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Microbiological leaching of a zinc sulfide concentrate Torma, Arpad Emil 1970

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MICROBIOLOGICAL LEACHING OF A ZINC SULFIDE CONCENTRATE by ARPAD EMIL TORMA Dipl.  Chem. Eng., Swiss F e d e r a l M.Sc., L a v a l  I n s t i t u t e of Technology, 19  U n i v e r s i t y , 1962  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n the Department of CHEMICAL ENGINEERING We a c c e p t t h i s t h e s i s as conforming t o t h e required  standard  THE UNIVERSITY OF BRITISH COLUMBIA May, 1970  In p r e s e n t i n g  this  thesis  an a d v a n c e d d e g r e e a t the L i b r a r y I  further  for  agree  scholarly  by h i s of  shall  this  written  the U n i v e r s i t y  make  it  freely  t h a t permission  for  It  financial  of  Columbia,  British for  gain  Columbia  the  requirements  reference copying o f  I agree and this  shall  that  not  copying or  for  that  study. thesis  by t h e Head o f my D e p a r t m e n t  is understood  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  of  for extensive  permission.  Department  fulfilment  available  p u r p o s e s may be g r a n t e d  representatives. thesis  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t my  Abstract  •  i  The applicability of microbiological oxidation  for the  recovery of zinc from a high-grade zinc sulfide concentrate has been investigated using a pure strain of Thiobacillus ferrooxidans.  Factors  affecting the bacterial activity and consequently the rate and extent of zinc extraction were studied.  These factors were:  temperature,  pH, nutrient and substrate concentrations, solid particle size and surface area.  The effect of carbon dioxide concentration in the air  supplied to the oxidation  was also studied.  Larger scale experiments  were carried out to simulate more closely possible industrial conditions. The optimum temperature was found to be 35°C, the optimum pH 2.3 . Nutrient levels of 89 mg phosphate P/l and 636 mg ammonia N/1 were sufficient to avoid rate limitation and provide for maximum extraction, respectively. Increasing the particle surface area, the pulp density, or the total surface per unit volume of leach liquor increased the rate of zinc'extraction up to a point beyond which further increases were not effective.  Increasing the carbon dioxide content of the air  had a similar effect. The larger scale experiments gave similar extraction rates to those observed i n shake flasks but the extent of zinc extraction was significantly  higher.  The final concentration of zinc in leach solutions  reached levels currently-employed  in commercial electrowinning procedures.  A form of the generalized logistic equation was shown to be capable of representing the complete extraction curve under a variety of experimental conditions.  ii  This d i s s e r t a t i o n i s dedicated to my w i f e , K a t a l i n , to whom s p e c i a l g r a t i t u d e i s expressed f o r her e n d l e s s standing  and  p a t i e n c e , under-  encouragement.  Acknowled gement s  i i  The author wishes  to express s i n c e r e a p p r e c i a t i o n to  Dr. C. C r a i g Walden and Dr. R i c h a r d M. R. B r a n i o n f o r t h e i r interest,  guidance and encouragement throughout A l s o , the author wishes  this  study.  to thank Dr. Douglas W.  Duncan,  B. C. Research, f o r h i s a d v i c e and s u g g e s t i o n s i n the f i e l d biological  tireless  of m i c r o -  leaching. Thanks are due  to Mr.  N i t r o g e n A d s o r p t i o n Apparatus";  Ron  Orr f o r the use of the "Dynamic  to the B r i t i s h Columbia  Technology f o r the use o f some of t h e i r f o r p r o v i d i n g the use of a l l of t h e i r  Institute  equipment, and to B. C.  f a c i l i t i e s n e c e s s i t a t e d by  of  Research this  investigation. The author i s i n d e b t e d to h i s employer,  the Quebec Department  of N a t u r a l Resources, f o r p r o v i d i n g him w i t h a l e a v e of absence d u r a t i o n of t h i s  for  study.  The work r e p o r t e d i n t h i s d i s s e r t a t i o n B. C. Research F e l l o w s h i p .  was  supported by a  the  Contents Abstract Dedication  i . . . .  i i  Acknowledgements  i i i  Contents L i s t of F i g u r e s  iv .  ix  L i s t of Tables  x  Nomenclature  j _ x i i  I.  INTRODUCTION  1  1. 2.  Nature of the problem Objectives  1 1  II.  MICROBIOLOGICAL BACKGROUND  III. 1. 2. 3. 4. 4.1 4.2 4.3 4.4 4.5 4.6 4.7  LITERATURE REVIEW  P  4 5 5 10  Temperature H Energy source S u r f a c e a c t i v e agents Carbon d i o x i d e Oxygen Nutrients  M i c r o b i o l o g i c a l leach techniques  6.  M i c r o b i o l o g i c a l leaching of mineral  1.  4  D e s c r i p t i o n and p h y s i o l o g y o f T_. f e r r o o x i d a n s O c c u r r e n c e o f T_. f e r r o o x i d a n s M i c r o b i o l o g y of T_. f e r r o o x i d a n s B i o c h e m i c a l a c t i v i t y o f T?. f e r r o o x i d a n s  5.  IV.  3  10 10 10 10 11 11 11 12 sulfides  14  BI0KINETIC MODELING  18  Introduction  2. D i f f i c u l t i e s i n b i o k i n e t i c modeling 3. C l a s s i f i c a t i o n of f e r m e n t a t i o n p r o c e s s e s 4. Development of b a c t e r i a l k i n e t i c s 4.1 O r d e r s o f b i o l o g i c a l (enzymatic) r e a c t i o n s 4.2 S u b s t r a t e l i m i t e d models . . . . . 4.3 Product l i m i t e d models 4.4 S u b s t r a t e and product l i m i t e d models  18 .  . . . .  18 18 19 19 21 23 24  Contents  v Page  5.  Proposed  V.  MATERIALS AND  1.  General  27  2. 3.  Organisms Substrate  27 27  3.1 3.2 3.3 4.  models  25  METHODS  27  Substrate f r a c t i o n a t i o n D e t e r m i n a t i o n of p a r t i c l e D e t e r m i n a t i o n of s p e c i f i c  size surface area  .  28 28 28  . . .  29  . . . . . . . . . .  C u l t u r e techniques  4.1  Shake t e c h n i q u e  29  4.2  Tank l e a c h i n g  30  5.  Chemical  analysis  5.1  Substrate  5.2  Leach s o l u t i o n s  6. VI.  Modeling  and  RESULTS AND  30 .  30 30  curve f i t t i n g  .  . . . . . . . .  DISCUSSION  31  35  1.  E f f e c t s of temperature  35  2. 2.1  E f f e c t s of pH E f f e c t of i n i t i a l  39 41  2.2 3. 4. 5. 6. 7.  E f f e c t of c o n s t a n t pH . . . . . . . . . . . . E f f e c t s of n u t r i e n t c o n c e n t r a t i o n s E f f e c t s of pulp d e n s i t y ( s o l i d ' c o n c e n t r a t i o n ) E f f e c t s of i n i t i a l p a r t i c l e diameter and s p e c i f i c E f f e c t s of carbon d i o x i d e c o n c e n t r a t i o n E f f e c t s of i n i t i a l p a r t i c l e diameter and s u r f a c e a r e a a t 1.0% carbon d i o x i d e L a r g e r s c a l e experiments. . . . . Modelling  8. 9. 9.1 9.2 9.3  10.  pH . surface area  . . . . .  43 50 53 59 69 73 78 83  General D e t e r m i n a t i o n of V and K v a l u e s under normal a i r conditions D e t e r m i n a t i o n of V and 1^ v a l u e s under carbon d i o x i d e e n r i c h e d a i r c o n d i t i o n s . . . . .  83  Mathematical  .96  m  m  86  m  d e s c r i p t i o n of b a c t e r i a l l e a c h c u r v e s  90  Contents  vi Page  VII.  VIII.  SUMMARY AND CONSLUSIONS  REFERENCES  99  . . .  101  APPENDIX 1 Experimental data T a b l e 1A T a b l e IB T a b l e 2A T a b l e 2B T a b l e 2C T a b l e 2D T a b l e 2E T a b l e 2F T a b l e 3A T a b l e 3B Table 4 T a b l e 5A T a b l e 5B T a b l e 5C T a b l e 6A T a b l e 6B T a b l e 6C T a b l e 7A T a b l e 7B T a b l e 7C T a b l e 7D T a b l e 7E T a b l e 7F T a b l e 7G T a b l e 7H T a b l e 8A T a b l e 8B . T a b l e 8C T a b l e 9A T a b l e 9B T a b l e 9C T a b l e 9D T a b l e ' 10A T a b l e 10B T a b l e 11A T a b l e 11B T a b l e 12A T a b l e 12B T a b l e 13A  E f f e c t of temperature Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect Effect  1  of temperature o f i n i t i a l pH of i n i t i a l pH of i n i t i a l pH . o f i n i t i a l pH of i n i t i a l pH of i n i t i a l pH o f c o n s t a n t pH of c o n s t a n t pH of n u t r i e n t c o n c e n t r a t i o n s o f ammonium c o n c e n t r a t i o n o f ammonium c o n c e n t r a t i o n o f ammonium c o n c e n t r a t i o n of phosphate c o n c e n t r a t i o n of phosphate c o n c e n t r a t i o n of phosphate c o n c e n t r a t i o n of p u l p d e n s i t y . o f pulp d e n s i t y o f pulp d e n s i t y of pulp d e n s i t y of pulp d e n s i t y of p u l p d e n s i t y . . .• o f pulp d e n s i t y of pulp d e n s i t y a t i n c r e a s e d a g i t a t i o n of p a r t i c l e s i z e of p a r t i c l e s i z e of p a r t i c l e s i z e of p a r t i c l e size of p a r t i c l e s i z e of p a r t i c l e s i z e . . . of p a r t i c l e s i z e of p u l p d e n s i t y a t 7.92% CO.2' of p u l p d e n s i t y a t 7.92% CO2 of pulp d e n s i t y a t 1.03% CO2 o f pulp d e n s i t y a t 1.03% CO2 of p u l p d e n s i t y a t 0.23% C 0 of p u l p d e n s i t y a t 0.23% CO2 of p u l p d e n s i t y a t 0.13% CO2  .  . .  2  •  2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39  vii  Contents  Page Table 13B Table 14A Table 14B  E f f e c t of pulp density at 0.13% CO2 E f f e c t of s p e c i f i c surface area at 1.0% CO2 E f f e c t of s p e c i f i c surface area at 1.0% CO2  - ... ....  40 41 42  APPENDIX 2 Curve f i t t i n g s Table Table Table Table Table Table Table Table Table Table Table Table  1 2A 2B 3A . 3B 4A 4B  5A 5B 6A 6B 7A .  Table 7B Table 8A Table 8B Table Table Table Table  9A 9B 10A 10B  Program f o r curve f i t t i n g E f f e c t of pulp density (16%) at 0.03% CO2 E f f e c t of pulp density (16%) at 0.03% CO2 E f f e c t of pulp density (16%) at 0.13% CO2 E f f e c t of pulp density (16%) at 0.13% C02 E f f e c t of pulp density (24%) at 0.23% C 0 E f f e c t of pulp density (24%) at 0.23%'CO2 E f f e c t of PUlp density (24%) at 1.03% CO2 E f f e c t of pulp density (24%) at 1.03% C02 E f f e c t of pulp density (24%) at 7.92% CO2 E f f e c t of pulp density (24%) at 7.92% CO2 E f f e c t of s p e c i f i c surface area at 1.0% CO2 • C y c l o s i z e r f r a c t i o n No. 1 E f f e c t of s p e c i f i c surface area at 1.0% CO2 • C y c l o s i z e r f r a c t i o n No. 1 E f f e c t of s p e c i f i c surface area at 1.0% CO2 ... E f f e c t of s p e c i f i c surface area at 1.0% C02 Bahco-sizer f r a c t i o n No. 1 Leaching i n unbaffled tank at 1.0% C02 Leaching i n unbaffled tank at 1.0% CO2 Leaching i n b a f f l e d tank at 1.0% CO2 Leaching i n b a f f l e d tank at 1.0% CO2 2  1 3 4 5 6 7 8  9 10 11 12 13 14 15 16 17 18 19 20  APPENDIX 3 Determination of s p e c i f i c surface area Determination of s p e c i f i c surface area 1. Experimental procedure Figure 1 Schematic diagram of the dynamic n i t r o g e n adsorption apparatus 2. C a l c u l a t i o n of s p e c i f i c surface area Figure 2 T y p i c a l adsorption and desorption curves . . . . Figure 3 C a l i b r a t i o n curves f o r c y c l o s i z e r f r a c t i o n No. 1 Figure 4 B.E.T. p l o t f o r C y c l o s i z e r f r a c t i o n No. 1 . . . Table 3 Summary of B . E . T . - s p e c i f i c surface areas ... Program 1 C a l i b r a t i o n Program 2 Determination of s p e c i f i c surface area ....  1 1 2 3 4 7 8 9 11 14  Contents  viii Page  T a b l e 1A T a b l e IB T a b l e IC T a b l e ID  Table 2  Curve f i t t i n g of c a l i b r a t i o n d a t a a t 25% N2 f o r C y c l o s i z e r f r a c t i o n No. 1 . . . . Curve f i t t i n g of c a l i b r a t i o n d a t a a t 15% N2 f o r C y c l o s i z e r f r a c t i o n No. 1 Curve f i t t i n g of c a l i b r a t i o n d a t a a t 5% N2 f o r C y c l o s i z e r f r a c t i o n No. 1 Output of d a t a d e r i v e d on C y c l o s i z e r f r a c t i o n No. 1 a t gas m i x t u r e ( c o n t a i n e d 5% 15% and 25% n i t r o g e n ) D e t e r m i n a t i o n of s p e c i f i c s u r f a c e a r e a of C y c l o s i z e r f r a c t i o n No. 1 .  16 17 18  19 22  List  ix  Figure 1  Typical  Figure 2  E f f e c t of temperature  Figure 3  E f f e c t of temperature on the m i c r o b i o l o g i c a l zinc  zinc  of F i g u r e s  s u l f i d e l e a c h curve •  extraction rate  36  37  Figure 4  E f f e c t of i n i t i a l  pH  Figure 5  E f f e c t of i n i t i a l  pH  Figure 6  E f f e c t of c o n s t a n t  Fiture  E f f e c t of pH on l a g time  7  32  . . . . . . . . on z i n c  pH  on z i n c  42  extraction  47  extraction  47' 48  Figure 8  E f f e c t of ammonium c o n c e n t r a t i o n  Figure  E f f e c t of phosphate c o n c e n t r a t i o n  54  F i g u r e 10  E f f e c t of pulp d e n s i t y  56  F i g u r e 11  Cyclosizer fractions  F i g u r e 12  Bahco-sizer  F i g u r e 13  E f f e c t of p a r t i c l e s i z e  9  '.  . . . .  52  62  fractions  63 (under normal a e r a t i o n  conditions  66  F i g u r e 14  E f f e c t of s p e c i f i c s u r f a c e a r e a  67  F i g u r e 15  E f f e c t of t o t a l s u r f a c e a r e a of s o l i d  68  F i g u r e 16  E f f e c t of pulp d e n s i t y a t d i f f e r e n t carbon dioxide p a r t i a l pressures E f f e c t of carbon d i o x i d e p a r t i a l p r e s s u r e s at d i f f e r e n t pulp d e n s i t i e s  72  F i g u r e 17 F i g u r e 18  E f f e c t of p a r t i c l e s i z e at 1.0%  74  carbon d i o x i d e  p a r t i a l pressure  77  F i g u r e 19  E f f e c t of s p e c i f i c s u r f a c e a r e a at 1.0%.carbon d i o x i d e  79  F i g u r e 20  E f f e c t of t o t a l s u r f a c e a r e a of  F i g u r e 21  f r a c t i o n s at 1.0% CO2 E f f e c t of pulp d e n s i t y Lineweaver-Burk p l o t  F i g u r e 22  Effect  size • • • • . . . . .  of s p e c i f i c s u r f a c e area Lineweaver-burk p l o t  .  8  0  88 89  List  of F i g u r e s  x Page  F i g u r e 23  E f f e c t of t o t a l s u r f a c e a r e a Lineweaver-Burk p l o t  . .  91  F i g u r e 24  E f f e c t of pulp d e n s i t y a t i n c r e a s e d carbon d i o x i d e p a r t i a l p r e s s u r e s Lineweaver-Burk p l o t . .  93  E f f e c t of pulp d e n s i t y at 0.13% Lineweaver-Burk p l o t  94  F i g u r e 25  F i g u r e 26  F i g u r e 27  CO2  E f f e c t of s p e c i f i c s u r f a c e a r e a a t 1.0% Lineweaver-Burk p l o t E f f e c t of t o t a l s u r f a c e a r e a a t 1.0% Lineweaver-Burk p l o t  C0  CO2 95 2  97  List  of T a b l e s  xi Page  Table 1  L i q u i d media f o r T_. f e r r o o x i d a n s  6  Table 2  Temperature c o e f f i c i e n t s and a c t i v a t i o n e n e r g i e s f o r z i n c e x t r a c t i o n from the z i n c s u l f i d e c o n c e n t r a t e by T_. f e r r o o x i d a n s  40  Table 3  E f f e c t of i n i t i a l pH  45  Table 4  E f f e c t s of c o n s t a n t pH  49  Table 5  E f f e c t of p u l p d e n s i t y and  Table 6  E f f e c t of s u b s i e v e f r a c t i o n s  Table 7  E f f e c t of p u l p d e n s i t y a t d i f f e r e n t carbon d i o x i d e  zinc concentration  p a r t i a l pressures  . . . .  58 61  . .  71  Table 8  E f f e c t of s u b s i e v e f r a c t i o n s  76  Table 9  Alterations  84  i n substrate during leaching  Nomenclature a ,  a ,  =  polynomial  constants  (equation  22)  a, b, c, d  =  polynomial  constants  (equation  16)  a, b  =  s l o p e and  d  =  p a r t i c l e diameter  B  =  constant  =  initial  =  enzyme c o n c e n t r a t i o n ,  c  E  s  ...,  a5  xii  D  E ES E  (equation  (equation  (equation  18)  29)  14)  enzyme c o n c e n t r a t i o n ,  g/1  g/1  enzyme - s u b s t r a t e complex c o n c e n t r a t i o n ,  =  =  r  intercept  g/1  energy r e q u i r e d f o r carbon d i o x i d e f i x a t i o n , calories/g  =  energy produced by s u b s t r a t e o x i d a t i o n , c a l o r i e s  FEE  =  f r e e energy e f f i c i e n c y ,  fl  =  f u n c t i o n depends on c e l l c o n c e n t r a t i o n ( e q u a t i o n  *2  =  f u n c t i o n depends on s u b s t r a t e consumption  P  /g  % 9)  (equation  10) fg  =  f u n c t i o n depends on product  G  =  g l u c o s e c o n c e n t r a t i o n ( e q u a t i o n 20),  =  a c t i v a t i o n energy, Kcal/mole  =  p r o p o r t i o n a l i t y constant  =  r a t e constants  Kj_, K 2  =  p r o p o r t i o n a l i t y constants  KJJJ  =  Michaelis-Menten  N  =  neomycin c o n c e n t r a t i o n ( e q u a t i o n 20),  P  =  product  PD  =  pulp d e n s i t y , g x 100/ml  P  =  maximum v a l u e of product  ,A H  a  K ki,  m  k2j k-j  formation  (equation  ( e q u a t i o n 12,  (equation g/1  29)  19 and  20)  (equation  15)  constant  concentration,  g/1  g/1  concentration,  g/1  11)  Nomenclature  xiii  Q  =  temperature  R  =  gas c o n s t a n t ,  S, S^,  =  substrate concentrations,  coefficient calories/°K mole g/1  2, SSA  =  specxfxc  s u r f a c e a r e a , m /g  t  =  time, h r  T^,  =  absolute  TSA  =  t o t a l s u r f a c e a r e a per u n i t volume of l i q u i d medium,  V  =  m^/ml s p e c i f i c growth r a t e , h r ^ or z i n c e x t r a c t i o n r a t e ,  temperatures, °K  mg/1 h r V  m  X  =  maximum v a l u e o f above  =  cell  (mass or number) c o n c e n t r a t i o n Appendix 3  c  =  P  =  constant p a r t i a l pressure mixture,  Pd  =  o f n i t r o g e n i n the He - ^  gas  mm Hg  s a t u r a t i o n pressure  of n i t r o g e n a t temperature  of  l i q u i d n i t r o g e n , mm Hg Vads  =  volume of n i t r o g e n adsorbed on sample. (STP), p i  Vm  =  volume o f adsorbed n i t r o g e n due t o monolayer  cover-  age, y l Vmspc  =  volume o f adsorbed n i t r o g e n due t o s p e c i f i c monolayer coverage, y l / g  I.  INTRODUCTION  1.  1.  Nature of the problem The discovery of the obligate chemoautotrophic bacterium,  Thiobacillus  ferrooxidans, opened up an area of research which has had  and w i l l continue to have considerable economic significance. organism  This micro-  can tolerate exceptionally high concentrations of most  cations and is involved in the leaching of sulfide ores and wastes. The possibility of using this microorganism in hydrometallurgical metal extraction processes was recognized early by a l l investigators. It represents a potential solution to the problem faced in many countries where continuing depletion of high-grade ore deposits has created a need to develop effective methods for recovering metal values from lowgrade jsulfide ores. The microbiological leaching process involves complex interactions between the microorganism, substrate and the trace nutrient concentrations, which are not yet completely understood.  Altogether, a more economic  use of this leaching process requires a better understanding  of the various  factors influencing bacterial grox^th and the microbiological metal dissolution processes. 2.  Objectives The present work investigates the microbiological extraction  of zinc from a high-grade zinc sulfide concentrate, using a pure strain of T^. ferrooxidans.  Conditions such as temperature, pH, pulp density,  nutrient concentrations, and specific surface area of solid substrate are studied in terms of their effects on zinc extraction rate and, in some instances, on the final zinc concentration in solution. Where appropriate, optimum conditions for leaching are specified.  In addition,  factors limiting  the r a t e of z i n c e x t r a c t i o n are d e l i n e a t e d  those c o n d i t i o n s  under w h i c h they become l i m i t i n g .  i s made to d e s c r i b e  the  Further,  as w e l l an  form of an e q u a t i o n s u i t a b l e f o r c u r v e  the d a t a o b t a i n e d i n these m i c r o b i o l o g i c a l l e a c h i n g  studies.  as  effort fitting  II.  3.  MICROBIOLOGICAL BACKGROUND  Most b a c t e r i a l s p e c i e s u t i l i z e complex o r g a n i c energy.  Such organisms are c l a s s i f i e d  species, called hydrates,  autotrophic  f a t s and  nitrogen.  autotrophic  (1  2)  Winogradsky  '  i n 1887  which were a b l e  b a c t e r i a , are a b l e  Only a  to s y n t h e s i z e  their  and  1888.  He  to grow by u t i l i z i n g  carbo-  i n o r g a n i c s o u r c e s of  concluded  ferrous iron.  that b a c t e r i a e x i s t  The  The  b a c t e r i a may  be d i s t i n g u i s h e d  o b l i g a t e forms o b t a i n  from o x i d a t i o n of i n o r g a n i c compounds, whereas the u t i l i z e organic  by  the energy l i b e r a t e d by o x i d a t i o n of  as o b l i g a t e or f a c u l t a t i v e a u t o t r o p h s .  t i v e forms a l s o may  few  c a p a b i l i t i e s of b a c t e r i a were e s t a b l i s h e d  reduced forms of s u l f u r and  energy s o l e l y  as the h e t e r o t r o p h s .  p r o t e i n s from carbon d i o x i d e and  The  compounds f o r  their faculta-  compounds, when i n o r g a n i c compounds  are not a v a i l a b l e . T. leaching,has  f e r r o o x i d a n s , which i s r e s p o n s i b l e f o r m i c r o b i o l o g i c a l been p l a c e d  i n the f i f t h  genus, T h i o b a c i l l u s , of the  family  (3) Thiobacteriaceae . T h i s organism p o s s e s s e s the f o l l o w i n g m o r p h o l o g i , . ' • „. (3, 4, 5) cal  characteristics  cell:  s h o r t rod;  0.5  diplobacilli; colony:  : by  1.5  microns; m o t i l e ;  granular  occur  s i n g l y or  Gram s t a i n - n e g a t i v e ,  (form when c u l t u r e d on s o l i d flat;  cells  s u r f a c e ; opaque.  media) minute; i r r e g u l a r -  v  edge;  as  III.  1.  LITERATURE REVIEW  4.  D e s c r i p t i o n and p h y s i o l o g y  of T_. f e r r o o x i d a n s  J_. f e r r o o x i d a n s was d i s c o v e r e d a c i d , i r o n - c o n t a i n i n g drainage described  by Colmer and H i n k l e  i n the  water of some bituminous c o a l mines, and  l a t e r by Colmer et_ a l ^ ^ and Temple and Colmer  as an  o b l i g a t e , chemoautotrophic, a c i d o p h i l i c , i r o n o x i d i z i n g b a c t e r i u m . o b t a i n s carbon and  ( i n form o f carbon d i o x i d e ) and oxygen from the atmosphere  derives i t s metabolic  sulfur  It  energy from the o x i d a t i o n of reduced i r o n and  compounds. T h i s organism i s m o r p h o l o g i c a l l y  thiooxidans.  similar  to T h i o b a c i l l u s  The fundamental d i f f e r e n c e between the two s p e c i e s i s  generally recognized  t o be the i n a b i l i t y  of T_. t h i o o x i d a n s  to o x i d i z e  f e r r o u s i r o n and i n s o l u b l e s u l f i d e s ^ ' ~*' ^ . Leathen and B r a l e y ^ ^  and Leathen et_ a l / ^ s t u d i e d an organism  which o x i d i z e d f e r r o u s i r o n but n o t e l e m e n t a l Because of i t s i n a b i l i t y was  considered  ferrooxidans.  s u l f u r or t h i o s u l f a t e .  t o u t i l i z e these reduced s u l f u r s u b s t r a t e s , i t  t o be a new genus and a s s i g n e d  the name F e r r o b a c i l l u s  S i m i l a r l y , K i n s e l ^ ^ assigned  the name F e r r o b a c i l l u s  sulfooxidans  t o an organism she i s o l a t e d , which u t i l i z e d  and  s u l f u r but not t h i o s u l f a t e .  elemental  ferrous  iron  Subsequent i n v e s t i g a t i o n s by Unz and Lundgren^"'"^ , Ivanov and / "I  /1 O \  Lyalikova  *3 "\  , Beck and Shaf i a  t h a t these  organisms  (1 and Hutchinson e_t jal "  (T. f e r r o o x i d a n s ,  V  F_. f e r r o o x i d a n s  were i d e n t i c a l and should be c a l l e d T_. f e r r o o x i d a n s . were capable  of o x i d i z i n g e l e m e n t a l  / \  indicated  and F_. s u l f ooxidans) A l l these  organisms  s u l f u r and t h i o s u l f a t e i n a d d i t i o n to  (14) ferrous iron continue  .  I n s p i t e of these  conclusive data,  t o use the name F. f e r r o o x i d a n s .  some authors  2.  Occurrence  of T. f e r r o o x i d a n s  5.  The organism, T_. f e r r o o x i d a n s , i s v i r t u a l l y u b i q u i t o u s i n nature.  Since i t s o r i g i n a l i s o l a t i o n ^ ' " ' ' ^ , i t has been i s o l a t e d i n  . . (15) _ , (16,17) . (18) „ ,(19) _ . ,(20) Australia , Canada , Congo , Denmark , England , Germany  ( 2 1 )  , Japan  ( 2 2 )  c ."(16) o j (21) Spam , Sweden N  3.  , Mexico  ( 2 3 )  , Scotland  . . (7,8,10,25-31) U.S.A.  ( 2 1 )  , South  Africa  ( 2 4 )  ,  , . ^ _ _ _ (32-36) and i n the U.S.S.R.  TT  7T  M i c r o b i o l o g y of T. f e r r o o x i d a n s . The a c t i v i t y of t h e s e b a c t e r i a i s i n f l u e n c e d by the n u t r i e n t s  a v a i l a b l e f o r i t s growth and  reproduction.  The  l i q u i d media most f r e q u e n t l y  (9) used f o r T_. f e r r o o x i d a n s are those of Leathen  et a l  and  Silverman  and  (37) Lundgren  support  .  These media a r e compared i n T a b l e 1. (37) Silverman and Lundgren d e s i g n a t e d t h e i r medium 9K. I t w i l l 8 8 6 2 x 10 to 4 x 10 c e l l s per ml compared to 7 x 10 c e l l s per ml  (9) f o r the medium of Leathen  et_ al_  .  During b a c t e r i a l growth, the f e r r o u s i r o n i s o x i d i z e d to f e r r i c iron  ( e q u a t i o n 1 ) , which has been c o n s i d e r e d to h y d r o l y z e to (37) h y d r o x i d e and s u l f u r i c a c i d ( e q u a t i o n 2)  4 FeS0  +  4  2Fe (S0 ) 2  4  2H S0 2  +  3  +  4  0  2  v~-  12H 0 2  =  2Fe (S0 ) 2  4Fe(0H)  4  3  +  3  +  ferric  2H 0  (1)  2  6H S0 2  (2)  4  R e a c t i o n 1 i s a m e t a b o l i c r e a c t i o n of the b a c t e r i a .  Reaction 2 i s a  c h e m i c a l r e a c t i o n , which r e s u l t s i n an i n c r e a s e i n the a c i d c o n t e n t  of  the medium. Leathen  et a l  s u l f a t e i s incomplete  have i n d i c a t e d t h a t the h y d r o l y s i s of  i n a c i d medium and b a s i c f e r r i c  the r e l a t i v e amounts of i r o n , h y d r o x y l and  ferric  s u l f a t e s are produced;  s u l f a t e w i l l depend upon the  6.  Table 1 L i q u i d Media f o r T. f e r r o o x i d a n s  (9) Components  Leathen e t a l  S i l v e r m a n and Lundgren in g  in g Basal  salts:  (NH ) S0 4  2  4  KC1 K HP0 2  MgS0  4  x 7H 0  4  2  Ca(N0 ) 3  Dist.  2  H 0 2  ION H S0, 2 4 o  Energy  0.05  3.00  0.05  0.10  0.05  0.50  0.50  0.50  0.01  0.01  1000 ml  to 700 ml  pH = 3.5  1.00 ml  source:  FeSO. x 7H„0 4 2  10 ml o f a 10% W/V s o l u t i o n  Where W/V  =  300 ml o f a 14.74% W/V s o l u t i o n  weight per volume  d i l u t i o n and the a c i d i t y d u r i n g h y d r o l y s i s .  They r e p r e s e n t e d the h y d r o l y -  s i s by the r e a c t i o n o f e q u a t i o n 3.  Fe (S0 ) 2  4  The  +  3  2H 0  \ —  2  j>.  2Fe(0H)S0  4  +  H S0 2  (3)  4  i r o n c h e m i s t r y i n v o l v e d i s c e r t a i n l y more complex than i s i n d i c a t e d  by the f o r e g o i n g e q u a t i o n s .  Observations  on m i c r o b i o l o g i c a l c h a l c o p y r i t e  (39) leaching  i n d i c a t e the f o l l o w i n g o v e r a l l r e a c t i o n f o r the f o r m a t i o n  of i n s o l u b l e f e r r i c  6CuFeS_  +  sulfate:  25 1/2 0„  I  +  9H 0 I  2HFe (S0 ) (0H) 3  A  >  o  I 2  6  +  2H S0 2  6CuS0, 4  + (4)  4  R e a c t i o n 4 r e s u l t s i n a r e d u c t i o n o f pH and of f e r r i c concentrations.  