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Continuous microbiological leaching of a zinc sulphide concentrate Gormely, Lynton Spencer 1973

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Il 111 CONTINUOUS MICROBIOLOGICAL LEACHING OF A ZINC SULPHIDE CONCENTB ATE bj LYHTCN SPENCER GORMELY B. A. S c . , U n i v e r s i t y of B r i t i s h C o l u m b i a , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOB TEE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Depar t n e n t o f CHEMICAL ENGINEERING 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 to the r e g u i r e d s t a n d a r d THE UNIVERSITY OF EBITISH CC1UMEIA F e b r u a r y , 1973 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t 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 f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may he g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f C h e m i c a l E n g i n e e r i n g The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date July 6. 1973 i Abstract A zinc sulphide concentrate was leached m i c r o b i o l o g i c a l l y by T h i o b a c i l l u s ferrooxidans i n a continuous s t i r r e d tank reactor. A model was developed to predict the leaching k i n e t i c s when the b a c t e r i a l growth rate was not limited by any substrate other than the zinc concentrate, and i t was modified to explain the observed r e s u l t s . It was possible to obtain stable steady-states over a range of d i l u t i o n rates. Because a s o l i d substrate was used, the s p e c i f i c growth rate of the bacteria was not a unique function of the substrate concentration, and conventional continuous culture theory based on the Monod equation therefore did not apply to t h i s system. The b a c t e r i a l concentration did not l i m i t the growth rates under the conditions of these experiments. The leaching rates and b a c t e r i a l growth rates are thus f i r s t order in mineral surface area concentration. The highest s p e c i f i c growth rate observed was 0.1038 h r - 1 ; the highest oxygen uptake c o e f f i c i e n t (QQ^(N)) calculated was 7650. Both of these values are higher than any reported previously for T : ferrooxidans growing on a s o l i d substrate. The highest zinc release rate obtained was 1.3 g/l-hr. None of these values i s necessarily the maximum achievable. i i T o tal carbon and n o n - d i s t i l l a b l e ammonium ion concentrations proved to be s a t i s f a c t o r y measures of biomass concentration. Yield c o e f f i c i e n t s calculated from these data were constant for the d i l u t i o n rates investigated, i n d i c a t i n g a low maintenance energy requirement for the organism. The value of the net ammonium ion y i e l d constant suggests that addition of ammonium ion above the l e v e l present in the medium 9K of Silverman and Lundgren should be b e n e f i c i a l when zinc concentrations exceed 68 g/1. Percentage zinc extractions increased with decreasing d i l u t i o n rate, but s u f f i c i e n t l y low d i l u t i o n rates to achieve extractions which would be competitive with conventional processes were not used. Recommendations are given for achieving competitive extractions by a l t e r i n g the process configuration. When the percentage zinc extraction was known for one d i l u t i o n rate, i t was possible to use a c a l c u l a t i o n method given by Levenspiel to predict the extractions at other d i l u t i o n rates. i i i Contents Page Abstract .- i Contents - i i i L i s t of Tables v i L i s t of Figures ix Acknowledgements x i i Nomenclature .«,.,-. x i i i I. INTRODUCTION 1 I I . LITERATURE REVIEW A. Mathematical Models for Microbial Growth 1. Types of models 3 2. Stochastic models 5 3. Unstructured deterministic models 7 4. Structured deterministic models 23 5. Models for heterogeneous fementations .... 29 B. B a c t e r i a l Leaching 1. Introduction 32 2. N u t r i t i o n a l requirements 33 3. Mechanism of b a c t e r i a l leaching 34 U. B a c t e r i a l leaching rates 38 5. Yield of bacteria 40 6 . Review of Torraa's work 44 I I I . DERIVATION OF MODEL ... 50 IV. APPARATUS AND MATERIALS A. Apparatus 56 B. Materials 60 V. PROCEDURES A. B a l l M i l l i n g 63 B. Surface Area Determination 63 C. Shake Flask Leaches 66 iv D. Analysis of the Zinc Concentrate .............. 67 E. Monitoring the Continuous Stirred Tank 1. Total organic carbon ...................... 69 2. N o n - d i s t i l l a b l e ammonium ion 70 3. Pulp density 71 4. Miscellaneous 72 VI. RESULTS AHD DISCUSSION A. Preliminary Experiments 1. Analysis of the 2inc concentrate .......... 75 2. Percentage extraction - m i l l i n g time experiment 81 3. Development of the non-distillafcle (net) ammonium icn method 83 4. Development of the pulp density determination procedure „ 84 5. Non-ideal product removal frem the tank ... 93 B. Continuous Leaching Experiments 1. Introduction .............................. 99 2. " S t e r i l e " run 100 3. Kinetic data a. Correlation of data 104 b. Wall growth 122 c. Generation time 123 d. Zinc concentrations and release rates . 123 e. Batch run 134 f . Oxygen uptake rates 134 g. Production of heat .................... 137 4. Yields 138 5. Percentage extractions .................... 144 6 . Mass balance on 2inc .. 146 7. Dissolved iron concentration and pII . . . . . . . 148 8. Acid and antifoam requirements ............ 148 9. Concentration of surface area in feed 151 10. I n d u s t r i a l applications ................... 151 VII. SUMMARY AND CONCLUSIONS 156 VIII. REFERENCES 159 APPENDIX I Calculation of percentage zinc extracted in batch shake flask experiments (Table VI) .... 164 APPENDIX II Regression analysis of tank and product dissolved zinc concentrations ............... 166 V APPENDIX I I I S t e r i l e run data 170 APPENDIX IV Continuous l e a c h i n g aata 173 APPENDIX V C a l c u l a t i o n s f o r s t e a d y - s t a t e achieved 22-11-71 to 27-11-71 i n c l u s i v e 190 APPENDIX VI C a l c u l a t i o n of f r a c t i o n a l e x t r a c t i o n u s i n g L e v e n s p i e l ' s model 199 vi L i s t of Tables Page Table I Geometric r a t i o s for s t i r r e d tank reactor (refer to Figure 3) 58 Table II Zinc, i r o n , and sulphur analysis of zinc concentrate (as received) .... 76 Table III Analysis of variance for zinc content of zinc concentrate 78 Table IV Analysis of variance for ir c n content cf zinc concentrate 79 Table V Analysis of variance for sulphur content cf zinc concentrate 80 Table VI Percentage extraction - m i l l i n g tine r e s u l t s 82 Table VII D i s t r i b u t i o n of organic material between s o l i d s and f i l t r a t e : 10% HCl wash 87 Table VIII D i s t r i b u t i o n of organic material between s o l i d s and f i l t r a t e : acetone wash 88 Table IX D i s t r i b u t i o n of organic material between s o l i d s and centrifugate: '\0% HCl wash ....... 90 Table X D i s t r i b u t i o n of organic material between s o l i d s and centrifugate: pH 2 wash 92 Table XI D i s t r i b u t i o n of zinc i n tank and product samples 95 Table XII Comparison of tank and product sample concentrations for steady-state 28-07-72 29-07-72 97 Table XIII Summary of slopes and intercepts for steady-state r e s u l t s ........................ 110 Table XIV Summary of percentage zinc extractions 117 Table XV Summary of mass balances on zinc 147 Table XVI Acid and antifoam requirements for i r o n -free 9K medium i 149 v i i Table XVII Concentration of surface in feed and product ..................................... 152 Table XVIII Regression analysis of tank and product dissolved zinc concentrations 168 Table XIX B a c t e r i a l growth rates for continuous leaching at d i l u t i o n rate = 0.0588 h r - 1 ( S t e r i l e Run) 171 Table XX Yield constants for continuous leaching at d i l u t i o n rate = 0.0588 hr" 1 ( S t e r i l e Run) ... 171 Table XXI Results for continuous leaching at d i l u t i o n rate = 0.0588 hr- 1 ( S t e r i l e Run) 172 Table XXII B a c t e r i a l growth rates for continuous leaching at d i l u t i o n rate = 0.0171 h r - 1 174 Table XXIII B a c t e r i a l growth rates for continuous leaching at d i l u t i o n rate = 0.0284 hr- 1 175 Table XXIV B a c t e r i a l growth rates for continuous leaching at d i l u t i o n , r a t e = 0.0595 h r - 1 ..... 176 Table XXV B a c t e r i a l growth rates for continuous leaching at d i l u t i o n rate = 0.1038 h r - 1 ..... 177 Table XXVI Y i e l d constants for continuous leaching at d i l u t i o n rate = 0.0171 h r - 1 (corrected for chemical leaching) .......................... 178 Table XXVII Yield constants for continuous leaching at d i l u t i o n rate = 0.0284 h r - 1 (corrected for chemical leaching) 179 Table XXVIII Yield constants for continuous leaching at d i l u t i o n rate = 0.0595 h r - 1 (corrected for chemical leaching) .......................... 180 Table XXIX Yie l d constants for continuous leaching at d i l u t i o n rate = 0.1038 h r - 1 (corrected for chemical leaching) 181 Table XXX • Results f o r continuous leaching at d i l u t i o n rate = 0.0171 h r - 1 (zinc values uncorrected for chemical leaching) 182 v i i i Table XXXI Results for continuous leaching at d i l u t i o n rate = 0.0284 h r - 1 (zinc values uncorrected for chemical leaching) ...................... 183 Table XXXII Results for continuous leaching at d i l u t i o n rate = 0.0595 hr- 1 (zinc values uncorrected f o r chemical leaching) 184 Table XXXIII Results for continuous leaching at d i l u t i c n rate = 0.1038 h r - 1 (zinc values uncorrected for chemical leaching) 185 Table XXXIV Results for continuous leaching at d i l u t i o n rate = 0.0171 hr ~ l (zinc values corrected for chemical leaching) 186 Table XXXV Results for continuous leaching at d i l u t i c n rate = 0.0284 h r - 1 (zinc values corrected for chemical leaching) 187 Table XXXVI Results f o r continuous leaching at d i l u t i o n rate = 0.0595 h r - 1 (zinc values corrected for chemical leaching) 188 Table XXXVII Results for continuous leaching at d i l u t i c n rate = 0.1038 hr-» (zinc values corrected for chemical leaching) ...................... 189 Table XXXVIII Product data for sample c a l c u l a t i o n 197 Table XXXIX Summary of daily tank data, 22-11-71 27-11-71 197 Table XL Summary of tank data for sample c a l c u l a t i o n . 198 Table XLI Calculation of f r a c t i o n a l extraction ........ 203 ix L i s t of Figures Page Figure 1 Luedeking*s graphical solution for continuous fermentation i n a single vessel (14) ............ 21 Figure 2 Schematic diagram of the continuous leaching apparatus 57 Figure 3 Schematic diagram of s t i r r e d tank reactor showing dimensions (refer to table I) ........... 59 Figure 4 Schematic diagram of nutrient medium feed c i r c u i t 61 Figure 5 Schematic diagram of the dynamic nitrogen adsorption apparatus 65 Figure 6 Steady-state net ammonium ion concentration vs. surface area concentration .................. 106 Figure 7 Steady-state t o t a l carbon concentration vs. surface area concentration 107 Figure 8 Steady-state net ammonium ion concentration vs. pulp density ................................ 108 Figure 9 Steady-state t o t a l carbon concentration ' vs. pulp density 109 Figure 10 Slope vs. r e c i p r o c a l d i l u t i o n rate f o r net ammonium ion - surface concentration plot (Figure 6) 112 Figure 11 Slope vs. r e c i p r o c a l d i l u t i o n rate for t o t a l carbon - surface concentration plot (Figure 7) .. 113 Figure 12 Slope vs. r e c i p r o c a l d i l u t i o n rate for net ammonium ion - pulp density plot (Figure 8) 114 Figure 13 Slope vs. r e c i p r o c a l d i l u t i o n rate for t o t a l carbon - pulp density plot (Figure 9) ........... 115 Figure 14 Growth rate expressed as net anmonium icn vs surface area concentrations .................. 120 Figure 15 Growth rate expressed as t o t a l carton vs. surface area concentrations ................. 121 X Figure 16 Steady-state zinc concentration vs. surface area concentration (not corrected for chemical leaching) 124 Figure 17 Slope vs. r e c i p r o c a l d i l u t i o n rate for uncorrected zinc - surface area concentration plot (Figure 16) 125 Figure 18 Steady-state zinc concentration vs. pulp density (not corrected for chemical leaching) ... 126 Figure 19 Slope vs. re c i p r o c a l d i l u t i o n rate for uncorrected zinc - pulp density plot (Figure 18) 127 Figure 20 Steady-state zinc concentration vs. surface area concentration (corrected f o r chemical leaching) 128 Figure 21 Slope vs. re c i p r o c a l d i l u t i o n rate for corrected zinc - surface area concentration plot (Figure 20) 129 Figure 22 Steady-state zinc concentraticn vs. pulp density (corrected for chemical leaching) ....... 130 Figure 23 Slope vs. r e c i p r o c a l d i l u t i o n rate for ' corrected zinc - pulp density plot (Figure 22) 131 Figure 24 Zinc release rate vs. surface area concentration (not corrected f o r . chemical leaching) 132 Figure 25 Zinc release rate vs. surface area concentration (corrected for chemical leaching) . 133 Figure 26 Dissolved z i n c vs. time curve for batch leaching i n the s t i r r e d tank reactor ............ 135 Figure 27 Net ammonium i c n y i e l d constant vs. d i l u t i c n rate 139 Figure 28 Total carbon y i e l d constant vs. d i l u t i c n rate ... 140 Figure 29 Ratio of t o t a l carbon yield to net ammonium ion y i e l d vs. d i l u t i c n rate 141 xi Figure 30 Banco size d i s t r i b u t i o n analysis of feed concentrate 201 Figure 31 Fractional extraction vs. ciimensionless residence time calculated from Levenspiel's model (17) 202 Figure 32 Measured f r a c t i o n a l extraction vs. f r a c t i o n a l extraction predicted by Levenspiel's model (17) . 206 x i i Acknowledgements With pleasure I acknowledge the contributions of the following people and organizations: Dr. D. H., Duncan, Dr. R. M. s. Branion, and Er. K. L. Pinder provided guidance, i n s t r u c t i o n and friendship throughout the course of this work. I am indebted to B. G. Research for allowing me f u l l use cf t h e i r , f a c i l i t i e s for the research program. The technical i n s t r u c t i o n of Hilde Kurtz and Margaret Lewis i s appreciated. I have had many valuable discussions with Dr. R., 0. McElroy which have given me a better perspective on the f i e l d of hydrometallurgy. The Chemical Engineering workshop and stores personnel have been most cooperative in a l l aspects of equipment design and maintenance. Mr. Bruce Bowen supplied a sample of s i l i c a spheres for one of the experiments. The zinc concentrate was provided by Cominco Ltd. I wish to thank my wife Pat for her support during my graduate studies. . Fi n a n c i a l support for t h i s research was provided by the National Research Council of Canada and Shell Canada Limited. x i i i NOMENCLATURE a = a c t i v i t y A = constant b = stoichiometric c o e f f i c i e n t B = constant D = d i l u t i o n r ate, F/V, or diameter E = rate constant f o r maintenance energy metabolism, or electrode p o t e n t i a l f = surface area occupied per unit of concentration of attached bacteria, or a polynomial function F - volumetric rate of removal of material from fermentor, or free energy FEE = free energy e f f i c i e n c y G = G-mass, struc t u r a l / g e n e t i c biomass, or G-mass concentration h = constant H = enthalpy, or height k = rate constant K = saturation constant L = length M = dead biomass N = c e l l number concentration pd •= pulp density P = P-mass, synthetic biomass, or P-mass concentration Q = oxygen uptake c o e f f i c i e n t r = growth rate, release rate, or substrate consumption rate s = surface area concentration xiv S = substrate, or substrate concentration SSA = s p e c i f i c surface area t = time, or residence time T = toxicant TC = t o t a l carbon concentration V = vi a b l e biomass, or viable biomass concentration, or volume of fermentor W = width X = c e l l mass concentration, or f r a c t i o n a l extraction y = an observation Y = y i e l d of c e l l mass or numbers based on substrate consumption GREEK a = constant A = change i n K = k - l / k l u = s p e c i f i c growth rate, r^/X, or r^/N v = s p e c i f i c growth rate for bacteria which are attached to mineral p = density o = concentration of bacteria attached to mineral x = time for t o t a l consumption of p a r t i c l e <J> = constant SUBSCRIPTS b baseline chemical leaching, or b a f f l e B b a r r e l c t o t a l carbon C c r i t i c a l d i l u t i o n rate CH chemical leaching G G-mass i impeller I i n h i b i t o r L l i g u i d IB maximum s p e c i f i c growth rate n net ammonium ion N c e l l numbers o i n i t i a l , or feed OX leaching of oxidized zinc mineral p P-mass s s l u r r y s substrate t tank T toxicant X c e l l mass z dissolved zinc 1 I. INTRODUCTION The bacterium T h i o b a c i l l u s ferrcoxidans i s of int e r e s t to the mining industry because i t par t i c i p a t e s i n the leaching of a variety of metals from their s u l f i d e ores. Much research e f f o r t has been directed towards developing processes using 1-. ferrcoxidans for microbiological leaching of heaps or dumps of low grade mineralization which cannot be handled economically by conventional mineral dressing techniques. It has teen proposed that microbiological leaching could be used to advantage in treating mineral concentrates as well as low grade material (1). This type of leaching would take place in a batch or continuous flow chemical reactor in which the process could be more re a d i l y controlled than could be a dump leaching system. In chemical engineering, i t i s common tc model processes mathematically. This permits mathematical rcanipulations to replace time consuming and costly experimentation in the search for the best configuration and optimum values of operating parameters for the process. In addition, because mathematical models may be based on hypotheses about the mechanisms which determine process behaviour, comparison of predicted and experimental results f i e l d s greater understanding cf these mechanisms. 2 The o b j e c t i v e c f t h i s work i s t o d e v e l o p a m a t h e m a t i c a l model f o r T_. f e r r c o x i j a n s g r o w i n g cn z i n c s u l p h i d e c o n c e n t r a t e i n c o n t i n u o u s c u l t u r e . 3 II . LITERATURE REVIEW A. Mathematical Models For Microbial Growth 1. Types of Models Many of the models to be considered seek to represent a l l phases of batch growth, and w i l l he judged in part cn whether or not they do t h i s . The importance of this c r i t e r i o n when the batch models are adapted to continuous culture l i e s in the fact that a l l aspects cf batch growth must manifest themselves in continuous culture (2). For example, i f we consider the lag phase to be a period of adaptation for the bacterium, then the transient response to a step change of a variable in continuous culture should show the ef f e c t of adaptation cf the bacterium to the new conditions e x i s t i n g in the fermentor. There are a number of d i f f e r e n t assumptions which can lead tc models which w i l l ( q u a l i t a t i v e l y ) predict a l l phases of batch growth. Tsuchiya et a l . (2) discussed possible approaches to the problem of dynamic modelling of microbial c e l l populations, and proposed several c l a s s i f i c a t i o n s for models. They noted that l i f e i s segregated into s t r u c t u r a l and functional units c a l l e d c e l l s which can only a r i s e from preexisting c e l l s . Therefore, in any complete theory cf c e l l u l a r population dynamics, the number of c e l l s per unit volume w i l l be the fundamental dependent variable. In b a c t e r i a l leaching of mineral sulphides, firm attachment of c e l l s to the surface of the mineral lakes c e l l counts v i r t u a l l y impossible. Thus, the c e l l number w i l l need to be replaced by some more e a s i l y attainable treasure of population such as b a c t e r i a l carbon or nitrogen analysis. The model for co r r e l a t i n g the data w i l l use such empirical measures of concentration of l i v i n g substance, and w i l l treat l i f e as something dis t r i b u t e d throughout the medium i n which the c e l l s are growing. This gives us the f i r s t means of c l a s s i f y i n g a model: i t may be either a segregated model or a di s t r i b u t e d model. A segregated model recognizes the existence of c e l l s and uses c e l l number as the fundamental dependent variable. A dis t r i b u t e d model does not recognize the segregation of biomass into c e l l s and uses a measure of biomass ether than c e l l numbers as the fundamental dependent variable. While the process of growth can be treated in both models, the process of reproduction can only be treated by segregated models. A second basis f e r c l a s s i f i c a t i o n i s that the l i v i n g material may be assumed to te either structured or unstructured. A segregated model contains structure i f some means i s sp e c i f i e d for distinguishing a c e l l from i t s fellows. A di s t r i b u t e d model contains structure i f the composition of the l i v i n g substance (or biomass) varies with conditions of propagation. The 5 inc l u s i o n of structure i s a recognition that a c e l l i s not of homogeneous composition; i t i s d i f f e r e n t i a t e d , and the proportions of the d i f f e r e n t i a t e d structures may vary. The physiological state cf a c e l l i s determined by i t s structure. In a structured model, s p e c i f i c a t i o n of the state of the population requires s p e c i f i c a t i o n cf mere than cne quantity. F i n a l l y , we may use either stochastic or deterministic models. In f a c t , a c e l l population i s always segregated and structured, and i t s growth and reproduction are random processes which should be treated s t o c h a s t i c a l l y . Predictions of stochastic models are in the form of freguency d i s t r i b u t i o n s ; there i s a range of possible r e s u l t s due to randomness of b i o l o g i c a l processes. Deterministic models predict only discrete r e s u l t s for any given set of conditions; they assume that i n a large c e l l population the randomness w i l l average out to the predicted r e s u l t s every time. A stochastic model containing a l l aspects of structure i s beyond the scope of our b i o l o g i c a l and mathematical s o p h i s t i c a t i o n , so that s i m p l i f i e d approaches are necessary to give useful r e s u l t s . 2. Stochastic Models Tsuchiya et al., (2) derived a segregated, unstructured, stochastic model. This simple model simulated the exponential phase of growth only. By investigating the moments of the' 6 d i s t r i b u t i o n , they concluded that for small inocula, observations on many i d e n t i c a l systems would te widely scattered about the mean. However, for inocula of the sizes usually encountered, they concluded that for p r a c t i c a l purposes the qrowth process can te regarded as deterministic. Fredrickson and Tsuchiya (3) presented a segregated, structured, stochastic model in which the structure was provided by considering age as an index of physiological state of the c e l l . C e l l d i v i s i o n , death, and autolysis p r o b a b i l i t y densities were thus considered as functions of c e l l age. The r e s u l t i n g equations were solved for the c e l l age d i s t r i b u t i o n in a continuous fernsentor at steady-state. The steady-state obtained was probably stable with no o s c i l l a t i o n s , but this was not proved. Expressions for c a l c u l a t i n g gross metabolic rates and c e l l size d i s t r i b u t i o n s were derived. Eakman et a l . (4) modified the above model by considering c e l l mass to be a better index of physiological state than c e l l age. This allowed them to treat the rate of increase of mass of a sing l e c e l l by existing deterministic models, so that e x p l i c i t account could be taken cf the i n t e r a c t i o n between population and environment. The equations were solved for the case of the steady-state continuous fermentor. They concluded that d i s t r i b u t e d models are adequate tc describe the results when the d i l u t i o n rate i s not near the c r i t i c a l d i l u t i o n rate. 7 The s t o c h a s t i c models which have been d i s c u s s e d a r e o n l y v a l i d when e n v i r o n m e n t a l c o n d i t i o n s a r e c o n s t a n t o r c h a n g i n g s l o w l y , t h a t i s , when growth i s b a l a n c e d (4). They c a n n o t p r e d i c t a l a g phase i n b a t c h c u l t u r e , nor c a n t h e y c o r r e c t l y p r e d i c t t r a n s i e n t c o n d i t i o n s i n c o n t i n u o u s c u l t u r e1. E l a b o r a t e e x p e r i m e n t s a r e n e c e s s a r y t o o b t a i n t h e d i s t r i b u t i o n f u n c t i o n s f o r c e l l d i v i s i o n and d e a t h ( e . g . s y n c h r o n o u s c u l t u r e s t u d i e s ( 3 ) ) . T h e s e o b j e c t i o n s , t o g e t h e r w i t h t h e m a t h e m a t i c a l c o m p l e x i t y o f t h e s t o c h a s t i c m o d e l s , have r e s u l t e d i n d e t e r m i n i s t i c models b e i n g more p o p u l a r i n t h e l i t e r a t u r e . 