuovinen and Kelly, 1973). Tne cell structure of T. ferrooxidans is similar to that of otner Gram-negative bacteria (Lundgren et_ al_, 1964 and Holt, et. _al_, 1974). Tne cell wall is semi-permeable to nutrient (Mitchell, 1957 and Csaky, 1965). It consists of six layers: tnree osmopnilic and three osmophobic (AvaKyan and KaravaiKo, 1970). Tne three outer osmopnilic layers are composed of a 1 ipoprotein-1ipopolysaccnaride layer; tne middle layer is a layer composed of glooular protein attacned to f ibr i l lar nucleopeptide; and tne innermost layer is tne cytoplasmic membrane (Remsen and Lundgren, 1966). The sugars common to 1ipopolysaccharides (LPS), namely neptose, glucose, galactose, mannose and 2-*eto-3-deoxy-octulosonate, were identified. Iron, mostly in tne ferric form, was associated witn tne LPS, suggesting tnat LPS might serve as tne init ial 9 binding site f o r tne energy substrate (Fe ) of tne organism (Wang _et aj_ 1970). Tne peptidoglycan layer consists of glutamic acid, a-e-diaminopiinel ic acid, alanine, glucosamine and muramic acid (Wang and Lundgren, 1968). Tne cytoplasm of T. ferrrooxidans abounds with internal memDrane structures ana contains ribosomes, nuclear materials and a numoer of cell inclusions of different sizes (Avakyan and KaravaiKo, 1970). Tne precise function of tne cell envelope and its relation to tne structure is not yet clearly identified. 2.3 Mineral-iMicrooe Interactions Tne necessity for direct contact between tne mineral particles and tne chemoautotropnic bacteria nas been established oy several worKers (Vogler and Umoreit, 1941); Umbreit _et a_l_; 1942; Silverman, 1967, McGoran et_ al_, 1967; Enrlicn and Fox 1967; Duncan and Drummono, 1973; Gormely and Duncan 1974). 2.3.1 Enumeration Tne usual methods encountered in microbiology are unsuitable for tne enumeration of tne cnemoautotropnic bacteria. Turbidity, the most common inetnod usea in bacteriology, is not often used to measure growtn of tne 10 cnemoautotropns as tne s u D s t r a t e s are themselves particulate in nature. Moreover, . tnere may be precipitation of inorganic substances as a result of bacterial growtn. Tne dry weight of tne bacteria cannot be used for ;tne same reasons. Direct counting of bacteria is diff icult and prone to error. Since, tney cannot be grown on solid agar plates witn reproducibility, even tne metnod of most probable number (MPM) suggested by Collins (1967) cannot oe used. In view of tnese difficulties several non-routine methods nave been used by different researchers. Becx (1960) used tne oxidation of ferrous iron as a measure of tne activity of T. ferrooxidans. A decrease in pH or increase in tne amount of titrable acid produced could oe used as measure of tne growtn of sulfur-oxidizing bacteria. Tne uptake of oxygen as tne bacteria oxidize tne substrate could oe measured using a manometric technique (Bhappu et_ al_, 1969; Umbreit et_ a_l_, 1972). Other metnods of measuring bacterial growth include monitoring the concentration of tne metal, analyzing for protein (Lowry e_t a l , 1951; Le Roux et_ 1973) or total cellular nitrogen (Le Roux et_ al_, 1973). A technique developed oy Smith et aj_ (1972, 1973) is 14 based on tne fixation ot CO2. Tms metnoo was used oy Brierley (1977) for the determination of tne activity of 11 T. ferrooxidans and Sulfolobus. It was found tnat tne method was suitable for mesopnilic chemoautotropns sucn as T. ferrooxidans. However, no correlation was ooserved Detween 14 tne CC^  uptake and Sulfo lobus counts as ascertained by ivlPN in 1iquid medium. Tuovinen and Kelly (1973) examined tne development of T. ferrooxidans colonies using memorane f i l ters on ferrous sulfate agar. Deposition of iron on tne memorane was eliminated by lowering tne pH of tne medium to, and maintaining it at, 1.3. In view of tne pH being so low tne T. ferrooxidans nad to oe adapted. Tne bacteria were separated from tne membranes, Dut toxicity of diffusiole soluble agar was noted. Only one strain of T. ferrooxidans was tested. It is likely tnat different strains and different organisms would nave different requirements. In tne circumstances tne appl icabi l i ty of tnis metnod for general purposes is douDtful (Brierly, 1978). Scnuler and Tsucniya (1975) useo tne Coulter Counter for determination of cell number and size of tnree strains of T. ferrooxidans grown in liquid medium. The autnors pointed out tnat tne Coulter Counter cannot oe useo to determine cell numbers attacned to mineral particles, as EDTA (oi-sodium ethylene diaminetetraacetate dinydrate), wnicn tney used to solubulize precipitated iron salts, will not remove tne bacteria from the mineral particles. Another problem encountered oy tne 12 autnors was tnat tne ba'cxground pulse neignt on tne Coulter Counter is almost tne same as tne pulse neignt encountered for small cel ls , such as tnose of T. ferrooxidans. Tne cost of tne Coulter Counter is so nigh ano its uti l i ty so l i t t le tnat tne cost-benefit of this method is low. Apel e_t _a]_ (1976) used an indirect fluorescent antibody (FA) staining technique for tne detection of T. ferrooxidans. Anti-T. ferrooxidans immunoglobulin was prepared in rabbits. The FA stain did not react witn J_. tniooxidans. The autnors 4 noted tnat tne cell density would have to oe greater tnan 10 cells per gram to observe one cell per microscopic f ie ld . To overcome tnis problem, samples were washed with pH 3 water, centrifuged and tne wasnea refuse was ground, sonicated, wasneo and tnen concentrated oy centrifugation. Altnougn, tne FA stain metnod nas the limitations of auto fluorescence and non-specific fluorescence (wnen applied directly to tne sample), it is applicable to tne study of cnemoautotropnic bacteria ana mineral particles. Holm-Hansen (1973) determined tne total microoial mass, by measurement of ATP, in aquatic, terrestrial, activated sludge, ano sediment samples. Tne metncd is cased on tne fact that, in vitro, lignt production oy f iref ly lantern extracts is dependent on luciferin, tne enzyme luciferase, oxygen, magnesium 13 and ATP. For eacn molecule of ATP nydrolyzed, one pnoton of lignt is emitted. To obtain tne amount of ATP present, tne amount of light per unit time is measured. Comparison witn a standard sample permits tne absolute values to oe calculated. ATP photometers whicn integrate tne lignt emitted over a certain period of time ano give a direct read-out are available. Brierly (1978) reported tnat tne ATP photometer metnod is Deing developed for enumeration of tne cnemolitnotropnic bacteria. Gormely and Duncan (1974) presented a metnod for estimating bacterial nitrogen as tne difference oetween tne total nitrogen determined oy Kjeldahl digestion and inorganic nitrogen (distillaole nitrogen) as determined oy steam dist i l l ing tne sample witn caustic. The autnors correlated tne non-distiliable nitrogen witn organic caroon (measured using an organic carbon analyzer) ano cell number estimated using a Petroff-Hausser counting chamber. The value reported for non-disti1Iable nitrogen content (0.157 x 10-"^ mg per cell) agrees with tnat reported oy Silverman ano Lundgren (195y). Tne cellular carbon value of 0.767 x 10"^ mg per cell corresponds to tne value ootaineo by Tuovinen and Kelly (1972, 1973). Based on tnis study tne autnors reported tnat 65 percent of tne population of T. ferrooxidans was attacnea to tne mineral wnen zinc sulphide concentrate was leached. Brierly (1978) listed tne disadvantages of this metnoo as (1) it measures all tne 14 organisms present (2) it is indirect and does not give a cell count and (3) it measures nitrogen containing organic Dy-products of microbial growtn. 2.3.2 Attacnment As mentioned earlier (Section 2.3) many early investigators noted tne need for direct contact between tne bacteria and tne mineral. In recent years researcners nave looked at tne minerals directly and studied tne attacnment of tne organisms to tne surface of tne mineral (Meadows, 1971; Weiss, 1973; Brierly ano Murr, 1973; Baldensperger et_ aj_, 1974; Berry and Murr, 1975; Brierly et aj_, 1975; Murr and Berry, 1976(A); Murr and Berry, 1976(B)). A significant feature of oacterial/mineral interaction involves tne mode and character of oacterial attacnment. Weiss (1973), Dugiud (1959) ana Hirscn ana PanKratz (1970) descriDed tne attacnment as occurring tnrougn a variety of holdfasts, including adhesive p i l i . Meadows (1971) ano Torma et aj_ (1970) suggested that tne attachment was due to surface adnesion. Duncan and Drummond (1973) proposed tnat cnemical and biological attack took place along mineral fractures and crystallograpnic planes. Silverman and Ehrlicn (1964) reported 15 tnat tne. crystal structure of a given mineral is an important factor in influencing tne oxidation of tnese minerals. Berry and Murr (1978) observed tne attachment of T. ferrooxidans, T. tniooxidans ana Sulfolobus-Iike microorganisms on low-graae copper ore ana drew tne following conclusions: (a) Tne attachment of Sulfoloous-1ike micro-organisms was more frequent than tne attachment of TnioDacilli. Tney attributed it as oeing due to tne difference in cell wall rigidity and tne absence of a f l age Hum on tne Sulfoloous—1iKe organisms. (o) Although attachment of bacteria was noticed at sites of dislocation, tne autnors felt tnat there was no proof tnat tne organisms preferred sucn locations. (c) The attachment of bacteria was specific to sulpnide pnase regions on a polisned waste rocx surface because tnese are regions offering an energy source. The authors also noted tnat there was no question tnat bacteria are attacned to mineral surfaces and tnat tney are attacned to specific areas in a waste rocK (from a copper mine) wnicn can function as an energy source, namely sulpnide pnases. However, tney go on to say, attachment does not always occur, and bacterial catalysis could oe very significant without direct attachment. 16 2.4 Bacterial Leacning Microbiological leacning of metal suipnides can De said to oe a dissolution process of tne metal eitner due to tne direct or indirect action of tne microorganisms. In one sense it is a biochemical oxidation process in wnicn tne bacteria acts as a catalyst and can be represented in a simplified form as follows: micro-MS + 202 • * MSO4. organism Tne sulfate is the end product of a complex biological reaction in wnicn tne bacteria acts upon the mineral sulphide, wnich serves as an energy source in tne presence of otner nutrients (see Section 2.5.1). 2.4.1 Direct Mecnanism Some microorganisms attacx certain mineral suipnides directly and oxidize tne sulphides. Berry and Murr (1978); Bennet and Tributscn (1978) and Tributscn (1976) nave snown oy scanning electron micrographs tnat a number of bacteria are capable of attacning themselves to the surface of tne sulpnioe minerals. Lundgren and Tano (1978) have presented a model to explain iron and sulphide oxidation. According to tnis model, tne cell envelope somehow establishes a micro-environment wnicn 17 is favorable to tne functioning of the enzymes required for tne oxidation. Tne enzymes are protected from tne mgnly acidic medium by T. ferrooxidans. Silverman (1967) postulated that tne oacteria nave two roles in the leacning of minerals. One role involves tne ferric-ferrous cycle (see Section 2.4.2) and tne other involves direct physical contact of tne organisms witn tne insoluoie sulpnide mineral. Mizogucni _et a_l_ (1976) nave snown that insoluble mineral sulphides can be oxidized by microorganisms in tne absence of ferric iron. However, Landesman e_t aj_ (1966 A and 6), Duncan et_ al_ (1967A) and BecK and Brown (1968) were ail of tne opinion that ootn oxidative processes contribute to metal leacning, if iron is present in tne lattice. Tnougn present knowledge of tne direct attack oy bacteria on mineral sulphides is incomplete, it is known tnat (a) microoial involvement is influenced Dy tne cnemical nature of ootn tne aqueous and solid crystal pnases (Berry and Murr, 1978). (b) bacteria appear to attach to tne sulpnide moiety of mineral rock surfaces, whicn are tne regions tnat contain tne energy supply for tne bacteria (Berry and Murr, 1978). (c) attacnment results in pitting of tne mineral surface. (d) tne extent of tne surface corrosion varies from crystal to crystal and is dependent on tne orientation of tne mineral (Tributscn (1976), Bennet ano Triouxscn (1978) ana Berry and Murr (1978)). 2.4.2 Indirect Mecnanism Silverman and Enr'Mcn (1964) nave suggested tnat several agents, sucn as oxygen, ferric-suIfate ano iron-oxidizing tniooaci l l i , can participate in tne oxidation of metal sulphide minerals. Dutrizac and MacDonald (1974) pointed out that ferric iron, eitner alone or in combination is tne most important chemical species involved in tne indirect attacks on sulpnide minerals. Tne role of ferric sulfate in mineral sulphide oxidation may be explained by one or botn of tne following reactions. MS + 8Fe 3 + + 4Ho0 > M 2 + + Sof + 8H" + 8 F e 2 + (2.2) MS+2Fe 3 + > M 2 + + 2Fe 2 + + S° (2'3> In the presence of iron-oxidizing bacteria, tne ferrous iron produced by tnis reaction would oe oxidized to ferric iron: 19 4FeS04+ 2H2S04+ 0 2 P a C t e r i d > 2Fe 2(S0 4) 3 + 2H20. ^ Thus a cyclic process is established. Tne overall reaction may be expressed by tne equation MS + 20 2—>M 2 + S04 (2.5) Tne rate of oxidation of metal suipnides oy ferric iron, in the absence of bacteria, at low pH values is low. Tuovinen and Kelly (1973) reported tnat tne oxidation in tne 5 6 presence of bacteria is about 10 - 10 times tnat ot tne oxidation in tne absence of bacteria. Ra'lpn (1979) stated tnat tnere is overwhelming evidence suggesting a unique role for ferric iron as an agent in indirect mecnanisms of oxidative attacK on tne minerals. He is also of the opinion tnat complex cuprous ions may play a similar role witn copper containing minerals. 2.4.3 Mecnanism of Oxidation of Elemental Sulfur ana Sulfur Compounds Tne classification as a member of tne genus Tniobaci11 us implies tnat tne organism is capable of using tne energy of oxidation of inorganic compounds of sulfur for its metabolism. LiK.e tne biochemistry of iron oxidation, the 20 biocnemistry and pnysiology of tne oxidation of compounds of sulpnur, particularly the oxidation of inorganic suipnides, nave been extensively investigated. Several reviews have appeared in tne literature (Visnniac and Santer, 1957; Pec*, 1962, 1968; Trudinger, 1967, 1969; Kelly, 1968, 1971; Trudinger, 1971; SuzuKi, 1974; Aleem, 1975 and Silver, 1978). Most of tne researcn on tne oiocnemistry of sulfur oxidation nas oeen carried out witn elemental sulfur ana witn soluble substrates sucn as nydrogen sulpnide, soluble suipnides, polysulphides, sulf i te, tniosulfate and polytnionate. Altnougn tnere are gaps in regard to tne exact mecnanisms in respect of certain reactions, tne specific intermediates and tne overall pattern, including tne enzymes involved are fairly well documented. Tne scheme shown in Figure 2.1 accounts for most of tne experimental information available. Tne oxygenation of elemental sulfur with tne formation of sulfite is catalyzed by a sulfur-oxidizing enzyme. Tniosulfate can either oe split with tne formation of sulfite and sulpnide or it may be oxidized to tetratnionate, wnicn in turn can yield sulfite ana tniosulfate. Sulfite can oe oxioizeo to sulfate eitner by a cytocnrome-c-mediated oxidation or via adenosine pnospnosulfate (APS). Rnodanese, tniosulfate oxidizing enzymes, tniosulfate reductase and APS reductase nave all oeen identified in reactions involving tniooacil1 i . FIGURE 2.1 GENERALISED SCHEME FOR THE OXIDATION OF ELEMENTAL SULFUR AND REDUCED COMPOUNDS BY THIOBACILLI ( SILVER, 1978) 22 2.4.4 Mecnanism of Oxidation of Ferrous Iron Tne reduced form of iron, wnicn is stable in acidic solutions is an energy source for J_. ferrooxidans. Pnysiological ly, tne following series of events occur: ferrous iron is oxidized to ferric iron, with tne release of electrons (Landesman e_t aj_, 1965; BrocK and Durland, 1970). 2Fe 2 + >2Fe 3 + + 2e~ (2.6) Tne reducing potential of the electrons is available for the reduction of molecular oxygen. 1/2 0o + 2e + 2H+-> H90. (2.7) Tne electron transfer yields enough energy for tne formation of ATP (oxidative pnospnorylation). A DP + P. .—> ATP (2.8) Tne process of electron transfer involves a numoer of 2+ Fe -dependent cytocnrorne reductions. It nas been proposed tnat tne oxidation involves transfer of electrons from iron to cytocnrorne c, cytochrome a, and oxygen in tnat sequence (BlaylocK and Nason, 1963; Vernon et_ aj_, 1966; and Yates and Nason, 1966) (See Figure 2.2). OXIDIZED CYTOCHROME c REDUCED CYTOCHROME c REDUCED CYTOCHROME a OXIDIZED CYTOCHROME a 2 0 2 + H 2 H 2 0 FIGURE 2 , 2 SCHEME FOR IRON OXIDATION ro 24 2.4.5 Fixation of Caroon Dioxide The iron oxidizing tniobacilli use tne reauctive pentose phosphate (Calvin-Benson) cycle and tne carooxy1 at ion of pnospno-enol-pyruvate for the assimilation of carbon dioxide (Maciag and Lundgren, 1964; Din et_ al_, 1967). Tne energy requirements are served oy tne oxidation of ferrous iron. However, tne oxidation of elemental sulfur, reduced inorganic sulfur compounds, and metal sulpnide minerals could also support C02 fixation (Margalitn et_ al_, 1966; Silver, 1970; Silver ano Torma, 1974). Eacn molecule of CO,, fixed oy tne Calvin cycle needs three molecules of ATP and two molecules of reduced pyridine nucleotide. Tne requirement of ATP is met oy tne oxiaation of tne growtn substrates and tne pyridine nucleotides are reduced by tne reversal of tne electron transport chain (Aleem et_ a l . , 1963; Aleem 1977). NAD+ + 2e~ + 2H+ + 2ATP—> NADH ++H + 2ADP + 2P j (2.9) NADH + H+ + NADP+—^ NAD + NADPH + H (2.10) 25 2.4.6 Toxicity of Metals and UV-Sensitivity TnioDacillus ferrooxidans nas a nign tolerance to metals compared to most otner microorganisms. Tne actual metal concentrations tnat would oe tolerated Dy tne organism are variable and are dependent on the particular strain and adaptation of tne bacteria. Sadler and Trudinger (1967) and Tuovinen and Kelly (1972) nave reviewed tne toxicity of metals. High concentrations of various cations nave oeen reported, e.g. , 40 g/1 of copper (Duncan et_ al_, 1967), 12 g/1 of uranium (Duncan and Bruynesteyn, 1971) 120 g/1 of Zinc (Torma et _a]_, 1972), ano 10 g/1 of arsenic (Pincnes, 1975). However, soluble uranium and thallium are moderately toxic to T. ferrooxidans (Tuovinen ano Kelly, 1974A, 1974B). Addition of 10 - 7 M AgNO^  (0.01 ppm Ag) to T\_ ferrooxidans in ferrous iron medium resulted in no growth occurring (Norris and Kelly, 1978). Hoffman ano Hendrix (1976) nave reported that death to tne entire culture occurred wnen tne soluole silver level reacned 5 ppm. 4 Mercuric ion at a concentration of 5 x 10 mM was reported to inhibit tne activity of T. ferrooxidans; out attempts to steril ize a column containing pyrite witn a single oose of 0.5 mM of Hg was only partially successful (Brierly, 1973). 26 Cnakraoartny (1978) nas reviewed some of tne genetic an.d biochemical bases for tne development of bacterial resistance and intracellular accumulation of metal ions. He suggests tnat genetic engineering of T. ferrooxidans oy tne introduction of plasmids specifically resistant to metal ions sucn as silver, cadmium, mercury etc. (assuming tney exist), and to UV- radiation, would De beneficial. Sucn mutants could be used for scavenging tne environment and also witn minerals wnicn nave toxic metals as a component. 2.5 Factors Affecting Metabolism ana Leacning of T. ferrooxidans All microbial cells contain caroon, nyorogen, nitrogen, oxygen, pnospnorous and sulfur (Luria, 1960). Otner elements sucn as potassium, calcium, magnesium, iron and trace quantities of manganese, cobalt, copper, rnolybaenum and zinc are found in tne ce l l . Tneir content varies widely reflecting tne nature of the medium and growth conaitions. Lixe all other l i fe processes leacning of ore by microorganisms is aependent on tne environment in wnicn tne organisms are growing. 27 2.5.1 Nutrients Ammonium-nitrogen, pnospnorus, sulfate, and magnesium are essential for growtn of ferrooxidans. A minimum of 2+ 2 mg Mg / i , is required for CO^  fixation (Tuovinen et _a_l_, 1971). Pnospnorus in the form of pnosphate is not only necessary for energy rnetaoolism out also for tne f i rst steps of ferrous iron oxidation outside tne cell wall (Dugan and Lundgren, 1965). Sulfur is required for tne syntnesis of proteins since it is a component of sulfur containing amino acids (e.g., cysteine). Lazaroff (1963) elaborated upon tne need for sulfate ions by T. ferrooxidans for iron oxidation. He postulated tnat sulfate controls tne entrance of ferrous iron into tne cell or tnat perhaps it is required in energy transfer for tne iron oxidase system. Steiner and Lazaroff (1974) demonstrated tne need for sulfate in ferrous iron oxidation. Tney observed tnat iron oxidation was innioited at sulfate concentrations above 0.22M (12g/l). Nitrogen appeared to be tne most important nutrient for tne thiobacil l i . Nitrogen is required for tne syntnesis of proteins and nucleic acids. Tne nitrogen-fixing abilities of certain T\_ ferrooxidans strains were suggested oy tne experiments of Mackintosh (1971) and unequivocally demonstrated recently by the same author (Mackintosh, 1976) 28 A number of workers nave suggested different media for tne growtn of ferrooxidans (Leatnen et _aj_, 1953; Bryner and Anderson, 1957 and Silverman and Lundgren, 1959). But tne most commonly used medium, popularly referred to as tne 9K medium, is that of Silverman and Lundgren (1959). Tne 9K medium, and for that matter all media used in tne laboratory, contain an excess concentration of tne required nutritional salts, including ammonia (as NH )^, sulfate, potassium, phosphate, magnesium and calcium. Otner trace element requirements are usually met by tne impurities present in tne minerals. Tne energy source is ferrous iron, sulfur or reduced sulfur compounds and tne caroon source is caroon dioxide present in tne air. . Tne concentration of in tne air used for aeration affects tne leacning rate (BecK and Snafia, 1964; Bruynesteyn e_t a_l_, 1971). Torma et a_l_ (1972) found that carbon dioxide enricned air up to a concentration of 0.23 percent gives tne optimum effect on zinc extraction. Torma et_ aj_ (1970) and Tuovinen et_ al_ (1971) nave + 2-snown tnat tne concentration of NH^  ions and PO^  ions affect the rate and yield of zinc extraction. 29 T. ferrooxidans are aerooic and limitation of oxygen affects tne rate of oxidation of iron (Guay et a l , 1975) ana extraction of metal (Guay et_ a_l_, 1977). According to Liu (1973), maintenance of an oxygen tension nigner tnan 6.5 mm Hg (or 0.29 mg oxygen per l itre at 35°C) is necessary to ensure tnat oxygen tension will not oe a rate-limiting factor in tne growth of ferrooxidans. 2.5.2 Temperature Temperature can exert an influence upon biological systems in three ways - f i rs t , by influencing tne rates of enzymatically catalyzed reactions; second oy affecting tne rate of diffusion of substrate to the ce l l ; third oy affecting tne rate of denaturation of enzyme as a protein. Growth of various bacteria has been observed between -18°C and 105°C (Valentyne, 1967). Tnis range of temperature is divided into tnree sectors. Organisms wnicn grow well, witnin the range 10-35°C, are called mesopnilic. Tne otner two groups are called psychrophi1ic and thermophilic. Optimal leacning -of metal sulphide ores oy tniooacilli nas been determined to occur between 25° and 45°C (Marcnlenwitz and Schwartz; 1961; CorricK and Sutton, 1965). Torma (1970) studied tne effect of temperature over tne range of 25° to 45°C on zinc sulpnide leaching oy T. ferrooxidans. 30 Tne maximum zinc extraction was ooserved to oe at around 35°C. Tne temperature coefficient (Q^Q) a n a t n e energy of activation (Ea) were determined to oe around 2 and 12.8 K cal/mole respectively. Guay et_ al_, (1975) ano Sakagucni et_ al_, (1975) found Q 1 Q to De around 2 and Ea to oe oetween 11.7 ana 16.3 K cal/mole for ferrous sulfate and copper sulpnide. Tne energies of inactivation for tnese substrates were found to De oetween 53.3 and 61.5 K cal/mole oy tne same researcners. 2.5.3 pH Silverman and Lundgren (1967) found tnat T. ferrooxidans was active in the pH range of 1.5-5.0. With adaptation tne bacteria will tolerate values aown to a pH of 1, out values below tnis may be detrimental to tne cells (Duncan et a l , 1966). Optimum pH for oxidation of cnalcopyrite (Razeli and Trussell, 1963), zinc sulphide (Torma, 1970), ferrous iron (Guay et a_l_, 1975) cooalt sulpnide (Torma, 1975) chalcolite and covellite (Sakagucni et_ aj_, 1976), galena (Tomizuka and Yagisawa, 1978) and pyrite (Atkins, 1978) was observed to be between 1.0 ano 2.5. 