The a c i d i t y o f the s o l u t i o n i s s t a b i l i z e d near  a c c o r d i n g t o the e q u i l i b r i u m  2HFe (S0 ) (0H) 3  The  4  2  6  and s u l f a t e i o n  + 5H S0 2  4  pH 2,  equation:  v—-  3Fe^(S0 ) 4  +  12H 0  (5)  2  e a r l y l i t e r a t u r e c o n c e r n i n g the c a p a b i l i t y o f t h i s microorganism  u t i l i z e d i f f e r e n t energy  sources i s somewhat c o n f u s e d .  to  The a b i l i t y of  X_. f e r r o o x i d a n s t o o x i d i z e f e r r o u s i r o n has been demonstrated by numerous authors5,14,37)  s i m i l a r agreement has not been o b t a i n e d c o n c e r n i n g the  u t i l i z a t i o n of d i f f e r e n t s u l f u r compounds as s u b s t r a t e s , because some a u t h o r s have f a i l e d 9)  t o demonstrate the o x i d a t i o n of e l e m e n t a l  sulfur^'"*'^'  . (8,9) or t h i o s u l f a t e ' .A p o s s i b l e e x p l a n a t i o n of t h i s l a c k of s u c c e s s by (14)  c e r t a i n authors i s g i v e n by H u t c h i n s o n importance  et_ a l  , who p o i n t e d out the  o f i n i t i a t i n g growth a t the c o r r e c t ph.  8. However, the m a j o r i t y ferrooxidans A  if  i s able u  -i,-  s u l f u r and  of i n v e s t i g a t o r s have shown t h a t T_.  to d e r i v e i t s energy from the o x i d a t i o n of -  thiosulfate  (3,10,11,14,16,21,40,41)  .  o x i d a t i o n of e l e m e n t a l s u l f u r ranges from 1 . 7 5 +u-  i  ,  w  A  /  t h i o s u l f a t e between 4 and f  These pH  c  pH  to 5  _  ,  optxmum f o r  '  and  the  for  .(11,14,42,43)  5.5  optima are h i g h e r  a c t i v i t y on f e r r o u s s u l f a t e media. c e l l u l a r pH  „  The  elemental  than those found f o r b a c t e r i a l  I t should  be noted t h a t the i n t e r n a l  of these organisms n o r m a l l y i s h i g h e r  than t h a t of  their  (44)  e x t e r n a l environment  .  Recently,  workers a t B. C. (42  have p u b l i s h e d  ferrooxidans.  o x i d i z e s o l u b l e and sulfide,  45-48)  a s e r i e s of communications  u t i l i z a t i o n by T.  Research  '  concerning  substrate  They have found t h a t these organisms  i n s o l u b l e f e r r o u s i r o n , s u l f u r , i n s o l u b l e and  t h i o s u l f a t e , t r i t h i o n a t e and  tetrathionate.  The  soluble  oxidation  rate  (41)  of s u l f u r was  always slower than the r a t e of i r o n o x i d a t i o n  A l t h o u g h the l i t e r a t u r e c o n c e r n i n g  the energy t r a n s f e r  mechanisms of t h i o b a c i l l i i s growing r a p i d l y , o n l y l i m i t e d i n f o r m a t i o n a v a i l a b l e concerning  e l e c t r o n t r a n s f e r from f e r r o u s i r o n and  compounds to m o l e c u l a r oxygen. and  p r o t e i n s present  published Peck^"^  Various  i n the organisms  (44  sulfur  t h e o r i e s e x i s t i n v o l v i n g enzymes '  49-63)  .  a review of the metabolism of i n o r g a n i c one  is  on energy c o u p l i n g mechanisms.  Trudinger  (64)  has  s u l f u r compounds  and  N o n e t h e l e s s , no o v e r a l l  u n d e r s t a n d i n g of the energy t r a n s f e r r e a c t i o n s i n T_. f e r r o o x i d a n s  has  y e t been a c h i e v e d . Biological cells transfer  tend to l o s e energy at a l l s i t e s of  , a measure of t h e i r e f f i c i e n c y  i n r e t a i n i n g the  a v a i l a b l e to them i s the f r e e energy e f f i c i e n c y dioxide  f i x a t i o n by T_. f e r r o o x i d a n s  may  be  (FEE).  evaluated  The  using  energy  energy F E E of  carbon  a relationship  proposed by Baas-Becking and  Parks  :  E  =  (%)  FEE  Y~  100  (6)  P  where E  r  Ep  Using  =  energy used f o r carbon d i o x i d e  =  energy produced by s u b s t r a t e o x i d a t i o n .  f e r r o u s i r o n as s u b s t r a t e , Temple and  fixation;  Colmerfound  t h a t the f r e e energy e f f i c i e n c y of carbon d i o x i d e f i x a t i o n f o r _T. (  f e r r o o x i d a n s was decreases with  about 3.2%.  the age  Lyalikova  of the c u l t u r e .  o b t a i n e d w i t h a two-day o l d c u l t u r e . ranging of 20.5%  from 13.8  to 28.6%  f.Q\  observed t h a t t h i s An  average v a l u e of 30%  Silverman^^  reported  f o r carbon d i o x i d e  pounds  (209, 210)  s o l u t i o n may wetting  ,_  ,  by a u t o t r o p h i c organisms from  r e l e a s e s amino a c i d s and  .,  ^ (70)  and _T. f e r r o o x i d a n s p y r u v a t e  a c t as c h e l a t i n g agents and  .  extent  phosphatidyl  . .  ...  com-  Amino a c i d s i n  phosphatidyl  compounds as  a  agent, p o s s i b l y a s e l e c t i v e advantage f o r these microorganisms  i n a t t a c h i n g themselves to s o l i d Under completely  surfaces.  anaerobic  c o n d i t i o n s , Pugh and  a b l e to demonstrate carbon d i o x i d e f i x a t i o n t h a t was o x i d a t i o n of a s p e c i f i c s u b s t r a t e . jC. f e r r o o x i d a n s  Umbreit^"^  associated  For example, these a u t h o r s  (F. sulfooxidans)showed  when f e r r o u s i r o n was support  efficiency  fixation.  carbon d i o x i d e are s e c r e t e d i n t o the medium to a s i g n i f i c a n t For example, T;. t h i o o x i d a n s  was  values  w i t h an average v a l u e of f r e e energy  C e r t a i n compounds s y n t h e s i z e d  '  efficiency  o x i d i z e d to f e r r i c  t h a t carbon d i o x i d e was iron.  Further,  these  were  with using fixed authors  the concept t h a t an e l e c t r o n t r a n s p o r t system i s i n t e r p o s e d between  10. the i n o r g a n i c s u b s t r a t e o x i d i z e d and mechanism 4.  was  given  Biochemical  the a c t u a l oxygen u t i l i z e d .  to e x p l a i n t h i s phenomenon.  a c t i v i t y of T..  ferrooxidans  B a c t e r i a are i n f l u e n c e d markedly.by t h e i r Factors  No  such as temperature, pH,  energy s o u r c e ,  environment.  pulp d e n s i t y ,  s i z e , oxygen, carbon d i o x i d e , n u t r i e n t c o n c e n t r a t i o n s  and  particle  agitation  be expected e i t h e r to s t i m u l a t e or suppress the m i c r o b i a l a c t i v i t y T.  of  ferrooxidans• For l e a c h i n g of m i n e r a l  f o l l o w i n g c o n d i t i o n s are r e p o r t e d 4.1  s u l f i d e s by T_. f e r r o o x i d a n s , i n the  the  literature:  Temperature The  optimum temperature has  b a c t e r i a are i n h i b i t e d f o r growth has  4.2  been found to be  35°C^^'^^',  the  40°C^^'^'^^; no minimum temperature l i m i t  at  been e s t a b l i s h e d .  pH The  f o l l o w i n g pH-values were r e p o r t e d  growth of T_. f e r r o o x i d a n s :  2 and  Silverman  The  it  may  i s at  and  Ehrlich^^.  to be  4 by R a z z e l l ^ " ^ and  optimum pH  the l i m i t s f o r 1 and  i s below 3 ^ ^ ;  5 by  more e x a c t l y  2.5^^'^'^^ . Above pH 6.0 b a c t e r i a l a c t i o n i s almost  com-  (72) p l e t e l y i n h i b i t e d and 4.3  above pH  9.0,  the b a c t e r i a are  destroyed  Energy source Substrate  o x i d a t i o n r a t e s are s a i d to be much h i g h e r  on  f e r r o u s i r o n than on i n o r g a n i c s u l f i d e s u b s t r a t e s .  T h i s organism o f t e n CJQ) r e q u i r e s a p e r i o d of a d a p t a t i o n to the new energy source . Sulfide m i n e r a l s are more r a p i d l y leached as f i n e p a r t i c l e s than as c o a r s e  (7,26,46,74,77) ones 4.4  ; Surface  ' no  .  .  optimum p a r t i c l e s i z e d a t a have been  ^  A  reported.  a c t i v e agents  Some s u r f a c t a n t s e x e r t a b e n e f i c i a l e f f e c t on m e t a l e x t r a c t i o n  11. 79 81) —  rates  and  reduce the l a g time  (82)  ; but  the p r e s e n c e of  surfactants  ( 83) diminishes  the l e v e l of f i n a l m e t a l e x t r a c t i o n  , possibly  through  l i m i t a t i o n of oxygen t r a n s f e r ^ ^ . 4.5  Carbon  dioxide  Normal a i r c o n c e n t r a t i o n s  are adequate  ; up  to 2% carbon  dioxide  (13) concentration 4.6  i n the gas  phase may  be  desirable  Oxygen Oxygen i s r e q u i r e d  as s u l f i d e , r e q u i r e s sulfate).  The  (46 process  two  supply  i n l a r g e q u a n t i t i e s (every  pounds of oxygen f o r complete c o n v e r s i o n  of t h i s oxygen i s the key  '  .  The  This necessitates  leaching  low  s o l u b i l i t y of oxygen and  carbon d i o x i d e  t r a n s f e r are  in  the  necessary.  the use.of some k i n d of a g i t a t i o n .  Nutrients The  n u t r i e n t r e q u i r e m e n t s of T_. f e r r o o x i d a n s  chemosynthetic a u t o t r o p h . inorganic and  problem i n the  to  78)  l e a c h i n g medium means t h a t h i g h r a t e s of gas  4.7  pound of s u l f u r  E a r l y r e p o r t s i n d i c a t e d a requirement f o r such  compounds as carbon d i o x i d e  dipotassium  f e r r o u s i r o n and  are normal f o r a  ( f o r c e l l growth), ammonium s u l f a t e  hydrogen phosphate (as n i t r o g e n  and  phosphate  s u l f u r compounds (as energy s o u r c e s ) ,  and  sources),  magnesium  (74) s u l f a t e , potassium c h l o r i d e and  However, experiments c a r r i e d out t h a t T_. f e r r o o x i d a n s  has  no  c a l c i u m n i t r a t e (as growth f a c t o r s )  (39)  at B.  C. Research  requirement f o r magnesium, c a l c i u m  potassium i o n s beyond those l e v e l s c o n t a i n e d sulfate,  dipotassium Of  have demonstrated and  i n reagent grade ammonium  hydrogen phosphate and  sulfide-minerals.  these f a c t o r s i n f l u e n c i n g m i c r o b i o l o g i c a l l e a c h i n g ,  important p r o b a b l y are (metabolism) and  temperature and  pH.  growth of the b a c t e r i a . .  o x i d a t i o n of s u l f i d e s by  the most  These d i r e c t l y a f f e c t a c t i v i t y Another requirement f o r  the b a c t e r i a i s the a v a i l a b i l i t y  of the  the substrate.  12. The  most i d e a l c o n d i t i o n e x i s t s when the s u b s t r a t e  i s s o l u b l e such as  are  ferrous  the s u l f i d e  iron salts.  For i n s o l u b l e s u b s t r a t e s ,  must have an adequate amount of exposed s u r f a c e  minerals  area.  A l t h o u g h the s u r f a c e phenomena have been observed by many ...  (7,26,46,77,78)  authors  .  ..  „.  ,  ,  ,  ,,  , no i n v e s t i g a t i o n s have been undertaken t o  e s t a b l i s h the r e l a t i o n s h i p between the s p e c i f i c s u r f a c e  area  and b a c t e r i a l  growth and the e f f e c t on the m e t a l e x t r a c t i o n r a t e . (39) However, experiments on m i c r o b i o l o g i c a l c h a l c o p y r i t e  leaching  have i n d i c a t e d t h a t , below a c e r t a i n p a r t i c l e s i z e , no b e n e f i t i n e x t r a c t i o n r a t e i s achieved is 5.  and, i n t h i s  instance,  only  the t o t a l  enhanced. M i c r o b i o l o g i c a l leach techniques (79) Prior  leaching described  to 1964  , laboratory  s t u d i e s on the m i c r o b i o l o g i c a l  of s u l f i d e o r e s were c a r r i e d out w i t h a i r l i f t  percolators,  by B r y n e r e t a l ^ ^ , the Warburg r e s p i r o m e t e r o r  stationary leach b o t t l e s ^ ^ .  The oxygen supply  with  i s poor i n both the  p e r c o l a t o r and the s t a t i o n a r y l e a c h b o t t l e t e c h n i q u e s ; and  extraction  whereas t h e s i z e  the p r i n c i p l e of the Warburg apparatus render i t u n s u i t a b l e f o r  practical  leaching. Using p e r c o l a t o r s  (25) Bryner e t a l  f o r the b a c t e r i a l l e a c h i n g o f c h a l c o p y r i t e ,  found 2.7% o f copper e x t r a c t e d  from one sample and (29) 6.1% of copper from another sample i n 70 days; Malouf and P r a t e r r e p o r t e d about 40% a f t e r 70 days and 60% e x t r a c t i o n a f t e r 470 days. (79) Duncan, T r u s s e l l and Walden d e s c r i b e d a p r a c t i c a l method, g y r a t o r y s h a k i n g , which produces r a p i d a e r a t i o n and an a c c e l e r a t e d r a t e (82) of l e a c h i n g . reported  Using the s h a k e - f l a s k  t h a t T_. f e r r o o x i d a n s  t e c h n i q u e , Duncan and T r u s s e l l  leached  72% of the copper from museum grade  c h a l c o p y r i t e i n 12 days and 100% i n 26 days.  T h i s comparison shows the  s u p e r i o r i t y of the s h a k i n g t e c h n i q u e .  13.  However, b e s i d e s the g y r a t o r y shaking many o t h e r types of mixers experiments, shakers.  a v a i l a b l e f o r use i n l a b o r a t o r y l e a c h i n g  e.g., a i r s p a r g e r s , magnetic  for  s t i r r e r s and r e c i p r o c a t i n g  The e f f e c t s of these t e c h n i q u e s on m i c r o b i o l o g i c a l  e x t r a c t i o n a r e compared by Duncan e t a l stirring  there are  .  They found  that  copper magnetic  and r e c i p r o c a t i n g shaking gave r e s u l t s comparable w i t h  those  gyratory shaking. (78  L a b o r a t o r y column l e a c h i n g t e c h n i q u e s commercial  procedures  f o r heap o r dump l e a c h i n g .  85^  '  may s i m u l a t e the  A sample o f o r e i s  p l a c e d i n a column and the l i q u i d medium i s c i r c u l a t e d t i n u o u s l y by an a i r l i f t .  One c o n c u r r e n t e f f e c t of t h i s t e c h n i q u e i s to  p r o v i d e the column w i t h oxygen and CO2 because of the h i g h oxygen requirement be a l i m i t i n g  through i t con-  s a t u r a t e d medium.  Although,  of the p r o c e s s , oxygen s t i l l  may  factor.  Another  l e a c h t e c h n i q u e which may be used  for laboratory  m i c r o b i o l o g i c a l m e t a l e x t r a c t i o n i s the tank l e a c h i n g t e c h n i q u e .  This  method i s p a r t i c u l a r l y u s e f u l f o r e v a l u a t i n g high-grade m a t e r i a l s and p r o v i d e s f o r easy c o n t r o l o f a l l t h e important parameters t h i s type o f l e a c h i n g . l e a c h i n g experiments bioleaching  influencing  The i n t e r p r e t a t i o n of the r e s u l t s of tank  a l s o may c o n t r i b u t e to a f u t u r e acceptance  technique f o r r e c o v e r y of metals  of the  from c e r t a i n o r e concen-  t r a t e s , which a r e p r e s e n t l y r e c o v e r e d by c o n v e n t i o n a l hydro- or p y r o metallurgy. So f a r , o n l y two m i c r o b i o l o g i c a l l e a c h t e c h n i q u e s have been applied  i n t h e commercial  r e c o v e r y of metals from s u l f i d e m a t e r i a l s .  These a r e dump o r heap l e a c h i n g and i n s i t u l e a c h i n g . The f i r s t . . , (86-94.211) . t e c h n i q u e i s used m a i n l y t o r copper r e c o v e r y m the western  14. states of U.S.A., where now more than 100,000 tons/year of copper are (78) produced in this manner  . The only other metal which is being leached  commercially  .  is uranium  It i s recovered by _in situ leaching in the  (95 96) ' in amounts of 10,000 lbs of U 0 per j o (24)  E l l i o t Lake area of Ontario  o  o  month, and in South Africa 6.  Microbiological leaching of mineral sulfides A l l living organisms require small quantities of trace elements  for protoplasm synthesis and for action of their enzyme systems. However, transformation of appreciable quantities of minerals is restricted . . (76) to certain groups of. microorganisms Mineral transformations can be effected not only by direct enzymatic interaction but also by interaction with the end product(s) of metabolism^*^.  This statement pertains also to the autotrophic lie  acidophilic organism, T?. ferrooxidans.  For example, Temple et a l  (4,5,6,  97 98) '  reported that T_. ferrooxidans and T_. thiooxidans were present in  the acid mine waters and were involved in acid formation in the coal mines. The process of the microbiological leaching of metal sulfides may be defined as a biochemical (biogeochemical) (123) catalyzed by a living organism  oxidation process,  . However , in nature, only the  insoluble sulfides are of consequence, and unless the oxidation product is soluble, such an oxidation would be of l i t t l e commercial consequence. T_. ferrooxidans oxidizes different mineral sulfides at different rates, the rate of oxidation of the mixture being the sum of (83) the rates of the individual components of the mixture _T. ferrooxidans has been found able to oxidize antimony sul... (25,8,3,99) . .... (99-101) , _ .... (18,99) fides , arsenic sulfides ,cobalt sulfides , copper sulfides< ' > ' -^ sulfidest ' ' 27,29,30,32,48,99,103-112) • f 6 28 29 85-113 114) • , -. , molybdenum s u l f i d e ^ ' > ' " > ' , nickel 1 6  2 5  2 6  2 8  7  2  D  z o  z y  X X J  ± X 4 ;  1 7  2 4  (7-7 82 83 85) '> » > '  sulfides  a r i (  j t i n sulfide  (83 85) ' .  Uranium i s a l s o  15. leached  • 4.1, r „!, • • (95,96,115-119) , ^ , . i n the p r e s e n c e of these microorganisms , but the mechanism of uranium e x t r a c t i o n i s due to a secondary c h e m i c a l e f f e c t not by d i r e c t a t t a c k on the c r y s t a l s t r u c t u r e by the b a c t e r i a as i s the case for  . -i (48,120) • s u l f i d e minerals . For  the b i o o x i d a t i o n o f z i n c s u l f i d e ,  the o v e r a l l e q u a t i o n can  be w r i t t e n as f o l l o w s :  ZnS  +  20„ 2  =  ZnSO. 4  +  E  (7)  p  Where E^ i s the f r e e energy of the r e a c t i o n d e s c r i b e d  by e q u a t i o n 7,  c o r r e s p o n d i n g to the removal of e i g h t e l e c t r o n s from the s u l f i d e as i n d i c a t e d by e q u a t i o n 8.  S  +  + 6  8e  (8)  (30 Some i n v e s t i g a t o r s  122) '  a t t r i b u t e the o x i d a t i o n of z i n c  s u l f i d e s o l e l y to the c h e m i c a l a c t i o n of a c i d i c f e r r i c According  to t h i s hypothesis,  f e r r o u s i r o n contained  iron solutions.  the organism o x i d i z e s to f e r r i c  i n most s u l f i d e m i n e r a l i z a t i o n s .  i r o n , the  The subsequent  o x i d a t i o n of s u l f i d e to s u l f a t e , i n t u r n , reduces the i r o n to the f e r r o u s form, which i s then r e o x i d i z e d by the b a c t e r i u m . Duncan  However,  et_ a l ^ ^ , by s e l e c t i v e i n h i b i t i o n of enzymes i n the organism,  s e g r e g a t e d f e r r o u s i o n and s u l f i d e i o n o x i d a t i o n s  and showed  s u l f i d e i o n o x i d a t i o n was the r a t e - c o n t r o l l i n g s t e p .  Support  the h y p o t h e s i s t h a t the b a c t e r i u m i t s e l f o x i d i z e s s u l f i d e is a v a i l a b l e ^  1 2 0  '  1 2 1  ).  t h a t the of  directly  16. I n f o r m a t i o n on the m i c r o b i o l o g i c a l l e a c h i n g of z i n c is  limited.  The e a r l i e s t  r e p o r t was embodied i n a p a t e n t i s s u e d t o  Zimmerly e t a l ^ ~ ^ i n 1958.  These i n v e n t o r s  c o u l d adapt to z i n c c o n c e n t r a t i o n s Marchlenitz  et^ al^^^  found t h a t T_.  noted t h a t a f t e r a d a p t a t i o n  S i l v e r m a n and E h r l i c h ^ ^ r e p o r t e d 7  ferrooxidans  as h i g h as 17 grams per l i t e r .  grew w e l l i n s o l u t i o n s having z i n c c o n c e n t r a t i o n s  concentrations  sulfide  these organisms of 25 grams per l i t e r .  t h a t the organisms can adapt t o z i n c  up to 40 grams per l i t e r .  On the o t h e r  hand, Moss and  (78) Anderson per  reported  liter  that zinc concentrations  a r e t o x i c to _T. f e r r o o x i d a n s .  concentration adaptation  i n the range 30 to 50 grams  They found a l s o t h a t the z i n c  t o x i c i t y l e v e l was dependent on the procedure used f o r  of these b a c t e r i a .  Recently  i n the l a b o r a t o r i e s of  (39) B. C. Research concentrations ability  , growth of T_. f e r r o o x i d a n s  has been observed i n z i n c  as h i g h as 56.5 grams per l i t e r ,  i n d i c a t i n g the adapt-  of t h i s  organism. (32) Ivanov ejt al r e p o r t e d t h a t T_. f e r r o o x i d a n s i n c r e a s e d the r a t e of s p h a l e r i t e (ZnS) l e a c h i n g , and t h a t the r a t e was f u r t h e r accelerated  by the a d d i t i o n of s o l u b l e i r o n .  U s i n g p e r c o l a t o r s , Malouf  (29) and  Prater  increased  the e x t r a c t i o n of z i n c from s p h a l e r i t e about  f i v e f o l d by m i x i n g i t w i t h p y r i t e . s o l u t i o n of s p h a l e r i t e c o n t a i n e d  A f t e r 340 days of l e a c h i n g , the  about 0.6 grams of z i n c per l i t e r  and  t h a t of s p h a l e r i t e p l u s p y r i t e about 3 grams of z i n c per l i t e r . Szolnoki  and B o g n a r ^ ^ ^  also reported  that  ferrooxidans  had a p o s i -  (99) t i v e e f f e c t on the r a t e of s p h a l e r i t e o x i d a t i o n . strated  that t h i s microorganism could  chemically  prepared z i n c s u l f i d e .  accelerate  Lyalikova  demon-  the o x i d a t i o n of  The p o s s i b i l i t y of u t i l i z i n g  this  organism i n the r e c o v e r y of s m a l l q u a n t i t i e s of m e t a l s (copper, from rougher t a i l i n g s has been c o n s i d e r e d Trussell^^ .  by Duncan, Walden  U s i n g a tank l e a c h i n g t e c h n i q u e  and  zinc)  17.  and  a zinc sulfide  ore  (85) c o n t a i n i n g 1.5 r a t e of 14 mg  to 2.8% per l i t e r  z i n c , Duncan e t _al per hour and,  30,  32,  39,  46,  76,  78,  85,  99 and  106,  have been d e r i v e d from p r e -  to the l e a c h i n g organism,  r e l a t i v e l y h i g h c o n c e n t r a t i o n s and  s u l f i d e ores i s t e c h n i c a l l y f e a s i b l e . t a i n l i m i t e d or no  _T. f e r r o o x i d a n s ,  t h a t the b i o l e a c h i n g of z i n c However, these r e f e r e n c e s  i n f o r m a t i o n on s p e c i f i c v a l u e s  f a c t o r s such as temperature, pH,  f o r the  pulp d e n s i t y , s p e c i f i c  and n u t r i e n t c o n c e n t r a t i o n s which w i l l  zinc extraction.  29,  A l t o g e t h e r , these s t u d i e s i n d i c a t e t h a t z i n c  c o n c e n t r a t i o n s are n o n t o x i c  solid  liter.  of the f o r e g o i n g d a t a which are a v a i l a b l e i n r e f e r e n c e s  l i m i n a r y experiments.  at  a zinc extraction  a f t e r 30 days of l e a c h i n g , a  f i n a l z i n c c o n c e n t r a t i o n of about 6 grams per All  obtained  con-  important  s u r f a c e area  l e a d to maximum r a t e s of  of  IV.  1.  BIOKINETIC MODELING  18.  Introduction Use  o f mathematical  models i n the d e s c r i p t i o n o f the  m i c r o b i o l o g i c a l l e a c h phenomena i s of g r e a t i n t e r e s t . models based  on the v a r i a b l e s i n f l u e n c i n g  the m e t a l  For example, the  s u l f i d e leaching could  p e r m i t one to study the e f f e c t of a v a r i a b l e w i t h o u t p e r f o r m i n g e x p e r i mental work.  Such t h e o r e t i c a l study c o u l d p r e d i c t r e s u l t s and save  m a t e r i a l and time, which a r e o f economic course 2.  t h a t t h e model had been a d e q u a t e l y  Difficulties  i n biokinetic  B i o k i n e t i c modeling  s i g n i f i c a n c e , p r o v i d e d of tested with experimental  data.  modeling i s especially d i f f i c u l t  because o f the  many d i f f e r e n t m e t a b o l i c pathways and s i d e r e a c t i o n s i n v o l v e d .  Major  c o m p l i c a t i o n s a r i s e because many o f the r e a c t i o n mechanisms o f the c e l l ' s m e t a b o l i c r e a c t i o n s a r e not c o m p l e t e l y understood.  Factors influencing  b a c t e r i a l growth a r e numerous and the b i o l o g i c a l knowledge and mathematic a l t o o l s necessary  f o r the f o r m u l a t i o n and study of a c o m p l e t e l y  g e n e r a l model do n o t e x i s t ^ " * " ^ . 2  An e x a c t k i n e t i c model f o r b a c t e r i a l  metabolism i s beyond the scope o f the p r e s e n t study. to m i c r o b i o l o g i c a l l e a c h i n g o f z i n c s u l f i d e s ,  Rather  with respect  those v a r i a b l e s which have  the g r e a t e s t economic i n t e r e s t have been i n v e s t i g a t e d w h i l e h o l d i n g other v a r i a b l e s constant.  '  The most commonly used v a r i a b l e s i n f e r m e n t a t i o n k i n e t i c s a r e the c o n c e n t r a t i o n s of c e l l s , composition  and the c e l l  R e c e n t l y , the c e l l  s i z e d i s t r i b u t i o n i n a g i v e n p o p u l a t i o n have  been r e c o g n i z e d as important 3.  s u b s t r a t e s and p r o d u c t s .  f o r this  C l a s s i f i c a t i o n of f e r m e n t a t i o n  purpose.  processes  The k i n e t i c c h a r a c t e r o f i n d i v i d u a l f e r m e n t a t i o n  processes  19. . d i f f e r s widely.  However, c e r t a i n c h a r a c t e r i s t i c s permit  • „v j . « _ xn t h r e e d x f f e r e n t ways; (128 kinetic of  classification  u ' i • 0-25,126) , . (127) phenomenologxc , thermodynamxc  , and  129) '  .  The  s p e c i f i c product  phenomenological approach i s based on a comparison  f o r m a t i o n r a t e w i t h a s s o c i a t e d growth phenomena.  In  the thermodynamic approach the a c t i v a t i o n e n e r g i e s of growth, resp i r a t i o n and of  b i o s y n t h e s i s are measured, whereas i n the k i n e t i c a n a l y s i s the r a t e product  formation  i s s t u d i e d i n r e s p e c t to the  fermentation  parameters. Another b a s i s f o r the c l a s s i f i c a t i o n p o p u l a t i o n has  been g i v e n by T s u c h i y a ej: al^^^.  p o p u l a t i o n model i s d e s c r i b e d as e i t h e r The  segregated  cal  s t a t e s among the c e l l s  model'does n o t .  may  In t h e i r  " d i s t r i b u t e d " or  In t h i s  i n the p o p u l a t i o n , w h i l e  the  The  physiologi-  distributed  d i s t r i b u t e d model i s the s i m p l i e r ,  o f r e p r o d u c t i o n i s not  i n v o l v e d i n the model.  i s either  the  "segregated".  cells since  Further, i t  s t r u c t u r e d or u n s t r u c t u r e d .  s t r u c t u r e d model r e c o g n i z e s the d i f f e r e n t compounds p r e s e n t  4.  system,  l a t t e r model, i t i s assumed t h a t a l l the  be assumed t h a t the c e l l  while  bacterial  model r e c o g n i z e s the d i s t r i b u t i o n of d i f f e r e n t  have the same p r o p e r t i e s . the p r o c e s s  of models of  i n the  The cell  the u n s t r u c t u r e d model does not.  Development of b a c t e r i a l  kinetics (124-  Rather than 126,130-133)  summarize e x i s t i n g reviews of b a c t e r i a l _ , . . • . ,. ^  , thxs s e c t x o n emphasxzes the s t e p s leadxng of 4•1  fermentation Orders If  evolutxon  kinetics.  of b i o l o g i c a l  (enzymatic)  reactions  the s u b s t r a t e l e v e l i s h i g h the b i o l o g i c a l r e a c t i o n r a t e  follows a zero-order falls,  to the  kinetics, -  course  (reaction rate i s constant).  e i t h e r because s u b s t r a t e i s used up  the r a t e more c l o s e l y  If this  or i s i n a d e q u a t e l y  approximates a f i r s t - o r d e r  level  replaced,  r e a c t i o n (the r e a c t i o n  20. Therefore, i t  r a t e i s p r o p o r t i o n a l to the c o n c e n t r a t i o n of s u b s t r a t e ) . is d i f f i c u l t ,  .  to c l a s s i f y  '  being  ...  the o v e r a l l b a c t e r i a l  ,  ..  