3. U n s t r u c t u r e d D e t e r m i n i s t i c M o d e l s In many o f the models t o be d i s c u s s e d b e l o w , t h e f o l l o w i n g c e l l mass ( o r c e l l numbers) b a l a n c e and l i m i t i n g s u b s t r a t e b a l a n c e e q u a t i o n s w i l l be combined w i t h an e x p r e s s i o n f o r growth r a t e t o d e r i v e e x p r e s s i o n s f o r b a c t e r i a l g r o w t h i n a c o n t i n u o u s s t i r r e d f e r m e n t o r w i t h no r e c y c l e o r f e e d o f b a c t e r i a . 1 T h e s e o b j e c t i o n s may be removed by t h e i n c l u s i o n o f a l i m i t e d amount o f b i o c h e m i c a l s t r u c t u r e i n t o t h e m o d e l s . The e q u a t i o n s f o r s u c h a model have been d e v e l o p e d , b u t not y e t s o l v e d (4). 8 = rX ~ DX (cell mass concentration) (1) = r^j - DN (cell numbers concentration) dS rX ^ = DSQ - DS - -y- (substrate concentration) (3) Tsuchiya et a l . (2) discussed two simple deterministic models in which the growth rate i s a function only of the number of c e l l s present. The f i r s t y i e l d s only the exponential phase in batch growth: r N = uN (4) If the bacteria are considered to be growing in a ccntinuous s t i r r e d fermentor, the c e l l number balance gives dN ? r = uN - DN (5) so that at steady-state 9 u = D (6) Since u i s a constant (here) there can be only one steady s t a t e , and the population density i s indeterminate. This contradicts the experimental observation that d i f f e r e n t steady-states may be attained over a range cf d i l u t i o n rates. The second model assumes the " l o g i s t i c law": where a and h are posit i v e constants. In batch growth (D = 0), t h i s may be integrated to give the l o g i s t i c curve: As t -»• 00 , N approaches 1/h, giving a stationary phase following the exponential growth. No lag phase i s predicted. In continuous c u l t u r e , at steady-state. r N = oN (1 - hN) (7) N = "oc  1 - hN (1 - eat) o (8) D = a (1 - hN) (9) In contrast to eguation 6, a steady-state can be obtained for 10 any d i l u t i o n rate less than a . At E = a , a steady-state i s also attained, but N = 0. This r e s u l t i s much more s a t i s f a c t o r y than the previous one, but i t i s suspect because no allowance i s made for the r e c i p r o c a l e f f e c t of bacteria on environment and environment on bacteria. This objection can be overcome by making assumptions f i r s t suggested by H'Kendrick and Pai (5). They postulated that exponential growth can occur only when unlimited nuttient i s ava i l a b l e , and that when this was exhausted, growth must stop. Their expression gave growth rate as r N = 4>NS (10) where S i s the growth l i m i t i n g substrate ccncentraticn. The concentration of growth l i m i t i n g substrate i s influenced by the rate of consumption of substrate which i s assumed to be rS = " T r N ( 1 1> In batch growth, equations 10 and 11 lead to the l o g i s t i c equation 8 where a = <j> (S + (1/Y)NQ) and h = (1/Y)/(S Q+ (1/Y)N ). Now a and h have a physical s i g n i f i c a n c e . Monod (6,7) improved on the theory of M'Kendtick and Pai in 11 two ways. He r e a l i z e d t h a t they were i n e f f e c t p o s t u l a t i n g a chemical r e a c t i o n between the c e l l m a t e r i a l and the s u b s t r a t e , so that c e l l mass c o n c e n t r a t i o n , not p o p u l a t i o n d e n s i t y should be the dependent v a r i a b l e ; i . e . , a d i s t r i b u t e d model was r e q u i r e d . He a l s o r e c o g n i z e d t h a t there was a l i m i t to hew f a s t a c e l l c ould grow, so he p o s t u l a t e d t h a t s u b s t r a t e dependence of growth f o l l o w the Michaelis-Menten enzyme k i n e t i c s e x p r e s s i o n : rx = TT~s ( 1 2 ) This", together with r x = - Y r s (13) c o n s t i t u t e d Monod's model. Moncd was very c a r e f u l t c e x p l a i n t h a t equation 12 was an e m p i r i c a l r e l a t i o n which was found to e x p l a i n the data q u i t e w e l l . Monad co n s i d e r e d i t to be an extremely remote p o s s i b i l i t y t h a t only one of a l l the r e a c t i o n s i n v o l v e d i n growth should be so slow as to be r a t e c o n t r o l l i n g . T h e r e f o r e equation 12 should not be co n s i d e r e d as r e p r e s e n t i n g the Michaelis-Menten k i n e t i c s of a one enzyme c a t a l y z e d "master r e a c t i o n " . In batch growth, X i n c r e a s e s e x p o n e n t i a l l y at f i r s t , but a s t a t i o n a r y phase occurs when s u b s t r a t e i s exhausted. There i s no 12 laq phase. The maximum concentration of protoplasm i s X = X + YS =- YS (14) o o o Herbert et al_. (8) developed Honod's model for the continuous case. Using equations 12 and 13 in eguations 1 and 3, they derived the d i f f e r e n t i a l eguaticns § " x { % icT-s - D> , 1 5 ) f - D(S0-S) -^(K-h) "6> Setting these to zero, they obtained the steady-state c e l l mass concentration and substrate concentration: S = K ( D n) (18) and also 13 S = SQ ,19) X = 0 . (20) Tsuchiya et al., (2) showed that the f i r s t steady-state (equations 17 and 18) i s stable i f > D < 2 1 ) and unstable i f the inequality i s reversed. When i t i s sta b l e , no o s c i l l a t i o n s w i l l be observed in the approach tc steady-s t a t e . The second steady-state (equations 19 and 20) i s stable i f m° < D ,22) K+S o and unstable i f the inequality i s reversed. This corresponds to complete washout of c e l l s , so that one i s normally more interested i n the f i r s t steady-state. The point of equality 14 " D = DC <23> g i v e s t h e c r i t i c a l d i l u t i o n r a t e . B e c ause the c r i t i c a l d i l u t i o n r a t e i s t h a t a t which c e l l s wash o u t , i t i s an o p e r a t i n g p a r a m e t e r o f c o n s i d e r a b l e p r a c t i c a l i m p o r t a n c e . H e r b e r t e t a l . (8) used A e r o b a c t e r c l o a c a e t o make q u a n t i t a t i v e e x p e r i m e n t a l t e s t s o f t h e m o d e l . The model was a d e q u a t e t o e x p l a i n t h e d a t a e x c e p t n e a r t h e c r i t i c a l d i l u t i o n r a t e . S t e a d y - s t a t e was o b t a i n e d a t d i l u t i c n r a t e s h i g h e r t h a n t h e p r e d i c t e d c r i t i c a l d i l u t i o n r a t e . The r e a s o n f o r t h e d i s c r e p a n c y was b e l i e v e d t o be n c n - i d e a l m i x i n g i n t h e f e r m e n t o r as w e l l a s w a l l g r o wth cn t h e f e r m e n t o r . The y i e l d c o n s t a n t was s i m i l a r t o t h e v a l u e o b t a i n e d i n b a t c h e x p e r i m e n t s f o r low d i l u t i o n r a t e s , but d e c r e a s e d a t h i g h e r d i l u t i c n r a t e s . Dabes e t a l . . (9) d e v e l o p e d a g e n e r a l model o f a s e r i e s o f l i n k e d r e v e r s i b l e e n z y m a t i c r e a c t i o n s d e p e n d e n t on t h e c o n c e n t r a t i o n o f a s i n g l e e x t e r n a l s u b s t r a t e . A p p l y i n g t h e mas t e r r e a c t i o n c o n c e p t and u s i n g d i f f e r e n t s i m p l i f y i n g a s s u m p t i o n s , t h e y were a b l e t o d e r i v e t h e f o l l o w i n g t h r e e m o d e l s : -when two s l o w e n z y m a t i c s t e p s a r e s e p a r a t e d by a s e r i e s o f 15 fast reactions that together can be described by an equilibrium constant that i s not large, B + + S - /(B + Ay-, + S)2 - 4 A % S V - " 2~K ' • <24> where A, B, and u m are defined in terms of parameters of the assumed enzymatic pathway. -when the equilibrium constant for the intermediate reactions i s larqe, Blackman k i n e t i c s r e s u l t : u = , when S < Au-j (25) u = u m , when S > AUj,, (26) -when the maxinum forward rate of one enzymatic reaction in the c e l l may be assumed to be much less than the maximum forward rate of any other reaction in the pathway, Mcnod*s model (equation 12) r e s u l t s . These workers then examined twelve sets of experimental data from the l i t e r a t u r e and showed that the Mcnod model gave a poorer f i t than the Blackman model in nine cf the twelve cases 16 as determined by a non-linear least-squares f i t t i n g technique. S i n c l a i r et al.. (10) have modified Mcnod's model to account for u t i l i z a t i o n of substrate to provide maintenance energy for the bacteria. The steady-state b a c t e r i a l concentration predicted i s This predicts that the y i e l d cf bacteria per unit of substrate consumed decreases at lew d i l u t i o n rates as a greater portion of the energy released i s diverted for maintenance reguireirents. Ware (11) developed Monod's model to handle mixed cultures (more than one s t r a i n of bacteria), mutations, and the addition of antimicrobial agents. I n i t i a l lag was introduced by creating an a r t i f i c i a l delay in the organism's response to substrate. A c e r t a i n maximum concentration of c e l l s (the M-concentration) could not be exceeded even i f substrate was net yet exhausted; a rate modifying factor was introduced to ensure t h i s . The e f f e c t of bactericides was given by another rate modifying factor. The actual growth rate at any time was calculated a f t e r considering these three modifying e f f e c t s . Other modifications included provision for death of c e l l s naturally and by bactericides, and adsorption of bactericides by dead c e l l s . The equations for batch culture were sclved i n Algol 60 on a d i g i t a l computer. X = 0 + E YD CD + E) "I - (D + E)J (27) 17 Continuous culture was not treated. It i s f e l t that Ware's simulation, although able to reproduce a l l phases of b a c t e r i a l growth and to account for numerous other factors, has l o s t much of i t s potential usefulness because of the a r b i t r a r y manner in which some of the e f f e c t s were taken into account. It may be useful in a predictive sense, but i t gives no insight into the reasons for the appearance of a lag phase or a maximum population. Consideration w i l l now be given to alternative unstructured deterministic models which give better understanding of how properties of the culture can determine the appearance of various batch growth phases. We have seen that the Monod model predicts exponential growth i n i t i a l l y while substrate concentration i s high, followed by a stationary phase when substrate i s exhausted. Andrews (12) observed that high concentrations of substrates could i n i t i a l l y be i n h i b i t o r y to organisms metabolizing them, and that this could r e s u l t i n a lag phase in their growth curve. Just as Monodfs empirical r e l a t i o n was s i m i l a r to the Michaelis-Menten expression for enzyme k i n e t i c s , Andrews chose an " i n h i b i t i o n function" s i m i l a r in form to one used to describe substrate i n h i b i t i o n in enzyme k i n e t i c s : 18 u = K + S + S2/KX (28) This expression was used in formulation of d i f f e r e n t i a l equations for batch and continuous growth. The equations were solved numerically on a d i g i t a l computer. In batch growth, substrates with low values of K_ produced pronounced lag phases. In continuous culture i t was fcund that there were two possible steady states, one of which was unstable. Successful startups required a minimum inoculum size below which the process f a i l e d . If start-up took the form of a ramp change i n substrate concentration rather than a step change, successful start-ups could be achieved with lower inoculum s i z e s . As with the Honod model, a stationary phase should occur at substrate exhaustion, although this was net demonstrated. Besides exhaustion of substrate, stationary phase iray occur as a res u l t of accumulation in the medium of toxic or i n h i b i t o r y products of the c e l l s ' metabolism. Thus, a phase of decline may occur as the c e l l s are k i l l e d by a toxicant. 19 Ramkrishna et a l . ,13) developed a model i n which the reactions representing growth were given as In reaction 29 viable biomass and substrate react to produce more viable biomass plus toxicant and other iretabclic products. In reaction 30, viable biomass and toxicant react to form dead biomass, and toxicant may be consumed or produced, depending on the sign of fc^. The k i n e t i c s for reaction 29 are assumed to be given by the Monod equation. With b-p-^  p o s i t i v e , a l l growth phases except lag phase are present in simulated batch growth. b-p^  negative or zero gives a curve showing no lag or stationary phases. In continuous culture, two steady-states are predicted by t h i s model; one i s at washout and the other i s the "normal" steady-state. A c r i t i c a l d i l u t i o n rate i s predicted equal to that predicted by Mcnod's model. Camped o s c i l l a t i o n s about the normal steady-state may occur, for smaller d i l u t i o n rates. V + bsS -> 2 V + b T T + . (29) V + T - M + (1 + bT1) T (30) 20 Luedeking (14) in a review of fermentation process k i n e t i c s presented a graphical method fer predicting continuous culture r e s u l t s from batch culture data. The method i s presented in Figure 1. The b a c t e r i a l growth rate i s plotted against the b a c t e r i a l concentration for the entire batch c y c l e . A l i n e having slope equal to the desired d i l u t i c n rate and passing through the o r i g i n (the operating line) i s then drawn over t h i s curve. The in t e r s e c t i o n of the operating l i n e with the growth curve represents a steady-state mass balance cn bacteria for a continuous s t i r r e d tank reactor operating at the chosen d i l u t i o n rate. The b a c t e r i a l growth rate and b a c t e r i a l concentration at t h i s point should be those e x i s t i n g in the continuous reactor i f the feed has the same conditions as the i n i t i a l conditions for the batch experiment. Luedeking and Piret (15) have v e r i f i e d t h i s method for a single-stage continuous l a c t i c acid fermentation. Assumptions necessary for the accurate prediction of continuous r e s u l t s by t h i s method are that conditions in the continuous culture are the same as those i n the corresponding stage of batch c u l t i v a t i o n and that b a c t e r i a l concentration i s a v a l i d parameter for determining the rate of b a c t e r i a l grewth. The second assumption i s r e a l l y an i n d i r e c t way of expressing b a c t e r i a l growth rate as a function of both substrate 21 F i g u r e 1 LUEDEKING'S GRAPHICAL SOLUTION FOR CONTINUOUS FERMENTATION IN A SINGLE V E S S E L ( 14) BACTERIAL CONCENTRATION, X 22 c o n c e n t r a t i o n and b a c t e r i a l c o n c e n t r a t i o n . As b a c t e r i a l c o n c e n t r a t i o n i n c r e a s e s , the s u b s t r a t e c o n c e n t r a t i o n d e c r e a s e s u n t i l e x h a u s t i o n o f s u b s t r a t e t e r m i n a t e s the f e r m e n t a t i o n . Such c u r v e s a r e t h e r e f o r e unique o n l y t o a q i v e n i n i t i a l s u b s t r a t e c o n c e n t r a t i o n . For t h e s p e c i a l case of the f e r m e n t a t i o n c f a heterogeneous s u b s t r a t e , t h e growth r a t e s h o u l d depend cn c o n c e n t r a t i o n of s u b s t r a t e s u r f a c e a v a i l a b l e to the b a c t e r i a , not cn the s u b s t r a t e c o n c e n t r a t i o n (16). The u t i l i t y c f t h i s method then depends on whether the r e l a t i o n between b a c t e r i a l growth r a t e and b a c t e r i a l c o n c e n t r a t i o n w i l l be the same i n both b a t c h and c o n t i n u o u s c u l t u r e under t h i s s p e c i a l c o n s t r a i n t . F o r a s i n g l e s u b s t r a t e p a r t i c l e exposed to b a c t e r i a l a t t a c k , t h e s u b s t r a t e s u r f a c e a r e a and amount of s u b s t r a t e used a r e a f u n c t i o n o f t h e t i m e the p a r t i c l e has been exposed to the b a c t e r i a . In a batch r e a c t i o n , i f a l l t h e p a r t i c l e s are the same s i z e i n i t i a l l y , one s i m p l y m u l t i p l i e s the s u r f a c e area and amount of s u b s t r a t e used f o r one p a r t i c l e by the t o t a l p a r t i c l e c o n c e n t r a t i o n t o o b t a i n . the r e l a t i o n between the r e d u c t i o n i n s u b s t r a t e c o n c e n t r a t i o n and the s u r f a c e area c o n c e n t r a t i o n a t any t i m e . In a c o n t i n u o u s r e a c t o r , however, t h e r e i s a d i s t r i b u t i o n of p a r t i c l e ages, and the s u r f a c e a r e a c o n c e n t r a t i o n f o r any 23 reactor residence time must be determined by summing the surface areas of the p a r t i c l e s over a l l the ages. S i m i l a r l y , the reduction i n substrate concentration roust be calculated by summing the reductions for p a r t i c l e s of a l l ages (17). Evidently, the relationship between surface area concentration (and hence b a c t e r i a l growth rate) and substrate u t i l i z a t i o n (and hence b a c t e r i a l concentration) w i l l not need to be the same in batch as i n continuous culture. It i s dependent on the d i s t r i b u t i o n s of residence times which are quite d i f f e r e n t for the twc cases. Therefore, conditions i n a batch culture at a p a r t i c u l a r time are not the same as those in a continuous culture having that residence time when bacteria are consuming a heterogeneous substrate, and the method should not successfully predict the continuous leaching r e s u l t s from the batch data. 4. Structured Deterministic Models Up to now we have considered only deterministic models which lack structure. When structure i s added to a model, the c e l l composition changes with changing culture conditions. Therefore the behaviour of the biomass may be affected by i t s his t o r y . This enables structured models to predict a large number of observed phenomena of b a c t e r i a l growth. 24 One of the simplest structured models tc appear in the l i t e r a t u r e i s that cf Williams (18). The viable bicmass i s divided into two components, G-mass and P-mass. G-mass i s the structural/genetic portion of the c e l l and P-mass i s the synthetic portion. G-mass i s seen as consisting mainly of protein and DNA, while P-mass i s thought of as the sum t o t a l of small metabolites in the c e l l , together with the ribosomal p a r t i c l e s and BNA involved i n protein synthesis. C e l l d i v i s i o n i s said to occur i f and only i f the G portion has doubled i t s s i z e . The reactions which comprise growth are Assuming bimolecular f i r s t order reactions in a ccntinuous ferraentor, the d i f f e r e n t i a l equations are G + bgS + P-*2P + G + • • • • (31) bpP + G -»- 2 G (32) dS dt = D (Sc - S) - kjSV (33) 25 = krSV - k 2 PG - DP ,34) § = *2 pG - DG ,35) where V = G+P and batch fermentation i s simulated by putting D 0. Adding eguations 33 and 34 dP dG dV . rar at+ ar = dT = i - <36> which in batch culture i s s i m i l a r tc eguation 10 with V substituted for N. Thus, in batch culture, the growth curve for viable biomass i s given by the l o g i s t i c eguation. The model therefore gives results l i k e those of M'Kendrick and Pai (5) except that viable biomass i s substituted for c e l l numbers. Because of i t s structure, however, t h i s model w i l l predict a lag based on c e l l numbers, with the increase in viable biomass going into making the existing c e l l s larger rather than increasing t h e i r number. No phase cf decline i s predicted. i This simple model i l l u s t r a t e s a number cf other experimentally observed features cf c e l l population growth. It shows differences in response lag of d i f f e r e n t c e l l u l a r 26 components following a change in environmental conditions, and general growth curve shapes for toth steady-state and transient conditions in either batch or continuous cultures. There i s an absence of lag phase when the culture medium i s inoculated with already r a p i d l y growing c e l l s . C e l l s are able to continue di v i d i n g after being placed in non-nutrient medium. Some shortcomings of the model include the d i f f i c u l t y of determining what s h a l l constitute G-mass and P-mass, the lack of provision for a maximum growth rate (e.g. as i n the Mcnod equation), and the f a c t that the lag phase i s net perfect -there i s always some c e l l d i v i s i o n occurring. We have already mentioned the f i r s t part of a paper by Ramkrishna et al_. (13) , in which they postulated that stationary phase and phase of decline are the r e s u l t of toxicants released into the medium by the growing c e l l s . In the second part of that paper, by adding structure to the model, they were able to predict a l l phases cf batch growth, including a lag phase i n the viable biomass. They divided the c e l l into two parts, G- and P-mass, as did Williams, but they formulated the growth reactions and the growth reaction k i n e t i c s in a d i f f e r e n t manner. Ignoring the toxicant, growth was postulated as 27 G + bsS + P - 2 G + P (37) G + be S + P + 2 P + G + ,38) Here, qrowth of G did net occur at the expense cf P as i t did in Williams 1 model. The k i n e t i c s for these reactions were given by a double substrate Michaelis-Menten type expression: u N S G P R G (K + S)(KG + G ) ( 3 9 ) ypSGP rP (K' + S)(K£ + G) K ' so that there was a maximum growth rate at high substrate concentrations. In another paper (19), these authors assumed that the stationary phase was a resu l t of exogenous substrate exhaustion, and that the decline phase did not begin u n t i l stores of an endogenous substrate were depleted. Using the same type of structure (G-mass and P-mass), a l l phases of batch growth could 28 be predicted. Which of these l a s t two models i s better for a given s i t u a t i o n should be determinable by experimentation since some differences in behaviour in both batch and continuous culture are expected, even though each can predict q u a l i t a t i v e l y the same batch curves. The toxicant model predicts a large change in growth pattern as the i n i t i a l substrate concentration i s changed, while the endogenous metabolism model predicts l i t t l e d ifference. With the toxicant model, viable biomass concentration at steady-state f a l l s off at low d i l u t i o n rates; with the endogenous metabolism model, a f a i r l y constant viable biomass l e v e l i s maintained. O s c i l l a t i o n s in continuous culture viable biomass concentration are possible with the toxicant assumption, but not with the endogenous metabolism assumption. One other i n t e r e s t i n g approach to the problem of modelling a growing b a c t e r i a l population i s that cf Swanscn et al._ ,20). They consider the problem of b a c t e r i a l growth to be sim i l a r to certai n optimization problems in economics, termed "bottleneck" problems. In t h i s view, the rate of growth of the bicmass i s controlled by the concentration in the c e l l of a c r i t i c a l intermediate which i s produced at the expense of substrate. I t is postulated that the bacteria produce the c r i t i c a l intermediate ("bottleneck product") in such a way as to traximize the net increase in biomass by the time that the l i m i t i n g 29 nutrient i s exhausted. Solution of thi s problem leads to two sets of d i f f e r e n t i a l equations; one for lag phase, when the concentration of bottleneck product i s building up but no growth occurs, and the other for the remaining phases when no bottleneck product i s produced. Since provision for c e l l death i s included, this mcdel can predict a l l phases of c e l l population growth. The model has been solved only for batch culture. Because the point at which lag phase gives over to exponential growth i s a function of the i n i t i a l concentrations of substrate and bottleneck product, adaptation to continuous culture i s not guite so straightforward as i t has been in some of the previous models. I n t u i t i v e l y , i t seems that i t should be possible, invoking lag equations cnly for transient behaviour. This model i s i n t r i g u i n g because i t assumes that natural s e l e c t i o n has led to an optimal growth pattern. The optimal growth pattern turns out to be (qu a l i t a t i v e l y ) that which i s observed experimentally. 