31 2.5.4 Oxidation-Reduction Potential (Eh) Tne oxidation-reduction potential is a measure of tne tendency of a substance to accept or donate electrons. En gives a measure of tne oxidizing ability of tne system. Low En values are indicative of low oxidising ability and nign En values of nign oxidising abil ity. Tne indirect mechanism (see Section 2.4.2) of bacterial leacning, with ferric ions, is dependent upon tne En. The well-Known En-pH diagrams, made popular by tne wor« of Pourbaix (1966), enable one to see at a glance tne range of stability of aqueous and solid pnases under specific conditions of Eh and pH. Moss and Anderson (1968) nave made use of tne EH-pH diagrams in tneir discussion of bacterial leaching. Figure 2.3 is a reproduction of the diagram, as drawn by Moss and Anderson. Tne environmental limits for bacterial growtn (Bass Becking et_ al_, 1960) are superimposed on tne En-pH diagram for iron systems. Diagrams constructed using En and pH as parameters are phase diagrams of tne free energies of tne constituent species. An area containing one species nas two degrees of freedom. A line represents an equilibrium between two species and nas only one degree of freedom. A point wnere three lines meet is an invariant point, and represents an equilibrium between tnree species. 32 F I G U R E 2 . 3 EH - PH D I A G R A M OF F E - S - H 9 0 S Y S T E M pH X- Limits for growth of thiobacilli Y - Limits imposed on the natural environment by the inorganic chemistry of normal soil constituents 3 3 According to the convention of tne International Union of Pure and Applied Cnemists, potential is normally expressed as a reduction potential. Consider tne equation aA + oB + mH+ + ne—>cC + dD. ( 2 . 1 1 ) wnere A, B, C and D are ionic or molecular solutes, gases or solids required to express tne reaction taking place at a single electrode. The equation giving tne standard free energy cnange is c d A G ° = -RT In a C dD - n FE. ( 2 . 1 2 ) a b m aA aB V Wnere AG ° is tne standard Gioos free energy cnange, R is tne gas constant, T is the temperature ("absolute) and E is tne single electrode potential. If RT is expressed in calories/g mole, tne value of tne Faraday, F must oe taken as 2 3 , 0 6 0 cals/volt. Tne term a with a suoscript refers to tne activity of component denoted oy tne subscript relative to its standard state. If all substances except hydrogen ions are in tneir standard states, equation ( 2 . 1 1 ) on rearranging gives E = E°- 2 - 3 . Rl . (m / n) . p H F ( 2 . 1 3 ) 34 There are a number of papers in tne literature wnicn give a ful l description of the metnod for tne calculations required for tne construction of the Eh-pH diagrams (Garrels, 1960; Garrels and Christ, 1965; Brook, 1971; Peters, 1976; Froming et _al_, 1976, Duby, 1976; Vernulst and Daby 1977 and Osseo-asare and Brown, 1979). An En-pH diagram for the Zn-S-h^O system is given in Figure 2.4. Although tne En-pH diagrams are very useful tools in the understanding of leacning tnere are a numoer of limitations wnich must oe borne in mind wnen using these diagrams. Tne diagrams do not give rates and nence tne transformations indicated by tne diagram may take seconds, days or geologic time periods. Secondly, as all sulpnide minerals are impure, it snould always be borne in mind tnat tne diagrams are constructed using thermodynamic data for pure compounds and ionic species. For example, tne actual oenaviour of spnalerite in an aqueous system might be quite different from tnat predicted from Figure 2.4 for tne reason tnat a significant amount of iron substitution is prevalent in tne crystal lattice of spnalerite. Moreover, tne En-pH diagrams, sometimes include metastaole products. 2.5.5 Particle Size and Surface Area Torma (1970) examined tne effect of particle surface area on oioleacning of zinc sulphide concentrate. Torma and F I G U R E 2 . 4 EH - PH D I A G R A M OF ZN - S - H S Y S I E M X - Limits for growth of thiobacilli Y - Limits imposed on the natural environment by the inorganic chemistry of normal soil constituents 36 Legault (1973) extended tne work on the effect of total surface area on tne bioleacning of other sulpnide minerals. Gormely et al , (1975) reported that tne rate of leacning of zinc sulphide concentrate is first-order witn respect to surface area. Torma and Guay (1976) studied tne biodegradation of sphalerite concentrate, applied the Monod equation and obtained tne maximum rate of zinc extraction to oe 9 mM/n. using tne smallest size fraction of about 2.2 micrometers. The nignest experimental value observed was 8 mM/n. Pincnes et aj_, (1976) also concluded tnat tne most important factor, on wnicn leacning of copper concentrate depended, was tne size of the particle. In tneir work tney observed that tne copper extraction was proportional to the specific surface area for particles larger tnan 7 um in size. They calculated a leacn "depth" on tne assumption tnat tne volume of the mineral leacned can oe taken as tne product of a leacn depth and the init ial surface area. Tney notea tnat the calculated, apparent leacn depths were constant for particles larger than 7 yin and that tne leacn deptn is snal lower for particles smaller than 7 yin. Bruynesteyn and Duncan (1974) proposed an "active leacning volume" wnicn is tne surface area multiplied oy tne depth of penetration by bacteria and lixiviant. Tney disagree with tne 37 snrinKing core model, oecause it has oeen snown oy electron micrograpn studies that minerals near tne surface are not always leacned before minerals deeper into the particles nave oeen oxidized (Duncan and Drummona 1973). The effect of specific surface area concentration on bacterial leacning nas been demonstrated by a numoer of researcners (Torma, 1970; Torma et_ a]_, 1973; Pinches, 1975 ; Gormely et a l , 1975; Torma ano Guay, 1976; Pinches et a l , 1976). 38 3. THEORY 3.1 Bacterial Kinetics and Modelling A study of microbial fermentation processes involves periodic sampling and measurement of oacterial growtn, suostrate utilization and product formation. Kinetic studies aid in tne interpretation of tne observations and in tne deduction of tne effects tnat various factors nave on fermentation and are a necessary prerequisite for tne design of a scaled up reactor. A model represents part of a reality. Only those aspects wnicn are of interest to tne modeller are considered. Moreover, manipulation of the model gives insignt to tne real system. For almost any biological process, modelling of tne intricate details of tne complete system is a hopelessly complex task. In fermentation a number of processes take place and their interaction determines the outcome. Tnese processes, 39 wnicn are tne main features of models in biochemical engineering can be classified as: transfer processes (or transport processes) transformation processes (or conversion processes) 3.1.1 Transfer Processes Transfer processes are dependent on tne system cnosen and its boundaries. Transfer processes describe tne transfer of matter or energy oetween tne system and tne environment or a boundary. Transfer processes are described by simple equations containing concentration, concentration difference or concentration gradient terms. One distinguishing feature of tne transport process is tnat the molecular structure remains unchanged. 3.1.2 Transformation Processes As a result of tne -metabolism of tne organisms, tne substrate is converted into metabolites, cellular mass, neat and 'products.' All tnese processes wnicn take place in tne system, are the transformation processes. Equations describing tne rates of these transformation processes are called kinetic equations. 40 In practice biochemical engineering problems are described by models involving ootn transfer and transformation processes. 3.1.3 BioKinetic Modelling An all inclusive oiokinetic modelling is diff icult in view of tne many metabolic patnways available and tne different side reactions that take place during tne life cycle of tne bacterial ce l l . Many of the reaction mecnanisms in tne metabolism of tne cell are not fully understood and factors affecting growth are numerous. Tuscniya et_ al_ (1966) nave expressed an opinion that present knowledge of tne oiology of cells and tne matnematical tools necessary for tne formulation and study of a completely general oiokinetic growtn model oo not exist. 3.2 Kinetics Two kinds of kinetic observations can be made in fermentation processes. These are obtained from dynamic or batch culture systems ano steady state or continuous systems. 3.2.1 Batch Culture Micnaelis ana Menten (1913) proposed a simple K ine t ic model for enzyme-suostrate interaction. In tnis model, tne enzyme, E, combines reversibly witn tne substrate, S, to form a complex, ES, wnich irreversibly decomposes to form product, P, and free enzyme, E, i .e. Kl k S > ES E + P. (3.1) t " l = rate constant of tne forward reaction = rate constant of tne oacKward reaction , k„ = reaction rate constant, and 2 Based on tnis nypotnesis tne Michaelis-Menten Equation was derived. It is usually expressed as E + wnere k l K - l V [S] = m L J (3.2) 42 where V = rate of reaction V = maximum rate of reaction m [SJ = concentration of substrate and K = Michaelis-Menten constant, An equation similar to equation (3.2) was proposed empirically by Monod (1949) for microbial growtn: LS] (3.3) Ks + LSJ where, p = specific growtn rate ymax = m a x " ' m u m specific growth rate [S] = concentration of substrate and = the saturation constant, Lineweaver and BurK (1934) proposed writing tne iMichael is-Menten equation as: Vm LSJ Vm (3.4; Tnus a plot of 1/V versus 1/[S] gives a straight line witn slope K [ n/Vm and an intercept on tne Y-axis of 1/V(n. Various modifications (Laidler and Socquet, 1950; Segal et al_, 1952; Spicer, 1955; Moser, 1958; Fujimoto, 1963) for Monod's equation nave oeen proposed. However, tney are not as popular as tne Monod equation. Equation (3.3) is applicable under conditions of one limiting nutrient. When tne substrate is available in non-limiting quantities, Silverman and Lundgren (1959) snowed that the growth of ferrooxidans is logaritnmic, nence tne rate of growtn can oe defined as dX = UX dt (3.5) wnere, X = tne number of cells per l i t re , n = specific growtn rate, and t = time. The rate of product formation was found by Silverman and Lundgren (1959) to be proportional to tne growtn rate of tne cel ls: wnere, ano dP 1 aX dt Y x / p dt (3.6) S = the concentration of substrate P = tne concentration of product Y v / D = yield coefficient. X/ r Integration of equations 3.5 and 3.6 gives In X = In XQ + yt (3.7) l n ^ p + ^ o ^ = l n ^ ^ o ^ + y t (3.8) Y Y TX/P X/P 3.2.2 Continuous Culture Consider a series of n equivolume vessels, eacn of capacity V l i tres, as snown in Figure 3.1. If tne flow rate is F 1/n., and it is assumed tnat tnere is no cnange in aensity due to substrate consumption or product formation, tne mass balance equations for concentrations of cell mass, X, product, P, and tne limiting substrate, S, can oe expressed as follows: For Cel1 Mass V. = F. Xn , - F. X + V , , (3.9) dt 1 1 dt 'growtn in ntn vesse1 - F - Xn-1 " F ' X n + V - n^ ' Xn Dividing by V, dX n = D (Xn_x - Xn) + pnXn (3.11) wnere, dt D = F = dilution rate, h ^ =1 = 1 = reciprocal of mean holding (retention) (V/F) 7 time of flowing medium in eacn vessel. and y = 1 . d X n = specific growth rate of cells in tne n t n  n "x dt vessel. Subscripts n and (n-1) refer to tne n t n and (n - l ) t n vessels respectively. x 0 ( = o) p 0 ( = o) s 0 t • — J — • CM—n F - Flow Rate of Medium X - Cell Mass Conors. P - Product Concn. S-Substrate Concn. Subscripts l,2....n denote the vessel number Xn - 1 Pn - 1 Sn - 1 Xn Pn Sn D - J — • FIGURE 3.1 N VESSELS IN SERIES Similarly, for proauct: wnere, ! ! l L = M P n _ l " p n ) + ( ^  ) (3- 1 2) dt V v ot 'product formation in tne tn , n vessel . - 0 ( V i " P n) + YP/X ' ^n • X n < 3 - 1 3 ) Y D / Y = A P = yield of product based on cell mass, and for suostrate: where, _^J1= £ (Sn i - Sn) + , (3.14) dt V v dt 'consumption in tne tn , n vessel D. ( S n _ x - S n ) - l _ - ^ n • Xn ( 3- 1 5) X/S D- ( S n _ l " S n ) - V£ • " n • X n (3.16) YP/S Yj,,r = - _AX =" yield of cell growth based on ' "AS limiting suostrate. Y p / c = - AP = ( AP ) . ( - A X ) N 1 7 , ?lb IS ( A X ) ( Isj (3-17) = Y P / X . Y X / S The above derivation is subject to tne following assumptions: 48 1. Each tank is wel 1 mixed, i.e. composition is uniform everywhere. In effect it means tnat tne entering feed is instantaneously mixed witn tne contents of tne tank and tnat the composition of tne material leaving tne tank has tne same composition as that of the tank as a whole. 2. Values of Y ^ , Yp/X> Yp^ are assumed to oe constant irrespective of tne number of tanks. At steady state, ^ n = ^ n = ^ n = 0 (3.18) dt dt dt combining equations (3.11) and (3.18) we have Xn - D ' Xn-1 (3.19) n (n * 1) (3.20) 49 Hence, 2 X = D , X n - l = D , X n-2  ° 3 • Xn-3 (D-un) (D - un_x) (D - u n _ 2 = D n _ 1 - Xx . (3.21) rv TT (D - u.) j=2 J For a single vessel Xn ^ = 0 ana therefore equation (3.11) at steady state gives, M l = D (3.22) Tne steady state equation for P is given by: P n = D ' Pn-1 + YP/x • yn • Xn (3.23) D P =0 for tne f i rst reactor, o therefore, P l = YP/x ' y l * X l ( 3 ' 2 4 ) Y p / X . X1 (3.25) (since D = ) 50 Finally, tne steady state S is given oy: \ = S n-1 " I . Wx . u. . X D YP/S = V l - I ' i ' n^ • Xn < 3 ' 2 6 )  D YX/S For n = 1 S l - S 0 - 1 . X i (3.27) YX/S From equation (3.9), assuming XQ = 0 at steaay state, dt ^ dt 'growtn V from wnicn X, = , d X l x . 1 (3.28) 1 1 dt jgrowtn F7"V Similarly, dX9 n dX, 1 (3.29) L = u = / i _ \ • ot * dt ;G F/V X = X„ , - dX„ . 1 n n-1 , n_ , 1 dt jG F/V (3.30) 51 3.3 Kinetics of Leacning Gonnely ( 1973) derived a model, oased on a growtn mode 1 for cultures witn two liquid pnases proposed oy EricKSon et_ aj_ (1970), for oiologicai leacning of concentrates in a single CSTR. In tne present work it is proposed to extend 'ms moael to 2 CSTRs in series, witn and witnout recycle to tne f irst one. 3.3.1 Derivation of Gonnely1s Model In Section 2.3.2 tne consensus of opinion existing amongst various workers on bacterial attacnment' for leacning was looked into in detail. Attacnment to tne mineral is considered an essential requirement for leacning of tne zinc from a zinc sulpnide mineral. It snail oe assumed tnat tne oniy limitation on tne oacterium's growtn is its access to sulpnide by attacnment to tne mineral. In tnese circumstances tne oacteria tnat are attacned to tne mineral should nave a constant growtn rate, wnicn is tne maximum possiole. It would also follow tnat tne bacteria tnat are not attached to tne mineral oo not grow. In tms assumption tne possibility tnat tne oacteria coulu ingest tne substrate, leave tne mineral and grow on tne ingested suostrate wnile it is swimming freely in tne liquid, is i gnored. Since we are considering steady states, it is reasonable to assume that tne surface area concentration, s, remains a constant. 52 Let i t oe assumed tnat tnere is a dynamic equi l ibr ium oetween tne bacter ia attacned to pa r t i c l e surfaces and tnose suspended f ree ly in tne so lu t i on . It is also assumed tnat tne rate of attachment of c e l l s to tne mineral is proport ional to tne product of c e l l concentration in tne l i qu id phase and tne surface area of tne mineral that is free of attachment oy bac te r ia , and tnat tne rate of detachment is proport ional to tne number of c e l l s on tne minera l . Assuming, f i r s t order K i n e t i c s we have, (S - of) (X - a) = K_ 1 a (3.31) wnere, f = tne surface area occupiea per unit of bac ter ia l concentration X = tne bac ter ia l concentration a = concentration of bacter ia attacned to tne surface of tne mineral K. ana •< , = rate constants 53 Expanding equation (3.31) gives, o 2 f - o ( s + Xf + K - l ) + Xs = 0 (3.32) K l a = (s + Xf + K) ± V ( S + Xf + K) 2 - 4fXs (3.33) 2T wnen s = o, a = o, tnerefore only tne negative radical is t a K e n . If growtn rate is assumed to oe proportional to tne nurnoer of attacned oactena, tne growtn rate, (r ) is: X r = va = v [ (s + Xf + K) - V ( s + Xf + K ) 2 - 4fXs j 2f (3.34) wnere, v is tne maximum specific growtn rate of tne oacteria wnicn are attacned and x K 1 ^ ~ — ' (3.34A) K l 3.3.2 Application of tne Model to a Single TanK in Section 3.2.2 tne equation for a single tanx was derived. Recal I equation (3.22) V xi = - D (3.22) Combining equations (3.22) ana (3.34) g ives , D - j , ( S l + X l f + K) - y ( S l + X-^ f + K) . 4 f X ] L s ( 3 > 3 5 ) Xj_ 2T~^ wnicn gives X, = K + v . sn- (3.36) 1 t'L(D/v) - 1] Df 1 In equation (3.36) K, v ana f are constants ana Xp D and s are va r iab les . Wnen one chooses two var iables tne th i rd would oe f i x e d . In p rac t i ce , one would Keep tne d i l u t i on rate constant and vary tne concentration of sur face, wnicn is eas i l y done by e i tner increasing tne pulp density or oy gr inaing tne concentrate for varying times to produce various levels of s p e c i f i c sur face. Tnen X could oe determined. Examination of equation 3.36 reveals tnat a plot of X^ against s , at constant D, would give a s t ra ignt l i ne witn slope v and intercept K . If several plots are maae for Df fL (D /v ) - I J d i f fe ren t d i l u t i on rates D and tne slopes ano intercepts were to oe reckoned, tnen one could plot tne rec iproca l of tne s lope, (Df /v ) , against tne d i l u t i on ra te , D, and ootain a s t ra ignt l ine througn tne o r ig in whose slope would oe ( f / v ) . ana Tne intercept = K X (3.37) f L(D/v) - IJ 55 therefore 1 = f . D - f . (3.33) Intercept Kv "R" Hence a plot of tne reciprocal of tne intercept against tne dilution rate D, snoulo give a straignt line witn slope (f/Kv) and (-f/K) as tne intercept. Tnus we nave f/v, fv and f/K. Hence tne constants f, K and v could oe calculated. 3.3.3 Application of Gormely's Model to Two TanKS in Series For two tanks in series tne equations for tne f irst tank are tne same as tnose developed in tne preceding section. RecalI equation (3.11) d x n • ( V l - V +*n xn ( 3 ' U ) Substituting n = 2, at steady state, C(dX /dt) = 0] gives D ( X X - X2) + y 2 X 2 = 0 • (3.39) i .e . , r x 2 = D ( X 2 - Xx) = D . (AX) (3.40) combining equation (3.34) ana (3.40) witn tne necessary subscripts, results in D . (AX) = ±^{SZ + X2f + K) ^/ (s 2 + X2f + K)" - 4fX 2s 2J (3.41) Equation ( 3 . 4 1 ) af ter lengtny manipulation (see Appendix 3 . 2 ) gives A X = s ? ( l - v ) + X,f + K ± / s ( 1-v) + X,f + K ] 2 - 4 X , s f ( l - v ) c D 1 V P 1 c P 2f [(D/v) - U ( 3 > 4 2 ) Since A X > 0 , taKe only tne negative r a d i c a l . 3 . 3 . 4 Appl icat ion of Model Wnen Recycling is Used As noted in Section 2 . 3 . 2 tne oacter ia tend to attacn tnemselves to tne minera l 's surface. Gonnely and Duncan ( 1 9 7 4 ) reported tnat 65 percent of tne c e l l s enumerated, wnen T. ferrooxidans were grown in continuous cul ture in an i d - l i t r e tanK using zinc sulpnide concentrate, were attacneo to tne minera l . Hence recycle of micro-organisms could eas i l y oe accomplisned oy al lowing tne outflow from a CSTR to sediment, permit t ing tne supernatant to flow to e i tner tne product receiver or to a second tank, i f any, and returning the sedimented port ion to the ( f i r s t ) reactor . Tnis method of recycle nas two advantages. F i r s t l y , tne CSTR could De operated aoove the c r i t i c a l d i l u t i on rate for tne once tnrougn system witnout wasn-out occurr ing and secondly, tne larger pa r t i c l es in tne concentrate would, as a resu l t of r ecyc l i ng , nave a longer residence time, and nence a nigner conversion than i f there were no recyc l i ng , m fac t Levenspiel ( 1 9 7 2 ) nas snown tnat i f tne 57 unconverted reactant can be separated from tne product stream and returned to the reactor tnen tne oest scneme is to use an ideally mixed reactor operating at tne point of maximum reaction rate. Let the recycle ratio, y, oe defined as, (see Figure 3.2) Y = volume of slurry returned to tne reactor entrance volume of slurry entering tne system (3.43) Let tne fraction of solios to recycle oe A mass oalance (see Appendix 3.3) on tne separator gives mass of solids to recycle = (1 + Y) FS^ 5 (3.44) concentration of solids in recycle = , 1 + 1 Y ( 1 : > V (3.45) mass of solids to tank 2 = (1 + Y) FS^ (1-S) (3.46) concentration of solids to tank 2 = (1 + Y) (1 - &) (3.47) wnere, F = flow rate s^ = surface area concentration in tan« 1. Similarly a oacterial oalance (see Figure 3.3) gives: bacteria to recycle stream = (1 + Y)F <5a + sF (X]_ - a) (3.48) Bacteria to tank 2 = (1 + Y)F (1 - &)a + F(x]_ - a) (3.49) (1+7) F ( 1 + 7 ) F f 7 F FIGURE 3 . 2 RECYCLE MODE OPERATION SHOWING MEANING OF RECYCLE RATIO cn CO F X 0 ( =0) S 0 (1+7) F S i *1 S i (1 +7) ( 1-5) a + ( X i -a) - (3 ( 1 - 5 ) 5 ! (1+7) 1» F X2 S2 V x 2 s 2 7 F (1 + ^;) 5(7 d +j_) 5 S i 7 + ( x i - a) FIGURE 3,3 DISTRIBUTION OF SURFACE AREA AND BACTERIAL CONCENTRATION DURING RECYCLE 3.3.4.1 Application of Model to First Tank When recycle is used a cell mass balance gives V • , d X l x = F . Xn + Y F [(1 + 1) 6.a + (X , - a , ) ] - (1 + Y) . F . X , + V. , ^1 , (3.50) 1 dt ;G dX Dividing by V, substituting , 1 . = M ,X 1 = va , , [ dt jG d X assuming X = 0, and assuming steady state , 1 - 0 * i Ves ^ dt ' y o, = D . X1 (3.51) v + D L U + Y) 6 - YJ 1 Combining equation (3.34) and (3.51) and inserting the necessary subscripts, we have (see Appendix 3.4), (sx+ Xxf + K) - ((sx+ Xxf + K) 2 - 4fX 1s 1) ) 1 / 2 /2f = D X 1 / ( u + [ ( 1 + Y) 5 - 6 ) JD ) (3.52) Expansion and simplification leads to X l = S l + K (3.53) AT f (A - 1) where, A = D . (3.54) v + L d + Y)« - Y JO When there is no recycle Y = s = 0, which gives, A = p_ . (3.55) v 61 Substituting (3.5b) in equation (3.53) yields equation (3.36), wnich is what is expected. 3.3.4.2 Application of Model to Second Tank Wnen Recyle is Used A cell mass balance gives, d X 2 dX V ( - ~ ) = F . 6 . - F . X + V , _ ^ 2 _ x (3.56) a z 6 K dt jG where 8 = (1 + y ) ( 1 - 6 ) Xx - ^ (3.57) Dividing by V, substituting , d X 2 x = y 7 X ? , [ dt jG d dX2 and assuming steady state, ( ) = 0 as before, we have u 2 = D_ (x2 - 6 ) (3.58) X 2 Combining (3.58) with equation (3.34) with tne necessary subscripts and remembering u2 = X 2 / X 2 leads to (see Appendix 3.5) C ± (C2 - 4efs ? ( 1 - v ) ) 1 / 2 _ D_ (3.5y) wnere 3 = v . X, (3.60) v + L d + y) « - Y J D 1 and C = s 9 , 1 - v x + 8f + K (3.61) 62 3.3.5 Review of Gormely's Work Gormely (1973) derived a model for leacning oasea on f i rst order K inet ics of attachment and release of tne oacteria. His equation derived on tnis assumption was equation (3.31) in Section 3.3.1. Tnis equation was comoined witn equation (3.22), wnicn is oased on tne assumption tnat tne reactor oenaves as if perfectly mixed. But it would appear tnat tne design of tne apparatus used Dy Gormely was sucn tnat tnis assumption was not borne out (see Sect-ion 4.1). Tne reasons for tnis suspicion are manifold, in Cnapter VI, Section 5 of nis tnesis Gormely states "It was suspected tnat removing product oy slurping it from tne surface of tne tanK to control tne liquid level might result in removal of material not representative of tne contents of tne OUIK of tne t a n K . " He then proceeded to do a least square f i t of tne results and accepted tne hypotnesis tnat tnere was no non-ideal product removal at 90 percent confidence level. However, it would appear tnat there was non-ideal product removal (see Section 4.1). Tne existence of a crit ical dilution rate coulo not be established by Gormely. It is suspected tnat three out of four of tne dilution rates used were over tne crit ical dilution rate. Tne experimental results obtained did not conform to tne analytical results predicted oy tne model and the,conclusion of the writer is that it was probably due to lack of complete mixing. 63 Gormely suspected that the concentrate particles may have bypassed the reactor by being carried in tne foam. Tne absence of wash-out, even though flow rates exceeded the crit ical dilution rate, may have been due to the presence of 'dead' regions. In the circumstances it would appear that the stirred tank Gormely used could De best described by a moael such as the one shown in Figure 3.4 (Cholette and Cloutier (1959)). A tracer study similar to the one described in Appendix 5.8 would have given a quantitative method of checking ideal mixing. Q Q b w vby-pass'flow Q active'region or completely mixed region 'dead region' FIGURE 3 . 