of. a s p e c i f i c o r d e r  (enzymatic) r e a c t i o n as  (134)  or r e a c t i o n  Most k i n e t i c models d e a l w i t h i n v o l v i n g l i m i t a t i o n of n u t r i e n t s and  c e l l growth and  products.  product  These models do  take i n account the d i f f e r e n c e between i n d i v i d u a l c e l l s , ing  may  ~  =  f  ||  =  -f  f  =  f  formation  and  not  the f o l l o w -  be w r i t t e n :  (X,S,P)  x  (9)  (X,S,P)  2  •  (10)  (X,S,P)  3  (11)  where X  =  cell  S  =  substrate  P  =  product  f^,  f  and  2  (mass or number) c o n c e n t r a t i o n ; concentration;  concentration;  f ^ are f u n c t i o n s which depend on c e l l  s u b s t r a t e consumption and If centration  these  equations  (X) e x p r e s s i o n s  consumption and  product 9,  concentration respectively.  10 and  11 are d i v i d e d by  s p e c i f i c product  T h i s should  c u l t u r e and may of a c u l t u r e .  not be  the c e l l  f o r s p e c i f i c growth r a t e , s p e c i f i c formation  apply e x p l i c i t l y  con-  substrate  are a t t a i n e d ^ ^ ^ ^ .  Constant s p e c i f i c growth r a t e i s the s i m p l e s t equations.  concentration,  to e x p o n e n t i a l  form of the r a t e growth of a  a p p l i c a b l e to o t h e r phases of the growth  curve  4.2  S u b s t r a t e l i m i t e d models  '  .21.  The h y p o t h e s i s t h a t the enzyme (E) and the s u b s t r a t e form a complex  (ES) i n enzyme c a t a l y z e d r e a c t i o n s , was d e r i v e d o r i g i n a l l y by  M i c h a e l i s and M e n t e n ^ * ^ ^ i n 1913:  E  +  k ~==± k  S  {ES}  k --—>  E  +  . P  (12)  2  Where k^  =  r a t e c o n s t a n t o f the forward  reaction for  enzyme-substrate  complex f o r m a t i o n ; k^  =  r a t e c o n s t a n t of the backward  k^  =  r e a c t i o n r a t e c o n s t a n t f o r d i s s o c i a t i o n of the enzymesubstrate  The  complex.  s p e c i f i c growth r a t e (V) of the r e a c t i o n o f e q u a t i o n 12 may be w r i t t e n  as f o l l o w s  V  V  reaction;  '  :  m [S]  K m  Where V m K  [S]  +  m  < > 13  =  maximum s p e c i f i c growth r a t e ; °  =  Michaelis-Menten  The v a l u e o f K m r e a c t i o n proceeds  constant,  i s e q u a l to the s u b s t r a t e c o n c e n t r a t i o n when the a t one h a l f  the maximum r e a c t i o n r a t e .  This K value m  r e p r e s e n t s a fundamental c o n s t a n t i n enzyme k i n e t i c s . The M i c h a e l i s - M e n t e n  e q u a t i o n 13 can a l s o be d e r i v e d  from  • 's a d As o r p t,i•o n i•s o t-hi e, r m Langmuir t h eio r y (138,139) T  An  e q u a t i o n analogous  to e q u a t i o n 13 has been proposed by  ,(131,140) • r ., ^ Monod f o r m i c r o b i a l growth. u and V by y m max J  respectively, r  J  T  • xr • 1 J 1. I n h i s e q u a t i o n V i s r e p l a c e d by  22 Lineweaver and Burk linearized;  i f one p l o t s 1/V  showed t h a t e q u a t i o n 13 c o u l d be versus 1/[S].  Then the i n t e r c e p t of  s t r a i g h t l i n e w i t h the' o r d i n a t e r e p r e s e n t s 1/V^J w h i l e t h a t w i t h a b c i s s a i s e q u a l to  this the  -1/K  and the s l o p e of t h i s l i n e i s K /V . There m mm e x i s t many a l t e r n a t e forms of the Lineweaver-Burk p l o t , c l a i m i n g a d d i t i o n a l , . (142-144) advantages Many workers  ' ^6) x  k  proposed  a v e  s p e c i f i c growth r a t e of microorganisms. ditions  these reduce  (147)  and  Fujimoto  (148)  c o n c e n t r a t i o n i n t o the growth r a t e e q u a t i o n ,  m  [S]  BX  +  V  V  Under c e r t a i n l i m i t i n g  to the Monod or M i c h a e l i s - M e n t e n  Other workers such as C o n t o i s cell  a l t e r n a t e models f o r the  =  type  con-  equations.  have i n c o r p o r a t e d the  e.g.:  [Sf  (  Monod's e q u a t i o n  ( h y p e r b o l i c r a t e equation)  s u b s t r a t e on the  growth r a t e .  fermentation processes  c o n d i t i o n i s not m a i n t a i n e d  and more than one  4  )  i s supposed to  d e s c r i b e the e f f e c t of a s i n g l e l i m i t i n g However, i n many important  1  specific this  s u b s t r a t e i s used.  For  these  (149) cases e q u a t i o n 13 has  to be m o d i f i e d .  a r a t e equation f o r a two-substrate independently  V  =  1  Socquet  derived  r e a c t i o n i n which each s u b s t r a t e  forms a complex w i t h a d j a c e n t s i t e s on the enzyme:  V fS ][S ]/((l m  L a i d l e r and  2  E q u a t i o n 15 reduces  +  K [S ]) 1  1  (1  +  K [S ])) 2  (15)  2  to the h y p e r b o l i c form when one  of the s u b s t r a t e  c o n c e n t r a t i o n s i s c o n s t a n t on i t s e q u i v a l e n t , i . e . , when the c o n c e n t r a t i o n of one  s u b s t r a t e g r e a t l y exceeds t h a t of the o t h e r .  e q u a t i o n f o r t e r n a r y complex f o r m a t i o n was  Similarly,  an  d e r i v e d by S e g a l e t a l ^ ^ .  23. Despite the fact that most workers(131,140,145,146,151 155) have regarded the specific growth rate of a microbial population as a single function of the concentration of the limiting substrate, Contois and Fujimoto^"'"^^ were able to show that i t i s also a function of the (212) population density ( X ) .  More recent work  suggests density effects  are due to limitations of a number of other factors. 4.3  Product limited models Inhibitory metabolic products normally are formed and accumulated  during any growth processes.  These may compete with substrates for  active sites on the enzyme molecules and can thus result in a diminution in the rate of product formation and in the number of viable organisms. Several models have been proposed in the literature to describe this relationship. i  In the area of population growth P r i t c h e t t u s e d a third  order polynomial to describe the growth as a function of time.  The  (122) same order of polynomial has been applied by McDonald bacterial ferrous iron oxidation curve.  Pearl  to describe the  demonstrated the  applicability of a logarithmic form to growth curve representation. Numerous models have been proposed in describing sigmoid-shape (158-172) growth curves  which were found useful in studies of growth  phenomena. The logistic type equation, for example ^^"^ : X  »  X /(1 m  +  exp (a  +  bt  +  ct  2  +  dt )) 3  (16)  where a, b, c and d are constants and t the time, may be written in a linearized form which i s more adaptable to certain computational techniques(173-180).  24. A generalized l o g i s t i c growth curves has been proposed  X  =  X /(l + m  Leudeking  a  1 dX I d T  e q u a t i o n 18  In for  , +  order  Edwards and  wilke^  limited  ,  x 8 x  ^  have d e s c r i b e d a model f o r product cultures:  '  •  STQ\  b  ( 1 8 )  the f i r s t  1 ' dP T T — -J— X at  a straight  d  polynomial.  term on the r i g h t hand s i d e i s an e x p r e s s i o n product  Based on e q u a t i o n 18,  a constant.  a n  (17)  s p e c i f i c growth-associated  * formation,  ± 3  and P i r e t  f o r m a t i o n i n product  =  by E d i r a r d s ^ " ^  exp(f(t)))  where f ( t ) i s a f i f t h  1 dP XdF  e q u a t i o n which can f i t many types of  f o r m a t i o n and  the second  term i s  a p l o t of the s p e c i f i c r a t e of  product  • ... ^ 1 dX . . . . . v e r s u s the s p e c i f i c growth r a t e , — - j — , should g i v e X dt :  ,  l i n e , where b i s the i n t e r c e p t and  a the s l o p e of the r e g r e s s i o n  line. 4.4  S u b s t r a t e and p r o d u c t The  simultaneous  l i m i t e d models effect  of p r o d u c t and  s u b s t r a t e on the r a t e of (183)  product  f o r m a t i o n has been demonstrated by Chen e_t a l k  2  EoS  1  +  =  r e a c t i o n r a t e c o n s t a n t f o r enzyme-substrate  =  i n v e r s e of M i c h a e l i s - M e n t e n  k^  =  desorption constant;  Eo  =  i n i t i a l enzyme c o n c e n t r a t i o n .  dt where k^ k  2  k S 2  +  k P  v  J  3  constant;  complex f o r m a t i o n ;  The authors  (183)  2.5 >  claim that equation 19 f i t their data better than the  simple substrate limited model. Using enzyme kinetic models, Maxon and Chen^"^^ have been able to solve complicated fermentation processes, such as semicontinuous substrate addition. Their models are oriented towards description of industrial fermentation processes (e.g., the production of neomycin) as shown by equation 20.  j dX dt Y  k x G 1 + k G + k N n  =  1  ( 2 Q ) v  1  Where the growth rate is based on glucose (G) concentration and inhibition is due to neomycin (N) concentration. 5.  Proposed models The current literature of biological kinetics contains many  examples of mathematical models derived for homogeneous systems.  In  general, in the choice of a model which quantitatively describes the biological phenomena, one has to be certain that i t has validity, generality and prediction a b i l i t y ^ ^ " ^ .  Further, the choice or design  of a valid mathematical model should depend on what is already known about the system and on what type of results one expects to obtain. A complete description of the bacterial kinetic processes w i l l not be possible until an exact and complete description of the metabolism of the organism is available. This could also require new biological principles which should be consistent with the physical principles but perhaps not derivable from them^^"^. In the case of the heterogeneous system of microbiological leaching of zinc sulfide, there are problems which are not evident in homogeneous systems.  The availability of substrate in the sulfide is not  o n l y a f u n c t i o n of the mass but Further, its  the s u r f a c e a r e a of  specific  surface area.  thus o n l y c e r t a i n s i t e s should  considered  m i c r o b i o l o g i c a l o x i d a t i o n of z i n c s u l f i d e ores may  as a m u l t i s u b s t r a t e  s u l f a t e and  of f e r r o u s i r o n to f e r r i c  i r o n take p l a c e .  Another major problem i n v o l v e d of the number of organisms.  of e s t i m a t i n g  be  system, i n which o x i d a t i o n of s u l f i d e  iron.  i n t h i s system i s the  Unfortunately  to  Commercial z i n c  s u l f i d e . o r e s always c o n t a i n a c e r t a i n q u a n t i t y of f e r r o u s  are  be  available for bacterial action. The  ability  26.  the z i n c s u l f i d e ore i s inhomogeneous i n  energy c h a r a c t e r i s t i c s and  considered  a l s o of the  avail-  t h e r e e x i s t s no method  the number of organisms i n systems where s o l i d  particles  involved. From t h i s i n t r o d u c t i o n i t i s o b v i o u s t h a t the m a t h e m a t i c a l  expressions  derived  so f a r f o r b a c t e r i a l k i n e t i c s are not  applicable  to t h i s heterogeneous system of m i c r o b i o l o g i c a l z i n c s u l f i d e Therefore,  a l l k i n e t i c data  throughout t h i s p r e s e n t  i n terms of p r o d u c t f o r m a t i o n  (zinc extraction).  oxidation.  work w i l l be  expressed  V.  MATERIALS AND METHODS  1.  General  27.  Because the number of v a r i a b l e s under c o n s i d e r a t i o n i s l a r g e (8 v a r i a b l e s ) , and because of the l i m i t e d a v a i l a b i l i t y o f some s u b s i e v e f r a c t i o n s o f the s u b s t r a t e , s t a t i s t i c a l l y designed used.  experiments  The procedure was t o study one v a r i a b l e a t a time.  were n o t  When t h e v a l u e  of t h e v a r i a b l e which gave maximum l e a c h i n g r a t e was determined, h e l d c o n s t a n t i n subsequent experiments  i t was  w h i l e o t h e r v a r i a b l e s were  examined. 2.  Organisms An  inoculum  o f T h i o b a c i l l u s f e r r o o x i d a n s (N.C.I.B. No. 9490),  i s o l a t e d by R a z z e l l and T r u s s e l l  W  a s  adapted  to a medium c o n t a i n i n g (37)  the b a s a l s a l t s o f t h e medium d e s c r i b e d by S i l v e r m a n and Lundgren  but  w i t h z i n c s u l f i d e c o n c e n t r a t e r e p l a c i n g f e r r o u s s u l f a t e as t h e energy source.  When growth i n b a t c h c u l t u r e reached  b a c t e r i a were m a i n t a i n e d  the s t a t i o n a r y phase the  by t r a n s f e r o r were used  as an e x p e r i m e n t a l  inoculum. 3.  Substrate A l l work has been c a r r i e d out w i t h a s i n g l e l o t of high-grade  zinc s u l f i d e concentrate.  T h i s m a t e r i a l was s u p p l i e d by Cominco L t d . ,  T r a i l , B. C. a f t e r s p e c i a l f l o t a t i o n t o remove excess p y r i t e . marmatic p r e p a r a t i o n was wet b a l l - m i l l e d  This  t o pass a 400 mesh s i e v e .  After  d r y i n g a t 45°C, a c h e m i c a l a n a l y s i s gave the f o l l o w i n g c o m p o s i t i o n : 60.78% z i n c , 33.23% s u l f u r , 2.50% i r o n , 1.79% l e a d , 1.29% c a l c i u m o x i d e and  some i m p u r i t i e s (Cd, Cu, Mg,...).  Corresponding  the z i n c s u l f i d e c o n c e n t r a t e i s 90.6% pure, as z i n c  to this sulfide.  analysis,  28. The d e n s i t y of the s u b s i e v e m a t e r i a l has been p y c n o m e t r i c a l l y to be 3.7990 gram per ml 3.1  Substrate  (186).  fractionation  In o r d e r t o study on  the e f f e c t of p a r t i c l e s i z e of s u b s t r a t e  the m i c r o b i o l o g i c a l z i n c e x t r a c t i o n , the s u b s i e v e  concentrate  determined  zinc  sulfide  (-400 mesh) was f r a c t i o n a t e d i n t o d e f i n i t e s i z e  fractions  u s i n g b o t h a wet and a d r y t e c h n i q u e . Wet s u b s i e v e f r a c t i o n a t i o n c o n s i s t e d of c o l l e c t i n g f r a c t i o n s , u s i n g a Warman C y c l o s i z e r A p p a r a t u s ^ ^ . x 8  s i x subsieve  This i s a hydraulic  c y c l o n e e l u t r i a t o r whose o p e r a t i n g p r i n c i p l e s have been d e s c r i b e d by K e l s a l l and McAdam^ ^ ^. X  8  The d r y t e c h n i q u e  c o n s i s t e d of c o l l e c t i n g  eight  subsieve  f r a c t i o n s u s i n g a Bahco No. 6000 M i c r o p a r t i c l e C l a s s i f i e r . d e v i c e i s a combination 3.2  Determination  This  of an a i r e l u t r i a t o r and a c e n t r i f u g e .  of p a r t i c l e  size  The main p a r t i c l e diameters  (Stokesian diameters)  of the C y c l o -  s i z e r f r a c t i o n s were o b t a i n e d from the o p e r a t i n g c u r v e s of the C y c l o sizer M a n u a l a n d  by m i c r o s c o p i c measurements, which c o n s i s t e d of  comparison of the p a r t i c l e images w i t h a g r a t i c u l e .  The B a h c o - s i z e r  f r a c t i o n s were i n v e s t i g a t e d by m i c r o s c o p i c measurements o n l y . In t h e s e m i c r o s c o p i c measurements, the p a r t i c l e diameter determined  was  as the average o f the two dimensions e x h i b i t e d by the p a r t i c l e .  F o r each f r a c t i o n t h i r t y  i n d i v i d u a l p a r t i c l e s were observed  and the  average v a l u e of these measurements r e g i s t e r e d . 3.3  Determination  of s p e c i f i c s u r f a c e a r e a  S p e c i f i c s u r f a c e a r e a , which i s the s u r f a c e a r e a per u n i t mass of s o l i d s , of the u n f r a c t i o n a t e d z i n c s u l f i d e c o n c e n t r a t e  (-400 mesh)  and of the v a r i o u s s u b s i e v e f r a c t i o n s mentioned the B.E.T.-technique^"'"^"^ T h i s apparatus was paper  samples,  determined  29. by  u s i n g a dynamic n i t r o g e n a d s o r p t i o n a p p a r a t u s .  b u i l t by Orr  and was  above, was  (192) ,  f o r s u r f a c e a r e a measurements of  made a v a i l a b l e f o r t h i s  study. (193-199)  The dynamic n i t r o g e n a d s o r p t i o n method a gas chromatographic solid  i n the normal  i s essentially  t e c h n i q u e i n which the sample powder r e p l a c e s the  chromatographic  the sample a t the temperature  column.  N i t r o g e n i s adsorbed  by  of l i q u i d n i t r o g e n from a c o n t i n u o u s  gas  stream of n i t r o g e n and helium, and desorbed upon warming the sample. The d i f f e r e n c e i n nitrogen c o n c e n t r a t i o n of the gas m i x t u r e i s measured by a c a l i b r a t e d  thermal c o n d u c t i v i t y c e l l .  The  s u r f a c e a r e a of the  i s e v a l u a t e d by a p p l i c a t i o n of the B.E.T.-equation. in  Appendix.3.  4.  C u l t u r e techniques  4.1  solid  D e t a i l s are g i v e n  Shake t e c h n i q u e The m i c r o b i o l o g i c a l l e a c h i n g experiments were c a r r i e d out  a g y r a t o r y shaker(200)^  u s  -L g n  a  on  . b a t c h t e c h n i q u e developed by Duncan e t  (79) al  .  The d e s i r e d q u a n t i t y of z i n c s u l f i d e c o n c e n t r a t e and  70 ml of  (37) i r o n f r e e medium  were p l a c e d i n b a f f l e d , 250 ml Erlenmeyer  flasks.  Then these f l a s k s were i n o c u l a t e d w i t h 5 ml of an a c t i v e c u l t u r e of T h i o b a c i l l u s f e r r o o x i d a n s p r e v i o u s l y adapted centrate.  to the z i n c s u l f i d e  con-  In the s t e r i l e c o n t r o l f l a s k s i n s t e a d of the inoculum, 5 ml  of a s o l u t i o n c o n t a i n i n g  two per cent of thymol  i n a l c o h o l , were added.  The f l a s k s were i n c u b a t e d a t c o n s t a n t temperature thermostated g y r a t o r y shaker. e v a p o r a t i o n was s u l f u r i c acid  P e r i o d i c a l l y any water l o s t  r e p l a c e d w i t h d i s t i l l e d water and  (IN) or sodium h y d r o x i d e  were not stoppered i n any manner.  on a through  the pH a d j u s t e d w i t h  (IN) i f n e c e s s a r y .  The  flasks  30. Constant equipped 4.2  pH experiments  were c a r r i e d out i n shake  with a pH-stat^^"^ .  Tank l e a c h i n g Large  s c a l e experiments  were c a r r i e d  d i o x i d e p a r t i a l p r e s s u r e i n a temperature a)  flasks  i n an u n b a f f l e d s t a i n l e s s s t e e l tank  24 i n c h e s deep l e n g t h ) equipped 1% carbon d i o x i d e was  out a t i n c r e a s e d  controlled  carbon  room:  (12 i n c h e s i n s i d e diameter  and  with a marine-impeller, a i r containing  i n t r o d u c e d i n t o the medium under the i m p e l l e r s a t  a f l o w r a t e of 10,000 ml per minute; b)  i n a baffled  same dimensions  ( t h r e e b a f f l e s 120°  as the u n b a f f l e d one)  t u r b i n e i m p e l l e r , a i r s u p p l y was 5. 5.1  Chemical  a p a r t ) p l e x i g l a s s tank equipped  (with the  with p H - s t a t ^ ^ ^ 2  and  a  the same as i n the u n b a f f l e d tank.  analysis  Substrate . Metal contents  (Zn, Fe, Pb,  s u l f i d e c o n c e n t r a t e were determined  CaO,  and  so on)  of the  zinc  on the s o l u t i o n s o b t a i n e d by  acidic  (202) digestion  u s i n g a P e r k i n Elmer Model 303  atomic  absorption spectro-  photometer. The  s u l f u r c o n t e n t of the z i n c s u l f i d e c o n c e n t r a t e  determined  gravimetrically(202)^  5.2  solutions  Leach  The  e x t r a c t e d z i n c c o n c e n t r a t i o n s were determined  d u r i n g the individua.l l e a c h e s by removing one ml t h e i r z i n c c o n t e n t s by atomic  a b s o r p t i o n spectrophotometry.  removed f o r z i n c d e t e r m i n a t i o n was , . ,. (37) of i r o n - f r e e medium f  samples and  was  periodically measuring The volume  r e p l a c e d w i t h an e q u i v a l e n t volume  6.  Modeling and curve f i t t i n g  31  In the work d e s c r i b e d  later  i n t h i s t h e s i s a r a t e of z i n c  e x t r a c t i o n i s r e l a t e d t o a v a r i e t y of parameters. z i n c concentration versus obtained.  Figure 1 i s a p l o t of  time and i s t y p i c a l of the l e a c h  curves  The s l o p e o f such a curve i s the r a t e of l e a c h i n g o r r a t e  of e x t r a c t i o n .  Obviously  a b l e from such a curve.  t h e r e i s a range of e x t r a c t i o n r a t e s The one used l a t e r  obtain-  f o r c o r r e l a t i v e purposes i s  the s l o p e o f the l i n e a r r e g i o n of the c u r v e of F i g u r e 1, t h a t i s the r e g i o n between a and b. by  The s l o p e o f t h i s l i n e a r p o r t i o n was determined  a l e a s t squares (203) computer program. Attempts were made f o r some o f the e x p e r i m e n t a l  mathematical expression  to the complete l e a c h i n g curve.  i o n chosen was the g e n e r a l i z e d and  P  l o g i s t i c equation  runs,  to f i t a  The e x p r e s s -  employed by Edwards ^ ~ ^ 3  Edwards and W i l k e ^ " ^ " ^ which i s w r i t t e n  =. P / ( 1 +  f(t)  where  m  =  a  P  Q  =  +  exp(f(t)))  a ^  product  +  a t  (21)  (zinc)  ^m =  maximum p r o d u c t  t  time;  =  +  2  2  +  a^t*  +  a^  (22)  5  concentration;  r  21 i s v e r y  3  concentration;  a , a,, a„, a „ , a., a • o 1 2 3 4 5 Equation  a.^  are constants  f l e x i b l e , having  7 constants,  the l e a c h c u r v e and f i v e o f them a d j u s t a b l e . reproduce a v a r i e t y o f sigmoid  f o r a p a r t i c u l a r leach. two o b t a i n a b l e  from  Thus i t i s a b l e t o  (S-shaped) curves(?Q4) .  to be e s p e c i a l l y u s e f u l f o r systems d i s p l a y i n g p r o d u c t  i t i s stated inhibition^ "^ 8  Pm the maximum product c o n c e n t r a t i o n i s o b t a i n a b l e d i r e c t l y from the l e a c h curve  33  ( e . g . , i t i s the z i n c c o n c e n t r a t i o n a t p o i n t d on F i g u r e 1 ) .  A t the s t a r t o f t h e l e a c h (time zero) t h e r e i s a s m a l l but finite  c o n c e n t r a t i o n of z i n c  (Po) which was i n t r o d u c e d w i t h t h e inoculum-  When t = 0, e q u a t i o n 21 reduces t o :  P P  °  ~  m  1 + exp(a  )  n  (  which a l l o w s e s t i m a t i o n of a  from knowledge o f P  G  to t h e e x p e r i m e n t a l d i f f i c u l t i e s l e a c h curve a least  involved i n the i n i t i a l  fitted  could d i f f e r e n t i a t e  -  i t to g e t the e x t r a c t i o n r a t e  using a  thus  =  &  l  < *> 2  +  2a t  +  2  3a t  0  ln(  In  the curve f i t t i n g procedure  P  )  =  a  Q  +  at ±  4a^t  +  5a t  /  •  5  (25)  e q u a t i o n , e q u a t i o n 21, may be converby t a k i n g l o g a r i t h m s .  x  =  +  3  to a polynomial e x p r e s s i o n ( 8 1 )  y  and  p a r t of the  an e q u a t i o n o f the form of e q u a t i o n 21, one  The g e n e r a l i z e d l o g i s t i c ted  )  However, due  p f >  where f ' ( t )  3  t e c h n i q u e d e s c r i b e d below.  Having  dt  and Pm.  was n o t measured i n t h i s work but was determined  G  squares  0  2  +  used P  ... +  m  a t  Thus,  5  5  was o b t a i n e d from the l e a c h curve  the r e m a i n i n g s i x c o n s t a n t s ( a , a^, ... , a^) were determined Q  (26)  by a  l e a s t squares f i t t i n g technique using a m u l t i p l e regression a n a l y s i s program w r i t t e n f o r the I.B.M. 360 d i g i t a l computer(205,  206)  Another program reproduced i n Table 1 of Appendix 2 was used to c a l c u l a t e the f i t t e d values f o r the data and to tabulate them alongsid of the measured values f o r comparison.  VI. 1.  RESULTS AND E f f e c t s of  DISCUSSION  3 5  temperature  The effect of temperature v a r i a t i o n on zinc extraction studied over a range of 25°C to 45°C. c o<v i J 5.3% pulp density J  adjusted to 2.5.  was  The leach suspensions contained  / mass s o l i d s x 100 . . . ... , ( = ,- . TZ ) with the i n i t i a l pH volume of l i q u i d medium  u  N  A l l experiments were done i n duplicate and with  s t e r i l e controls.  The experimental data are given i n Table 1 (A and B)  of Appendix 1. The s t e r i l e controls show the extent of chemical d i s s o l u t i o n of zinc from the zinc s u l f i d e concentrate.  The zinc concentrations i n  there s t e r i l e controls can be seen from Table 1 (A and B) of Appendix 1 to be much lower than those obtained i n the presence of T\ ferrooxidans, thus establishing the role of the bacteria i n such leaching. The e f f e c t of temperature  on the microbiological zinc  extraction i s presented graphically i n Figure 2.  Each point on t h i s  graph i s the average of the duplicate runs reported i n Table 1 (A and of Appendix 1.  B)  From Figure 2 i t i s e a s i l y seen that the fastest zinc  extraction rate was achieved at 35°C. The zinc extraction rates i n mg/1 temperature  i n Figure 3.  hr are plotted against  A maximum i n this extraction rate curve i s d i s -  cernible at around 35°C. Subsequent experimentation was done at 35°C.  This  value i s i n agreement with values reported by other workers for oxidation •  •  of ferrous iron m  i  A  - n-  U - J  (16,72,74,77,207)  solution and m e t a l l i c s u l f i d e ores  These workers have quoted optimum temperatures  i n the range 28°C to 40°C.  Figure 3 indicates extremely limited micorbiological leaching a c t i v i t y at temperatures  above 45°C.  Bryner e_t  found that b i o l o g i c a l  Figure EFFECT  I  0  .  I  40  JL  2  OF TEMPERATURE  __-J______^_j__J___  80  100 TIME  160 ( hr )  200  37  oxidation of chalcopyrite ceased at around 55°C and that at higher  38  temperatures only chemical oxidation occurred. The value obtained for the optimum temperature (35°C) would place T_. ferrooxidans in that class of organisms called mesophiles.  This temperature optimum is greater than  the values usually found for s o i l microorganisms, which generally are psychrophilic. The shape of the zinc extraction rate versus temperature plot is typical of biological reactions.  There are two competing rate  processes to be considered, the usual kinetic rise in reaction rate with increasing temperature and at the same time an increase in the rate of thermal death of the microorganisms  f  Thus as  temperature increases the rate of thermal death of the microorganisms increases more rapidly than does the increase in extraction rate.  The net  result i s a maximum in the extraction rate versus temperature plot. Using the data summarized in Figure 3 values for the temperature coefficient (Q^Q) °f  t n e  zinc extraction rate process were  calculated from equation 2 7 : 10 (27)  where T^ and and  a r e  temperatures in absolute units;  are the extraction rates corresponding to temperatures T^ and  v ... Also,values for the activation energy defined by:  39 AH  12 T  a  2  - T  were c a l c u l a t e d ,  The  ln(-  (28)  )  1  where R i s the gas c o n s t a n t .  r e s u l t s o f these c a l c u l a t i o n s over f o u r  are p r e s e n t e d i n T a b l e 2.  temperature ranges  For temperatures of up to 35°C, the Q ^ ^  v a l u e s a r e o f the o r d e r of 2 which i s a t y p i c a l v a l u e f o r many c h e m i c a l reactions  and i s the b a s i s  f o r the r u l e of thumb t h a t  r e a c t i o n r a t e s double f o r a 10°C i n c r e a s e  i n temperature.  f o r Q ^ Q over the range 25°C to 35°C a  values obtained  b i o l o g i c a l and n o n b i o l o g i c a l  reactions.  typically  r e  So t h e  " t y p i c a l f o r both  The a c t i v a t i o n e n e r g i e s found  f o r the temperature range 25 to 35°C (12.8 Kcal/mole) a r e a l s o t y p i c a l of a wide v a r i e t y o f b i o l o g i c a l and n o n b i o l o g i c a l  reactions.  