5. Models for Heterogeneous Fermentations Chakravarty et a l . (21) have presented a k i n e t i c mcdel for growth on a s o l i d hydrocarbon substrate. The model i s based on the assumption that a metabolite produced by the qrowinq c e l l s helps the dis s o l u t i o n of the s o l i d substrate in the aqueous medium so that i t can be used by the bacteria. The growth rate 30 of the bacteria i s related to the concentration of dissolved hydrocarbon according to the Moncd model. The concentration of the metabolite in the medium i s assumed to be proportional to the number of c e l l s present. The l i n e a r behaviour of the growth curve predicted by the model was v e r i f i e d experimentally. Erickson and Humphrey (22) have formulated three batch models for growth on a substrate which forms a second phase in the fermentor. The second phase i s assumed to be a pure substrate, and the i n t e r f a c i a l area i s assumed to decrease due to substrate consumption. No c e l l s are in the continuous phase u n t i l the surface of the dispersed phase becomes saturated with c e l l s . The f i r s t model assumes a l l growth occurs at the interface of the dispersed phase, and the s p e c i f i c growth rate for c e l l s at the surface i s a constant. The second model assumes substrate equilibrium between the two phases and growth occurs both at the in t e r f a c e and in the continuous phase. The t h i r d model assumes substrate consumption in the continuous phase i s limited by mass transfer of substrate into, that phase, and growth occurs both at the interface and in the continuous phase. By comparing these models to experimental re s u l t s they conclude that the concept of a growth rate proportional to the surface area of the dispersed l i q u i d phase itay be useful in 31 e x p l a i n i n g r a t e s of growth on n - a l k a n e s . S u r f a c e a r e a may l i m i t growth e i t h e r by a l l o w i n g o n l y a f r a c t i o n of t h e t o t a l c e l l p o p u l a t i o n t o be at a drop s u r f a c e or by l i m i t i n g the r a t e o f s u b s t r a t e t r a n s p o r t t o t h e c o n t i n u o u s phase, o r b o t h . They o b s e r v e d w i t h y e a s t c u l t u r e s t h a t a l a r g e number o f c e l l s a r e i n the c o n t i n u o u s phase even when t h e r e a r e not enough c e l l s t o c o v e r the drop s u r f a c e . An e q u i l i b r i u m s h o u l d e x i s t between t h o s e c e l l s at t h e drop s u r f a c e and those i n the c o n t i n u o u s phase. E r i c k s o n et a l . (23) d e v e l o p e d a model f o r growth cn a hydr o c a r b o n s u b s t r a t e which i s d i s s o l v e d i n a d i s p e r s e d phase. The model a c c o u n t s f o r drop s i z e d i s t r i b u t i o n , c o a l e s c e n c e and r e d i s p e r s i o n , growth i n the c o n t i n u o u s phase and a t the i n t e r f a c e , and a d s o r p t i o n and d e s o r p t i o n of b a c t e r i a a t the i n t e r f a c e . The a d s o r p t i o n r a t e i s assumed t o be p r o p o r t i o n a l t o the p r o d u c t o f t h e c e l l c o n c e n t r a t i o n i n the c o n t i n u o u s phase and the f r e e s u r f a c e a r e a per u n i t volume. The r a t e c f d e s o r p t i o n i s assumed t o be p r o p o r t i o n a l to t h e number o f c e l l s on the drop s . The d i f f e r e n t i a l e g u a t i o n s d e s c r i b i n g the model have been s o l v e d n u m e r i c a l l y f o r t h e case o f b a t c h growth o n l y . I t s h o u l d be p o s s i b l e t o adapt t h i s mcdel t o the case of c o n t i n u o u s b a c t e r i a l l e a c h i n g of s u l p h i d e m i n e r a l s . I f a s o l i d o r l i q u i d d i s p e r s e d phase s u r f a c e were s a t u r a t e d w i t h c e l l s and no qrowth were o c c u r r i n g i n t h e c o n t i n u o u s phase, 32 then the reaction could be modelled by the methods provided by Levenspiel (17) for heterogenecus reacting systems. His model for a shrinking spherical p a r t i c l e when chemical reaction at the surface i s c o n t r o l l i n g should apply to this system. He supplies the solutions for both batch reactors and continuous s t i r r e d tank reactors. B. B a c t e r i a l Leaching 1. Introduction Throughout the discussion of models, bacterium-environment in t e r a c t i o n has been described by means of inte r a c t i o n between the bacterium and a l i m i t i n g substrate. Thus, the models have been concerned not only with growth rates but also with y i e l d s of bacteria when a given amount of substrate has been consumed. We now wish to consider s p e c i f i c a l l y the bacterium used in this study, T. ferrgoxidans, i t s n u t r i t i o n a l requirements, possible l i m i t i n g substrates, and y i e l d and rate data which have appeared in the l i t e r a t u r e . We w i l l conclude by reviewing the work done by Torma (16) which was the basis for the present study. While examining a c i d i c coal mine drainage waters for a poll u t i o n study, Colmer and Hinkle (24) noted the presence of a bacterium involved in the oxidation of ferrous iron to the f e r r i c form. In subseguent papers, Colmer et al.. (25), and 33 Temple and Calmer (26) described morphological and c u l t u r a l c h a r a c t e r i s t i c s of the organism, demonstrated i t s autotrophic nature on thiosulphate and ferrous iron media, and suggested the s p e c i f i c name T t ferrqcxidans. Two organisms si m i l a r to T. ferrcoxidans have been is o l a t e d and described ( 2 7 , 2 8 ) . These were given the names Ferr o b a c i l l u s f grrcpx id ans and F_. sulfcoxidans, tut the v a l i d i t y of t h i s new genus has been questioned ( 2 9 , 3 0 ) . It i s now generally accepted that the three are the same organism. Moreover, any s l i g h t differences between them are ne g l i g i b l e in mineral applications ( 3 1 ) . They are, however, d i s t i n c t from the morphologically similar T.. tjjicoxidans due to the l a t t e r ' s i n a b i l i t y to oxidize ferrous iron ( 3 2 ) . 2. N u t r i t i o n a l Requirements N u t r i t i o n a l requirements of T_. ferroo xidans have been reviewed by Tuovinen and Kelly ( 3 3 ) . Enerqy i s derived from oxidation of i r o n , sulphur, and reduced sulphur compounds. The ultimate electron acceptor in the oxidation cf these substances i s oxygen dissolved in the medium. Carbon for the creation of biomass can be supplied e n t i r e l y by carbon dioxide dissolved in the medium. Nitrogen may be supplied as ammonium ion; some amino acids may be substituted as a nitrogen source. Fixation of atmospheric nitrogen has been c i t e d . Phosphate requirements are 34 s a t i s f i e d by orthophosphate ion. Magnesium i s required as a trace element t h e o r e t i c a l l y , but no one has demonstrated a measureable requirement. Sulphate i s required as a source of sulphur for biosynthesis; an additional role in the metabolism of T^ ferrooxidans as a complexing agent in ferrcus iron oxidation has been postulated. For purposes of modelling, we may consider only those nutrients whose concentrations might exert an e f f e c t on the leaching rate; i . e . , the possible l i m i t i n g substrates. The most l i k e l y l i m i t i n g substrates are sulphide mineral (expressed as surface area), oxygen, and carbon dioxide. A l l other nutrients can be made to be in excess. 3. Mechanism of B a c t e r i a l Leaching The release cf zinc ion into solution during b i o l o g i c a l leaching i s due to b a c t e r i a l oxidation cf the sulphide sulphur to sulphate: ZnS + 2 0 2 ZnS04 (41) Zinc sulphide concentrates usually cgntain some iron, and this w i l l also be released into s o l u t i c n during sulphide oxidation by the bacteria. Since ferrous iron i s an acceptable energy source for the bacteria, i t may be oxidized by them either d i r e c t l y on 35 the mineral surface (34) or in solution according to Fe+ + + 1/4 02 + H+ •* 1 / 2 H20 + Fe + + + (4 2) Some investigators (35,36) att r i b u t e the oxidation of metallic sulphides s o l e l y to the chemical action of a c i d i c f e r r i c iron solutions: MS + 2 Fe + + + •*• M++ + S° + 2 Fe + + (43) The bacteria would part i c i p a t e in the process only by regenerating the f e r r i c iron which becomes reduced to ferrous iron during the leaching reaction. sulphur produced may be oxidized by the bacteria to give sulphuric a c i d : s ° + 3 /2 °2 + H2° fySty There i s considerable evidence to show that the bacteria are able to attack the sulphide minerals d i r e c t l y . Tj, ferrooxidans has been shown to accelerate metal release from sulphides containing no iron (32,37). Duncan et a l ^ (34) used s e l e c t i v e i n h i b i t i o n of enzymes in the bacteria to show that the iron and sulphide in chalcopyrite and pyrite were attacked simultaneously and independently by the bacteria and that 36 sulphide oxidation was the rate c o n t r o l l i n g step. Additional support of the direct action theory i s provided by the carbon dioxide f i x a t i o n e f f i c i e n c y studies of Beck and Brown (38) who found that the e f f i c i e n c y of carbon dioxide f i x a t i o n by T.. ferrooxidans growing on pyrite and chalcopyrite was higher than would be expected i f the bacteria were simply regenerating f e r r i c iron in the system. Levels of f e r r i c iron in the l a t t e r two experiments were not reported but they were probably not too high. Duncan and walden (39) have determined that high levels of f e r r i c iron contribute l i t t l e to release of copper and zinc from sulphide minerals in a microbiological leaching system. There i s thus l i t t l e doubt that d i r e c t b a c t e r i a l attack of the mineral i s the major contributor to leaching of sulphide ores when conditions are favourable for growth of the organisms. Evidence for the attachment of bacteria to the mineral surface has been given by McGoran et al.. (40). They state that in excess of 96% of a b a c t e r i a l population grown on chalcopyrite and 77% of a population grown cn sulphur were associated with insoluble material. The chalcopyrite data are suspect (41) since i t has been shown that inorganic nitrogen may be precipitated as ammonio-jarosite, NH^Fe^ (SO^ )^ (°H)^ (42). This would have reported as b a c t e r i a l nitrogen in t h e i r procedure. 37 MacDonald and Clark (36) encountered severe wall growth on t h e i r fermentor, which demonstrates the a b i l i t y of the bacterium to attach to s o l i d surfaces. Duncan et al.. (43) have shewn that the lag that occurs before leaching of chalcopyrite begins can be shortened by addition of the surfactant Tween 20. They concluded that the a b i l i t y to contact the sulphide surface apparently was aided by the surfactant. Jones and Benscn (44) i s o l a t e d phosphatidyl g l y c e r o l from medium in which T,. thipoxidans had been growing. They concluded that t h i s l i p i d could provide surfactant a c t i v i t y e s s e n t i a l f e r metabolic attack at sulphur surfaces. Agate et al_. (45) have isolated similar compounds from medium in which F_. f errco xidans had been growing. Schaeffer et al.. (46) presented electron micrographs of r e p l i c a s of sulphur c r y s t a l s before and after attack by l i thiopxidans which shewed that the bacteria eroded the c r y s t a l immediately adjacent to the c e l l . Since direct contact appears to be necessary, the observed increase in leaching rate with mineral surface area (16,31,35,47,48,49) i s e a s i l y explained, The metabolism of sulphur compounds by t h i o b a c i l l i has been reviewed by Trudinger (50). In elemental sulphur oxidation, available evidence indicates that the i n i t i a l reaction i s between the sulphur surface and a c e l l u l a r component at the b a c t e r i a l surface. P a r t i c i p a t i o n of an e x t r a c e l l u l a r sulphur s o l u b i l i z i n g enzyme appears doubtful. If this i s also true for sulphides, then a d i f f u s i o n resistance to mass transfer could 38 not exist between the bacterium and the surface, and shculd not appear i n the model. The nature cf the i n i t i a l reaction for sulphur attack i s not known, but may involve formation of polysulphides. Attack at s o l i d sulphide surfaces i s not d iscussed. 4. B a c t e r i a l Leaching Rates Rate data for b a c t e r i a l leaching systems has been presented in at least three ways. Ba c t e r i a l growth rates are normally reported as doubling times or s p e c i f i c growth rates. Investigators performing manometric experiments report oxygen uptake values ( Q Q ^ ( N ) ) in m i c r o l i t r e s of S.T.P. oxygen per milligram of c e l l nitrogen per hour. This quantity i s c l o s e l y related to the s p e c i f i c growth rate (51). Leaching rates are usually reported as milligrams of metal ion released per l i t r e per hour. This guantity may be nearly proportional to the b a c t e r i a l growth rate. Tuovinen and Kelly (33) have summarized the ranges cf c e l l doubling times usually encountered on various media. For oxidation of elemental sulphur they report doubling times of 10 to 25 hours, for a ferrous iron substrate, 6.5 to 15 hcurs, and for a thiosulphate substrate, 36 hours. McGcran et a l . (40) reported a doubling time of 7-8 days for sulphur oxidation by T. ferrooxidans. Their data for doubling times on chalcopyrite 39 are suspect, since p r e c i p i t a t i o n of ammonic-j'arosite probably invalidated the b a c t e r i a l nitroqen values (41). Lacey and Lawscn (52) f i t Mcnod's model to the i r batch data for TT. fQrrooxidans growing on ferrous iron and determined % values of 0.12 h r - 1 at 20«C and 0.2 hr- 1 at 31<>C. They found that the saturation constant K was in the range of 1 to 2 g/1. MacDonald and Clark (36) determined % to be'0.115 hr~» at 32°C in batch culture and 0.161 hr- 1 at 28<>C in continuous culture. Their continuous experiments yielded a K value of 0.402 g/1. Many oxygen uptake values have been reported in the l i t e r a t u r e as a r e s u l t of manometric experiments with Tm_ ferrooxidans but the highest values reported appear to be those by Landesman et al._ (53,54). For ferrous iron oxidation they reported values in the range of 19,000 tc 22,5C0 p i O2 per mg N per hour, for cbalcopyrite oxidation, 3200, for bornite, 450, and for py r i t e , 1600. Representative maximum release rates for b a c t e r i a l leaching have been reported by Bruynesteyn and Duncan (1). They reported a copper release rate of 725 mg/l-hr cn a chalcopyrite • concentrate and 1300 mg/l-hr on a zinc sulphide concentrate. 40 5. Yield of Bacteria Yield data for fjgrrcoxidans have been reported as the r a t i o of carbon dioxide fixed to oxygen consumed, the y i e l d of c e l l number or dry weight per mole of substrate consumed, and as the free energy e f f i c i e n c y . Interpretation cf y i e l d data i s complicated by the f a c t that the bacteria may have a high maintenance energy requirement in order to maintain low i n t r a c e l l u l a r hydrogen and metal ion concentrations which occur in excessive l e v e l s in i t s environment (33). As a r e s u l t , one expects higher yield values at higher growth rates, when the maintenance energy requirement i s a small f r a c t i o n of the t o t a l energy requirement (10,51). Beck (55) reported carbon dioxide f i x a t i o n e f f i c i e n c i e s of 2.1 to 3.0 u moles CO^ per 100 pinoles C 2 for growth on ferrous i r o n . Beck and Brown (38) reported 22 u moles C O 2 per 100 u moles O 2 for growth on sulphur. Nielsen and Beck (56) reported 1.5 preoles CO 2 fixed per 100 umoles O 2 for oxidation of chalcocite to c o v e l l i t e . Temple and Colmer (26) reported that T. ferrcoxidaris fixed 16.05 mg of carbon while oxidizing 120 g of FeSO^^R^O. Silverman and Lundgren (57) reported f i x a t i o n of 0.97 umoles of CO 2 per 50 "J moles ferrous iron. Tuovinen et al.. ,58) grew the bacteria on a medium containing 2 g/1 ferrous iron and measured 4 1 a resultant b a c t e r i a l concentration of 10 8 c e l l s per ml. MacDonald and Clark (36), growing the bacteria i n continuous culture measured a c e l l y i e l d of 4.7 X 10 1 0 c e l l s per g of ferrous iron oxidized. Free energy e f f i c i e n c y i s the r a t i o cf the minimum chemical work required to create the biomass tc the maximum amount of chemical work which could be obtained from the substrate that was used. The minimum chemical work required to synthesize the biomass i s usually taken to be the free energy change for the f i x a t i o n of carbon dioxide into glucose as given by Baas-Eecking and Parks (59): 6 C02 (0.0003 arm) + 6 H20 (1.) •* 6 0 2 (0.2 atm) + C 6H 1 2°6 t s') <45> AF = 708.9 kcal/mole The maximum amount of chemical work which i s available by oxidizing a substrate i s the free energy change for the oxidation reaction for the conditions under which the reaction i s taking place. Tuovinen and Kelly (33) have summarized some of the values which have been used for the free energy of ferrous iron oxidation and accept the c a l c u l a t i o n of Lees et aJU (60) as being the most representative value for the conditions under which bacteria w i l l mediate the reaction. We believe that Lees' c a l c u l a t i o n i s incomplete and present the following one in i t s stead: 42 We begin by assuming that the f e r r i c iron produced pr e c i p i t a t e s as f e r r i c hydroxide, for which the s o l u b i l i t y product given by Latimer (61) i s 1 0 - 3 8 . Using the ion product of water as 10- 1*, we can express the a c t i v i t y cf f e r r i c ion as a function of hydrogen ion a c t i v i t y : i a p e + + + = 104 a 3 + (46) The oxidation of ferrous ion i s given by the following equation: Fe + + + V 4 0 2 + H+ - 1 / 2 H20 + Fe*""" (47) for which the electrode potential at 25°C can be calculated from a F e + + + E = 0.458 - 0.059 l o g i n ( TJJ ) (48) 1 0 a F e + + a 0 2 V Substituting for f e r r i c ion a c t i v i t y , and assuming the a c t i v i t y of atmospheric oxygen tc be .2, E = 0.212 + 0.059 [2 pH + l o g 1 0 ape++] (49) which i s e a s i l y converted to the free energy change per mole of ferrous iron oxidized by multiplying by -23,060. This expression shows an increase in absolute value of molar free energy change with pH due to decreased s o l u b i l i t y of f e r r i c icn as pH 4 3 increases, as opposed to the expression derived by Lees et ajU The value of -11.3 kcal/mole used by Temple and Colmer (26) and subsequent workers (33) for the free energy change for reaction 47 appears to have been taken from Bichcwsky and Rossini (62) as the difference of the heats of formation of aqueous f e r r i c ion and aqueous ferrous ion, and as such i s a standard enthalpy change, not a free energy change. It has been observed that the majority of the f e r r i c iron generated i n b a c t e r i a l cultures p r e c i p i t a t e s as the basic f e r r i c sulphate mineral, j a r o s i t e , AFe^ (SO 4) 2 (OH) g , where A can be Na, K, Rb, NH4, Ag, Pb/2, or H3O (16,42,65). Duncan and Walden (39) show curves suggesting that NH^, K, and H^ O are the most probable candidates. In view of the uncertainty of the form in which the f e r r i c iron p r e c i p i t a t e s in b a c t e r i a l cultures and the fact that eguilibrium p r e c i p i t a t i o n i s slow to be obtained, i t seems best to simply use the standard free energy change at 298°K for the oxidation of aqueous ferrous ion. This can be calculated from the standard electrode potentials qiven by Latimer (61) to be -10.6 kcal/mole. Assuming a free energy change of -11.3 kcal/mole for ferrous iron oxidation. Temple and Colmer (26) reported a free energy e f f i c i e n c y of 3.2%, Silverman and Lundgren (57) reported 20.5%, and Lyalikova (79) reported 30*. Lyalikova noted a 44 decrease in e f f i c i e n c y with age of culture. 6. Review of Torma's Work Torma (16,63,64) optimized a number of variables in batch leaching of a zinc sulphide concentrate. Optimum conditions were defined as those which gave maximum rates of zinc release and minimum lag times. Zinc release rates were calculated from the l i n e a r portion of zinc extraction vs. time curves. No attempt was made to explain why t h i s portion of the curve should be l i n e a r instead of showing the exponential increase usually associated with batch b a c t e r i a l growth. A constant rate of zinc release i s suggestive cf a mass transfer l i m i t e d process, but the rate change with temperature suggests that a chemical or b i o l o g i c a l reaction was l i m i t i n g . Two other p o s s i b i l i t i e s a r i s e . The surface a v a i l a b l e for leaching may remain r e l a t i v e l y constant for most of the batch experiment, decreasing rather sharply near the end of the leach. A l t e r n a t i v e l y , the increase in b a c t e r i a l population may balance the decrease in surface area u n t i l near the end of the leach. Some support for the former hypothesis i s provided by Levenspiel (17) who has modelled the case of a single shrinking sphere where the reaction rate for d i s s o l u t i o n cf the sphere i s proportional to the surface of the sphere only. His plot of f r a c t i o n of the o r i g i n a l sphere undissolved vs.. dimensionless 45 time shows an approximately l i n e a r decrease in the f r a c t i o n undissolved up to atout 60% of the time fer complete d i s s o l u t i o n of the p a r t i c l e , a f t e r which the di s s o l u t i o n rate decreases markedly. If either of these hypotheses i s true, then i t i s l i k e l y that under a l l conditions where linear leach curves were encountered, either surface area er mass transfer rates were l i m i t i n g the observed release rates. If surface area was l i m i t i n g the release rates, the ef f e c t s of the other variables investigated would s t i l l be f e l t ; the release rate per unit surface area could s t i l l be sensi t i v e to temperature, pH, nutrient concentrations, etc. Torma determined the optimum temperature to be 36-37°C, the optimum pH to be 2.3. The absence of added potassium chloride, magnesium sulphate, or calcium nit r a t e from the basal s a l t s medium did not af f e c t the f i n a l zinc concentrations achieved or the zinc release rates. Ammonium ion and phosphate i c n were required; l e v e l s in the medium 9K of Silverman and Lundgren (66) were s u f f i c i e n t for maximum release rates and zinc concentrations. 1$ carbon dioxide in the a i r supplied to the leaching vessels was s u f f i c i e n t to achieve maximum rates. The release rates were l i n e a r in i n i t i a l concentrate pulp density. I n i t i a l concentration of surface area of mineral was shewn to be the fundamental variable for c o r r e l a t i n g the release rates measured on both varying pulp densities and varying p a r t i c l e s i z e s . 4 6 The highest release rate measured in this study was 1150 mg/l-hr, measured i n a shake flask for the f r a c t i o n of the concentrate having the highest s p e c i f i c surface area. The highest zinc concentration achieved was about 120 g/1, measured in a baffled s t i r r e d batch tank containing 12 1 of concentrate s l u r r y at a pulp density of 24$. It was concluded that after suitable pretreatment the product solution would be suitable for recovery of zinc by e l e c t r o l y s i s . One attempt was made to measure the e f f e c t of the bacteria on the substrate. Three samples were taken, from a batch leach at appropriate time i n t e r v a l s , the s o l i d s were recovered by f i l t r a t i o n and washing with d i s t i l l e d water, and then fractionated by s i z e . The zinc content of representative size f r a c t i o n s was determined. The results indicated that the smallest f r a c t i o n s leached faster than the largest f r a c t i o n , while p a r t i c l e s in the large f r a c t i o n shrank to become part of the smaller f r a c t i o n s . The smallest p a r t i c l e s . should not disappear completely due to the inert material i n i t i a l l y present in the concentrate. No attempt was made to measure the surface area concentration while a leach was in progress, and tc correlate i t with the observed leach rates. From the data presented, i t would appear that the surface area concentration in a sl u r r y that was ac t i v e l y leaching could t»7 be s u b s t a n t i a l l y d i f f e r e n t than that in the s l u r r y i n i t i a l l y . In p a r t i c u l a r , the weight of the f i n e s t f r a c t i o n , which would contribute a great deal of the t o t a l surface concentration, becomes a small f r a c t i o n of i n i t i a l value as leaching progresses. This is one of several instances where Tcrma has estimated the effect of the environment on the bacteria, but f a i l e d to estimate the r e c i p r o c a l e f f e c t cf the bacteria on the environment. Two other examples of t h i s occur in the determination of ammonium and phosphate requirements, fts the b a c t e r i a l population grows, the concentration of ammonium ion drops (39) and the phosphate concentration probably drops as well. Therefore, although there was enough of these nutrients in the basal s a l t s medium for the conditions under which the experiments were performed, for very high b a c t e r i a l populations (and as a r e s u l t , high zinc concentrations), i t may prove necessary to make additions of these nutrients. The bacteria are responsive to the concentration cf carbon dioxide in the medium, not that in the a i r supply. For a given concentration i n the a i r supply under constant conditions for mass transfer, the concentration cf carbon dicxide in the medium w i l l be a function of hew fast i t i s being consumed by the bacteria; i . e . , i t w i l l be a function cf the growth rate. Torma's measurements are therefore s p e c i f i c to the type of 48 leaching vessel he used (shake f l a s k s ) , and the maximum release rate achieved i n his carbon dioxide experiments (650 mg/l-hr). Higher growth rates may reguire higher gas phase C O 2 concentrations, or increased provisions for mass transfer of C O 2 into s o l u t i o n . As noted by Torma, his use of the Monod equation tc f i t his data i s empirical. Its conventional use i s to f i t s p e c i f i c growth rate data as a function of substrate concentration in the c u l t u r e . Torma used i t to f i t zinc release rates as a function of i n i t i a l substrate concentration i n batch leaches. Under these conditions i t f a i l s to take into account the r e c i p r o c a l e f f e c t s of bacteria on substrate and substrate on bacteria, making i t impractical for predicting continuous culture r e s u l t s . Torma also points out that the usual requirement fer one substrate to be l i m i t i n g when thi s eguation i s used i s not always met by his data. Some of Torma's data would appear to have been f i t better by Blackman ki n e t i c s (9). Torma modelled his leach curves with a generalized l o g i s t i c equation proposed by Edwards and Wilke (67): [Zn] = [Zn] m / {1 + exp (f (t))} (50) where f(t) i s a f i f t h order polynomial. Torma did not give F values for each power of t included in the model, but his use of 49 a l l f i v e suggests that he f e l t each was s i g n i f i c a n t . With so many constants in the model, i t i s doubtful i f physical s i g n i f i c a n c e could be assigned to them a l l . There i s nc obvious way i n which t h i s model takes into account bacterium-environment i n t e r a c t i o n . 