4 FLOW DIAGRAM OF A. MODEL SHOWING COMPLETE MIXING SHORT - CIRCUITING AND DEAD SPACE 65 4. EXPERIMENTAL METHODS AND PROCEDURES 4.1 Preliminary Experiments Tne apparatus used for tne preliminary experiments consisted of two reactors of 50 litre capacity each and a product receiver of 40 l itre capacity. All vessels were made of AISI 316 stainless steel. Tne reactors nad 4 oaffles eacn and tne product receiver nad a Lucite l id . Tne reactors were provided witn tubes to enaole tne tanKs to oe aerated. Provision was made to agitate tne contents of tne reactors oy single, nuo-mounteo turoine impellers (witn six olades). Tne tanKs were provided witn cooling/neating coi ls. Yellow Spring Instrument Company Tnermistemp Mode 63 temperature controllers maintained tne contents of tne tan«s at a predetermined constant temperature. Tne slurry was transferred from reactor 2 to tne product receiver oy suction. Tne product receiver was under constant suction and tne tuoe connecting tne reactor to tne product receiver hao a solenoid valve wmcn was opened intermittently for a predetermined lengtn of time oy a 'Flexopulse' timer. Tne transfer of tne slurry from tne f irst tanK to tne second tanK was oy a Cole-Parmer flow inducer pump. Tne positioning of tne suction tuoe was sucn tnat it permitted control of tne level in tanK 1. Wnen tne level dropped oelow tne eno of tne tuoe, air was pumpeo to tanK 2, instead of slurry. 66 Air, enricned witn 1 percent CO^  and saturated witn water at tne same temperature as tne contents of tne tanK, was sparged under tne turbine impellers. The zinc sulpnide concentrate was fed to tanK 1 by a volumetric disc feeder (Manufactured by BIF). Tne medium was pumped from a reservoir to a constant level neao tanK. Tne overflow from tne constant-level neao tanK was returned to tne reservoir. Medium from tne constant level nead tank was allowed to flow to tank 1 tnrougn a neeole valve wnicn controlled tne amount of nutrient medium. 67 4.2 Development of the Apparatus 4.2.1 E f f i c i e n t Mixing Two runs were performed witn tn is set up and tne resu l ts are presented in Appendix 4 .1 . A perusal of run 2 snows tnat tne pulp densi ty of tne s lu r r y in tne product receiver was nigner than tne pulp density in tne second tanK. This led to tne suspic ion tnat the tanxs were not well mixed. It was also f e l t that so l ids may nave been, r id ing on tne foam leading to ' by -pass ing . 1 In view of tne douot created as deta i led in tne previous paragraph, a second, nub-mounted, pitcned blade turbine impel ler was added, one impeller diameter above tne turbine impel ler . To cnecx the e f f i cacy of tne modi f icat ion a ser ies of experiments was performed witn pulp dens i t ies varying from 1 percent to 25 percent. It was observed tnat samples withdrawn at 12 d i f fe ren t neignts at in te rva ls of one incn s ta r t ing from 1/8 of an incn above tne bottom of tne tank had tne same pulp densi ty as tnat in tne tank at tne 99 percent confidence l e v e l . 4.2.2 Transfer of Slurry Between Reactors When a flow inducer pump was used for t ransfer of tne s l u r r i e s i t was observed tnat tne tubing nad a tendency to break at frequent, i r regu la r i n t e r v a l s . A number of experiments wnicn were almost near steady state had to be abandoned due to tne 68 d isrupt ion of tne t ransfer of the s lu r ry as a resu l t of tne tubing g iv ing way, mostly at times wnen tne apparatus was unattended. To overcome tn is d i f f i c u l t y an intermediate tank was used for tne express purpose of t rans fer r ing s l u r r y . Figure 4.1 snows a diagramatic lay-out of tne intermediate tanK and tne necessary inter-connect ing pipe-worK and va lves. Tne intermediate tanK consisted of a Q.V.F. p ipe-sect ion 150 mm in diameter and 80 mm nign. The top and bottom were closed by 0.6 cm tn icK s ta in less steel d iscs bolted in place using a f lange, inser t and gasKet. The top s ta in less s tee l plate had a s p e c i a l l y designed gland, wnicn permitted an impel ler to be inserted to prevent tne so l ids from s e t t l i n g , but wnicn was s t i l l proof against pressure or vacuum. Figure 4.2 snows de ta i l s of tne construct ion of tne f lange. The interconnect ing s ta in less steel pipeworK of 1/4 incn (0.6 cm) nominal diameter pipe was connected to tne tank oy "SwAGELOK" f i t t i n g s . Transfer of s lu r r y between tanks was cont ro l led using a s ta in less steel Wnitey Ba l l Valve Model SS-43 X S4 coupled to a Whitey A i r Operated Ba l l Valve Model MS-131SR. Plugging and corrosion wnicn were plaguing tne o r i g i n a l l y i ns ta l l ed solenoid valve were avoided wnen i t was replaced by tne above mentioned ba l l va lve. Tne ba l l valve nad Teflon inser ts wnicn prevented tne s lu r ry from gett ing oetween tne moving metal par ts , and abrading tne sur face. The a i r operated ba l l valves were governed by compressed a i r . Solenoid valves cont ro l led tne flow of compressed a i r . COMPRESSED AIR I B> FIGURE 4 . 1 DIAGRAMATIC LAY IT. OUT OF THE INTERMEDIATE TANK FIGURE 4 . 2 DETAILS OF CONSTRUCTION OF THE GLAND 71 The air-operator A-^  actuated tne ball valves and B^  (see Figure 4.1). However, wnen B^  is open B^  was closed ano vice versa. To effect transfer of tne slurry from reactor, R ,^ to tne intermediate tanK, IT, valve B-^  was open, B^  was closed and suction was applied to tne intermediate tanK. Tnis sucKed tne slurry into tne intermediate tank wnere stirring prevented tne slurry from settling. Wnen sufficient quantity nad oeen sucKed B^  was closed, 8^  was opened. Compressed air was tnen forced into tne intermediate tanK, wmcn in turn forced tne slurry into reactor, R ,^ tnereoy effecting tne transfer of slurry from R^  to R .^ Tne operations of tne air-operator and tne solenoid valves were directed oy a custom designed, and built, sequential timer (see Section 4.2.5). A level controller, LC^ (see section 4.2.3 and Appendix 4.2) was aole to override tne transfer of slurry from tne intermediate tanK to reactor R ,^ if necessary. 4.2.3 Recycle Simple recirculation of tne product stream nas l i t t le effect in most cases as tnis is inoistinguisnaole from internal circulation of tne contents of tne fermenter. However, recirculation in conjunction witn concentration of microbial mass nas a beneficial influence on performance (AtKinson, 1974). In concentrate leacning, the oacteria attacn tnemselves 72 to tne mineral surface (see Section 2.3.2). Advantage was taken of tnis pnenomenon ana concentration of tne organisms for recycle was acnieved oy allowing tne slurry to sediment in tne intermediate tank. Tne supernatant was airected to tne secona reactor, and tne concentrated portion returned to tne f i rst reactor. Tnis resulted in effective recycle of micro-organisms and also recirculated tne larger size particles to tne f i rst tank, thereoy increasing tneir residence time tnerein. Figure 4.3 is a scnematic diagram of tne intermediate tank, tne reactors and tne product receiver snowing tne necessary modifications to permit recycle. Tne oasic cnanges were a larger intermediate tank, a QVF pipe-section 300 mm in diameter and 150 mm nign, tne aosence of a stirrer, and provision for return of tne sedimented slurry oack to reactor 1. Some additional valves were necessary. 4.2.4 Sequential Timer Tne orain of tne equipment was a custom designea ana Duilt, sequential timer. Tnis sequential timer consisted of seven timers cascaded to proauce tne sequential timing pulses (see Appendix 4.3). SUCTION AIR, ^7 4 B1 R i 4 I.T. S 5 -C^O- -a-AIR AIR AIR -4> ^ ft s 4 | R 2 B 5 A - Air Operated Ball Valve B - Stainless Steel Ball Valve S ~ Solenoid Valve R - Reactor IT. - Intermediate Tank Subscripts denote serial numbering - ( g ) — — « s f - AIR 1 L SUCTION PRODUCT RECEIVER FIGURE 4 . 3 MODIFICATION FOR RECYCLE 74 Taole 4.1 gives tne valves actuated oy tne various timers. Tne variable potentiometers of tne timers 1 to 7 will oe referred to nereafter as P-^  to P ,^ respectively. 4.3 Description of tne Reactor System 4.3.1 Straignt Tnrougn, Two Stage Operation Figure 4.4 is a diagram of tne lay-out of tne apparatus for tnis mooe of operation. Tne reactors, Rp and R ,^ were made of stainless steel and had an inside diameter of 30.0 cm. Tne geometric ratios for tnese stirred tanK reactors are given in Table 4.2 and a scnematic drawing is given in Figure 4.5. Eacn tanK nad four oaffies. Agitation was provided oy two, nub-mounted, turoine impellers, wnicn were separated oy a distance equivalent to tne impeller diameter. Tne upper turbine nad its, blades pitcned at 45° to tne vertical. Air was sparged into tne reactors tnrougn l/4_incn stainless steel pipes. To reduce evaporational losses tnis air, enricned witn 1 percent CO ,^ was numidified oy passing i t tnrougn water wnicn was maintained at a temperature of 35°C. TABLE 4.1 Valves Actuated oy tne Timers Valve See Fig. 4.4 S 1 S 2 S 3 S 4 S 5 S 6 S 7 T i merv 1 Open Open Open Closed CIoseo Closed Closed 2 Open Open Closed Closed Closed Closed Closed 3 Closed Closed Closed Open Closed C losed Closed 4 Closed Closed Closed Closed Open Closed Closed 5 Closed Closed Closed Closed Closed Closed Closed 6 Closed Closed Closed Closed Closed Open Open 7 Closed Open Closed Closed Closed Closed CIoseo I.T - Intermediate Tank ST.- Sequential Timer n i — Reactor 1 R2 - Reactor 2 R -Rotameter G - Pressure Gauge T.C-Temperature Controller T. - Thermocouple Ai j Air - Operated A 2 J Ball Valve L.C - Level Controller H. - Humidifier G 3. COMPRESSED AIR I.T. S5,l,COMPRESSEDl AIR SUCTION CO., f 1 AIR COM -PRESSED AIR "0 S T . © © © © SUCTION PRODUCT RECEIVER AIR F I G U R E t\J\ LAY - OUT OF THE A P P A R A T U S FOR S T R A I G H T THROUGH MODE OPERATION F I G U R E 4 . 5 S C H E M A T I C DRAWING OF TANK 3 0 0 mm £ E o o CO WATER OUTLET WATER INLET 6.25 air inlet n PITCHED BLADE TURBINE 100 mm 100 mm -I {^TURBINE J 25 mm I P P BAFFLE BRACKETS(4) 1.56mm x 25mm BAFFLES 550 mm Long 25mm SPACING 3 turns of 6.25mm SS coil threaded through baffles Stainless steel construction throughout Geometric Ratios For Stirred Tank Reactor (Refer to Figure 4.6) 0 t / D i = 3.0 H L / D t = 1.2 H i / D i = 1.0 w b / D t = 0.08 rt'i/Di = 0.25 F I G U R E 4 . 6 GEOMETRIC RATIOS OF THE REACTOR w b 80 The temperature of tne reactors was maintained at 35°C oy Yellow Springs Instrument Company Tnermistemp Mooel b3 temperature controllers. Tnese controllers operated solenoid valves wnicn permitted tne flow of not and cold water tnrougn stainless steel neating-cooling coils wnicn were immersed in tne tam<s. Tne transfer of slurries from one reactor to tne otner was via tne intermediate tanK as described in Section 4.2.2. Tne transfer of product to tne product receiver from tan* 2 was acnieved by maintaining tne product receiver under a constant vacuum ano opening tne oail valve B5 for a pre-determined iengtn of time set on tne sequential timer. Tne concentrate was added to reactor 1 oy a B.I.F. Volumetric Disc Feeder, Model 22-01. To ensure tnat tne disc feeder delivered a constant amount of concentrate to tne tan<, it was necessary to Keep tne amount of concentrate in tne nopper at a constant weignt. Tms was acnieved oy replenishing tne nopper daily witn tne exact weignt of concentrate fed to tne reactor. 3.2 Two Stage witn Recycle to Reactor 1 Please see Section 4.2.3 for tne necessary modification tne apparatus. Plates 1 to 4 snow different views of tne apparatus. 4.4 Operation 4.4.1 Straignt Tnrougn Two Stage Operation Tne operation of tne system is oest aescrioea oy reference to Figure 4.4 and Taole 4.1. Tne f i rs t step is to set tne total cycle time (say 15 minutes). Tnis could oe acmevea oy setting tne individual timing perioas of tne seven cascaded timers tnat constitute tne sequential timer (see Section 4.2.5). Tne period of eacn timer could oe varied from milliseconds to nours oy varying its potentiometer. Tne duration of tne f irst period - tne lengtn of time during wnicn valve B5 is open - is cnosen in sucn a manner as to acnieve tne desired dilution rate. For example, if tne volume of liquid in tne reactor is 25 litres and it is desired to operate tne system at a dilution rate of 0.020 n - ^ tnen tne volume of slurry F to oe transferred in one nour from reactor 2 to product receiver is calculated from tne following equation: 63 F = D (4.1) V wnere, F = flow rate V = volume of liquiu in reactor ana 0 is tne ailution rate. In tne example considered, F would oe 520 ml per nour. If tne (total) cycle time is set at 15 minutes tnen eacn suction to tne product receiver snould transfer 130 ml, since tnere would oe four cycles per nour. Potentiometer 1 is adjusted to give tnis suction rate. Reference to Taole 4.1 snows tnat during tnis period valves S^, ana are open. Solenoid valve S^ controls tne supply of compressed air to air operator wmcn opens oail valve, B ,^ and closes oa I "I valve, . Solenoid valve connects tne intermediate tanK to suction. Solenoid valve supplies air to air operator A , wnicn actuates oail valve, B,-, tnereoy permitting tne flow of slurry from reactor, R to tne proauct receiver. Tne penoa of tne secona timer is selectea so as to ensure tnat tne volume of slurry transferred from reactor, R p to tne intermediate tanK is in excess of tne volume of slurry transferred to tne product receiver during tne f i rst period. Tnis ensures tnat tne level in reactor, R^, will oe maintained at tne desirea level. During tnis perioa valves S-^  ana remain open. Tnus tne transfer of slurry from R^ to IT commences during tne f irst perioa and continues into tne secona. d4 Tne tnira ana fiftn periods are dummy events included, so as to enable tne desirea cycle time to oe acnieved. During tne straignt tnrougn operation tne potentiometer is set to zero, so tnat tnis period is almost zero and valve nas no time to open and close. All valves remain closed during tnese two periods. Tne fourtn timing period enables tne transfer of slurry from tne intermediate tanK to reactor R . Tne duration of tnis period is so selected tnat it is more tnan enougn to transfer sufficient slurry to replenish reactor R .^ During tnis period Sg opens sending compressed air into tne intermediate tanK. Since valve S^  is closed, oal I valve will oe open allowing tne transfer of tne slurry to reactor K However, tne level controller of tne second tanK nas an overiae on tne transfer and could cut it off wnenever tne pre-determinea level is reacned in tne reactor R .^ However, tne duration of tne period is unaffected, tnereby ensuring tnat tne total cycle time remains unaffected. Potentiometers P. ana P., are set to zero during tne b 7 straignt tnrougn operation. P^  is set so as to acnieve tne desired cycle time. Tne impeller in tne intermediate tanK is 'on' tnrougnout, tnus ensuring tnat tne slurry left oenind in tne intermediate tanK does not settle. 85 Tne level controller of reactor R^, nas an over-riding influence on valve Sg, wmcn controls tne flow of medium from tne constant level neao tanK to reactor R,.S is l a connected to an interval timer. Tnis enables tne liquid in tne manometer, attacneo to tne level controller, to give a steady reading. 4.4.2 Recycle In recycle studies tne intermediate tanK and tne interconnecting pipe wor< were modified (See Section 4.3.2). As solids are to oe sedimented in tne intermediate tanK no agitator was used. As for straignt tnrougn operation, tne sequence starts witn tne setting of tne dilution rate in tne f i rst period. Tne second period is extended to permit more slurry to oe t a K e n into tne intermediate tanK. In fact, tne recycle ratio, 6, (see Section 3.3.4), would determine tne duration of tnis period. During tne tnira period tne slurry is allowed to settle. Ideally tnis period would oe determined oy tne cnoice cib of 6, tne f rac t ion of so l ids to recycle (See Section 3 .3 .4 ) . However, in tne present study, 6 was ca lcu la ted for an a r b i t r a r i l y cnosen per iod. A l l valves except S^ remain closed during tn is per iod. Openiny of valve S^ during tn is per ioa permits tne vacuum to oe re leased. If tne vacuum is not released i t was founo tnat tne entry of compressed a i r in tne fo l lowing period was so v io lent tnat tne sedimented pa r t i c l es were s t i r r e a up. Tne fourtn t iming period permits tne t ransfer of tne supernatant to reactor R Tnis i s accornp I isnea by opening valve S(-, wnicn permits compressed a i r to surge into tne a i r operator, A^, wnicn actuates tne ba l l valves B^ ana B^. Compressed a i r f lowing tnrougn 8^  enters tne intermediate tan* ana blows tne supernatant witn f ines to reactor R . Tne leve l con t ro l le r of R„ over- r ides tne solenoid valve S c wnen tne 2 5 level in R reacnes tne preset l eve l . However, as in tne s t ra ign t tnrougn operat ion, tne over- r ide does not a f fect tne duration of tn is t iming per iod. As mentioned e a r l i e r tne f ' i f tn period was a aummy a c t i v i t y to make up tne cycle time. A l l valves are closed during t n i s penoo . 87 During tne sixth period, tne remnants of tne intermediate tanK are mixed well, so as to prevent a ouilo up of solids, and forced into reactor, R .^ Tnis was achieved oy opening tne solenoid valves Sy and Sg. Tne opening of valve Sy allows compressed air to ouoble into tne slurry tnereoy mixing tne contents of tne intermediate tanK. Opening of valve Sg activates tne air operator, A ,^, wnicn in turn opens tne oal I valve E^. Hence tne slurry in IT is forced out tnrougn into R^. Tne duration of tnis period is cnosen in sucn a manner tnat it is more tnan adequate to flusn out all tne slurry collected oy suction, in tne intermediate tanK during tne f i rst and second periods. This is necessary to prevent a buildup of tne slurry in tne intermediate tanK, with passage of time. Tne final period is anotner dummy activity to use up tne remainder of tne cycle time. However, tnis period is used to evacuate tne intermediate tanK and to create a vacuum. Tne only valve wnicn remains open during tnis time is S 2- All otner valves remain closed. 4.5. Materials 4.5.1 Organisms Tne inoculum used was a strain of Tmooaci 11 us  ferrooxidans (N.C.I.B. No. 9490), isolated by Razzell and Trussell (1963). It was grown in snaKe f'lasK cultures on zinc concentrate and adapted to tne ZnS substrate for over tnree years. 88 4.5.2 Suostrate Tne preliminary experiments were carried out witn tne zinc concentrate useo oy Gormeiy (1973). However, tne DUIK of tne worK reported in tnis study was done using a single lot of nign-grade, zinc sulphide concentrate. This material was supplied oy Cominco Ltd., Trai l , B.C. Its origin was tne Pine Point Mine, in tne Nortnwest Territories. 4.5.3 Culture Medium Tne liquid medium feo to reactor R ,^ was tne 9K medium described oy Silverman and Lundgren (1959). However, zinc sulpnide concentrate replaced the ferrous iron salts, useo Dy tnem, as tne energy source. For most of tne runs tne pH of tne medium was not ar t i f ic ia l ly reduced to tne optimum range of 2.0 - 2.5. The acid-producing potential of tne organism (witn this suostrate) was utilized to reduce tne pH of tne medium to the optimum value. 4.5.4 Antifoam During oaten growtn periods foaming was encountered. Altnougn Dow Polyglycol 15 - 200 was found to suppress tnis foaming, its effect was temporary. Reduction of tne aeration rate helped to oring tne foaming under control. But once the organism started growing vigorously tnere was no need for any antifoam. 89 4.6 Procedures 4.6.1 Mixing Characteristics of tne reactors j Tne preliminary experiments indicated tnat tne reactors were not well mixed as set up in i t ia l ly . (See Section 4.1). After tne modifications described in Section 4.2.1 were made tne efficiency of mixing nao to oe verified. Tnis was done in two ways. Efficiency of mixing in a oaten mode was cnecKed oy withdrawing samples at one incn intervals witn varying pulp densities. (See Section 4.2.1). Tne efficiency of mixing ano ideal-product removal during continuous runs were verified oy liquid and solid phase tracer studies. Most of tne tracer systems reported in tne literature are liquid, gas and liquid-gas. Tne use of a solid tracer in a solid-liquid system is somewnat rare. A suitaole tracer for tne system under investigation was eitner: (a) radioactive spnalerite or (o) cnalcopyrite yo Altnougn r a d i o a c t i v e s p h a l e r i t e was eminently s u i t a b l e as a t r a c e r , tne cost of i r r a d i a t i n g a sample and tne cost of tne necessary mod i f i ca t ions to enaoie tne precaut ions tnat nad to De ooserved in order to secure tne necessary permits ru led out the possioility of i t s use. In tne circumstances i t was decided to use c n a l c o p y r i t e as tne t r a c e r . Tne c n a l c o p y r i t e t r a c e r nelped to c h a r a c t e r i z e tne mixing of tne solids. Tne c n a l c o p y r i t e used as tne t r a c e r was a lso b a l l m i l l e d to tne same s i z e (-400 mesn) as tne z inc concent ra te . Tne s p e c i f i c g rav i ty of c n a l c o p y r i t e is about 4.1 wn i ls t tnat of s p n a l e r i t e is 3 . 8 . Since ootn s p n a l e r i t e and c n a l c o p y r i t e nave d e n s i t i e s wnicn are s i m i l a r and s ince tne p a r t i c l e s i z e was tne same, tne benavioural c h a r a c t e r i s t i c s of ootn substances would be similar .Tne l i q u i d mixing was Character ized s imultaneously by measurement of KCl c o n c e n t r a t i o n , v i a conductance, of tne samples at var ious times a f te r tne in t roduct ion of a pulse of t r a c e r . 91 Zinc sulpnide concentrate was added from tne disc feeder into a slurry consisting of disti l led water and tne concentrate. After tne tanK nad reached steady state, weighed quantities of cnalcopyrite and potassium chloride were added in pulse loading. Samples drawn at uniform intervals were assayed for copper . and tne conductance was measured. Tne sample was digested and tne copper assayed on a PerKin Elmer Mouel 303 atomic absorption spectrophotometer. Tne conductance was determined using a Yellow Spring Instrument Model 30 S-C-T (Salinity, Conductivity, Temperature) Meter. 4.6.2 The Concentrate Tne Concentrate was delivered Dy Cominco in two oarreis eacn containing about 225 K g . 4.6.2.1 Blending tne Concentrate Tne concentrate was blended according to a procedure detailed in Appendix 4.4 to ensure tnat it was well mixed. 4.6.2.2 Analysis of tne Concentrate About a naif-gram of tne sample of concentrate to oe analysed was weigned accurately into a 250 ml oeaKer. 5 ml eacn 92 of concentrated nydrocnloric acid and concentrated nitric acid were added ana tne mixture was evaporated to dryness on a not plate. Wnen tne mixture was dry 5 ml eacn of concentrated nitric and concentrated sulfuric acics were added and evaporated to dryness again. Tne residue was ooiled witn disti l led water and a drop or two of nitric acid (to dissolve any ferric hydroxide tnat mignt have precipitated), allowed to cool, made to volume and analysed for zinc and iron using an atomic absorption spectrophotometer. For analysis of tne sulphur content of tne concentrate, the concentrate was f i rst washed witn pyridine to remove any flotation cnemicals left oenind (Gormely, 1973). Tne pyridine was supplanted oy etnanol followed oy disti l led water. Tne concentrate was tnen dried at 60°C for tnree days. About 50 mg of tne concentrate was weighed exactly and mixed witn 1 gram eacn of vanadium pentoxioe catalyst, (tfurxe, 1962) and 1 gram of low sulpnur, iron powder - accelerator. The mixture was comousted in a stream of oxygen in a Leco Moael 521 93 induction furnace. Tne sulphur dioxide generated oy tne combustion was aosoroed in a solution containing 30 ml of concentrated nydrocnloric acid, 5 ml of 10 percent potassium iodide solution, and 1 ml of 2 percent starcn solution per l i t re. Tne product was titrated against standard (0.025N) potassium iodate. KI03 + 5KI + 6HC1 » 3I2 + 6KC1 + 3H20 (4.1) Sulphur dioxide absorbed in tne solution reduced tne iodine to iodide: S02 + I2 +2H20 » H2S04+2HI (4.2) Excess iodine in tne solution was detected as a dar< blue colour oy tne starcn. 