The  a c t i v a t i o n energy o b t a i n e d f o r the 40 to 45°C range i s much l a r g e r and opposite i n sign.  T h i s v a l u e i s t y p i c a l of the v a l u e s found f o r the  denaturation of proteins.  I t i s also  the r e a s o n f o r the low v a l u e of  Q^Q because the r u l e o f d o u b l i n g t h i s r e a c t i o n r a t e f o r a 10°C temperature i n c r e a s e 10 and 20 Kcal/mole. region 2.  of F i g u r e  i s only v a l i d  i f the a c t i v a t i o n energy i s between  The s i g n i s n e g a t i v e because the r a t e  3 decreases with increased  i n this  temperature.  E f f e c t s o f pH After  ferrooxidans rise.  i n i t i a l pH adjustment and i n o c u l a t i o n w i t h T_.  the pH o f the l e a c h  s o l u t i o n s , u n l e s s c o n t r o l l e d , tends t o  T h i s may be due t o the b u f f e r i n g n a t u r e of the a l k a l i n e  c o n c e n t r a t e o r t o the i n h e r e n t  pH o f z i n c s u l f a t e .  However, d u r i n g the  40  Table 2 Temperature c o e f f i c i e n t s and a c t i v a t i o n e n e r g i e s f o r z i n c e x t r a c t i o n from the z i n c s u l f i d e c o n c e n t r a t e by T_. f e r r o o x i d a n s  Temperature range (°C)  * a H  Kcal/mole  25-30  2.05  12.8  25 - 35  2.02  12.8  30 - 35  2.00  12.8  40 - 45  0.05  -57.6  period  of r a p i d m e t a l r e l e a s e  the pH,  u n l e s s ' c o n t r o l l e d , tends to  ^  become more a c i d i c . 2.1  E f f e c t of i n i t i a l  pH  The  e f f e c t s of i n i t i a l  pH  ( v a r y i n g from 1.5  to  4.0)  on m i c r o b i o l o g i c a l z i n c e x t r a c t i o n were s t u d i e d on l e a c h s u s p e n s i o n s cont a i n i n g 5.3%  s o l i d s incubated  s o l u t i o n s was value was  as  not  adjusted  but  left  to seek i t s own  hydrogen i o n , z i n c and times.  and  l e a c h i n g s t a r t e d the pH  rose  partially  level,  and  In t h i s F i g u r e  dropped and The  the  the f i n a l pH  contributed  and  Duncan  (39)  iron concentration,  to the drop i n pH. and  2.5)  pH  the pH  rose  to very  been suggested  T h i s p r e c i p i t a t i o n of i r o n may  run,  the pH  throughout the l e a c h .  the  When the  which was  not  by  have  of i n i t i a l  pH  significant.  tended to be  higher  However, i n a l l the  remainder of t h i s s e r i e s of experiments (pH u n c o n t r o l l e d started)  seen t h a t  added.  However, a t lower v a l u e s  1.5  of  have p r e c i p i t a t e d  i r o n p r e c i p i t a t i o n p r o b a b l y was I n the pH  than the i n i t i a l  .  to 2F of Appendix  as f u n c t i o n s  a c i d was  i n the form of b a s i c i r o n s u l f a t e s as has (38)  leaching  were measured at  4 i t can be  I r o n may  pH  value  D u r i n g the  zinc concentration  then d e c r e a s e d .  initial  Subsequently the  iron concentration  tends to r i s e u n l e s s  stable level.  initially  L e a t h e n et. al  2.0,  4.  these  the pH back to the  iron concentrations  z i n c and  by F i g u r e  e s t a b l i s h e d pH  reach a f i n a l ,  of  These r e s u l t s are p r e s e n t e d i n T a b l e 2A  time i s p r o v i d e d initially  pH  c h e m i c a l s t a b i l i z a t i o n of the system.  A t y p i c a l p l o t of pH  (1.5,  initial  n e c e s s a r y , u n t i l the r e a c t i o n s t a r t e d .  process,  low,  The  c o n t r o l l e d manually a d j u s t i n g  representing  various  a t 35°C.  u l t i m a t e l y s t a b i l i z e d a t about 2.1.  after reaction  T h i s may  be  1.  4 2  Figure EFFECT  O F I N I T I A L "pH  (pH  5.3%  1.0  4  • 3.5 )  Pulp Density  20  4.0  f * , x X" x  0.8 •zp0.6  <  0.4  o o z  o  3.5  IG ^' y  pH  g  i - 12  3.0  <  cc  g  0 1  UJ  o o o  8  2.5  2.0  0 2 N o O ~ o - o o  ,0-0-  A ^ A - A - A H A - A — A °  0  100  A  '  200 TIME  300 ( hr )  400  500  1.5  43 characteristic to a degree of this particular medium and strain of T_. ferrooxidans for in other environments such as acid mine waters the pH has been reported to be maintained at various values ranging from 1.5 to 3.5 . Figure 5 presents plots of zinc concentration versus time for various values of i n i t i a l pH.  It shows that the most significant effect  of i n i t i a l pH i s on the lag (initiation) time. rates are more or less constant.  The zinc extraction  This lag time (defined in point c of  Figure 1) is the time i t takes for the reaction to reach the rapid, constant zinc extraction rate.  It i s a period in the microbiological growth  cycle wherein the organisms adapt themselves to their environment at the end of the lag period or phase and rapid c e l l division of the organisms begins.  Although i n this work c e l l reproduction rates were not measured,  the curves of Figure 4 would suggest that the lag phase ended at the time that significant amounts of zinc begin to be released.  Table 3  summarizes the data given in Figure 4 and in Tables 2A to 2F of Appendix 1.  The shortest lag times were observed in leach solutions which were  i n i t i a l l y at pH 2.0.  The calculated extraction rates were only slightly  dependent on i n i t i a l pH.  The fastest extraction rate (119.5 mg/1 hr)  in this series of experiments was observed with an i n i t i a l pH of 2.5 . 2.2  Effect of constant pH The effects of controlled, constant pH oh microbial zinc  extraction were studied on leach suspensions containing 16% of solid substrate.  These suspensions were maintained at 35°C in shake flasks.  The 16% pulp density (solids concentration) i s , as w i l l be shown i n Section 4, an optimum value for substrate concentration.  The pH values  Figure  5  E F F E C T O F INITIAL pH ON ZINC 5.3%  Pulp  TIME  Density  ( hr )  EXTRACTION  Table 3 E f f e c t of I n i t i a l  Initial pH  Final  Lag  time  pH  Zinc  extraction rate (mg/1 hr)  pH  (hr)  1.5  1.75  252  99.7  2.0  2.05  10  106.4  2.5  2.2  18  119.5  3.0  2.1  74  116.3  3.5  2.05  192  108.4  4.0  2.2  390  96.9  46 of these at  s o l u t i o n s were i n i t i a l l y  adjusted  0.5 pH u n i t i n t e r v a l s and maintained  values  t o v a l u e s between 1.5 and 4.0  to w i t h i n - 0.1 pH u n i t s of these  a u t o m a t i c a l l y u s i n g a pH stat^*"*"^ .  T h i s s e r i e s of experiments  was c a r r i e d out w i t h s i n g l e samples o n l y except f o r the run a t pH 1.5 which was d u p l i c a t e d .  No s t e r i l e c o n t r o l was made.  r e s u l t s a r e summarized i n T a b l e presented  i n F i g u r e 6.  experimental  3 (A and B) of Appendix 1, and a r e  T h i s f i g u r e shows t h a t the e x t r a c t i o n r a t e was  s i g n i f i c a n t l y a f f e c t e d o n l y a t the extreme v a l u e s studied  The  ( i . e . 1.5 to 4.0).  of the pH range  The s h o r t e s t l a g time and maximum z i n c con-  c e n t r a t i o n s were o b t a i n e d when the pH was c o n t r o l l e d a t 2.0 and 2.5. Maximum z i n c c o n c e n t r a t i o n s experiments where pH was o r was n o t  differed  considerably  i n those  c o n t r o l l e d ( F i g u r e s 5 and 6 ) .  d i f f e r e n c e s , i . e . 20 t o 70 g/1, were a t t r i b u t e d almost e n t i r e l y  These  to the  d i f f e r e n t pulp d e n s i t i e s employed and not to the d i f f e r e n c e i n pH c o n t r o l . However, when pH was c o n t r o l l e d , t h e f i n a l  z i n c c o n c e n t r a t i o n and maximum  e x t r a c t i o n dropped o f f s h a r p l y a t pH v a l u e s 2.5 range.  above and below the 2.0 t o  No attempt was made to a s s e s s whether t h i s e f f e c t was on the  organism o r was due t o s u b s t r a t e m o d i f i c a t i o n o r both. The  r e l a t i o n s between pH and l a g time f o r both t h e i n i t i a l pH  runs and the c o n s t a n t lag  time o c c u r s  A d e f i n i t e minimum  a t around pH 2.3 f o r both s e t s o f d a t a .  somewhat sharper data.  pH runs a r e shown i n F i g u r e 7.  This value  f o r the i n i t i a l  pH d a t a  T h i s minimum i s  than f o r the c o n t r o l l e d pH  (pH = 2.3) i s i n good agreement w i t h  the optimum  Figures E F F E C T OF CONSTANT pH ON ZINC EXTRACTION 16% Pulp Density  70  pH.2.5^V  y'pH —  2.0  60  pH' 3.0 0= O  a a a  O ° 0=0  0 3  50 z  pH 3.5  o  Si o o o  40  o'  pH 4.0  30  o N  20  A ^ A ^ A ^ A ^ A " A  -  -j  pH 1.5  0 80  160 TIME  240 ( hr )  320  400  Figure EFFECT  0  1  OF  2  7  pH ON L A G  3  TIME  Table 4 E f f e c t s of constant  Lag  time  pH (hr)  Zinc  pH  extraction rate (mg/1 hr)  F i n a l zinc extraction  (g/D  1.5  116  99.2  19.8  2.0  12  369.6  70.3  2.5  12  375.9  71.4  3.0  42  373.7  54.1  3.5  93  326.8  49.3  4.0  154  255.1  36.4  50 * ^ r e p o r t e d by  pH's  i (16, o t h e r workers  m e t a l l i c s u l f i d e s and  72,  77,  f e r r o u s i r o n by T_.  122,  207)  , . f o r the o x i d a t i o n of  ferrooxidans.  T h i s minimum l a g time i s of some p r a c t i c a l s i g n i f i c a n c e s i n c e i n a commercial b a t c h , m i c r o b i o l o g i c a l l e a c h i n g of z i n c , s u f i d e the l a g time, which i s u n p r o d u c t i v e time, would be At and in  constant  pH measurements, the f i n a l z i n c  the z i n c e x t r a c t i o n r a t e s were much h i g h e r the i n i t i a l  pH measurements.  the i n c r e a s e i n s u b s t r a t e The of pH  on  being  able  The  improvements can be a t t r i b u t e d to  concentration  above d a t a  and  T^. f e r r o o x i d a n s .  concentrations  than those d e r i v e d  from 5 . 3  to 16% pulp d e n s i t i e s .  those of o t h e r s have shown the  importance  T h i s organism i s r e l a t i v e l y unique i n  to s u r v i v e at such low pH's.  T h i s f a c t i s of  economic s i g n i f i c a n c e because, u n l i k e many o t h e r does not  minimized.  considerable  fermentations, t h i s  r e q u i r e an expensive s t e r i l i z a t i o n of the medium p r i o r  one  to  inoculation. 3.  E f f e c t s of n u t r i e n t  concentrations  A study of the e f f e c t s of v a r i o u s  concentrations  of n u t r i e n t s  (37) in  the b a s a l medium  c e n t r a t i o n s was  on  performed u s i n g  m a i n t a i n e d at pH  2.3  and  ments were c a r r i e d out The on  z i n c e x t r a c t i o n r a t e s and  first  35°C.  f i n a l z i n c con-  z i n c s u l f i d e concentrate The  pulp d e n s i t y was  16%.  suspensions A l l experi-  in duplicate.  group of these experiments demonstrates the e f f e c t s  the l e a c h i n g a c t i v i t y of T[. f e r r o o x i d a n s  n u t r i e n t s from the b a s a l medium, which has  of the absence of c e r t a i n been d e s c r i b e d  i n Table  1.  These experiments were c a r r i e d out by withdrawing ammonium s u l f a t e , dipotassium  hydrogen phosphate, and  the r e s t of the n u t r i e n t components  51 (potassium c h l o r i d e , magnesium s u l f a t e , and l i q u i d medium^ ?) one  at a time.  3  T a b l e 4 of Appendix In the  rate  r e s u l t i n g d a t a are r e c o r d e d  final  zinc concentration  (351.7 mg/1  hr)  are  (69.5  g/1)  and  the  the d a t a t y p i f i e d by T a b l e 7E  and  zinc  of  1.  hydrogen phosphate from the b a s a l medium had the  concentration  a c t i v i t y of the and  bacterial activity nitrogen  in  comparable to those a c h i e v e d when  However, the absence of e i t h e r ammonium s u l f a t e or  e f f e c t on  the  1.  these s a l t s were p r e s e n t ; e.g., Appendix  from  absence of potassium c h l o r i d e , magnesium s u l f a t e  c a l c i u m n i t r a t e the extraction  The  calcium n i t r a t e )  and  These s m a l l  the  organism.  a considerable,  In both cases the  z i n c e x t r a c t i o n r a t e were reduced.  that d i d occur i n d i c a t e s  that small  inoculum which c o n s t i t u t e d The  e f f e c t s of the  of the  measured The  limited  with  of  the  s u s p e n s i o n volume.  c o n c e n t r a t i o n s of the n i t r o g e n  phosphorus s o u r c e s were i n v e s t i g a t e d  zinc  organism.  p r o b a b l y were s u p p l i e d  a p p r o x i m a t e l y 7%  deleterious  quantities  phosphorus must have been a v a i l a b l e to the  q u a n t i t i e s of n u t r i e n t s  dipotassium  and  f u r t h e r over a range encompassing  (37) 0 to 3.5  times the The  amounts c o n t a i n e d i n the b a s a l medium  d a t a on  the v a r i a t i o n of ammonium s u l f a t e c o n c e n t r a t i o n  g i v e n i n T a b l e 5 (A to C) of Appendix 1 and Ammonium s u l f a t e c o n c e n t r a t i o n zinc concentration.  had  I t s e f f e c t on  are graphed i n F i g u r e  i t s p r i n c i p a l e f f e c t on the  zinc extraction rate  the  8.  final  was  virtually negligible. In s t u d y i n g centration,  the  the  e f f e c t s of v a r i a t i o n s i n phosphate con-  inoculum was  grown on reduced phosphate l e v e l media  are  52  F i g u r e s E F F E C T O F AMMONIUM  CONCENTRATION  80(  ( N H ) S 0 g/1 3.75-10.50 4  70  2  4  .00  A — 0.75 J  0.00  150 TI M E  300  350  53 and was t r a n s f e r r e d twice b e f o r e i n o c u l a t i o n i n t o the l e a c h This s e r i e s of i n v e s t i g a t i o n s i n d i c a t e d that dipotassium a t e c o n c e n t r a t i o n had l i t t l e e f f e c t on the f i n a l d i d i n f l u e n c e the z i n c e x t r a c t i o n r a t e . by  the d a t a of T a b l e  suspension.  hydrogen phosph-  z i n c c o n c e n t r a t i o n but  These statements a r e supported  6 (A t o C) of Appendix 1 and F i g u r e 9. ( 3 7 )  S i n c e the make up of the b a s a l medium was p r e s e n t e d only l i m i t e d  i n f o r m a t i o n has been p u b l i s h e d c o n c e r n i n g  requirements  o f T_. f e r r o o x i d a n s .  the n u t r i t i o n a l requirements s u l f i d e minerals.  i n 1959  the n u t r i t i o n a l  S t u d i e s have not been undertaken on  of t h i s organism w h i l e l e a c h i n g z i n c  The d a t a summarized i n F i g u r e s 8 and 9 i n d i c a t e t h a t  the n u t r i e n t l e v e l s c a l l e d f o r i n the b a s a l medium (3 s u l f a t e and 0.5 g/1 of d i p o t a s s i u m The minor n u t r i e n t s (potassium  g/1 of ammonium  hydrogen phosphate) a r e adequate.  c h l o r i d e , magnesium s u l f a t e ,  calcium  n i t r a t e ) were r e q u i r e d by the organism i n such s m a l l q u a n t i t i e s t h a t any  requirement  beyond the amounts c o n t a i n e d  as i m p u r i t i e s i n the ammon-  ium  and phosphate s a l t s o r i n the z i n c c o n c e n t r a t e  c o u l d n o t be  demonstrated. S i m i l a r evidence dipotassium  f o r the e f f e c t s of ammonium s u l f a t e and  hydrogen phosphate has been found  f o r the o x i d a t i o n o f (208  c h a l c o p y r i t e by T_. f e r r o o x i d a n s i n the l a b o r a t o r i e s o f B. C. Research 4.  E f f e c t s o f pulp d e n s i t y ( s o l i d The  concentration)  i n f l u e n c e o f the i n i t i a l  pulp d e n s i t y or s o l i d s  concentra-  t i o n on the r a t e of z i n c e x t r a c t i o n has been s t u d i e d over a range of 1 t o 26.6%.  A l l experiments were d u p l i c a t e d and s t e r i l e c o n t r o l s were  maintained  i n almost a l l c a s e s .  No e f f o r t was made i n t h i s s e r i e s of  experiments to determine the change i n pulp d e n s i t y d u r i n g the course -  Figure EFFECT  OF P H O S P H A T E  9 CONCENTRATION  400  0.4 INITIAL  0.8 K HP0 2  4  1.2 1.6 CONCENTRATION  2.0 (g / I )  55 of a l e a c h . and  pH  2.3  The  r e s u l t s of these experiments which were run a t 35°C  are p r e s e n t e d i n T a b l e 7 (A to G)  of Appendix 1.  T a b l e 7R of  Appendix 1 p r o v i d e s some d a t a on a s e r i e s of l e a c h e s done by the speed of the g y r a t o r y No  incubator  from the  s t e r i l e c o n t r o l s were run w i t h the The  s t a n d a r d 280  latter  increasing  to 400  rpm.  set.  r a t e s of z i n c e x t r a c t i o n c a l c u l a t e d from the  averaged  d a t a from the d u p l i c a t e runs are p l o t t e d v e r s u s p u l p d e n s i t i e s i n . Figure  10.  As  can be  seen z i n c e x t r a c t i o n r a t e s i n c r e a s e w i t h  ing pulp d e n s i t y  up  to about 16%.  d e n s i t i e s of 13%  i s marginal.  At  The low  tion rate i s d i r e c t l y proportional taper  improvement i n r a t e above pulp pulp d e n s i t i e s the  to the p u l p d e n s i t y  o f f at higher pulp d e n s i t i e s .  increas-  At  still  zinc  but  extrac-  tends  h i g h e r v a l u e s the  to extraction  rate decreases. At  low  doubt l i m i t e d by  s o l i d s concentration  the e x t r a c t i o n r a t e of z i n c i s no  the amount of s u b s t r a t e  (ZnS)  r a t e of growth of the organism i s l i m i t e d by energy s o u r c e . s o u r c e and  by  are assuming i s p r o p o r t i o n a l  That i s , the  the a v a i l a b i l i t y of i t s  At higher pulp d e n s i t i e s there  the r a t e bf organism growth and  r a t e , which we  available.  i s a s u r f e i t of  hence the  zinc  energy  extraction  to growth, becomes l i m i t e d  some o t h e r f a c t o r . If  t h i s o t h e r l i m i t i n g f a c t o r were the mass t r a n s f e r  from a i r to the l e a c h s o l u t i o n of the g a s e s ( c a r b o n d i o x i d e which the organism r e q u i r e s shaker speed would i n c r e a s e degree of a g i t a t i o n . r e s u l t s and  the  one  and  rates oxygen)  would a n t i c i p a t e t h a t i n c r e a s i n g  the mass t r a n s f e r r a t e due  However, t h i s d i d not  tentative conclusion  was  to an  the  increased  produce markedly d i f f e r e n t  reached t h a t such mass  56  Figure  10  OF P U L P  400i  DENSITY  ~T O  t 300  E  LU  200 o  fo <  cc X UJ o  2  o  Normal Shaker Speed ( 2 8 0 r p r n )  •  Increased Shaker Speed ( 4 0 0 r p m )  1001  N  i  0  J.  10 15 20 PULP DENSITY (g x 100 /ml )  25  30  57 transfer was not limiting.  It should be noted that these experiments  were done before those reported in the previous section on nutrient requirements.  When i t became evident that under these conditions  nutrient concentrations were not limiting, further work on carbon dioxide requirements was begun.  This i s repotted in section 6 of this work.  The decline in extraction rate at high pulp densities probably can be attributed to the interference of the solids with the mass transfer of oxygen or carbon dioxide to the organism. At 16 - 20% solids the zinc extraction rates were highest (ca 350 mg/1 hr) implying that i f the i n i t i a l pulp density were 16% or greater that pulp density would not be rate limiting.  The final zinc  concentrations achieved were of the order of 50 to 70 g/1 for pulp densities ranging from 16 to 26.6%. !  Behaviour  of the organism at high i n i t i a l zinc concentrations  was studied by adding fresh quantities of the solid substrate (ZnS concentrate) to liquors decanted from the leaches already carried out at 18 and 20% pulp density.  In other words leaches were done at i n i t i a l  pulp densities of 18 and 20%.  When extraction ceased the liquors were  separated from the leached solids and new solids added.  The zinc  concentrations after the f i r s t leach were 70.1 g/1 for the 18% suspension and 70.6 g/1 for the 20% one.  The data given in Table 5 show that these  concentrations increased to 91.9 g/1 and 90.8 g/1 respectively during the second extraction. These concentrations, as w i l l subsequently be shown, do not represent the maximum tolerance toward zinc of this organism. These high zinc concentrations approach those used in direct recovery of zinc from solution by electrowinning.  Thus a new possibility for  Table 5 E f f e c t o f pulp d e n s i t y and z i n c  Time (hr)  concentration  ZINC EXTRACTIONS (g/1) Pulp  density 18%  Pulp  density 20%  0  66.1  64.2  22  66.4  64.8  45  67.6  73.6  68  78.2  80.3  92  89.5  84.5  102  91.6  89.3  117  91.7  90.3  127  91.9  90.8  59 h y d r o m e t a l l u r g i c a l e x t r a c t i o n has been demonstrated which i n v o l v e s a m i c r o b i o l o g i c a l treatment sulfide 5.  i n the r e c o v e r y of z i n c from a high-grade  concentrate.  E f f e c t s of i n i t i a l In  leaching  p a r t i c l e diameter  and s p e c i f i c s u r f a c e area  t h i s s e c t i o n of t h i s work we c o n s i d e r the e f f e c t s on  of the p a r t i c l e s i z e and s p e c i f i c  zinc s u l f i d e concentrate.  s u r f a c e a r e a of the s o l i d  P a r t i c l e s of a v a r i e t y of s i z e s and s p e c i f i c  s u r f a c e areas were o b t a i n e d from by wet  zinc  the u n f r a c t i o n a t e d s u b s i e v e  concentrate  ( C y c l o s i z e r ) and d r y ( B a h c o - s i z e r ) s e p a r a t i o n t e c h n i q u e s .  s e c t i o n V. 3.1 . s t e r i l e controls.  A l l experiments  were c a r r i e d out i n d u p l i c a t e w i t h  The l e a c h suspensions were m a i n t a i n e d  and had a p u l p d e n s i t y of 16%.  See  a t pH 2.3, 35°C  The l e a c h i n g d a t a o b t a i n e d w i t h the  C y c l o s i z e r f r a c t i o n s a r e g i v e n i n T a b l e 8 (A to C) of Appendix 1 and those o b t a i n e d w i t h the B a h c o - s i z e r f r a c t i o n s i n T a b l e 9 (A to D) of t h a t Appendix.  Note t h a t w i t h the C y c l o s i z e r f r a c t i o n s and w i t h the f i r s t  f o u r B a h c o - s i z e r f r a c t i o n s the l a g time was abnormally be a t t r i b u t e d  long.  T h i s can  to the u s e of an o l d inoculum which r e q u i r e d a p r o l o n g e d  p e r i o d of time f o r a d a p t a t i o n . T a b l e 6 summarizes the e f f e c t s of the s u b s i e v e f r a c t i o n s on the m i c r o b i o l o g i c a l z i n c e x t r a c t i o n s u s i n g normal a i r f o r a e r a t i o n .  The  f i n a l z i n c c o n c e n t r a t i o n s of both the i n o c u l a t e d samples and the s t e r i l e c o n t r o l s as w e l l as the z i n c e x t r a c t i o n r a t e s were s t r o n g l y dependent on the s p e c i f i c s u r f a c e a r e a o r the p a r t i c l e  size.  Table 6 also includes  d a t a taken from T a b l e 7E of Appendix 1 which were o b t a i n e d u s i n g the u n f r a c t i o n a t e d -400 mesh z i n c s u l f i d e c o n c e n t r a t e a l s o h a v i n g a p u l p d e n s i t y of 16%.  60 As  p a r t i c l e s i z e decreased and  the amount of z i n c s o l u b i l i z e d i n the surface thus the  a r e a of these p a r t i c l e s may f i n e r f r a c t i o n s may  o x i d e which d i s s o l v e d  due  s p e c i f i c surface  s t e r i l e controls  10.9  g/1  f o r the  increased.  The and  have c o n t a i n e d l a r g e r q u a n t i t i e s of  to the a c t i o n of s u l f u r i c a c i d .  finest Cyclosizer  s i z e f r a c t i o n r e s p e c t i v e l y ) may e f f e c t but  increased  have been p a r t i a l l y o x i d i z e d  r e l a t i v e l y h i g h z i n c c o n c e n t r a t i o n s i n the and  area  be  p o s s i b l y a l s o to an  s t e r i l e controls  s i z e f r a c t i o n and  a t t r i b u t e d not  increased  T  only  n e r e  zinc  f° e»  the  r  (e.g.,  2.49  Bahco-sizer  to the  size  amount of a i r o x i d a t i o n  of  the  finer particles. Figure and  uniformity  The  coarsest  11 and  of  the  12 are photographs showing the  Cyclosizer  size fraction (CS.  i n such s m a l l  quantities  that  relative size .  and  Bahco-sizer f r a c t i o n s  No.  6) from the  i t was  not  respectively.  C y c l o s i z e r was  used i n b a c t e r i a l  obtained  leaching  experiments. D e s p i t e the d i f f e r e n t t e c h n i q u e s used i n d e t e r m i n i n g p a r t i c l e d i a m e t e r s of  the C y c l o s i z e r  good agreement between the  two  f r a c t i o n s , Table 6  techniques.  the  indicates  These t e c h n i q u e s were m i c r o (209)  s c o p i c measurement and The  the method d e s c r i b e d  i n the  C y c l o s i z e r Manual  p a r t i c l e s i z e s of the B a h c o - s i z e r f r a c t i o n s were measured by  scope.  The  m i c r o s c o p i c measurements f o r b o t h s e t s of p a r t i c l e s are  the ones used  subsequently.  Figure microbiological  13 demonstrates the zinc extraction  rate.  d a t a which suggests a l o g a r i t h m i c logarithmic  micro-  e f f e c t of p a r t i c l e s i z e on Figure  13A  relationship.  r e l a t i o n which i s of the  form  i s a p l o t of Figure  13B  the the  shows t h i s  Table 6 Effect  of s u b s i e v e  fractions  •  FINAL ZINC CONCENTRATION  Zinc extraction rate  Specific surface area  In S t e r i l e  (mg/1 hr)  (m /g)  (g/D  Sample  In presence of b a c t e r i a  2  MEAN PARTICLE DIAMETER (micron) Microscopic Measur.  Cyclosizer Manual  8.9 12.2 18.6 26.7  C.S.* No. 1 2 3 4 5  70.1 63.1 51.8 37.4 33.0  2.49 1.32 1.16 0.97 0.86  496.2 359.8 263.6 204.3 158.0  6.04 1.20 0.66 0.55 0.45  3.5 8.8 12.6 19.1 25.6  B.S.* No. 1 2 3 4 5 6 7 8  72.8 70.0 65.4 61.3 53.0 46.0 38.9 27.7  10.9 8.9 4.24 3.21 2.74 0.84 1.02 1.27  516.8 484.2 446.2 349.3 ' 274.3 173.1 132.7 73.4  6.90 4.11 2.85 1.25 0.73 0.47 0.39 0.29  2.2 3.6 5.4 9.0 13.6 21.7 27.8 39.9 . •  -400 mesh  1.20  63.7  *  C.S.  =  1.37 .  343.3  Cyclosizer fraction;  B.S.  =  Bahco-sizer  fraction  FIGURE 11  C Y C L O S I Z E R  F R A C T I O N S  62  FIGURE 12  B A H C O - S I Z E R  63  F R A C T I O N S  64  V  v  =  where  m  x exp (K x d)  V  =  z i n c e x t r a c t i o n r a t e (mg/1 h r ) ;  V  =  maximum z i n c e x t r a c t i o n r a t e (mg/1 h r ) ;  m  K  =  constant;  d  =. p a r t i c l e diameter  L e a s t squares f i t t i n g  InV  As  =  (29)  6.34  -  5.24  (micron).  of the d a t a p a i r s r e s u l t e d i n  10~ x d  (30) .  2  x  the p a r t i c l e diameter tends t o zero the s o l i d  s u b s t r a t e would become  so f i n e l y d i v i d e d t h a t i t would approach m o l e c u l a r be c o n s i d e r e d  t o be i n s o l u t i o n .  I f t h i s were s  0  dimensions which c o u l d one would expect  then  t h a t as d goes to zero the maximum e x t r a c t i o n r a t e would be o b t a i n e d . Following  t h i s l i n e of reasoning  the maximum e x t r a c t i o n r a t e was found  f r o m . e q u a t i o n 30 to be 569 mg/1 h r .  Thus, whereas f o r maximum e x t r a c -  t i o n r a t e s the o r e should be ground as f i n e l y as p o s s i b l e , commercially t h i s would have to be balanced The  against  the i n c r e a s e d c o s t s of g r i n d i n g .  z i n c e x t r a c t i o n r a t e data of Table  F i g u r e 14 t h i s time u s i n g  the i n i t i a l  specific  6 are replotted i n  s u r f a c e area of the  d i f f e r e n t s i z e f r a c t i o n s as the dependent v a r i a b l e . point representing  Also plotted i s a  the u n f r a c t i o n a t e d s u b s i e v e m a t e r i a l .  The curve of  F i g u r e ' 14 suggests t h a t where s p e c i f i c s u r f a c e i s low(with  large  p a r t i c l e s ) the e x t r a c t i o n r a t e i s l i m i t e d by the a v a i l a b i l i t y o f s u r f a c e . The  b a c t e r i a must c o n t a c t  effect  the s u r f a c e of the s o l i d m i n e r a l p a r t i c l e t o  the s o l u b i l i z a t i o n o f z i n c and i f o n l y so much s u r f a c e i s a v a i l a b l e  65 it  can be the r a t e l i m i t i n g f a c t o r .  