50 I I I . DERIVATION OF HO DEI Despite i t s a b i l i t y to account only for the log and stationary phases, flonod's model i s most often used in discussions of continuous culture theory. It has been used in analyses of continuous culture i n several reactor systems besides the single stage continuous perfectly s t i r r e d tank reactor which we have discussed. Examples are: multiple stage continuous s t i r r e d fermentors (68,69), single fermentcrs with feedback (68), tubular reactors (68), and b i o l o g i c a l film and f l o e reactors (70,71). It i s desired to derive a model which w i l l predict the growth rate of the bacteria and the release rate of zinc when the sulphide surface i s the l i m i t i n g substrate. Since one cannot r e l i a b l y estimate c e l l numbers, and w i l l have to measure some quantity proportional to c e l l mass, a distributed model should be chosen. Structure should not be needed since the prediction of steady-state r e s u l t s i n a continuous culture i s the major concern. For s i m p l i c i t y of f i t t i n g , i t should be deterministic. Attachment to the mineral surface appears to be prerequisite to zinc release and b a c t e r i a l growth; thus consideration must be qiven to the manner in which the bacteria become attached to the mineral. This i n turn establishes how much biomass i s attached to the surface. If i t i s assumed that 51 growth i s not limited hy any other component cf the system, the bacteria which are attached should grow at their maximum s p e c i f i c growth rate, which i s constant. The bacteria which are not attached to sulphide mineral have no access to substrate and can be assumed not to grow. Because i t considers the adsorption and descrption of bacteria at a dispersed phase surface, the model of Erickson et a l . (23) o f f e r s the most promise for describing b a c t e r i a l leaching k i n e t i c s . It can be s i m p l i f i e d to account for the constant substrate concentration in a sulphide mineral p a r t i c l e . I t w i l l be necessary to account for the change i n surface area as substrate i s consumed, and to adapt the model to continuous culture. Following Erickson et al._ (23) we assume the b a c t e r i a l concentration i s x, and a of these are attached to the surface. If a dynamic equilibrium between those bacteria attached and those in solution i s postulated, and i f one assumes that the rates of attachment and release follow f i r s t order k i n e t i c s , then \ (s - of) (X - a) = k_xo (51) where f i s the surface area occupied per unit of b a c t e r i a l concentration. This says that the rate of attachment i s 52 proportional to the concentration of bacteria-free surface and the b a c t e r i a l concentration in so l u t i o n ; the rate of release i s proportional to the b a c t e r i a l ccncentration attached. Solve for a : a 2f - (s + fX + {j^}) a + sX = 0 ( 5 2 ) fs + fX + tc) ± / (s + fX + K ) 2 - 4 fsX a = T i (53, For s=0, a=0, therefore take only the negative r a d i c a l . Assume that growth rate i s proportional to the number attached: r x = va = v (Cs + fX + <) - / ( S f + fX + K ) 2 - 4 j j ^ ( 5 1 | ) v i s thus the maximum s p e c i f i c growth rate f c r the t a c t e r i a which are attached. Equation 54 i s quite s i m i l a r in forti tc equation 24 obtained by Dabes et al.. (9) , but d i f f e r s in that equation 54 does not give u uniquely i n terms of substrate concentration. To c a l c u l a t e the steady-state conditions in a continuous backmix reactor, the k i n e t i c model w i l l have to te solved toqether with the mass halance on bacteria over the reactor. At steady state the mass balance on bacteria (equation 1) gives the 53 r e l a t i o n u = D (55) Solving the model with the b a c t e r i a l mass balance gives n = v r ( s + f X + K) - / Cs + fX + K ) 2 - 4 f s X , X 1 2 f To see how X depends on s and D we square equation 56 tc get ( M l - ) 2 . 4J2I2 (S + fx + <) + 4 fXs = 0 (57) V v Divide through by X and discard the zero root: 4 ( H ) 2 X - 4 - 4 S f S . 4 2 f E + 4 £s = 0 (58) Solve for x: To f i t the model, we have to determine three constants, v , ic , and f. We have three variables any two of which determine the t h i r d . We can vary the d i l u t i c n rate; or we can vary X and s for a constant d i l u t i o n rate by changing the pulp density or 54 grinding for a d i f f e r e n t length cf time. Equation 59 shews that for a constant D, a plot of X versus s should be a straight l i n e with slope v/Df and intercept ic/f (D/v - 1 ) « Several cf these plots can be made for other d i l u t i o n rates. If we now plot the r e c i p r o c a l of the slope versus d i l u t i o n rate, we should get a straight l i n e having zero intercept and slope (f / v ) . The r e c i p r o c a l of the intercept should be a linear function of the d i l u t i o n rate: Intercept VK K The l i n e should give f/vic as the slope, and (-f/< ) as the intercept. We now have estimates cf ( f / v ), (f/ VK ), and (f/ < ) • from which the three constants may be calculated. The r e l a t i o n which has been derived gives the steady-state b a c t e r i a l concentration as a function of d i l u t i o n rate and steady-state surface concentration. The steady-state zinc concentration can be determined from the b a c t e r i a l concentration by measuring the y i e l d of bacteria as a function of zinc released. Prediction of performance for a given d i l u t i o n rate and feed w i l l reguire that the steady-state surface concentration be calculated from the size d i s t r i b u t i o n of the feed in conjunction with the determined k i n e t i c s , the residence time d i s t r i b u t i o n in the reactor, and some simplifying assumptions regarding the geometry of the p a r t i c l e s . A prototype f o r t „ u c - , a . . i . 1 , 7 1 • 56 IV. APPARATUS AND MATERIALS A. AfiEa'catus y A schematic diagram of the leaching apparatus i s given i n Figure 2. The s t i r r e d tank reactor was made of l u c i t e p l a s t i c , and had an inside diameter of 11.25 inches. A schematic drawing of the tank i s given i n Figure 3. The r a t i o s of the dimensions are given i n Table I. The tank had four b a f f l e s , and the a g i t a t i o n was provided by a six-bladed turbine. The turbine was driven by a Graham N30MR2.U variable speed transmission. Air was sparged into the tank through a 1/U inch s t a i n l e s s s t e e l pipe nipple. To avoid plugging, no a i r d i s t r i b u t o r was used i n the tank. To avoid excessive evaporation i n the tank, the a i r was humidified by babbling through water before entering the tank. Carbon dioxide was added to the a i r stream at a rate adequate to increase i t s concentration in the a i r to 1% by volume. Solids were fed to the tank using a B. I. F. Volumetric Disc Feeder, Model 22-01. Product was removed in t e r m i t t e n t l y by suction into a F i g u r e 2 SCHEMATIC DIAGRAM OF THE CONTINUOUS LEACHING APPARATUS "Flexopulse" timer Vacuum Product receiver Solids Stirred tank reactor ] Temperature controller Hot/cold water Nutrient medium Flow meter C0 2 Mano-meter cH—• I Compressed air o -O _ on Table I. Geometric Ratios For Stirred Tank Reactor (Refer Figure 3) . Dt/Di HL / D i V D i »b/Dt L./D. W i / D i = 3 = 3 = 1 = 0 . 10 = 0 . 2 5 = 0 . 2 0 59 F i g u r e 3 SCHEMATIC DIAGRAM OF STIRRED TANK REACTOR SHOWING DIMENSIONS (Refer to Table I) W b _ X L U X 1 1 1 > Dt 60 s t a i n l e s s s t e e l product receiver. The i n t e r v a l of sampling was controlled by a Plexopulse Interval Timer (Eagle Signal D i v i s i o n of E. W. B l i s s Company) which opened a solenoid valve p e r i o d i c a l l y . Level control was achieved by positioning the suction tube at the desired l e v e l , and arranging to remove more material than was fed. When the l e v e l dropped below the end of the tube, a i r was taken into the product receiver instead of product. Vacuum was maintained by a water aspirator. Temperature i n the tank was controlled by a Yellow Springs Instrument Company Thermistemp Model 63 temperature c o n t r o l l e r . This c o n t r o l l e r operated a solenoid valve which permitted hot (or cold) water to flow through a s t a i n l e s s s t e e l c o i l i n the tank. A schematic diagram of the nutrient medium flow c i r c u i t i s given i n Figure 4. The medium was re c i r c u l a t e d through the constant head tank by a Cole-Parmer No. 85-07 magnetic drive c e n t r i f u g a l pump. The constant head was maintained by allowing the medium to flow over a weir i n the constant head tank, and return to the reservoir. Some medium was taken from the head tank and passed through a needle valve to the reactor. B. Materials. The concentrate was a single 1000 l b . l o t of Sul l i v a n Mine 6 1 F i g u r e 4 SCHEMATIC DIAGRAM OF NUTRIENT MEDIUM FEED CIRCUIT Head tank Nutrient V^-_-_ medium \— tank Flow meter Recirculation pump To reactor 62 zinc concentrate supplied by Corainco Limited. The inoculum for the tank was a pure s t r a i n of T h i o b a c i l l u s f§:£E22£idans (N.C.I.B. 9490) obtained from B.C. Research (48). It was grown in shake f l a s k cultures on the test concentrate to acclimatize the bacteria to the new substrate. The l i q u i d medium fed to the tank was the medium 9K described by Silverman and Lundgren (66) with water added i n place of the ferrous iron s o l u t i o n . The proportion of sulphuric acid was varied to maintain the tank pH between 2.0 and 2.5. Antifoam, when used, was Dow Polyglycol 15-200. 63 V. PROCEDURES A . B a i l H i l l i n g For the preliminary experiments a 0.5 pound portion of concentrate was placed in a No. 2 U.S. Stcneware porcelain b a l l -m i l l along with 0.25 pound of water and 5.0 pounds of 1/2 inch s t e e l b a l l s . Successive batches were milled at 65 rpm for 15, 30, 45, 60, and 90 minutes. The r e s u l t i n g s l u r r i e s were dried at 60°C overnight and the dry cakes were homogenized with a mortar and pestle and stored in p l a s t i c bags. Concentrate for the continuous experiments was milled in a 20 inch diameter s t e e l b a l l m i l l containing 350 pounds of 1/2 inch s t e e l b a l l s . A 35 pound batch of concentrate was milled with 8 l i t r e s of water at 46 rpm for 1.5 hours. The concentrate was dried at 60°C and pulverized in a rotating disc pulverizer (Cave S Co.). B. Surface Area Determination The s p e c i f i c surface area of a mineral sample was determined by f i t t i n g the Brunauer, Emmett and T e l l e r equation (72) to an adsorption isotherm for the material. The adsorption isotherm was determined by a dynamic method, usinq equipment designed and b u i l t by Orr (73). A schematic diagram of the 64 apparatus i s given in Figure 5. About half a gram of the mineral sample was placed in a tared U-tube made of 5 mm 0.D. glass tubing. The sample was dried i n the tube at 110OC for 12 hours. After cooling, three tubes of concentrate were weighed and mounted in the apparatus. A mixture of 5 volume % nitrogen in helium was passed through the tubes at 20 ml/min and the power to the thermal conductivity c e l l was turned on. After about one half hour warm up time, the f i r s t sample tube was immersed in l i q u i d nitrcgen. After the adsorption peak had been recorded, the instrument was c a l i b r a t e d with known volumes of nitrogen. Atmospheric pressure and temperature were noted for each c a l i b r a t i o n peak. While the c a l i b r a t i o n peaks were being taken, the probe of the nitrogen thermometer was immersed in the l i q u i d nitrogen bath. The pressure on the manometer was noted just before desorption, and the probe was removed. The l i q u i d nitrogen bath was removed and a desorption peak was recorded. The procedure was repeated on the other two samples. The gas mixture was changed to 15 and 25 volume % nitrogen in helium to complete the data for the three samples. F i g u r e 5 SCHEMATIC DIAGRAM OF THE DYNAMIC NITROGEN ADSORPTION APPARATUS 12 V power source c-Back pressure manometer He~N2 mixture-**-Exhaust**— Thermoconductivity / cell 7 To millivolt °-recordero-Dewar flask •^Sample holder tubes Liquid nitrogen E L Pure nitrogen Back pressure manometer Oil filled syringe caps for calibration <y o ••— o E o c o E QJ w (/) tn a> cL u» o Q. Nitrogen thermometer Exhaust 66 C. Shake f l a s k Leaches For shake flask studies, 5 g portions of concentrate and 70 ml of iron free medium 9K were placed in baffled 250 ml Erlenmeyer f l a s k s and 3 ml of 12N H2 S C4 w e r e added. One day was allowed for the pH to s t a b i l i z e due to acid ccnsumpticn by the concentrate, and additional acid was added as required to bring the f l a s k contents to pH 2.5. The flasks were then inoculated with 5 ml of bacteria previously grown on this concentrate. S t e r i l e control f l a s k s were carried in which 5 irl of the nutrient medium were added in place of incculum, and a c r y s t a l of thymol was added to maintain s t e r i l i t y . The f l a s k s were incubated at 35°C on a gyratory shaker, and the pH and dissolved zinc and iron concentrations were determined at convenient i n t e r v a l s . The f i n a l extraction was determined aft e r removing the leached out s o l i d s by f i l t r a t i o n on a Buchner funnel with Whatman No. 5 f i l t e r paper. The residue was washed several times with pH 2 water (water a c i d i f i e d to pH 2 with sulphuric a c i d ) , the f i l t r a t e was made to volume and analyzed for zinc. The c a l c u l a t i o n was corrected for the zinc removed in sampling, and for the zinc added with the inoculum. 67 D. Analysis Cf The Zinc Concentrate The concentrate was delivered in f i v e barrels containing about 200 pounds each. In addition, there had been delivered e a r l i e r two smaller cans t o t a l l i n g about 300 pounds of concentrate. The following procedure (known as coning and guartering) was adopted to mix the concentrate. A l l the concentrate was placed in one p i l e . This cone shaped p i l e was flattened, roughly quartered, and each guarter p i l e d into i t s own separate cone. Shovelsful of concentrate were then taken sequentially from each of the smaller cones u n t i l a l l of the material had been recombined into a single cone. This procedure was repeated for a t o t a l of three times. The thoroughly mixed concentrate was then replaced in the f i v e barrels. The samples for analysis were dried f c r about one week at 600C and then each sample was homogenized with a Cave S Co. pulverizer. Duplicate aliquots cf each sample (about 0.5 g) were weighed out for a n a l y s i s . The 0.5 g portion was placed in a 250 ml beaker with 10 ml of concentrated n i t r i c acid . and 5 ml of concentrated hydrochloric a c i d . The mixture was evaporated to dryness on a hot plate and then 5 ml of concentrated n i t r i c acid and 5 ml of 68 concentrated sulphuric acid were added to the residue, which was again evaporated to dryness. The residue was dissolved in about 30 ml of pH 2 water, made to volume, and analyzed for 2inc and i r o n . For the sulphur analysis, the concentrate was f i r s t washed with pyridine to remove any f l o t a t i o n chemical which might contribute sulphur to the analysis (41). The pyridine was displaced with ethanol followed by d i s t i l l e d water. The concentrate was dried at 100°C for 16 hours. The concentrate was combusted i n a stream of oxygen gas using a Leco Model 521 induction furnace. Vanadium pentcxide was added as a c a t a l y s t (74), and powdered iron was added as an accelerator. The sulphur dioxide produced was absorbed in a solution containing 30 ml of concentrated hydrochloric acid, 5 ml of 10^ potassium iodide solution, and 1 ml of 2% starch solution per l i t r e . Iodine was generated by t i t r a t i n g 0.025 N potassium iodate into the reaction vessel: KI0 3 + 5 Kl + 6 HCl -*• 3 I 2 • 6 KCl + 3 H20 (61) Sulphur dioxide absorbed in the solution reduced the iodine to iodide: 69 S0 2 • _ 2 + 2 « 20 + H 2 S O 4 • 2 HI (62) Iodine in the solution was detected as a dark blue colour by the starch. Two blanks and six standards using reagent grade zinc sulphide were run with the concentrate samples. E« Monitoring The Continuous S t i r r e d Tank 1. Total Organic Carbon B a c t e r i a l concentration was estimated as t o t a l organic carbon concentration using a Beckman No. 915 Total Organic Carbon Analyzer. Total organic carbon concentration i s the difference between t o t a l carbon concentration and inorganic carbon concentration in a sample. Total carbon was determined by i n j e c t i n g a 20 u1 sample into a bed of cobalt n i t r a t e catalyst at 800°C. An oxygen stream passing through the bed picked up the carbon dioxide generated by i n c i n e r a t i o n of the organic carbon and decomposition of the carbonates in the sample. The carbon dioxide was detected by i t s absorption of infra-red l i g h t . Each sample injected generated a peak on a chart recorder. The height of the peak was proportional to the amount of carbon injected. 70 A separate low temperature (150°C) furnace containing a phosphoric acid wetted packing liberated any inorganic carbon from another 20 u 1 sample as carbon dioxide. The oxygen stream from t h i s furnace could be fed into the same detector yieldi n g a peak on the recorder whose height was proportional to the amount of inorganic carbon i n the sample. In practice, the inorganic carbon in the tank s l u r r y was about 2 mg/1, n e g l i g i b l e when compared to the t o t a l carbon readings. Therefore, inorganic carbon readings were done only infreguently. 2. N o n - d i s t i l l a b l e Ammonium Ion Ba c t e r i a l concentration was also estimated by the "non-d i s t i l l a b l e " or "net" ammonium ion concentration. This i s the difference between the t o t a l ammonium ion concentration after Kjeldahl digestion and the steam d i s t i l l a b l e ammonium ion concentration, and i s thus an estimate of b a c t e r i a l nitrogen concentration i n the sample. To determine the t o t a l ammonium ion, the sample was digested in a Kjeldahl flask with concentrated sulphuric acid and a Hengar selenized b o i l i n g granule. The digestion was carried out over a*Bunsen flame for about two hours. This digestion converted the organic nitrogen to ammonium ion. After the digestion, the sample was washed into a micro-Kjeldahl steam s t i l l (W. Buchi, Switzerland) with s u f f i c i e n t sodium hydroxide tc make the mixture strongly 71 al k a l i n e . The mixture was steam d i s t i l l e d , and the d i s t i l l a t e was co l l e c t e d in a flask containing 5 ml of saturated bc r i c acid and 3 drops of an indicator s o l u t i c n . The indicator was made up of one part 0.2% methyl red and f i v e parts 0.2% brcmocresol green in ethanol. After about 50 ml of d i s t i l l a t e had been c o l l e c t e d , the flask contents were t i t r a t e d tc a colourless end point with 0.01 N HCl. The ammonium ion equivalent of the hydrochloric acid was calculated. The d i s t i l l a b l e ammonium ion i s an estimate cf the inorganic ammonium ion i n the s l u r r y . I t was determined by placing the tank slurry in the s t i l l without digesting i t , and repeating the above procedure. 3. Pulp Density The pulp density was determined by pipetting a known guantity of s l u r r y into a glass centrifuge b o t t l e . The s l u r r y was centrifuged at low speed to s e t t l e the s o l i d s but leave the bacteria suspended. The centrifugate was decanted and 10% HCl was added to the s o l i d s . The bottle was stoppered and shaken to dissolve precipitated iron compounds. The s l u r r y was centrifuged and decanted as before. The procedure was repeated for a t o t a l of two HCl washes and one d i s t i l l e d water wash. The s o l i d s were then resuspended in d i s t i l l e d water and f i l t e r e d on a Buchner funnel using Whatman number 5 f i l t e r paper. The f i l t e r cake was 72 dried over night at 105°C. It was cooled, weighed, and stored for surface area analysis and digestion for -zinc and iron analyses. 4. Miscellaneous Zinc and iron concentrations were determined on a Perkin Elmer Model 303 atomic absorption spectrophotometer. Daily samples of tank s l u r r y were centrifuged in a c l i n i c a l centrifuge and the clear centrifugate was sampled f c r zinc and iron analysis. Whenever the product receiver was being emptied, a sample of the s l u r r y was taken for dissolved zinc and dissolved iron analysis. In doing a mass balance on zinc over the tank, the concentration of zinc i n the product was used to determine the amount of soluble zinc removed from the tank. To complete the mass balance on zinc over the tank, the s o l i d residues from the tank were analyzed for zinc content by the procedure given in section V.D. 10 ml of slurry and 10 ml of centrifugate from the tank were weighed for determination of densities. From these two densities and the pulp density, i t was possible to estimate the volume f r a c t i o n of l i q u i d in the s l u r r y . This was e s s e n t i a l in order to determine true extraction rates. It was also possible to correlate the centrifugate density with dissolved zinc 73 concentration, and to correlate the difference in the two densities with the pulp density of the s l u r r y . These co r r e l a t i o n s provided a quick check cn the tank c o n d i t i c n . The amount of concentrate collected over a measured i n t e r v a l of about 20 minutes was weighed to qive an estimate of s o l i d feed rate. The tank depth was measured with the a i r flow and agitation on and again with the a i r and agitation switched o f f . The measurement with the agita t i o n and a i r switched off allowed determination of the volume of s l u r r y i n the tank, and the difference between the two readings provided a measure of the gas holdup in the tank. The s t a i n l e s s s t e e l product receiver was c a l i b r a t e d to a centimeter dip s t i c k so that the volume of the product could be noted as a function of time. This allowed c a l c u l a t i o n of the product flow rate, from which the d i l u t i o n rate was calculated. The a i r flow was maintained at about 1 0 1/min, the C O 2 flow at about 95 ml/min, measured at the conditions of flow. The agitator turned at about 450 rpm. The flew of l i q u i d medium was checked on a rotameter. The temperature and pH of the tank slurr y were noted d a i l y . 74 The mean temperature was controlled to 36°C. One siz e d i s t r i b u t i o n analysis was performed on a feed sample using a. Bahco 6000 Microparticle C l a s s i f i e r . Six frac t i o n s were produced, and the representative maximum p a r t i c l e diameter for each f r a c t i o n was calculated by averaging the maximum and minimum diameter of ten p a r t i c l e s as determined with an ocular micrometer. C e l l numbers were estimated in a Petroff-Hausser counting chamber. The number of bacteria in nine of the smallest squares was counted in ten f i e l d s frcm each cf two s l i d e s . From the average number per smallest square, the c e l l number concentration could be calculated. 75 VI. RESULTS AND DISCUSSION A. Preliminary Experiments 1. Analysis of the Zinc Concentrate To characterize the zinc concentrate used i n these studies, i t was assayed for zinc, iron, and t o t a l sulphur. It was impartant that the feed concentrate be as uniform i n composition as possible, so that upsets i n the continuous process would not be traceable to changes i n the feed composition. The concentrate was sampled in such a way that a s t a t i s t i c a l measure of the variance of the assays could be made. Two samples (a and b) were removed from each of the f i v e b a r r e l s . An e f f o r t was made to take one sample near the bottom of the bar r e l and the other near the top. The r e s u l t s of the chemical analysis of the zinc concentrate are presented i n Table II. These data were analyzed by the h i e r a r c h i c a l c l a s s i f i c a t i o n , a s t a t i s t i c a l design permitting the testing of the s i g n i f i c a n c e of heterogeneity in the concentrate (75). In these experiments, each observation was broken down into the general mean, the barrel e f f e c t , the e f f e c t of the samples a and b within each b a r r e l , and the error e f f e c t of the duplicates: Table II. Zinc, Icon, And Sulphur Analysis Of Zinc Concentrate (As Received). Sample Percent Zinc 1a1 56.44 1a2 55.99 1b1 55.76 1b2 55.54 2a1 55. 