1 ml of 0.025 N potassium iooate was equivalent to 0.24 mg. of sulpnur. Two b i a n K S ano five standard . reagent grade zinc sulphide samples were also combusted for comparison purposes. A sample of the concentrate (after ball milling, pulverizing and drying) was analysed at Cominco Ltd., by X-ray spectrometry. 4.6.2.3 Determination of tne specific surface area In biological leacning processes, tne rate of metal extraction is usually a function of tne specific surface area. (See Section 2.5.4). Hence it was necessary to determine tne specific surface area of tne unleacneo concentrate ano ieacneu samples from eacn run. Torma (1970) and Gormely (1973) used tne Brunauer-Emrnett-Teller (1938) metnod for tne determination of tne specific surface area. Tnis metnod cased on tne adsorption of nitrogen on tne surface of tne concentrate measures tne s u r f a c e s due to pores, c r a c K s , and fissures wnicn may not oe available to tne bacteria. Lawrence (1975) and Pincnes et a_l_ (1976) nave used tne air permeability metnod for tne determination of specific su r f ace area. Tne air permeaoility metnoa was used in tnis study and is discussed in Appendix 4.5. 4.6.2.4 Ball Milling of tne Concentrate Gormely (1973) conducted bail milling tests and concluded tnat ball milling for 45 minutes was sufficient to Obtain maximum extraction. He found tnat maximum specific surface area was obtained after about 90 minutes. In tnis study, using tne same 50 cms (20 incnes) ball mill as Gonnely, 13.5 kg of tne concentrate, 135 K g of 1.25 cm (1/2 incn) steel balls and about 7 litres of water were milled at 46 rpm for about 90 minutes. Tne milled concentrate was decanted and dried at 60°C for at least 24 nours. Tne dried cake was pulverized in a rotating disc pulverizer and stored in' plastic containers until needed. 4.6.2.5 Concentrate Fractionation In order to study tne effect of particle size on tne microoiological zinc extraction in snaKe f l asKS, tne subsieve (_400 mesn) concentrate was fractionated into definite size fractions using a Banco No. 6000 Microparticle Classifier. Tnis device is a combination of an air elutriator ano a centrifuge. It gave eight subsieve fractions. 4.6.3 Tne Organism Tne organism was routinely maintained on tne 9K medium of Silverman and Lundgren (1959) in wnicn tne ferrous iron energy source was replaced oy tne zinc sulpnide concentrate. Tne organisms were maintained on zinc concentrate for more tnan 3 years. This ensured tnat tne organisms were adapted to tne substrate and tolerant of nigh concentrations of zinc. 96 Tne medium used- nad tne composition given in Taole 4.3. Bacteria for use as inocula were ta«en from tne late exponential or early stationary phase of growtn. Altnougn tne glassware and media were ini t ia l ly sterilized to prevent contamination oy otner organisms, asepsis, per se, was not ooserved. 97 TABLE 4.3 (Modified) 9K medium of Silverman and Lundgren (1959) (NH4)2S04 3.0g K2HP04 0.5g MgS04 7H20 0.5g KC1 O.Og Ca(N03)2.4H20 O.Olg Distilled Water to 1.0 ]. (Total Volume ) 98 4.6.3.1 Evaluation of Bacterial Growth Brierly (1978) had criticized the ammonia nitrogen method of determining cell numbers (See Section 2.3.1). In our opinion it is unlikely that any organism other than T. ferroxidans would grow at the pH and with the energy source available in the present study. Moreover, in a steady state system it is assumed tnat the number of non viable cells are minimal. Finally tne amount of nitrogen containing organic by-products of microbial growth is considered to be small and to be constant at steady state and so would have no impact on the conclusions drawn. Therefore it was decided to use this method because of its simplicity, rel iabi l i ty and low cost. Detailed experimental procedures are given in Appendix 4.6. 4.6.4 Leaching Techniques 4.6.4.1 Continuous Experiments Although the capacity of each reactor was 50 l i t res, the actual volume of slurry during operations was only 26 l i t res. Tne experiments were commenced by preparing the slurries in both tanks at a pulp density of about 5 percent. Sulphuric acid was added to bring the pH of tne slurry to 2.5, 99 air was spargea in and tne contents of the reactor agitated. The system was allowed to equilibriate overnight. Then more acid was added, as needed until the pH attained a steady value of 2.5. Once the pH nad reached its steady value inoculum was added and tne growth of the organism monitored by measuring tne zinc extraction. The cultures were grown in batcn mode oy feeding more substrate (Feed-Batch Culture Mode) until the desired zinc concentration was reached. The desired product removal rate was set by disengaging all the valves except and also setting all the potentiometers except to zero. The cycle time of the sequential timer in this mode of operation would be only a few seconds. The quantity of slurry transferred during four such reduced cycles was measured and the dilution rate calculated as explained in Section 4.4.1. Tne actual dilution rate achieved was checked by resetting the sequential timer to normal operation (15 minutes cycle time) ano measuring the slurry transferred to the product receiver over a period of an hour or two. The rate of concentrate feed for tne continuous run was calculated from a knowledge of the composition of the feed, the zinc in solution and the pulp density of tne slurry. 4.6.4.2 Pulp Density Samples (125 ml) were withdrawn daily from tne reactors, tne product receiver and, during recycle, the sedimented slurry returned to reactor R^  from the intermediate tank. 100 50 ml of tne . slurry were pipetted into a plastic centrifuge bottle. Tnis was tnen centrifugeo in a SORVAL superspeed Model RC2B centrifuge at 1500 rpm for 10 minutes. At sucn low speeds tne oacteria remained in suspension but tne solids settled down. Tne centrifugate was decanted and tne settled solids were resuspended in 10 percent HCl, and sna«en well to dissolve any precipitated iron salts. It was tnen centrifuged again and decanted as oefore. Tnis process was repeated two more times, once witn HCl ana tne last time witn dist i l led water. To cnecK if zinc containing solids were lost during decantation, tne decanted centrifugate was filtered tnrougn Millipore RAWD 0 47 00 f i l ters on Millipore f i l tration equipment and tne increase in weignt was found to be of tne oroer of 0.25 percent of tne weight of tne precipitate. Tnis was deemed to oe negligible. After tne final wasn witn disti l led water tne solios were transferred to an evaporating disn witn disti l led water and dried at 60°C for 2 or 3 oays and weighed to determine tne pulp density. 101 A quicker metnod for tne determination of pulp density was tne use of tne HP 41C calculator program given in Appendix 4.6. Knowledge of any three of tne parameters specific gravity of f lu id, specific gravity of concentrate, percent solias oy weignt of slurry, percent solids Dy volume of slurry, specific gravity of slurry gave tne other parameters. This program was used to ootain tne pulp density of tne slurry quickly. 4.6.4.3 Sampling Procedures and Miscellaneous Daily Housekeeping Chores Zinc and iron concentrations in tne reactors ano tne product receiver were monitored daily. Tne samples were analysed for zinc and iron on a Perk in Elmer Model 303 atomic aosorption spectrophotometer. Tne pH, En and temperature of tne reactors were recorded daily. Tne solios feed rate was cnecxed oy collecting tne amount delivered for a measured period of time. To ensure a constant feed rate tne disc feeder was maintained witn approximately tne same weignt of concentrate in its nopper every day. I 102 Tne efficiency of tne level controllers was cti'ecKed daily Dy measuring tne depth of slurry in tne tanK witn tne airflow and agitation switcned off. Samples were withdrawn from tne product receiver after measuring tne volume of product collected. Since tne product receiver nad oeen caliorated witn a meter sticK tne measurement of its content was easy. The product receiver was emptied of its contents daily. The constancy of tne dilution rate was cnecKed from tne measured volume ana tne time elapseo oetween sampling intervals. Fresn iron free 9K medium was preparea ana pumped to tne overhead tanK daily. 5. RESULTS AND DISCUSSION b.l Mixing Characteristics of tne Reactor Preliminary experiments snowed tnat tne init ial set-up of tne apparatus gave rise to incomplete mixing ano oy-passing (See Section 4.1). Hence it was necessary to modify tne apparatus. Tne init ial step in tne modification was to ensure tnat tne reactors were completely mixed. So a second nub-mounted, pitcned-0 lade, turbine impeller was fixed one impeller diameter above tne original turoine impeller. Slurries of different pulp densities (varying from 1 percent to 25 percent) were made up and put into tne reactor. Samples were witndrawn from tne tanK at 12 different levels starting one eigntn of an incn above tne bottom of tne 'tan*. Tne specific gravities of tne samples witndrawn were determined using a density bottle. Taole 5.1 presents typical findings for one of tnese tests. Tne remainder of tne results are presented in Appendix 5.1. Tne statistics presented snow tnat it is safe to assume tnat tne tanxs are perfectly mixed at tne y9 percent level. TABLE 5.1 Data for Pulp Density of 10 Percent Height of sampling Weight of 50 ml point from bottom of sample of tanK (inches) (g) 0.125 54.9789 1.125 54.9784 2.125 54.9828 3.125 54.9614 4.125 54.9776 5.125 54.9638 6.125 54.9774 7.125 54.9644 8.125 54.9817 9.125 54.9818 10.125 54.9712 11.125 54.9732 Average weight (W) = 54.9737 Standard deviation (a) = 0.0765 99 percent confidence interval Max = Min = 54.9902 54.9572 105 A quantitative method of analysing tracer data to determine dead space and the efficiency of mixing has been described by Rebhun and Argaman (1965). Using this metnod a solid tracer (chalcopyrite) and a liquid tracer gave tne results in Table 5.2. The details of tne method, results and plots are in Appendix 5.8. From these results it is clear that the mixing in the tanK is close to ideal. TABLE 5.2 Summary of tne Results of Tracer Study Solid Liquid tracer tracer (percent) (percent Dead Space 0 4.4 Perfect Mixing 95.2 94.3 Plug flow and By-passing 4.8 1.3 107 5.2 Analysis of the Concentrate To ensure that the concentrate was uniform, the randomized block design was used to test statistically if tnere is any variation in the analytical results of samples drawn from the plots (see Figure A.45-Appendix 4.3). Tne analytical results for zinc and iron are given in Table 5.3 and the Analysis of Variance (ANOVA) for zinc and iron respectively are presented in Tables 5.4 and 5.5. The results snow that the row effects and the column effects are zero at the 0.01 level of significance. In otner words, the mixing of tne concentrate can oe assumed to oe uniform at the 99 percent confidence level. Since both zinc and iron assays showed conclusively that the concentrate was mixed thoroughly it was felt that the analysis for sulphur need not be performed on eacn of tne samples from tne plots. TABLE 5.3 Analytical Results of Concentrate Percentage Composition Zinc 60.84 Iron 2.36 Sulphur 32.98 Total 96.18 109 TABLE 5.4 Analysis of Variance - Zinc Tota i Mean 1 30.50 30.34 30.44 30.46 30.46 132.20 30.44 2 30.35 30.46 30.40 30.42 30.39 152.02 30.40 3 30.29 30.29 30.42 26.38 30.58 151.96 20.3y 4 ' 30.33 30.39 30.40 30.50 30.61 152.23 30.45 5 30.51 30.34 30.45 30.70 30.40 152.50 20.50 6 30.43 30.29 30.44 30.52 30.39 152.07 20.41 7 30.40 30.23 30.48 30.45 30.59 152.13 30.44 3 30.39 30.38 30.32 30.46 30.23 151.33 20.37 Total 243.30 242.77 243.35 243.39 243.63 1216.99 Mean 30.41 30.35 30.42 30.49 30.46 30.42. ANOVA TABLE aegrees of freedom Sum of Squares Mean Sauare F Rows 7 0.091 0.013 i.o67 Columns 4 0.058 0.014 1./95 Error 23 0.218 0.0773 Total 39 0.367 FQ.QIF (7,139) = 3.133 110 TABLE 5.5 Analysis of Variance - Iron 3 4 5 Total Mean 1 i .12 2 1.22 3 1.17 4 l . i S 5 1.15 6 1.2b 7 1.20 8 1.14 Total 9.42 Mean 1.18 1.14- 1.22 1.24 1.24 1.22 1.14 1.17 1.17 1.20 1.21 1.15 1.23 1.17 1.13 1.15 1.15 9.44 9.49 1.18 1.19 1.17 1.15 1.13 • 1.16 1.24 1.14 1.13 1.20 1.22 1.23 1.17 1.12 1.22 1.16 1.23 1.14 9.57 9.31 1.20 • 1.16 5.31 1.16 5.yy 1.20 5.91 1.13 5.90 1.13 6.02 1.20 5.90 1.13 5.39 1.1b 5.31 i . l b 47.23 1.13 ANOVA TABLE Degrees of freedom sum of Sauares Mean Sauare :' Rows 7 0.0223 0.00319 i.GO Columns 4 0.0390 0.00975 3.05 Irrzr 2S 0.2509 0.0032 Total 39 • o.or { ' J • • J - - S u I l l A sample of the ball milled and pulverized concentrate was analysed at Cominco Ltd., Tra i l , B.C. by x-ray spectrometry and found to have the composition given in Table 5.6. Tne difference between tne two results is due to some iron from the steel balls finding its way into the concentrate during ball milling (Bond, 1943; Norman and Loeb, 1949) and due to errors in calibration etc. of the x-ray spectroscope. TABLE 5.6 Results of x-ray Spectroscopic Analysis of Concentrate Percentage Cadmium 0.12 Lead 2.1 Zinc 58.2 Iron 4.3 Sulpnur 32.5 Si l ica . 0.3 Calcium oxide 1.2 Manganese oxioe 0.43 Antimony <0.01 Arsenic <0.01 113 5.3 Shake Flask Experiments Torma (1970) studied the effect of the important factors that affect the leacn rate of zinc sulfide concentrate by T. ferrooxidans. Scrutiny of his results on tne effects of particle size on leaching rates showed that maximum extraction rates were obtained after varying lengths of time nad elapsed since inoculation. For example, in the case of particles having a diameter of less tnan 5 um (micrometers) the highest extraction rate was obtained after a lag of 280 hours. The larger particles with a diameter of 28 um and over gave the maximum extraction rate almost immediately after inoculation. It is felt that in the case of the smaller particles the inoculum lacked the number of micro-organisms needed to initiate rapid leaching. Moreover since the studies were made at different times and on different batches of concentrate it was thought that these experiments should be repeated. A series of tests were performed using the various Bahco size fractions. In the tests performed the size of the inoculum was varied in such a manner as to give approximately a constant number of bacteria per unit specific surface area using a pulp density of 16 percent, the same value as used by Torma. 114 Gormely and Duncan (1974) reported a non-disti11 able nitrogen content of 0.157 x l O - ^ mg per ce l l . Based on tnis value and a knowledge of the specific surface area, the quantity of inoculum was adjusted so that there were about 1.5 x 10^  cells per square centimeter of surface area. The results of these experiments are presented in Table 5.8. It was observed that the lag times were mucn snorter tnan Torma's (See Figure 5.1). In other respects the results were similar. The results are plotted in Figure 5.2 wnerein zinc extraction rate is plotted against specific surface area. As observed by Torma the zinc extraction rate increases in 2 proportion to the specific surface area up to 1.1 m /g (see Table 5.9) and thereafter increase in specific surface area has almost no effect on zinc extraction rate showing that some factor other tnan substrate is rate limiting. Figure 5.3 is a plot of the zinc extraction rate against particle diameter. 115 116 FIGURE 5 , 1 ZINC EXTRACTION RATES OF THE BAHCO FRACTIONS 118 TABLE 5.9 Banco Fractions Banco Average Specific Terminal Weight Cumulative Fractions Particle Surface Vel. Fraction Fraction Dia. Area Run No. ym m2/g in/min. Percent Percent 1 2.1 1.8300 1.19 2.2 2.2 2 3.5 1.1637 3.29 16.2 14.0 3 5.3 0.8264 7.55 16.8 33.0 4 9.0 0.5549 21.77 24.7 57.7 5 13.0 0.3212 50.45 20.2 77.9 6 21.5 0.1815 124.24 12.3 90.2 7 27.5 0.1409 218.23 5.5 95.7 8 35.0 0.1113 356.26 4.2 99.9 F I G U R E 5 . 3 Z I N C E X T R A C T I O N RATE V E R S U S P A R T I C L E DIAMETER T — \ 1 1 1 1 1 1 1-0 « 5 10 15 20 25 30 35 Size of PARTICLE DIA p bacteria 120 5.4 Continuous Leaching Experiments 5.4.1 Introduction Gonnely (1973). set out to study tne K ine t ics of leaching in a single tank. His study failed to snow the existence of a crit ical dilution rate, and ne could not determine the parameters v, f and K in equation (3.36), since his results did not agree witn the model (See Section 3.3.5). because of this the present study was designed to obtain tne data necessary to obtain the parameters v, f and K; extend the K ine t i cs to a two-tank system; to modify the apparatus to increase the dilution rate (and thereby shorten the residence time) over the crit ical dilution rate of the two tank system; and to increase the percentage extraction and thereby make the process more attractive. 5.4.2 "Sterile" run In Gormely's (1973) study, he made a sterile run to determine tne contribution of chemical leaching, relative to the total amount of leacning. A similar study was conducted in this work to establish tne necessary corrections for chemical 1eaching. 121 As was observed by Gormely (1973), the characteristic yellowish-orange ferric iron precipitate was absent, En values remained low indicating low levels of ferric iron. A slight pale green tinge was observed in the liquid medium, indicative of tne presence of ferrous iron rather than ferric iron. The leaching results are presented in Table 5.10. Tne baseline chemical leaching rate was calculated on the assumption that tne dissolution of zinc is tne sum of the amount of readily soluble zinc and a slow but steady chemical leaching component. When 5 grams of concentrate were agitated for 15 minutes in pH 2 water, 0.0318 gram of zinc (0.636 percent of the weignt of concentrate) were solubilized. The rate of zinc dissolution, rDI, may be expressed in terms of the feed pulp density, Fpd, (g/1 ) and tne dilution rate, D, (h-''") as follows: r D I = 0.00636. D. Fpd.gl 1 h 1 ^ ^ TABLE 5.10 Data for Continuous Run (sterile) at a Dilution Rate of 0.0130 h"1 Fu lu Density Spec i fic Surface Area ') s 2 in /1 PH El) [Fe] [Zn] Z r IS 1 Percen t c in /g_ 9/1 9/1 g/i.ii g/h.m 20.120 0.57B 116.2936 2.1 320 1.05 3.5 4.55 x 10-2 3.9135 x 10-4 123 The feed pulp density for the sterile run was 21.02 percent (or 210.2 g/1) and tne dilution rate was 0.0130 h _ 1 . Substitution of these values in.equation 5.1 gives r^^O.01737 g . l " 1 h" 1 . The sterile run gave a release rate of 0.0455 g.l -"'' h"1. If the readily soluble rate of 0.01737 g . l " 1 h" 1 is taken away the rate of zinc release due to cnemical oxidation of the zinc sulphide concentrate is (0.0455 - 0.01737)=0.02813 g . l - ^ h ^. The rate of zinc release due to chemical oxidation of concentrate, r^. may be described by the equation: r C H = k. [SA] g . l " 1 n"1 (5.2) where, k is a constant and [SA] is the surface area concentration. Substituting tne value of 0.02813 for and 116.2936 m 2 / l , the surface area concentration for the sterile run, the value of tne constant k becomes 2.419 x 10"4 g . n - 1 rn"2. 124 Hence the Dase line chemical leaching rate, r , may now be expressed by the equation: r = r + r b CH DI = 2.419 xlO" 4 [SA] + 6.36 x 10"3x D. Fpd. g . l - 1 . h " 1 (5.3) This may be converted to a concentration by dividing by tne dilution rate D. i.e. [r ] = 2.419 x 10 4 [SA] + 6.36 x 10 3 . Fpd. g.l 1 D (5 .4 ) where [r^] is the concentration of zinc due to baseline leaching. The sterile run gave a net ammonium ion concentration of 11.5 ppm. On the assumption that the ammonium ion was from the concentrate fed, a baseline correction for net ammonium ion was calculated. Tne feed pulp density, Fpd. for the sterile run was 125 21.0123 percent. Hence tne net NH* baseline correction, NBL, (expressed as ppm) for the sterile run is (11.5/21.0123 = 0.547). The correction for other runs was calculated on tne basis of tne following equation: NBL = 0.547 x Fpd, (5.5.j 5.4.3 Straight Through Mode Runs The data for the continuous leaching runs witnout recycle are tabulated in Appendix 5.2. A sample calculation for one steady state achieved is given in Appendix 5.3. 5.4.3.1 The First Reactor Tne bacterial concentration in the f i rst tank is given by tne equation: X, K + v_ . s , (3.36) 1 f[(D/v) - 1] Of 1 According to the equation (3.36) a plot of X^  versus S^  should give a straight line with a slope of v/Df ano an intercept of K/f((D/v) - 1) 126 Therefore, as D increases the slope term v/Df snoula decrease and the intercept should become more negative. In addition D must be less than v to avoid washout, hence 0/\j <1 ano K / f ( ( D / v ) - 1) should be negative. A summary of tne results in respect to Tank 1 are presented in Table 5 . 1 1 and are plotted in figure 5 . 4 . In figure 5 . 4 tne net ammonium ion concentration is plotted in lieu of X-^  + since it is assumed that net NH^  is a measure of the bacterial concentration. 127 TA3LE 5.11 Data for F i r s t Tank I Run 1 No. u i l u t i o n Rate h ?u i p Oens i t y burrace Area Cone. fn2/i I ^inc j Cone. g/i i Net. 1 0.0113 2.5003 23.4508 15.33 163 0 0.0098 5.234 32.6966 33.73 249 3 0.0098 7 ..5335 41.0200 45.46 326 0.0098 9.9108 51.6134 60.35 424 5 0.0085 13.3194 105.2281 • 59.40 451 6 0.013 10.7715 53.2371 63.92 413 7 0.013 5.9643 31.2660 30.5 155 8 0.013 11.3005 43.0547 37.00 272 9 0.013 11.9992 57 .5687 49.05 339 10 0.013 13.831 71.1570 52.75 433 l i 0.015 3.096 20.0235 24.23 50 \2 0.015 7.195 37.2449 46.38 154 13 0.015 3.2741 44.3650 53.53 197 1 28 F I G U R E SA PLOT OF NET C N H ^ l V E R S U S LSAJ -100 H 1 1 1 1 1 1 1 1 r 0 10 20 30 40 50 60 70 80 90 SURFACE AREA CONCENTRATION m 2 / l 129 As suggested oy the model the points for each and every run at the different dilution rates l ie on a straight line. Tne lines all nave negative intercepts and the numerical value of the intercept decreases with increasing dilution rate. Similarly tne slope decreases as the dilution rate increases. A summary of the dilution rate, intercept and slope values is presented in Table 5.12. Equation 3.36suggests that if the reciprocal of tne slopes were to be plotted against the dilution rates we should get a straight line passing through tne origin. The line in Figure 5.5 passes through the origin and its slope is 11.05, a measure of f /v. The intercept of the line is K/ f (D/v - 1). Rearranging, 3 3 2. i l i O —•} — \n '—' u '_) — "J 3 — 1) •0 -j TJ 3 -a —i O 131 FIGURE 5 . 5 RECIPROCAL SLOPE VERSUS DILUTION RATE DILUTION RATE * 10 3 (h"1) 132 Equation (5.6) indicates tnat the reciprocal of the intercept is a linear function of the dilution rate. Figure 5.6 is a plot of the negative reciprocal of intercept againsc dilution rate. It is a straight line as required, with a negative slope and a positive intercept. Tne intercept of 0.0274 is a measure of f/K and the slope of 0.88372 is a measure of - f/vK. We have: f/v = 11.05 m2/h.mg (5.7) f/K = 0.0274 1/mg (5.8) and f/vK = 0.8837 l.h/mg (5.9) Equation 5.8 divided by 5.9 gives: v = 0.0310 h"1 (5.10) wnere v is tne maximum specific growth rate for tne bacteria wnich are attached. Thus an evaluation of the data for the f i rst tank in the straight through mode suggests that the crit ical dilution rate is 0.0310 hour ^. Substitution of equation 5.10 in equation 5.7 gives: f = 0.343 m2/mg (5.11) which is the surface area occupied per unit of bacterial concentration, and from equation 5.8 and equation 5.11 we have: 12.504 m 2/l (5.12.) F I G U R E 5 , 6 R E C I P R O C A L I N T E R C E P T V E R S U S D I L U T I O N RATE DILUTION RATE x 1 0 " 3 ( h _ 1 ) 134 k ^ and are the rate constants of equation 3 -31 kx (S-af)(X-o) = k_L a ( 3 . 3 1 ) and since K = k ^ / k p it is evident that tne release of the bacteria from the mineral surface (k )^ is 1 2 . 5 times faster than the attachment (k )^ to the mineral surface. Such a situation seems reasonable in tnat the bacteria are produced (grow) on the mineral surface and should oe able to easily release themselves from the surface of tne mineral. Attachment in an agitated slurry would be more diff icult for the bacteria to accomplish. This task is made even more diff icult if tne organism has to orient itself and attach only at specific sites on the mineral (See Section 2 . 3 . 2 ) . + Figure 5 . 7 is a plot of net NH^  concentration against pulp density. A linear relationship between X and pulp density is observed. In Figures 5 . 8 and 5 . 9 zinc concentration is plotted against surface area concentration. In Figure 5 . 8 tne zinc concentration is not corrected for cnemical leaching, whereas the correction has been made in Figure 5 . 9 . Similarly in Figures 5 . 1 0 and 5 . 