the r a t e tends toward, a c o n s t a n t f a c t o r has become r a t e l i m i t i n g .  At higher  value,  values  suggesting  of s p e c i f i c  surface  t h a t some o t h e r  Thus these experiments c a r r i e d out on  the s i z e d f r a c t i o n s of the s u b s i e v e  zinc s u l f i d e concentrate  have been  a b l e t o demonstrate the e f f e c t s of p a r t i c l e diameter and s p e c i f i c s u r f a c e a r e a on m i c r o b i o l o g i c a l l e a c h i n g r a t e s which were p r e d i c t e d by v ( 7 , 16, 27,46) a number o f i n v e s t i g a t o r s These data  relating particle specific  r a t e complement those o b t a i n e d extraction rate  i n the pulp  (V) i s p l o t t e d a g a i n s t  surface  to l e a c h i n g  d e n s i t y experiments.  initial  I f zinc  t o t a l s u r f a c e a r e a of  s o l i d s per u n i t volume of l i q u i d medium ( T S A ) the c u r v e s from the pulp d e n s i t y v a r i a t i o n experiments and from the p a r t i c l e s i z e v a r i a t i o n experiments c o i n c i d e i n the r e g i o n of low a r e a per u n i t volume. i s a t low pulp surface that  d e n s i t i e s or f o r p a r t i c l e s h a v i n g low v a l u e s  the curves o v e r l a p  as evidenced by F i g u r e 15.  the t r u e r a t e l i m i t i n g f a c t o r a s s o c i a t e d w i t h  That  of s p e c i f i c  Thus i t appears  the energy  source  ( z i n c s u l f i d e ) i s the amount o f s u r f a c e a r e a a v a i l a b l e per u n i t volume of l e a c h s o l u t i o n .  The organisms cannot a t t a c k  i n t e r i o r o f the c o n c e n t r a t e Increasing surface the  the pulp  particle until  density  i n the  the outer m a t e r i a l i s d i s s o l v e d .  puts more p a r t i c l e mass of f i x e d  specific  ( s u r f a c e a r e a p e r u n i t mass) i n t o a u n i t volume thus i n c r e a s i n g  t o t a l available surface.  Increasing  p u t s the same p a r t i c l e mass w i t h volume, a g a i n of pulp  the s u b s t r a t e  increasing specific  i n c r e a s i n g the t o t a l a v a i l a b l e s u r f a c e .  d e n s i t y other  i n s e c t i o n 4.  the p a r t i c l e s p e c i f i c surface  surface  into a unit  At higher  values  f a c t o r s become r a t e l i m i t i n g as p r e v i o u s l y mentioned  "Figure  13 •  E F F E C T OF PARTICLE (UNDER N O R M A L AERATION)  I  SIZE CONDITIONS  i  1  SECTION  A  600  LU CC  2 1* 4 0 0  I— -c O <  or  \  *  E  ° +  \  Cyclosizer Fractions Bahco F r a c t i o n s  V V= V  m  exp ( K x d )  200  o  N  0  I  I  | SECTION  B  —  4  1  0  10 PARTICLE  1  20  1  30  DIAMETER = d  L  40  (microns)  50  67  Figure  14  E F F E C T OF S P E C I F I C S U R F A C E A R E A  600  £400 LLI  !S 2  o  1— o  2 200 L  o  4  rX Ul  u 2 N  O  4  I  o  Cyclosizer Fractions  .+  Bahco-sizer Fractions  •  - 4 0 0 Mesh Z n S (Unf ractionated)  +  J_ 2 SPECIFIC  3 SURFACE  4 AREA  5 (rn /g ) 2  68  Figure  15  E F F E C T OF T O T A L S U R F A C E A R E A O F SOLID  600  500  •400  Cft  E  §300 z o  BY C H A N G I N G P A R T I C L E  \-  x  o < £ 200 x UJ  Bahco-sizer Cyclosizer  BY C H A N G I N G S O L I D S  o ®  o 2 N  SIZE  CONCENTRATION  Standard Conditions Increased A g i t a t i o n  100  o  /  o  0.3  0.6  T O T A L SURFACE AREA  0.9 (m /cm ) 2  3  1.2  69 No s i g n i f i c a n t d i f f e r e n c e s were observed between the e f f e c t s of the wet and d r y c l a s s i f i e d rate.  Also  subsieve  f r a c t i o n s on the z i n c e x t r a c t i o n  the u n f r a c t i o n a t e d m a t e r i a l showed s i m i l a r  the s i z e d f r a c t i o n s when compared on a s p e c i f i c s u r f a c e per u n i t volume b a s i s .  s u r f a c e or t o t a l  The maximum z i n c e x t r a c t i o n r a t e s  observed were about 517 mg/1 hr which was o b t a i n e d having  behaviour to  the l a r g e s t s p e c i f i c s u r f a c e .  with  the f r a c t i o n  E x t r a p o l a t i o n of the r a t e -  p a r t i c l e diameter curve suggested a maximum r a t e of about 570 mg/1 h r . 6.  E f f e c t s of carbon d i o x i d e In order  concentration  t o f u r t h e r d e l i n e a t e the r a t e l i m i t i n g  factors i n zinc  e x t r a c t i o n a s e r i e s of experiments was c a r r i e d out a e r a t i n g the l e a c h suspensions with dioxide;  a i r c o n t a i n i n g a v a r i e t y of c o n c e n t r a t i o n s  the s o l e carbon source f o r T_. f e r r o o x i d a n s .  of carbon  These experiments  were d u p l i c a t e d and were done a t 35°C and pH 2.3 on l e a c h s u s p e n s i o n s w i t h v a r i o u s pulp d e n s i t i e s i n the range 5.3 to 26.6%. concentrations  i n the a i r s u p p l i e d  to the e n c l o s e d ,  The carbon  thermostated,  dioxide gyratory  shaker were c o n t r o l l e d a t between 0.13 and 7.92 volume per c e n t . The given pulp The  i n Table  experimental  data obtained  a t 7.92% carbon d i o x i d e a r e  10 (A and B) of Appendix 1.  The 16, 18, 20 and 24%  d e n s i t y experiments were done i n d u p l i c a t e w i t h r e s u l t s obtained  e f f e c t of i n c r e a s e d  with  the s t e r i l e  s t e r i l e controls.  c o n t r o l s showed no s i g n i f i c a n t  carbon d i o x i d e l e v e l  (7.92%) on the z i n c e x t r a c t i o n  i n the c o n t r o l s , as can be seen by comparison o f r e s u l t s t o those obtained  w i t h normal a i r (0.03% carbon d i o x i d e ) , i . e . , i n T a b l e  7 (A t o  G) o f Appendix 1. The  e f f e c t s of pulp d e n s i t y on z i n c e x t r a c t i o n r a t e a t the  70 different  carbon d i o x i d e l e v e l s  a r e summarized i n T a b l e study  7.  [ T a b l e 10 to 13 (A and B) of Appendix 1]  T h i s t a b l e a l s o i n c l u d e s the pulp  r e s u l t s under normal a e r a t i o n c o n d i t i o n s ; transposed  density  from F i g u r e 10.  A t carbon d i o x i d e l e v e l s o f 7.92%, 1.03% and 0.23% the z i n c e x t r a c t i o n rates are v i r t u a l l y  identical,  indicating  c e n t r a t i o n of 0.23% i n a i r i s s u f f i c i e n t rate. with about  t h a t a carbon d i o x i d e  to i n s u r e a maximum e x t r a c t i o n  The h i g h e s t e x t r a c t i o n r a t e (about  640  mg/1 h r ) was o b t a i n e d  l e a c h s u s p e n s i o n s of 24 and 26.6% pulp d e n s i t i e s . 280 mg/1 h r h i g h e r than o b t a i n e d  (360 mg/1 h r ) . were s l i g h t l y  con-  This value i s  under normal a e r a t i o n c o n d i t i o n s  A t 0.13% carbon d i o x i d e the maximum z i n c e x t r a c t i o n r a t e s inferior  concentrations.  to those maxima o b t a i n e d  at higher  carbon d i o x i d e  For t h i s experiment the maximum r a t e was 570 mg/1 hr  o b t a i n e d w i t h pulp d e n s i t i e s of 24 and 26.6%. These d a t a a r e p r e s e n t e d e x t r a c t i o n rate versus  p u l p d e n s i t y curve  d e n s i t i e s of about 22%. suggesting  g r a p h i c a l l y i n F i g u r e 16. . The z i n c  Atf h i g h e r pulp d e n s i t i e s t h i s r a t e l e v e l s out  t h a t pulp d e n s i t y i s no l o n g e r  carbon d i o x i d e e n r i c h e d  i n c r e a s e s l i n e a r l y up to pulp  limiting.  with  a i r the l i n e a r p o r t i o n of the p l o t extends past  the l i n e a r p o r t i o n o f the z i n c e x t r a c t i o n r a t e v e r s u s was o b t a i n e d  Note t h a t  w i t h normal a i r ( F i g u r e 10).  pulp d e n s i t y which  T h i s suggests t h a t i n F i g u r e  10 the carbon d i o x i d e c o n c e n t r a t i o n was the l i m i t i n g  f a c t o r f o r pulp  d e n s i t i e s above 12%. A l e a s t squares f i t o f the l i n e a r p a r t of F i g u r e 16 (pulp d e n s i t i e s up t o 20%) gave  V  =  30.0  x  PD  -  30.6  (31)  71  : Table 7 Effect  of pulp d e n s i t y a t d i f f e r e n t  00  pressures  ZINC EXTRACTION RATE (mg/1 hr)  Pulp Density  carbon, d i o x i d e p a r t i a l  7.92% C 0  2  1.03% C 0  2  0.23% C 0  2  0.13% C 0  2  0.03% C 0  141.3  133.9  118.5  107.6  121.0  12  355.1  339.8  339.4  331.3  312.5  14  383.0  405.2  399.7  414.3  335.4  16  438.8  438.5  439.8  444.2  343.3  18  488.1  513.3  496.5  490.7  364.3  20  577.8  574.6  589.0  549.0  353.4  24  640.8  644.4  636.0  576.2  327.5  26.6  640.6  636.9  636.5  563.6  297.1  5.3  2  72  Pi g u f e  IS  E F F E C T OF P U L P DENSITY AT D I F F E R E N T CARBON DIOXIDE PARTIAL  PRESSURES  700  8 PULP  12 DENSITY  16 20 ( g x 100 / m l )  where V PD The  =  z i n c e x t r a c t i o n r a t e (mg/1 h r ) ;  =  pulp d e n s i t y i n  negative  real,  73  %.  e x t r a c t i o n rate obtained  at very  low pulp d e n s i t i e s i s not  i s of d o u b t f u l s i g n i f i c a n c e and p r o b a b l y  error.  i s due to  '  experimental  -  At the h i g h e s t v a l u e s of pulp d e n s i t y the i n t r i n s i c r a t e of the r e a c t i o n expressed i n t e r f e r e with oxygen.  by e q u a t i o n  7 may be l i m i t i n g or the s o l i d s may  the r a t e of mass t r a n s f e r of carbon d i o x i d e or even  The carbon d i o x i d e content  not i n the l i q u i d phase.  was measured o n l y i n the gas phase,  However, i t i s r e a s o n a b l e  gas phase c o n c e n t r a t i o n i s r a i s e d , o t h e r  to assume t h a t i f the  t h i n g s b e i n g e q u a l , the l i q u i d  phase c o n c e n t r a t i o n a l s o w i l l be i n c r e a s e d .  Mass t r a n s f e r r a t e s were  not measured. F i g u r e 17 i s a c r o s s p l o t of the d a t a g i v e n  i n Table  7 where  z i n c e x t r a c t i o n r a t e i s p l o t t e d a g a i n s t carbon d i o x i d e c o n c e n t r a t i o n pulp d e n s i t y as a parameter.  The pulp d e n s i t y or s u b s t r a t e  concentration  a f f e c t s the l e v e l a t which s l o p e of the e x t r a c t i o n r a t e curve zero.  with  approaches  The l a t t e r l e v e l r i s e s as the pulp d e n s i t y increased, up to pulp  d e n s i t i e s of 24%. 7.  E f f e c t s of i n i t i a l p a r t i c l e diameter and s u r f a c e area a t carbon d i o x i d e I n view of the d a t a  1.0%  observed f o r l e a c h i n g r a t e s w i t h  carbon d i o x i d e l e v e l s the e f f e c t s of p a r t i c l e s i z e and s p e c i f i c a r e a on l e a c h i n g r a t e s were reexamined a t an i n c r e a s e d  increased surface  concentration  (1.0%) of carbon d i o x i d e i n a i r . A l l of these experiments were done i n s i n g l e runs i n 16% pulp d e n s i t y l e a c h suspensions subsieve 2.3  concentrate  f r a c t i o n s described  and the temperature 35°C.  u s i n g the v a r i o u s  i n s e c t i o n 5.  The r e s u l t s a r e p r e s e n t e d  A g a i n the pH was i n Tables  14  74  Figure EFFECT  17  OF C A R B O N DIOXIDE P A R T I A L P R E S S U R E S AT D I F F E R E N T P U L P D E N S I T I E S  CARBON DIOXIDE IN VOLUME  PERCENT  (A and  B)  of Appendix 1. Table  unfractionated  75  8 summarizes the e f f e c t s of the v a r i o u s f r a c t i o n s and ore c o n c e n t r a t e  on  the m i c r o b i o l o g i c a l z i n c e x t r a c t i o n  r a t e ; both under normal a e r a t i o n and  under a e r a t i o n w i t h carbon  enriched  air.  i n Table  smallest  size particles  The  dioxide enriched air.  r e s u l t s presented  a e r a t i o n was  8 i n d i c a t e that f o r  the z i n c e x t r a c t i o n r a t e s o b t a i n e d  a i r were more than double those o b t a i n e d  Thus f o r example, the h i g h e s t 516.8  mg/1  dioxide  with  the  carbon  u s i n g normal  z i n c e x t r a c t i o n r a t e under normal  hr o b t a i n e d  with  the f r a c t i o n having  the  2 highest  s p e c i f i c surface area  a e r a t i o n contained  (6.90  m /g) whereas when the a i r used f o r  1% carbon d i o x i d e  to an e x t r a c t i o n r a t e of 1,152.3 mg/1 lower s p e c i f i c able  t h i s same s i z e f r a c t i o n gave r i s e hr.  With the p a r t i c l e s i z e s  s u r f a c e a r e a s the i n c r e a s e s  to i n c r e a s e d  availability  in extraction rate  attribut-  of carbon d i o x i d e became m a r g i n a l .  these c o n d i t i o n s the a v a i l a b i l i t y of s u r f a c e i s r a t e l i m i t i n g  having  Under  rather  than the a v a i l a b i l i t y of carbon d i o x i d e . The with  p l o t of z i n c e x t r a c t i o n r a t e a g a i n s t p a r t i c l e  carbon d i o x i d e e n r i c h e d  shows t h a t i n i t i a l l y  the  a i r , i s given  13B  a semilog  s u b s e q u e n t l y more s l o w l y .  p l o t of these d a t a ,  does not produce a s t r a i g h t l i n e . obtainable  Figure  18A  z i n c e x t r a c t i o n r a t e decreases r a p i d l y with  i n c r e a s e i n p a r t i c l e diameter and Figure  i n F i g u r e 18.  diameter,  Unlike  as can be seen from F i g u r e  p a r t i c l e s i z e p l o t to zero p a r t i c l e diameter o n l y those d a t a  versus  for  p a r t i c l e diameters l e s s than 10 microns were used. T h i s p a r t of the by  the f o l l o w i n g  18B,  In an attempt to p r e d i c t a maximum  e x t r a c t i o n r a t e by e x t r a p o l a t i n g the e x t r a c t i o n r a t e  c o u l d be d e s c r i b e d  an  equation.  curve  76  Table 8 E f f e c t of s u b s i e v e  fractions  -—>——  Sample  Particle Diameter (micron)  Specific Surface area (m /g) 2  ZINC EXTRACTION (mg/1 h r ) 0.03% C 0  2  RATE  1.0%  co  2  C.S. No. 1 2 3 4 5  3.5 8.8 12.6 19.1 25.6  6.04 1.20' 0.66 0.55 0.45  ' 496.2 359.8 263.6 204.3 158.0  1,115.5 441.9 268.7 198.6 170.2  B.S. No. 1 2 3 4 5 6 7 8  2.2 3.6 5.4 9.0 13.6 21.7 27.8 39.9  6.90 4.11 2.85 1.25 0.73 0.47 0.39 0.29  516.8 • 484.2 446.2 439.3 274.3 173.1 132.7 73.4  1,152.3 1,068.3 989.8 460.9 271.6 184.1 157.6 107.0  1.37  343.3  438.5  -400 mesh  .  Figure AT  1.0%  18  E F F E C T OF P A R T I C L E S I Z E C A R B O N DIOXIDE P A R T I A L T  i  1200  ; f SECTION  ;SURI  A  1000 v. cn  E  800  > UJ  o Cyclosizer Fractions X Bah co Fractions  600  <  cc Z O  h-  O <  400  CC  H X Ul o 200 N  ,  > w  c  6  10 PARTICLE  20  .  30  DIAMETER = cl  40 (microns)  50  78 ln V  =7.52  -  (32)  0.152 x d  T h i s l e a d s t o a maximum e x t r a c t i o n r a t e of V  =  1,840 mg/1 h r .  m Because of the l i m i t a t i o n s imposed on the e x t r a p o l a t i o n t h i s f i g u r e i s o n l y to be c o n s i d e r e d mately air  as a v e r y rough e s t i m a t e .  t h r e e times the e s t i m a t e  Note t h a t i t i s a p p r o x i  made p r e v i o u s l y ( s e c t i o n 5) f o r normal  conditions. F i g u r e 19 p r e s e n t s  specific  z i n c e x t r a c t i o n r a t e as  s u r f a c e area of the o r e c o n c e n t r a t e  carbon d i o x i d e e n r i c h e d  a i r conditions.  a f u n c t i o n of  p a r t i c l e s under normal and  Where carbon d i o x i d e  enriched  a i r has been used the z i n c e x t r a c t i o n r a t e i s p r o p o r t i o n a l t o the s p e c i f 2 s u r f a c e , f o r v a l u e s below 2.5 m /g. F u r t h e r i n c r e a s e s i n s u r f a c e a r e a become l e s s , and l e s s e f f e c t i v e i n i n c r e a s i n g the e x t r a c t i o n r a t e . normal a e r a t i o n the p r o p o r t i o n a l i t y h o l d s  o n l y up to s p e c i f i c  For  surfaces  2 of around 0.75 m /g.  A l s o F i g u r e 19 shows c l e a r l y  s p e c i f i c s u r f a c e range the r a t e s i n e n r i c h e d those  t h a t i n the h i g h  a i r a r e more than double  observed i n normal a i r . Figure  20 i s the curve  of zinc e x t r a c t i o n rate versus  s u r f a c e a r e a p e r u n i t volume o f l i q u i d medium. the data o b t a i n e d  with  1.03% carbon d i o x i d e e n r i c h e d  of pulp d e n s i t y and by u s i n g p a r t i c l e s having surface areas.  This plot  total  indicates a l l  a i r by v a r i a t i o n  a v a r i e t y of s p e c i f i c  The v a r i o u s d a t a p o i n t s f i t w e l l onto a s i n g l e curve  save f o r those p o i n t s o b t a i n e d  a t h i g h pulp d e n s i t i e s where some i n t e r -  f e r e n c e w i t h mass t r a n s f e r has been p o s t u l a t e d . 8.  Larger  s c a l e experiments All  o f the p r e v i o u s l y d i s c u s s e d  experiments were c a r r i e d out  79  Figure  19  E F F E C T OF SPECIFIC SURFACE A R E A A f 1.0% CARBON DIOXIDE  SPECIFIC  SURFACE  AREA  (m /g ) 2  80  Figure  20  E F F E C T OF T O T A L S U R F A C E A R E A OF S I Z E F R A C T I O N S AT 1.0% C 0  l  0  _  _  i  0.2  i  I  0.4 0.6 TOTAL SURFACE AREA  l  0.8 (m /cm ) 2  3  2  l  1.0  1.2  i n Erlenmeyer procedure  f l a s k s on a g y r a t o r y shaker.  As a p r e l i m i n a r y s c a l e - u p  to a p o t e n t i a l l y commercial-sized i n s t a l l a t i o n some e x p e r i -  ments were undertaken suspension.  in stirred  tanks, w i t h much l a r g e r volumes of  These were undertaken  to a s c e r t a i n the r e l e v a n c e of d a t a  o b t a i n e d i n shake f l a s k s f o r s c a l e - u p purposes.  These l a r g e s c a l e  l e a c h e s were done a t a pulp d e n s i t y of 24% u s i n g u n f r a c t i o n e d -400 c o n c e n t r a t e a t pH 2.3, The suspension  first  35°C and w i t h carbon d i o x i d e e n r i c h e d a i r ( 1 % ) .  experiment  d a t a o b t a i n e d are p r e s e n t e d  636.9 mg/1 the f i n a l was  was  i n an u n b a f f l e d tank.  t i o n r a t e was  calculated  hr found  done w i t h 30 l i t e r s of l e a c h The  pH was  c o n t r o l l e d manually.  i n T a b l e 2 of Appendix 2.  to be 635.3 mg/1  The  s i g n i f i c a n t l y g r e a t e r than Another experiment  hr i n good agreement w i t h  i n the s t i r r e d  t h a t observed  was  tank  i n the shake f l a s k  done i n a b a f f l e d , s t i r r e d 2.3,  w i t h automatic  The  i n T a b l e 3 of  Appendix 2. agreed  The  z i n c e x t r a c t i o n r a t e observed  w e l l w i t h the shake f l a s k  z i n c c o n c e n t r a t i o n was observed unbaffled  measured as 119.8  i n the u n b a f f l e d tank. tanks are minimal.  d i f f e r e n t but  t h i s was  These f i n a l t h i s work and c u r r e n t l y used  g/1  (70.4  35°C, 1% CO  (651.4 mg/1  r e s u l t . (636.9 mg/1  g/1)  tank u s i n g  (24% pulp d e n s i t y , pH r e s u l t s are noted  the  However,  (112.2  12 l i t e r s of ore s u s p e n s i o n control.  The  zinc extrac-  f o r s i m i l a r c o n d i t i o n s i n the shake f l a s k .  z i n c c o n c e n t r a t i o n observed  pH  mesh  hr)  hr).  )  again  The  final  s l i g h t l y s u p e r i o r to t h a t  The d i f f e r e n c e s between b a f f l e d  A g i t a t o r power consumption might  and  be  not measured. z i n c c o n c e n t r a t i o n s a r e the h i g h e s t observed  are i n the range of z i n c c o n c e n t r a t i o n s (80 - 160 i n .the commercial e l e c t r o w i n n i n g of z i n c from  in  g/1)  solution.  g/1).  Samples of the l e a c h l i q u o r s have been sent to Cominco L t d . f o r e v a l u a t i o n of t h e i r s u i t a b i l i t y  for electrowinning.  or y i e l d s i n the u n b a f f l e d and b a f f l e d and  82.1%  respectively.  stirred  The  32  zinc recoveries  tank l e a c h e s were  76.9  R e s u l t s o b t a i n e d by Cominco L t d . i n d i c a t e d  s a t i s f a c t o r y q u a l i t y of cathode  z i n c , produced  a f t e r pretreatment  a  to  remove i r o n by p r e c i p i t a t i o n of the f e r r i c  form a t pH 5 and  of o t h e r minor i m p u r i t i e s w i t h z i n c dust.  C u r r e n t e f f i c i e n c i e s of 79 -  83% were lower sidered  than a c c e p t a b l e commercial l e v e l s  (90%).  I t was  con-  t h a t t h i s d e f i c i e n c y c o u l d be overcome by minor m o d i f i c a t i o n of  p u r i f i c a t i o n procedures, The  prior  to e l e c t r o w i n n i n g .  reason f o r the d i f f e r e n c e i n the f i n a l  i n the shake f l a s k and  stirred  the e x t r a c t i o n p r o c e s s or perhaps the d i f f e r e n t tanks r e s u l t e d  p r o d u c i n g more s u r f a c e .  zinc concentrations  tank l e a c h e s i s not r e a d i l y e v i d e n t .  P e r i o d i c s t o p p i n g of the shaker f o r sampling may  stirred  cementation  have i n t e r f e r e d type of m i x i n g  with  i n the  i n some s e l f - g r i n d i n g of the c o n c e n t r a t e , However, no d e f i n i t i v e e x p l a n a t i o n i s a v a i l -  able. During  these l a r g e s c a l e experiments  as time p r o g r e s s e d  a l t e r a t i o n s which o c c u r r e d  i n the s i z e d i s t r i b u t i o n and  chemical  of the s u b s t r a t e ore p a r t i c l e s were i n v e s t i g a t e d . 400 ml  samples from  the l e a c h s u s p e n s i o n ,  and were washed t h r e e times w i t h one  liter  The  and  of d i s t i l l e d water.  tank.  out  After  on the B a h c o - s i z e r  the z i n c c o n t e n t s of f r a c t i o n s 1, 3, 5 and  r e s u l t s are i n T a b l e 9.  i n the b a f f l e d  A f t e r removal of  the s o l i d s were f i l t e r e d  d r y i n g at 45°C these s o l i d s were f r a c t i o n a t e d apparatus  composition  These were o b t a i n e d from  8  determined.  the l e a c h done  From T a b l e  9, most of the z i n c i s l e a c h e d  from the  smaller  p a r t i c l e s because t h e i r z i n c c o n c e n t r a t i o n drops most r a p i d l y w i t h Also  t h e r e i s a s m a l l e r p e r c e n t a g e of the s m a l l e s t p a r t i c l e s  a f t e r 338  hours of l e a c h i n g .  p a r t i c l e s i n c r e a s e s and  The  r e l a t i v e p r o p o r t i o n of the  the c o m p o s i t i o n  These f a c t s a r e c o n s i s t e n t w i t h having  remains more or l e s s an i n i t i a l p a r t i c l e  the s m a l l e s t f r a c t i o n s of which a r e l e a c h e d f r a c t i o n while to  p a r t i c l e s w i l l not i n i t i a l l y present Modelling  9.1  General The  completely i n the ore  conditions.  disappear  The due  distribution  smallest  fraction  to the i n e r t m a t e r i a l  concentrate.  pulp  t o t a l s u r f a c e a r e a per u n i t volume of  A t r e l a t i v e l y low v a l u e s  carbon d i o x i d e  enriched  of the v a r i o u s dependent  the z i n c e x t r a c t i o n r a t e s are d i r e c t l y p r o p o r t i o n a l to  dependent v a r i a b l e s .  At higher values  z i n c e x t r a c t i o n r a t e s l e v e l o f f and the s i m p l e s t  equations  m i.  ,  .  tend  to become independent.  ( e q u a t i o n 13) M  the  of the dependent v a r i a b l e s  which can be used to d e s c r i b e t h i s k i n d  b e h a v i o u r i s the h y p e r b o l i c e q u a t i o n (131,140)  constant.  f a s t e r than the l a r g e s t  l e a c h l i q u o r a r e s i m i l a r both under normal and  variables  large  shapes of the p l o t s of z i n c e x t r a c t i o n r a t e s v e r s u s  d e n s i t y , s p e c i f i c s u r f a c e , and  air  remaining  those p a r t i c l e s i n the l a r g e f r a c t i o n d i m i n i s h i n s i z e  become p a r t of the s m a l l e r f r a c t i o n s .  9.  time  .  ,  ..  the One  of  of  suggested by Monod  •  . • T h i s i s a l s o known as the M i c h a e l i s - M e n t e n  (136) equation  (see s e c t i o n IV.4.2). Equation  13 has been adapted i n t h i s work to d e s c r i b e  the  e f f e c t s of v a r i o u s f a c t o r s on the k i n e t i c s of m i c r o b i a l z i n c e x t r a c t i o n  Table 9 A l t e r a t i o n s i n substrate during Time  0 hr  Y i e l d of Zn - e x t r .  0%  Bahcofractions  Weight  Weight  Weight  %  Zinc content %  g  1  • 5.3  60.85  2  2.7  3  11.3  4  14.7  . ' 5 '.  19.0  60.63  60.89  leaching  212 h r  338 hr  47.0%  82.1% Weight  %  Zinc content %  0.7  0.8  14.73  0.1  1.0  1.9  4.2  6.7  5.8  9.7  10.2  22.7  Weight  %  Zinc content %  g  5.3  1.3  18.79  2.7  2.0  11.3  8.0  14.7  11.0  , 19.0  19.3  41.51  58.96  Weight  g  0.3 38.74  1.2 1.7  53.20  4.1  '6  19.3  19.3  21.7  11.5  16.7  3.0  7  . 6.3  6.3  8.0  4.2  10.3  1.8  8  21.3  21.3  28.7  15.2  21.3  TOTAL  99.9  99.9  100.0  52.9  100.1  60.92  *  60.21  60.45  5.6  17.8  C a l c u l a t e d from average y i e l d  oo  85 Thus the s u b s t r a t e c o n c e n t r a t i o n  (S) i s r e p l a c e d by pulp d e n s i t y (PD),  specific  surface area  Equation ^  13 i s used i n t h i s work to e s t i m a t e  cularly  (SSA), o r t o t a l s u r f a c e a r e a per u n i t volume (TSA) values  for K  and V , p a r t i m m  the l a t t e r which i s an i n d i c a t i o n of the maximum r a t e a t t a i n a b l e  T h i s maximum r a t e would be of c o n s i d e r a b l e importance i n an i n d u s t r i a l scale  operation. Monod^  ± 3 ±  '  specified  met when u s i n g e q u a t i o n all  of these  13 t o c h a r a c t e r i z e b a c t e r i a l growth c u r v e s .  a r e met i n the p r e s e n t work which renders  more e m p i r i c a l i n n a t u r e . product  a number o f c o n d i t i o n s which must be  (zinc) formation  treatment  Not  thereof  In t h i s work we were concerned w i t h a r a t e r a t h e r than a b a c t e r i a l c e l l growth r a t e .  In Monod's work the growth r a t e was the growth r a t e observed i n the l o g a r i t h m i c phase o f the c e l l p o p u l a t i o n growth. product  r a t e used was the product  I n t h i s work t h e  r a t e which appeared as the l i n e a r  p o r t i o n of a p l o t of z i n c concentration versus  time.  Monod assumed t h a t a l l n u t r i e n t s and/or s u b s t r a t e s were present The  i n excess save one which was s a i d  limiting  13 by S. and  to be the l i m i t i n g  s u b s t r a t e c o n c e n t r a t i o n i s the one r e p r e s e n t e d  I n the p r e s e n t  study  substrate. i n equation  both the a v a i l a b i l i t y of energy  carbon d i o x i d e can be l i m i t i n g .  As has been shown i n s e c t i o n 4  t h e r e can be a t r a n s i t i o n from one l i m i t i n g f a c t o r t o another. t h i s study  equation  13 was a p p l i e d w i t h o u t  as w i l l be shown below.  represent  source  Thus the V and K m m  s o l e l y the e f f e c t s o f a l i m i t i n g  regard to t h i s values  In  limitation  observed may not  substrate.  However, under  c o n d i t i o n s where carbon d i o x i d e was i n excess t h e Monod c o n d i t i o n of a single limiting  substrate probably  substrate i s insoluble zinc  i s met.  sulfide.  In t h i s case the l i m i t i n g  In t h i s heterogeneous system the s u b s t r a t e c o n c e n t r a t i o n should be expressed organism  as a s u r f a c e because the energy  i s o n l y a v a i l a b l e through  this surface.  source f o r the  Hence as suggested by  (78) Moss and Andersen used  s p e c i f i c s u r f a c e or t o t a l s u r f a c e a r e a s have been  as w e l l as z i n c s u l f i d e c o n c e n t r a t i o n s expressed Due  t o the c o m p l i c a t i n g f a c t o r s l i s t e d  work should be regarded  as p r e l i m i n a r y .  