69 2a2 55.03 2b1 54.78 2b2 54.95 3a1 54. 67 3a2 55.53 3b1 56. 16 3b2 56.21 4a1 56. 19 4a2 56.09 4b1 55.96 4b2 54.90 5a1 55. 69 5a2 56. 10 5b1 56. 15 5b2 56.02 Percent Percent Iron Sulphur 4. 872 31.77 4.770 33.27 4. 852 31.26 4.817 31.05 4.554 31.16 4.552 30.96 4. 964 31.37 4.869 4. 713 32.61 4.801 31.25 4. 536 30.82 4.647 32.52 4.491 31.86 4.546 31.11 5.774 32.28 4.971 31.93 4. 726 30.42 4.613 31.33 5.704 31.35 4.451 32. 18 77 y = y + (y B- y) • (f - ?B) * (y - y) <63) where y = an observation y = the general mean y = the mean of four observations D from a barrel y = the mean of two duplicates The analyses of variance for zinc, ir o n , and sulphur analyses are given i n Tables I I I , IV, and V. They show that neither the variance contributed by the barrels, nor the variance contributed by the samples a and b within each barrel i s s i g n i f i c a n t l y d i f f e r e n t from zero at the 95% l e v e l . We may therefore conclude that there should not be s i g n i f i c a n t v a r i a t i o n of the concentrate composition from, b a r r e l to ba r r e l , or from sample to sample within each barrel, when compared to the variance of the a n a l y t i c a l method (the variance contributed by the duplicates). The assay values used in these experiments were 55.69% zinc, 4.81235 i r o n , and 31.61% sulphur. 78 Table I I I . Analysis Of Variance For Zinc Content Of Zinc Concentrate. Source S.S. d.f. M.S. Barrels Sa mples Error Total 1.974 2.282 1.388 5.644 4 5 10 19 0.4935 0.4564 0. 1388 0.297 1 1.08 3.29 F (4r5,.95) = 5. 1922 F(5,10,.95) = 3.3258 Neither Barrel Not Sample Eff e c t S i g n i f i c a n t At The 95% Level. Average Zinc Composition Of Concentrate Is 55.69%. 95% Confidence Limits: Upper: 55.44% Lower: 55.95% Table IV. Analysis Of Variance For Ircn Content Of Zinc Concen trate. Source S.S. d.f. ti.S, Barrels 0.1872 4 0.04679 0.222 Samples 1.0555 5 0.2111 1.859 Error 1. 1357 10 0. 1 136 Total 2.3783 19 0.1252 F (4,5,.95) = 5. 1922 F(5, 10,.95) = 3.3258 Neither Barrel Nor Sample E f f e c t S i g n i f i c a n t At The 95% Level. Average Iron Composition Of Concentrate Is 4.812/* 95% Confidence Limits: Upper: 4.978* Lower: 4.647* 80 Table V. Analysis Of Variance For Sulphur Content Of Zinc Concen trate. Source S.S. d.f. K.S, Barrels Samples Error Total 1.422 3. 171 a.639 9. 232 4 5 9 18 0.3555 0.6342 0.5154 0.5605 1.231 F (4,5,-95) = 5. 1922 F(5,9,.95) = 3.4817 Neither Barrel Nor Sample E f f e c t S i g n i f i c a n t At The 955? Level. Average Sulphur Composition Of The Concentrate Is 31.61%. 95% Confidence Limits: Upper: 31.96% Lower: 31.26% 81 2. Percentage Extraction - M i l l i n g Time Experiment A portion of the concentrate used i s not zinc sulphide, and t h i s gangue material may prevent b a c t e r i a l contact with otherwise leachable material. Grinding should overcome t h i s by exposing more sulphide mineral to the bacteria. In addition, the sulphide mineral may have to be stressed in order to render i t susceptible to b a c t e r i a l attack. More grinding should subject the c r y s t a l structure to more stress. F i n a l l y , the surface to volume r a t i o for the coarser sulphide material may be so small that a f t e r the f i n e s have been dissolved, the leach rate drops to a n e g l i g i b l e value. The extraction would then appear to be le s s than the true p o t e n t i a l of the concentrate. To determine the b a l l m i l l i n g time required . to produce maximum extraction, portions of the zinc concentrate were b a l l milled for various lengths of time and then leached i n shake f l a s k s (duplicate batch t e s t s ) . Determining the s p e c i f i c surface area provided a measure of the effectiveness of the m i l l i n g . A sample c a l c u l a t i o n of percentage extraction i s given i n Appendix I. The r e s u l t s i n Table VI show that m i l l i n g for 15 minutes was s u f f i c i e n t to obtain the maximum extraction. Values for 60 and 90 minutes were not s i g n i f i c a n t l y higher. Maximum extraction was obtained with a s p e c i f i c surface area of about 1.7 m2/g. 82 Table VI. Percentage Extraction - M i l l i n g Time Results Washed Dried Milled Bacteria y Extraction Average S p e c i f i c 1 Surface Extraction Area (n>2/g) — — - 41.3, 44.6 43.0 0.820 - + - + 46. 4, 63. 5 55. 0 + • - • 40.3, 40.3 + 15 min • 69. 5, 71. 5 70.5 1.116 + 30 nin + 71.8, 78.5 75.2 1.569 + + 45 min + 80. 6, 84. 1 82. 4 1.676 + • 60 a i n • 80.9, 79.8 80.4 2.026 + + 90 min + 80.9, 84. 5 82. 7 2.373 + 90 min - 12. 1 , 12. 1 2.373 83 M i l l i n g foe the continuous experiments was done i n a larger m i l l . After 90 minutes i n the larger m i l l , the s p e c i f i c surface area of the material t y p i c a l l y was of the order of 3 m2/g; a f t e r 90 minutes m i l l i n g in the smaller test m i l l , i t was 2.373 m2/g, ind i c a t i n g that the larger m i l l was more e f f e c t i v e than the small m i l l . Batch shake flask tests on concentrate from the large m i l l had an average percentage extraction of 88.6%, s l i g h t l y higher than predicted from the data i n Table VI. Washing and drying the unmilled concentrate had no e f f e c t on extraction. 3U Development of the Non-D i s t i l l a b l e (Net) Ammonium Ion Method To determine how much of the nitrogen associated with the bacteria could be d i s t i l l e d as ammonium ion without digestion, the following experiment was performed. Duplicate aliguots of a washed c e l l suspension were digested by the Kjeldahl procedure and d i s t i l l e d . The average t o t a l ammonium ion content of these aliguots was 0.5484 mg. Duplicate aliquots of the suspension were d i s t i l l e d without digestion, and the average d i s t i l l a b l e ammonium ion content was found to be 0.02346 mg, or 4.28% of the t o t a l . Thus, le s s than 5% of the b a c t e r i a l nitrogen w i l l report as d i s t i l l a b l e ammonium ion. 84 A second experiment was performed to determine i f the ammonium ion trapped as j a r o s i t e would be released by the caustic d i s t i l l a t i o n without digestion, and thus not report as b a c t e r i a l nitrogen. A sample of j a r o s i t e was obtained from B.C. Research. Duplicate portions were weighed out and completely dissolved in 35% HCl s o l u t i o n . Aliquots of these solutions were d i s t i l l e d with caustic. The ammonium ion content of the j a r o s i t e determined by t h i s method was 0.677%. When samples of the j a r o s i t e were d i s t i l l e d with caustic without any prior treatment to dissolve the s o l i d s , the ammonium ion content averaged 0.693%. The r e s u l t s show that ammonium ion trapped as j a r o s i t e w i l l report as d i s t i l l a b l e ammonium ion, and not as net ammonium ion. Thus, formation of ammonio-jarosite should not a f f e c t the estimation of b a c t e r i a l nitrogen. 4. Development of the Pulp Density Determination Procedure In these studies we are interested in the pulp density and surface area of the sulphide mineral, excluding any pre c i p i t a t e d iron s a l t s . Therefore, a procedure was necessary to dissolve the iron s a l t s before the s o l i d s were weighed and the i r s p e c i f i c surface area determined. Another potential problem was that the bacteria attached to the surface of the mineral might a f f e c t the measurement of surface area by the B. E. T. method, either by 85 a l t e r i n g the actual surface area presented to the adsorbing nitrogen, or by a l t e r i n g the e f f e c t i v e surface area covered by a nitrogen molecule. A procedure was therefore necessary to remove the attached bacteria from the mineral surface. Four procedures to achieve these two objectives were evaluated: (a.) Wash with 10% HC1, f i l t e r . (b.) Wash with 10% HCl and acetone, f i l t e r . (c.) Wash with 10% HCl, centrifuge. (d.) Wash with pH 2 water, centrifuge. In these procedures, the HCl wash was intended to dissolve precipitated iron compounds and cause the bacteria to leave the surface due to the unfavourable environment. Two 20 ml samples were removed from the leach tank, and made to 10% HCl with concentrated acid. They were stoppered, shaken well, and allowed to stand for 13 hours. The s o l i d s were recovered by f i l t r a t i o n on Whatman No. 5 paper, and dried at 105°C. One f i l t e r cake was digested by the Kjeldahl procedure and the t o t a l ammonium ion was determined. The other f i l t e r cake was resuspended i n pH 2 water, and analyzed for d i s t i l l a b l e ammonium ion and t o t a l carbon. A l l washings and f i l t r a t e s were 86 co l l e c t e d and made to volume. Dissolved zinc and iron, non-d i s t i l l a b l e ammonium ion, and t o t a l carbon were determined i n the o r i g i n a l s l u r r y and i n these f i l t r a t e s . The res u l t s are summarized in Table VII, where a l l the concentrations have been corrected to the basis of the concentrations in the o r i g i n a l sample. (Note that the determinations on the resuspended cake are of low accuracy due to the d i f f i c u l t y of resuspending the cake homogeneously.) Table VII shows that the HCl treatment increased the dissolved iron l e v e l s u b s t a n t i a l l y while the dissolved zinc l e v e l decreased s l i g h t l y . 3555 of the net ammonium ion remained associated with the s o l i d s . I t was concluded that the 10% HCl wash procedure dissolved some of the iron p r e c i p i t a t e , but was not successful in removing the bacteria from the s o l i d s . To improve the removal of bacteria from the s o l i d s i t was decided to include an acetone washing step. Acetone might be able to dissolve the bond between the bacteria and the mineral and should lyse the c e l l s . To t h i s end, the HCl washing procedure was repeated on two 50 ml samples from the leach tank. Following f i l t r a t i o n , the f i l t e r cakes were washed with acetone, then d i s t i l l e d water. The r e s u l t s are presented in Table VIII. The data in Table VIII support the conclusion that the 10% 87 Table VII. D i s t r i b u t i o n Of Organic Material Between Solids And F i l t r a t e : 1051 HCl Wash. 15-07-71 Two Samples, 20 ml Zn = 20100 mg/1 Fe = 890 mg/1 Net NHj = 131 mg/1 Total C = 435 mg/1 Wash With 10* HCl, F i l t e r . F i l t e r Cakes: I II (digest) (resuspend) O r i g i n a l Tank Product Total NH4 = 47 mg/1 Net NH;t = 46 mg/1 D i s t i l l a b l e NH4= 1 mg/1 T c t a l C = 295 mg/1 F i l t r a t e : Zn 19475 mg/1 Fe 1275 mg/1 Net HHt 69 mg/1 Total C 2 17 mg/1 88 Table VIII. D i s t r i b u t i o n Of Organic Material Between Solids And F i l t r a t e : Acetone Wash Or i g i n a l Tank Product 22-09-71 2 Samples, 50 nil Zn = 38100 mg/1 Fe = 1086 mg/1 Net NHj = 196 mg/1 Total C = 750 mg/1 Wash With ^0% HCl, Acetone, F i l t e r . F i l t e r Cakes: (digest) Total NHj = 124 mg/1 Net NH 4 = 117 mg/1 II (resuspend) D i s t i l l a b l e NH4 = 7 mg/1 T c t a l C = 252 mg/1 Zn = Fe = Net NHT = 37720 mg/1 3422 mg/1 69 mg/1 F i l t r a t e s : II P r e c i p i t a t i o n Of Zinc Sulphate Due To Acetone Addition Invalidates Analysis. Total Carbon Not Possible Due To Acetone Wash 89 HCl dissolves a sub s t a n t i a l amount of iron p r e c i p i t a t e while di s s o l v i n g very l i t t l e of the zinc in the mineral. The acetone wash was unsuccessful i n removing bacteria from the s o l i d s ; 60% of the net ammonium ion remained associated with the s o l i d s . When acetone was added to f i l t r a t e II a white p r e c i p i t a t e was formed. This p r e c i p i t a t e was found to contain 25% zinc, and was te n t a t i v e l y i d e n t i f i e d as a hydrated zinc sulphate. It was possible that the bacteria were su c c e s s f u l l y removed from the surface by the 10% HCl treatment, but that the suspended bacteria were p a r t i a l l y removed from the f i l t r a t e with the s o l i d s during f i l t r a t i o n . This would account for the high net ammonium ion and t o t a l carbon l e v e l s in the f i l t e r cake. The washing procedure was therefore modified as follows: 50 ml of s l u r r y were pipetted into a centrifuge bottle and centrifuged at low speed to s e t t l e the s o l i d s but leave the bacteria suspended. The centrifugate was decanted and 10% HCl was added to the s o l i d s . The bottle was stoppered and shaken, and then centrifuged and decanted as before. The procedure was repeated for a t o t a l of two HCl washes and one d i s t i l l e d water wash. The s o l i d s were resuspended i n d i s t i l l e d water and f i l t e r e d . The re s u l t s of t h i s experiment are presented in Table IX. The data i n Table IX show that the zinc concentrations i n 90 Table IX. Dist r i b u t i o n Cf Organic Material Eetweer Solids And Centrifugate: 10% HCl wash. Or i g i n a l Tank Product 18-11-71 T\»o Samples, 50 ml Zn = 46350 mg/1 Fe = 1565 mg/1 Net NH4 = 360 ng/1 Total C = 1400 mg/1 Wash With 10% HCl, Centrifuge. S o l i d s : (digest) Total NH4 = 69 mg/1 Net NHt = 65 mg/1 4 II (resuspend) D i s t i l l a b l e N H J = 4 mg/1 Total C = 252 mg/1 Centrifugates: Zn = Fe = Net NH4 = Total C = 48050 mg/1 4545 mg/1 296 mg/1 1104 mg/1 II 47500 mg/1 4548 mg/1 304 mg/1 1144 mg/1 9 1 the f i l t r a t e s were s l i g h t l y higher than in the o r i g i n a l sample; the iron concentrations were about three times that in the o r i g i n a l sample. The zinc dissolved represents d i s s o l u t i o n of about 5% of the f i l t e r cake weight. The r a t i o of zinc to iron dissolved i s 0 . 4 8 ; the r a t i o of zinc to iron i n the zinc concentrate i s about 1 0 . It was concluded that the increase in dissolved iron was due to di s s o l u t i o n of iron p r e c i p i t a t e , not due to d i s s o l u t i o n of zinc concentrate. 18% of the net ammonium ion remained in the f i l t e r cake, a marked improvement over the previous procedures. To show the eff e c t of the 10% HCl i n these procedures, an experiment was performed where pH 2 water was substituted for 1 0 % HCl, and the s o l i d s were recovered by ce n t r i f u g a t i o n . The re s u l t s i n Table X show that there was some increase i n the iron l e v e l s i n the f i l t r a t e s , no increase in the zinc l e v e l s , and 65% of the net ammonium ion remained i n the cake. The d i s t i l l a b l e ammonium ion i n the resuspended cake was s u b s t a n t i a l l y higher than i n the HCl washed cakes, suggesting that some ammonio-j a r o s i t e had not been dissolved by the pH 2 water wash. These four experiments are not s t r i c t l y comparable, since the conditions in the tank were not i d e n t i c a l in each case. However, they indicate that the objectives of removing bacteria and iron p r e c i p i t a t e from the s o l i d s were most nearly achieved by a 1 0 % HCl wash and centrifugation. This method i s summarized 92 Table X. Di s t r i b u t i o n Of Organic Material Between Solids And Centrifugate: pH 2 Wash. Or i g i n a l Tank Product 18-03-72 2 Samples, 50 nil Zn = 31500 mg/1 Fe = 671 mg/1 Net NHj = 384 mg/1 Total C = 1416 mg/1 Wash With pB 2 Water, Centrifuge. S o l i d s : (digest) Total NHj = 285 mg/1 Net NH^  = 251 mg/1 II (resuspend) D i s t i l l a b l e NB-J = 34 mg/1 T c t a l C = 447 mg/1 Centrifugates: Zn = Fe = Net NH4 = Total C = 34975 mg/1 838 mg/1 144 mg/1 470 mg/1 II 33850 mg/1 813 mg/1 135 mg/1 452 mg/1 93 in the Procedures section (page 71). In an attempt to evaluate the ef f e c t of bacteria attached to the mineral surface on the s p e c i f i c surface area determination, a washed c e l l suspension was incubated with a sl u r r y of s i l i c a spheres of diameter one micron (76). A s l u r r y of the same spheres was incubated with pH 2 water as a control. After three days incubation the spheres were recovered by low speed centrifugation and washed twice with pH 2 water. They were resuspended i n pH 2 water and f i l t e r e d . The f i l t e r cakes were digested for t o t a l ammonium ion. The test spheres and the control spheres analyzed 0.093% and 0.0035% ammonium ion respectively; thus, some bacteria had attached to the test spheres. The s p e c i f i c surface of the test spheres and the control spheres was found to be 4.14 m2/g and 4.55 m2/g respectively. Therefore, bacteria on the surface may reduce the s p e c i f i c surface area determined by the B„ E. T. method by about 10%. 5. Non-Ideal Product Removal from the Tank It was suspected that removing product by slurping i t from the surface of the tank to control the l i q u i d l e v e l might r e s u l t in removal of material not representative of the contents of the bulk of the tank. Accordingly, experiments were performed on several occasions to determine the difference, i f any, i n 94 composition between material removed d i r e c t l y from the tank, and material removed through the product removal l i n e . Table XI shows the d i s t r i b u t i o n of zinc i n samples taken at the same time, one d i r e c t l y from the tank, and one from the product removal l i n e . The undissolved zinc was determined by measuring the pulp density of each sample and analyzing the s o l i d cake for zinc content. The data for 17-06-72 and 24-06-72 show a higher l e v e l of undissolved zinc in the product sample than i n the tank sample. This i s not due to the HCl washing of the tank s o l i d s ; the discrepancy i s larger than the maximum of 5% dissolved by HCl washing. It i s l i k e l y due to the fact that the product removal slurper removed some of the foam along with the material from the bulk of the tank. The material in the foam had a higher undissolved zinc l e v e l than the material i n ei t h e r the tank or product samples. The data for 19-07-72 and 29-07-72 show that careful adjustment of the removal slurper cycle so that mostly tank material was removed could eliminate t h i s problem. Since the product was removed i n pulses, the duration of the pulse and the length of time between pulses could be adjusted so that the slurp tube was submerged for most of the ,pulse, minimizing sampling of the foam. Table XI. Di s t r i b u t i o n Of zinc In Tank And Product Samples Dissolved Undissolved Total Zinc Zinc Zinc (g/1) (g/1) (g/1) 17-06-72 Tank 6.40 8.18 14.57 Product 10.07 Foam 24-06-72 Tank 14.22 18.34 32.56 Product 13.89 21.04 34.93 Foam 14.09 75.00 89.09 19-07-72 Tank 7.62 16.13 23.75 Product 7.78 16.33 24.11 Foam 8.10 31.32 39.42 29-07-72 Tank 12.68 27.68 40.36 Product 12.35 27.24 39.59 Foam 13.33 68.10 81.43 96 As further proof that t h i s adjustment was successful, the data i n Table XII are presented. This summarizes the net ammonium ion, t o t a l carbon and dissolved iron values i n the tank and product samples for the steady state of 28-07-72 29-07-72. The pot e n t i a l for d i f f e r e n t values i n the product was there: a sample of the foam taken during t h i s period had a net ammonium ion l e v e l of 200 rag/1, a t o t a l carbon l e v e l of 798 mg/1, and an iron concentration of 0.531 g/1, a l l s u b s t a n t i a l l y d i f f e r e n t from the l e v e l s i n the tank or i n the product. The high l e v e l s of undissolved zinc in the foam may be due to the production by the bacteria of a surfactant with a c o l l e c t o r action, or presence of f l o t a t i o n reagents on the concentrate. The tank then acted as a f l o t a t i o n c e l l , concentrating the hydrophobic mineral in the foam. The organic material which concentrated in the foam may have been surface active products of the c e l l s ' metabolism, c e l l s themselves, antifoam, f l o t a t i o n reagents, or c e l l s attached to the hydrophobic mineral. Although there i s no data s p e c i f i c a l l y demonstrating i t , i t i s quite probable that when the product material contained higher l e v e l s of undissolved zinc than the tank material (indicating sampling of the foam), i t also contained higher l e v e l s of organic matter, since organic matter concentrated in 97 Table XII. Comparison Of Tank For Steady State 2 Sample 28-07-72 1 Tank Product 28-07-72 2 Tank Product 28- 07-72 3 Tank Product 29- 07-72 1 Tank Product 29-07-72 2 Tank Product And Product Sample Concentrations -07-72 29-07-72. Net Total [ I e ] Ammonium Carbon Icn (mg/1) (mg/1) (g/1) 116 506 0.681 148 503 0.702 145 498 0.699 149 502 0.708 154 506 0.662 153 511 0.699 151 516 0.715 151 499 0.741 153 516 0.717 152 50 4 0.716 98 the foam. The lowered iron concentration i n the foam may be due to d i l u t i o n of the foam by nutrient medium f a l l i n g through i t as i t entered into the tank. Levels of dissolved zinc for the steady states obtained between 22-06-72 and 29-07-72 were not s i g n i f i c a n t l y d i f f e r e n t in the tank and product samples. A least squares l i n e was f i t to product dissolved zinc concentrations as a function of tank dissolved zinc concentrations, and i t was impossible to r e j e c t the hypotheses that the slope was one and the intercept was zero at the 90% l e v e l (Appendix II) . Unfortunately, there are not enough data to indicate what percentage of the time the non-ideal product removal was a problem. It i s l i k e l y that i t was a greater problem at higher d i l u t i o n rates when the foaming was greatest. The data in Table XI suggest that once the problem was discovered i t could be eliminated, so that the data for the d i l u t i o n rate of 0.1038 hr-* are probably not affected. The data for the d i l u t i o n rate of 0.0595 h r - 1 probably have been biased, but they correlate quite well with the data from the other three d i l u t i o n rates, so the non-ideality was not too great. When non-ideal product removal was occurrinq, the b a c t e r i a l 99 growth rates were ac t u a l l y higher than those calculated, since the rate at which bacteria were removed from the tank was actu a l l y greater than that calculated. Higher l e v e l s of undissolved zinc in the product stream than i n the tank make the residence time of the concentrate p a r t i c l e s i n the tank less than that calculated from the d i l u t i o n rate due to a higher throughput rate of concentrate. B. Continuous Leaching Experiments 1 . Introduction Because the proposed applications of concentrate leaching are i n continuous processing, a k i n e t i c study was done in continuous culture. To make the study as easy to analyze as possible, an i d e a l reactor had to be chosen. Two i d e a l continuous reactor types are the plug flow reactor, and the perfectly s t i r r e d tank reactor. The plug flow reactor was ruled out because of the d i f f i c u l t y of maintaining true plug flow of a three phase mixture for the high residence times required. As well, most of the b i o k i n e t i c models that had been developed to describe continuous fermentations had considered the fermentation to be taking place i n a chemostat, a continuous s t i r r e d tank reactor. The variables of pH and temperature were studied in batch 100 culture by Torma (16), and i t was f e l t that the optima determined i n batch culture should apply to continuous culture as well. Other variables such as l e v e l s of dissolved oxygen, carbon dioxide, and nutrient in the nutrient medium could be important l i m i t i n g factors i n the continuous process, but were not studied because of the desire to measure the e f f e c t of the concentration of substrate surface area. To t h i s end, i t was decided to maintain oxygen, carbon dioxide, and nutrients at l e v e l s which would not l i m i t the b a c t e r i a l growth rate. 2. " S t e r i l e " Run To evaluate the contribution of the bacteria to the continuous leaching r e s u l t s , one run was made where no bacteria were i n t e n t i o n a l l y introduced. Since i t was not possible to s t e r i l i z e the tank and keep i t s t e r i l e , the added precaution of eliminating ammonium sulphate from the nutrient medium was taken. Thus the only sources of nitrogen for any stray bacteria in the system would be that entering with the concentrate, or nitrogen i n the a i r supplied to the tank. The re s u l t s for t h i s run are tabulated in Appendix I I I . Although the occasional bacterium was evident under a microscope, the correction factors calculated were s l i g h t l y less than those which had been previously calculated by determining d i r e c t l y the net ammonium ion and t o t a l carbon content of the 101 concentrate. Therefore the contribution of the observed bacteria to these measurements was probably very small, and the l e v e l of bacteria during the s t e r i l e run was a very small f r a c t i o n of the le v e l s observed during the continuous leaching runs. Further evidence of the low l e v e l of b a c t e r i a l a c t i v i t y during t h i s run i s the low l e v e l of f e r r i c i r o n . Duncan and Walden (39) indicated that there i s seldom any ferrous iron present when the leaching bacteria are active. The low level of f e r r i c iron was indicated by a low Eh value of +290 mv (measured r e l a t i v e to a Ag/AgCl reference electrode) as