1 1 the unccrrected and correctea zinc concentrations are plotted against pulp density. Tne chemical leaching correction does not nave any profound effect on tne curves obtained. In tne circumstances, it was proposed to ignore tne effect of chemical leaching in the data for otner runs. 135 PULP DENSITY % 136 137 13fi F I G U R E 5 , 1 0 UNCORRECTED [ Z N ] V E R S U S P U L P D E N S I T Y 70 H PULP DENSITY (%) 139 140 5.4.3.2 The Second Reactor Table 5.13 presents the inlet, outlet, and differences between inlet and outlet values of pulp density, surface area concentration and the concentration zinc for the secona reactor. Figure 5.12 is a plot of tne difference in surface area concentration against difference in zinc concentration. The plot shows that the differences are directly proportional. Similarly from Figure 5.13 it can oe concluded that tne increase in zinc concentration is directly proportional to tne change in the pulp densities for each dilution rate. The bacterial concentration, X , in tne second tanK is given by equation (3.42) X2 = Xx +[x -Jx1 - 4X 1 s 2 f (1 - (v/D)] / 2f((D/v - 1) (5.14) where x = s 2(l - (v/D)) + X]_f + K ($.v*>) The equation has four variables X 2 > X^, D and s 2 . It is non-linear and second-order in X2- Even if D were to be kept constant, tnere would oe three variables ana hence any plot TABLE 5.13 DATA FOR SECOND TANK RUN PULP DENSITY Per :ent fFF7~ SURFACE AREA CONCN. m2/g CONCN. OF ZINC 9/1 NO. IN OUT 5 IN OUT DIFF. IN ffUT DIFF. 1 2 .5003 0.6456 1 .855 23 .4508 6 439 1/ .0118 19.0 32.5 13.5 2 B .284 u.6358 3 .748 32 .6966 12 .303 20 .3936 36.5 60.7 24.2 3 7 .5336 3.1U47 4 429 41 0200 15 635 25 3850 50.0 80.0 30.0 4 y .9108 3.8398 6 071 51 .6134 15 588 36 .0254 65.0 106.5 41.5 5 IH 3197 11.8527 6 467 105 2281 66 299 38 9291 77.5 117.5 40.0 6 IU .7716 5.2446 5 527 68 2871 44 629 23 6581 67.5 100.U 32.5 7 6 9643 2.3030 4 661 31 2660 5 794 25 4 720 32.6 62.5 29.9 8 11 3005 6.1655 5 135 48 0547 22 484 25 5707 40.0 72.0 32.0 y 11 9992 5.5600 6 439 57 6687 24 923 32 7407 52.5 93.0 40.5 10 l i l 8810 9-y711 8 910 71 1670 25 725 45 4320 57.5 112.5 55.0 l l 3 U96 0.8676 2 228 20 0235 7. 735 12 2885 25.5 39.5 14.0 12 7 195 4.1634 3 032 37 2449 21 995 15 2499 48.5 67.0 18.5 13 8 2711 2.7965 5. 478 44. 3650 16. 342 28. 0230 61.25 94.0 32.75 F I G U R E 5 . 1 2 D I F F E R E N C E IN CZNI V E R S U S D I F F E R E N C E IN [ S A J 60 H 0 10 20 30 40 CHANGE IN SURFACE AREA (m 2 / l) 143 F I G U R E 5 , 1 3 D I F F E R E N C E I N Z N V E R S U S D I F F E R E N C E I N P U L P D E N S I T Y of versus X^  and s^ would have to be a three-dimensional surface. In these circumstances one metnoo available for checking the experimental results would be to calculate the value of X^, by substitution of tne various parameters determined from data taken on the f i rst tanK and the variables 0, X^  and s^, and compare this calculated X^  with the experimental measured value. Table 5.14 summarises the values of D, X^, s^, X2 (calculated) and X 2 (experimental) in respect of the second tank for tne tnirteen straight through mode runs conducted. A perusal of X2 (calculated) versus X2 (experimental) values in Table 5.14 shows significant differences. So it was concluded that perhaps the values of f, v and K as determined from tanK 1 data were not applicable to tank 2. Thus non-linear optimization techniques were adapted to calculate the values of v, f and K. Two optimization programmes - POWELL and FLETCH (modified version of the subprograms VA 06 A and VA 10 A respectively from the Harwell Subroutine Library, Tne Atomic Energy Research Establishment, Harwell, England) were used to determine the values for the parameters v, f and K wnicn gave minimum least squares between calculated and observed values of X 2- Table 5.15 compares, the calculated and experimental values of X2 based on these calculations. The agreement between tne calculated and measured values is good except for run 5. The values for the parameters, wnen compared to tne values obtained 145 in section 5.4.3.2 for tank 1, snow that f is about the same, K is slightly smaller but v is decidedly lower. The value of 0.0198 obtained now seems more reasonable. (See Section 5.4.5). How can we justify the nigner value of 0.031 obtained in section 5.4.3.1. A closer IOOK at the pulp densities and tne amount of concentrate added to tne f i rst tank inaicates tnat presumably more concentrate was addea to the f i rst reactor than the organism could handle in relation to its acio-proauction potential and hence tne elevated value for v. In fact run 5 clearly snows that due to the addition of an excessive amount of concentrate the results obtained in that run do not f i t the model. 146 TABLE 5.14 Oata for Secona TanK Straignc Througn Mode .J,un MO. J I lucion n 1 .'•las .-iH d From T r u g / 1 i u r raca A r e a Cone. m~ < 1 ;ie r- .'IH | d 1 Calculataa T i g / 1 1 1 :;ec 'in i ixaerimsn Z21 rag/ i 1 0.0113 171 5.439 212.51 193 2 0.0093 ~-l 12.503 359.03 320 3 0.0098 15.535 466.30 415 * 0.0093 1 ^  n 15/533 572.51 - - ,~ 3 L 3 5 0.0035 473 56.299 1157.44 6 0.012 424 44.529 715.32 509 ! - 0.013 1:3 5.794 131.41 ! 135 i 3 ii. ^1" 22.434 i •-i ! 3 79 i 1 0.013 ! 347 24 -923 507.04 i t j 10 0.013 1 25. .'25 513.70 i i - 1 0.015 1 i 34 7.735 ! 34.52 i •' -| 1? 0.015 L52 21.595 ; i 230 1 ,-. <M ; l ' v . u l : 1 i 207 15.342 292.99 252 147 TABLE 5.15 NET AMMONIUM ION VALUES CALCULATED ON THE BASIS OF THE FOLLOWING VALUES FOR THE CONSTANTS f , K AND v f= 0.348 m2/mg v = 0.0198 r> - 1 K = 11.032 m 2/l f<UN NO. CALCULATED EXPERIMENTAL VALUE VALUE 1 197.43 198 2 321.38 320 3 417.72 415 4 522.90 519 5 903^.09 620 6 607.39 609 7 179.28 185 8 373.40 379 9 447.73 449 10 556.71 555 11 73.04 72 12 232.89 230 13 261.18 262 148 5.4.3.3 Conclusions from tne Straignt Througn Mode Runs Table 5.16 presents a summary of the feea rate, proauct removal rate, dilution rate, concentration of zinc in solution in each of tne reactors, percentage extractions and the rate of zinc production in respect to each run. It can be observed that zinc concentrations as high as 117.5 g/1 were recorded in continuous runs. However, it should be pointed out that such a nign concentration was not accompanied by high percentage extraction. Nor did the highest extraction rate of 1527.5 mg/l.h recorded in these runs, produce a nign percentage extraction. The highest percentage extraction recorded was 93.8 which occurred at tne lowest extraction rate A summary of zinc mass balances is given in Table 5.17. In the f i rst run tne losses were hign due to condensation of moisture on tne canvas cloth which was directing the concentrate from tne disc feeder to the tank. Concentrate tended to adhere to tne canvas and did not get into the tank. In tne subsequent runs tne canvas was replaced by a plastic material and the l ia covering the disc feeder just above the tank was left sligntly open to allow any moisture to escape. Care was taken to scrape and wash any solids on the tank walls ana baffle plates back into the tank. After that the loss of zinc was less than 1 percent for 12 out of the 13 runs. TABLE 6.16 SUMMARY OF TWO STAGE CONTINUOUS STRAIGHT THROUGH RUN RUN NO. FEEO RATE PRODUCT REMOVAL DILUTION RATE CONCN. OF IN SOLUTN ZINC PERCENTAGE EXTRACTION RATE OF ZINC ION PRODUCTION II/in in RATE 1/h Ii 1 1 stage 9/1 2 stage 9/1 1 stage 2 stage iuq/1 II 1 0 310 0.309 0.0118 19. 0 32 5 54 4 93 8 386.8 L . 0 5S0 0.265 0 0098 36. 5 60 7 48 7 81 4 594.9 3 0 710 0.256 0 0098 50. 0 80 0 51 8 83 8 784.0 '1 u 1J20 0.255 0 0098 66. 0 106 5 51 8 85 2 1043.7 5 1 200 0.220 0 0085 77. 5 117 5 41 0 62 7 998.8 6 1 2i>o 0.340 0 0130 67 5 100 0 52 .1 77 I 1310.0 1 0 720 0.34U 0 0130 32. 6 62 5 43 3 84 8 812.5 8 1 ObU 0.340 0 0130 40 0 72 0 37 .1 66 9 1527.5 y 1 212 0.339 0 0130 62. 5 93 0 42 0 74 9 1209.0 lu 1 650 0.338 0 0130 57 5 112 .5 33 .7 66 2 936.0 11 0 493 0.390 0 0150 26. 5 39 5 57 .6 90 1 592.5 12 0 .9UU 0.388 0 .UlbO 48 6 67 .0 55 .1 76 .3 1005.0 13 1 196 0.390 0 0150 61 3 94 0 57 .1 88 3 1410.0 150 TABLE 5.17 SUMMARY OF ZINC MASS BALANCES Loss Input Output Loss Percent g g j j 254.039 257.791 5.243 2.30 463.457 465.759 2.593 0.56 504.736 598.703 6.023 0.97 733.501 730.377 3.224 0.40 1,022.088 1,012.033 9.093 0.37 1,073.192 1,065.244 7.943 0.72 613.253 510.735 2.517 0.40 394.323 392.212 2.115 0.23 1,032.309 1,025.432 6.327 0.64 1,405.401 1,400.543 5.327 0.54 0 . 9 ; 419.908 415.714 4.194 334.706 332/519 2.087 ' 0.24 1,046.935 1,017.320 7.590 0.73 151 5.4.4 Two Stage Continuous Runs in Recycle Mode Tne data for the continuous leaching experiments witn recycle are tabulated in Appendix 5.4. A sample calculation for one steady state is given in Appendix 5.5. 5.4.4.1 The First Reactor The equation whicn gives X ,^ tne microbial concentration in reactor 1 when the microorganisms and tne sedimented slurry are recycled is: (3.53) AT" f (A - 1) where, A = 0 (3.54) V + 1(1 + Y ) « - Y JD 152 Trie parameters K, f and v are constants. If the recycle ratio, y and tne fraction of solids to recyle 6 are constant, then, the variables are X, and D. As before (See Section 5.4.3.1) for various dilution rates, series of values for X-^  ano coulo oe obtained and plotted to obtain values for v, K and f. Figure 5.14 shows the plot of Net NH^  concentration against surface area concentration. However due to tne lack of sufficient data points it was felt tnat tne optimization procedure described in Section 5.4.3.2 would give a more reliable value for the parameters v, K ano f. Table 5.18 gives a summary of the data obtained in runs 14 to 19 from the f irst reactor. Tne optimization program Powell referred to in Section 5.4.3.2 gave the following values: v = 0.029 n . - 1 f = 0.345 m2/mg and K = 12.4 m 2/l It can be observed that even at "steady state", tnere was a slight change in tne pulp density in the f i rst reactor whicn increased over a day's operation by the percentages given 153 TABLE 5.18 Summary of Data from F i r s t lank in Recycle Mode Operation Residue Pulp SSA S from 1.1. Densi ty 1 to T in T 1 1 2 2 g_ percsn I: m / j !!L_/_L 14 0.0188 32.5 17.652 7.169 0.5315 37.5186 16 U.U188 48.1 11.297 0.5212 58.881 16 0.0188 68.75 39.432 15-679 0.5254 82.3775 17 0.0255 32.6 85.840 11.891 0.5387 58.6644 18 U.0255 72.1 22.365 0.5228 116.9242 19 0.0255 47.5 53.932 14.612 0.5359 78.2521 Kim Di Iuf ion 7 inc Mo. Rate Cone. in I -1 1 Il g/ I X X Extraction 1 1 Experimental Calculated mg_/_l IE9/J Po rcoji 150 150.6 66.0 260 260.0 6 7.1 111 410.8 67.3 199 199.4 63.1 491 493.5 68.0 303 308.I 63.8 155 in Table 5.19. Tnis indicates that tnere was accumulation of tne slurry in the f i rst reactor due to addition of excess concentrate. The increase in the pulp density was between 0.26 percent - 0.36 percent of the contents of tne tank. Altnough tne increase was only slight, it should be pointed out that the rate of addition of the concentrate was in excess, albeit marginally, of what was required for the system to attain steady state. As was pointed out in Section 4.5.3 occasionally tne pH of tne tanK could not be maintained below 2.5 by the organisms and acid was added periodically to ensure that the pH of the slurry in reactor 1 was below 2.5. Altnough the rate of addition of concentrate was slightly more than what was required, steady state was attained in spite of the excess concentrate mainly because the amount by wnich it was exceeded was small and also because tne addition of acid helped the organism to continue leaching. However, it is felt that the higher value obtained for the parameter x> may be due to the excess concentrate added in certain runs. 156 TABLE 5.19 Increase in pulp density in First Tank Run Increase in pulp density Number Percentage 14 0.315 15 16 0.264 17 0.361 18 19 0.355 157 5.4.4.2 Tne Second Reactor Equation (3.59) gives the microoial concentration in tne second tank, when the system was running in tne recycle mode. X„ = 28f [D/v - 1] + C* ( C 2 - 46fS9 [1- v / D ] ) 1 / 2 2 £ (3.59) 2f [D/v - 1] where, = v + L U + Y ) 5-YJ D X L ( 3 ' 6 0 ) C = S2 (1 - v/D) + K + Sf (3.61) This is a non-linear, secono-order equation in tne variable X-?. The other variables are Xp S 2 , y, 6 and D. Even if y» <$ and D are kept constant the resultant equation has three variables. As before (See Section 5.4.3.2) tne best metnod would be to use the optimization program to obtain the optimum values for tne parameters v , K, ano f. Table 5.20 summarizes the results of tne six runs conducted with recycle. Table 5.21 compares the experimental values obtained for X2 amd also gives the optimum values of v , K and f. The values obtained for the parameters are in gooo agreement with tne values obtained for the second reactor in the case of the straight through run. Table 5.22 gives a summary of tne values obtained for the parameters, v , K and f. TAISLE !i.20 Summary of Data from Second lank in Recycle Node Operation Run No. 0 i hit ion Recycle Fract ion Concn.of S Exper i men la 1 Calcula'.ed Extract k Kale Rat i o , y of sol iris SA in Value X 2 stage to Recycle Stream for X 2 i to T 2 2 -1 h 2 2 2 in 1) in / 1 my / l my /1 Percent T l 0.11188 11 .296 0.9587 19.0289 7.51 15 118 118.86 "81 3 lb /i 0.9522 34.5900 16.7773 227 226.42 87.0 16 n Ii 0.9571 43.1231 19.3260 333 333.71 81.7 17 U.()2bb 8.1631 0.9507 26.2323 8.7767 131 130.61 82.6 18 t\ I I 0.9530 49.8274 24.1077 331 329.75 86.2 19 it I I 0.9554 31.61)04 16.0776 203 202.83 80.6 c n CO 159 TABLE 5.21 Comparison of Experimental and Calculated Values of X„ f = 0.346 m2/mg v = O.0195 h"1 K = 11.125 m2/l Run No. X 2 (Experimental) X2 (Calculated) 14 118 118.86 15 227 226.42 16 333 333.71 17 131 130.51 18 331 329.75 19 203 202.83 Table 5 . 2 2 Values Obtained for v , f and K v f K h - 1 m2/mg m 2/l Straight through mode Tank 1 0 . 0 3 1 0 . 3 4 3 1 2 . 5 0 4 Tank 2 0 . 0 1 9 8 0 . 3 4 8 1 1 . 0 3 2 Recyle mode Tank 1 0 . 0 2 9 0 . 3 4 5 1 2 . 4 0 Tank 2 0 . 0 1 9 5 0 . 3 4 5 1 1 . 1 2 5 161 5.4.4.3 CONCLUSIONS FROM RECYCLE MODE RUNS Table 5.23 is a summary of tne recycle runs. Tne concentration of zinc in the outlet solution from tank 2 was generally lower than that obtained when tne system was run in tne straight through mode (Taole 5.16). However, the percentage extraction was less variaole at each stage for tnese recyle runs. In the f irst stage the extraction was between 65 percent and 68 percent. In the second stage it was between 80 and 87 percent. In contrast the extraction in the f irst stage in the straignt through mode varied between 37 and 58 percent and tnat for the second stage it was between 62 percent and 93.8 percent. Tne highest leach rate in the straight tnrougn mooe was 1527.5 mg/l/h. whereas in the recycle mode it was 2326.9 mg/1 n. The reason for sucn a nign extraction rate could be explained as due to the recycle of tne microorganisms and tne larger particles. Tne result of the recycle is to increase tne concentration of micro-organisms and also to increase tne residence time of the larger particles even though tne hydraulic TABLE 5.23 SUMMARY OF TWO STAGE CONTINUOUS RECYCLE MODE OPERATION RUN NO. FEED RATE PRODUCT REMOVAL DILUTION RATE CONCN OF ZINC IN SOLUTION PERCENTAGE EXTRACTION RATE OF ZINC PRODUCT ION g/min RATE 1/h -1 h 1 stage g/i 2 stage 9/1 1 stage 2 stage mg/1.h 14 0.684 0.488 0.0188 32.5 40.0 66.0 81.3 752.0 15 0.992 0.489 0.0188 48.0 62.0 67.4 87.0 1165.6 16 1.420 0.488 0.0188 68.75 86.25 67.3 84.4 1621.5 17 0.968 0.662 0.0255 32.5 42.5 63.1 82.5 1083.8 18 1.988 0.661 0.0255 72.0 91.25 68.0 86.2 2326.9 19 1.400 0.662 0.0255 47.5 60.0 63.8 80.6 1530.0 CT> [\3 163 residence time is shorter. The recycling also permits tne dilution rate to exceed tne straight tnrough crit ical dilution rate without wash-out occurring. Table 5.24 is a summary of tne mass balance of zinc of the runs with recycle. The loss was less than 1 percent in each of the runs. Table 5.24 Summary of Zinc Mass balance for Run No. Input Output g/per day g/per day 14 582.5605 578.7030 15 844.9266 840.4999 16 1209.4716 1197.5372 17 824.4848 821.4159 18 1693.2602 1678.3270 19 1192.4367 1181.7024 Recycle Runs Loss g percent 3.8975 0.67 4.4267 0.52 11.9344 0.99 3.0689 0.36 14.9332 0.88 10.7343 0.90 165 5.4.5 Wash-out Micro-organisms nave a definite doubling (or generation) time. As the dilution rate increases in a continuous culture the concentration of microbial mass in the tank decreases t i l l it reaches zero. The dilution rate at which this happens is called tne cr i t ical dilution rate. If the dilution rate exceeds tne crit ical dilution rate the micro-organisms get washed out. The generation time is tne residence time at wash-out. Wnen the system was operating in the straight tnrougn mode the maximum dilution rate was 0.015 hr \ corresponding to a generation time of 66.7 hours. In one of the preliminary experiments the microorganisms were washed out at a dilution rate of 0.0215 hours (See Fig. 5.15), corresponding to a generation time of 46.5 hours. Hence the actual generation time of T. ferroxidans growing on zinc sulphide concentrate would appear to be between 46.5 and 66.7 hours. The generation time according to the model is: ^ = 52.2 nours. 0.01915 Corrans (1974) found a generation time between 50.0 and 58.8 hours for T^ _ ferroxidans growing on nickel sulpnide. Gormely (1973) reported that the generation time corresponding to tne nignest dilution rate used in nis study was 6.7 nours. As mentioned earlier this was probably due to improper mixing. 166 F I G U R E 5 , 1 5 HASH - OUT OF BOTH REACTORS AT A D I L U T I O N RATE OF 0 . 0 2 1 5 h" 1 60 4 03 - o - O -' i i 1 1 r -60 30 100 120 140 160 130 TIME IN HOURS 167 Other values of generation time for T. ferroxidans include 6.5 to 10 nours on ferrous iron, 7 to 8 days on sulfur, ano 14 to 17 nours on chalcopyrite concentrate (McGoran et_ a1_, 1969). 5.4.6 Dissolved Iron Concentration The dissolved iron concentrations during the various runs are summarised in the tables presented in Appendix 5.2. The dissolved iron concentration in all runs remained quite low. The highest concentration recorded was 4.85 g/1. In general the dissolved iron concentration was proportional to the dissolved zinc concentration (See Fig. 5.16), since tne ratio of iron to zinc in the concentrate was constant and since the pH of the medium was kept around tne same value it follows that the ratio of the metals in solution due to Teaching by the micro-organisms should be tne same for all experiments. In the sterile run, since there were no micro-organisms to oxidise the ferrous iron to ferric iron (which precipitates out) the ratio of iron to zinc was observed to be higher. 5.4.7 Yield Constants Plots of AX VS AS, A[Zn] vs AS , and A[Znj vs AX were made for each tank for both straight through and recycle runs (See Appendix 5.3 and 5.5). 169 The Yield Constants: Y v , = A X X / S A ? Y Zn/s = A [ Z n ] ; A X  Y Z n / X = * ^ ] / A X were determined as the slopes of straight lines fitted to the data. Tne results are presented in Table 5.25. The data is scattered about tne fitted lines, thus the yield coefficients are by no means exact. Tnere is no clear trend in the data wnen yield coefficients are plotted as functions of dilution rate. This is in agreement witn Gormely's (1973) observation. 5.4.8 Nitrogen Fixation When the total nitrogen was determined by tne Kjeldanl procedure (Section 4.6.3.1) it was observed that the amount of nitrogen expressed as ammonium ion in the slurry was in excess of the 820 mg/1 with which the experiment was started. The only explanations possible for this observation were: or (i) a relative increase in the amount of 9K medium due to evaporation. (ii) the T. ferrooxidans fixed atmospheric nitrogen. 170 TABLE 5.25 Average Y i e l d C o e f f i c i e n t s at D i f f e r e n t D i l u t i o n Rates -1 U i 1 u t i o n R a t e (h ) Y i e l d 0.0098 0.013 0.015 0.019 0.026 Constan ts Tank 1 Y X / s 5.93 5.28 3.75 S t r a i g h t Y Z n / s 1.03 0.88 1.09 through Y Z n / X 0 .20 0.20 0.24 mode Tank 2 Y X / s 4 .13 3.89 3.25 __ s t r a i g h t Y Z n / s 0.92 1.23 1.17 — — througn Y Z n / X 0.25 0.27 0.31 , mode Tank 1 Y X / s — 5.32 5.80 Recyc le Y Z n / s — — 1.29 1.40 riode Y l n / X — — 0.19 0.23 Tank 2 Y X / s — 4.81 2.72 Recyc le Y 2 n / s — — 0.82 0 .80 Mode Y Z n / X — — 0.21 0.26 171 To determine wnicn of tne above two phenomena actually took place a batcn run was conducted. In this Datcn experiment a slurry having a pulp density of approximately 10 percent was inoculated and continued as a fed-batch (with ZnS) run. Samples were withdrawn periodically and analysed for zinc and tne total and distil lable nitrogen were determined. Evaporational losses were replenisneo witn disti l led water. The results are presented in Table 5.26. Tne dissolved zinc concentration reached a maximum level of 139.91 grams per 1itre. When the experiment terminated tne total nitrogen concentration in the tank was 26 percent more than tne init ial concentration. Hence it is clear tnat the strain of T. ferrooxidans used in this study was capable of fixing atmospheric nitrogen. A perusal of Table 5.26 shows tnat tnere was about 220-240 mg of disti l lable nitrogen remaining in tne system. It was originally postulated that this ammonia was tied up as ammonio-jarosite and thus was only slowly available to the bacteria (Duncan, 1970). The tank snowed tne characteristic yellow colour. However an evaluation of soluble iron data from tne various continuous runs suggests tnat almost all tne iron was in solution ano thus it is unlikely tnat sufficient iron had precipitated (the equivalent of 2.1 g/1 of iron) to tie up tnat amount of ammonium ion as jarosite. Thus tnere is insufficient evidence available to state whetner the distil lable ammonia 172 TABLE 5.26 Fed-Batch Culture Sample Pulp Zinc Nitrogen Concentration No. Density Cone. + [NH4 ] mg/1 Distillable Total Non d is t i l l able*  Percent g/1 Uncorr- Corrected** ected 1 3.15 17.5 663 826 163 160 2 5.10 27.9 605 821 216 213 3 5.70 31.0 590 825 235 232 4 6.50 35.9 564 817 253 249 5 8.50 46.3 510 821 311 306 6 10.35 56.2 465 326 361 355 7 11.52 62.5 438 826 388 382 8 12.70 70.2 397 830 433 426 9 15.53 85.3 316 826 510 502 10 17.75 96.9 262 830 568 558 11 19.05 103.6 226 830 604 594 12 21.15 115.2 235 898 663 651 13 23.06 125.8 239 956 717 704 14 24.70 135.7 243 1015 767 753 15 25.59 139.9 253 1042 789 775 x Assumed to be nitrogen incorporated into the bacteria **Base line correction (See Section 5.4.2) 173 levels found represent free ammonia readily available to tne bacteria and thus the threshold value at which nitrogen fixation begins or whether the ammonia is bound up in some form whicn makes it unavailable or at best slowly availaole to the organism. 5.4.9 Reduction of Concentration of Surface Area in Feed Table 5.27 gives the surface area concentration of tne feed to reactors 1 and 2. The percentages of surface area concentration reduction in tnese tanks are also included. A perusal of tne data snows that the surface area concentration was reduced by about 50 percent in the f i rst reactor and 80 percent in ootn reactors when run in the straight-tnrough mode. Table 5.28 presents similar data for the runs using recycle. Since material was being recycled to tank 1 the percent reduction in surface area nas no meaning but the data for tank 2 indicates about an 80 percent reduction was achieved during the recycle mode of operation. It is curious that the reduction of surface area concentration in our two reactor system was around 80 percent irrespective of the percentage of zinc extraction and independent of whether the system was operating in a straight through or recycle mode. Gormely (1973) also observea an 80 percent reduction in surface area concentration, regardless of the level of extraction in his single tank reactor. However, interpretation of his oata is complicated by high zinc losses (up to 18.5 percent). TABLE 5.27 Reduction of Surface Area Concentrat ion in the Reactors Operating in St ra ight Through Mode 174 Run Feed Reactor Percentage Reactor Percentage No.. [SA] [SA] Used up 2 Used up 2 2 CSA] 1 32.915 23.451 28.3 6.439 80.4 2 72.064 32.697 54.6 12.303 . 