as p u l p  densities.  above t h i s m o d e l l i n g  F u r t h e r work should be under-  taken to p r o v i d e a more a c c u r a t e s i m u l a t i o n of the l e a c h i n g c u r v e s . In the f o l l o w i n g the v a l u e s o f the c o n s t a n t s V and K were m m estimated  through  least  squares  fitting  of the d a t a u s i n g the  9.2 D e t e r m i nand a t i oBurk n oft Ve c and a tiiro c nditions Lineweaver h n iK q uv ael tu eos under l i n e a r inormal z e equa n o 13. m m The density  r e l a t i o n between z i n c e x t r a c t i o n r a t e (V) and p u l p  (PD) was w r i t t e n as  V  x < > ro  m  K + (PD) m  V  V m K  (  =  maximum z i n c e x t r a c t i o n r a t e (mg/1 h r ) : °  =  Michaelis-Menten  constant  (% pulp  .  form  3  )  .. .  density).  When the d a t a of F i g u r e 10 were p l o t t e d 1 (—  .  3  i n the l i n e a r i z e d  1  vs  )  a s t r a i g h t l i n e was n o t observed  save i n the  r e l a t i v e l y narrow r e g i o n between p u l p d e n s i t i e s of .12 to 18%. Lineweaver-Burk  plot  the v a l u e o f V i s d e r i v e d from m  of t h e s t r a i g h t l i n e on the 1/V a x i s .  I t was f e l t  the i n t e r c e p t r  t h a t the d a t a p o i n t s  from p u l p d e n s i t i e s between 12% and 18% c o u l d be used a b l e e s t i m a t e of V .  From the  to g e t a r e a s o n -  Data p o i n t s f o r h i g h e r pulp d e n s i t i e s which l a y  87 closer to the 1/V axis were not useful because the high solids concentration apparently reduced the rate. and  =  The values found were V  =  574 mg/1 hr  10.1% pulp density; see Figure 21. The K value represents the pulp density which i s half the m  pulp density required to achieve maximum rate.  Thus i f this were the  correct model, the maximum rate should be achieved at a pulp density of 20.2%.  The fact that at this pulp density the rate was lower than  574 mg/1 hr means that some unaccounted for factor has interfered. This has already been commented upon when discussing Figure 10. The extraction rate data from Figure 14 were studied using specific surface area (SSA) to represent substrate concentration in equation 13. Thus V  x (SSA)  = jK" + (SSA) .oca m  V  (34)  From the plot of Figure 22 the maximum zinc extraction rate and MichaelisMenten constant were determined to be V m  =  2 566 mg/1 hr and K = 0.77 m /g. ° m  The data corresponding to particles having low surface areas deviated from the straight line and were not used in drawing the straight line. In Figure 22, similar extrapolation of the tangent to the dotted line, suggests a difference in reactivity of large particle size substrates. Similarly total surface area per unit volume (TSA) can represent substrate concentration and x (TSA)  V v V  =  \  JE K + (TSA) m  (35) V  .  The linearized plot of equation 35 i s given in Figure 23 which includes points from the various pulp density experiments and points from the  Figure  21  E F F E C T OF P U L P D E N S I T Y L I N E WE AVER - BURK P L O T  RECIPROCAL OF PULP DENSITY [ m ! / ( g x 100)] x I O "  2  F i g u r e 22 EFFECT OF SPECIFIC SURFACE A R E A LINEWEAVER-BURK PLOT  i  O ><  12 E  x Cyclosizer Bahco-sizer - 4 0 0 Mesh  ,10 ui  6  8  CC  Z o Io  < cc H X  UJ  u 4 z  N U.  o  UJ  to  5 6 5 . 7 rng / L 0 . 7 7 rn -/g  vc  -UJ  ?  > 2  -2  -I  0  ±  1  2  3  4  INVERSE OF INITIAL SPECIFIC SURFACE AREA ( 1 /SSA ) in g/m2  90 v a r i o u s s u b s i e v e f r a c t i o n experiments. range the d a t a from from  I n the 12 to 18% p u l p d e n s i t y  the p u l p d e n s i t y experiments  the s u b s i e v e f r a c t i o n experiments.  agree w e l l w i t h  The v a l u e s found  for V  2 were 566 mg/1  h r and  d e v i a t e d markedly from t i o n of V  and K m  .  0.12  m /ml r e s p e c t i v e l y .  Again  the s t r a i g h t l i n e were not used  This V  m  and m  1  K  those  the d a t a which  i n the computa-  v a l u e i s the same as the one  obtained f o r  m  the z i n c e x t r a c t i o n r a t e as a f u n c t i o n of s p e c i f i c s u r f a c e a r e a e q u a t i o n ( e q u a t i o n 34). However,.this i s not unexpected s i n c e much of the same d a t a were used.  The  different units  used.  d i f f e r e n c e s i n the v a l u e s of K  m  are due  to the  The v a l u e s o b t a i n e d f o r the maximum e x t r a c t i o n r a t e , 574 mg/1 from  the pulp d e n s i t y experiments  s u r f a c e a r e a and  and  566 mg/1  t o t a l s u r f a c e a r e a experiments,  w i t h the maximum e x t r a c t i o n r a t e (569 mg/1 the p a r t i c l e diameter All  No  Determination  and K  m  diameter.  done under normal comparison.  v a l u e s under carbon d i o x i d e  enriched a i r conditions The  to zero  l i t e r a t u r e d a t a are a v a i l a b l e f o r m  specific  hr) o b t a i n e d by e x t r a p o l a t i n g  v e r s u s e x t r a c t i o n r a t e curve  of V  the  are i n good agreement  of these v a l u e s were o b t a i n e d from experiments  air condition. 9.3  hr from  .  -  e f f e c t s of p u l p d e n s i t y on z i n c e x t r a c t i o n r a t e s under  carbon d i o x i d e e n r i c h e d a i r c o n d i t i o n s have been demonstrated i n F i g u r e 16. and  7.92%  The  r a t e s o b t a i n e d at carbon d i o x i d e l e v e l s of 0.23,  are s i m i l a r .  Thus these d a t a a r e p l o t t e d  the d e t e r m i n a t i o n of the V m i s a s i m i l a r p l o t based of 0.13%.  and K m  1.03,  i n F i g u r e 24 f o r  c o n s t a n t s of e q u a t i o n 33.  F i g u r e 25  on the d a t a o b t a i n e d a t a carbon d i o x i d e l e v e l  hr  91  Figure  23  E F F E C T OF TOTAL S U R F A C E A R E A L I N E WE AVER - BURK P L O T  /o  I  ro i  O x 12  BY C H A N G I N G : PULP DENSITY  • Standard Agitation ©Increased Agitation •  E  SPECIFIC SURFACE  AREA  x Cyclosizer Fractions O Bahco-sizer Fractions  -10  o LU  0  4  8  V  m  K  m  =• 5 6 5 . 7 mg / L hr = 0.12 r n / m l 2  .J.  12  J L _ _ ± _ „  16  20  RECIPROCAL OF T O T A L SURFACE AREA ( T S A ) PER UNIT VOLUME (ml/m ) 2  24  For the 0.13% carbon to.be  d i o x i d e experiments V was e s t i m a t e d m  2,796 mg/1 hr and K to be 85.4% pulp d e n s i t y . m  o b t a i n e d f o r the h i g h e r carbon 107.8% pulp d e n s i t y . carbon  As expected  probably  dioxide l e v e l .  the V  and K v a l u e s were lower m m  o n l y be approximated i n p r a c t i c e .  and'216%.  E q u a t i o n 33 p r e d i c t s t h a t the  these maximum r a t e s w i l l be about  These v a l u e s a r e so h i g h t h a t they w i l l  to l i m i t a t i o n s .  a t the  These h i g h maximum e x t r a c t i o n r a t e s can  pulp d e n s i t i e s r e q u i r e d to achieve 170  The v a l u e s  d i o x i d e l e v e l s were 3,457 mg/1 h r and  r  lower  92  The r e l a t i v e l i m i t a t i o n  lead  inevitably  free s i t u a t i o n existed at  normal a i r c o n d i t i o n s i n a narrow pulp d e n s i t y range of 12 t o 18% only.  T h i s range was expanded to 20% a t i n c r e a s e d carbon  p a r t i a l pressures.  At higher pulp d e n s i t i e s  pulp d e n s i t i e s ) , t h e s o l i d  (as a t these  concentrations probably w i l l  t i o n s on the mass t r a n s f e r r a t e of oxygen and carbon  dioxide extreme  impose  limita-  d i o x i d e to t h e  organisms. The  e f f e c t s of s p e c i f i c  s u r f a c e a r e a and t o t a l s u r f a c e area  on the m i c r o b i o l o g i c a l z i n c e x t r a c t i o n r a t e s were demonstrated i n F i g u r e s 19 and 20 a t carbon of the l i n e a r i z e d  forms of e q u a t i o n s  i n the f o l l o w i n g v a l u e s area V m  =  d i o x i d e c o n c e n t r a t i o n s of 1%. A p p l i c a t i o n  =  2  8.98 m /g, and f o r t o t a l  surface  surface  2  3,586 mg/1 h r and K m  maximum r a t e s agree w i t h t h a t observed (3,457 mg/1 h r ) a t carbon  resulted  (see F i g u r e s 26 and 2 7 ) : f o r s p e c i f i c  3,586 mg/1 hr and K = m  a r e a p e r u n i t volume V m  34 and 35 to these d a t a  »  1.44 m /ml.  These  i n t h e pulp d e n s i t y experiments  d i o x i d e l e v e l s of 0.23, 1.03, and 7.92%.  However, these v a l u e s a r e almost  double  the rough v a l u e  (1840 mg/1 h r )  o b t a i n e d by e x t r a p o l a t i n g the z i n c e x t r a c t i o n r a t e - p a r t i c l e diameter  curve.  Figure  24  OF P U L P D E N S I T Y A T I N C R E A S E * ! CARBON DIOXIDE PARTIAL L I N E WE AVER - BURK P L O T EFFECT  i  1  -  '  to  o  i  PRESSURES  i  i  3.0  X  cn  E \ 2.5  -  /  t» _•  LU ^ „  -  H  /  2.0  EXTRACTION  <  o N  '-0  /  U. O  x 0.23%-! o 1.03% 4-C0 • 7.92%  / /  < U  2  J  § 0.5 n  LJL.  /  O LU  v  m = 3456.9 mg / L hr  K -2  0  m  = 107.8% Pulp Density  I . . . . . . . .!.__ _ 1 1 2 4 6 8 . RECIPROCAL OF PULP DENSITY  [ r n l / ( g x 1 0 0 ) ] x IO"  2  Figure  2S  E F F E C T OF S P E C I F I C S U R F A C E A R E A AT •LINEWEAVER-BURK PLOT  -I  .  0 . 1 2 RECIPROCAL OF SPECIFIC  (g/m ) 2  1.0% CO  3 SURFACE  4 AREA  96 The p u l p d e n s i t y d a t a agree w e l l w i t h the d a t a o b t a i n e d the s u b s i e v e f r a c t i o n s , as shown i n F i g u r e 27. necessary of  Whereas pulp  with  densities  to approach maximum r a t e s are i m p r a c t i c a l e x c e s s i v e g r i n d i n g  the ore c o n c e n t r a t e to i n c r e a s e the s p e c i f i c  more p r a c t i c a l .  s u r f a c e a r e a s may  be  T h i s c o u l d be combined w i t h a h i g h e r p u l p d e n s i t y .  However, the i n c r e a s e d g r i n d i n g c o s t s would have to be b a l a n c e d the improved r a t e of e x t r a c t i o n .  against  The h i g h e s t e x t r a c t i o n r a t e observed  i n any of the work r e p o r t e d i n t h i s t h e s i s was  about 1,160  mg/1  hr;  a c h i e v e d w i t h the s m a l l e s t s i z e f r a c t i o n h a v i n g a s p e c i f i c s u r f a c e 2 a r e a of 6.90 10.  m /g .  Mathematical The  to  d e s c r i p t i o n of b a c t e r i a l l e a c h curves  generalized l o g i s t i c  equation  ( e q u a t i o n 21) was  l e a c h curves o b t a i n e d under a v a r i e t y of c o n d i t i o n s .  are presented  i n T a b l e s 2 (A .and B)  to 10  The  results  (A and B) of Appendix  The A t a b l e s c o n t a i n the r e g r e s s i o n c o e f f i c i e n t s associated s t a t i s t i c a l  fitted  2.  and  parameters as computed by a m u l t i p l e r e g r e s s i o n  (205) a n a l y s i s program fed  .  E x p e r i m e n t a l d a t a from a p a r t i c u l a r  i n t o the p r o g r a m ^ ^ " ^ and  fitted  to e q u a t i o n 26.  o b t a i n e d f o r the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s squares  suggest  equation.  The  l e a c h were  The h i g h v a l u e s  (R v a l u e ) and  a good f i t of the d a t a by the g e n e r a l i z e d  logistic  goodness of t h i s f i t can be seen i n the B t a b l e s where  the e x p e r i m e n t a l d a t a are compared to the f i t t e d  data.  The  program  reproduced  i n T a b l e .1 of Appendix 2 was.used to compute these B  by f i t t i n g  the e q u a t i o n s r e c o r d e d i n each A t a b l e .  v a r i a b l e i s time tration  for their  (mg/1) .  The  independent  (hr) and Y the dependent v a r i a b l e i s the z i n c The maximum d e v i a t i o n observed  tables,  between f i t t e d  concenand  97  27  Figure  E F F E C T OF TOTAL S U R F A C E A R E A AT 1.0% C 0 L I N E W E A V E R - B U R K PLOT  BY  2  G  C H A N G I N G  SIZE FRACTIONS :  x Cyclosizer o Bahco-sizer PULP  DENSITIES AT  • 1.03% C 0  •  2  • •  -4  4  V K  8  m  m  = 3 5 8 5 . 6 mg / L hr = 1.44 m /mL 2  12  J.  16  RECIPROCAL OF TOTAL SURFACE AREA  1  20  -(ml/m ) 2  98 observed v a l u e s of z i n c c o n c e n t r a t i o n was 5.5 g/1; agreement between most o t h e r d a t a p a i r s was b e t t e r . Thus the g e n e r a l i z e d l o g i s t i c e q u a t i o n as expressed by e q u a t i o n 21 can be used t o f i t a m i c r o b i o l o g i c a l l e a c h c u r v e . confirms  the c o n c l u s i o n s o f E d w a r d s ^ w h o 3  b a c t e r i a l growth c u r v e s .  suggested  This  i t f o r use w i t h  I t i s of some importance t h a t t h i s k i n d of  curve can f i t the e n t i r e l e a c h curve i n c l u d i n g the p a r t s c o r r e s p o n d i n g to the l a g phase and the s t a t i o n a r y phase. Leaching fitted. air,  curves o b t a i n e d under a v a r i e t y of c o n d i t i o n s were  The r e s u l t s i n T a b l e 2 of Appendix 2 were o b t a i n e d i n normal  those of T a b l e s 3 to 10 w i t h carbon d i o x i d e e n r i c h e d a i r and  v a r i o u s pulp d e n s i t i e s .  Under them some were f i t t e d  with various size f r a c t i o n s larger scale, stirred  to data  obtained  ( T a b l e 7 and 8) and t o d a t a o b t a i n e d i n the  tank experiments ( T a b l e s 9 and 10).  VII.  SUMMARY AND  The  CONCLUSIONS  99  technological f e a s i b i l i t y of a batch m i c r o b i o l o g i c a l  leach-  ing process using T_. ferrooxidans f o r e x t r a c t i n g zinc from a high-grade z i n c s u l f i d e concentrate has been demonstrated.  This study provides  u s e f u l information about the r e a c t i o n mechanism involved i n the  oxida-  t i o n process and explains c e r t a i n phenomena, observed i n t h i s and  other  s t u d i e s , which occur during the b i o l o g i c a l leaching of i n s o l u b l e metal sulfides. a)  These f a c t o r s can be summarized as f o l l o w s : The  zinc e x t r a c t i o n rate was  strongly dependent on temperature.  Best r e s u l t s were observed at around 35°C. b)  The optimum pH was  c o n t r o l to be about 2.3 e x t r a c t i o n rate was  .  observed using both manual and automatic pH  At pH 2.3  the lag time was  shortest, the zinc  f a s t e s t and the f i n a l zinc concentration  highest. (37)  c)  The n u t r i e n t concentrations present i n the l i q u i d medium  were found to be adequate and thus should not be rate l i m i t i n g .  Ammonium  concentration c o n t r o l l e d the f i n a l zinc concentration i n s o l u t i o n  and  phosphate concentration c o n t r o l l e d the rate of zinc e x t r a c t i o n . d)  Zinc e x t r a c t i o n rates were r e l a t e d to pulp density,  specific  surface area of the ore p a r t i c l e s , mean diameter of the s i z e f r a c t i o n s , and  t o t a l surface area of .ore per u n i t volume of leach l i q u o r under  various l e v e l s of carbon dioxide concentration i n a i r .  The  results  i n d i c a t e d that at low l e v e l s of these independent variables the t i o n rates were p r o p o r t i o n a l  to these independent v a r i a b l e s .  extracAt higher  values of the independent v a r i a b l e the influence on the zinc e x t r a c t i o n rates decreased.  The use of t o t a l surface area permitted combination of  100 d a t a from experiments  on p u l p d e n s i t y v a r i a t i o n s w i t h those  obtained  using ore p a r t i c l e s of v a r i o u s s p e c i f i c s u r f a c e s . The maximum a t t a i n a b l e z i n c e x t r a c t i o n r a t e i n c r e a s e d as the carbon d i o x i d e content of the a i r used  f o r . a e r a t i o n of the f e r m e n t a t i o n  increased. Attempts were made to use a form o f the M i c h a e l i s - M e n t e n or Monod e q u a t i o n to c o r r e l a t e some of these d a t a .  T h i s was  reasonably  s u c c e s s f u l but i t should be c o n s i d e r e d as an e m p i r i c a l means o n l y o f d e t e r m i n i n g maximum e x t r a c t i o n r a t e s .  Maximum r a t e s of 570 mg/1 h r ,  2,796 mg/1 h r , 3,457 mg/1 hr were e s t i m a t e d  f o r carbon d i o x i d e l e v e l s  of normal a i r , 0.13%, and 0.23 to 7.92% r e s p e c t i v e l y . rates are a t t a i n a b l e only e)  Probably  these  theoretically.  L a r g e r s c a l e experiments  have shown t h a t t h i s  microbiological  l e a c h i n g t e c h n i q u e c o u l d produce z i n c concentrations of the o r d e r of 120 g/1 which are s u i t a b l e f o r d i r e c t e l e c t r o w i n n i n g of z i n c . larger scale stirred to those observed  tank experiments  gave s i m i l a r z i n c e x t r a c t i o n r a t e s  i n shake f l a s k s f o r s i m i l a r c o n d i t i o n s .  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Experimental data  T a b l e 1A E f f e c t of temperature  Time  V  (hr)  A  .B  Sterile  25  0 25 46.5 70.5 100.5 118.5 143 166 191  1.62 1.77 3.18 5.81 6.60 8.40 9.30 10.4 12.2  1.54 1.73 3.10 5.69 6.60 8.30 9.10 10.6 12.2  0.196 0.202 0.205 0.212 0.223 .0.255 0.270 0.283 0.294  Zn-extr . rate 30  0 19 46 67 91 115 140 163  Zn-extr . rate 35  Zn-extr.  0 19 46 67 91 115 140 163 rate  Zinc  extractions  (g/D  Temperature  58.5 mg/1 h r 1.40 1. 70 4.50 6.10 8.10 10.6 11.8 14.3  1.50 1.90 •4.30 5.90 8.30 10.2 11.8 14.4  0.178 0.208 0.351 0.368 0.375 0.380 0.385 0.392  83.7 mg/1 h r 1.45 1.80 5.40 7.50 10.5 13.8 16.5 19.0  1.45 1.80 5.40 7.70 10.3 13.8 17.4 19.2  121.0 mg/1 h r  0.161 0.205 0.222 0.399 0.417 0.430 0.432 0.433  -  T a b l e IB  E f f e c t o f temperature  Temperature  Time  °C  (hr)  A  B  Sterile  40  0 19 46 67 91 115 140 163  1.50 1.80 4.90 7.10 10.1 13.1 15.8 18.0  1.50 1.80 5.10 7.10 10.1 13.3 15.8 18.1  0.168 0.200 0.390 0.395 0.418 0.434 0.438 0.439  Zn^-extr. 45  Zn-extr .  rate 0 18 39 63 88 112 135 159 186 208  rate  Z i n c e x t r a c t i o n s (g/1)  114.5 mg/1 h r 1.62 2.10 2.84 2.92 4.18 4.60 5.66 6.12 6.45 7.15  1.62 2.30 2.80 3.04 4.18 4.80 5.82 6.04 6.45 7.35  24.7 m g/1 h r  0.180 0.205 0.218 0.219 0.235 0.245 0.255 0.265 0.270 0.278  Time (hr)  0 21 46 72 93 121 141 169 189 215 240 262 289 310 338 359 383 407 430 456 481 Zinc-extr. rate (mg/1 h r )  A PH 1.5 " 1.6 1.7 1.75 1.8 1.85 1.9 1.95 2.05 2.1 2.0 1.8 1.7 1.7 1.75 1.75 1.75 1.75 1.75 1.75 1.75-  B  Zn(g/1)  Fe(g/1)  1.32 2.02 2.14 2.37 2.49 2.73 2.80 2.82 3.07 3.08 3.10 3.38 7.80 10.4 12.8 14.4 16.9 18.7 18.8 18.8 18.9  0.071 0.165 0.185 0.194 0.207 0.214 0.225 0.230 0.235 0.240 0.238 0.236 0.315 0.388 0.422 0.456 0.475 0.512 0.575 0.685 0.670  i.  pH 1.5 1.6 1.75 1.8 1.9 1.95 2.05 2.10 2.10 2.1 2.0 1.75 1.7 1.7 1.75 1.75 1.75 1.75 1.75 1.75 1.75 v •• 99.7  Sterile  Zn(g/1)  Fe(g/1)  Zn(g/1)  Fe(g/1)  1.32 2.00 2.06 2.33 2.45 2.75 2.86 2.87 3.09 3.10 3.06 3.48 8.00 10.6 13.4 14.5 17.2 18.8 19.0 19.2 19.3  0.070 . 0.168 0.190 0.200 0.210 0.221 0.230 0.207 0.222 0.226 0.230 0.231 0.319 0.385 0.449 0.465 0.477 . 0.491 0.583 0.660 0.687  0.168 0.705 0.900 1.10 1.28 1.50 1.67 1.79 1.80 1.82 1.88 1.95 1.96 1.96 1.97 1.95 1.99 2.02 2.04 2.04 2.05  0.026 0.077 0.120 0.120 0.128 0.142 0.145 0.149 0.153 0.156 0.157 0.154 0.155 0.148 0.135 0.124 0.116 0.102 0.098 0.092 0.-080  /  Time  STERILE  B  A pH  Zn(g/1)  Fe(g/1)  pH  Zn(g/1)  Fe(g/1)  Zn(g/1)  Fe(g/1)  0  2.0  1.28  0.054  2.0  1.28  0.041  0.207  0.025  21  2.3  2.42  0.077  2.3  2.45  0.075  0.384  0.052  46  2.1  5.49  0.164  2.15  5.28  0.156  0.470  0.024  72  2.1  9.5  0.341  2.15  9.1  0.343  0.480  0.014  93  2.1  11.5  0.513  2.1  11.5  0.504  0.481  0.011  121  2.1  14.9  0.722  2.1  14.7  0.702  0.486  0.009  141  2.05  16.6  0.757  2.1  16.8  0.747  0.500  0.008  169  .2.1-  18.1  0.800  2.1  18.3  0.787  0.510  0.010  189  2.05  20.2  0.929  2.05  20.6  0.897  0.530  0.009  215  2.05  20.5  0.942  2.1  20.4  0.931  0.532  0.009  240  2.05  20.8  0.934  2.05  20.8  0.895  0.539  0.010  262  • 2.05  20.9  0.921  2.05  20.9  0.938  0.540  0.009  (hr)  Zn-extr.rate (mg/1 hr)  S-  Y  106.4  J  (hr) 0 21  PH 2.5 2.8 — > 2 . 5  Zn(g/1)  Sterile  B  A  Time  pH  Fe(g/1)  1.29  0.039  1.74  0.042  2.5 3.0  — > 2 . 5  Fe.(g/1)  Zn(g/1)  Fe(g/1)  1.26  0.034  0.200  0.022  1.72  0.052  0.209  0.010  Zn(g/1)  46  2.45  3.94  0.076  2.45  4.26  0.070  0.213  0.009  72  2.35'  8.40  0.271  2.35  8.00  0.265  0.222  0.009  93  2.3  10.2  0.446  2.3  9.8  0.424  0.232  0.009  121  2.25  13.3  0.656  2.25  13.1  0.648  0.272  0.008  141  2.25  14.7  0.670  2.2  14.9  0.687  0.285  0.010  169  2.2.  16.8  0..761  2.2  17.1  0.769  0.287  0.012  189  2.2  17.9  0.862  2.2  18.1  0.868  0.301  0.011  215  2.2.  18.6  0.895  2.2  ' 18.9  0.912  0.312  0.016  240  2.2  19.9  0.897  2.2  20.1  0.875  0.329  0.017  262  2.2  20.0  0. 902  2.2  20.1  0.888  0.410  0.011  Zinc-extr. rate (mg/1 hr)  V  119.5  T a b l e 2D E f f e c t of i n i t i a l pH pH = 3.0  60  QJ  oo 00 o o o o  ON  o o  o o  rH  o O  o rH o  ON  m  VO co  -tf  O  st  co o  CN  CN  CN  CN  CN  CN  CN  CN  CO  O  O  O  o  O  O  O  O  O  ,r-~ vO CN m o O CN o o O  CN CO CO  rH  o  ON  CN  -tf  o  o  o  S t  rH CM  CO  O  o o  O  O  CN  CN  CN  CN CN  O  O  O  O  00  rH rH  o o  o rH o o  rH rH O  00  rH ON  -tf  o o  rs O  o o  o rH o  rH rH  st rH  vO rH  oo rH  ON rH  CO  CO  CO  o  O  O  -tf •tf  o  o  •H  f-i  CD  60  rH 60  QJ  60  a  o o  o o o  vO  vO  CN  CO  rH  r-H  o o o  ON  CN  -tf 00  CN  rH  rH  CN  -tf  vD  vO  00  in  rH  in m o  CN  o  o in o  CO  m o  ON  CN  oo  CN  -tf  rH  vO  VO  00 rH  00 rH  ON rH  ON rH  ON rH  in  rH CN  CN  CN  CN  00 CO  CN VO  00 00  CO rH  o  o  ON  VO  S t  CO  CN  CO  co  CN  CN  CN  CN  CN  CN  VO O O  00 O O  rH rH  CO CO  CO vO CN  CN r-H CO  rH 00 CO  vO sj-  in  ON  O  o  o  O  o  ON  m m  -tf O rH  tN  ON  in in o  -tf  'OT  pq  ON 00  rH  m  rH  rH  in  in o  O  jn CO  o  ON rH  o CO  o CO  A I CO  rH  rH CN  CN  CO  60  Pn  r-H ro  O O  rH 60  CN  ^0  rH  -tf rH  rH  O O  in  00 rH  o o  o  ON  CN  o  CN r^.  CN  rH  rH CN  -tf  -tf  O  m . in o o  CN  rH  CO  ON  cn  ON  -tf  CO rH  in  rH  rH  00 rH  00 rH  ON  ON  ON  CO  CN  in  CO  in rH  rH  rH  rH  rH  rH  CN  CN  CN  CN  CN  CN  CN  CN  CN  CN  rH st rH  ON VO rH  ON CO rH  m  O st CN  CN vO CN  ON 00 CN  O rH  00 CO CO  ON  rH  00  in o  in o  in o  rH  -tf O  rH  co O  rH  o CO  o  A  1  CO  o  o  ON  VO  CO  CO  CN  CN  VO st  CN  co  in  rH  CO  QJ  e  •rl  EH  ^  u X  w  ON  rH CN  co  in CO  (hr)  0 21 46 72 93 ' 121 141 169 189 215 240 262 289 310 338 359 383 407 430 . 456 481 Zinc-extr. rate (mg/1 h r )  pH 3.5 3. 8 - >3.5 3. 75 - >3.5 3. 75 - >3.5 3. 7 - >3.5 3. 7 - >3.5 3. 85 - >3.5 3. 75 - >3.5 3.45 2.85 2.55 2.4 2.3 2.2 2.2 2.15 2.1 2.1 2.05 2.05 2.05  Sterile  B  A  Time  Zn(g/1)  Fe(g/1)  1.23 1.37 1.43 1.53 1.62 1.79 1.84 1.92 ' 2.61 4.9 8.0 10.8 14.0 16.1 • 17.3 18.5 18.9 19.2 19.3 - 19.3 19.4  0.029 0.007 . 0.008 0.008 0.013 0.008 0.012 0.017 0.020 0.098 0.274 0.363 0.439 0.452 0.486 0.554 0.562 0.584 0.402 0.365 0.315  PH  .  3.5 3.8 - >3.5 3.75 - >3.5 3.75.- >3.5 3.7 - >3.5 3.7 - >3.5 3.8 - >3.5 3.75 - >3.5 3.45 2.85 2.50 2.4 2.3 2.2 2.2 2.15 2.1 2.1 2.05 2.05 2.05  V 108.4  Zn(g/1)  Fe(g/1)  Zn(g/1)  Fe(g/1)  1.24 1.37 1.42 1.54 1.70 1.78 1.87 1.96 2.73 5.20 8.1 11.3 15.4 16.2 17.6 18.4 19.0 19.3 19.5 19.6 19.6  0.025 0.007 0.008 0.007 0.012 0.009 0.011 0.014 0.025 0.112 0.291 0.364 0.445 0.461 0.488 0.537 0.541  0.174 0.190 0.196 0.220 0.240 0.261 0.269 0.272 0.286 0.287 0.289 0.290 0.304 ' 0.305 0.324 0.341 0.345  0.013 0.006 0.008 0.008 0.010 0.008 0.009 0.010 0.010 0.011 0.012 0.008 0.009 0.009 0.015 0.012 0.015 0.016 0.010 0.012 0.015  J  .0.531 0.408 0.354 0.330  0.381 0.401 0.407 0.432  Time  A  (hr)  PH  0 21 46 72 93 121 141 169 189 215 240 262 289 310 338 359 383 407 430 456 481 . 505 526 552 557  4.00 3.85 3.80 3.75 3.80 3.80 3.85 3.95 4. 05->4.00 4. 25->4. 0 - 4.35->4.0 4. 30->4. 0 4. 30->4. 0 4. 30->4.0 4. 20->4. 0 3.80 3.7 3.7 3.1 2.6 2.3 2.3 2.2 2.2 2.2  Zn-extr.rate . . (mg/l.hr) .  Zn(g/1) 1.23 1.37 1.42 1.54 1.59 1.74 1.84 1.91 1.98 1.97 1.96 1.97 2.04 2.06 2.09 2.10 2.14 3.87 6.7 9.9 11.7 14.3 16.4 17.7 18.0  B Fe(g/1) 0.029 0.006 0.007 0.008 0.012 0.006 0.010 0.012 0.016 0.022 0.023 0.026 0.026 0.029 0.030 0.038 0.036 0.074 0.240 0.310 0.488 0.557 0.538 0.556 0.537  pH 4.00 . 3.85 3.80 3.80 3.80 3.80 3.85 3.95 4.15->4. 0 4.25->4.0 4.35->4. 0 4.30->4.0 4.30->4.0 4.30->4.0 4.20->4. 0 3.8 3.8 3.8 3.4 2.7 2.5 2.3 2.2 2.2 2.2  ~T  96.9  Zn(g/1) 1.24 1.41 1.40 1.47 1.56 1.70 1.82 1.84. 1.92 1.96 . 1-97 1.98 2.02 2.07 2.09 2.08 2.18 3.92 6.5 9.8 11.9 14.5 16.2 17.8 18.0  Sterile Fe(g/1) Zn(g/1) 0.025 0.007 0.007 .0.009 0.009 0.009 0.011 0.014 0.012 0.016 0.019 0.021 0.026 0.029 0.028 0.040 0.042 0.068 0.198 0.305 0.435 0.514 0.527 0.541 0.532  0.185 0.192 •0.194 0.200 0.204 0.233 0.240 0.262 0.264 0.268 0.269 0.270 0.291 0.310 0.322 0.341 0.364 0.394 0.411 0.435 0.472 0.480 0.484 0.488 0.492  Fe(g/1) 0.021 0.006 0.008 0.009 0.011 0.008 0.009 0.011 0.009 0.010 0.012 0.008 0.009 0.012 0.009 0.011 0.013 0.017 0.008 0.010 0.011 0.013 0.013 0.012 0.012  T a b l e 3A E f f e c t o f constant pH  pH= 1.5 . Zn( g/1)  Time (hr)  B  A  Time  pH=2.0  pH=2.5  (hr)  Zn(g/1)  Zn(g/1)  0  1.83  1.81  0  24  2.13  2.18  46  2.76  69 92 '  1.34 •  1.35  21  6.4  6.5  2.74  46  14.3  14.8  3.24  3.30  73  24.4  24.9  3.91  3.98  93  31.2  31.1  117  4.5  4.4  116  40.1  40.3  • 141  6.8  6.9  141-  50.6  50.8  165  9.7  9.9  164  59.1  •60.4  189  11.3  11.5  195  67.4  68.2 '  213  13.4  13.3  217  69.6  69.9  243  17.0  16.8  238  70.3  71.4  265  19.5  19.7  288  19.9  19.8  369.6  375.9  311  19.7  19.9  340.  19.8  19.8  Zn-extr.rate  99. 2 mg/1 h r  Zn-extr.rate (mg/1 h r )  :  T a b l e 3B E f f e c t of constant pH  Time  pH=3.0  Time  pH=3.5  Time  pH=4.0  (hr)  Zn(g/1)  (hr)  Zn(g/1)  (hr)  Zn(g/1)  0 17 43 69 96 117 • 141 168 187 212 236 259 290 309 321  1.61 2.07 3.42 13.0 23.2 30.4 40.0 50.2 53.6 54.0 54.2 54.1 54.3 54.2 54.4  Zn-extr.rate (mg/1 h r )  373.7  •  0 17 43 69 96 122 149 170 194 221 240 265 289 312 343 362  Zn-extr.rate (mg/1 h r )  1.65 1.82 1.96 2.02 3.18 12.8 22.2 30.5 38.2 47.1 48.3 49.0 49.2 49.4 49.3 49.5  326.8  0 17 43 70 91 115" ' 142 169 190 214 241 260 285 309 321 345  Zn-extr.rate (mg/1 h r )  1.60 1.74 1.88 1.91 1.97 2.06 3.88 8.9 14.8. 21.0 28.3 33.4 35.6 36.2 36.3 36.4  255.1  o  Table Effect of nutrient  4 concentrations  ZINC EXTRACTIONS ( g / 1 ) Time ABSENT FROM THE BASAL MEDIUM ( 3 7 ' ) : (hr) K HP0  (NHO2SO4  B  A  0  23 50 73  2.42 2.59 2.82 14.2  123 143 167 192 216 246 273  19.6 24.3  Zn-extr.rate (mg/1 h r )  2.45 2.52 2.79 6.3 14.4 19.5 24.6 26.4 26.6 26.6  6.2  101  2  26.2  26.5 26.6 26.8 27.5  27.0  27.3  258.9  MgSOit, C a ( N 0 ) 3  2  A  B  A  B'  2.48 2.52 2.77 3.70 4.80  2.50 2.54 2.82 3.60 4.70  2.48 2.52 . 6.15  2.52* 2.52 6.26  8,1  8.2  11.3  12.4  12.6  21.0 -  21.7  29.6  11.4 15.2  29.4 36.5 45.0  45.1  19.8  52.8  25.0  63.0  53.6 62.8  29.2  29.7  33.5  34.0  68.8 69.3  15.6 19.5 24.7 .  KC1,  4  171.8  36.2  69.2  69.6  351.7  T a b l e 5A E f f e c t of ammonium c o n c e n t r a t i o n  ZINC EXTRACTIONS -  Time (hr)  (NH ) S0^ = 0.75g/l Lf  2  . B  A  0 19 43 68 95 119 140 164 187 . 212 235  Zn-extr.rate (mg/1 h r )  (g/D  1.94 2.28 7.0 15.2 22.3 31.7 36.6 38.8 40.9 40.9 41.0  1.89 2.30 6.9 15.4 22.7 31.8 36.6 38.7 40.8 41.0 41.1  319. 5  (NH ) S0 Lf  2  lf  = 1.50 g/1  (NH ) S0 Lf  2  4  = 2.25g/l B  A  A  1.95 2.49 7.2 16.3 25.8 33.9 42.1 50.3 54.7 58.0 57.9  1.96 2.41 7.2 16.6 25.7 34.2 ' 41.9 51.0 54.5 57.6 ' 57.8  357.5  1.96 2.37 7.5 17.0 26.3 35.2 42.6 5.1.2 59.7 62.6 62.7  1.91 • 2.36 7.4 16.9 26.2 34.9 42.8 51.6 60.1 62.4 62.9  363 .3  T a b l e 5B E f f e c t of ammonium c o n c e n t r a t i o n  ZINC EXTRACTIONS (g/1) Time  •  ( N H ) S 0 ^ = 3.00g/l 4  2  (NH ) S0 t+  2  1+  •  4.50g/l  = 3.75g/l  (hr) B  A  0 19 43 68 95 119 140 164 187 212 235  .  