compared to values of about +440 mv measured when active bacteria were present. There was no evidence of the usual yellow-orange f e r r i c iron p r e c i p i t a t e , and the centrifugate from the leach s l u r r y was a pale green colour, i n d i c a t i v e of ferrous rather than f e r r i c ion in solut i o n . The dissolved iron values were r e l a t i v e l y high i n comparison with the dissolved zinc values, i n d i c a t i n g that l i t t l e iron was being removed from the soluti o n by p r e c i p i t a t i o n . As a r e s u l t of the f a i l u r e of iron to p r e c i p i t a t e with accompanying generation of acid, the reguirement for acid to maintain the low pH was higher for t h i s run than for any other run. From a l l these observations, we may conclude that the l e v e l of b a c t e r i a l a c t i v i t y was very low, and the s t e r i l e run did measure chemical leaching of zinc. Two objections may be raised to t h i s method of estimating the contribution of chemical leaching to the t o t a l amount of 102 leaching observed. One i s that the l e v e l of f e r r i c iron in solution during the s t e r i l e run was quite low, while i n the continuous leaching runs a l l the iron i n solution was probably in the f e r r i c form. Insofar as the f e r r i c iron can contribute to the o v e r a l l leaching observed with a zinc concentrate (Duncan and Walden (39)), the s t e r i l e run should give a low estimate for the chemical leaching contribution. However, the l e v e l s of dissolved iron observed i n our continuous leaching runs were considerably lower than the 22.4 g/1 used by Duncan and Walden in t h e i r experiments. The other objection i s that i t i s conceivable that one may have either chemical leaching or b a c t e r i a l leaching but not both simultaneously. I f the surface of the leachable mineral i s completely covered with bacteria, then the access of the chemical leaching agents to the surface may be r e s t r i c t e d . If t h i s objection i s v a l i d , the estimates of chemical leaching given by the s t e r i l e run should be too high. Ignoring these two objections, the chemical leaching k i n e t i c s have been assumed to involve a fast d i s s o l u t i o n of acid l a b i l e zinc compounds (e.g. zinc oxide, zinc sulphate), followed by a slow, steady leaching of the sulphide. It has been assumed that the l a t t e r process would exhibit a rate proportional to the exposed surface area. 103 For the present purposes, the amount of re a d i l y soluble zinc was defined to be the amount which dissolves i n pH 2 water in 15 minutes. By washing 5 g of feed concentrate i n pH 2 water for 15 minutes, t h i s was determined to be 2.06% of the feed weight. The release rate a t t r i b u t a b l e to t h i s mechanism may be calculated by r Q X = (0.0206) (feed pd, g/1) D (64) For the s t e r i l e run, t h i s was 0.0750 g/l-hr. The average release rate for the s t e r i l e run was 0.2185 g/l-hr, so the rate a t t r i b u t a b l e to the slow chemical leaching of the concentrate i s 0.1435 g/l-hr. Assuming that the slow chemical leaching component may be described by r C H = ks (65) the constant k may be calculated from the release rate of 0.1435 g/l-hr and the average steady-state surface area concentration of 107.7 mz/1 to be 1.33 x 10~ 3 g/hr-m*. The baseline chemical leaching rate may now be determined as the sum of the two contributions: 1 0 4 rb = rOX + rCH = ° - n o ] : 5 3 3 s + n-0206 (feed pd, g/1) (66) This may be converted to a concentration by div i d i n g by the d i l u t i o n r a t e . The s t e r i l e run data also were used to provide a baseline correction to the net ammonium ion and t o t a l carbon concentrations measured i n the other continuous runs. It was assumed that the net ammonium ion and t o t a l carbon concentrations measured i n the s t e r i l e run were contributed by the incoming concentrate. The baseline correction was therefore calculated as mg/1 net ammonium ion or t o t a l carbon per percent feed pulp density. 3. Kinetic Data a. Correlation of Data A l l the data for the continuous leaching runs are tabulated in Appendix IV. A sample c a l c u l a t i o n for one steady-state run i s given i n Appendix V. i The theory (page 53) suggests that the steady-state data should be plotted as b a c t e r i a l concentration versus substrate 105 surface area concentration, with d i l u t i o n rate as a parameter. These plots are given i n Figures 6 and 7. In addition, in Figures 8 and 9 the data are plotted as a function of pulp density, so that the e f f e c t s of substrate concentration and substrate surface area concentration may be compared. The l i n e s which have been drawn through the data are the l i n e s of l e a s t squares f i t . k summary of the slopes and intercepts of these l i n e s i s given in Table XIII. In Figures 6 and 8 b a c t e r i a l concentration i s estimated by net ammonium ion concentration; i n Figures 7 and 9 i t i s estimated by t o t a l carbon concentration. The data show a good c o r r e l a t i o n between the two measures of b a c t e r i a l concentration, and accordingly they are discussed interchangeably. The most important single feature about Figures 6 - 9 from the point of view of b a c t e r i a l k i n e t i c s i s that there i s a range of substrate concentrations or substrate surface area concentrations f o r a given d i l u t i o n rate for which v a l i d steady-states may be obtained. This i s because, unlike homogeneous fermentations, the s p e c i f i c growth rate i s not a unique function of the substrate concentration. If there were only one s p e c i f i c growth rate which would be supported by a given steady-state substrate concentration (e.g. as in the Honod model), then there could be only one substrate concentration for steady-state at a given d i l u t i o n rate, since at steady-state the s p e c i f i c growth F i g u r e 6 1 0 6 STEADY-STATE NET AMMONIUM ION CONCENTRATION Vs SURFACE AREA CONCENTRATION X D = OiOI7l hr O D = 0,0284 hr • D A D -i - I -i 0.0595 hr 0,1038 hr"1 500 - 400 £ * 300 I— UJ 200 100 I 1 i 1 25 50 75 100 125 SURFACE CONCENTRATION, m 2 / l -100 F i g u r e 7 1 0 7 STEADY-STATE TOTAL CARBON CONCENTRATION Vs SURFACE AREA CONCENTRATION -250L 108 F i g u r e 8 STEADY-STATE NET AMMONIUM ION CONCENTRATION Vs PULP DENSITY -100 109 F i g u r e 9 STEADY-STATE TOTAL CARBON CONCENTRATION Vs PULP DENSITY I750r I500H 1250k c? 1000 o CD < O 750 500h 250h 2 3 4 5 PULP DENSITY, % -250 110 Table XIII. Summary Of Slopes And Intercepts For Steady-State Results Figure Variables D i l u t i o n Slope Ordinate Abscissa Rate Intercept N 16 18 20 22 'N Fd pd Uncorrected [Zn] Oncorrec ted [Zn] Corrected [Zn] Corrected [Zn] pd Fd 0.0171 5.50 29.5 0.0284 4. 55 -24.2 0.0595 2.61 6.75 0. 1038 1. 44 13.7 0.0171 20. 1 104 0.0284 17. 2 -104 0.0595 8.58 42.4 0. 1038 3. 82 88.2 0.0171 86. 2 33.4 0.0284 83. 5 -36.2 0.0595 45. 4 0. 134 0. 1038 35. 4 -7.68 0.0171 319 113 0.0284 316 - 151 0.0595 149 21.5 0. 1038 94. 7 28. 1 0.0171 0. 629 2.66 0.0284 0. 426 - 1.23 0.0595 0.244 1. 20 0. 1038 0. 103 2.97 0.0171 10.0 2.90 0.0284 7. 82 -2.33 0.0595 4. 24 0.560 0.1038 2. 57 1. 30 0.0171 0. 517 2.45 0.0284 0. 350 -1. 14 0.0595 0. 202 0.977 0. 1038 0.0770 2.75 0.0171 8.22 2.63 0.0284 6. 42 -2.01 0.0595 3. 52 0.434 0. 1038 1. 94 1.45 111 rate equals the d i l u t i o n rate (equation 55). In t h i s case, the l i n e s on our plots would a l l be v e r t i c a l . Our model (equation 54) predicts that s p e c i f i c growth rate should depend not only on substrate surface area, but also on the b a c t e r i a l concentration: „ = £X - v .fs + fX + K) - / fs + fX * K)2 - 4 fsxT y X X ( 2 f J ( b / ) The dependence of s p e c i f i c growth rate on substrate surface concentration i s thus not unique. In t h i s important respect our model i s therefore borne out by the experimental data. Our model predicts that the l i n e s for each d i l u t i o n rate should have no curvature (equation 59), and t h i s prediction appears to be borne out by the experimental data. Our model predicts that the slopes of the l i n e s when plotted against the r e c i p r o c a l of the d i l u t i o n rates should define a straight l i n e passing through the o r i g i n . Figures 10 and 11 plot the data i n t h i s manner with surface area concentration as the independent variable; i n Figures 12 and 13, pulp density i s the independent variable. Since only four d i l u t i o n rates were used, there are only four points to define the l i n e . It would appear, however, that i f the l i n e i s to go through the o r i g i n , the l i n e must curve downward at higher F i g u r e 10 SLOPE Vs RECIPROCAL DILUTION RATE FOR NET AMMONIUM ION -SURFACE CONCENTRATION PLOT (Figure 6) ~ 5 CM £ 4 CP w B Q_ O CO I 10 20 30 40 1/D, hr 50 60 70 80 F i g u r e 11 SLOPE Vs RECIPROCAL DILUTION RATE FOR TOTAL CARBON -SURFACE CONCENTRATION PLOT (Figure 7) 25r ~ 20 CM E 15 3 ,0 «• LU Q_ O (/> 5 i 10 20 30 40 50 60 70 80 1/D, hr F i g u r e 12 SLOPE Vs RECIPROCAL DILUTION RATE FOR NET AMMONIUM ION -PULP DENSITY PLOT (Figure 8) I25r-100 - 75 £ UJ GL O - J CO r50 25 1 10 20 30 40 50 1/D,hr 60 70 80 115 F i g u r e 13 SLOPE Vs RECIPROCAL DILUTION RATE FOR TOTAL CARBON-PULP DENSITY PLOT (Figure 9) 350 300 250 - 2 0 0 v. cn £ UJI50 CL O - J CO 100 50 J I L 10 20 30 40 50 60 1/D, hr 1 1 6 values of r e c i p r o c a l d i l u t i o n rate. In addition, when pulp density i s the independent variable, the l i n e s appear to have a positive intercept. The downward curvature at high r e c i p r o c a l d i l u t i o n rates (residence times) may be explained by noting that not a l l the concentrate fed i s leachable. At higher residence times, the percentage extraction increases, and the f r a c t i o n of the surface area exposed that i s "a c t i v e " becomes smaller. For any given d i l u t i o n rate, the percentage extraction i s approximately constant (Table XIV), so that the f r a c t i o n of active surface w i l l be a constant which w i l l decrease with decreasing d i l u t i o n rate. The e f f e c t of applying such a correction factor to the measured surface concentrations i s to increase the slope of the l i n e for a given d i l u t i o n rate. Since the correction factor would become smaller as the d i l u t i o n rate became smaller, the greatest increase i n slope should occur for the smallest d i l u t i o n rate. The e f f e c t would be to help straighten out the l i n e in these plots. A l l the leach residue analyses f e l l in the range 54.2% to 58.5% zinc, independent of percentage extraction. This range includes residues that were both HCl and pH 2 water washed. These data indicate that the explanation for the curvatures in Figures 10 - 13 may not be v a l i d , as a l l the residues probably contained a high percentage of leachable zinc. 117 Table XIV. Summary Of Percentage Zinc Extractions. Dates Di l u t i o n Total Soluble % Rate Output Output Zinc Extracted (hr-M (g) (g) 22-11-71 27-11-71 0.0171 5005 3312 66.2 15-12-71 17- 12-71 0.0167 850. 4 514. 0 60.4 24-02-72 28-02-72 0.0284 2101 1087 51.7 11-04-72 14-04-72 0.0273 3298 1832 55.5 4-05-72 9-05-72 C.0294 2002 1117 55.8 16-05-72 18-05-72 0.0603 2490 1111 44.6 14-06-72 17-06-72 0.0595 1194 517. 0 43.3 21-06-72 23-06-72 0.0588 857. 0 344. 6 40.2 12-07-72 13-07-72 0. 1040 1370 467. 0 34. 1 16-07-72 19-07-72 0. 1034 1364 439. 2 32.2 21-07-72 23-07-72 0. 1040 2360 785. 1 33.3 28-07-72 29-07-72 0.1038 2307 748. 3 32.4 10-09-72 12-09-72 0.0588 1904 204. 8 10.8 17-12-72 21-12-72 0.0171 514. 0 369. 6 71.9 1 18 The theory predicts that the intercepts of the l i n e s in Figures 6 and 7 should become more negative as d i l u t i o n rate increases. None of the intercepts appears to be s i g n i f i c a n t l y d i f f e r e n t from zero. P o s i t i v e intercepts are not possible i n terms of the theory presented. With no substrate fed to the tank, the only possible steady-state should be with no bacteria in the tank. The intercepts show no clear trend with d i l u t i o n rate. How can we reconcile these r e s u l t s with the predicted model? The steady-state r e s u l t s are predicted by eguation 59: x - f o>£ -1) * & s ( 5 9> Zero intercepts suggest that the constant < i s n e g l i g i b l y small. If t h i s i s so, k_^i s much smaller than k^. Consideration of eguation 51 shows that i n t h i s case the equilibrium between the bacteria attached and the free swimming bacteria i s such that the surface i s v i r t u a l l y completely occupied by bacteria. Putting K equal to zero in equation 54 makes the b a c t e r i a l qrowth rate f i r s t order i n surface concentration, which i s expected i f the surface i s completely occupied by the bacteria. If the growth rate i s f i r s t order i n surface concentration, then a l l the growth rate data should be correlated by plotting 119 growth rate as a function of surface concentration. Figures 14 and 15 show that the growth rate data for net ammonium ion and t o t a l carbon are well correlated by t h i s type of plot, giving a stra i g h t l i n e intercepting near the o r i g i n . The slope of thi s l i n e i s an estimate of v / f , and t h i s i s a better estimate than would be obtained from the slope of the plot of slopes versus r e c i p r o c a l d i l u t i o n rate (Figure 10 or 11) since a l l the data are used d i r e c t l y . There appears to be an e f f e c t due to d i l u t i o n rate on these plots, with higher d i l u t i o n rates giving a higher growth rate for a given surface concentration. This may possibly be explained by the observation that at lower d i l u t i o n rates and higher percentage extractions a lower f r a c t i o n of the surface i s activ e . Because the intercept plot suggested by the theory could not be made, i t was not possible to make estimates of the three constants i n the model. We have an estimate of v/f, and we know that K i s much smaller than f(D/v-1) for the range of d i l u t i o n rates investigated. According to the model, i f the d i l u t i o n rate were made high enough, the intercept term should become s i g n i f i c a n t as D/v approaches unity. We may therefore conclude that v i s somewhat larger than the greatest value of d i l u t i o n rate used i n t h i s study, 0.1038 h r - 1 . The upper l i m i t on d i l u t i o n rate at which a steady-state b a c t e r i a l population can F i g u r e 14 1 2 n GROWTH RATE EXPRESSED AS NET AMMONIUM ION Vs SURFACE AREA CONCENTRATIONS 20 L - I 18 t 16 |> 14 LU a: O or o 12 10 8 LU X u o • L A D = OiOITI hr D = 0,0284 hr D = 0,0595 hr - i D= 0,1038 hr"1 Slope = 0,139 Intercept = 0.252 J 25 50 75 100 125 SURFACE AREA CONCENTRATION, m2/L F i g u r e 15 1 2 1 GROWTH RATE EXPRESSED AS TOTAL CARBON Vs SURFACE AREA CONCENTRATIONS Slope = 0i445 Intercept = 2.33 X D=0.0I7I hr"1 O 0=0.0284 hr"1 • D=0.0595 hr"' A Dso.iosshr1 J L 50 100 150 SURFACE AREA CONCENTRATION, m2/L 122 be maintained i n the reactor i s v , the maximum s p e c i f i c growth rate for the bacteria which are attached. Evidently t h i s work has not covered the f u l l range of possible d i l u t i o n rates. For comparison, Hempfling and Vishniac (77) have grown l i Q§.a.E2li£a.nus i - n continuous culture on a thiosulphate medium and determined a maximum s p e c i f i c growth rate of about 0.45 h r - i . ' -b. Wall Growth It may be argued that wall growth i s responsible for the lack of appearance of a c r i t i c a l d i l u t i o n rate (36,71). Two observations suggest that t h i s i s unlikely: The t o t a l mineral surface area i n the tank was usually greater than 300 m2. The surface of the walls of the tank i n contact with the slurry was only 3.2 m2. Thus growth on the walls of the tank i s un l i k e l y to make a s i g n i f i c a n t contribution to the t o t a l growth measured. While i t i s l i k e l y that bacteria were associated with the scale which formed on the tank sides, these bacteria would not be able to grow at a s i g n i f i c a n t rate, since the only substrate available was the zinc concentrate. Bacteria attached to the walls would be dependent on soluble substrate for growth. Dissolved iron in b a c t e r i a l leaching systems i s normally in the 123 f e r r i c form (39), and thus i s not a substrate. There did not appear to be any dead areas in the tank shere concentrate could accumulate and support b a c t e r i a l growth above the c r i t i c a l d i l u t i o n rate. c. Generation Time The generation time corresponding to the highest d i l u t i o n rate used in t h i s work i s about 6.7 hr and i s the shortest generation time which has been reported for £. ferrcoxidans when growing on a s o l i d substrate. We may conclude from the above argument that t h i s does not represent the minimum generation time for the organism. d. Zinc Concentrations and Release Rates Similar plots for zinc concentrations and release rates, both corrected and uncorrected for chemical leaching are given in Figures 16 - 25. They show the same general features as the b a c t e r i a l concentration and growth rate plots, a ccnseguence of the close associaticn of b a c t e r i a l growth with sulphide oxidation. The chemical leaching correction does not appear to have much ef f e c t on the degree cf c o r r e l a t i c n of the data. Like the b a c t e r i a l concentration data, the zinc concentrations show a better c o r r e l a t i o n with surface concentrations than with pulp dens i t i e s . F i g u r e 16 STEADY-STATE ZINC CONCENTRATION Vs SURFACE AREA CONCENTRATION (NOT CORRECTED FOR CHEMICAL LEACHING) X D = O.OI7I hr""1 O D = 0.0284 hr"1 • D= 0,0595 hr"1 A D = 0,1038 hr"1 SURFACE AREA CONCENTRATION, m2/l 125 F i g u r e 17 SLOPE Vs RECIPROCAL DILUTION RATE FOR UNCORRECTED ZINC-SURFACE AREA CONCENTRATION PLOT (Figure 16) .8r-,7 _,6 csT w . 4 LU o.3 CO .2 ,1 10 1 1 20 30 40 1/D,hr 50 60 F i g u r e 18 STEADY-STATE ZINC CONCENTRATION Vs PULP DENSITY (NOT CORRECTED FOR CHEMICAL LEACHING) X D = 0,0171 hr"' O D = 0.0284 hr"1 • D = 0.0595 hr - 1 PULP DENSITY, % F i g u r e 19 127 SLOPE Vs RECIPROCAL DILUTION RATE FOR UNCORRECTED ZINC-PULP DENSITY PLOT (Figure 18) A 101 8 * 5 UJ Q_ o 4 CO J I I I 10 20 30 40 50 60 1/D,hr F i g u r e 20 STEADY-STATE ZINC CONCENTRATION Vs SURFACE AREA CONCENTRATION (CORRECTED FOR CHEMICAL LEACHING) F i g u r e 21 129 SLOPE Vs RECIPROCAL DILUTION RATE FOR CORRECTED ZINC "SURFACE AREA CONCENTRATION PLOT (Figure 20) .8r-.7 .6 £ .5 Cn UJ , Q_ tO O -I CO .2 ,1 A J L 10 20 30 40 50 60 1/D,hr F i g u r e 22 STEADY-STATE ZINC CONCENTRATION Vs PULP DENSITY (CORRECTED FOR CHEMICAL LEACHING) 131 F i g u r e 23 SLOPE Vs RECIPROCAL DILUTION RATE FOR CORRECTED ZINC-PULP DENSITY PLOT (Figure 22) 9 i -8 3 6 C 5 cn o. o _l <o3 J L 10 20 30 40 50 60 1/D, hr F i g u r e 2 4 1 3 2 Z I N C R E L E A S E R A T E V s S U R F A C E A R E A C O N C E N T R A T I O N ( N O T C O R R E C T E D F O R C H E M I C A L L E A C H I N G ) X D = 0,0171 h r "1 O D = 0 , 0 2 8 4 h r "1 • D = 0 , 0 5 9 5 h r "1 A D = 0 , 1 0 3 8 h r "1 l ,6r -L 1-4 #» LU !5 tc LU CO < LU -J LU CC O 1.2 1.0 ,8 N ,6 o LU H O LU a: ,4 S a ,2 S l o p e = 0.0122 Intercept = 0 , 0 9 2 2 1 1 J 0 2 5 5 0 7 5 100 125 S U R F A C E A R E A C O N C E N T R A T I O N , m2/ l F i g u r e 25 ZINC RELEASE RATE Vs SURFACE AREA CONCENTRATION (CORRECTED FOR CHEMICAL LEACHING) • D^O.OSSShr"1 A D=O.I038hr"1 I I I I I I I I 0 50 100 150 SURFACE AREA CONCENTRATION, m2/L 13a e. Batch Run The maximum zinc release rate observed in t h i s study was about 1.3 g/l-hr, which agrees well with the value reported for batch leaching of a zinc sulphide concentrate by Bruynesteyn and Duncan (1). Figure 26 presents the leaching curve for a batch run in the apparatus used for the continuous experiments. The slope of the l i n e a r portion of the leaching curve gives a rate of 1.2 g/l-hr. Concentrate was fed continuously to t h i s batch experiment, so that the rate was probably li m i t e d to t h i s value . by mass-transfer of oxygen or carbon dioxide into the s l u r r y . The continuous experiments have thus demonstrated the hiyhest rate that the combination of agitator speed and a i r flow would permit. Since the release rate i s f i r s t order in surface area, there would appear to be no l i m i t to the rate which can be achieved by increasing the surface area. P r a c t i c a l l i m i t a t i o n s might be the a b i l i t y to transfer s u f f i c i e n t oxygen or carbon dioxide to the bacteria, or generation of high concentrations of toxic products, e.g. zinc ions. f. Oxygen Uptake Rates In order to compare our rates with values of Q n (N) which u2 F i g u r e 26 DISSOLVED ZINC Vs TIME CURVE FOR BATCH LEACHING IN THE STIRRED TANK REACTOR 0 10 20 30 40 50 60 70 TIME, hr 136 have been reported in the l i t e r a t u r e , we have calculated such a value from the net ammonium ion y i e l d c o e f f i c i e n t and the di l u t i o n rate. The net ammonium ion y i e l d c o e f f i c i e n t represents the r a t i o of net ammonium • ion concentration to zinc concentration in the tank at any steady-state. If we define a Q (Ntf*;) analogously tc Qn~ (N) as the rate of zinc release by a Zn 4 unit amount of net ammonium ion in the tank, then To convert the zinc release rate to an oxygen uptake rate, we can assume that 2 moles of oxygen are required to release one mole of zin c , and we can correct the net ammonium ion l e v e l to an organic nitrogen l e v e l by the r a t i o of the molecular weights. Since the. uptake rate i s usually expressed volumetrically, we assume that the oxygen i s a perfect gas at STP: QZn CNHp = S -D [Zn] X N D (68) Qo2W (18) (2) (22.4) 1Q6 p 0.882 x 106 D ul 0? (STP) (14) 65.4 YN ~ YN mgN - hr (69) Our highest Q n (N) i s then U2 tb2CN) -(0.882)(106)(.1038) 12 = 7650 yl 02 (STP) mgN - hr (70) which i s s i g n i f i c a n t l y higher than any value reported previously for this organism growing on a s o l i d substrate. 137 g. Production of Heat Whenever the release rate of zinc was greater than about 0.8 g / l - h r r i t was necessary to cool the tank in order to control the temperature. The heat being removed under these circumstances was produced by the leaching reaction as shown by the following c a l c u l a t i o n : If i t i s assumed that a l l the carbon dioxide i s fixed as glucose, the reactions taking place in the tank may be approximated by the following coupled reactions: ZnS + 20 2 •+ ZnS0 4 AH = -208.4 kcal/mole (71) 6C02+6H20 •* "6H]2°6 + 6 0 2 AH = +673.0 kcal/mole (72) A representative value of the y i e l d constant Yc i s 43 milligrams t o t a l carbon per gram of zinc released (Figure 28). Therefore release of one mole of zinc r e s u l t s in f i x a t i o n of (65.4) (43) = 0.0391 moles glucose (73) (72) (1000) The net change in enthalpy for the two reactions i s then 138 -208.4 + (.0391) (673.0) = -182. 