82.9 3 92.273 41.020 55.5 15.635 83.1 4 120.743 51.613 57.3 15.588 87.7 5 181.670 105.228 42.1 66.299 63.5 6 123.614 68.287 44.8 44.629 63.9 7 7U.372 31.266 55.9 5.794 91.3 3 103.535 48.055 53.6 22.484 78.3 9 119.351 57.669 51.7 24.928 79.1 10 163.435 71.157 56.5 25.725 34.3 11 42.056 20.024 52.4 7.735 31.5 12 S4.232 37.245 o 5 • 3 21.995 73.9 13 102.202 44.365 56.6 16.302 34.1 175 TABLE 5.28 Reduction of Surface Area Concentration in the Reactors Operating with Recycle Feed Reactor 1 Reactor 2 Percentage Run [SA] [SA] [SA] Used up 2 2 ? nT/1 rrT/1 rrT/1 14 45.802 37.519 7.51 30.0 15 67.315 58.880 15.777 73.2 15 96.820 82.378 19.326 76.5 17 48.951 58.664 8.777 85.0 13 100.059 116.924 24.108 79.4 19 70.423 78.252 16.078 79.5 .176 5.4.10 The Shrinking Core Model According to Levenspiel (1972) the percentage extraction from a solid substrate is a function of tne initial particle size and the dilution rate. Appendix 5.6 gives the details of tne calculations of percentage extractions in reactor 1 for tne 13 straignt through mode runs. The results are summarised in Table 5.29 and plotted in Figure 5.17. The results show that the experimental values are generally greater than the calculated values. Possible reasons for this discrepancy are: 1. The concentrate particles are of irregular shape and hence probably have a specific surface area greater than that of a sphere of tne same diameter. 2. Although one diameter was assigned to each Banco fraction, in practice the fraction consisted of a distribution of sizes. Moreover, tne diameter assigned to each fraction of material is toward tne higher end of the distribution range. 177 TABLE 5.29 Comparison of the Calculated Values of Extraction in Tank One (based on the Shrinking Core Model) with Experimental Values Zinc Extraction No. Di lution Rate -1 Calculated Experimental (h ) Percent Percent 1 0.0118 63.0 54.4 2 0.0098 49.15 48.66 3 0.0098 43.48 51.83 4 0.0098 37.58 51.8 5 0.0085 31.98 40.98 6 0.013 31.25 52.11 7 0.013 43.03 43.31 8 0.013 36.60 37.06 9 0.013 31.87 42.01 10 0.013 25.99 33.70 11 0.015 51.78 51.60 12 0.015. 29.71 55.10 13 0.015 32.12 57.10 178 F I G U R E 5 , 1 7 PLOT OF C A L C U L A T E D E X T R A C T I O N V E R S U S E X P E R I M E N T A L E X T R A C T I O N 65 179 3. Aggregates of small particles could have been classified as large particles curing Banco fractionation. However, in the reactors due to agitation, tney may have been separatee into the component smaller particles. Attrition during agitation could also nave caused a similar phenomenon. It is concluded the shrinking core mooel does not exactly f i t tne experimental data. However in 12 out of 13 runs the shrinking core model predicts extractions tnat are equal or less than tne experimental values (maximum difference is 25 percent). Tnus the shrinking core mooel could be used for design purposes in that it would give a reactor size that would be big enough for tne required extraction. It would be too oig in some cases but would be unlikely to be too small (a more serious defect). Tne design calculations in Section 5.4.11.2 snow now the calculations based on shrinking core model could be used for reactor design purposes. 5.4.11 Economic Considerations of Continuous Leacning Considerable research work has been done on tne bacterial leaching of copper sulpniae minerals ano to a lesser extent on zinc sulphide minerals. Most of the work done has been on the recovery of metal values from low grade or waste 180 material. Concentrates of zinc and copper are conventionally subjected to pyrometallurgical treatment for the recovery of tne metals. At the present state of the art it is most unlikely that bacterial leaching in a, continuous stirred tank would be considered as an economical substitute for the more conventional processes being used. However, bacterial leaching nas a number of advantages which warrant the need to consider it as an alternative method in tne future. 1. Biological leaching can oe used to treat concentrates which are not amenable to conventional treatment due to the presence of otner constituents, (example lead-zinc concentrates). 2. The leaching process can be useo rignt at tne mine site, thus reducing transport costs. 3. The method is air-pollution free. 4. The waste acid produced can be used for the treatment of oxioe minerals or for enhancing microbiological leaching of alkaline metal 'bearing waste rock. 5. Capital and operating costs, in comparison to smelter operations, are low (Corrans et_ al_, 1972). 181 6- The scale of operation could be increased by tne addition of more units without much additional cost. 5.4.11.1 Feasibility For the bacterial leacning of zinc concentrates to oe economically feasible, hign metal extractions and nigh metal concentrations must be achieved. It has been demonstrated tnat metal concentrations as high as 117 g/1 could be achieved in biological oxidation systems, by using finely ground concentrates in continuous stirred tank reactors. It is well Known that T. ferroxioans is an aerobic organism tnus 0^  is required for tne leaching process. Moreover it gets its carbon from CO^  in the supplied air. Thus gas to liquid to organism transfer of 0^  and CC^ is an important aspect of the design of any microbiological leaching process. In the present study gas was spargea into tne leacn tanK under tne impeller, Duncan et_ al_ (1964) have suggested tne use of equipment similar to that used in activated sludge plants, Duncan and Bruynesteyn (1970) proposed the use of surface cone aerators. Tnus a variety of techniques is available. In any 132 system design the aeration equipment selected must be able to suppy the required amounts of and Cil, keeping tne concentrate particles in suspension at minimum cost. In commercial operations tne most easily controlled factor is the pH. In batch or continuous operations there are a number of concentrate properties that affect the pH. Tne presence of acid-consuming gangue in the mineral will tend to raise the pH. Further, certain oxidative reactions involving zinc sulpnide could be acid consuming. However, as found by Duncan and Trussell (1964) and observed in tne present study, a favourable pH could be maintained even in tne presence of alkaline gangue if tne concentrate contained pyrite or some otner form of iron sulphide. Most zinc sulphide concentrates contain varying amounts of iron sulphide and the amount contained is usually more than enough to generate the acid needed. • 183 Torma (1970) stated that the leacnate solution is suitable for zinc recovery by electrowinning if tne concentration of zinc is between 80 and 120 grams per l i t re . Seven out of the 13 runs in the straight through mode and 2 out of tne 6 runs in the recycle mode gave final zinc concentrations of over 80 grams per l i t re . Although these experiments were not conauctea witn the idea of obtaining the highest concentration of zinc possible it has amply demonstrated that it is possible to ootain the nign concentrations approaching that required for electrowinning. Due to the inherent nature of continuous stirred tanK reactors it is not possible to obtain very high concentrations of zinc and very high extractions at one and tne same dilution rate and pulp density without recycle of microorganisms, solids, or liquid product (zinc solution). It is necessary to s t r i K e a mean between high extraction rates and very high concentrations. It would appear from tnis worK tnat one of tne serious drawbacks in continuous biological leaching in stirred tanKs is the long residence times required. Tnis arises from tne fact that each system has a crit ical dilution rate and exceeding tne cri t ical dilution rate results in wash-out. The present study has shown that the crit ical dilution rate can be exceeded, without wasn-out, by a very simple, inexpensive process of 184 sedimentation and recycle. Tne equations derived for tne recycle system could oe used to determine the optimum recycle ratio, y, and tne fraction of solids to recycle 6 (in view of tne complexities of equation (3.59), an analytical solution to maximise and X2 is not possible. . Tne optimization routines referred to in section 5.4.3.2 could be used in a case where the numerical values for all other variables are known). 5.4.11.2 Design Calculations As an example of how the results of this study could oe used for designing a large scale reactor the following calculations are presented. Assume that the concentrate contains 60 percent zinc. As we have seen in this study tne concentrate will have to oe ground in a call mill (or preferably in an attrition grinder) to -400 mesh. The particle size distribution would be determined. If it is- determined that tne grinding resultea in a size distribution similar to the one obtained in this study (See Table 5.9) the overall contribution (or percentage extraction) could be calculated in respect of the f irst reactor for various dilution 185 rates and varying pulp densities using the shrinking core moael of Section 5.4.9 and Appendix 5.6. Table 5.30 gives a summary of the calculations made for feed pulp densities of 20 percent and 25 percent and for dilution rates varying from 0.01 h -^ to 0.019 h -'''. (See Appendix 5.6 for details of tne ShrinKing Core Model calculations). Once the contribution of eacn fraction in tne f i rst reactor is calculated, it could be used to determine the diameter of the resulting fractions assuming that each fraction consists of mono-disperse spheres. In other words one can calculate tne particle size distribution of the solios out of tank 1. In tnis calculation it assumed that the overall contribution is due to the leaching of the particles in tne ShrinKing core region. Since the representative diameter of each new fraction is known the new surface area concentration could be calculated (See Appendix 5.7). 186 TABLE 5.30 E x t r a c t i o n on Rates C a l c u l a t e d Us ing the S h r i n k i n g Core Model ^ ^ s . Feed Pu lp ^ v j J e n s i t y E x t r a c t i o n Percen tage D i l u t i o n Rate 20 Percent 25 Percen t 0.010 38.08 33.38 o . o n 36.03 — 0.012 34.22 29.79 0.013 32.58 1 i i 0.014 31.10 1 i 26.93 j 0.016 28.56 j i 24.59 1 0.018 26.41 1 22.66 ; 1 0.019 — 21.78 j i 187 The calculations could be repeated for each fraction and the overall extraction in both tanks can be calculated. Summary of calculations made for a dilution rate of 0.01 h~^  ana feea pulp densities of 20 percent, 25 percent and 30 percent (to tne f irst taak) are presentea in Table 5.31. High pulp density leads to high percent extraction. Too high a pulp density leads to extra expense for mixing ana may interfere with 0^ and CO2 transfer (Torma 1970). So cnoose a pulp density of 25 percent as being within tne acceptable range. Table 5.31 indicates that 57 percent extraction ana a zinc concentration of 85 g/1 could oe calculated from tne snrinking core model. Once the dilution rate (in this case 0.01 n-''") and feed pulp density (in this case 25 percent) are chosen the size of tne tank is easily determined. 25 percent feed pulp density is 25g per lOOrnl which is equivalent to 1 kg/4 l i t res. To nandle 1 Tonne of concentrate per day the volume of each of the two reactors needed is (4000/24) x (1/0.01=) 16,667 l i tres. Tnis reactor volume is definitely very large and therefore seems to be a deficiency of the process. 188 As was observed in Section 5.4.9 tne shrinking core model generally predicts a lower extraction rate tnan tnat observed experimentally. In practice one could expect a higher percentage extraction and zinc concentration. For instance in this study Run No. 4 had a dilution rate of 0.0098 n-''" and a feed pulp density of 20.9587 percent. This run gave an overall extraction of 85 percent and a product naving a concentration of 106 g/1. Tnese can. be compared to tne above figures of 57 percent extraction and 85 g/1 calculated using a ailution rate of O.Oln-''' and a feed pulp density of 25 percent. Tne reactor volume would oe more or less tne same since the dilution rates are practically the same. 189 TABLE 5.31 Summary of Calculations Made on the Basis of the Shrinking Core Model DILUTION RATE: 0.01 h" FEED PULP DENSITY 20 percent 25 percent 30 percent Extraction (Percent) 38.08 33.38 27.79 in Tank 1 Extraction in tanK 39.75 35.34 29.65 (Percent) in Tank 2 of Orig. 24.61 23.54 21.41 Feed . Total (Percent) Extraction 62.69 56.92 49.20 Line Concentration in Proauct 9/1 75.23 85.38 88.56 6. SUMMARY AND CONCLUSIONS 1. A novel two stage reactor configuration for small scale leacning of concentrates was designed and shown to work well. Tne salient features of tne apparatus were a level controller suitable for agitated, aeratea slurries ana a sequential timer wnich was capable of controlling tne automatic operation of tne apparatus. 2. Tne reactors were proven to be uniformly mixed by: (a) withdrawing samples at different heights for different pulp aensities and cnecking tne specific gravities of the slurry samples. and (o) tracer studies using both 'a liquia phase tracer (KC1) and a solid phase tracer (cnalcopyrite). The results indicated near ideal mixing conditions. 3. Continuous microbiological leaching of zinc sulphide concentrate in the two stage reactor was conducted in a straignt through mode and stable steady-states were achieved. 191 The reactors (CSTR) in series were modified for recycle of the slurry/microorganism witn a view to decreasing tne hydraulic residence time in tne reactors to a value less than tne doubling time, without encountering wasn-out. 4. A model was devised for the leaching of zinc concentrate in two CSTR in a straight through mode. Tne various parameters of the model were evaluated using tne experimental data generated:-The maximum specific growtn rate of tne bacteria whicn were attacned to tne concentrate, v, was found to be 0.019b-''" giving a generation time of about 52.2 hours. The surface area occupied by the attached bacteria, f, was 0.345m /mg, or 100 percent ot the surface area of tne residue in tank at steady state. The rate constant, K, (which is a ratio of tne rate of backward reaction to the rate of tne forward reaction represented by equation (3.31) was found to be between 11.0 and 12.5. 5. The model was extended to tne leaching of zinc concentrate in two CSTR in tne recycle mode. The parameters y, f and K were calculated from the data obtained. The values obtained were similar witnin limits of experimental error to those noted in 3. above. 192 6. The maximum specific growth for J_. ferrooxidans growing on zinc concentrate was determined experimentally to lie between 0.015 and 0.021 h - ^. The model predicted a value of 0.019 n-''". These results are in close agreement to those obtained for growth on nickel concentrate i.e. between 0.017 and 0.020 n" 1 (Corrans, 1974). 7. Tne organism T. ferrooxidans used in this study exhibited the ability to fix atmospheric nitrogen wnen tne ammonium ion concentration in the medium was depleted. 8. Although the residence times required for straignt througn runs are of the order of 50 hours, this could oe improved by a simple inexpensive recycle of tne slurry and the organisms. The recycle allows nign dilution rates and hence a bigger throughput and a better conversion. 9. It was snown that the amount of leaching could generally be predicted by the application of the shrinking core model of Levenspiel (1972). 10. A design procedure based on tne snrinking core model is given. 193 6.1 Recommendations for future studies 6.1.1 Optimum numoer of Tanks In the case of f i rst order reactions it has been shown that for a given conversion in a tank (CSTRR) system in series, the two reactors snould be of equal size (Coulson and Ricnardson). In tne present study two reactors of equal volume were used. When recycle was used the second reactor did not have sufficient substrate. Grieves and Kao (1968) nave shown that a three-stage continuous-culture system with a volume distribution of 0.6 : 0-2 '• 0.2 and an input distribution of eitner 1.0 : 0 : 0 or 0.7 : 0.3 : 0 gives optimum utilization of tne substrate. The system studied by tnese autnors is the straight through type. It is recommended tnat future studies examine the optimum numoer of tanks, their volume distribution and the optimum input distribution. 194 6.1.2 Optimum Recycle Ratio As pointed out in section 5.4.9.1 the optimum recycle ratio and the fraction of solids recycled could not be determined. The present study was undertaken without a model being available to guide the aesign of the experiments. 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Appendix 3.1 Derivation of Gormely's Model Recall Equation 3.31: k (s - of) (X - a) = k_x o (3.31) Multiplying k 1 (XS - Xaf - aS+a2f) = k^a (A.l) Dividing ootn siaes oy k-^  XS - Xaf - as + a f = k^.a/k^ i .e. a 2f - a [s +Xf + + Xs = 0 Therefore a = (s + Xf + K) ± L(s +Xf + K) 2? wnere K = K _]_/k Q_ (A.2) (A.3) - 4Xfs] -,1/2 (A.4) Wnen s = 0, a = 0 o = (s + Xf + K) - f(s + Xf + K) 2 - 4 X f s l 1 / 2 2f ( Assume growth rate is proportional to the number attacned: Growth rate r = v.a (A.6) X Substituting for a, we have rx= (v/2f) [(s + Xf + K) -((s + Xf + K) 2 - 4 fXs) 1 / 2 ] (A.7) where v is the maximum specific growtn rate for the bacteria attached. At steady state, (dX /dt = 0) D ( X n_ x - X J + pn Xn = 0 Equation (3.11) For a single tank tne equation becomes D = u x (A.8) 1 ' (A.9) 208 Combining equations (A.7), (A.8) and (A.9) we have D = (v /X r 2f) [( S l+ X :f + K) - (S l+ Xxf+ K ) 2 - 4 f X S l ) 1 / 2 ] (A.10) I .e. 1/2 (2DX1f/v) = (s 1 + X xf + K) - (s x +Xxf + K) 2-4fXs x] (A.11) Squaring both sides of the equation gives (sx+ X :f + K) 2 - 4fs 1X 1= (sx+ X xf + K)2+ (2 DX^/v) 2 - 4(D Xf/v)(s 1 +X]f + K) (A.12) Cancelling common terms -4fs 1X 1 = (4D2 X 2f 2 /v 2)-(4DX 1f/v)(s 1+X 1f + K) (A.13) Dividing botn sides oy 4fX-, on tne assumption that 0 and f ^ 0 - S X = (D 2f.X 1/v 2)-(D/v)(s 1 + Xxf + K) (A.14) Regrouping, X 1 [ ( 0 2 f / v 2 ) - (Df/v)] = S 1 [(D/v) - 1] + (D/v) K (A.15) (Xx Df/v) [(D/v) - 1] = S 1 [(D/v) - 1] + DK/v (A.16) i > e ' Xx = (v/DfJ.S^ K/f[(D/v) - 1] (A.17) Appendix 3.2 Derivation of Equation (3.42) Recall Equation 3.41: D . (AX) = __L(s 2 + X 2f + K) - ( (s 2 + X2f + K) 2 - 4 f X 2 s 2 ) 1 / 2 ] i .e. 2 f D.(Ax).(2f/v) = (s + x„f + K) -[(So + X9f + K ) 2 - 4 f X 9 s „ ] 1 / 2 L L <• 1 1 (A.18) Rearranging [ ( s 2 + X2f + K) 2 - 4 fX 2 s 2 J 1 _ 2 (s 2 + X2f + K) - 2Df(Ax)/v (A.19) Squaring ootn sides, (s2+ x 2f + K) 2 - 4fx 2 s 2 = (s2+ x 2f + K)2+ 4 D 2 f 2 ( A x ) 2 / v 2 - 4(Df/v)(Ax)(s 2+ x 2f + K) (A.20) Cancelling common terms and dividing oy 4f on tne assumption tnat f£0, we nave ( D 2 f / v 2 ) . ( A x ) 2 - (D/v).(_x).(s2+ x 2f + K) + x 2 s 2 = 0 (A.21) 2 1 1 i .e. ( D 2 f / v 2 ) ( A X ) 2 - ( D / V ) ( A / X ) [ S 2 + ( A X ) f + K + X x f j + ( A X ) . s 2 + X X s 2 = 0 ( A . 2 2 ) i .e. ( D f / v ) ( A X ) 2 [(D/v) -IJ - L D ( A X ) / V ] [ S 2 + X x f + K - v . s 2 /D j + X X s 2 = 0 ( A . 2 3 ) i .e. (Df/v)[(D/v) - 1 ] ( A X ) 2 - (D/v) [ s 2 ( l -v/D) + x xf + K ] . ( A X ) + X X s 2 = 0 ( A . 2 4 ) i .e. AX = (D/v) [ s 2 ( l - v/D) + X x f + K] 2(Dt/v)LD/v) - IJ ± (D 2/v 2) [ s 2 ( l - v/D) + X x f + K] 2 - 4 (D2/v) ( A . 2 5 ) 2(Df/v) L(D/v) - IJ Since AX > 0 and (D/v) - 1 < 0 take only tne negative radical. Multiplying the numerator and denominator oy v/D gives: AX = s 2(l-v / D ) + X X f + K - LS 2(l-v/D) + X 1 f + K j 2 2(Dt/v) L(D/v) - Ij 4(Df/v) [(D/v) - IJ X 1 s 2 2(Df/v) L(D/v) - IJ ( A . 2 5 ) 212 Appendix 3.3 Recycle Mass Balances 1. Mass Balances on solids. Taking mass balance on tne intermediate tank gives: Solids in = (1 + YJ.F.SJ^ (A.22) Fraction of solids to recycle = <s (A.23) Fraction to tank two = 1 - 6 (A.24) Mass of solids to recycle = (1 + y).F .s^.6 (A.25) Cone, of solids in recycle= (1 - Y ) .F.S^6/YF = [1 + U M j . s r s (A.26) Mass of solids to tank 2 = (1 + Y) F . S 1 (1 - s) (A.27) Cone, of solids to tank 2 = (1 + Y) S 1 (1-S) (A.28) 2 1 3 2 . Bacterial Balance Taking mass balance on tne intermediate tank gives: IN Mass of bacteria = ( 1 + Y ) . F . X 1 ( A . 2 9 ) RECYCLE Flow of solids x Mass of oacteria so I ias ~ + flow of liquia x Mass bacteria Vol. of liquid ( A . 3 0 ) ( A . 3 1 ) ( A . 3 2 ) i .e . , [ ( 1 + Y ) . F . S ^ . 6 . O / S ^ ] + Y F (x1 - a) = F L U + Y) 6.a + Y ( X r a)] To TanK 2 ( 1 + Y ) F . S 1 ( 1 - 6).a/S 1 + F (x1 - a) ( A . 3 3 ) = F [ ( 1 + Y ) d - 6).a + ( x r a)] ( A > 3 4 ) As a cneck sum up recycle and tank 2 : F [ ( 1 + Y) Aa + Y ^ - a) + ( 1 + Y ) ( l - A ) a + X 1 - a] = F[Aa + Y A O + Y X ^ - yo + ya - Aa - Y A O + X^- a = F [ x ^ l + Y ) ] = Same as IN Summary Bacteria on Bacteria solids liquid I N (1 + Y ) . F . < J (1 + Y ) . F Recycle (1 + Y).F.5.O Y F (x^ -Tank 2 (1 + Y) F (1-6).a F (x1 - a Appendix 3.4 215 Derivation of Equation 3.53 A cell mass balance on Tank 1 gives: V.ldX^dt) = F.XQ + YF[(1 +(1/ y)).6.O 1 + (X1 - a^j - (1 + Y ) . F . X ] _ + V.(d X^dt) . (A.35) Dividing by V and substituting (dX^/atJg = u ^ X; we nave (dX1/dt) = YDL(1 + ( l / y)).6 . a 1 + (X1 - c )^] - (1 + 1 /Y)) D1 X X + V l X 1 (A.35) At steady state, (dX^/dt) = 0 i . e . D [ ( Y + 1) 6.ox + Y ( X 1 - o 1 ) - X 1 ( l + Y)] + u x X X = 0 (A.35) But ^ = va^ i .e. o x [D(l + Y ) .6 -Y) + v] - Xx D[(l + Y) - Y] = 0 (A.38) i .e. a 1 = D.X^L'v + D((l + Y ) « - Y ) J (A.39) Recall equation A.7: r x = a .v.= (a/2f) [ S + Xf + K) -((s + Xf + K) 2 - 4 fXs) 1 / 2 j (A.7) Substituting A.39 in above and inserting tne subscripts, we nave [ ( s 1 + Xxf + K) - ( (s 1 + x : f + K) 2 - 4 f x 1 s 1 ) 1 / 2 ] / 2 f ( A > 4 Q ) = D.X1/[v + D ( ( l + Y) 5 - Y) (s,+ X,f + K)-[(s,+ X-f + K) 2 - 4 f X 1 s 1 ] i / 2 = 2f.A.X, 1 1 1 1 1 1 1 ( A > 4 1 ) wnere A = D/[v + ((1 + Y) 5 - Y) DJ (A.42) 217 Rearranging, L(s 1 + X : f + K) 2 - 4 . f X 1 s 1 ] 1 / 2 = (s 1 + Xxf + K) - 2 A.f Xx (A.43) Squaring botn sides, (s 1 + Xx f + K) 2 - 4fX]_s1 = (s x + Xxf + K) 2 + 4 A 2f X2-4 A.f x (sx + Xjf+K) (A.44) Cancelling common terms, we nave: -4 f Xx s x = 4 A 2 fX 2 - 4AfXx ^ + X^ + K) (A.45) Dividing Dotn sides oy 4 f X^  (X^ i 0, f ^ 0) and rearranging gives: A2 f X1 - A(s + X^ + K) + s 1 =0 (A.46) 218 ,2, i .e. X^A^f-Af) - A (s + K) + s 1 _ 0 (A.47) i .e. Xi = A(s +lK) s l At(A - 1) (A.48) sx(A - 1) + AK At (A - 1) Af (A - 1) (A.49) = (s x/Af) + K / f ( A - l ) (A.50) Appendix 3.5 Derivation of Equation 3.59 Mass oalance on tank 2 gives: V ( d x 2 / d t ) = F.8 - F.X 2 + V ( d X 2 / d t ) = F.8 - F.X 2 + V . p 2 X 2 wnere 8 = (1 + Y ) ( 1 - 6) + (x -^Dividing oy V and rememoering F/V = D, dX 2/dt = D.6 - DX2 + u 2 X2 At steady state dX2/dt = 0 Therefore X2 = De/(D - u2) i .e. (D - p2) X2 = D8 i .e. y 2 = D(X2 - B ) / X 2 Recalling equation A.7 and introducing the subscripts, r x = (v/2f) [(s2+ X 2f + K) -((s 2+ X 2f + K ) 2 - 4 f X 2 s 2 ) I / 2 ] ( A . 5 8 ) Combining A.57 and. A.58, we have, D(X2- e) = (v/2f) C(s 2 + X 2f + K)- ((s 2 + Xgf + K) 2-4fX 2 s 2 ) 1 / 2 ] (A.59) Let X2 - s = AX. (v/2f) [ ( s 2 + X 2f + K) 2 - 4fX2 s 2 ] 1 i 2 (v /2 f ) (s 2 + X 2f + K) - D ( A X ) (A.60) Squaring both sides, (\>2/4f2) [ ( s 2 + X 2f + K)2 - 4fX 2s 2) = (v 2 / 4 f 2 ) ( s+ X 9f + K)2+ D 2 ( A X ) 2 - (v /f)(s 9+ X 9f + K)] (AX) 2 2 2 2 (A.61) Cancelling common terms, gives - (v 2/4f 2)(4f X2 s 2) = 0 2 ( A X ) 2 - (v/f).(AX).D.(s 2+ X 2f + K) (A.62) Rearranging, ( D 2 f / v 2 ) ( A X ) 2 - ( D / v ) ( s 9 + X 9 f + K ) (AX) + X 9 s 9 = 0 L 2 2 (A.63) i.e. ( D 2 f / v 2 ) ( A X ) 2 - ( D / v ) , [s2+ (AX ) f + K + 6 f ] ( A X ) + S 2 (AX) + ss 2 = 0 (A.64) i.e. ( D f 7 v ) [ ( D / v ) - l ] ( A X r - (D/v) [s2+ K + B f - (V/D )S 2J (AX ) + B S 2 = 0 (A.65) Therefore AX = (D2/v) [s + K + 8f - (v2/D) s J / Z ± L ( D 2 / v 2 ) [ S 2 + K + 8f - ( v / D ) S 2 J 2 - 4(Df/v)[D/v) - l j 8 . S 2 J 1 / 2 / (A.66) wnere Z = 2 (D/v ) f [(D/v) - 1] (A.67) Si nip 1 i fying, AX = [s2+ K + ef - (v/D).s 2) / 2f[(D/v) - l j ± [(s?+ K + 8f - ( v / D ) . S 9 ) 2 - 4 8 S 9 f - ( v / D ) J 1 / 2 / 2 f [ ( D / v ) - 1] 1 L L (A.68) 8 = (1+Y)(1-S) a +. ( X R 0 L ) (A.69) i .e. 8 = (Y - 5 - Y 6 ) a x + X X (A.70) But a x = D X x / [ v + ((1 + y)& - Y ) D J Suostituting 8 = (Y — 6 — Y « ) ( D X 1 ) / [ V + ((1 + Y) fi - Y ) D ] + X 1 (A.71) i.e. u = [ ( Y - 6 - Y 6 ) D + v + ((1 + Y ) « - Y J D ] X X/ [ v + ((1 + Y ) DJ (A.72) = [ D ( Y - 6 - Y 6 + 6 + Y 6 - Y) + V] X X / [ V + ((1 + Y ) 5 - Y ) D J (A.73) = v x x / [ v + ((1 + Y ) 6 - Y ) D ] (A.74) (A.75) Substituting A.75 in A.58 gives, X 9 = 8 + [C ± C 2 - 48S 9f (1 - (v/D))] / 2f L(0/v) - I J 6 1 (A.76) wnere C = s 0 [1 - (v/D)] + Sf + K and 8 = v X X / [v + ((1 + y) & - y) Dj ( A ' 7 7 ) 223 Appendix 4.1 Results of Two Runs Made Prior to tne Modifications of tne Apparatus Tne data obtained from tne runs are presented in Taole A4.1. I'AUl.t A4.1 I1AIA fllOM PULI. IMIHAUY UIIN'i Tank 1 Tank 2 Product Kece iver It UK NO. Dale Pulp Z inc Pulp Z inc Pulp Z"inc Dens i ty Cone. Dens i ty Cone. IJeiiS i ty Cone. •%• (g/1) ( g / i ) % (g/D 1 23-05-/6 2.5204 10 2.2306 20 0.491? 