Zn-extr.rate (mg/1 h r )  1.95 2.21 7.4 17.0 25.9 35.3 42.7 52.0 60.8 63.2 63.6  1.95 2.20 7.6 17.2 26.4 35.1 42.5 51.6 60.7 66.0 65.8  B  A  1.94 2.42 7.5 17.1 26.2 35.6 42.6 51.8 60.2 64.7 67.8  -  1.96 2.44 7.8 17.3 26.0 35.4 42.6 51.9 60.5 65.0 68.2  A  B  1.96 2.44 7.9 17.2 26.1 35.4 43.0 52.0 60.4 63.8 67.9  1.94 2.39 7.8 17.0 26.6 35.7 42.4 51.7 60.7 64.2 67.8  •  367.0  364.5  362.1  T a b l e 5C E f f e c t of ammonium c o n c e n t r a t i o n  ZINC EI{TRACTIONS (g/1) Time (NH^)250^=6.00g/l  (NHtt)2S04= 7.50g/l  (NH ) S0 = lf  2  It  9.00g/l  (NH ) S0^ 4  2  10.50g/l  (hr) A  0 19 43 68 95 119 140 164 187 212 235  Zn-extr.rate (mg/1 h r )  1.93 2.32 7.9 17.4 26.0 35.8 43.1 51.9 60.6 64.3 68.4  B  1.91 2.32 7.9 17.1 26.3 35.6 • 42.7 51.8 60.4 64.7 68.2  364.3  A  B  1.94 2.40 8.0 17.6 26.5 35.7 43.0 51.7 60.7 64.8 68.5  1.93 2.41 8.4 17.3 26.6 35.9 43.2 51.6 60.8 64.5 68.5  362.5  A  B  1.92 2.36 8.0 17.6 26.3 35.8 43.0 52.3 60.9 64.4 68.5  1.94 2.36 8.2 17.4 26.9 35.3 43.1 52.4 60.3 64.2 68.8  364.1  A  1.92 2.32 7.9 17.3 26.8 35.5 43.3 52.4 • 60.5 64.5 68.9-  B  1.94 2.38 8.0 17.7 26.7 35.9 43.3 52.5 60.7 64.5 69.4  365.3  T a b l e 6A E f f e c t of phosphate c o n c e n t r a t i o n  ZINC EXTRACTIONS (g/1) Time K HP0 z  =  4  0.1g/l  K2HPO4  =  0.2g/l  KZHPOLJ  =  0.3g/l  (hr) B  A  0  23 46 72 96117 • 147 169 190 214 241 261 292 '  Zn-extr.rate (mg/1 h r )  0.63 1.48 1.96 4.20 6.7 8.8 11.7 13.8 16.7 19.0  21.8 23.8 26.7  104.1  0  1 1 4 6 8 11 14 16 18 22 23 26  A  65 50 93 30 5 7 4 0  9 7 0  6 9  B  .62 1 .28 3 .90 8. 0 12 .9 16 .8 22 .4 26 .5 30 .4 34 .8 39 .9 43 .7 48 .9 0  66 1. 40 3 60 8 2 12 8 16 8 22 1 26 6 30 2 ' 34 9 39 7 43 6 49 4  186.9  0.  A  0  1 4 12 20 27 36 44 50 58 62 66 68  B  71 44 7 9 5 4 9 0  6 1 5 8 7  315.8  68 1. 56 4. 8 12. 6 20. 7 27. 9 36. 5 39. 8 50. 2 58. 5 62. 9 67. 4 68. 3 0.  Table 6B E f f e c t o f phosphate  concentration  ZINC EXTRACTIONS (g/1) Time K HP0 2  4  = 0.4g/l  K^HPO^ = 0 . 5 g / l  K^HPO^ = 0.75g/l  (hr) B  A  0 23 46 7296 117 147 169 190 214 241 261 292  '  Zn-extr. r a t e (mg/1 h r )  0.66 1.46 4.9 14.1 22.6 30.2 40.9 48.7 55.5 61.2 64.5 67.4 68.5  354.8  0.72 1.52 4.9 14.2 22.3 30.0 41.0 49.0 55.8 61.1 64.8 67.3 68.6  A  0.66 1.48 5.2 14.8 23.7 31.5 42.6 50.8 58.1 63.2 66.7 68.0 68.3  B  0.63 1.43 5.4 14.4 23.8 31.9 42.4 50.5 58.3 63.6 66.5 68.3 68.7  369.7  B  A  0.63 1.41 5.0 14.9 23.9 31.3 42.5 50.7 57.9 62.9 67.3 68.2 69.0  0.62 1.44 5.1 14.6 24.1 31.6 42.4 50.6 58.1 63.3 67.0 68.5 68.7  368.0  T a b l e 6C E f f e c t of phosphate  concentration  ZINC EXTRACTIONS (g/1) Time K2HP0  = 1.00g/l  4  K HP0i 2  = 1.25g/l  t  K HP0 2  = 1.50g/l  4  K^HPO^ = 1.75g/l  (hr) A  0 23 46 72 96 117 147 169 190 214 241 261 292  Zn-extr.rate (mg/1 h r ) ,  B  0.66 1.45 4.8 14.3 23.6 31.8 42.3 50.2 57.7 62.7 66.5 . •, 67.3 68.1  368.5  0.63 1.44 4.6 14.5 23.3 31.4 43.0 50.4 57.3 63.5 67.1 67.4 68.4  A  B  0.63 1.46 4.9 14.7 24.8 31.3 42.3 50.7 57.7 63.1 67.2 68.3 68.8  0.69 1.46 5.3 14.9 24.2 31.4 42.6 50.4 57.8 63.0 ' 67.1 69.0 69.2  365.6  B  A.  0.68 1.46 4.9 14.2 24.5 31.2 42.5 50.3 56.9 62.9 66.5 67.4 68.5  365.6  0.66 1.48 4.8 14.6 24.3 31.1 42.3 50.7 57.6 63.4 67.2 67.7 68.7  A  B  0.67 1.50 5.2 14.5 24.5 31.2 • 42.2 50.5 57.8 ' 63.2 66.9 67.5 69.2  366.3  0.68 1.47 5.3 14.3 24.7 31.0 42.5 50.5 58.0 62.8 66.7 67.3 68.7  Table 7A E f f e c t o f pulp d e n s i t y P u l p d e n s i t y = 2%  Pulp d e n s i t y = 1%  ZINC EXTRACTIONS (g/1)  ZINC EXTRACTIONS (g/1) Time (hr)  Time (hr) B  A  0 13 37 61 85 109 134 158  Zn-extr.rate (mg/1 h r )  1.34 1.77 2.24 2.38 2.35 2.68 2.98 3.20  1.34 1.74 2.19 2.31 2.45 2.71 2.95 3.25  8. 5  Sterile  0.050 0.155 0.239 0.240 . 0.242 0.258 0.305 0.338  0 13 37 61 85 109 134 158  Zn-extr.rate (mg/1 h r )  A  B  Sterile  1.41 2.04 2.68 3.40 4.60 5.40 6.40 7.20  1.31 2.05 2.62 3.32 4.65 5.60 • 6.20 7.30  0.069 0.174 0.250 0.320 0.346 0.387 0.412 0.428  35.8  oo  T a b l e 7B E f f e c t o f pulp d e n s i t y Pulp d e n s i t y = 5.3%  P u l p d e n s i t y = 4%  ZINC EXTRACTIONS (g/1)  ZINC EXTRACTIONS (g/1) .  0 13 37 61 •  8  Time (hr)  Time (hr)  5 109 134 158  Zn-extr.rate (mg/1 h r )  .A  B  Sterile  1.40 2.22 4.38 8.1 9.8 11.3 13.1 15.5  1.38 2.19 4.26 7.7 9.9 11.2 13.3 15.9  0.076 0.231 0.395 0.432 0.496 0.518 0.552 0.574  88.6  0 24 49 70 94 118 143 166  Zn-extr.rate (mg/1 h r )  A  B  Sterile  1.39 2.42 5.4 7.7 10.5 13.8 17.4 19.0  1.40 2.44 5.4 7.5 10.3 13.8 17.5 19.2  0.163 0.179 0.218 0.384 0.397 0.412 0.427 0.436  121.1  I—  1  VO  Table 7C E f f e c t of pulp d e n s i t y Pulp d e n s i t y = 8%  Pulp d e n s i t y = 6%  ZINC EXTRACTIONS (g/1)  ZINC EXTRACTIONS (g/1) Time (hr)  Time (hr) - A  0 13 37 61 85 109 134 158  Zn-extr.rate (mg/1 h r )  1.44 2.36 6.48 10.6 13.9 16.5 19.6 22.2  > 126.0  B  Sterile  1.48 2.31 6.96 10.9 13.8 16.9 19.8 22.1  0.156 0.277 0.297 0.317 0.385 0.473 0.594 0.682  0 13 37 61 85 109 134 158  Zn-extr.rate (mg/1 h r )  A  B  Sterile  1.72 2.20 6.8 13.5 17.5 21.5 26.6 30.9  1.65 2.16 6.9 13.1 17.8 21.6 27.1 31.2  0.201 0.358 0.492 0.577 0.653 0.681 0.688 0.699  195.2  O  Table 7D E f f e c t of pulp d e n s i t y Pulp  Pulp d e n s i t y = 10%  ZINC EXTRACTIONS  ZINC EXTRACTIONS (g/1) Time (hr)  0 13 37 61 85 109 134 158  Zn-extr.rate (mg/1 h r )  1.64 2.30 7.8 17.4 20.9 27.2 33.6 40.2- '  253.9  1.63 2.12 8.3 18.2 21.0 27.1 33.9 40.4  (g/1)'  Time (hr)  -  B  A  d e n s i t y = 12%  0.252 0.374 0.425 0.534 . 0.612 0.704 0.763 0.802  B  A  Sterile  0 19 30 44 53 67 77 101 116 143 163 188 212 241 262 285 316 477  Zn-extr.rate (mg/1 h r )  2.00 2.68 4.08 8.2 9.3 15.2 18.3 25.8 30.5 35.6 39.7 45.9 50.3 50.6 51.2 51.4 51.8  2.03 2.56 4.02 8.3 9.2 15.0 18.4 25.9 30.3 35.0 39.4 48.8 50.4 . 50.9 51.1 51.5 51.6 52.3  312.5  Sterile  0.56 0.58 0.59 0.62 0.63 0.66 0.68 0.69 0.71 0.73 0.78 0.81 0.83 0.87 0.93 0.96 1.05  Table 7E E f f e c t of pulp  density Pulp  Pulp d e n s i t y = 14%  ZINC EXTRACTIONS (g/1)  ZINC EXTRACTIONS (g/1) Time (hr)  Time (hr) A  0 19 30 -44 53 67 77 101 116 143 163 ' 188 212 241 262 285 316 477  Zn-extr.rate (mg/1 h r )  d e n s i t y = 16%  1.97 2.58 4.16 8.5 11.6 16.4 19.5-. 28.6 33.0 41.9 44.2 50.0 51.2 51.9 ' 52.5 53.0 53.8  335.4  B  Sterile  2.03 2.57 4.34 8.4 11.7 16.2 19.8 28.5 33.2 41.1 44.9 49.2 51.4 52.2 52.8 53.2 54.0 54.7  0.50 0.54 0.56 0.68' 0.70 0.72 0.75 0.76 0.78 0.79 0.80 0.82 0.83 0.89 0.96 1.02 1.09  0 1930 44 53 67 77 101 116 143 163 188 212 241 262 285 316 477  Zn-extr.rate (mg/1 h r )  A  B  2.10 2.58 4.2 9.1 12.4 17.0 20.4 29.9 35.3 42.3 49.8 57.4 59.4 61.9 ' 62.6 63.2 63.6  2.15 2.60 4.3 9.0 12.3 17.1 • 20.4 29.8 . 35.1 41.6 50.4 . 58.2 60.1 61.7 62.8 63.3. 63.5 63.7  Sterile  0.57 0.61 0.64 0.69 0.74 0.77 0.81 0.84 0.89 0.90 0.91 0.93 0.96 . 1.04 1.12 1.17 1.20  343.3  ro to  Table 7F E f f e c t of pulp d e n s i t y  Pulp d e n s i t y = 18%  P u l p d e n s i t y = 20%  ZINC EXTRACTIONS (g/1)  ZINC EXTRACTIONS (g/1) Time (hr)  Time (hr) A  0 19 30 44 53 67 77 101 116 143 163 188 212 241 262 285 316 477  2.19 2.70 4.5 9.4  12.5 •  Zn-extr.rate (mg/1 h r )  17.3 21.132.0 37.2 46.2 52.9 59.9 63.2 64.8 66.7 ' 68.2 69.6  364.3  B  Sterile  2.08 2.65 4.4 9.5 12.5 17.4 20.6 31.2 37.0 44.1 51.2 59.4 62.6 64.5 66.1 68.5 69.4 70.1  0.64 0.67 0.70. 0.74 0.77 0.79 0.85 0.88 0.92 0.93 0.94 0.95 0.96 1.04 1.14 1.26 1.32  B  Sterile  2.33 2.55 4.3 9.3 • 12.3 17.0 20.9 • 30.4 . 36.9 43.7 50.9 • 59.2 61.4 64.6 68.3 69.3 70.4 70.6  0.71 0.76 0.77 0.80 0.82 0.85 0.89 0.94 0.97 0.99 1.00 1.02 1.08 1.17 1.23 1.35 1.44  A  0 19 30 44 53 67 77 101 116 143 163 188 212 241 262 285 316 477  Zn-extr.rate (mg/1 h r )  •  2.42 2.54 4.2 9.2 12.1 17.0 .20.4 30.7 36.8 44.0 50.4 58.8 61.2 . 64.9 67.1 69.6 70.2  353.4 to  T a b l e 7G E f f e c t of pulp d e n s i t y  Pulp d e n s i t y = 24%  0 22 45 68 92 117 142 165 189 213 236 260 284 308 333  Zn-extr.rate (mg/1 h r )  Time (hr)  •  A  2.25 2.86 3.04 4.18 6.8 15.2 23.6 31.3 39.4 46.1 54.2 60.4 64.2 66.7 68.9 ''  d e n s i t y = 26.6%  ZINC EXTRACTIONS (g/1)  ZINC EXTRACTIONS (g/1) Time (hr)  Pulp  B  Sterile  2.31 2.74 3.07 4.30 6.7 15.3 23.4 31.5 39.1 46.5 54.4 61.0 64.7 67.0 69.0  0.66 0.74 0.86 0.87' 0.90 0.94 0.96 0.97' 0.98 1.03 1.05 1.10 1.15 1.22 1.30  0 19 30 • 44 . 53 67 77 101 •116 143 163 188 212 241 ' 262 285 316 477  A  B  Sterile  2.55 2.61 2.92 4.20 6.4 6.8 8.2 10.4 14.5 23.5 33.3 39.0 45.0 50.3' 55.4 60.5 63.7  2.52 2.58 2.96 4.40 6.6 7.0 8.6 10.7 14.3' 24.2 31.6 38.7 45.1 50.7 55.5 60.9 63.4 69.9  0.79 0.82 0.86 0.88 0.91 0.94 0.95 0.99 1.03 1.04 1.05 1.07 1.12 1.26 1.37 1.48 1.54  327.5 Zn-extr.rate (mg/l.hr)  297.1  N3  T a b l e 7H E f f e c t of pulp d e n s i t y a t i n c r e a s e d a g i t a t i o n  pulp density  Time (hr)  Zinc e x t r a c t i o n  (g/D  Zinc extraction  (g/D  B  0 23 47 71 - 95 120 147 167 192 216 240 265  Zn-extr.rate (mg/1 h r )  1.42 2.50 9.8 17.2 24.5 32.0 40.4 47.0 50.1 51.6 51.4 51.8  1.40 2.54 9.8 17.1 24.7 32.0 40.5 47.2 50.3 51.4 51.5 51.6  309.2  20  16  12  (%)  1.48 2.76 11.4 19.8 28.6 37.6 47.2 55.0 63.8 67.4 68.1 68.4  363.8  Zinc e x t r a c t i o n  (g/D B  A  B  1.50 2.79 11.2 20.0 28.4 37.4 47.3 55.2 64.1 67.7 68.3 68.3  1 ,62 2 ,84 11 ,4 19 ,6 28 ,4 37 ,3 46.8 54.6 63. 68. 69. 69.  1.58 2.86 11.1 20.0 28.4 37.2 46.7 54.6 63.1 68.3 69.9 69.5  359.4  T a b l e 8A Effect  Sample  Cyclosizer fraction No. 1  Time (hr) 0 23 47 70 98 143 167 190 214 238 262 288 312 340 362 383 411 435 455 480 507 527 550 575 Zn-extr. rate (mg/1 h r )  of p a r t i c l e  size  Cyclosizer fraction No. 2  ZINC EXTRACTIONS (g/1) A  B  1.59 3.15 4.02 4.66 • 5.15 5.82 6.1 6.9 7.0 7.2 7.2 7.5 7.8 8.5 10.5 20.7 34.1 45.3 55.0 65.4 66.8 .68.4 70.2 70.3  1.60 3.08 4.01 4.70 5.15 5.84 6.2 6.9 6.9 7.1 7.2 7.5 7.9 8.6 10.6 20.9 34.8 45.8 55.8 68.5 69.0 69.1 69.5 69.8  496 .2  Sterile 0.36 1.00 1.83 • 2.04 2.17 2.19 2.20 2.21 2.21 2.22 2.23 3.27 2.24 2.25 2.28 2.32 2.35 2.38 2.40 2.41 2.46 2.47 2.47 2.49  A  B  1.26 1.30 1.45 1.50 1.87 1.80 1.98 . 2.08 2.15 2.14 2.52 2.46 2.62 2.68 2.90 3.04 3.08 2.95 2.96 3.09 3.01 3.10 3.24 3.24 3.28 3.29 3. 70 3.65 5.12 5.18 12.5 12. 8 22.6 22.9 31.4 31.8 39.2 39.0 48.0 47.6 56.8 57.2 62.8 63.0 62.5 62.9 63.0 63.1 .  359 .8  Sterile 0.16 0.29 0.42 0.51 0.57 0.75 0.80 0.92 0.93 1.07 1.10 1.24 1.25 1.27 1.27 1.27 1.28 1.29 1.29 1.28 1.29 1.30 1.31 1.32  27  T a b l e 8B Effect  Sample  Cyclosizer No.  of p a r t i c l e  fraction 3  Time (hr) 0 23 47 70 98 143 167 190 217 238 262 288 312 340 362 383 411 435 455 480 507 527 550 575 Zn-extr. rate (mg/1 h r )  1INC  A 1. 23 1. 41 1. 68 1. 82 1. 94 2. 06 2. 25 2. 46 2. 49 2. 50 2. 51 . 2.54 2. 55 2. 90 4. 29 10. 4 18. 6 25. 9 31. 9 39. 0 46. 2 51. 8 51. 6 51. 8  263. 6  B 1. 26 1. 39 1. 65 1. 79 1. 91 2. 03 2. 21 2. 43 2. 50 2. 52 2. 53 2. 56 2. 58 2. 94 4. 36 10. 6 18. 9 25. 6 31. 7 38. 6 46. 0 51. 3 51. 8 51. 8  size  Cyclosizer fraction No. 4  E X T R /V C T I O N S  Sterile 0 11 0 22 0 36 0 41 0 50 0 51 0 61 0 78 0 79 0 80 0 82 0 89 0 92 0 97 1 01 1. 05 1 06 1. 07 1. 08 1. 09 1. 12 1. 13 1. 14 1. 16  (  g/D  A 1. 22 1. 45 1. 58 1. 72 1 89 1. 90 2 08 2 22 2 26 2 28 2 29 2 30 2. 31 2. '63 3 64 7 6 13 2 18 2 22. 6 27 3 32 8 36. 3 37. 1 37 2  204. 3  B 1 24 1 49 1 61 1 73 1 85 1. 91 2 06 2 30 2 32 2 29 2 30 2 32 2 34 2 60 3 62 7 5 13. 1 18. 0 22. 4 27. 4 32 3 36 8 37. 4 37 5 A  Steril e 0 12 0 22 0 30 0 36 0 42 0 50 0 57 0 65 0 66 0 67 0 68 0 70 0 71 0 74" 0 78 0 79 0 79 0 78 0 78 0. 81 0 86 0 90 0 94 0. 97  T a b l e 8C Effect  of p a r t i c l e  Sample  Cyclosizer  Time  size  f r a c t i o n No. 5  ZINC EXTRACTIONS  (g/D  (hr)  A  B  Sterile  0 23 47 70 98 143 167 190 214 238 262 288 312 340 362 383 411 435 455 480 507 527 550 575  1.24 1.48 1.60 1.77 1.86 1.91 1.96 2.09 2.10 2.18 2.17 2.18 2.17 2.58 3.32 6.64 11.1 14.8 17.8 21.9 26.3 29.4 32.6 32.9  1.24 1.52 1.61 1.86 1.88 1.90 1.96 .2.15 2.17 2.25 2.26 2.27 2.28 2.64 3.43 6.66 11.3 15.1 18.2 21.8 26.5 29.9 33.1 33.0  0.13 0.25 0.28 0.33 0.37 0.44 0.51 0.59 0.60 0.62 0.65 0.67 0.69 0.73 0.76 0.77 0.80 0.81 0.83 0.84 0.84 0.85 0.85 0.86  Zinc-extr. rate (mg/1 h r )  158.0  T a b l e 9A Effect  Sample  0 23 47 70 94 118 142 166 191 215 238 262 286 310 335 359 382  Zn-extr. rate (mg/1 h r )  size  Bahco f r a c t i o n No. 1  Bahco f r a c t i o n No. 1  ZINC EX'fR/ACTIONS  Time (hr)  of p a r t i c l e  A  Sterile  2.86 4.5 7.8 9.6 11.4 11.9 13.7 14.3 15.0 16.7 20.9 29.2 42.6 56.4 68.9 69.4 69.9  516 .8  2.96 4.8 . 7.9 9.5 11.5 11.8 13.9 14.2 15.8 16.2 19.8 30.2 42.2 56.9 69.9 72.2 75.7  1.48 2.19 2.39 3.42 4.43 4.7 5.3 6.1 7.4 7.9 8.1 8.6 9.7 10.6 10.7 10.8 10.9  (g/1)  A  B  Sterile  2.53 3.66 4.82 6.8 7.8 8.3 10.1 10.8 11.9 13.0 16.5 28.0 40.4 52.1 62.8 68.9 69.8  2.61 3.85 4.97 6.7 7.9 8.7 10.1 10.9 12.0 13.2 17.0 28.5 40.2 52.6 63.8 69.5 70.2  1.13 2.28 2.32 2.99 3.62. 3.89 4.72 5.4 6.3 7.3 7.5 7.8 7.9 8.0 8.3 8.8 8.9  484.2  T a b l e 9E Effect  Sample  size  Bahco f r a c t i o n No. .3  Time  Bahco f r a c t i o n No. 4  ZINC EXTRACTIONS (g/1)  (hr)  A  B  0 23 47 70 94 118 142 166 191 215 238 262 286 310  1.96 2.73 3.36 4.86 5.8 6.7 7.8 12.6 22.5 . 33.9 45.8 54.8 64.9 65.2  1.96 2.85 3.37 4.90 5.8 6.5 7.7 11.3 22.0 34.1 45.2 54.6 64.7 65.6  Zinc-extr. rate (mg/1 h r )  of p a r t i c l e  446.2  Sterile  0.62 0.99 1.18 1.35 1.85 2.27 2.82 2.86 2.91 3.26 3.58 3.72 4.04 4.24  A  B  1.'91 2.26 3.96 10.4 17.2 25.9 36.4 46.7 51.8 56.8 59.0 60.2 60.8 61.4  1.90 2.14 3.87 10.6 17.9 25.7 36.3 47.2 51.4 57.2 59.2 60.6 61.2 61.2  349.3  Sterile  .  0.46 0.61 0.65 0.93 1.36 1.73 1.88 2.00 2.10 2.33 2.58 2.87 3.04 3.21  T a b l e 9C Effect  Sample  of particle  Bahco f r a c t i o n No. 5 ZINC EXTRACTIONS  Time  (g/D  (hr)  A  B  Sterile  0 23 47 70 94 118 142 166 191 215 238 262 286 310  1.92 2.09 4.65 12.2 19.4 25.2 33.4 39.2 43.9 50.9 52.5 52.6, 52.7 52.9  1.91 2.04 4.84 11.6 19.0 24.9 33.1 39.4 44.1 51.6 52.2 52.6 52.8 53.0  • 0.42 0.45 0.51 0.88 1.26 1.39 1.50 1.62 1.71 • 1.94 2.04 2.18 2.61 2.74  Zinc-extr. rate (mg/1 h r )  •  274.3  size  Sample  Bahco f r a c t i o n No. 6  Time  ZINC EXTRACTIONS (g/1)  (hr) •  0 24 " 47 72 96 120 144 171 195 215 244 288 408 432  Zinc-extr. rate (mg/1 h r )  A 1.28 4.85 9.2 ' 13.5 17.6 22.2 26.7 31.2 34.3 37.5 39.9 41.8 45.9 45.9  173.1  B  Sterile  1.34 4.92 9.3 13.6 17.8 22.7 26.6 31.1 34.4 37.7 40.6 42.0 * 46.0 46.1  0.21 0.42 0.67 0.68 0.69 0.70 0.76 0.75 0.77 0.78 0.79 0.81 0.83 0.84  '  T a b l e 9D E f f e c t of p a r t i c l e  Sample  Bahco f r a c t i o n No. 7  Time  Bahco f r a c t i o n No. 8  ZINC EXTRACDTIONS  (hr)  A  B  0 24 47 72 96 120 144 171 195 215 244 288 408 432  1.18 4.16 7.2 10.5 . 13.6 . 16.9 21.4 23.2 27.4 29.3 31.9 32.9 38.9 39.0  1.30 4.11 7.4 10.6 13.4 17.2 21.5 ' 23.4 27.0 29.2 31.5 32.8 38.4 38.8  Zinc-extr. ' rate (mg/1 h r )  size  132.7  Sterile 0.13 0.40 0.63 0.71 0.76 0.80 0.83 0.84 0.83 0.84 0.84 0.85 1.00 1.02  (g/1)  A  B  1.21 2.65 3.17 5.4 6.4 7.7 10.0 12.4 14.2. 15.3 18.4 20.3 27.7 27.9  1.28 2.72 3.26 4.9 6.6 8.1 9.7 12.2 14.0 15.6 18.0 20.2 26.9 27.4  73 .4  Sterile  '  0.13 0.39 0.62 0.64 0.73 0.76 0.83 0.84 0.88 0.92 0.94 0.94 1.20 1.27  T a b l e 10A Effect  Pulp Density  0 21 28 44 71 80 92 103 116 126 144 167 189 198  B  A  .  Zinc-extr. rate (mg/1 h r )  1.30 ' 1.32 1.58 2.12 3.46 4.02 4.9 6.0 7.7 8.9 11.7 15.3 18.0 19.1  141 .3  1.28 1.34 1.56 2.16 3.44 . 4.04 4.9 6.1 7.9 9.0 11.6 15.4 18.2 18.9  A  26.6%  14%  12%  5. 3%  • Time  (hr)  of pulp d e n s i t y a t 7.92% CO  ZINC EXTRACTIONS (g/1) A B 1.68 2.31 2.92 5.6 15.9 22.9 27.2 30.7 35.1 39.7 45.8 53.3 58.9 62.6  1.71 2.18 2.90 5.40 16.0 23.1 27.1 30.8. 35.3 39.6 45.7 53.6 59.1 62.4  355.1  1.85 2.36 3.01 5.5 18.2 25.9 30.6 34. 3 39.9 43.5 50.2 59.5 64.3 66.2  B 1.82 2.32 3.03 5.7 18.0 26.1 30.6 34.7 40.0 43.6 50.4 59.1 64.7 66.3  383. 0  B  A  2.20 2.37 3.25 6.1 19.1 28.7 36.2 42.9 51.6 57.9 63.9 . 67.7 69.2 70.7  2.23 2.45 3.37 5.9 18.9 28.436.1 43.0 51.4 57.8 63.6 68.0 69.1 70.3  640.6  T a b l e 10B E f f e c t o f pulp d e n s i t y a t 7.92% C 0  Pulp Density  0 . 21 28 44 7.1 80 92 103 116 126 144 167 189 198  Zinc-extr. rate (mo71 h r )  ZINC EXTRACT IONS  B  Sterile  1.96  0.52  2.35 3.05 5.8 18.7 28.0 33.6 38.6 43.7 48.3 56.5 62.2 66.9 68.4  0.66 0.75 0.81 0.82 0.83 0.85 0.91 0.92 0.93 0.97 1.02 1.03 1.07  A 1.92 2.30 3.00 . 5.6 18.9 28.2 33.3 38.2 43.9 48; 3 56.2 62.5 66.4 68.3  438 8  B  Sterile  1.96  1.98  0.64  2.33 3.05 5.7 18.8 28.2 34.0 39.3 45.9 50.6 58.9 66.7 68.9 69.8  2.31 3.10 5.6 18.9 28.1 34.2 39.5 45.7 50.5 60.1 66.3 69.1 69.7  0.67 0.69 0.71 0.74 0.78 0.80 0.81 0.84 .0. 86 0.90 0.93 0.96 1.07  A  488.1  24%  20%  18%  16%  Time (hr)  2  (g/1) A  B  Sterile  2.10 2.33 3.20 5.8 18.9 28.3 35.5 41.6 49.0 55.0 62.7 67.3 68.8 69.7  2.00 2.36 3.30 5.9 19.0 28.2 35.0 41.6 49^2 54.8 62.5 67.7 68.9 69.9  0.70 0.77 0.80 0.88 0.89 0.92 0.93 0.94 0.99 1.01 1.03 1.10 1.12 1.16  577.8  B  Sterile  2.10 2.41 3.28 6.0 19.0 28.4 35.8 42.9 51.5 57.8 63.6 67.9 69.0 69.7  0.73 0.77 0.78 0.82 0.87 0.90 0.92 0.93 0.97 0.99 1.03 1.10 1-.16 1.17  A 2.10 2.38 3.20 5.9 19.0 28.2 36.0 42.8 51.3 57.4 •. 63.7 67.8 68.9 69.8  640.8  CO  4>-  T a b l e 11A E f f e c t o f pulp d e n s i t y a t 1.03% C02  Pulp Density Time (hr) 0 22 31 ' 46 56 73 96 105 117 129 144 171 190 Zinc-extr. rate (mg/1 h r )  A 1.26 1.60 2.03 2.83 3.17 4.30 6.4 7.7 9.5 10.8 12.8 • 16.5 19.1  133. 9  B  A  1.27 1.62 2.01 2.84 3.22 4.20 6.6 7.8 9.4 10.9 12.7 16.3 19.3  1.39 2.33 3.50 5.8 8.6 16.4 28.2 31.4 35.6 40.1 44.4 53.9 60.3  ZINC EXTRACTIONS (g/1) A 3 1.41 2.45 3.34 5.9 8.5 16.6 28.1 31.8 35.7 39.9 44.2 54.0 60.5  339 .8  16%  14%  12%  5.3%  1.44 2.50 3.61 7.0 9.4 19.2 38.4 41.8 46.5 51.1 57.9 65.2 68.7  B 1.48 2.47 3.66 7.1 9.3 19.6 37.8 42.0 46.6 51.0 57.7 65.0 68.9  405.2  A  B  1.56 2.42 3.72 7.1 9.6 19.7 37.8 41.8 47.0 52.3 58.9 66.3 69.4  1.57 2.46 3.71 7.1 9.7 19.8 37.7 41.9 47.2 52.1 58.8 66.5 69.7  .438.5  CO  T a b l e 11B E f f e c t o f pulp d e n s i t y a t 1.03%  Pulp Density  0 22 31 46 56 73 96 105 117 129 144 171 190 Zinc-extr. rate (mg/1 h r )  ZINC EXTRACTIONS B  B 1.61 2.44 3.72 6.8 9.9 21.0 38.1 43.5 49.9 55.3 61.6 67.3 70.1  1 59 2 43 3 65 6 9 10 1 21 2 38 3 43 4 49 6 55.0 61.7 67.8 69.8  513.3  1.71 2.45 3.72 7.1 10.3 21.2 38.7 43.5 50.6 57.4 65.1 68.9 70.0  1.72 2.45 3 75 7 0 10 2 20.8 38.5 43.7 50.7 57.6 64.7 68.8 70.2  574.6  26.6%  24%  20%  18%  Time (hr)  CO2  (g/D A  B  A  B  1.78 2.41 3.74 6.8 10.1 21.3 38.7 44.6 52.3 60.0 66.2 68.9 70.5  1.79 2.43 3.71 6.9 10.2 21.2 38.8 44.8 52.1 60.2 66.5 69.0 70.3  1.86 -2.48 2.7' 7.2 10.2 21.4 38.8 44.5 52.2 59.8 65.4 68.9 70.4  1.92 2.44 2.80 7.0 10.4 21.3 38.8 44.6 52.0 59.9 65.7 69.3 70.7  644.4  636.9  T a b l e 12A E f f e c t o f pulp d e n s i t y a t 0.23% C02  Pulp Density Time  0 21 44. 70 80 102 120 140 164 189 212 236 Zinc-extr. rate (mg/1)  ZINC EXTRACTIONS B  B  (hr)  1.39 1.48 2.24 3. 40 4..3 5..8 8.,2 10.,5 13.,2 ' 16.119.1 20.3  38 45 20 30 2 9 1 10 6 13 1 16 2 19.0 20.1  118.5  1.68 1.83 4.45 11.3 15.2 25.2 31.3 38.1 46.3 54.8 62.6 65.4  16%  14%  12%  5.3%  1.69 1.86 4.41 11.3 15.3 25.1 31.2 38.3 46.4 54.7 62.3 64.9  339.4  (g/D A  B  1.73 2.03 4.5 12.2 16.0 26.4 33.5 41.5 51.0 61.1 66.1 68.5  1.71 2.05 4.6 12.1 15.9 26.1 33.6 41.4 51.2 61.0 65.9 68.3  • 399.7  B 1.77 2.15 4.67 12.5 16.5 26.8 34.7 43.5 54.0 65.1 69.3 70.2  1.79 2.13 4.65 12.7 16.4 26.7 34.8 43.5 54.3 64.9 69.6 69.8  439.8  T a b l e 12B E f f e c t o f pulp d e n s i t y a t 0.23%  Pulp Density  18%  20% ZINC  CO2  24%  26. 6%  EXTRACT! ONS (g/1)  Time (hr)  A  B  A  B  A  B  0 21 44 70 80 102 120 140 164 189 212 236  1.87 2.20 4.8 12.8 16.9 26.8 35.7 45.6 57.5 64.5 68.8 69.9  1.83 2.21 4.9 12.8 16.6 26.9 35.6 45.7 57.7 64.6 68.3 70.0  1.91 2.25 5.1 13.0 17.1 27.3 37.6 49.1 63.9 67.4 69.8 70.4  1.95 2.24 5.2 13.2 17.0 27.1 37.7 49.0 63.7 67.6 69.9 70.2  2.03 2.27 5.2 13.3 17.3 27.5 39.0 51.8 67.0 69.7 70.8 72.1  2.04 2.30 5.2 13.1 17.3 27.7 38.8 51.5 67.1 69.9 71.0 71.6  Zinc-extr. rate (mg/1 h r )  496.5  589. 0  '636.6  A  B  '  2.17 2.31 5.2 13.2 17.4 27.8 39.0 51.7 67.1 69.8 70.9 71.2  2.05 2.33 5.3 13.3 17.2 27.6 39.1 51.9 67.2 69.5 71.0 • 71.4  636. 5  T a b l e 13A E f f e c t o f pulp d e n s i t y a t 0.13% G 0  Pulp Density Time (hr) 0 23 33 47 59 72 95 106 120 131 148 168 192 216 Zinc-extr. rate (mg/1 h r )  ZINC A  B  A  1.32 1.96 2.60 4.35 5.8 7.4 10.1 11.4 13.2 14.6 16.5 18.9 19.5 20.2  1.36 1.92 2.63 4.28 5.7 7.3 10.0 11.5 13.0 14.5 16.6 18.7 19.7 20.1  1.66 2.18 2.99 5.2 7.4 11.6 19.4 23.1 27.8 31.6 37.3 43.4 51.7 60.3  107 .6  14%  12%.  5.3%  EXTRACTIONS (g/1) B A 1.71 2.23 3.01 5.1 ' 7.6 11.3 19.6 23.0 27.9 31.8 37.3 43.4 51.8 60.5  331. 3  2  1.52 2.41 3.10 5.3 7.8 12.1 20.8 25.7 32.2 36.5 43.3 51.2 60.7 66.2  414 .3  .  16%  B  B  A  1.58 2.37 3.20 5.4 7.6 12.0 20.9 25.6 32.6 36.2 43.6 51.0 60.5 66.6  1.88 2.28 3.41 5.8 9.1 15.0 . 26.2 31.1 37.3 42.2 49.7 58.6 66.4 69.8  1.93 2.26 . 3.44 5.8 9.0 15.2 26.5 31.0 . 37.2 42.0 49.9 58.8 66.3 67.7  444 .2  T a b l e 13B E f f e c t o f pulp d e n s i t y a t 0.13% CO2  Pulp  18%  Density Time (hr) 0 23 33 47 59 72 95 106 120 . 131 148 168 192 216 Zinc-extr. rate (mg/1 h r )  20%  B  A  1.88-  1.91 2.34 3.20 5.4, 11.7 22.2 28.7 33.7 40.5 46.3 54.3 64.1 69.0 70.8  2.31 3.20 5.7 12.1 21.9 28.3 33.8 40.6 46.1 54.5 ' 64.4 68.7 70.2  490  7  26.6%  24%  ZINC EXTRACTIONS (g/1) A B A 1.95 2.33 3.20 6.1 9.9 17.2 27.1 33.2 40.8 46.8 56.2 62.4 66.8 69.7  549. 0  1.98 2.35 3.25 6.3 9.8 17.4 26.9 33.3 40.9 46.5 56.3 63.0 66.5 69.5  B 2.06 2.35 3.53 6.2 10.2 17.7 27.3 33.8 42.0 48.1 . 58.0 65.3 68.1 70.0  2.08 2.36 3.42 6.1 10.3 17.5 27.4 33.9 41.9 48.2 57.9 65.1 68.4 69.9  576  2  A  B  2.14 2.19 2.31 2.33 3.45 3.44 6.1 6.3 10.2 ' 10.4 17.7 17.6 27.5 27.3 33.8 33.5 41.7 .• 41.6 47.8 • 47.8 ' 57.4 57.1 66.5 66.3 68.4 68.7 69.3 • 69.8  563.6  41  Table 14A E f f e c t of s p e c i f i c surface area at 1.0% CO  Cyclosizer Fraction  No. 1  time (br) 0 22 34 50 58 70 81 94 106 118 130 145 Zinc Extraction Rate (mg/1 hr)  No. 2  No. 3  No. 4  No. 5  Zinc E x t r a c t i o n s (g/1) 2.68 5.2 18.6 36.3 45.3 58.8 67.3 68.7 69.3 69.6 70.1 70.3  1,115.5  1.68 2.97 5.2 12.1 15.2 20.5 25.6 31.5 36.9 42.5 47.7 53.1  441.9  1.49 2.32 4.3 9.4 11.6 14.8 17.8 21.3 24.6 27.7 30.9 34.9  268.7  1.42 2.15 4.10 7.3 8.9 11.3 13.5 16.1 18.6 20.8 ' 23.2 26.1  198.6  1.36 2.05 3.65 6.4 7.8 9.9 11.8 14.0 16.1 18.0 20.2 22.4  170.2  T a b l e 14B E f f e c t of s p e c i f i c s u r f a c e a r e a a t 1.0% CO j  0  Bahco-sizer Fraction  No.l  No.2  Time (hr) 0 22 34 50 58 70 .' 81 94 106 118 130 145 Zinc Extraction Rate (mg/1 h r )  No. 3  Z i n c  3.35 5.4 20.3 38.4 47.5 60.9 68.2 70.5 70.8 71.1 71.3 71.3  1,152.3  2.96 5.2 17.9 35.1 43.7 56.5 64.3 67.7 69.1 69.8 70.1 70.4  1,068.3  2.47 5.1 17.3 33.1 41.0 52.9 63.5 66.7 68.0 69.4 69.9 70.2  989.8  No. 4  No. 5  E x t r a c t i o n s  1.82 3.32 4.90 12.3 15.9 21.5 26.6 32.6 38.1 43.6 49.2 56.0  460.9  1.63 • 2.31"' 4.20 9.4 11.6 14.9 17.8 21.4 24.7 28.1 31.3 34.9  271.6  No. 6  No. 7  No. 8 .  (g/D 1.51 2.25 3.63 6.6 8.1 10.3 12.3 14.7 16.9 19.2" 21.4 24.0  184.1  1.47 2.14 3.57 6.0 7.2 10.1 11.7 13.6 15.3 17.1 18.8 20.9  157.6  1.39 2.11 3.27 5.0 5.8 7.1 8.2 9.6 10.9 12.2 13.5 15.2  107.0  APPENDIX 2  Curve f i t t i n g s  Table 1 Program f o r curve f i t t i n g  n i N E N S I CN X ( 2 ? 0 ) f Y < 2 2 0 ] , Y F ( 2 2 O J , X l ( 2 2 O ) , X 2 ( 2 2 0 ) , X 3 { 2 2 O ) , 1X4(22G),X5(22C)»A(53) REAL K  C K-F I NAL EXTRACTION C • Y(I)^EXTRACTION .100 RE AC ( 5 , DN 1 FORMAT(13) READ(5,6)K 6 FORMAT if 10.0) WRI TE (6 , 8 B ) 88 FORMAT? 17'HF INAL EXTRACTION:) WRTIE(6 ,5)K WRITE'. A,?! 2 F O R M A T ( 5 X , 1 5 F N 0 OF OATAPAIRS,/) WR IT!" (6,3 ) N .. 3 FORMAT! 1QX,I 3,//) DO 10 1=1,N R E A o ( 5 ,4 ) X < I ! , Y { I ) 4 FORMAT(2F10.C) • 10 C O M INOF ' ' DO 40 1=1, IM X l ( I )=X( I ) 'X2 { I ) = X ( I ) * X l ( I ) X 3 ( I ) = X( I ) * X 2 M ' ) X'« ( I ) = X ( I )*X3( I )  X5( I ) = X ( I ) * X 4 (I ) 40 CONTINUE  Table 1 Continuation  . DO 60 1=1 ,6 RF AD( 5 , 5) A( I ) 5 FORMAT( E13.6 ) 60 CONTINUE WRITE (6,18) 1 8 ' FORMAT(IX t 2 5HP0LYNQMIAL PARAMETERS ARE,/) DO 70" I =1 .6 70 * R I T F ( 6 , 15 3A! T ) 15 FORMAT ( 4 X , F ] 3 .6 ) HP I TF (6,19) 19 FORMAT{5X,//) DO 20 31. YF{ I ) = K/ (1 .+EXP( A( 1 ) + A (2 )*X1 ( I) + A ( 3 )*X2< I ) + A(4 )*X3 t I ) + A( 5 ) *X4( I ) •+ 1 A(6 )*X5 ( I ) ! ) 20 CONTINUE WR I T E ( 6 , 7 ) 7 F O R M A T ( 5 0 H VALUES OF X VALUES OF Y FITTED VALUES OF Y ) DO 3 0 .1-1 » N WR IT E ( 6 , 8 ) X ( I ) , Y ( I ) , Y F ( I ) . 8 FORMAT{IX,8G15.5) 30 CONTI NUE. VJRITE(6,9) ... _ 9 FORtVAT ( 1 HI ) GO TO 100 P N C  .  '  Table 2A Effect of pulp density (16%) at 0.03% C 0  INDEPENDENT VARIABLE X X2 X3 X4 X5  2  REGRESSION COEFFICIENT  STANDARD DEVIATION  -0.456878D-01 0. 17 80170-03 - 0 . 7360800-06 0. 136661D-G8 -0.7 509410-12  0.6340350-02 " 0. 1G6921D-03 0 .7070010-06 0.19460QD-08 0. 1842 760-11  CONSTANT TERM = 0.361672E G l STANDARD ERROR OF ESTIMATE = 0.184501E 00 RESIDUAL VARIANCE •= C.340408E-01 MULTIPLE CORRELATION COEFFICIENT = C.99804 R . SQUARED = . 0.99603 The logistic equation describing these data i s : P  =  64000/(1 + exp(f(t)))  where f(t) = 3.6167 - 4.5688 * I O  -2  * t + 1.7801 * I O  -4  + 1.3666 * 10~ * t - 7.5094 * 10~ 9  4  * t - 7.3608 * 1 0 2  13  *t  5  _7  *t  3  T a b l e 2B E f f e c t o f pulp d e n s i t y  V A L U E S OF X . . 0.0 0.0 19.000 19.000 . 30.000 3G.000 44.000 44.000 53.000 53.000 67.00 0 67.000 . .... 7 7 . 0 0 0 77.000 1C1.C0 101 .00 116.00 116.00 143.00 143.00 163.00 163.00 188.00 188 .00 212.00 212.00 241 .00 241.00 262.00 262.00 .285. 00 285.00 316.00 v 3 16.00 4 77.OC  (16%) a t 0.03% CO  VALUES CF Y ... . 2 1 0 0 . 0 2150.0 2 58 0.0 2600.0 4 2 0 0 .0 4300.0 9100.0 9 0 0 0 .0 12400. 12300. 1.7000 . 17 1.00. 20400. 20400. 29900. 29800 . 35100. 35100. .. .' .42300. 41600. 49800. 5 0 4 0 0. 57400. 58200. . .59400. 60100. 61700. 61900. 626,00. 62800. 632 0 0 . 63 3 0 0 . • 63600. 6^500. 63700 .  FITTED .. .  .  V A L U E S OF 1 6 74.7 1674.7 3 641.0 .3 6 4 1 . 0 5 38 4.3 5 3 8 4 .3 8374.c 8 3 74.9 1.0785 . 1G785. 15276. 15276. 18974. 18974 . 28904. 289 0 4 . 3 52 6 8 . 3 5 2 6 8. 45.5 30... 4 5530. 51442. 51442. 56642. 56642. . 59748. 5 974 0. 61848. 6,18 48 . 62679. 6 267 9 . 6 32 0 9 . . 632C9. 63576. 63576. 6 3699.  Y  Table 3A Effect of pulp density (16%) at 0.13% CO  INDEPENDENT VARIABLE X X2 X3 X4 X5  , I  R EGR ESS I ON C O E F F I C I E NT 0.2179 350-01 -0.172928 0-02 0. 19 52130-04 -0.906010 0-07 0. 146010 0-09  STANDARD DEVIATION 0. 200241D-01 • 0.6532940-03 0-81430 70-05 0.426204D-07 0.7904590-10  CONSTANT TERM = 0 .357914E 01 STANDARD ERROR OF ESTIMATE 0.2S1981E 00 RESIDUAL VARIANCE •= 0 . 79 5 13 5E - 01 . MULTIPLE CCRREI.ATI CN COEFFICIENT = 0 . 9394 R SQUARED = 0.98792 rj  The generalized logistic equation describing these data i s : P where f(t) -  =  70000/(1 + exp(f(t)))  3.5791 +2.1794 * I O  -2  * t - 1.7293 * I O  - 9.0601 * 10~ * t + 1.4601 * I O 8  4  -3  - 1 0  * t + 1.9521'* 10~ * t Z  * t  5  3  3  T a b l e 3B E f f e c t o f pulp d e n s i t y  V A L U E S OF X 0.0 0. 0 23.000 2 3.000 3 3.000 33.000 ... 4 7 . GOG 47.000 5 9.000 59.00 0 7 2.000 72 .000 95.0GC 95.000 106 .00 106.00 120.00 120 .00 131.00 131.00 148.00 14 8.00 1.68 .00 168.00 192.00 192.00 216.00 216.00  VALUES  OF Y 18 8 0.0 1930.0 2280.0 2 2 6 0 .0 3410.0 3.44 0.0 5 8 0 0 .0 5300.0 9 10 0.0 9000.0 15000. 