1 kcal/mole Zn (74) which i s removed as heat. 4. Yields The y i e l d constants for a l l the continuous runs are plotted versus d i l u t i o n rate i n Figures 27 and 28. There i s no clear trend i n the data when plotted as a function of d i l u t i o n rate. I f there were a large maintenance energy requirement, the y i e l d constants should be lower at lower d i l u t i o n rates (51). Our data suggest that the maintenance requirements for t h i s organism were guite low, and i t may be concluded that T^ ferrooxidans probably does not use energy to maintain low i n t r a c e l l u l a r concentrations of hydrogen and metal ions (33). This conclusion i s supported by the observations of Beck (55) and Landesman et al.. (53) that endogenous a c t i v i t y was not detectable in Warburg respirometer experiments. However, an in v e s t i g a t i o n covering a wider range of d i l u t i o n rates might reveal a stronger trend i n the values of the yield constants. The r a t i o of t o t a l carbon to net ammonium ion remained constant at about 3.6 mg t o t a l carbon per mg net ammonium ion for the range of d i l u t i o n rates investigated (Figure 29). NET AMMONIUM ION YIELD CONSTANT m g N H 4 + / ( ^ Z n ^ ^ oi o oi o oi 1 1 1 1 1 or 1 — 1 o oo m I 1 o I to o o " 7 <D m - I co - o l I 1 rj ro (A O m i 1 601 F i g u r e 2 8 T O T A L CARBON Y I E L D CONSTANT Vs DILUTION R A T E 50 Z c O N " c40l UJO >|- 3 0 l O E CD <r 201 I i 10 1 1 ,02 ,04 .06 DILUTION RATE, hr"1 ,08 ,10 3 F i g u r e 29 RATIO OF TOTAL CARBON YIELD TO NET AMMONIUM ION YIELD Vs DILUTION RATE 5i ^ z cn_. Z cn 8 621 » i I 1 i 1 ,02 ,04 ,06 DILUTION RATE, hr"1 ,08 ,10 142 An attempt was made to correlate the t o t a l carbon and net ammonium ion measurements with c e l l numbers. Total carbon, net ammonium ion, and c e l l numbers were determined on a washed c e l l suspension prepared from the product from a continuous run. The t o t a l carbon was 7240 mg/1, the net ammonium ion was 1904 mg/1, and the concentration of c e l l numbers was 9.44 x 1 0 1 3 c e l l s per l i t r e . From these r e s u l t s we may calcu l a t e that there should be 0.779 x 10-»o m g T C / c e l l , and 0.202 x 10~»o m g net ammonium i o n / c e l l . The r a t i o of TC to net ammonium ion i s 3.80 which agrees f a i r l y well with the values measured in the continuous runs (Figure 29). The c e l l eguivalent of net ammonium ion agrees f a i r l y well with the r e s u l t s of Silverman and Lundgren (66) who reported 10*° c a l l s to contain 0.191 mg nitrogen. There i s no y i e l d data i n the l i t e r a t u r e for Tj, f§EE22xidans growing on a zinc sulphide substrate. To compare our data with l i t e r a t u r e values, we should express i t in a form which i s independent of the substrate used. Two ways of doing t h i s are to convert the data to r a t i o s of carbon dioxide fixed for oxygen consumed and to calcu l a t e free energy e f f i c i e n c i e s . The y i e l d constant Y c may be converted to a carbon dioxide f i x a t i o n e f f i c i e n c y by assuming that when one mole of zinc was released, two moles of oxygen were consumed (equation 71). Assuming that Y i s 43 mg TC/g Zn the e f f i c i e n c y can be 143 calculated to be 11.7 y moles of C0 2 fixed per 100 y moles of 0 2 taken up. This i s larger than the value of 2.1-3.0 reported by Beck (55) for growth on ferrous iron, but less than the value of 22 reported by Beck and Brown (38) for growth on sulphur. Calculation of the free energy e f f i c i e n c y f or the reaction requires a value for the free energy change for the oxidation of zinc sulphide to zinc sulphate i n aqueous so l u t i o n . We s h a l l use -163.9 kcal/mole, the standard free energy change for the reaction at 25°C as evaluated from the free energies of formation of the reactants and products (6 1). Correction for the e f f e c t of the concentrations of the reactants and product was not thought to be warranted i n t h i s case since the corrections are not very large and are d i f f i c u l t to evaluate i n a system having so many i o n i c species. For the free energy change for f i x a t i o n of carbon dioxide as glucose we s h a l l use the value of +118.2 kcal/mole of CO 2 given by Baas-Becking and Parks (59). Taking Y c as 43 mg carbon fixed per g of zinc released, the free energy e f f i c i e n c y (FEE) i s FEE = (43) (118.2) (65.4) (100%) (1000) (163.9) (12) = 16.9% (75) iaa This value l i e s between the values of 3.1% of Temple and Colmer (26) and 30% of Lyalikova (79), and i s close to the value of 17.8% which may be calculated from the c e l l numbers yield c o e f f i c i e n t of McDonald and Clark (36). The above three values are a l l for growth on ferrous i r o n . I f the net ammonium ion y i e l d constant stayed constant at about 12 mg net ammonium icn/g Zn released, the 820 mg/1 ammonium ion i n the medium 9K would be exhausted at a dissolved zinc concentration of about 68 g/1. The maximum l e v e l obtained by Torma (16) was 120 g/1, so that the yi e l d constant must have been d i f f e r e n t for his concentrate, or the y i e l d constant may have become smaller as ammonium icn became a l i m i t i n g substrate. This points to the p o s s i b i l i t y of increasing the maximum concentrations attainable by addition of ammonium icn tc the medium. 5. Percentage Extractions The percentage extractions for a l l the runs are summarized in Table XIV. The percentage extraction increases with decreasing d i l u t i o n rate as expected. The maximum percentage extraction achieved was 71.9% which i s i n s u f f i c i e n t to make th i s process competitive with the conventional e l e c t r o l y t i c zinc process. It w i l l be necessary either tc use tanks i n serie s or recycle of unleached residues to bring the percentage 145 extraction above the maximum batch extraction of 88.6%. The percentage extractions should be a function of the i n i t i a l p a r t i c l e size and the d i l u t i o n rate (17). Therefore any variation s within a given d i l u t i o n rate may be i n part a t t r i b u t a b l e to va r i a t i o n i n the guality of the grinding from run to run. An attempt was made i n Appendix VI to calcu l a t e the percentage extraction from a knowledge of the leaching k i n e t i c s , the d i l u t i o n rate, and the feed p a r t i c l e size d i s t r i b u t i o n . This procedure f a i l e d , predicting low by a factor of ten. Possible reasons for t h i s discrepancy are presented in Appendix VI-Once one knows the percentage extraction at an intermediate d i l u t i o n rate, one can make simp l i f y i n g assumptions and predict the percentage extractions at other d i l u t i o n rates with f a i r accuracy. The method i s included in Appendix VI. It does not appear to be possible to estimate the time (x ) for complete leaching of a representative concentrate p a r t i c l e from batch data. T for the concentrate used i n these experiments was 65 hours; batch experiments took about 144 hours to go to completion once i n i t i a t i o n of growth was obtained. This does not appear to be explainable by the necessity to build up an active population of bacteria i n order to achieve the maximum 146 release rate; the rate reached a maximum soon aft e r i n i t i a t i o n of zinc release and the leach curve was l i n e a r from that time u n t i l the leach was nearly complete. Torma's (16) re s u l t s were s i m i l a r . 6. Mass Balance on Zinc The mass balance r e s u l t s f o r a l l the runs are summarized i n Table XV. There was a net loss of zinc in every case, ranging from 0.6% to 18.5% of the amount fed into the tank. These losses appear to be a t t r i b u t a b l e to concentrate caking on the sides and top of the reactor above the surface of the leach s l u r r y . Not a l l the concentrate fed into the tank found i t s way into the s l u r r y ; some stuck to the moist sides of the tank or blew back out the top with the escaping sparging a i r . The measured feed rates did not take t h i s into account. This conclusion was tested by attempting to recover the amount of s o l i d s which were c o l l e c t e d on the tank sides and top aft e r the run for 14-06-72 17-06-72. It was not possible to c o l l e c t a l l t h i s material, but 320 g were recovered containing 189 g zinc. This accounts for a substantial portion of the loss for t h i s run. During the run of 28-07-72 29-07-72 care was taken to knock as much material as possible o f f the sides of the tank into the s l u r r y . This procedure was r e f l e c t e d i n sharply reduced losses for the run. 147 Table XV. Summary Of Mass Ealances On Zinc. Dates Zinc Zinc Zinc % Input Output loss Loss (g) (g) (g) 22-11-71 _ _ _ _ 27- 11-71 5353 5005 348 6.5 15-12-71 17- 12-71 985.0 850.4 34.6 13.6 24-02-72 28-02-72 2356 2101 255 10.8 11-04-72 14-04-72 3538 3298 240 6.8 4-05-72 9-05-72 2237 2001 235 10.5 16-05-72 18-05-72 2815 2490 325 11.5 14-06-72 17-06-72 1470 1 197 273 18.5 21-06-72 23-06-72 933.2 863.3 69.9 7.5 12-07-72 13-07-72 1465 1377 87 6.0 16-07-72 19-07-72 1405 1364 41 2.9 21-07-72 23-07-72 2519 2367 152 6.0 28-07-72 29-07-72 2333 2318 15 0.6 10-09-72 12-09-72 2090 19 10 180 8.6 17-12-72 21- 12-72 574.7 519.4 55.3 9.6 ma 7. Dissolved Iron Concentration and pH The dissolved iron concentration and pH data are summarized in Tables XXX - XXXIII i n Appendix IV. The iron concentration remained quite low for a l l the runs, never exceeding 1.8 g/1. The l e v e l correlated quite well with the zinc concentration l e v e l s in the tank, occasionally modified by the e f f e c t of pH (e.g. 15-12-71 17-12-71). The iron l e v e l i n solution at any time should be determined by the r e l a t i v e rates of release from the mineral by leaching and of p r e c i p i t a t i o n as hydrated f e r r i c compounds. The iron release rate, l i k e the zinc release rate, i s determined by the concentration of surface present; the p r e c i p i t a t i o n rate w i l l be a function of the f e r r i c iron concentration and pH. The much higher r a t i o of iron to zinc in solut i o n for the s t e r i l e run (Table XXI) i s due to the fact that the iron was in the ferrous form and so did not p r e c i p i t a t e . 8. Acid and Antifoam Requirements The acid and antifoam requirements for the nutrient medium are summarized in Table XVI. The addition rates of both of these quantities were determined by t r i a l and error i n order to achieve the desired process r e s u l t s . 149 Table XVI. Acid And Antifoam Requirements For Iron-Tree 9K Medium. Date S o l i d Feed Rate (9/hr) 22-11-71 27-11-71 45. 6 15-12-71 17-12-71 26. 0 24-02-72 28-02-72 42. 9 11-04-72 14-04-72 65. 2 4-05-72 9-05-72 27. 8 16-05-72 18-05-72 105. 5 14-06-72 17-06-72 36. 5 21-06-72 • 23-06-72 70. 3 12-07-72 13-07-72 72. 9 16-07-72 19-07-72 82. 5 21-07-72 23-07-72 102. 4 28-07-72 29-07-72 135. 1 10-09-72 12-09-72 73. 6 17-12-72 21-12-72 14. 0 Product Sulphuric Antifoam Rate Acid (1/hr) (m/201) (drops/201) 0.311 50.' 0. 0.300 0. 0. 0.518 15. 10. 0.494 25. 20. 0.535 10. 20. 1.098 35. 20. 1.075 35. 20. 1.074 35. 20. 1.894 35. 20. 1.885 35. 20. 1.893 40. 20. 1.879 45. 25. 1.082 100. 0. 0.313 20. 0. 150 In general, the acid requirement increased with d i l u t i o n rate and with feed pulp density. The increase i n requirement with feed pulp density i s due to the acid consuming nature of the concentrate. This property of the concentrate was noted in the preliminary batch experiments, where i t was necessary to keep taking the pH down to the optimum l e v e l u n t i l leaching began. Thereafter, the pH would stay down or even decrease as p r e c i p i t a t i o n of f e r r i c i r o n generated acid i n the medium. - At the higher d i l u t i o n rates and lower percentage extractions the r a t i o of acid consumption by concentrate to acid generation by p r e c i p i t a t i n g f e r r i c iron should increase due to the higher r a t i o of pulp density to f e r r i c i r o n concentration. This explains why the acid requirement increased with increased d i l u t i o n rate. The high acid requirement for the s t e r i l e run i s due to the lack of acid generation by p r e c i p i t a t i n g f e r r i c compounds in t h i s case. Antifoam (Dow Polyglycol 15-200) had to be added to keep the s l u r r y from foaming out of the tank at higher d i l u t i o n rates. The foaming was evidently due to b a c t e r i a l a c t i v i t y as there was no antifoam requirement for the s t e r i l e run which was performed under conditions that otherwise would have required 151 addition of 20 drops of antifoam to each 20 1 of nutrient medium. 9. Concentration of Surface Area i n Feed The feed surface area concentrations and the average product surface area concentrations are summarized in Table XVII. The surface concentration was reduced by about 80% by passage through the tank. Elution of fine s as the feed f e l l into the tank may have been a contributing factor, although the dust accumulation i n the laboratory was minimal. The remainder i s due to reduction in both pulp density and s p e c i f i c surface area of the concentrate as i t was leached. 10. I n d u s t r i a l Applications Torma (16) has shown that the solutions produced by b a c t e r i a l leaching of a zinc sulphide concentrate are suitable for zinc recovery by electrowinning. In t h i s study, the technical f e a s i b i l i t y of a continuous b a c t e r i a l leaching process has been demonstrated. Stable steady-states with high leaching rates have been obtained. The data show that there should be no upper l i m i t placed on leach rates by surface area. It should always be possible to provide enough surface area by grinding or increasing the pulp density so that some other factor w i l l l i m i t the rate. 152 Table XVII. Concentration Of Surface In Feed And Product. Dates Dilution Feed Product Pate s s (hr-M ( i » z / l ) (II V I 22-11-71 27-11-71 0.0171 437. 9 73.3 15-12-71 17-12-71 0.0167 276.6 46.0 24-02-72 28-02-72 0.0284 280.4 55.2 11-04-72 14-04-72 0.0273 406.9 94.0 4-05-72 9-05-72 0.0294 150. 1 35.7 16-05-72 18-05-72 0.0603 289.0 77.3 14-06-72 _ 17-06-72 0.0595 89. 5 21.8 21-06-72 23-06-72 0.0588 182.2 50.7 12-07-72 13-07-72 0. 1040 10 2. 3 34.0 16-07-72 19-07-72 0.1034 118.2 46.6 21-07-72 23-07-72 0. 1040 151.7 65.8 28-07-72 29-07-72 0.1038 237.3 87.2 10-09-72 12-09-72 0.0588 ie8.o 1C7.7 17-12-72 21-12-72 0.0171 130.4 17.7 1 5 3 High percentage extractions and high zinc concentrations have not been obtained due to the residence time d i s t r i b u t i o n i n the reactor type chosen. To achieve maximum extractions and zinc concentrations, the residence time d i s t r i b u t i o n of a plug flow reactor i s necessary. P r a c t i c a l l y , i t would be d i f f i c u l t to maintain plug flow of the three phase mixture for the high residence times required. The desired residence time d i s t r i b u t i o n can be approached by connecting a number of s t i r r e d tanks i n s e r i e s . In the l i m i t of an i n f i n i t e s e r i e s of s t i r r e d tanks, the plug flow residence time d i s t r i b u t i o n would be achieved. Levenspiel (17) shows that the t o t a l residence time requirement decreases s u b s t a n t i a l l y for a qiven percentage extraction when two s t i r r e d tanks are connected i n s e r i e s . An a l t e r n a t i v e would be to separate the leachable s o l i d s by f l o t a t i o n or density methods af t e r one stage of leaching i n a s t i r r e d tank and recycle them through the tank. In t h i s way s u f f i c i e n t residence time i n the tank would be provided to achieve the t o t a l recovery of a l l the leachable zinc in the concentrate. Disadvantages of t h i s method would be the cost of making the separation and the losses of leachable mineral i n the separation step. The data which have been taken in t h i s work are representative of reactor performance when the rate of leaching 1 5 4 i s l i m i t e d by the amount of mineral surface area a v a i l a b l e . Since the major process expense i s expected to be the aeration and a g i t a t i o n required to transfer oxygen and carbon dioxide into the s l u r r y (78), i t i s unl i k e l y that a l l the tanks i n a series would be operated at a surface l i m i t i n g condition. S u f f i c i e n t surface would be provided to support a reaction rate capable of using a l l the oxygen and carbon dioxide that could be transferred. Surface would only be permitted to become l i m i t i n g at the end of the ser i e s , i n order to bring the t o t a l extraction up to the maximum which could be achieved. Since the concentration of leachable s o l i d s leaving the l a s t reactor should be quite low, the leaching rate i n t h i s l a s t reactor w i l l be l i m i t e d by mineral surface area, and the aeration capacity of the e a r l i e r reactors w i l l not be needed. The data taken i n t h i s work should permit determination of the stage in a se r i e s of reactors where the surface area becomes l i m i t i n g . This work has not been able to demonstrate the existence of a c r i t i c a l d i l u t i o n rate. The bacteria used in these studies should have a maximum s p e c i f i c growth rate, and so i n the absence of wall growth or non-ideal mixing there should be a c r i t i c a l d i l u t i o n rate above which the bacteria w i l l wash out of the reactor. Further studies should be undertaken to determine what th i s i s , so that design studies can take into account the f u l l range of poten t i a l d i l u t i o n rates. Although the t o t a l residence, time requirement w i l l be quite high to ensure high 155 extractions and dissolved zinc concentrations, t h i s residence time may be divided up among a series of s t i r r e d tanks, and so the d i l u t i o n rate in any given tank may be r e l a t i v e l y high. In a series of equal sized s t i r r e d tanks, i f washout occurs i n the f i r s t tank, i t w i l l progress through the whole se r i e s , with consequent process f a i l u r e . Thus, i t may prove necessary to recycle a portion of the leach liquor to ensure a supply of bacteria for the whole reactor t r a i n . Consideration of the net ammonium ion y i e l d constant determined i n t h i s work shows that i t w i l l probably be necessary to increase the amount of ammonium ion in the nutrient medium. The amount to add w i l l be determined by the zinc concentration required i n the feed to the electrowinning plant. The concentrate tested i n t h i s work w i l l require a d d i t i o n a l grinding i n order to achieve extractions i n excess of 90%. Foaming may be a problem, but i t may be cont r o l l e d by addition of Dow Polyglycol 15-200 to the leach s l u r r y . This compound does not appear to ba i n h i b i t o r y to the bacteria at l e v e l s necessary for successful foam control. There w i l l be a requirement for sulphuric acid addition to control pH; th i s may be supplied by recycling spent electrowinning solution. Recycle of t h i s solution w i l l minimize losses of dissolved zinc and the nutrients i n the medium. 156 VII. SUMMARY AND CONCLUSIONS 1. Continuous microbiological leaching of the test concentrate i s t e c h n i c a l l y f e a s i b l e . Stable steady-states may be obtained i n a continuous s t i r r e d tank reactor. 2. The s p e c i f i c growth rate of the bacteria was not a unique function of the substrate concentration or the surface area concentration. Thus conventional continuous culture theory does not apply to t h i s system. There was a range of steady-state substrate concentrations attainable for a given d i l u t i o n rate. This was a consequence of using a s o l i d substrate. 3. The b a c t e r i a l concentration did not l i m i t the leaching rates under the conditions of these experiments. The leaching rates and b a c t e r i a l growth rates were thus f i r s t order i n surface area. t». The model which was derived suggested that b a c t e r i a l concentration should l i m i t leaching rates at higher d i l u t i o n rates. There should be a maximum d i l u t i o n rate beyond which washout should occur. 5. The maximum s p e c i f i c growth rate was not approached in these experiments. The highest s p e c i f i c growth rate obtained (0.1038 h r - 1 ) i s the highest rate which has been observed for T. ferrooxidans growing on s o l i d substrates. 6. The maximum oxygen uptake coeffecient ( Q Q ^ ^ ) ) calculated from these experiments was 7650, about twice as great as 157 the highest reported for growth of t h i s organism on a s o l i d substrate. 7. Total carbon and net ammonium ion concentrations correlated with each other and were s a t i s f a c t o r y measures of the biomass concentration. 8. The b a c t e r i a l y i e l d s remained constant for the range of d i l u t i o n rates investigated, indicating a low maintenance energy requirement for t h i s organism. 9. The y i e l d c o e f f i c i e n t value of 12 mg net ammonium ion per g zinc released suggests that addition of ammonium ion above the l e v e l s present in the medium 9K of Silverman and Lundgren (66) should be b e n e f i c i a l when dissolved zinc concentrations exceed 68 g/1. 10. The bacteria fixed about 43 mg carbon per g zinc released. 11. When the percentage extraction for one d i l u t i o n rate was known, i t was possible to use a c a l c u l a t i o n method given by Levenspiel (17) to predict the r e s u l t s at other d i l u t i o n rates. 12. It was necessary to grind the concentrate to obtain the maximum batch zinc extraction of 88.6%. 13. The contribution of chemical leaching to the t o t a l amount of zinc leached was estimated to be 20 - 25 %. 14. Heat produced at higher release rates necessitated cooling the reactor. 15. At higher d i l u t i o n rates when bacteria were present, foaming was a problem. Addition of Dow Polyglycol 15-200 1 58 to the nutrient medium controlled the foam. When b a c t e r i a l growth was suppressed by withholding ammonium ion, foaming was not a problem. 16. I t was necessary to add sulphuric acid to the nutrient medium to maintain the pH in the optimum range for the bacteria. The requirement for acid increased with increasing d i l u t i o n rate and increasing pulp density. 17. The bast process configuration to achieve high extractions and zinc concentrations i n continuous processing w i l l be s t i r r e d tanks i n s e r i e s , with or without s o l i d s recycle. 159 VIII. REFERENCES 1. Bruynesteyn, A., and tuncan, E. W., Can. Met. Quart. JO, 57-63 (1971) 2. Tsuchiya, H. M. , Fredrickson, A. G., and A r i s , R., Advan. Chera. Eng. 6, 125-206 (1966) 3. Fredrickson, A. G., and Tsuchiya, H. M., A. I. Ch. E. J. 9, 459-468 (1963) 4. Eakman, J. M., Fredrickson, A. G., and Tsuchiya, K. M. , Chem. Eng. Prcgr. Symp. Ser. 62, 37-49 (1966) 5. M'Kendrick, A. G,, and Pai, M. K., Proc. Roy. Soc. Edinburgh 3J, 645-655 (1910-1911) 6. Mcncd, J., "Recherches Sur l a Croissance des Cultures Bacteriennes", Masson Et Cie., Paris (1942), cited in reference 2 7. Mcncd, J . , Ann. Rev. Microbiol. 3, 371-394 (1949) 8. Herbert, D. , Elswcrth, R., and T e l l i n g , R. 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H. , and T e l l e r , E., J. Amer. Chem. Soc. 60, 309-319 (1938) 73. Orr, R., Ph. D. Thesis, University of B. C. (1969) 74. Burke, K. E., Anal. Chem. 34, 1747-1751 (1962) 75. L i , J . C. R., " S t a t i s t i c a l Inference", p. 374, Edwards Bros., Ann Arbor, 1964 76. Stober, W., Fink, A., and Bchn, E., J. C o l l o i d Interface S c i . 26, 62-69 (1968) 77. Hempfling, ». P., and Vishniac, W., J. E a c t e r i o l . 93, 874-878 (1968) 78. McElroy, R. O., Personal Conmunication. 79. Lyalikova, N . N., Mikrobiolcgia 27, 556-559 (1958) APPENDIX I Calculation Cf Percentage Zinc Extracted In Batch Shake Flask Experiments (Table VI) 165 Appendix I. Calculation Of Percentage Zinc Extracted In Batch Shake Flask Experiments (Tafcle VI), Estimated Ore Composition Is 55.69 % Zinc. 5. g Ore Contains (.5569) (5.) = 2.785 g Zinc Total Zinc Extracted = Eissclved zinc Recovered At The End Of The leach + Dissolved Zinc Remcved By Sampling The Flasks (1 ml Samples) - Dissolved Zinc Introduced With The Inoculum. = 1.24G0 • 0.0016 + C.C033 + 0.0036 • 0.0044 + 0.0057 + 0.0070 + 0.0112 + 0.0125 • 0.0161 • 0.0151 • 0.0141 -0.042 = 1.293 g Zinc Percentage Zinc Extracted = (1.293) (100%) = 46.4 % ( 2 . 7 a * ) 166 APPENDIX II Regression Analysis Of Tank And Product Dissolved Zinc Concentrations 167 Appendix II. Regression Analysis Cf Tank And Product Dissolved Zinc Concentrations. The data for the regression analysis are giver in Tatle XVIII, Sum Of X = 251 .79, Sum Cf If = 219.68, Sum Cf XY = 2483.5, Sum Of Squares X = 2500.3, Sum Cf Squares Y = 2468.1, (Sums Of Squares Uncorrected For The Mean) Analysis Of Variance Source Sum cf Sguares d.f, Mean Sguare Regression (to) Regression ( t i l b 0 ) Residual Total 2149.7 317. 1 1.4 2468. 1 1 1 27 29 317.12 0.0506 6272. Hypothesis: Slope = 1.0 t = b 1 - 1.0 fS_2_ s <? where SS = [Sum Of Sguares X] - [Sum Cf X] 2/n t = 1.C024 - 1.00 / 0.0506 /250C.3 - [251. 70 ]V29 = 0.190 t (.05,27) = 1.703 The slope i s not s i g n i f i c a n t l y d i f f e r e n t from 1.0 at the 90% l e v e l . Hypothesis: Intercept = 0.0 168 Table XVIII. Regression Analysis Of Tank And Product Dissolved Zinc Ccncentraticns. Date Tank Product F i t t e d Concentration Concentration Product Concentration (g/i) (g/i) (g / D 12-09-72 2 3.77 3.74 3.69 12-09-72 1 3.78 3.75 3.70 11-09-72 2 3.78 3.70 3.70 11-09-72 1 3.70 3.47 3.62 10-09-72 1 3.35 3.26 3.27 29-07-72 2 12.68 12. 35 12.62 29-07-72 1 12.58 12.97 12.52 28-07-72 3 12.41 12.66 12. 35 28-07-72 2 12.40 12.66 12.34 28-07-72 1 12. 36 12. 30 12.30 23-07-72 2 8.98 9.13 8.91 23-07-72 1 8.97 8.86 8.90 22-07-72 2 9.24 8.99 9. 17 22-07-72 1 9.62 9.52 9.55 21-07-72 1 8.74 8.90 8.67 19-07-72 1 7.61 7.78 7.54 18-07-72 1 6.80 6.55 6.73 17-07-72 2 7.70 7.90 7.63 17-07-72 1 7.91 7.75 7. 84 16-07-72 1 8. 31 7.92 8.24 13-07-72 2 6.50 6.38 6.43 13-07-72 1 6.68 6.68 6.61 12-07-72 3 6.87 6.72 6.80 12-07-72 2 6.68 6.52 6.61 12-07-72 1 6.65 6.54 6.58 24-06-72 1 14.22 13.89 14. 16 23-06-72 1 13.36 13.08 13.30 22-06-72 2 12.96 13. 17 12.90 22-06-72 1 13.06 12.51 13.00 169 t = :0 r s u t D of x]« t nZZZ i S2 Since the intercept cannot be negative (implies a negative concentration in the prcduct sample) this should te a c c e - t a i l e d t e s t , and cnly positive values of t should be s i g n i f i c a n t . The calculated bp i s negative, so t cannct be s i g n i f i c a n t in a cne-t a i l e d test. We cannct reject the hypotheses that fc-l = 1.0 b 0 = 0.0 at the 90% s i g n i f i c a n c e l e v e l . APPENDIX III S t e r i l e Run Data 171 Table XIX. Ba c t e r i a l Growth Rates For Continuous Leaching At Dilut i o n Rate = 0.0588 Hr-*. ( S t e r i l e Run) Date Net * H4 Net Rate Total Carbon T c t a l Carbon Rate (mg/1) (mg/l-hr) (mg/1) (mg/l-hr) 11-09-72 1 11- 09-72 2 12- 09-72 1 12-09-72 2 5 4 5 4 0.294 0.235 0.294 0.235 47 55 3 3 45 2.76 3.23 1.94 2.64 Table XX. Yield Constants For Continuous Leaching At Di l u t i o n Rate = 0.0588 Hr-*. ( S t e r i l e Run) Bate Net N H 4 Yield Total Carbon Yield Ra t i o ^ mg N H A - J r mg TC. *-g Zn J rmq TC . '-mg NHj-> 11-09-72 1 1. 35 12.7 9.40 11-09-72 2 1.06 14. 5 13.76 12-09-72 1 1.32 8.7 6.60 12-09-72 2 1.06 11.9 11.26 \ Table XXI. Results For Continuaus Leaching At Di l u t i o n Rata = 0.0583 H r - 1 ( S t e r i l e Run) Date Pulp Spe c i f i c Density Surface Area pH [ F a ] [Zn] r z / s (m2/g) ( t n 2/l) (g/ D (g/1) (g/l-hr) (g/hr-m*) 11-09-72 1 11- 09-72 2 12- 09-72 1 12-09-72 2 5.3760 5.2548 5.1958 5. 1816 2.0817 2.2425 1.8106 2.0637 111.91 117.84 94. 08 106.93 2. 05 2.00 2. 10 2.00 1.052 1.121 1. 159 1. 164 3. 70 3.79 3. 79 3. 77 0.218 0. 