21 -1-05-76 2.2554 10 1.9330 20 0.6430 20 25-0S-/6 2.0300 10 !.6002 20 1 .014? 20 26-05-/6 2.U632 10 1.5348 20 0.0264 20 27-05-/6 2.0090 10 1.3660 20 20-05-/6 1.0910 10 1.6660 20 0.9/10 20 29-05 76 1.0/52 10 1.3004 20 0.0620 20 2 7-06-/6 0.6160 12 0.4260 1? 0-06-76 1.1642 12 0.6452 12 U.2662 I 2 9-06-/6 1.1006 11 0.54/6 11 0.464? 1? 10-06-/6 1.2526 12 0.66 36 12 0.6616 12 11-U6-/6 1.1066 12 0.6110 12 0.6194 1? 12-06-/(i 1.263b 12 0.6462 12 0.7406 12 Appendix 4.2 Development of a Level Controller 225 To minimize concentrate 'by-passing' it was tnougnt necessary to nave tne inlet of tne slurry transfer pipe submerged oe'low tne slurry surface. Tnen it became imperative tnat a reliable level control be inccrporated into tne design of tne apparatus. Tne needle valve used ini t ia l ly to set tne flow rate of tne medium to Reactor 1 was found to be unreliable in maintaining a constant flow rate and was replaced by a metering valve. Tnis necessitated tnat a Nupron SS-2F-T7-7 model f i l ter oe added to protect tne orifice of tne metering valve from getting plugged up, due to crystallisation of tne 9K medium salts. Finally, wnen tne level controller described in tnis section was developea, tne metering valve was by-passed. All tne conventional metnods of level control (or modifications tnereof) reported in the literature were tried ana found to oe unsuitable. Any metnoa based on a float activatea aevice failed due to turbulence caused by aeration ana agitation of tne slurry. Any metnod oased on electrical contact witn tne slurry was unsuitaole as it promoted electrolytic corrosion. 226 Metnoas based on sonic sounding could not be used due to tne presence of foams. Init ial ly, a modified method based on tne ouooie-tube system of Perry (1973) was found to be somewhat satisfactory. In this system a constant flow differential regulator was employed in order to eliminate or reduce pressure drop due to cnanges in the gas flow-rate. Since the flow of gas tnrougn tne bubble tuoe prevents entry of the slurry into tne bubble tuoe tnis system is said to be suitaole for slurries. In practice nowever tnere was a slow ouild up of solids in tne dip-tube causing tne system to OIOCK up. The bacx pressure, wnicn was registered by a manometer, could oe converted into a level control device oy tne addition of a lignt source and a photocell. Tne response from the photocell was amplified and used to open or close tne valve controlling tne transfer of medium or slurry to tne reactor. In tne long run, when tnis device was used for level control several snags were encountered. Wnen water or any otner liquid wnose specific gravity was less tnan 1, was used, the level in tne manometer fluctuated violently due to the agitation and aeration in the reactor. This was overcome by using FIGURE A4.1 T Y P I C A L L E V E L CONTROLLER I N S T A L L A T I O N rv> ro xi 228 glycerine as tne manometric f luid. Anotner problem encountered was tnat tne air would escape tnrougn the manometer, olowing out tne manometric liquid instead of bubbling tnrougn tne slurry. On several occasions experiments nad to oe abandoned oue to failures of tne level controller in tnis manner. Even tne incorporation of a 1/3 psi relief valve in tne line did not alleviate tne problem as tne relief valve failed to open at times due to nysteresis in tne valve springs. A specially designed ana constructed relief valve whicn utilized the weight of a suitable stainless steel ball nad to oe abandoned as tnis system was too sensitive to vibrations. Finally tne replacement of tne bubble tube by a Moore Model 19L1 level transmitter resulted in a dependable, and nighly accurate level control system (See Figure A4.1). Tne Mooel 19L1 is a simple, force balance level transmitter device. Tne pressure on tne instrument side of tne diapnragm builds up until it equals tne process pressure, at wnich time the exhaust nozzle opens, maintaining tne instrument pressure equal to tne process pressure (See Figure A4.2). Tne spring rate of tne diapnragm is so low tnat it is extremely sensitive. Tne resulting back pressure is transmitted tnrougn tne manometer whicn in turn controls the feed flow valve. MODEL 62V FLOW C O N T R O L L E R OR NEEDLE VALVE SUPPLY PIPE FOR AIR VENT -MOD 19K1 FIGURE A ' l . 2 LEVEL TRANSMITTER ro to 230 Appendix 4.3 Description of tne Sequential Timer A diagramatic representation of tne seven timers ana tne connections to tne seven relays is shown in Figure A4.3. A scnematic circuit diagram for eacn timer is snown in Figure A4.4. The IC chip XR-2242 (Exar Integratea Systems, Inc., California) is a monolitnic timer capable of producing precision time delays from microseconas to days. In monostable or "self-resetting" mode, tne timing pulse nas a auration of 128 RC Wnen a potentiometer is used to supply the R, tne lengtn of eacn pulse becomes variable. Tne sequential timer was so aesignea tnat once tne timer is triggered it would continue to operate in its astaole or "free-running" mode indefinitely. 231 F I G U R E A 4 . 3 BLOCK DIAGRAM OF TIMERS AND THE CONNECTIONS TO THE RELAYS 0.1 F I G U R E A M SCHEMATIC C I R C U I T DIAGRAM OF ONE T I M E R 233 Appendix 4.4 Procedure for Mixing the Concentrate To ensure tnat tne concentrate was well mixed and uniform in composition it was poured from tne two drums to one pile shaped in the form of a cone. Tne cone was flattened and divided into four parts. Eacn part was piled into a cone snape. Shovelfulls of concentrate from eacn cone were taken sequentially and passed tnrougn a splitter (1:1 ratio). All tne concentrate from the four cones was sent tnrougn tne splitter and tne output of tne splitter including tne reject was piled into a single cone. This process was repeated tnree times. The splitter ensures uniform splitting of tne concentrate. To ensure furtner olenoing of tne concentrate the splitter was rotated oetween eacn shovelful! so tnat the output of tne splitter fel l in different positions on the neap. Tne concentrate was made into a rectangular oed aoout 6 feet (1.8m) long, 3 feet (0.9m) wide and aoout 4 incnes(10 cms) nign. The oed was partitioned into forty plots as snown in Figure A4.5. 234 F I G U R E A4.5 P A R T I T I O N I N G OF T H E P L O T C 1 2 C 1 3 C 1 4 C 1 5 C 2 1 C 2 2 C 2 3 C 2 4 C 2 5 C 3 1 C 3 2 C 3 3 C 3 4 C 3 5 C 4 1 C 4 2 C 4 3 C 4 4 C 4 5 C 5 1 C 5 2 C 5 3 C 5 4 C 5 5 C 6 1 C 6 2 C 6 3 C 6 4 C 6 5 C 7 1 C 7 2 C 7 3 C 7 4 C 8 1 C 8 2 C 8 3 C 8 4 C 8 5 ~< — 0-9 m _ 235 The concentrate in eacn plot was passed tnrougn a splitter (1:20 ratio) and samples withdrawn from eacn split were accumulated, composited, and labelled Dy tne plot designation. The split samples were pulverized individualiy, and dried in tne oven at 60°C for three days. 236 Appendix 4.5 Air Permeaoility Method for tne Determination of Specific Surface Area Specific surface area (surface area per unit mass of solids) of the concentrate and of the various leacn residues from eacn ana every run were determined according to tne method described in A.S.T.M. C.204-75 using tne Blaine air permeaoility apparatus (Figure A4.6). Tne Blaine air permeability apparatus consists essentially of a means of drawing a defined quantity of air tnrougn a oed of defined porosity. The number and size of tne pores in tne prepared bed of defined porosity is a function of tne size of tne particles and determines the rate of air flow through the bed. The procedure for tne determination of tne specific surface area using tne Blaine apparatus was relatively simple. The permeaoility cell nas a plunger ana after a few repeated tests one could ootain a feel for tne required compaction. Tne volume of tne prepared oed was determined using mercury to f i l l tne void space above tne bed and anotner determination with no sample. FIG. A4 .6 BLAINE AIR PERMEABILITY APPARATUS r Male Valve of clamp 14.5 cm 16.,0 cm I 4 .0cm T 5.5cm| 1.5cm fcoup l in < fit bott (.of cell g to om 1.6cm I d ia »• PLUNGER Flat,-0.3 cm wide .G lass tube, 0.9 cm 0 0 Length to give 1.5 ± 0.1 c m depth of bed Clearance between plunger and ceil not more than 0.01cm 1.27 ± 0 . 1 cm di; 3 0 - 4 0 , m m holes distributed Perforated brass disc couplinq to fit top of manometer 0.9 ± 0.1 mm Filter paper MANOMETER CELL AND PLUNGER 238 Tne weignt of sample required to produce a oed naving a porosity of 0.500 ± 0.005 was then calculated using tne equation: W = p V (1-e) (A4.3) wnen, W = grams of sample required p = specific gravity of sample 3 V = bulk volume of tne prepared oed in cm and e = desired porosity of oed (0.500 ± 0.005) The time for a definite quantity of air to oe drawn tnrougn the oed was measured to tne nearest 0.5 seconds. Tne instrument was calibrated using a Standard Reference Cement Sample ootained from National Bureau of Standards, Washington D.C. 20254, U.S.A. The time of flow witn tne standard sample was measured five times witn separately prepared oeds of tne standard sample. Only values of tests wnicn were witnin 2 percent of eacn otner were accepted. For tne concentrate samples tne tests were 239 also repeated until two determination gave values wnicn were witnin 2 percent of eacn otner (ASTM requirement). Tne specific surface area was calculated using tne following formula: ss _ [ss s .p s . ( l - e s ) . e 3 . T]/[p(l-e) e 3 . T $ wnere: (4-4) 2 ss = specific surface of tne test sample cm /g ss s = specific surface of tne standard sample used in calibration of tne apparatus, cm /g T = measurea time interval in seconds for tne manometer to drop tnrougn tne specified neignt for test sample T$ = measured time interval in seconds for tne manometer to drop for tne stanaard sample used in calibration of tne apparatus e = porosity of prepared oed of test sample 240 e $ = porosity of prepared Ded of standard sample used in calibration of apparatus p = specific gravity of test sample and P s = specific gravity of standard sample 241 Appendix 4.6 Experimental Procedure for tne Determination of Nitrogen Tne metnod involves tne determination of total ammonium ion concentration and distilIable ammonium ion concentration. Tne oisti l iable ammonium ion concentration is a measure of tne inorganic nitrogen and tne total ammonium ion concentration would give an indication of ootn inorganic and organically oouno nitrogen. Hence tne difference gives an estimate of organically Dound nitrogen wnicn snould oe proportional to tne oacteria! concentration. To determine tne total ammonium concentration, 2ml of slurry sample are digested in a Kjeldanl flasK with 5ml of concentrated sulphuric acid and a Hengar selenized ooiling granule. Tne digestion is carried out in a fume hood over a Bunsen flame over 3 to 4 nours. Tne digested sample i s transferred to a micro-Kjeldan! steam s t i l l (W. Buchi, Switzerland); about 10ml of 50 percent sodium nyoroxide is aadea to ensure that tne mixture is strongly alkaline ana is tnen steam dist i l led. Tne disti l late is collected in 250ml Erlenmeyer flasks containing 5ml of saturated D o r i c acio and 3 drops of an indicator which is made up of one part 0.2 percent metnyl red and five parts 0.2 percent bromocresol green in ethanol. After aoout 242 75mI of disti l late nas been collected, it is titrated against 0.01N HCl. For tne determination of tne disti l laole ammonium, a 2ml sample is transferred to tne micro-Kjeldanl steam s t i l l followed oy 5ml of 50 percent sodium nydroxioe. Tne rest of tne procedure is tne same as for total ammonium ion determination. Appendix 4.7. Properties of Slurries A Calculator Program (for HP 41C) was developed on tne oasis of these equations: M = 100 P L - S G S G = n o W T 7 S F ^ L 7 L M.W  W = 100[(M.pL - l)/,Mj [s/(s p L - l ) j ( M > 3 ) W = V . S G / M (A4.4) S G = 100.M. - (100-V) P L V (A4.5) V S G +(100-V) p. M _ L_ TW (A4.6) V = 100[(M - P L ) / ( S G - P ^ J (A4.7) wnere, SG - specific gravity of solias W - percent solids oy weignt M - specific gravity of tne slurry V - percent solids Dy volume p.- specific gravity of liquid Tne algoritnm of tne program may oe followed easily oy tne Flow Chart given in Figure A4.7. Tne program is as follows: F I G U R E A 4 . 7 FLOW CHART FOR CALCULATOR PROGRAM 15 SF m za sio u zi * v = ?• 2b ' iV a C-" J.8JJ C'v' * vitLBi. "SLURRY* 54 &L 83 CLRG 84 CF St, 85 CF Si 3c 188 66 Cf 82 59 RCL 82 6? CF 83 ce -Hit CF 22 bl kCw 63 83 • oi * 18 Sit 85 b2 RCL 82 11 "SF. SR. Or RES!' M RCL 85 12 "riiH ••" 13 F'ROilFT 14 FS?C £2 Kl x 66 r ?? B5 JJ sT0 68 69 RCL 82 16 ' H = ?" - •« 1? PROMPT * 16 FS?C 22 71 &3 72 / 73 STO 81 74 XES 93 22 PROMPT ^ L B L 22 23 FS?C 22 76 M 24 SF 11 7? 16S 25 STO il * 79 188 27 PRQfi?! 68 KCi. Cl 28 FS?C 22 8*. -29 SF-62 62 RCL 85 38 STO 82 63 * 31 • s * r ft -32 PROMPT 85 ftlL 81 33 FS?C 22 So • 34 Sf 83 8? STO 83 35 STO 63 63 RCL 81 36*LEL 88 69 * 37 FS? 88 58 KCL 88 3b GTC 8: 51 ••' 33 FS? 81 52 SFO 82 48 GTO 62 53 XES 93 42n.fei. 81 5v K: 88 43 FS? 61 Si K L 82 44 XE6 22 5? * 45 FS? 62 98 166 4b XES 23 59 RCL 62 47 X£y 2- 168 -4g*LSl 62 161 KCL 66 43 FS? 82 i&2 RCL 65 58 XZ« 25 163 * 51 XE« 26 164 3 52»LBL 2: 163 106 53 KCL 63 l6o KOv 54 RCL 85 Ia? -16b / 247 189 STO 63 lie RCL 22 111 RCL 88 112 * i 13 K/V i 14 / 115 ST ii 8i 116 X£y 99 i i r *LSL 2'4 lib' RCL 66 i i $ RCL 85 126 * 121 1 . 122 -123 RCL.68 124 / 125 RCL 83 126 RCL 83 12? RCL 85 i i O * 12=? 1 13o -i 3 : / 132 * 133 188 134 * 136 RCL 89 137 * l3e RCL 63 139 / 148 STO 81 141 x£§ 9'? 14*i*LSL 143 188 i •»» R\j'L 81 i4-j -146 188 14c fiUL 62 i 4 r / iod KCL 85 151 * 132 370 88 153 RCL 62 154 •* 155 RCL 81 15b / 83 iOvi X£Q 99 159^ L8;. 26 iii RCL 83 162 * ia3 1S8 164 RCL 81 1 •' c _ i O J -166 RCL 65 167 * It-:? r 169 188 i?9 / 171 STO 88 172 RCL 81 173 RCL 63 174 * 175 XOr 17b / 177 .STO 82 173 X£8 99 i?9*LBL 99 138 * ft=-1S1 "h-132 SRCL 38 1S3 XE5 SS 184." V=' 185 'r-' 13b BRCL 31 187 X£S 83 188 * K=" 159 " r \ 198 fiRCL 82 191 X£S S3 193 194 fiRCL 83 135 XEfi 83 136 G70 98 137*LBL 85 138 HY'lEa 288' PS£-281 R7H 292*LBL 38 283 CF 38 284 CF 81 285 CF 32 286 Cf 83 287 CF 21 28o CLfi 289 flOFF 218 STO? 211 EHB 248 Appendix 5.1 Detailed Experimental Data for Mixing Characteristics Experiment Taole A5.1 gives tne detailed results of tne oata ootained from tne experiments. rat'lo A5.1 D a t a f rom M i x i n g C h a r a c t e r i s t i c s f. \\ter intpnI. AI'PROX. PULP DENSITY HE Hil l I or SAMPLIMG POINT KKUH HOT 1OM OE TANK ( III INCHE.s) WE I BUT OF 50 ml SAMPLE III GRAMS 10 12 11 l f i 25 0 . 125 5 0 . 1 1 8 3 507'jfifiH 7 / 5 9 6 52 .5659 63 .3692 51 . 1669 51 . 9 / 8 9 55 . 763 3 56 .68.16 57 .3991 6 l .0013 1 .125 5 0 . 1 4 8 8 5 0 . 9 6 9 0 51 .7492 52 .5649 53 .3586 54 . 1 / 1 5 51 .9701 55 .7672 56 .6791 5 7 . 3 9 5 5 61 .0121 2 . 1 2 5 50.15-12 50 .9642 51 .7501 52 .5502 • 53 . 3574 51 .1602 54 . 9 8 2 8 55 . 7693 66 . 5 / 0 0 5 7 . 3 9 4 / 61 . 0063 3 . 1 2 5 50 .1482 5 0 . 9 6 2 3 51 .7167 52 .6672 53 . 3646 51 .1635 61 .9611 55 . 7 5 / 8 56 . 5 7 8 / 5 7 . 3 0 7 9 61 . 0 0 5 6 1 . 1 2 5 50.112.1 5 0 . 9 6 1 8 51 . 7 1 9 0 52 .5656 53 . 3605 54 .1711 54 . 9 7 7 6 55 . 7573 56 .6731 5 7 . 3 9 0 5 61 .0061 5 . 1 2 5 5 0 . 1 3 6 / 50 .9632 51. .7531 52 .5586 53 .3628 61 .1739 51 .9638 55 . 7523 56 .5762 5 7 . 3 9 6 5 61 .0064 6 . 1 2 5 5 0 . 1 5 4 / 50 .y6O1 51 . 7621 52 .5625 53 . 3546 54 .1757 54 .9771 ' 55 . 7513 56 . 5715 5 7 . 3 9 6 9 60 .9999 / . 1 2 5 50 .1501 5 0 . 9 5 8 3 '51. .7118 52 .5621 53 .3638 54 .1681 51 .9611 55 , .7551 66 , .6672 5 7 . 3 9 8 6 61 .0161 8 . 1 2 5 5 0 . 1 5 6 9 5 0 . 9 6 8 0 51 .7473 52 .5670 53 .3514 54 .1619 51 .9817 55 .7641 56 .5750 5 7 . 3 8 9 1 61 .0072 9 . 1 2 5 50.15.14 50 . 9198 51 . ,7611 52. .5551 5 3 . . 3 5 0 / 54, . 1703 5 1 . .9818 65 . .7603 56 . 6922 5 7 . 3 8 5 2 61 . 0 0 / 6 1 0 . 1 2 5 50 .1191 5 0 . 9 1 8 5 51 .7659 52 .6582 63 .3571 51 .1655 51 .9712 55 . .7611 56 , . 6902 5 7 . 3 9 5 0 61 . 0129 11 .125 5 0 . 1 5 5 / 50 .9631 5 1 . 7503 52 . 5524 5 3 . 3586 5 1 . 1653 5 1 . 9 / 3 2 5 5 . 7684 6 6 . 5819 5 7 . 3 8 7 2 61 . 0011 A v e r a g e W e i g h t (W) 5 0 . 1 4 9 8 5 0 . 9 6 1 6 51 . 7525 62. .561.1 5 3 . ,3691 54. , 1 6 7 / 5 1 , . 9 / 3 7 55 . 7606 56 . 6785 5 7 . 3 9 3 2 61 .0073 S t a n d a r d d e v i a t i o n ( n ) 0.011,5 0 .0161 0 . 0166 0 . 0135 0 . 0135 0 . 0191 0 . 0165 0 . 0135 0 . 01907 0 . 0 1 6 6 0 . 0191 99 p e r c e n t C o n f i d e n c e I n t e r v a l Max 50 .1634 50 .9752 5 1 . /661 5 2 . 5723 5 3 . 3706 5 1 . 1831 5 4 . 9902 6 5 . 7718 5 6 . 5976 5 7 . 1 0 6 0 61 . 02 31 Min 5 0 . 1 3 6 ? 6 0 . 9 4 8 0 5 1 . 7389 5 2 . 5499 5 3 . 3182 5 1 . I 520 5 4 . 9 6 / 2 7191 5 6 . 6591 57 .8804 61 . 9815 Appendix 5.2 Results of Continuous Straignt Tnrougn Mode Operation Tne results of tne continuous straignt tnrougn mode are presented in tne Taoles A5.2 to A5.4. Table A5.2 gives tne uncorrected zinc concentrations for tne f irst tank wnile table A5.3 gives tne corrected data for Tank 1. TAIiLt A6.2 DA IA fkllM IANK ONE LOU CONTINUOUS I.EACIH lllj IN S IKAI Gil I fllKOlltill MODE (ZINC V AL DL S ONCOKKEC IT D IOH CHEMICAL LEACHING) M-1 CHIC KDM IINiSLK DU III IDU KAIL HI 1151 1 Y rtKCLMI 5IIKf ACE AKI: A '> 2 _ / ! I'M Eh [Fej t Zn] r Z Z in / I J in ' J / ' 1L/1 i |/ 1 Ii L. _._il/J'^!L 9.6x10" 3 . 1 (J .ul ia 2 .6003 0.93/9 23 .1600 2.1 540 0 .760 19 .0 0 .2212 0 .0090 Ii . 2 0 4 O.620J J2 .6966 2.4 496 1 .45 36 .5 0 .2501 I . 1 x10" 2 0 .0098 / .1)336 0.6415 41 .0200 2.1 560 1 .95 60 .0 0 .4910 1 .19x10"^ 'i 0 . 0091! 9 .91011 O.52U0 61 .6131 2.3 520 2 .60 66 . 0 0 .6 15/ 1 . 2 3 x l u " 2 0 .0085 ia .319/ 0.5/11 106 .2201 2.00 460 2 .00 / / .5 0 .1)549 6 . 2 x i i r 2 i> ( 1 .0130 10 .//It) 0.6340 60 .2671 2.3 465 2. .6 67 .5 0 . 1 1 / / ! . , 1 .2x10 ? 7 0 .0130 c . 964 J 0.1409 31 . 2otiO 2.5 610 1 . .26 32 .6 0 .4231! 1.36x10"" a O .0130 11 .3006 0.1252 • 1 0 .054/ 2.1 610 1 . .66 40 .0 II .6200 l . o o x i o " 2 9 U .0130 11 .999.' U.-10U6 6/ .550/ 2.6 500 1 . .95 52 .6 0 .1.825 1. lax I ii"'-' ID 0. .01 30 ia .aai 0.3/69 7! .15/0 2.5 160 2. .26 67 .6 t) . / 1 /5 1.05x10 11 tl. .U13U 3 . I ) 9 I J 0.6160 20 .02 36 2.3 600 0. .95 26 .6 11. .3015 1.91x10"' 1 2 1). .011)0 7 . 19', 0.5l/t> 37 .2149 2.6 530 1 . 06 40 .5 0 . . /25b 2 . I2x l0" 2 i j U. .011)0 a .2 / ' I I 0 .5362 41 .36511 2.1 610 2 . 60 61 .25 0 . .9 In 1 2 . 0 / / H f 2 . . - - . ro on rAIM.if IIAIA II (OM I/UIK ONE TDK am I INUOUS LLACIIi NG IN SlKAiGll i TIIKOUGII HOW: (ZINC VACUL5 CUKUEC 11:11 I OU CHEMICAL EEAC'IIING) I'W.I' specific HUH llll 01 I UN DENSITY SURFACE IIUMIiEK KAIE I'IKi I UI AKEA "Lill in / 1 1 0.01 in 2 . 5.003 0.03/0 23.460H 2 .4 O.UU<J!) 6 .;:u4 0.5203 32.6066 2 .1 3 O.OO'JH / . M i l . 0.6445 11 .0200 2 .1 4 o.oooa 'J .'Jltin 0.520a !.l .6131 2 .3 5 0 . U U H 5 lit . i l o / 0.6//4 106.22HI .4 1. o.o i n 10 ./"/Id 0.6340 6a. 2a / i 2. .3 / O.UI 3 i. .Ol>4 3 0.44HO 31 .266 2. ,!) a o.o i ;i 11. . 300!. 0.4262 l a . o s i y 2. .4 !) 0.013 II. .0002 o.iao6 !>7.66a/ 2. 6 10 0.013 l a . Mill 0.3/1.0 /I .15/ 2. !) 1 1 O.OI 5 3. O'Jti O.Oblli 20.0235 2. 3 12 O.OI!', /. 1 'J!, 1 0.1)1/0 34.2440 2. 6 I.I O.OI!. Ii. 2/11 0.5362 44.3660 2. 1 • fill [Pe l i: /,,| r I r / s I g/1 l i / i J/I h 2 y/h -in !)10 0 ./!. 15 .HH o. i a /4 a.oxio~ J 405 1 .45 33 . /3 0. i Hit, 1 . U l x l O - 2 560 1 .'Jb 45 .16 0.451)2 l . U x l U ^ 620 2 .50 60 .35 n.5002 1.14x10"'"' 160 2 .HO 6'J .4 o.SaoU 5.6x10"^ 16!) 2 .60 63 .02 o.Ui'l 1 .22xlO" 2 f.lO 1 .25 30. .5 o. ioi>5 I . 2 / x l O ~ 2 !)10 1 . .65 3 / . .0 li.4f.llO 1 .OOx lU - 2 500 1 . .05 40. 05 0 . 63 / / 1.11x10 2 11)0 2. 25 52 . /6 o.cu50 U . % x l U - 2 tiiiO 0. 05 24. 23 0.jo25 i . a i x n r 2 1.30 1 . 115 16. 3H O.r.'j sn 2 . 0 J x l O " 2 MO 2. 50 5a. 6H o.!j'//'J 1 .OHxIO'"1 IV) TAl i i . I : A 6 . 4 I IAIA I K O H i A N K 'IHO EOK C O I I i l N U O U S L E A C H I N G IN S i K A I G I I i T l lKOl lGI I MODE KLIN IIUMItLK D I L U T I O N K A I L I'lll I' III N'i I IY I'l K l I III . I ' l . L l i II. j U K I A C l : A K E A 2 E l i r Is 1 in in _/_L • i / I !• C j / l l - l l l 1 0 .01 l i l 0 . 6 4 6 6 0 . D O M 6 . 4 3 0 0 2 . 1 5 6 0 0 1 . 3 5 3 2 . 6 0 0 . . i l l 3 5 5 . 0 6 x ) l f 2 2 0 .01108 2 . 5 3 6 8 0 . .•Ul!) 2 1 2 . . 3 0 3 0 2 . . 0 6 2 5 2 . 6 0 6 0 . 7 O . 6 0 4 0 4 . 8 4 x l O ~ 2 3 0 . 0 0 0 8 3 . . 104 / 0 . . 5 0 3 6 11). . 6 3 5 1 .a 6 0 0 3 . 2 5 8 0 . 0 o. /114 6 . 0 1 x l G " 2 4 0 oooa i . l iJ ' ja 0 . , ' 1060 IS. . 5UU 1, .a 6 6 5 4 . 3 5 1 0 6 . 6 1 . 0 4 3 7 6 . 6 0 X 1 U " 2 ii 0 , . 0 0 8 5 11 .111,2/ 0 . . 6 6 04 6 6 . . 2 0 0 2 , . 2 5 2 0 4 . 8 6 1 1 7 . 6 O . 0 0 8 8 i . 5 x i u ~ 2 Ii 0 . .01 3 5 . . 2 4 1 6 LI. .11510 4 4 . . 6 2 0 . 0 6 2 5 3 . 0 0 1 0 0 . 0 1 . 3 0 2 . 9 4 x 1 0 " 2 / 0 . . o n 2 . .30.1 U. . 2 6 1 6 !). . 704 2 . . l 5 0 0 2 . 6 6 6 2 . 6 U . 8 I 2 5 14 . 0 2 x l O " 2 11 0 . ,ot 3 i). .11,!)!, 0 . . 364 / 2-2. . 484 2 , . I 6 5 0 3 . 0 6 7 2 . 0 1 . 0 36 4 . 1 6 x l O ~ 2 0 0 . . o n !i. , !)( ,00 0 . .41113 2 4 . , 0 2 8 2 , . I 6 6 0 3 . 7 6 0 3 . 0 1 . 2 0 0 4 . 8 6 X 1 0 " 2 10 0 , .01 3 !). , ' J / I 1 0 . . 2 5 8 0 2 5 . . 7 2 6 2 . .1 5 2 0 4 . 6 0 1 1 2 . 6 1 . 4 0 i 6 . 6 0 x l O " 2 11 0 . .01! ) 0 . .lll>7(i 0 . 11015 /. , 7 3 6 2 . . l 6 3 0 1 . 6 0 3 0 . 6 0 . 6 0 2 6 / . 6 6 x l O " 2 12 0 . .01! ) ' 1 . It) I'l 0 . !)2!13 21 . , 0 0 5 0 •> , 0 6 2 0 ?.. /() 6 7 . 0 1 . 0 0 5 1 . 6 / x l u " ' ' 1.1 0 . .01! ) 2 . . / 0 6 5 0 . 6 8 2 0 I d . 3 0 2 1 , .0 6 / 0 3 . 0 5 0 4 . 0 1 . 4 1 0 8 . 0 6 x 1 0 " ' ' ro cn Co Appendix 5.3 Calculation for Steady State Run No. 5 PERIOD 1979.07.20 to 1979.07.25 DILUTION RATE (a) Average Tank Deptn (o) Tank Volume (c) Volume of Product Collected (d) Total Time (e) Product Removal Rate (f) Dilution Rate D = F/V = 0.220/26.073 = 0.00845 n" 1 Residence Time = 1/D = 118.514 n TANK 1 SPECIFIC GROWTH RATE By Steady State Assumption, v = D Generation Time, tn= In 2/u = 81.547 n 36.0 cms 26.073 1 21.065 1 95.75 n 0.220 1/n 255 4. SURFACE AREA CONCENTRATION LSAJ pd SSA [SA] 10 x pd. x SSA = 18.3197 percent (g/100 ml) = 0.5466 m2/g = 105.2281 m 2/l 5. BACTERIAL GROWTH RATE Base line Correction (See Section 5.4.2) for [NH4J (See Taole 5.10) 0.547 x pa = 14.25pprn n dX / dt 461 mg/1 = 3.919 mg/1 n 256 6. ZINC EXTRACTION RATE Uncorrected Corrected Concn. of Zinc [Zn] g/1 = 77.5 69.40 (See Taole 5.10) Rate of Zn.extraction, a LZn] / at ( » Y Z ) ( G / 1 _ N ) (See Taole 5.10) 0.6549 0.5809 [SA] in2/ 1 = 105.2281 105.2281 r z/[SA] g/m2-n = 0.0062 0.0056 7. YIELD CONSTANTS (Corrected for Cnemical Leacning) r n , mg/l-n = 3.919 r z , g/l-n = 5.849 x 10"1 Yx/Zn = r n / r z , mg NH4 / g Zn = 6.643 257 8. ZINC BALANCE OVER TANK INPUT Feed Rate = 1.20 g/rnin Total Amount of Concentrate Fed 1.20 x 50 x 24 = 1728.00 g/oay Corrected for moisture 1728.00 x 0.9722 = 1679.9616 g Weignt of Zinc Fed x 0.6084' = 1022.0886 g OUTPUT SoluDle Zinc 5.405 1@ 77.5 g/1 = 4/8 .888 g Residue 5.405 lx 2x9.1598 percent 990.1776g Weignt of Zinc in Residue 990.1776 x 0.60 = 594.107 g Total Zinc Output = 1012.995 g ZINC LOST 9.0936 g or 0.90 percent 258 9. EXTRACTION = (Sol.Zn./Input Zn.) x 100 = 40.98 percent 10. CORRECTION FOR CHEMICAL LEACHING (See Section 5.4.2) (a) Rate of base line chemical leacning, CLB (rate), = 2.419 x 10 4 x [SA] + 6.36 x 10"3 x D x Fpa. [CLB] = CLB (rate) / D = 2.419 x 10 4 x [SA] ) / D + 6.36 x 10"3 x Fpa, (o) Output of Zinc = 1012.995 g/day 1012.995 1 C C C n 1 , 0.6084 = 1^65.014 g ot Cone. / day Product Rate 0.220 1/hr. 259 Feed Pulp Density 1665.014 24 x 2.2 SSA Feed 31.5344 percent 0.5761 m2g [SA] Feed 10 x 0.5761 x 31.5344 181.6695 nf (c) Dilution rate -1 0.00845 n [CLB] = 2.419 x 10 4 x[SA] ) / D + 6.36 x 10"3 xFpo 0968 (a) Net NH4 Base Line Correction 8.0967 g/1 0.547 x Fpa, TANK 2 17.25 mg/lNH. SURFACE AREA CONCENTRATION ISA] pd SSA [SA] 10 x pd. x SSA 11.8527 percent (g/100 ml) 0.55936 m2/g 66.299 m 2/l 260 13. BACTERIAL GROWTH RATE 622 mg/1 5.287 x mg/l-n. 14. ZINC CONCENTRATION Concentration of Zinc g/i Rate of Zinc extraction, d(Zn)/dt D x [Zn] (g/l-nr.) [SA] m2/l rz I [SA] g/m2- -n . 15. YIELD CONSTANTS r n mg/l-nr. = 5.287x r ? g/l-nr. = 0.9988 Xn dX/dt 117.5 0.9988 66.299 0.0151 YX/Zn = r n / r z mg NH^  / g Zn 5.293 261 16. ZINC BALANCE OVER TANK INPUT Soluble Zinc 5.405 1 77.5 g/1 = 418.888 g Residue 5.405 1 18.3197 percent pa 990.1776 g Weignt of Zinc in resiaue 990.1776 x 0.60 = 594.107 g Total Zinc Input = 1012.995 g OUTPUT Soluole Zinc 5.405 1 117.5 g/1 = 635.088 g Residue 5.405 1 11.8527 percent pd 640.638 g Weignt of Zinc in resiaue 640.638 x .589 = 377.336 g Total Zinc Output = 1012.424 g 17. EXTRACTION Soluole Zinc/Input Zinc = 62.69 percent 18. RATE OF ZINC PRODUCTION = 998.8 mg/l"" (per 1itre of reactor) 262 Appendix 5.4 Results of Continuous Recycle Mode Operation Tne data of tne recycle mode runs are in tne accompanying taOles A5.5, A5.6 and A5.7. Taole A5.5 gives tne zinc concentration values of Tank 1 wnicn are uncorrected for chemical leaching. r/Uil.L AL.!) DATA I-'KIIH TANK UNI- l:UI< CONTINUOUS ILACllINU IN KECYI.L MODE (/INC VALUES UNCOKKECIEI) l:UI( CMIMICAL LEACHING) KUN Jl-llil: K III LUI Hill KAIL I'll! IJ UL'NSI IY I'EliCENl MM i l i 11: 5UIUACE AULA I'll LM 1 > V | [ /u l r / r /s 7 III / IJ in J[ 9/1 ' l / l ' j / l I... JJ/II-III I'l u.oioa / .059 0.631!) 