223 0.223 0.222 0.0019 0.0019 0.0024 0.0021 173 APPENDIX IV Ccntinuous Leaching Data 174 Table XXII. Bacterial Growth Rates For Continuous Leaching At D i l u t i c n Rate = 0.0171 Hr* 1. Date Net NHj Net N H J Rate Total Carbon Total Carbon Rate (mg/1) (mg/l-hr) lmg/1) (mg/l-hr) 22- 11-71 23- 11-71 24- 11-71 25- 11-71 26- 11-71 27- 11-71 440 434 458 434 451 7.53 7.43 7.84 7.43 7.72 161 1 168 1 160 1 161 1 160 1 1609 27.59 28.79 27.42 27.60 27.42 27.56 15- 12-71 16- 12-71 17- 12-71 242 235 243 4. 3, 4. 02 91 04 878 894 884 14.6 1 14.88 14.71 17- 12-72 18- 12-72 19- 12-72 20- 12-72 21- 12-72 150 133 133 135 137 2.56 2.27 2.27 2. 31 2.34 598 51 1 476 456 443 10.21 8.73 8. 13 7.79 7.57 175 Table XXIII. B a c t e r i a l Growth Sates For Ccnti nuous Leaching , Dilution Rate = 0.0284 Hr- 1. Date Net Net Total Total NH + N H 4 Carbon Carbo Rate Rate (rcg/1) (mg/l-hr) (mg/1) (mg/l-h 24-02-72 222 6. 30 902 25.60 25-02-72 221 6.27 800 22.71 26-02-72 218 6. 18 812 23.05 27-02-72 221 6.27 793 22.51 28-02-72 216 6. 13 849 24.10 11-04-72 406 11.06 158 8 43.28 12-04-72 408 11.12 1532 4 1.76 11-04-72 413 11.25 1472 40. 12 14-04-72 414 11.28 1550 42.25 4-05-72 147 4. 32 514 15.13 5-05-72 136 4.00 50 2 14.77 6-05-72 134 3.94 496 14.60 7-05-72 131 3.85 490 14.42 8-05-72 149 4.3 8 53 1 15.63 9-05-72 139 4.09 50 8 14.95 176 Table XXIV. Bact e r i a l Growth Sates For Continuous Leaching At Dilution Rate = 0 . 0 5 9 5 Hr-i. Date Net Net Total Total N H J Carbon Car bo Rate Rate (mg/1) (mg/l-hr) (mg/1) (rcg/l-h: 1 6 - 0 5 - 7 2 1 2 0 0 1 2 . 0 6 7 1 6 4 3 . 1 8 1 6 - 0 5 - 7 2 2 2 0 3 1 2 . 2 4 7 2 2 4 3 . 5 4 1 7 - 0 5 - 7 2 1 2 0 4 1 2 . 3 0 7 1 6 4 3 . 1 8 1 7 - 0 5 - 7 2 2 2 0 8 1 2 . 5 4 7 1 6 4 3 . 1 8 1 8 - 0 5 - 7 2 1 2 1 6 1 3 . 0 2 7 1 6 4 3 . 1 8 1 4 - 0 6 - 7 2 2 4 8 2 . 8 5 2 0 8 1 2 . 3 6 1 5 - 0 6 - 7 2 1 6 5 3 . 8 6 2 2 6 1 3 . 4 4 1 5 - 0 6 - 7 2 2 6 4 3 . 8 0 2 4 6 1 4 . 6 2 1 7 - 0 6 - 7 2 1 4 6 2 . 7 3 2 2 5 1 3 . 3 8 2 1 - 0 6 - 7 2 1 1 4 7 8 . 6 4 4 8 1 2 8 . 3 0 2 1 - 0 6 - 7 2 2 1 5 4 9 . 0 6 5 0 0 2 9 . 4 2 2 2 - 0 6 - 7 2 1 1 3 7 8 . 0 6 4 6 8 2 7 . 5 3 2 2 - 0 6 - 7 2 2 1 5 8 9 . 2 9 4 6 8 2 7 . 5 3 2 3 - 0 6 - 7 2 1 1 4 5 8 . 5 3 4 2 1 2 4 . 7 7 177 Table XXV. Ba c t e r i a l Growth Rates For Continuous Leaching At D i l u t i c n Rate = 0. 1038 Hr- 1. Date net Net Total Total NH+ NH4 Carbon Carbon Rate Rate (mg/1) (mg/l-hr) (mg/1) (mg/l-h: 12-07-72 1 72 7.48 230 23.92 12-07-72 2 59 6. 13 226 23.50 12-07-72 3 66 6.86 226 23.50 13-07-72 1 73 7.59 222 23.08 13-07-72 2 58 6.03 215 22.36 16-07-72 1 77 7.96 280 28.95 17-07-72 1 85 8.78 277 28.64 19-07-72 1 79 8. 16 259 26.78 21-07-72 1 106 11.02 315 32.76 22-07-72 1 103 10.71 326 33.90 22-07-72 2 105 10.92 339 35.25 23-07-72 1 101 10.50 310 32.24 23-07-72 2 103 10.71 308 32.03 28-07-72 1 141 14.63 436 45.25 28-07-72 2 140 14.53 428 44.42 28-07-72 3 149 15. 46 436 45.25 29-07-72 1 146 15. 15 446 46.29 29-07-72 2 148 15. 36 446 46.29 178 Table XXVI. Yield Constants For Continuous Leaching At C i l u t i o n Rate = 0.0171 H r - 1 . (Corrected For Chemical Leaching) Date Net NH$ Yi e l d Total Carbon Yield Ratio rmg HHJfs ^g Zn J ("9 T C) (£3_rc+) g Zn TC mg NH^  22- 11-71 23- 11-71 24- 11-71 25- 11-71 26- 1 1-71 27- 11-71 10. 54 10.62 10. 50 10.60 10.51 38. 6 41.1 36.7 38.0 39. 1 37.5 3. 66 3. 87 3. 50 3. 69 3.57 15- 12-71 16- 12-71 17- 12-71 12. 14 11.91 12.07 44. 1 45. 3 43. 9 3. 63 3.80 3. 64 17- 12-72 18- 12-72 19- 12-72 20- 12-72 21- 12-72 10.72 9.79 9.97 10. 47 10.80 42. 8 37. 6 35.7 35. 4 34. 9 3.99 3. 84 3.58 3.38 3.23 179 Table XXVII. Yield Constants For Continuous Leaching At Di l u t i o n Rate = 0.0284 H r - 1 . (Corrected For Chemical Leaching) Date Net Total Ratio NHj Carbon Yield Yield ,£g_NR_4s rmg TC. r_rng_TC . '-g Zn j lg Zn J '•mg NH+J 24-02-72 12. 10 49.2 4.06 25-02-72 13. 32 48. 2 3.62 26-02-72 12. 15 45.3 3.73 27-02-72 13.01 46.7 3. 59 28-02-72 13.02 51.2 3.93 11-04-72 12.26 47. 9 3.91 12-04-72 13.28 49.9 3.76 13-04-72 12. 53 44. 6 3. 56 14-04-72 12.50 46.8 3.74 4-05-72 12. 93 45. 2 3. 50 5-05-72 11.85 43.7 3.75 6-05-72 12.08 44.7 3. 70 7-05-72 11.25 42. 1 3.74 8-05-72 12.62 45.0 3. 56 9-05-72 11.16 40.8 3.66 Table XXVIII. Yield Constants For Continuous Leaching At Dil u t i o n Rate = 0.0595 Hr-*1. (Corrected Fcr Chemical Leachin Date Net Total Ratio NH4" Carbcn Yield Yield rjng_NH+ ,mg TC^ mg TC 1 g Zn i} lg Zn J Ug NH+J 16-05-72 1 12.03 43. 1 3.58 16-05-72 2 11.89 42. 3 3.56 17-05-72 1 12. 18 42.7 3.51 17-05-72 2 12.38 42.6 3.44 18-05-72 1 12.01 39.8 3.32 14-06-72 2 9. 14 39.6 4.33 15-06-72 1 11.86 41.2 3.48 15-06-72 2 11.31 43.5 3. 84 17-06-72 1 8.62 42.2 4.89 21-06-72 1 14. 19 46.4 3.27 21-06-72 2 13.95 45.3 3.25 22-06-72 1 12.84 43.9 3.42 22-06-72 2 14.95 44.3 2.96 23-06-72 1 13.22 38.4 2.90 181 Table XXIX. Yield Constants For Continuous Leaching At E i l u t i o n Rate = 0.1038 H r - 1 . (Corrected For Chemical Leaching) Date Net Total Ratio UH| Carbon Yield Y i e l d mg_NHJ mg TC mg TC Ig Zn J g^ Zn J Ug NHy 12-07-72 1 13.21 12. 2 3. 19 12-07-72 2 10.76 11.2 3.83 12-07-72 3 11.64 39.9 3.12 13-07-72 1 13.32 10.5 3.01 13-07-72 2 10.91 10.6 3.71 16-07-72 1 11.27 11.0 3.61 17-07-72 1 13.21 13.0 3. 26 19-07-72 1 12.88 12.2 3.28 21-07-72 1 15.17 46.0 2.97 22-07-72 1 13.32 12.2 3.17 22-07-72 2 11.29 46. 1 3.23 23-07-72 1 11.27 13.8 3.07 23-07-72 2 11.53 43.4 2.99 28-07-72 1 11.12 11.6 3.09 28-07-72 2 11.26 43.6 3.06 28-07-72 3 15.16 11.1 2.93 29-07-72 1 11.60 44.6 3.06 29-07-72 2 11.65 11.2 3.01 Table XXX. Results For Continuous Leaching At D i l u t i o n Rate = 0.0171 Hr- 1 (Zinc Values Uncorrected For Chemical Leaching) Date Pulp Spec i f i c s pH [Fe] [Zn] r z r 7/s Density Surface u Area (mVg) (mVl) (g/i) (g/i) (g/l-hr) (g/hr-m 22-11-71 4.7304 1.5911 75.27 2. 10 1.740 50.25 0.8608 0.0114 23-11-71 4.7164 1.5242 75. 10 2. 10 1.715 49.40 0.8462 0.0113 24-11-71 4.8720 1.6086 75. 10 2. 25 1.635 52. 15 0.8933 0.0 119 25-11-71 4.5588 1.6819 76.67 2. 10 1.610 50.95 0.8728 0.0 114 26-11-71 4. 3.080 1.5796 68.05 2. 05 1.785 49.45 0.8471 0.0125 27-11-71 4.4242 1.5742 69.65 2. 10 1.740 51.45 0.8813 0.0127 15-12-71 2.9900 1.6154 48. 30 2. 45 0. 154 25. 15 0.4187 0.0087 16-12-71 2.9164 1.6606 48.43 2. 30 0.300 24.95 0.4154 0.0086 17-12-71 2.6142 1.5776 41. 24 2. 05 0.548 25.35 0. 422 1 0.0 102 17-12-72 1.1184 1.6403 18.35 0.677 16.20 0.2767 0.0151 18-12-72 1.1 168 1.6877 18.85 2. 20 0. 691 15.80 0.2699 0.0143 19-12-72 1.0568 1.4938 15.79 2. 20 0.666 15. 55 0.2656 0.0168 20-12-72 1.0800 1.6629 17.96 2. 15 0.664 15. 10 0.2579 0.0144 21-12-72 1.0782 1.6477 17.77 2. 20 0.690 14.90 0. 2545 0.0143 co t-o Table XXXI. Results For Continuous Leaching At D i l u t i o n Rate = 0.0284 H r - 1 (Zinc Values Uncorrected For Chemical Leaching) Date Pulp S p e c i f i c s pH [Fe] [Zn] rZ r ? / s Density Surface Area (m2/g) (m 2 /D (g/i) (g/i) (g/l-hr) (g/hr- m 24-02-72 3.2866 1.6257 53.43 2.35 0. 190 22.45 0.6 374 0.0119 25-02-72 3.5100 1.6920 59. 39 2.50 0. 175 20.70 0.5877 0.0099 26-02-72 3.3754 1.5765 53.21 2.45 0.203 22. 05 0.6260 0.0118 27-02-72 3.2320 1.6480 53.26 2.40 0.246 21.10 0.5990 0.0113 28-02-72 3.3532 1.6895 56.65 2.40 0. 288 20.70 0.5877 0.0104 11-04-72 5.0574 1.7929 90.67 2.25 0.735 40.25 1.0972 0.0121 12-04-72 5.0906 1.7391 88.53 2.40 0.743 37.85 1.0318 0.0117 13-04-72 5.2812 1.7278 91.25 2.25 0.770 40. 10 1.09 31 0.0120 14-04-72 5.3028 1.9896 105.51 2.25 0. 749 40.25 1.0972 0.0104 4-05-72 1.9364 1.9229 37.24 2.50 0. 256 13.94 0.4104 0.0110 5-05-72 1.8720 1. 8774 35. 15 2.45 0.247 14.05 0.4136 0.01 18 6-05-72 1.9072 1.8906 36.06 2.55 0. 242 13.66 0.4022 0.0112 7-05-72 1.9608 1.8081 35.45 2.45 0.239 14.21 0.4183 0.01 18 8-05-72 2.1300 1.7999 38.34 2.40 0. 236 14.38 0.4233 0.0110 9-05-72 2.0098 1.5944 32. 04 2.40 0.280 15.02 0.4422 0.0138 co Table XXXII, Results For Continuous Leaching At Dilu t i o n Rate = 0.0595 H r - 1 (Zinc Values Uncorrected For Chemical Leaching) Date Pulp S p e c i f i c s pa [Fe] [Zn] r7 r 7 / s Density Surface L L Area (%) (m2/g) (n>2/l) (9/1) (g/ D (g/l-hr) (g/hr-m 16- 05-72 1 4.5520 1.6045 73.04 2.40 0.464 20.08 1.2110 0.0166 16- 05-72 2 4.4698 1.5980 71.43 2. 40 0.479 20. 53 1. 2382 0.0173 17- 05-72 1 4.5110 1.7566 79.24 2.40 0.487 20. 21 1.2189 0.0154 17- 05-72 2 4.8622 1.8313 89.04 2.45 0. 454 20.26 1.22 19 0.0137 18- 05-72 1 4.7744 1.5437 73.70 2.40 0.467 21. 45 1.2936 0.0176 14- 06-72 2 1.3235 1.6583 21.95 2. 10 0. 402 6.310 0.3753 0.0 171 15- 06-72 1 1.4001 1.6764 23.47 2.05 0.424 6. 540 0.3889 0.0 166 15- 06-72 2 1.3938 1.5374 21.43 2.05 0. 434 6. 720 0.3996 0.0187 17- 06-72 1 1.2562 1.6264 20.43 2.00 0. 425 6. 395 0. 380 3 0.0 186 21- 06-72 1 3.1878 1.7311 55. 18 2.30 0.689 12.75 0.7502 0.0136 21- 06-72 2 3.2232 1.5770 50.83 2.50 0. 677 13. 43 0.7902 0.0156 22- 06-72 1 3.0330 1.6366 49.64 2.35 0.700 13.06 0.7685 0.0155 22- 06-72 2 2.9516 1.6451 48.56 2. 35 0. 703 12.96 0.7626 0.0157 23- 06-72 1 2.9666 1.6570 49. 16 2.40 0.737 13. 36 0.7861 0.0160 CO Table XXXIII. Results For Continuous Laaching At Dilution Rate = 0.1038 Hr" 1 (Zinc Values Uncorrected For Chemical Leaching) Date Pulp S p e c i f i c s pH [Fe] [Zn] r7 r / s Density Surface L L Area (mVg) (mz/l) (g/i) (g/i) (g/l-hr) (g/hr-m 12-07-72 1 2.0710 1.6780 24.75 2. 15 0. 349 6. 650 0.6916 0.0199 12-07-72 2 2.0836 1.6886 34.77 2.10 0.368 6. 685 0.6952 0.0200 12-07-72 3 2. 1960 1.8622 40.89 2.20 0. 357 6.870 0.7 145 0.0174 13-07-72 1 2. 1361 1.7202 36.75 2.10 0.355 6. 680 0.6947 0.0189 13-07-72 2 2.0155 1.6217 32.69 2. 10 0. 347 6. 500 0.6760 0.0207 16-07-72 1 2.5272 1.7429 44.05 2.30 0.4 18 8.310 0.8593 0.0195 17-07-72 1 2.5577 1. 7053 43.62 2.25 0. 393 7.915 0.8184 0.0188 19-07-72 1 2.5797 2.0163 52. 01 2.30 0.463 7. 615 0.7874 0.0151 21-07-72 1 2.9350 2.0046 58.84 2.20 0.515 8. 740 0.9090 0.0155 22-07-72 1 3.0692 1. 9324 59. 31 2.20 0.524 9.620 1.0005 0.0169 22-07-72 2 3.0468 2.3306 71.01 2.20 0. 532 9. 240 0.9610 0.0135 23-07-72 1 3. 1262 2. 1348 66. 74 2.25 0. 514 8. 970 0.9329 0.0140 23-07-72 2 3.0590 2.3881 73.05 2.20 0. 495 8.980 0.9339 0.0128 28-07-72 1 4.2682 1.9613 83.71 2. 30 0. 681 12. 36 1. 2830 0.0153 28-07-72 2 4.3786 2.0617 90.27 2.30 0.699 12. 40 1.2871 0.0143 28-07-72 3 4.4136 1.9829 87. 52 2.40 0.662 12.41 1.2832 0.0147 29-07-72 1 4.2328 1.8522 78. 4 0 2.35 0.715 12. 58 1.3058 0.0167 29-07-72 2 '4. 4098 2. 1800 96. 13 2. 35 0.717 12. 68 1.3162 0.0137 oo Tabla XXXIV. Results For Continuous Leaching At D i l u t i o n Rata = 0.0171 Hr-i (Zinc Values Corrected For Chemical Leaching) Date Pulp S p e c i f i c s pH [Fa] [Zn] r z / s Density Surface Area {%) (m2/9) (mVl) (g/D (g/D (g/l-hr) (g/hr-m 22 -11-71 4.7304 1.5911 75.27 2. 10 1.740 41.73 0.7148 0.0095 23 -11-71 4.7164 1.5242 75. 13 2. 10 1.715 40. 88 0.7003 0.0 09 3 24 -11-71 4.8720 1.6086 75. 13 2. 25 1.635 43.63 0.7474 0.0100 25 -11-71 4.5588 1.6819 76. 67 2. 10 1.610 42.43 0.7263 0.0095 26 -11-71 4.3080 1.5796 68.05 2. 05 1. 785 43.93 0.701 1 0.0103 27 -11-71 4.4242 1.5742 69.65 2. 10 1. 740 42.93 0.7354 0.0 106 15 -12-71 2.9900 1.6154 4 8.33 2.45 0. 154 19.93 0.3318 0.0069 16 -12-71 2. 9164 1.6606 48.43 2. 30 0. 300 19.73 0.3285 0.0068 17 -12-71 2.6142 1.5776 41.2'4 2. 05 0.548 20.1 3 0.3352 0.0381 17 -12-72 1.1184 1.6403 18.35 0.677 13.99 0.2389 0.0130 13 -12-72 1.1168 1.6877 18. 85 2. 20 0.691 13.59 0.2321 0.0123 19 -12-72 1.0568 1.4938 15.79 2. 20 0. 666 13. 34 0.2278 0.0144 23 -12-72 1.0830 1.6629 17.95 2. 15 0.664 12.89 3.2202 0.0123 21 -12-72 1.0782 1.6477 17.77 2. 20 0.690 12.69 0.2167 0.0122 CO Tab-la XXKV. Results For Continuaus Laaching At D i l u t i o n Rata = 0.0284 Hr~ l (Zinc Values Corrected For Chemical Leaching) Date Pulp Spaci f i c s pH [Fe] [Zn] rZ r 7 / s Density Surface Lt L, Area (mVg) (mz/l) (g/i) (g/i) (g/l-hr) (g/hr- m 24-32-72 3.2866 1.6257 53. 4 3 2.35 0.190 13.34 0.5207 0.0097 25-02-72 3.5100 1.6920 59. 39 2.50 0.175 16. 59 0.47 10 0.0079 25-02-72 3.3754 1.5765 53. 21 2.45 0. 203 17. 94 3.5093 0.0096 27-02-72 3.2 320 1.6483 53.25 2.40 0. 246 16. 99 0.4823 0.009 1 23-02-72 3.3532 1.6895 56.65 2.40 0.288 1 6. 59 0.4713 0.0383 11-04-72 5.0574 1.7929 90.57 2.25 0. 735 33. 12 0.9029 0.0100 12-04-72 5.3936 1.7391 88. 53 2.40 0. 743 30.72 0.8374 0.0095 13-04-72 5.2812 1.7278 91.23 2.25 0. 770 32. 97 0.8988 0.0099 14-04-72 5.3028 1.9896 105.51 2.25 0. 749 33.12 0.9029 0.0086 '4-05-72 1.9 364 1.9229 37. 24 2.50 0.256 ' 11.37 0/3347 0.0090 5-05-72 1.8720 1.8774 35.1 5 2.45 0.247 11.48 0.3380 0.0096 5-05-72 1.9072 1.8906 36. 36 2.55 0. 242 11. 09 0.3255 0.009 1 7-05-72 1.9608 1.8081 35. '45 2.45 0.239 1 1. 64 0.3427 0.0097 3-35-72 2.1330 1.7999 38. 34 2.40 0.236 11.81 0.3477 0.009 1 9-05-72 2.0098 1.5944 32.34 2.40 0. 280 12. 45 0.3665 0.0114 rabla XXKVI. Results Foe Continuous Laaching At Di l u t i o n Rata = 0.0595 Hr- 1 (Zinc Values Corrected For Chemical Leaching) Date Pulp S p e c i f i c s pH [Fe] [Zn] rZ r z / s Density Surface Area (m*/g) (m2/l) (?/D (g/i) (g/l-hr) (g/hr-3i 16-05-72 1 4.5520 1. 6045 73. 04 2.40 0. 464 16. 62 1.0024 0.0137 16-05-72 2 4.4698 1.5980 71.43 2.40 0.479 1 7. 07 1.0295 0.0144 17-05-72 1 4.5110 1.7566 79. 24 2. 40 0. 487 16.75 1.0 102 0.0123 17-05-72 2 4.8622 1.8313 89. 04 2.45 0.454 16. 80 1.0132 0.0114 18-05-72 1 4.7744 1.5437 73. 70 2.40 0. 467 17.99 1.0853 0.0147 14-06-72 2 1.3235 1.6583 21.95 2.10 0.402 5. 250 0. 3122 0.0 142 15-36-72 1 1. 400 1 1.6764 23. 47 2.05 0. 424 5. 480 0.3259 0.0139 15-06-72 2 1.3938 1.5374 21*43 2.05 0. 434 5.660 0.3356 0.0157 17-06-72 1 1.2562 1.6264 20.43 2.00 0. 425 5.335 0.3 173 0.0155 21-06-72 1 3. 1378 1.7311 55. 18 2.30 0. 689 10.36 0.5096 0.0111 21-06-72 2 3.2232 1.5770 50. 33 2.50 0.677 11.04 0.6496 0.0128 22-06-72 1 3.0330 1.6366 49. 54 2.35 0. 700 10. 67 0.6278 0.0127 22-06-72 2 2.9516 1.6451 48.56 2.35 0.703 10. 57 0.6219 0.0128 23-06-72 1 2.9666 1.6570 49. 16 2.40 0.737 10.97 0.5455 0.0131 Table XXXVII. Results Fer Continuous Leaching At E i l u t i o n Rate = 0.1038 Hr~ l (Zinc Values Corrected For Chemical Leaching) Date Pulp S p e c i f i c s pH [Fe] [Zn] rZ r z / s Density Surface Area (m2/g) (m2/l) (g/D (g/i) (g/l-hr) (g/hr-a 12-07-72 1 2.0710 1.6780 24.75 2.15 0.349 5.450 0.5668 0.0163 12-07-72 2 2.0836 1.6886 34.77 2. 10 0.368 5.485 0.5704 0.0164 12-07-72 3 2. 1960 1.8622 40.89 2.20 0.357 5. 670 0.5897 0.0144 13-07-72 1 2.1361 1.7202 36.75 2. 10 0. 355 5.480 0.5699 0.0155 13-07-72 2 2.0155 1.6217 32.69 2.10 0.3 47 5.300 0.5512 C.016S 16-07-72 1 2.5272 1.7429 44.05 2.30 0.418 6.830 0.7062 0.016C 17-07-72 1 2.5577 1.7053 43.62 2.25 0.393 6.435 0.6654 0.0153 19-07-72 1 2.5797 2.0163 52*01 2.30 0.463 6. 135 0.6344 0.0122 21-07-72 1 2.9350 2.0046 58.84 2. 20 0. 515 6.850 0.7124 0.0121 22-07-72 1 3.0692 1.9324 59.31 2.20 0.524 7.730 0.8039 0.0136 22-07-72 2 3.0468 2.3306 71.01 2. 20 0.53 2 7.350 0.7644 0.0108 23-07-72 1 3. 1262 2. 1348 66.74 2.25 0.514 7.080 0.7363 0.011C 23-07-72 2 3.0590 2.3881 7 3.05 2.20 0. 495 7.090 0.7374 0.0101 28-07-72 1 4.2662 1.9613 83.71 2.30 0.681 9.780 1.0 152 0.0121 28-07-72 2 4.3786 2.0617 90. 27 2. 30 0.699 9.820 1.0193 0.0113 28-07-72 3 4.4136 1.9829 87.52 2.40 0.662 9.830 1.0204 0.0117 29-07-72 1 4.2328 1. 8522 78.40 2.35 0.715 10.00 1.0380 0.0132 29-07-72 2 4.4098 2.1800 96.13 2.35 0.717 10. 10 1.0484 0.01CS co 190 APPENDIX 7 Calculations For Steady-State Achieved 22-11-71 To 27-11-71 Inclusive Appendix V. Calculations For Steady-State Achieved 191 22-11-71 To 27-11-71 Inclusive 1. D i l u t i o n Rate^ (a) Average Tank Depth With Air Off: (2.54) r(11.25) (5) + 1 1.3125-) 6. (b) Average Tank Volume For Test: (0.63616) (28.601) - 0.020 (c) Average Product Rate Total Volume Collected = 22.8 • 22.5 + 20.4 Total Time Span 20-11-71 29-11-71 1500 1030 Subtract .5 Hr f o r Power Outage Product Rate = 65.70 (D) Average Dil u t i o n Bate Residence Time 211. = 0.31 14 18.175 = 28.601 cm = 18. 175 1 = 65.70 1 211.5 hr 211.C hr 0.3114 1_ hr 0.01713 h r - i 58.37 hr 2. S p e c i f i c Growth Rate: By steady-State assumption, u = D = 0.01713 hr~* t = ln2 = 40.464 hr y 1. Surface Area Concentrations: s = 10 (pd) (SSA) 192 Date pd SSA s % (n>2/g) (mVD 22-11-71 4. 7304 1.5911 75.27 23-11-71 4. 7164 1.5242 75.10 * 24- 11-71 4. 8720 1.6086 75.10 25-11-71 4. 5588 1.6819 76.67 26-11-71 4. 3080 1.5796 68.05 27-11-71 4. 4242 1.5742 69.65 * Not sure which pd goes with which.SSA due to l a b e l l i n g error (23-11,24-11). Therefore average pulp d e n s i t i e s and s p e c i f i c surface areas: Average pd = 4.7942 % s = 75.10 in*/! Average SSA = 1.5664 m2/g 4. B a c t e r i a l Growth Rate: r v = DX Baseline Correction: Net N H 4 = (13.68) (.72) = 10. mg/1 Total Carbon = (13.68) (7. 26) = 99. mg/1 Corrected Values Date r n X c r c (mg/1) (mg/l-hr) (mg/1) (mg/l-hr) 22-11-71 440 7.53 1611 27.59 23-11-71 434 7.43 1681 28.79 24-11-71 458 7.84 1601 27.42 25-11-71 1611 27.60 26-11-71 434 7.43 160 1 27.42 27-11-71 451 7.72 1609 27.56 5- Zinc Production Rate: (Dissolved Zinc) r z = D[Zn] Not Corrected For Chemical Leaching Date [Zn] rZ s r z / s (g/i) (g/l-hr) <m2/l) (g/hr-ro2) 22-11-71 50.25 0.8608 75.27 0.0111 23-11-71 19.40 0.8462 75. 10 0.0113 21-11-71 52. 15 0.8933 75. 10 0.0119 25-11-71 50.95 0.8728 76.67 0.0111 26-11-71 19.15 0.8471 68.05 0.0125 27-11-71 51.45 0.8813 69.65 0.0127 Correction For Chemical Leaching: = (.001333) (73. 31) + (.0206) (136.8) = 8.52 g/1 (.01713) Corrected For Chemical Leaching Date [Zn] rZ s r z / s (g/i) (g/l-hr) (mVl) (g/hr-m2) 22-11-71 11.73 0.7148 75.27 0.0095 23-11-71 10.88 0.7003 75. 10 0.0093 21-11-71 13.63 0.7474 75.10 0.0100 25-11-71 12.13 0.7268 76.67 0.0095 26-11-71 10.93 0.7011 68.05 0.0103 27-11-71 42.93 0.7354 69.65 0.0106 6- Yi e l d Constantsi Date • n mg/1 H H 4 h r 7 mg/1 TC hr. (g/l-hr) 22- 1 23- 1 24- 1 25- 1 26- 1 27- 1 7.709 7.606 8.017 7.606 7. 897 29.29 30.49 29. 12 29.29 29.12 29. 26 0.861 0.846 0.893 0.873 0.847 0.881 Date 22- 1 23- 1 24- 1 25- 1 26- 1 27- 1 n lg Zn > 10.54 10.62 10.50 10.60 10.51 TC lg zn J 38.6 41. 1 36.7 38.0 39. 1 37.5 *c/*n _mg_T£ 1 rag NH+J 4 3.66 3.87 3.50 3.69 3.57 Volume Fraction Liquid In Tank pd • (Volume Fraction Liguid) (Density Of Liquid) = (Density Of Slurry) .'. (Volume Fraction Liquid) = (Density Of Slurry) - pd (Density Of Liguid) Date p p pd Fraction s L Liquid (g/ml) (g/ml) (g/ml) 22-11 1. 162 1. 123 .0473 0.993 23-11 1. 166 1. 127 .0472 0.993 24-11 1. 177 1.131 .0487 0.998 25-11 1. 165 1. 126 .0456 0. 994 26-11 1. 163 1. 127 .0431 0.994 27-11 1. 170 1. 128 . 0442 0.998 195 Note that t h i s c a l c u l a t i o n ignores the weight of j a r o s i t e which i s dissolved in the HCl wash of the pulp density sample. 8- Zinc Balance Over Ta nk: 20-1 1-71 29- 11-71 Input: Average Feed Rate = ((0-7671) (6) +0.7392 + 0.7761*0.7290+0.7463) 10. = .759 g/min Over 211 hr. Feed (21 1) (60) (0.7593) = 9613 g Concentrate Composition Of Concentrate = 55.69? Zn. Therefore Total Height Of Zinc Fed = (0. 5569) (9613.) = 5353 g Zinc Output Soluble Zinc: 22.8 1 3 -49.00 g/1 = 1117 g 22.5 1 2 51.75 g/1 = 116*4 g 20.4 1 3 48.40 g/1 = 987 g Total = 3268 g Residue Analysis: Average Residue Analysis = 55.303 Zn. Residue Production: 65.70 1 3 4.603 pd (average) Total Residue Produced = (65.70) (0.0460) (1000) = 3022 g Total Zinc In Residue = (3022) (0.553) = 1671 g Zinc Zinc Removed In Daily Sampling: 20 ml Centrifuged For Clear Sample And Analysis 10 ml Mixture For Dist. NH^, TC, Density 196 10 ml Mixture For pH 4 ml For Kjeldahl Digestion 50 ml For Pulp Density 94 ml Daily Removed 9 Samples Or 876 ml Containing (49.72) (0. 876) + (0. 553) (46. 0) (0. 876) = 65.8 g Zinc Total Zinc Output = (3268+1671+66) = 5005 g Zinc Loss = (5353-5005)/5353 9. Percent Extraction: Percent Extraction = Soluble Zinc Out = 6.503 (1003) = 66.23 Total Zinc Out (3312) (1003) (5005) 10. Concentration Of Surface Area In Feed: (Feed Of 29-11-71) Average Feed Rate Based On Recovered Zinc = 5005 (.5569) (211) = 42.59 g/hr Product Rate = 0.3114 1/hr , >993S Liquid By Volume. pd = 42.59 = 13.683 (0.3114) (10) SSA Feed 29-11-71 = 3.2012 m2/g Therefore s = (0. 1368) (3.20 12) (1000) = 437.9 m2/l 197 Table XXXVIII. Product Data For Sample Ca l c u l a t i o n . Date Time Product [Zn] Volume (1) (g/i) 20-11 1500 0.0 23-11 1445 22. 8 49.00 23-11 1445 0.0 26-11 1415 22.5 5 1.75 26-11 1415 0.0 29-11 1030 20.4 48. 40 Table XXXIX. Summary Of Daily Tank Data, 22-11-71 27-11-71. Date pH T [Zn] (°C) (g/i) 22-11 2. 12 35.8 1.740 23-11 2.08 35.8 1.715 24-11 2.25 36.0 1.635 25-11 2.09 35.9 1.610 26-11 2.06 35.9 1.785 27-11 2.08 35.5 1 .740 Table XL. Summary Of Tank Data For Sample Calculation Date Depth Solids Slurry Liquid Feed Density Eensit Rate (inches) (g/min) (g/ml) (g/ml) 20-11 11.313 0.7392 1. 159 1.118 21-11 11.250 0.7761 1.161 1. 116 22-11 11. 250 0.7859 1. 162 1. 123 23-11 11.313 0.8024 1. 166 1. 127 24-11 11.250 0.7588 1.177 1. 131 25-11 11.250 0.7634 1. 165 1. 126 26-11 11.250 0.7660 1.163 1. 127 27-11 11.250 0.7259 1. 170 1. 128 28-11 11.250 0.7290 1. 168 1. 114 29-11 11.250 0.7463 1. 167 1. 120 199 APPENDIX VI Calculation Of Fractional Extraction Using Levenspiel's Model 200 Appendix VI. Calculation Of Fractional Extraction Using Levenspiel's Model. A. Calculation From Bahco Size D i s t r i b u t i o n Of Feed An attempt has been made to estimate the f r a c t i o n a l extraction at various d i l u t i o n rates using Levenspiel's shrinking sphere model for the case of chemical reaction c o n t r o l l i n g (17), by assuming that the feed consists of six f r a c t i o n s of monodisperse spheres corresponding to the six Dahco fr a c t i o n s (Figure 30). Using a release rate per unit surface area of 0.01 g/hr-m2, the time for t o t a l reaction for p a r t i c l e s of each s i z e , T , i s calculated from Using a d i l u t i o n rate of 0.0595 hr~» (t equals 16.8 hr), the f r a c t i o n a l extraction for p a r t i c l e s of each s i z e i s given by T pd0/2 rjs (76) X = 3-£- 6 C--)2 + 6 £ ) 3 (1 - e" T / €) (77) This equation has been plotted in Fiqure 31. The mean f r a c t i o n a l extraction for the feed i s calculated by summing the f r a c t i o n a l extraction for each times the f r a c t i o n of the feed which i s that s i z e : then size F i g u r e 30 BAH CO SIZE DISTRIBUTION ANALYSIS OF FEED CONCENTRATE 1 1 1 1 10 15 20 25 30 MAXIMUM SIZE ELUTED FOR EACH CUT, p 35 40 .8 |x .5 z o H O 2 .2 X UJ 1 .1 z o b <,05 < UJ ,02 ,012 F i g u r e 31 FRACTIONAL EXTRACTION Vs DIMENSIONLESS RESIDENCE TIME CALCULATED FROM -O' LEVENSPIEL'S MODEL (17) 0 0 3 ' . 0 0 5 . 0 1 T02 .05 .1 .2 DIMENSIONLESS MEAN RESIDENCE TIME, * / T I I I I I I M .5 I tv) O 203 Table XLI. Calculation Of Fractional Extraction. Size Fraction Of Total t X Overall Contribution (hr) 1.8 0.091 3.5 0.116 7.2 0.308 13.0 0.266 19.0 0.161 27.7 0.058 369 0.0455 718 0.0234 1476 0.01138 2665 0.00630 3895 "0.00431 5679 . 0.00296 0.125 0.0114 0.067 0.0081 0.033 0.0102 0.019 0.0051 0.013 0.0021 0.009 0.0005 0.0374 X measured for t h i s d i l u t i o n rate i s 0.427; X calculated by the above method i s 0.037. Possible reasons for t h i s discrepancy are: The concentrate p a r t i c l e s are of i r r e g u l a r shape and thus may have a greater surface area than spheres of the same diameter. 204 The s i z e s assigned to each f r a c t i o n of material were the representative maximum sizes for that f r a c t i o n . The smallest sized p a r t i c l e s in each f r a c t i o n may be completely eluted out of the equipment during the s i z i n g operation, making i t impossible to c a l c u l a t e a v a l i d average p a r t i c l e size for the f r a c t i o n . Consequently, the only thing one can do with any certainty i s measure the dimensions of the largest p a r t i c l e s one can f i n d in a f r a c t i o n . The material fed to the Bahco siz e r may not have been decaked to the point where each p a r t i c l e was c l a s s i f i e d i n d i v i d u a l l y . Clumps of small p a r t i c l e s could report as larger p a r t i c l e s . F i n a l l y , the B. E. T. surface area may not represent the surface area on which the leaching reactions are occurring. If the 5. E. T. surface area i s too high an estimate, the reaction rate per unit surface used would be too low, and t h i s could account for part of the discrepancy. B. Calculation From Results Of a Continuous Run At One D i l u t i o n Rate If we assume a raonodisperse feed of spheres having the observed reaction rate per unit surface area, we can develop a 205 method to predict the extraction at other d i l u t i o n rates once the extraction for one d i l u t i o n rate i s known. To improve the accuracy of t h i s method, we can express the extractions as f r a c t i o n s of the maximum amount of zinc extractable from the concentrate, not as f r a c t i o n s of the t o t a l amount of zinc in the concentrate. The maximum f r a c t i o n a l extraction obtainable from our sample of zinc concentrate was determined to be 0.886. On t h i s basis, the extraction for the d i l u t i o n rate of 0.0595 h r - 1 i s 0.482. Using Figure 31 we find T = 64.6 hr, and d Q = 0.315 u . Using t h i s value of j and Figure 31, we can get extractions for the three other d i l u t i o n rates used and compare them with the achieved extractions. A plot of measured extractions as a function of predicted extractions i s given in Figure 32. The agreement i s f a i r ; thus, t h i s method should prove hel p f u l in making design decisions when s o l i d substrate concentration i s l i m i t i n g the growth rate. 206 F i g u r e 32 MEASURED FRACTIONAL EXTRACTION Vs FRACTIONAL EXTRACTION PREDICTED BY LEVENSPIEL'S MODEL (17) 0 .2 .4 .6 .8 1.0 FRACTIONAL EXTRACTION PREDICTED 

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