3/. 61(16 2 !) 610 1 26 32.!) O.I,II 1.63x1 IT2 16 {).01(111 11 . ; ."J/ 0.!.21i.' 6u.aa 2 4 600 1 'JO la.o 0.9021 1.63xlO" 2 II) o.oiaa l!).l)/'J 0.5264 a::.3//6 u 2 160 2 liO 6a. /5 I .293 1 . 5 / x l O ~ 2 1 / H.U266 lO.tl'J 0.63(1/ 5(1.6641 2 1 630 I 25 32.06 o.a^aa 1 .1 l3xl ( )" 2 1(1 U.1)265 22.366 0.622)1 116.9242 o (. 3 600 3 06 72.0 i .a 16 1 .67x10^ I'J 0.0266 1 4. 602 0.536J '/a. 2621 2 4 610 1 ao 17.6 1 .2 1 1 3 1 .61xlO~ 2 ro IMlil.I: A6.6 HAIA IKUM TANK UNI I OK CONTINUOUS IhAClllNG IN KLCYLL MOIiL" (/INC VAl.UtS COKKLCICI) I UK CllLHICAI. I.LACllING) I'lll.l' SI'LCIIIC S KUN 1)11 III 11)11 WJllSIIY SIIKIACt pll HUWlUU KAIL" riKCLIll AULA 2 2 MI hj m /I I'I / .U69 0.1)31!) 3/.1)186 2.6 15 l l . ; : ' J / U.62I2 511.(1(1 2 A ID 16.6/9 0.5261 H2.3//S 2.2 1/ lo.tl'J 0.53(1/ 5(1.6611 2.1 l!i 22.366 0.62211 1 16.9212 2.3 111 11.002 0.636'J /a.2621 2.4 III ,• / s / 1 <j/l 9 / ! •J/ ! 6 2 <l/li -in 510 1.25 31 .55 0.693 i .6ax io~ 2 600 1.90 46.62 0.(1/66 1 .49xl l )" 2 460 2.(10 66. / 6 I .2!)6 l .62xlO~ 2 630 1.25 31 . / 5 0.(1099 l .3(11x10" 520 3.05 /0 .5 1 . /9I'I 1 .64x11)"2 61 0 1.1)0 15.1 1 . 1(132 1 .57xlO~ 2 2 ro cn i A I S L E A S . 7 U A I A L K O H T A N K I WO F U R C O N T I N U O U S L E A C H I N G I N R E C Y L E M U U E KIIH nn III mn IMIiEK KATE I'OI |' IIINSI TY T'tKCENl si'ECii-n; SURFACE AULA c »! /9. s 2 in / I I'll Eh J / ' i l / ' r / r / s I 2 t|/li-ni I'l O.li'J/ o.ar / ' i 7.5116 1 .9 640 1 .55 40.0 0./62 lO . O x l u " IS 1 . / H / l l 0.(1825 15.7/2 1 .11 620 2 .65 62.0 1 . In 5 6 /.19xlU ''• If i tso 0.(164/ 19.326 1 .9 600 3 .50 66.26 1 .622 (1.39x10""'' 1 / 0.02 s;.' 0.0561 8.7767 2.1 640 1 ./5 42.6 1 .0113(1 I2.36xl0"~ 2 Iii 2.6(116 U.ii'JTtO 24.10// l .a sao 3. .75 91 .25 2.3269 9.652xlO~ 2 I'J 1 .926 0.8362 16.0//6 1 .9 630 2. .60 60.0 1 .6 10 9.52x10 "?-266 Appendix 5.5 Calculation for Steady State Run No. 16 1. PERIOD 1980.04.11 to 1980.04.18 2. DILUTION RATE (a) Average Tank Deptn (b) Tank Volume (c) Volume of Product Collected (d) Total Time (e) Product Removal Rate (f) Dilution Rate D = F/V = 0.488/26.073 = 0.0188 n" 1 Residence Time = 1/D = 53.19 n 3. SPECIFIC GROWTH RATE By Steady State Assumption, y = D Generation Time, t n = In 2/y = 36.87 n 36.0 cms 26.073 1 23.420 1 48 n 0.488 1/n 2o7 4. SURFACE AREA CONCENTRATION LSA] 10 x pa. x SSA pd = 15.679 percent (9/100 ml) SSA = 5254 cm2/g [SA] = 82.3775 rn2/ I 5. BACTERIAL GROWTH RATE (See Section 5.4.2) Base line Correction = 0.547 x pd 9.2 ppm Xn = 411 mg/1 dX / dt = 7.729 mg/1 n 268 6. ZINC EVALUATION RATE Uncorrected Corrected Concn. of Zinc [In] g/1 = 68.75 66.75 (See Taole 5.12) Rate of Zn.extraction, (D x [Zn]) / dt = 1.293 1.255 (g/l-n) (See Taole 5.12) [SA] r n 2 / 1 = 82.3775 82.3775 »*Z/[SA] g/m2-n = 0.0157 0.0152 7. YIELD CONSTANTS (Corrected for Cnemical Leacning) r n , mg/l-n = 7.729 rz, g/l-n = 1.255 Yx/Zn , r n / r z , mg NH4 / g Zn = 6.157 269 8. ZINC BALANCE OVER TANKS INPUT Arnt. of Cone.Fed to T-, 1.420 x 60 x 24 = 2044.80 g/1 Corrected for moisture 2044.80 x 0.9722 = 1987.9546 g Wt. of Zinc in Feed 1989.9546x0.6084 = 1209.4716 g OUTPUT Soluble zinc T Soluole zinc T. Total Vol. x [Znj 11.712 x 68.75 11.712 x 17.50 = 813.7938 g = 207.1475 g = 1020.9413 g Residue to Product Receiver Vol.x p.d. x 10 11.712 xO.2235 x 10 = 261.7632 g Zinc in Residue to P.R. 0.524 X261.7632 = 137.1639 g Increase in p.d. of T-, = 0.2644 percent Residue to T-, 26.073 x 2.644 = 68.937 g Zinc in Residue 68.937 x 0.572 39.4320 g Zinc lost (0.99 percent) = 11.9344 g Total = 1209.4716 g 270 9. EXTRACTION = (Sol.Zn./Input Zn.) x 100 = 40.98 percent 10. CORRECTION FOR CHEMICAL LEACHING (See Section 5.4.2) (a) Rate of oase line cnemical leacning, CLB (rate), 2.419 x 10 4 x [SAJ + 5.36 x 10 3 x D x Fpa. [CLB] = CLB (rate) / D + 6.4 x 10~3 x Fpa. = (2.419 x 10~4 x [SAj)/D + 6.36 x 10~3 x Fpd, (o) Output of Zinc = 1197.528 g/day 1197.528 1 Q . Q _ 0 <. n n , 0.6084 = 1^8.326 g of Cone. / oay ProOuct Rate = 0.488 1/n. Feed Pulp Density 1968.326 24 x 4.88 = 16.806 percent 271 SSA Feed = 0.5761 m^ g L'SA] Feed = 96.820 in2J -1 (c) Dilution rate = 0.0188 n [CLB] = 3.366 x 10 x[SA] + 6.4x IO"3 x Fpd 1.97 g/1 (d) Net NH* Base Line Correction = 0.547 x Fpd. 9.193ppriiNH* 11. SURFACE AREA CONCENTRATION T 9 LSA] pd SSA [SA] 12. BACTERIAL GROWTH RATE Xn = 284 nig/1 dX/dt = 5.33y mg/'l-nr. 10 x pd. x SSA 2.2350 percent (g/iOO ml) 8647 cm2/g 19.326 m 2/l 272 13. ZINC CONCENTRATION Concentration of Zinc g/1 = 86.25 Rate of Zinc extraction a(Zn)/at a x LZnj (g/l-nr.) = 1.622 LSAj m 2/l = 19.326 r z / LSAJ g/m2 -nr. = 8.39 x 10"2 14. YIELD CONSTANTS r n ing/l-nr. r^  g/l-nr. 5.339 1.622 Yx/Zn = r n / r z (mg NH^  /g Zn)= 3.293 15. EXTRACTION Soluole Zinc/Input Zinc 1 Stage = 67.3 percent 2 Stages = 84.4 percent 16. RATE OF ZINC PRODUCTION = 1621.5 mg/1 (per 1itre of reactor) 273 Appendix 5.6 Calculation of Fractional Extraction Using Levenspiel's Snrinxing Core Moael Table 5.8 gives tne zinc extraction rates for eacn of tne 8 fractions ootained from tne Banco-sizer. Taole 5.9 gives tne corresponding equivalent diameters specific surface area ano tne weignt fraction respectively for eacn of tne fractions. According to Levenspiel (1972) tne fractional extraction Z, for particles of eacn size is given Dy tne equation: Z = 3(t/T) - 6(t/T) 2 + 6 ( t / T ) 3 . ( l - e _ ( T / t ) ) (A5.1) wnere, T = oo_ . 1 (A5.2) P = specific gravity of concentrate do = init ial particle diameter c z/s = release rate of zinc per unit surface area and = average residence time 274 Tne overall extraction for tne feed is tnen calculated by summing tne fractional extraction for eacn fraction multiplied by tne weignt for each fraction. T^e calculated extractions for eacn of tne 13 straignt tnrougn runs are given in Tables A5.8 to A5.20. F|)il = 5-/136 TAISLE A5.0 Calculated Extraction lor Run Ho. 1 -1 0 = U.1)110 Ii t = 1/D Uia. iiiii 1 2. "i /'J rZ g/l.h 3 S rZ/s 2 2 in / l g/h. in Ii. 6 t / T Kract Ion of Total Overa11 Contribution 10 2. . 1 1. .830 1 . ,2167 2, .3003 0. ,5209 7. .5415 11.2372 0. .9/01 U. .022 0, .0215 3 .5 1 .164 1 .0098 9 .3109 0, .11/0 56. .0004 1.4920 0, .0526 0 .140 0 .1194 S. .3 0. 824 u. ,9/45 7. .9095 0. .1232 01. ,7100 1.03/1 0. .7989 0. , 160 0. .1342 9 .0 0. .SSS 0 .4741 7 .0325 0. .0605 202. .6702 0.2999 0. .5161 0. .24/ 0 .1275 13. .0 0. 321 0. ,2910 3, .7040 U. 0/08 313. ,5180 0.2703 0. ,4801 0. .202 0. ,0986 21 . 5 0, .182 0 .1912 1 .2/90 0. .1495 273, .1972 0.3102 0. .6252 0 .12.3 0 .0646 2'/. 5 I). 141 0. 1504 0. ,4431 0. 3.394 153. 0919 0.550/ 0. 6715 0. 065 0. ,0369 3S. .0 0. .111 0, .1054 0 .2664 U, ,3957 160, .0153 0.5044 0. .6606 0, .042 0, 0. .02/3 ,6300 Calculated - 63 percent Experimental = 54.4 percent ro cn EpU = 12.5009 TABLE A5.9 Caleu la Led Extraction Lor Run No. 2 n = 0.0090 i r 1 L = t/u = 102.040a Oia. SSA rZ rZ/s Fraction Overall 2 (j/h. 111 t/T of Contribt iilil in 2/<j 9/ I.ll n 2 / 1 lota 1 1 3 4 5 6 7 a 9 10 1 2. .1 1 .830 1 .216/ 5 .0361 0.2416 16.5108 6.1802 0.9608 0.022 0 .0211 •'• 3 .b 1 .1 b4 1 .0898 20 .3845 0.0535 124.3543 0.8206 0.7568 0.140 t) .1059 3 i, .3 0.824 0 .9/45 17. .3163 0.0563 178.8912 0.5704 0.679/ 0. 168 0, .1142 4 •J. 0 U.:>:, . 0 .4 741 17 .14/8 0.0276 618.3308 0.1650 0.3586 0.247 0 .0086 5 13. .0 0.321 0. .2918 a. .1110 0.0360 686.3931 0.1487 0.3331 U.202 0. .0673 ii 21. .5 0.182 u .1912 2. .8002 0.0683 598.1161 0.1706 0.3669 0.123 0, .0451 / 27. 5 0.141 0. . 15U4 0. 9701 0.1550 336.9187 0.3029 0.5188 U.U55 0. .0285 M 36. ,0 0.1 11 0. .1054 0. ,5851 0.1801 369.0741 0.2765 0.4942 0.04 2 0. 0. JJ208 4915 Calculated ~- 49.15 percent Experimental = 40.66 percent ro Epd = lb.016 TAISLE A5-10 Calculated Extraction for Kun No. 3 1) = 0.0098 h"1 t = 1/0 = 102.0408 Ilia. SSA rZ 5 rZ/s T Z fraction Overall t/i of Contribution 2 2 2 Mni in /y g/1 .h HI / I g/li. in h. lotal 1 2 3 4 5 6 7 8 9 10 I 2. . 1 1. 830 1. .216/ 6. .448 0. .1887 21.1399 4. .8269 0. ,9503 0. ,022 0.0209 I 3 .6 1. .164 1 .0898 26 .0997 0, .0418 169.2193 0. .6409 0, .7059 0, .140 0.0988 3 6. 3 0. .824 0. .9745 22. .1713 0. ,0440 229.0466 0. .4455 0. .6200 0. 168 0.1042 4 9 .u 0 .555 0 .474 1 21 .9358 0 .0216 790.9794 0. .1290 0. .3000 0, .247 0.0741 5 13. .0 0. .321 0. .2918 10. .3748 0. ,0281 878.0458 0. .1162 0. ,2770 0. .202 0.0560 6 21 .6 0 .182 0 .1912 3 .5853 0 .0533 765.8029 0 .1332 0 .3074 0, .123 0.0378 7 2/. .6 0. .141 0. .1504 1. 2332 0. .1220 428.32U6 0. .2382 0. ,4541 0. 055 0.0250 8 36 .U 0 . 1 II 0 .1064 0 .7467 0 .1412 470.9698 0 .2167 0, .4288 0, .042 0.0180 0.4348 Calculated = 43.48 percent Experimental = 51.83 percent ro TABLE A6 . i l Calculated Extraction for Run No. 1 Epu = 20.958"/ U = 0.0098 h~ t = l/u = 102.040a D i a . pin 1 SSA 2 in /ij r/_ 9/1.1' 3 2 in / I rZ/s g / l i . m 5 2 t/.T t r a c t ion of Total CalcuI a ted Exper Iuienta I -- 37.58 percent = 51.8 percen t OveraI1 Contr ihution 10 1 2. .1 1 , .830 1 . 216/ 8, .4380 0, .1442 27, .6639 3, .6886 0, .935/ 0, .022 0 .0206 L 3 . 5 1 .164 1 .0808 34 .1543 0 .0319 208 .3559 0 .4897 0 .6435 0 .140 0 .0901 3 5. .3 0. ,824 u. .9/45 28, .4954 0. .0342 294. .3804 0. ,3466 0. .5549 0. . 168 • 0. .0932 4 9 .0 0 . 566 0 .4/41 28 .7312 0 .0165 1036 .0152 0. .0985 0, .2430 0. .24/ 0 .0600 i: 13. .0 0. ,321 0. 2lJl8 13. .5900 0. ,0215 1150. ,0537 0. 088/ 0. ,2231 0. 202 0. ,0451 ii 21. .5 0. .182 0, .1912 4 .6918 0, .0408 1002. .145.3 0. .1018 0. ,2496 0. ,123 0, .0307 7 2/. 6 u. 141 0. 1504 1. 6253 0. U925 564. 5083 0. 1808 0. 3815 0. 055 0. 0210 8 36. ,0 0. ,111 0, .1.054 0, .97/1 0. .10/9 616. .3169 0. ,1656 0. .3594 0. ,042 0. 0. ,0151 3758 -•4 CO TABLE A5.12 Calculated Extraction for kuu No. 5 Dia. SSA rZ S rZ/s T - 1 Fraction Overall t/T o f Contribution 2 2 2 '" U l Min 1 1 1 / 3 g/l.h 111 / ] g/h.m h. 1 2 j 4 5 G 7 8 0 10 2.1 1.030 1.2167 12.6957 0.0950 11.6303 2.0256 0.9174 O.U22 U.D202 3.5 1.164 1.0098 51.3085 O.U212 313.5967 0.3752 0.5758 0.140 0.0806 5.3 0.824 0.9745 43.6537 0.0223 451.4607 0.2606 U.4782 0.168 0.0803 9.0 0.656 0.4741 43.2289 0.0110 1654.1364 0.0767 0.1953 0 .247 0.0482 13.0 0.321 0.2918 20.4475 0.0143 1726.8182 0.0681 0.1787 0.202 0.0360 21.5 0.182 0.1912 7.0593 0.0271 1506.9834 0.0781 0.2U06 0.123 0 .0247 27.5 0.141 0.1504 2.4455 0.0615 . 849.3699 0.1385 0.3163 0.055 0.0174 35.L) 0.111 0.1054 1.4701 0.0717 927.2315 0.1269 0.2963 O.U42 0.0124 0.3198 Calculated = 31.98 percent Experimental = 40.90 percent TABLE AG.13 Calculated Extraction for Kun No. 6 l'-'pd = 21 ./lb'/ 0 = 0.013 h" t = 1/D = 76.9231 Ilia 5SA " i 2 / 9 rl 9/1-11 S in 2/1 rZ/s 2 g/li. in T h. t/T 2 Erac t ion of Total Overal1 Contribut ion 1 2 3 4 5 6 7 8 ) 10 1 2. .1 1.630 1.2167 8. .6386 0.1408 28. ,3216 2.7161 0. ,9143 0. 022 0. .0210 2 3 .5 1.164 1.0898 34 .9663 0.0312 213 .3097 0.3606 0. .5674 0. ,140 0 .0792 3 5. ,3 0.624 0.9745 29. .7034 0.0328 306. ,859 0.2507 0. .46/8 0. 168 0, .0786 4 9 .0 0.555 0.4741 29 .4143 0.0161 1060 .6468 0.0725 0. .1883 U . ,247 0 .0465 5 13. .0 0.321 0.2918 13. .9131 0.0210 117/. ,3966 0.0645 0. .1701 i). 202 0, .0344 6 21. .5 0.162 0.1912 4 .8034 0.0398 . 1025 .9717 0.0750 0. .193/ 0. 123 0 .0238 / 27. ,6 0.141 0.1504 1. ,6640 0.0904 577. ,9296 0.1331 0. 30/1 0. U55 0. .0169 11 35. .0 0.111 0.1.054 1 .0003 0.1054 630, .969 0.1219 U, .28/4 U. 042 0 0. .0121 .3125 Calculated = 31.25 percent Experimental = 52.11 percent ro co o Fpd = 12.302 TABLE A5.14 Calculated Extraction for Run No. 7 I) = 0.013 h"1 t = 1/0 = 76.9231 I l ia. iiiii 1 '55 A iii"/9 rZ g/l.h 3 in2/I rZ/s g/h. MI 5 t/T h. 6 Fraction of T o t a l 9 Calculated = 43.03 percent Experimental = 43.31 percent Overall Contribut ion 10 1 2. .1 1. .1130 1. .2167 4 .9528 0. .245/ 16. .2377 4, .73/3 0. .9494 0. .022 0, .0209 2 3 .6 1 .164 1 . 0698 20 .0473 0 .0544 122 .2974 0 .6290 0 .7018 0 .140 0 .0982 3 5, .3 0. 824 0. .9745 17. .0299 0. .05/2 175. .9323 0. ,4372 0. .6152 0. .168 0. .1034 4 9 .0 0. .555 0 .474 1 16 .8642 0. .0281 608. .1035 0. .1265 0, .2956 0. .247 0 .0730 6 13. .0 0. 321 0. 2918 7, .9769 0. 0366 675. .0400 0. ,1140 0. 2728 0. ,202 0. .0551 6 21 .6 0. .182 0, . 1912 2 .7539 0, .0694 588, .2231 0. .1308 0, .3031 0, .123 0 .0373 7 27. .5 0. 14 1 0. 1504 0. .9540 0. 1676 331 . 3460 0. 2322 0. 4472 0. 055 0. .0246 a 35. .0 U. .111 0. .1064 0 .5735 0. .1838 361, .7552 0. .2126 0. .4238 0. .042 0 0. .0178 ,4303 ro co TABLE A5.15 Calculated Extraction for Run Mo. 8 Epd = 17.971/ D = 0-013 h"1 Ilia. SSA rZ S rZ/s Z traction Overall tyT of Contribution 2 „i2/,j y / l . h ».2/1 y/ l i . in I). T o t a l pin I 2 3 1 5 6 9 10 Calculated = 36.6 percent Experimental = 37.06 percent 2. 1 1. 830 1. 2167 7.2354 0. 1682 23. 7155 3. 2136 0. 9274 0. 022 0. 0204 3. .5 1. ,161 1. ,0898 29.286/ 0. ,0372 178. .7164 0. 1301 0. ,6113 0. ,140 0. ,0856 5. .3 0. ,824 0. 9745 24.8/9 0. 0392 256. ,8202 0. 2995 0. 5158 0. 168 0. 0856 9 .0 0 .556 0, .1711 16.7568 0, .0283 604 .0813 0, .1273 0. .2970 0, .247 0, .0734 13. .0 0. ,321 0. ,2918 11.6532 0. ,0250 987, .710 0. ,0779 0. ,2001 0. .202 0. .0401 21 .5 0 .182 0 .1912 4.0231 0 .0475 859 .7737 0 .0895 0 .2247 0 .123 0 .02/6 27 .5 0 .141 0. .1504 1 .393/ 0, .1079 184 .1172 0, .1589 0 .3492 0 .055 0, .0192 35 .0 0 .111 0 .1054 0.83/8 0 .1258 528 .17/7 0 .1456 0 .3281 0 .042 0 • 01_38 0 .3660 r o oo r o TABLE A5.16 Calculated Extraction for Run No. 9 f| J l 1 = 20.717 0 = 0.013 It - 1 t = 1/0 = 76.9231 0 i a. Mill 1 6 6 A III2 / ij 2 rZ 9 /1 -1 ' 3 m2/l rZ/s <j/h. in 5 t/T Calculated = 31.87 percent Experimental = 12.01 percent fraction Overall of Contribution Total 10 1 2 .1 1 .830 1 .2167 a .3407 U .1459 27 .3449 2 .8131 0 .9171 0 .022 0 .0202 2 3. . 6 1. ,164 1 . .0898 33. .7604 0 .0323 205. .9531 0, .3735 0. .5746 1), .140 0, .0804 3 5 .3 0. .824 0 .9745 28 .6790 0 .0340 296 .2761 0 .2696 0, .4772 U. .168 0 .0802 1 9. , u 0. 555 0. .4741 28. .3999 0. .0167 1024. ,0677 0. ,0751 0. .1940 0. ,24 7 0. ,0479 5 13 .0 0. .321 0 .2918 13. .4333 0 .0217 1136 .7910 0. .0677 0. .1774 0, .21)2 0. .0358 6 21. . 6 0. 182 0. 1912 4. ,6377 0. 0412 991. ,2439 0. 0776 0. 1996 0. 123 0. 0245 7 27. .5 0. .141 0. .1504 1. 6066 0, .0936 557, .9982 0. .1379 0. .3152 0. .055 0. .0173 8 35. 0 0. 111 0. 1064 0. 9658 0. 1091 609. 2084 0. 1263 0. 2952 0. 042 0. 0. 0124 .310/ ro oo CJ TABLE A5.17 Calculated Extraction for Kurt No. 10 E|id = 20.3/78 0 = 0.013 h"1 t = 1/0 = 76.9231 U ia pin 55A 2 . »i /g r 9/1 z .6 in /I rZ/s 2 g/li. in T h. t/T Z tract ion of Total Overa 11 Contribution 1 2 3 4 5 6 7 8 9 10 2. .1 1 .830 1 .2167 11. .4249 1.0650 37. .4565 2.0537 0. ,8092 0.022 0.0196 3 .5 1 .161 1 .0090 46 .2445 0.0236 202 .1112 0.2727 0, .4904 0.140 0.068/ 5. .3 0.82'1 0 .9745 39. ,2840 0.0248 405. ,0341 0.1895 0. ,3937 0.168 0.0661 9 .0 0.566 0 .4741 30, .9017 0.0122 1402 .7508 0.0548 0 .1475 0.24 7 0.0364 13. .0 0.321 0 .2918 18. ,4007 0.0159 1557. .1673 0.0494 0. ,1343 0.202 0.0271 21 .6 0.182 0 .1912 6 .3527 0.0301 1356 .8914 0.0567 0, .1519 0.123 0.0107 27. ,6 0.141 0 .1604 2. ,2007 0.0683 764. ,3366 0.1O06 0. 2473 0.055 0.0136 35, .0 0.111 0 .1054 1 .323 0.079/ 034, .4834 0.0922 0. .2303 0.042 0^ 0097 0.2599 Calculated = 25. 99 percent Experimental - 33 .70 percent TABLE A5.18 Calculated Extraction for Run No. 11 fpd - 7.3001 D = 0.013 h _ 1 t = 1/0 = 76.9231 Uia. SSA r7 S rZ/s T - I fraction Overall t/T of Contribution 2 Total Ii. 1 Z 3 1 5 6 7 8 9 10 2 2 pin in / I J <j/1.6 in /1 y/h. in Ii.Calculated = 51.78 percent Experimental = 57.6 percent 1 2. . 1 1 . .830 1. ,2167 2.939 0. .414 9. .635 6. .9162 0. .9649 0. .022 0.0212 z 3. .6 1 . . 164 1 .0898 11.896 0 .0916 1Z. 579 0, .9185 0, .7778 0 .140 0.1089 3 5. ,3 0. 821 0. .9/45 10.130 0. .0960 104. .868 0. .6357 0. ,7011 0. .168 0.1183 4 9. .0 0. .566 0 .474 1 10.007 0 .0174 360 .660 0, .1848 0 .3872 0 .247 0.0966 5 13. .0 0. .321 0. .2918 4.737 0. .0616 400. .869 0. .1663 0. .3605 0 . .202 0.0728 6 21 . 5 0 .182 (J .1912 1.6342 0 .1170 349 .053 0. .1910 0 .3957 0 .123 0.0487 7 27. .5 0. .141 0. . 1 504 0.666 0. .2657 196. .599 0. ,3391 0. ,5191 0. .065 0.0302 8 35 .0 0 .111 0 . 1064 0.340 0 .3100 214 .460 0. .3109 0 .5250 0 .042 0.0221 0.5178 ro oo cn TABLE AS.19 Calculated Extraction tor Run No. 12 Fpd = 14.6211 0 = 0.015 h _ 1 t = l/D = 66.667 Uia. tint 1 S5A in 2 / (j rZ 9 / 1 - 6 3 r/_/s 2 <j/li. HI 6 t/1 Fraction Overall of Contribution Total 10 2. .1 1 . .630 1 . 2167 6. .1540 0. ,1977 20. .1760 3. ,3043 0. ,9287 0. ,022 0. ,0204 3 . 6 1 . 1 u4 1 .0898 23 .8265 0 .0457 145 .3522 0 .4570 0, .1262 0 .140 0 .0175 5. .3 0. .824 0. .9745 20. .2403 0. .0481 209. .0980 0. ,3188. 0. ,5326 0. ,168 0. ,0895 lJ .0 0. .556 0. .4741 20 .0433 0. .0237 722 .7396 0. .0922 0, .2304 0 .247 0 .0569 13. ,0 0. 321 0. 2918 9. .4806 0. .0308 802. .2945 0. ,0831 0. 2113 0. ,202 0. ,0427 21 0. .182 0. .1912 2 .5357 U. .0754 541 .6193 0. .1231 0, .2896 0 .123 0 .0356 27. .5 0. 141 0. 1604 1 . .1339 0. .1326 393. .8093 0. ,1693 0. ,3649 0. ,055 0. ,0201 35 .0 0, .111 0, . 1064 0 .6816 0, .1646 4 29. 9511 0. .1551 0. .3432 0. .042 0, 0. .0144 ,2971 Cal cu 'I a Led = 29.71 percent Experimental = 55.1 percent ro co CTl TABLE A5.20 Calculated Extraction for Run Mo. 13 fpd = 17.710 0 = 0.015 Ii""1 t = 1/D = 66.557 S S A rl S rZ/s 1 - Z Fraction Overall t/T of Contribution 2 iota I h. • m2/9 y/1 .h in2/1 g/li. in •5 4 5 6 7 8 y 10 1 .1 1. .830 1. .2167 7. .1421 0. .1704 23 .1154 2, .8471 0. .9180 0. .022 0 .0202 2 3 .5 1 .164 1 .0808 28 .9091 0 .0377 176 .3580 0 .3780 0 .5778 0 .140 0 . 0809 3 5. .3 0. ,824 0. .9715 24. .5578 0. .0397 253, .7017 0. .2628 0. .4805 0. , 1 bt'l 0, .0807 4 'J. 0 0. .665 0 .474 1 24 .3189 0, .0195 876 .9108 0 .0760 0. .1960 0, .247 0 .0487 5 13. .0 11. 321 0. ,2918 11. ,5030 0. 0254 973. .4359 0. ,0685 0. 1792 0. 202 o; .0362 6 21. .5 0. .182 0. .1912 3, .9713 0. .0481 818 .2424 0. .0786 0. .2016 0. ,123 0. .0248 7 27. .6 0. 111 0. 1 604 1. 3757 0. 1093 177. .8148 0. 1395 0. 3181 0. 055 0. 0175 6 35. .0 0. 111 0, . 1054 0. .8270 U. .1274 521, .6661 0. .1278 0. .2979 0. 042 0. .0125 0.3212 Calculated = 32.12 percent Experimental =57.1 percent ro co Appendix 5.7 Application of tne Shrinking Core Model to tne Secona TanK Tne method described in Appendix 5.6 was used for tne f i rs t Banco fraction witn a diameter of 2.1 for a feed pulp density of 20 percent and a dilution rate of 0.01 n" 1 . Data: Diameter 2.1 vm SSA 1.830 Y z (release rate) 1.216 [surface area] 8.0520 Results: Extraction 0.0206 or 2.06 percent Step 1 3 Hence a particle naving an init ial volume of 100 (um) will end up witn a volume of [(100 - 2.06) x 100 = J . . 100 97.94 (yin) . Hence new diameter of tne particle wouia 3 0.9794 x (2.1)3 = ) 2.085 Mm. 289 Step 2 From tne plot of release rate versus diameter cne new release rate r is obtained. Step 3 Assume tnere were n pa r t i c l es in tne f i r s t f r a c t i o n . Since tne number of pa r t i c l es at tne end of leacn in tne f i r s t tanK would remain tne same n would not cnange. Since tne i n i t i a l and f i n a l diameters are Known, tne new surface area concentration can oe ca lcu la ted . 2 d_ x s 0 d 0 (A5.3) wnere, s = surface area concentration S Q = i n i t i a l surface area concentrat ion d = diameter of tne p a r t i c l e , ym 2 d^ = i n i t i a l diameter of tne p a r t i c l e . In th is case, (2.085) 2x 8.0520 = 7.9374 ( 2.1) 2 290 Once d, and s are Known tne formulae in Appendix 5.6 could oe used to calculate tne extraction rate. Tables A5.21 and A5.22 give tne summary of tne results of calculations for a 20 percent feed pulp density ano a dilution rate of 0.01 n - 1 . = 20 TABLE A5.21 D = 0.010 I = 100 6 rZ/S T t/T V Fraction Overall Contribution 2 2 in /1 y/iii Ii Ii 4 5 6 7 IS 9 10 1 2 .1 I .830 1 .2167 8 .0620 0 .1511 26 .3994 3 . 7880 0 .9373 0 .022 0 .0206 2 3. ,b 1. .164 1. 0898 32. .5920 0. .U334 199. .0494 0. .5024 0. .649/ 0. .140 0, .0910 3 5 .3 0 .824 0 .9745 27 . 6864 0 .0352 286 .0043 0, .3496 0 .65/2 0 .168 0 .0936 4 9. ,0 0. 665 0. .4741 27. .4170 0. .0173 988. .1792 0. .1012 0. .2484 0. ,24 7 0, .0613 5 13 .0 0. .321 0 .2918 12 .9684 0. .0225 1097 .4889 0, .0911 0, .2281 0. .202 0 .0461 6 21. b 0. 182 0. .1912 4. .4772 0. .0427 956. .4227 0. 1046 0. 2649 0. ,123 0. .0314 7 27. .b 0. .141 u. . 1504 1 .5510 0. .0970 538. .5180 0. .1857 0. .3884 0, .055 0 .0214 0 3b. 0 0. 111 0. 1054 0. .9324 0. 1130 688. 3407 0. 1700 0. 36oO 0. 042 0. ,0154 0.3808 Calculated = 38.08 percent ro Uia. S5A rZ 11 tit 1 2 ill /(j 9/1 Ii 3 .011) TAISLE A5.22 Second Tank (Tank 1 Fpd: 20) iiiii SSA 2 in /y r/. y/1 ii 2 in / I r/_/S 2 y/m ii t/T Fract ton 39.75 percent = 21.61 percent of original Total Extraction is 62.69 percent 75.23 g/ Overal1 Contr ibut ion 1 2 3 4 5 6 7 8 9 10 2.085 1.2702 7.9374 0.1600 . 24.7529 4.0399 0.9411 0.022 0.0207 3.390 1.1048 30.5760 0.0361 178.3741 0.5606 0.6767 0.140 0.0916 5.128 U.9911 25.9315 0.0382 254.9905 0.3922 0.58/1 0.168 0.0987 8.810 0.4816 26.2734 0.0183 914.4587 0.1094 0.2o12 0.24 7 0.0652 12.791 0.2962 12.5603 0.0236 1029.7544 0.0971 0.2102 0.202 0.0485 21.2661 0.1932 4.3803 0.0441 915.9811 0.1092 0.2638 0.123 0.0324 27.293 0.1059 0.9221 0.1148 5/5.9224 0.1736 .0.J/13 0.042 0.0]56 0.3975 ro ro 293 Appendix 5.8 Quantitative Metnod for tne Evaluation of Mixing Efficiency A one-snot tracer is injected to tne inflow of a stirred tank reactor and tne concentration of tne tracer at tne outlet is determined as a function of time. The results of tne tracer study coula be plotted as dimensionless values C/Co versus t/T, in wnicn C is tne concentration of tracer at the outlet at time t; CQ is tne weignt of tne tracer divided by tanK volume, t is tne time; and T is tne residence time (Volume of tanK divided oy flow rate). Tne curve obtained is usually referred to as tne flow curve. A typical flow curve is snown in Figure A.5.1, Curve B. In an ioeal tank witn perfect mixing can oe descrioed oy a curve (Figure A.5.2, Curve A). Co (A5.4) In a real tanK tne flow is composed of plug flow, mixing, and dead space. Reonun and Argaman (1965) introduced a function F(t), wnicn is defined as a fraction of fluid witn retention time less tnan t. Values of tnis function can oe computed oy measuring tne area confined by tne residence time F I G U R E A 5 . 1 A T Y P I C A L R E S I D E N C E T I M E D I S T R I B U T I O N CURVE distribution curve to a value of t. In a real system tne function F(t) was found oy tne autnors to nave tne form, F ( t) - 1 - . ^ ' T » - J ( A 5 , > in wnicn a ano & and constants for a given system. Tne constants a ano o express tne ratio oetween eacn of plug, mixed flows ana dead space. In tne literature referred to above it is snown tnat Function F(t) was of tne form, Lt/T- p (l-m)J/(l-p)(l-m) F(t) = 1 - e " . . v (Ab.b) in wnicn m = dead space fraction of tank volume, 1 —in = effective fraction of tank volume, p = plug flow fraction of tne effective part, and 1-p = perfect mixing of tne effective part. Equation A5.6 is similar to Equation A5.5 in wnicn, a = l/(l-p)(l-m) (A5.7) o = p (1-m) (A5.8) 296 tnus giving a pnysical meaning to tne constants a and ». Rearranging Equation A5.2 and taKing logaritnms of ootn sides yields, log Ll-F(t)] = (-log e)[(t/T) - p ( l -m)j/( l -m ) ( l -p) (A5.9) . Plotting [ l -F ( t )J versus t/T on semi-log paper yields a straignt line witn a slope (log e)/(l-m)(1-p). For F(t) = 0, log Ll-F(t)] = 0 and F(t) = 0; t/T = p(l-m). From tne slope of tne straignt line and tne value of t/T for F(t) = 0 m and p can oe computed. Results ootained witn tne tracers are given in Taole A5.23 and tne semi-log plots are given in Figure A5.2. 297 TABLE A5.23 C/C o t /T ~ Sphalerite ;<C1 0.0138 0.1964 0.2313 0.0276 0.5532 0.5520 0.0552 0.9218 0.9325 0.0690 0.9473 0.9556 0.1381 0.9655 0.9657 0.2762 0.3636 0.8611 0.4144 0.7573 0.7444 0.5525 0.6300 0.7000 0.6906 0.6013 0.5111 0.3237 0.5345 0.5333 1.1050 0.4132 0.4200 1.3812 0.3255 0.3298 1.6575 0.2600 0.2557 1.9337 0.2164 0.2167 2.209S 0.1709 0.1770 2.^362 0.1255 0.1273 2.7624 0.0962 t ^ m 0 . J O O / 0.U732 3.1763 0.0691 F I G U R E A 5 - 2 P L O T O F l - F ( t ) V E R S U S t / T t / T PLATE 2 301 302 

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