15 2 0 0 . . .26200 . 265CC. 31100. 3 1 0 0 0. 37300. 37200. 42200. 4 20 0 0 . 497 00 . 49900. 58600. 53800. . .66400. 66300. 6980.0 . 67700.  (16%) a t 0.13% CO  F l T T E D . V A L U E S OF 1900.0 1 9 0 0 .0 2 30 7.7 2 30 7.7 3272.9 3272.9 5 813.6 . 5 81.3.6 94 19.9 9419.9 14784. 14 7 8 4 . 2 5934.. 2 59 34. 3 10 7 9 . 3 1079. 3 72 4 2 . 37242. . . 41999 . 4 19 9 9. 49632 . 4 96 3 2 . 5 85 8 9 . 58589. . . 66139. 66139. 68998. 68998.  Y  Table 4A Effect of pulp density (24%) at 0.23% CO INDEPENDENT VARIABLE X X2 X3 X5  STANDARD . OFVI AT ION  REGRESS I ON CCEFFICIENT -Q..240356C-02 -0.6318 700-03 •0 . 595578D-05 -0.2 509210-07 O.412513D-10  0 . 1701250-01 0.4928530-03 0. 55276413-05 0 . 2630250-07 0.4452350-10  CONSTANT TERM = 0.360096E 01 STANDARD ERRO-R OF ESTIMATE = 0. 242196E 00 RESIDUAL VARIANCE -0 .5S6590E-01 MULTIPLE CORRELATION COEFFICIENT = 0.99583 R SQUARED 0.99368 The generalized logistic equation describing these data i s : P where f(t)  =  =  72800/(1 + exp(f(t)))  3.6010 - 2.4036 * 10~ * t - 6.8187 * 10~ * t + 5.9558 * 10~ '* t 3  4  - 2.5092 * 10" * t + 4.1251 * 1 0 8  4  _ 1 1  2  *t  6  3  T a b l e 4B E f f e c t of p u l p d e n s i t y (24%) a t 0.23% CO  VALUES  OF  X  VALUES  0.0  .  0.0 2 1 . CCO 21.000 44.000  44.COO . . .  .  70.000 7C.000  ac.ooo 80.000 1C2.0C 1C2.00 120 .00 120.CO 140.00 140.00 164.CO 164  .00  189.00 189.00 212.00 212.00 236.00 236  .00  .  OF  Y  FITTED  VALUES  2030.0 2040 .0 2 270.0 2300 .0 5 2 00 .0 5200.0 13300.. 13100. 17300.  5055.8 5 05 5 . 8 12216. 12216. 16832.  17 3 0 0 . 27500.  168 3 2 . 30601 .  277CG. 39000. . 3 fl F C C . 5100C. 51500.  306C1. 4 34 35  .._  4 34 3 5 . 5 5666. 5 5666. 64997. 6 4 9 9 7.  67000. 67100. 6 9 7 0 0 ... 69900. 70800. 71000. 7 2 1 CO. 71600.  OF  Y  19 3 4 . 5 1934.5 2 5 39.0 2589. C  69571. 69571. V  71249.  7 1249. 71822. 71322.  .  ,  Table 5A Effect of pulp density (24%) at 1.03% CO  •  STANDARD DEVI AT ION  I N 0 E P F N D P N T REGRESSION COEFF IC IE NT VARIABLE  •  X X?  X3 X4 X5  0.1369090-02  - 0 . 1128580-02 0 .117 1^00-04 -0.56*931 0-07 0. 10 721 50-09  0.8270 120-0 2 0. 3 0 8 0 4 6 0 - 0 3 0.4343110-05 0 . 2574240-07 0.5420160-10  CONSTANT TER^ = 0.3695110 01. STANDARD ERROR OF ESTIMATE = 0.100037E 00 RESIDUAL VAR T AN Q F = 0 . 100075E-01 MULTIPLE C OR R E LA F r CN COEFFICIENT = 0.99931 R SQUARED = 0.99863 The generalized logistic equation describing these data i s : P where f(t)  =  =  72400/(1 + exp(f(t)))  3.6951 +.1.3691 * 10~ * t - 1.1286 * 10~ * t + 1.1713 * 10~ * t 3  . -5i6493 * I O  -8  3  * t + 1.0722 * 1 0 ° * t 4  _1  2  5  5  T a b l e 5B E f f e c t o f p u l p d e n s i t y (24%) a t 1.03% CC>  2  VALUES OF X 0.0 0 .0 22.GOO 2 2.000 3 1 .000 31.000 46.000 46.000 56.GCC 56.000 7 3.0 00 73.000 96.000 96.000 1 C 5. C0 105.00 117.00 1 17.00 . 1 29 .0 0 129.00 144.00 144 .00 17 1.00 1 7 1 .00 190.00 190.on  VALUES OF Y FITTED VALUES OF Y. 17S0.C 17 5 5.2 17 5 5.2 1790 .0 2410.0 2 5 97.7. 2 59 7. 7 24 3 0.0 3 5 9 1.3 3 74 0 . 0 3 591.3 3 710.0 6800.0 6 72 2.8 6900 .0 6 7 2 2.8 101.00. 10332 . 1 03 3 ?..' 102C0. 21300. 201. 13 . 212 G 0 . 2 0113. 387 CO. 38650. 3 8650. 38800 . 4 57 92 . 446C0. 44800. 45792. 52300. 53905. 521C0. 539C5 . .60000. 6GC24.. 60 200 . 6 00 2 4 . 6 6 2 C 0. 65G97. .665CO. 6 5097. 6 9 37 2 . 689C 0. 69372. 690 CO. 70500. 70 32 2. 7 C.3 0 0 . 7 0322. v  Table 6A Effect of pulp density (24%) at 7.92% CO RE ORE SSI OH COEFE IC I ENT  STANDARD DEVIATION  0.156638D-G1 -0.3 46 5 72 0-02 0. I 4 46 63 0-04 -0.627694D-07 0 . 101.0 64 C-0 9  G. 8001850-02 0 .2 S l 4 2D-0.3 n 3876740-05 0. 224352D-07 0 .4594 140-10  IM GF.P ENOENT VARIABLE X X2 X3 X4 X5  -  CC VST ANT STANDARD R ES I DUAL M M "I PLE R SQUARE n  T FR'M ERROT OF VAR 1.1*NCE OCR R.E LATI  Q  \J  .  0.3^9736F 01 n . 106098E 00 EST I MATE •= 0. 1125£ «F-.01 IN Cf-EFPIC i E "\ T = 0.99932  • —  The generalized logistic equation describing these data i s : P where f(t)  =  =  70600/(1 + exp(f(t)))  3.4974 + 1.5664 * 10~ * t - 1.4657 * I O 2  - 6.2769 * 10  * t + 1.0106 * 10  -3  * t + 1.4466 * 10~ * t 2  5  *t  H  1  I—  1  T a b l e 6B E f f e c t o f p u l p d e n s i t y (24%) a t 7.92% CO  VALUES OF X VALUES OF Y FITTED VALUES OF Y 0.0  2100.0  2074.8  0. c  2100  .0  207 4 . 6  21.000  2 38 0 . 0  2 50 6 . 3  21  2410  .0  3200  .0  2 50 6 . 3 3 139.3  .000  28.000 28.000  3280.0  313  6 0 7 6 ..3  44.0C0  5900.0 6000.0  71.000  190CC.  1918 6.  71.000  19000 .  1918 6.  282C0.  2604 8.  .  4 4.000  80.000  .  358C0.  35889 .  103.00 103.00  42800.  44351.  42900 .  44351.  116.00 116.00  513C0. 51500.  52576.  126.00  .  2 604 8. 3 , 5 8 8 9 ..  ..36000.  9 2.000 92. 000  •.  6076.3  2 8 4 C C  80.000  9.3  .  .  52576. 57423.  57400.  126.00 144 . 0 0  57800.  57423.  63700 .  634C5.  144.00  63600.  6 3405 .  167.00  67800.  167  67900 . 6 8 9 0 0 . ...  .00  189.00 189.00 19R  .00  198.00  „  6900 0.  67505. - 675G5. 6.9271 V  . :  69800 .  6 9 271. 69644.  697CG.  69644.  .  Table 7A Effect of specific surface area at 1.0% C0„.Cyclosizer fraction No. 1 INDEPENDENT VARIABLE X X2 X3 X4 X5  RFGR ESSI ON COEFFICIENT - 0 . 124841D-C1 -0.165177D-02 0. 1 122 5 50-04 0 . 1 87 5960— 07 -0.2122280-09  STA NOARO CF.V I AT FON . 0.4.194840-01 _, 0.20655 TO-0 2 0.3784580-04 • 0. 2909160-06 0 .7936350-09  CONSTANT TERM = 0.326576E 01 STANDARD ERROR OF ESTIMATE •= 0. 2442 58 F 00 RESIDUAL VARIANCE = C.596519E-Q1 MULTIPLE CORRELATION COEFFICIENT = 0.99774 R SQUARED = 0.99543 The generalized logistic equation describing these data i s : P where f(t)  =  =  71200/(1 + exp(f(t)))  3.2658 - 1.2484 * I O  -2  * t - 1.6518 * I O  -3  * t + 1.1226 * 10~ * t  " + 1.8760 * 10~ * t - 2.1223 * 1 0 ° * t 8  4  _1  2  5  5  r— OO 1  14  T a b l e 7B Effect  of s p e c i f i c s u r f a c e a r e a a t 1.0% CO C y c l o s i z e r f r a c t i o n No. 1  VALUES OF X . ... .0.0 2 2.00 0 34.000 5 0.000 58.000 70.000 81.000 94.000 106.00 ]18.00 130 .00 14 5.00  VALUES OF Y 26 8 0.0 520C.0 18600 . 363C0. 45300. 58800. 6 7300. 68700. 69300 . 69900. 70100 70300  FITTED VALUES OF V 2 617.6 6 4C3.1 14 2 1 5 . 36201. 4 83 83. 60728. 6 6 041 . 6 8 5 9 8. 6 9 5 13. 6 9895. 70075. 70303 .  Table 8A Effect of specific surface area at 1.0% CO . Bahco-sizer fraction No. 1  INDEPENDENT V ARI A BL E • -  x  X2 X3 X4 X5  REGRESSION CCEFF 10 IFNT -Q.7113310-02 - 0 . 1501620-02 . O.8403870-05 0.3273780-C7 -0.2094680-09  STANDARD DEVIATION 0.4489370-01 . .0. 2 2 10 5 40-0 2 0 .4050300-04 0. 3 113470-06 0.849358D-C9  CONSTANT TERM = 0.305298E 01 STANDARD ERROR OE ESTIMATE •= 0 .261408E 00 RESIDUAL VARIANCE = C.633339E-Q1 MULTIPLE CORRELATION COEFFICIENT = 0.99771 R SQUARED = 0.99542 The generalized logistic equation describing these data i s : P where f(t)  =  =  71900/(1 + exp(f(t)))-  3.0530 - 7.1133 * 1 0  _3  * t - 1.5916 * 10~ * t + 8.4039 * 10" * t 3  + 3.2738 * 10" * t - 2.0947 * 10~ 8  4  10  2  *t  5  6  3  16  Table  8B  E f f e c t of s p e c i f i c s u r f a c e a r e a at 1.0% Bahco-sizer  VALUES CF X ..  .0.0  2?.000 34. 000  5 0.coo  58 .000 70.000 8 1.000 94 .000 1C6.00 118.00 130.00 14 5.0 0  f r a c t i o n No.  CO  1  FITTED V A L U E S OF VALUES OF Y 3 241.9 ... 335C. 0 7 02 9.9 5400 .0 149 70 . 20300. . 37604. 3 3 4 0 0. 5 02 37.. 4 7500. 6 09 00. 6 27 6 6 . 67858. .6 8 2 0,0. 70132. 70500. 70 80 0. 7 08 84. . 71174. 7110 0. 71 30 0 . 7 12 7 3. 7 1299. 71300.  v  Table 9A Leaching i n unbaffled tank at 1.0% CO REGRESSION COEFFIC IENT  STANDARD DEVIATION  -0.360925D-01 0.3672400-03 -0.2397290-05 0.9366910-08 -0.110220D-10  0.620146D-02 0. 1 126040-03 0.813377D-06 0.2503950-08 0,2747280-1L  INDEPENDENT VARIABLE X X2 X3 X4 X5 CONSTANT TERM = 0.424634E 01 STANDARD ERROR OF ESTIMATE = 0.119222E 00 RESIDUAL VARIANCE = 0. 142140E-01 ' MULTIPLE CORRELATION COEFFICIENT = 0.99933 R SQUARED = 0.99866  The generalized logistic equation describing these data i s : P where f(t) =  =  112500/(1 + exp(f(t)))  4.2463 - 3.6093 * 10~ * t + 3.6724 * 10~ * t - 2.8973 * ' l ( f 2  4  + 9.3669 * 10~ * t - 1.1022 * 1 0 9  4  _ 1 1  2  *t  5  6  *t  Table 9B Leaching i n unbaffled tank at 1.0% CO  VALUES OF X . 0.0 2C. 000 24.000 44.000 4 8.000 68.000 7 2.000 92. COO • 96.000 120 .00 144.00 164.00 168.00 188.00 192.00 212.00 216.00 240 .00 2 6 0.00 264 .00 28 8 .00 312.00 336.00 3 60 . 0 0 365.00  VALUES OF Y FITTED VALUES 0 F Y . . 158 7.9 . . 1440 .0 2 0 50.e 3060 .0 330C.0 3127.2 4 55 7.4 4800 .0 4912.5 5200 .0 66CC.0 6 67 5.0 7081.6 7300.0 8600.0 9560 .9 10174. 92 0 0.0 150 8 8 . 14300. 20 8 0 0. 2 3014. 3268G.. .344 0 0 . 34963. 37 8 0 0 . 47827. 510 00. 545C0. 50611. 6 4761 . 64200. 6 7 525. 67500. 82558 . 82500. 9 24 1 3 . .. 9 1 4 0 0 . 92300. 940 81. 0.10070E 06 0 . 10 2 2 0 E 06 0.107 50F 06 0. 10759E 06 0.11074F 06 0 . U 1 2 0 E 06 0.112 10F 06 0.11210E 06 0. 11220E . 06 _ 0. 1 122 3 f-.06  Table 10A Leaching in baffled tank at 1.0% C0 INDEPENDENT V AR I 4P.L E  .  X X7 X3 X4 X5  ' '. CONSTANT'TERO~~ ="  2  •STANDARD DE VI AT I ON  RcGRESSION COEFF I 0 I ENT  -0. 2768.13D-01  0.416 342 0-03 -0.45 5 2 910-05 0.1836 330-07 -0.2565700-10  0.6418200-02 0. 1196120-03 0.9012200-06 0. 293 19 7 0-08 0 . 34 29 620- 1. 1  0. 406040E"01  STANDARD ERROR OF ESTIMATE = 0. 119072E 00 R F S I DUAL VARIANCE = 0.I41782E-01 MULTIPLE CORRELATION COEFFICIENT = 0.99930 R SQUARED = 0.99860 The generalized logistic equation describing these data i s : P where f(t)  =  =  120000/(1 + exp(f(t)))  4.0604 - 2.7681 * 10~ * t + 4.1684 * 10~ * t - 4.5529 * 1 0 2  4  + 1.8383 * 1 0 ~ * t - 2.5657 * 1 0 8  4  _ 1 1  2  *t  5  _6  *t  20 i  Table 1 0 B Leaching i n b a f f l e d tank at 1 . 0 % CO  VALUES OF X 0.0 20.000 26.000 43.OCO 49.000 67.000 72. COO 91.000 97.COO 116.00 121 .00 141.00 '. . 147 .00 163.00 174.00 187.00 198.00 212.00 . .. 21.7 .00 222.00 2 35.00 240 .00 246.00 • 259.OC 265.00 270.0 0 2 8 5.00 . 292.00 3C7.00 314 .00 32 7.00 3 33.00 338 .00  VALUES OF Y FITTED VALUES OF Y 210C.0 2 034.0... 2900.0 3 069.9 310 0.0 3 348 .9 4300 . 0 4 115.14700.0 4 4 0 2.5 5800 .0 5460.3 .. 61.00.0 5 83 7.8 ' 8000.C 7 824. 1 8 69 7.7 8 500 .-0 1010 0. 126 16. 13500. 14 013. 21500. . 2 1.572 . 24523.. 2 560 0.. • . 36300. 3 39 3 3 . 4 3 8 0 0. 4 148 5. 52100. 5 1042. 59700 . 59 2 10. 68500. 6 916 1. .. 7 1 9 0 0 . 72521.. . 73500. 7 57 66. 83500. 33 6 84. 86400 . 86552. 89900. 89891 . 96600. 96811. 0 .10 1 30 E .06 9 98 8 1 . 0.10250E C6 0. 102.37E 0 6 0.1091.0E 06 0. 10 93 2E 06 0. L1150F 06 0. U 2 1 2 E 06 0.11630E C6 0. 1.166 8E 06 0.11810E C6 C. 118C4F. 06 0.1195CE C6 0.1194 3 E 0 6 0.11980E C6 ' 0.11972F 06 0,1198 6F 06 0 . U 9 8 0 E 06  APPENDIX 3 D e t e r m i n a t i o n of s p e c i f i c  s u r f a c e area  APPENDIX 3 • Determination The  C y c l o s i z e r and  of s p e c i f i c  Bahco-sizer  c h a r a c t e r i z e d by d e t e r m i n a t i o n o n l y r e g u l a r p a r t i c l e s , e.g.,  contained  subsieve  area f r a c t i o n s have been  surface area.  Irregular particles  12)have a d e f i n i t e volume and  a b e t t e r c h a r a c t e r i z a t i o n of the s u b s i e v e  m a t e r i a l can be a c h i e v e d  However,  spheres or c y l i n d e r s , p o s s e s s a d e f i n i t e  i n the s i z e f r a c t i o n s (see t h e i r  p i c t u r e s i n F i g u r e 11 and Therefore,  surface  of the mean p a r t i c l e diameter.  diameter as w e l l as known volume and such as those  1  through d e t e r m i n a t i o n  microscopic surface area  zinc  sulfide  of i t s s p e c i f i c  a r e a , which i s the s u r f a c e a r e a per u n i t mass of  only.  surface  solids.  F i g u r e 1 i s a schematic r e p r e s e n t a t i o n of the dynamic n i t r o g e n a d s o r p t i o n a p p a r a t u s used f o r d e t e r m i n a t i o n the u n f r a c t i o n a t e d -400 the d i f f e r e n t 1.  subsieve  Experimental  mesh s u b s i e v e size  of s p e c i f i c  surface area  zinc s u l f i d e concentrate  ( C y c l o s i z e r and  Bahco-sizer)  and  procedure  sample-holders and  placed  A known m i x t u r e of helium flow  (12 ml  present. recorder  and  When t h i s was chart.  i n the c i r c u i t as i n d i c a t e d i n F i g u r e n i t r o g e n content  achieved  Then the f i r s t Adsorption  the r e c o r d e r  chart.  l i n e p o s i t i o n , the p o l a r i t y advantage of the f u l l of n i t r o g e n .  into  was  passed at a  1.  constant  per minute) through the system to r e p l a c e the a i r o r i g i n a l l y  n i t o r g e n bath. peak on  of  fractions.  Three d i f f e r e n t samples of known weight were i n t r o d u c e d the  of  The  a steady  base l i n e was  sample was  of n i t r o g e n by  slowly-Immersed the s o l i d was  A f t e r the r e c o r d e r pen s w i t c h was  reversed  range of the r e c o r d e r  sample tube was  l i q u i d n i t r o g e n bath, while  obtained i n the  on  the  liquid,  i n d i c a t e d by  returned  a  to i t s base  i n order  to  take  scale, prior  to  desorption  then warmed up by removal from  the d e s o r p t i o n peak f o r the n i t r o g e n  the was  Z "O  CO  q m i  o  a  >  o  o m  1 O H  o m '2. >  a o  -1 73 13  22 >  CO  3  r.  3 recorded.  The  areas under t h e s e txro peaks ( a d s o r p t i o n and  were equal and The  c o n s t i t u t e a measure of the amount of adsorbed  complete sequence of t h i s procedure  enhance the v a l i d i t y  of the r e s u l t s .  r e p e a t e d on the second Was  desorption)  and  the t h i r d  was  repeated  nitrogen.  s e v e r a l times  Then the e n t i r e procedure samples.  to  was  C a l i b r a t i o n of the  apparatus  a c h i e v e d by i n j e c t i n g known volumes of pure n i t r o g e n i n t o the system  under a d s o r p t i o n c o n d i t i o n s . In a d d i t i o n the whole p r o c e s s was mixtures.  In t h i s study, gas m i x t u r e s  repeated w i t h two more gas  c o n t a i n i n g 25, 15 and  5% of  n i t r o g e n i n helium were used. F i g u r e 2 shows some t y p i c a l examples of a d s o r p t i o n , d e s o r p t i o n and  calibration  disc integrator 2.  (due  to i n j e c t i o n of n i t r o g e n ) peaks t o g e t h e r w i t h  t r a c e s , used  C a l c u l a t i o n of s p e c i f i c The  to determine  their  peak a r e a .  s u r f a c e area  computer programs 1 and  2 p r e s e n t the c a l c u l a t i o n s of  s p e c i f i c s u r f a c e a r e a of the s u b s i e v e z i n c s u l f i d e  the  samples.  I n program 1, the r e l a t i o n s h i p between i n j e c t e d volume, of pure n i t r o g e n and  a r e a under the a d s o r p t i o n and  by  squares  the l e a s t  n i t r o g e n adsorbed standard  technique.  and p r e s s u r e c o n d i t i o n s .  c o o r d i n a t e s are c a l c u l a t e d . out on d a t a o b t a i n e d a t 25, In program 2,  equation:  Using t h i s r e l a t i o n s h i p ,  on the sample i s determined,  temperature  calculated  d e s o r p t i o n c u r v e s was  determined  the volume of  then i t i s r e c a l c u l a t e d f o r T h e r e a f t e r , the B.E.T.-  A l l these d e t e r m i n a t i o n s have been c a r r i e d 15 and  57* ^  the s p e c i f i c  levels.  s u r f a c e a r e a of the samples has been  through a p p l i c a t i o n of the Brunauer, Emmett and  Teller  (B.E.T.)  5 V „ ads  (Po - P)  where P  =  +  V C m  Tr~n V C m  (1)  Pci  v  p a r t i a l p r e s s u r e of n i t r o g e n ( i n the gas  Po =  mixture)  s a t u r a t i o n p r e s s u r e of n i t r o g e n a t temperature of  liquid  nitrogen ^ads  C  =  v  °l  °f n i t r o g e n adsorbed  u m e  =  volume of adsorbed  =  constant  on the sample  n i t r o g e n due  to monolayer coverage  T h i s i s the e q u a t i o n of a s t r a i g h t as the dependent and P/Po Through l e a s t  squares  the i n t e r c e p t  mspc  fitting  factor  F  =  a c  of these data  When t h i s l a t t e r  (P° ~ P)  g  (B.E.T.-coordinates)  the s l o p e  ((C - 1)/V C) m  (1/V C) of the s t r a i g h t l i n e were a s c e r t a i n e d .  ) were d e r i v e d .  the s p e c i f i c  l i n e having P / ^ j  as the independent v a r i a b l e  v a l u e s , the monolayer c a p a c i t y (V ) and (V  (STP)  From  and  these  the s p e c i f i c monolayer c a p a c i t y i s m u l t i p l i e d with a f a c t o r (F), . r  s u r f a c e a r e a of the sample i s o b t a i n e d .  The v a l u e of  the  (F) i s g i v e n i n the f o l l o w i n g form:  6.02  *  10 i ^ 2 3  —  *  16.2 22 414  *  10  2  ^  *  10 ^ =  4  ,  3  5  3  2  *  -3 1  0  <  2)  23 where  6.02  *  10  =  Avogadro's number  16.2  =  a r e a covered  by a  (molecules/mole) molecule  (square Angstroms/  molecule) -20  10 10 ^  = =  c o n v e r s i o n of square Angstroms to square meters c o n v e r s i o n of m i c r o l i t e r s to l i t e r s i n V mspc  22.414  =  volume of a mole of n i t r o g e n gas under conditions  ( l i t e r per mole)  standard  Determination  of the s p e c i f i c  f o r C y c l o s i z e r f r a c t i o n No. The  output  squares  1.  of computer program 1 f o r the c a l i b r a t i o n  o b t a i n e d a t 25, 15 and IC and  s u r f a c e area w i l l be demonstrated  5% n i t r o g e n l e v e l s i s p r e s e n t e d  the c o r r e s p o n d i n g B . E . T . - c o o r d i n a t e s f i t of the B.E.T."data and  as the output of computer program 2. d a t a i n T a b l e s 1A to IC and  i n T a b l e 1A  i n T a b l e ID.  The  The  1, are p r e s e n t e d  surface i n Table  f i t t e d v a l u e s f o r the  the B . E . T . - c o o r d i n a t e s  to  least  the v a l u e f o r the s p e c i f i c  a r e a of the sample, C y c l o s i z e r f r a c t i o n No.  data  2,  calibration  i n T a b l e 2 are i n c l o s e  agreement w i t h those d e r i v e d e x p e r i m e n t a l l y . The  c a l i b r a t i o n d a t a are graphed i n F i g u r e 3.  the i n d i v i d u a l p l o t s f o r 25, average  15 and  Each p o i n t of  5% n i t r o g e n l e v e l s , i s the a r i t h m e t i c  of a l l measurements made under the i n d i c a t e d c o n d i t i o n s .  For a l l  three nitrogen concentrations a p r e c i s e s t r a i g h t l i n e r e l a t i o n s h i p i s o b t a i n e d , w i t h a zero  intercept.  The B . E . T . - p l o t i n F i g u r e 4. measurements. The  f o r the C y c l o s i z e r f r a c t i o n No.  Here again,each An  i n t e r c e p t and  1 i s presented  p o i n t r e p r e s e n t s the average  of numerous  e x c e l l e n t s t r a i g h t l i n e r e l a t i o n s h i p has been o b t a i n e d . the s l o p e of t h i s s t r a i g h t l i n e were used  for deter-  m i n a t i o n of the monolayer c a p a c i t y . The  specific  s i z e r f r a c t i o n s and  s u r f a c e areas of the r e s t of C y c l o s i z e r and  of the -400  c o n c e n t r a t e were determined The  mesh i n f r a c t i o n a t e d  i n a s i m i l a r way  subsieve zinc  to t h a t o u t l i n e d  a r e a of the t h i r d s i z e f r a c t i o n produced  the s p e c i f i c  shows, the d u p l i c a t e  d a t a agree w e l l , e.g.,  twice.  v a l u e s f o r the  To  surface  by both C y c l o s i z e r and  s i z e r f r a c t i o n a t i o n t e c h n i q u e s , has been determined  sulfide  above.  r e s u l t s of these d e t e r m i n a t i o n s a r e summarized i n T a b l e 3.  demonstrate the r e p r o d u c i b i l i t y of the r e s u l t s ,  Bahco-  Bahco-  As T a b l e 3 specific  F i o ts  i' o  4  B. E.T. PLOT FOR CYCLOSIZER FRACTION  No.  Table 3 Summary o f B . E . T . - s p e c i f i c s u r f a c e  Sample Weight  Sample  Slope  " Vmc c  (g)  1  * io  Intercept - 2  V  c  areas  V mspc (micro-liter/g)  Q  _>  4 5  B.S. No. 1 2  0.1323 0.1582 0.3452 0.2670 1.1916 1.5117.  4 5 6 7 8  0.3900 0.5632 0.2490 0.3953 0.6975 0.7575 1.1588 1.4055 1.5627  -400 mesh  0.3357  3  . •'  area (m /g) 2  m C.S. No. 1 2  Spec, s u r f a c e  0.5376 2.2446 1.9001 2.4915 0.6375 0.6211  0.4058 4.4764 3.7863 4.1861 2.6739 1.9115  1,395.45 276.11 149.48 147.84 126.35 103.32  6.07 1.20 0.65 0.64 0.55 0.44  0.1583 0.1865 0.5812 0.3845 0.4914 0.7768 0.7872 0.7832 0.9549  0.3403 0.1723 3.0918 0.3992 0.7220 1.3267 1.7079 1.8476 0.8913  1.585.95 943.17 656.10 651.16 287.53 167.09 107.30 88.75 66.39  6.90 4.11 2.86 2.83 1.25 0.73 0.47 0.39 • 0.29  0.9339  1.0370  315.48  1.37  Where C.S. = C y c l o s i z e r f r a c t i o n s B.S. = B a h c o - s i z e r f r a c t i o n s  s u r f a c e area of the C y c l o s i z e r f r a c t i o n No. and  3 were 0.65  f o r the c o r r e s p o n d i n g B a h c o - s i z e r f r a c t i o n ,  2.86  and  and 2.83  0.64 m  2  Program 1  C C  LEAST SQUARES F I T CALIBRATION DIMENSION X ( 2 0 0 ) , Y ( 2 0 0 ) ,YF(200) , W ( 2 Q 0 ) , E l ( 5 0 ) , E 2 ( 5 0 ) , P ( 5 0 ) 1 , C I F F ( 2 0 0 ) , X X ( 2 0 0 ) , Y Y ( 2 0 0 ) , V S T P ( 2 0 0 ) , P0(2CC) 2 i X l ( 2 0 0 ) , Y l (200) 3 R EAD ( 5 1 > N , M, N I 1 FORMAT(315) DO 3 9 1=1,5 39 Pi I ) = C . 0 DO 57 I=1»N READ(5,2)X( I ) , Y I I ) 2 FORMAT(8F10.0) 57 CONTINUE EXTERNAL AUX CALL LQF( X, Y, Y F , W , E 1, E 2 , P , C » , N , H, NI ,N0,EP,AUX) ,_ IF(NC.EC.O) GO TO 3 • WRITE(6,40) 40 FORMAT(6 6 H ESTIMATES OF ROOT MEAN SQUARE STATISTICAL ERROR IN THE 1 PARAMETERS) W R I T F ( 6 , 5 ) ( E 1 ( I ) ,I = 1,M) WRITE (6,4) 4 F 0 R M A T ( 6 0 H ESTIMATES OF ROOT MEAN ' S CU AR E TOTAL ERROR IN THE PARAME • ITERS) T  . WRITE (6 5 T  M E 2 U  ) t 1=1  f  M)  5 F 0 R M A T( 1X,8G 1 5. 5 ! W R IT E ( 6 , 6 ) 6 FORMAT (65HMICRCL ITER CF N2  CHART PEAK AP.EA FITTED VALUE OF CHART  Program 1  (continued - 1)  1PEAK A R FA ) CO 7 1=1,N 7 WRITE(6,5 >X( I >,Y(I 5 , Y F ( I ) C=l./P(2) D = -P(1  C C C  DO  C C  C C C C  )/Pi2)  READ(5,1)NN READ(5,2)PitTtS P l IS THE AT M. PRESSURE(MMHG) T IS THE A 8 S . T E M P . 'lN KELVIN-DEGREE S IS THE NITROGEN CONTENT OF GAS MIXTURE 60  •  I=1TNN  READ(5,2) D I F F ( I ) , YY.( I ) ; . CONTINUE" D I F F ( I ) IS THE PARTIAL PRESSURE OF LIQUID NlTRCGEN DO 6 1 1=1,NN 61 XX( I)=D+C*YY( I) X X I I ) . IS.THE VOLUME' OF ADSORBED NITROGEN DO 62 1 = 1, NN . VSTP( I)=0.359408*(Pl/T)*XXm 62 CONTINUE ' '' THE CONSTANT TERM IS EQUAL TO 2 7 3 . 1 5 / 7 6 0 . PP=S*P1 PP I S THE PARTIAL PRESSURE OF NITROGEN IN GAS FIXTURE PO IS THE SATURATION PRESSURE OF NITROGEN "AT TEMPERATURE OF LIQUID NITROGEN (MNHG) DO 64 I=1,NN PO ( I ) = P1 + D.I FF-("l )  60  Program 1  ( c o n t i n u e d - 2)  DETERMINATION OF THE B.E.T.-COGRDINATES XI(I)=PP/FC<I) 64 Y1<I ) = P P / ( V S T P ( I ) * ( P O ( I )-PP }) WRITE ( 6 1 8 8 ) 8 8 FORMAT(1H1) WRITE (6, 70) 70 F 0 R Ri A T ( 7 5 H A D S. PEAK AREA VOL. ACS. N2 VOLUME IN ST P 1 P/(VADSiPC-P))t//) DO 5 5 I = 1 , N N 55 WRIT E ( 6 5 5 ) Y Y ( I ) > X X ( I ) , V S T P ( I ) , X 1 ( I ) , Y 1 ( I ) WR I T E ( 6, 8 ) FORMAT(1H1) GO TO 3 EN C  FUNCTION AUX(PtC»X»L) DINENSICN P(50),C(50)  D ( 1 ) = 1. AUX=P(1 )  00 10 J = 2 5 0( J )=D( J - l ) * X T  10  AUX=AUX+P(J)*D(J)  RETURN END  P/PO  Program 2  r  C C C  '  DETERMINATION CF SPECIFIC. SURFACE AREA LEAST SQUARES F I T ' . DIMENSION X( 200 ) , Y I 2 0 0 ) , YF ( 2 0 0 ) , W ( 2 C O ) , E 1 ( 5 0 ) , E 2 ( 5 0 ) t P ( 5 0 ) 3 READ ( 5 , 1 > N , M , N I 1 FORMAT(315) DO 3 9 1 = 1 , 5 39 P ( I ) = 0 . 0 DO 5 7 1 = 1 , N READ ( 5, 2 )X ( I ) , Y { 1) 2 FORMAT ( 4 F 1 5 . 5 ) 57 CONTINUE R.EAD( 5 , 22 )WE 22 FORMAT (8F 1 0 . 0 ) EXTERNAL AUX CALL L Q F ( X , Y , Y F , W , 6 1 , E 2 , P , 0 . , N , M , N I , N D , E P , A U X ) I F ( h D . E C O ) GO TO 3 KR I T E ( 6 , 4 C ) 40 FORMAT(66H ESTIMATES OF ROOT MEAN SQUARE S T A T I S T I C A L ERROR I N THE 1PARAMETERS) WR I TE-< 6 , 5 ) ( E 1 ( I ) , 1 = 1 , M) • WR IT E (6 , 4 ) 4 FORMAT(6CH ESTIMATES CF ROOT MEAN SQUARE TOTAL ERROR I N THE P AR AM E ITERS 5 WRIT E (6 ,5 ) ( E 2 ( I ) , 1 = 1 , M ) 5 FORMAT( 1 X , 8 G 1 5 . 5 ) WRITE(6,93) ;  Program 2  (continued - 2)  ~ 93 F C P M A T ( 3 7 H E.E.T.-COORD I N A T E S j < ' W R I T E ( 6 , 6) 6 FORM A T { 5 3 H V A L U E S OF P/PG P/(VADS(PC-P) ) F I T T E D P / ( V A D S I P O - P ) ) ,/) DC 7 I=1,N • 7 KR I T E ( 6 , 5 ) X ( I ) t V ( I ) , YF{ I ) VM=1 . / < P ( 1 ) + P < 2 ) ) VM£PC=VM/KE SS A = 0 . 0 0 4 3 532*VM SPC WR I T E ( 6 ,41 ) 41 FORMAT! 1H0, 57H'*EI GHT . CF SAMPLE MONOLAYER C A P A C I T Y S P E C I F I C SURFACE lAR'EA,/) h P I TE ( 6 5 ) V < E , VM ,S SA • WRITE(6,8) 8 FORMAT C1F.1) GO TO 3 END T  FUNCTION  AUX(P,D,X,L)  D I M E N S I O N P ( 5 0 ) ,C(5C5 D( 1 ) = 1 . AUX = P ( 1 ) DC" 10 J = ? i 5 10  D U )=D( J-1)*X AUX=AUX +P( J . ) * 0 ( J )  RETURN END  16  T a b l e 1A Curve f i t t i n g  o f c a l i b r a t i o n d a t a a t 25% N  for Cyclosizer  f r a c t i o n No. 1  INTEFMECIATE ESTIMATES OF PARAMETERS, SUM OF SQUARES 0.0 0. 14 117E 07 C. C -C.47469E- 01 1.3721 2 53.38 FINAL ESTIMATES OF PARAMETERS -C.46432E- 01 1.3721 SUM OF SQUARES 253.38 ESTIMATES OF ROOT MEAN SQUARE STATISTICAL ERROR IN THE PARAMETERS 0 .46 29 1 0.24495E-C2 ESTIMATES OF ROOT MEAN SQUARE TOTAL ERROR IN THE PARAMETERS 0. 894 52E-C2 1.690 5 MICROLITER OF N2 CHART PEAK A RE A FITTED VALUE OF CHART PEAK AREA 50.00068 .556 64.3C0 68.556 7 C. 5 C 0 . 50.000 67.200 68.556 50.000 7c0. 7 00 68 . 556 50.000 1 39.00 ICO.00 137.16 100.00 140 . 10 137. 16 137.16 ICG.OC 137.CC 100.00 137. 10 13 7.16 2 0 5.76 150.CC 211.30 150.00 2C5.76 207.80 2 0 5.76 150 .00 205.40 150.00 2C5.3C 205.76 274.36 200 .00 275 .6C 200 .00 273 .10 274.36 267.30 274.36 2 CO.CO 266 .00 2 7 4.36 200.00 416 .40 4 11.57 3C0.0C 411.57 3CC .CO 4 11.CC 411.57 300 .00 407.80 415.50 411.57 3CC.00 . 411.57 412.80 3C0.0C  17  T a b l e IB Curve f i t t i n g  of c a l i b r a t i o n d a t a a t 15% N  f o r C y c l o s i z e r f r a c t i o n No. 1  INTER?-PC I f i r E S T I M A T E S OF PARAMETERS? SUM OF SQUARES 0. C 0.29163E 0 6 0.0 0.92 2 32 C.485 I C E - 0 1 7 2.151 FINAL C  ESTIMATES 4 8 G 8 4 E - 01  OF  PARAM ET ERS 0.92 23 3  SUM OF SCUARFS 72.151 E S T I M A T E S OF R 00 T MEAN SQUARE S T A T I S T I C A L ERROR IN T H E PARAMETERS 0 .55 73 6 0.4O406E-C2 E S T I M A T E S CF ROOT MEAN SQUARE T O T A L ERROR IN THE PARAMETERS 1.18 36 0.858C4E-C2 M I C R O L I T E R OF N2 CHART PEAK AREA F I T T E D VALUE OF CHART PEAK AREA 4 6.164 5C.OCO 48.7GC 4 6.164 4 8 . ICC 50.000 45 .900 50.000 4 6.164 5C.CCC 4 8.4 00 4 6.164 4 6. 164 4 4 .6 00 5 0.00 010C.C0 92 .500 9 2.281 ICC.c c 92.28 1 8 9. 2 C 0 100.00 9 1. 500 9 2.281 ICO.00 90.300 9 2.28 1 1 4 0 . 10 13 8.40 150.CC 150 .0 0 137.20 138 . 4 C 150.00 138.40 13 7.60 1 5 0 . DC 13 5.30 13 3.40 200.00 186 .00 184.51 2CC.00 181.50 184.51 2C0.CC 184.ac 184.51 2C0.C0 187 .10 18 4.51 184.5 1 2C0.CC 187.3C  18  T a b l e IC Curve f i t t i n g  of c a l i b r a t i o n d a t a a t 5% N  f o r C y c l o s i z e r f r a c t i o n No. 1  I N T E R M E D I A T E E S T I M A T E S OF P A R A M E T E R S , SUM OF SQUARES 0.0 0 . 2 6 6 2 7 E 06 0 .0 56.982 C. 407 1 0 E - C 1 1.0 4 32 FINAL ESTIMATES C. 4 0 6 C 5 E - 0 I  OF  SUM OF SQUARES EST I MATES CF ROOT 0.45337 E S T I M A T E S CF ROOT C.51466 M I C R O L I T E R OF N2 30.000 3C. 0CC 30 .000 3C.-000 30.000 50.000 5 C. C C C ICO.00 100.00 ICO.CO 150.0C 150.0C 2CC.00 200 .00 200*00 2C0.00  PARAMETERS 1 .0432  56.982 MEAN S GUAR c S T A T I S T I C A L ERROR IN THE PARAMETERS 0.36 67 6 E - 02 MEAN SQUARE TOTAL] ERROR IN THE PARAMETERS 0 . 7 3 9 9 1 E - 02 CHART PEAK AREA F I T T E D VALUE OF CHART PEAK AREA 31.336 3 0.7 00 31.336 31.CCC 3 1.336 30.500 31.100 3 1 .33 6 3 1.336 3 0 . £ CO 52 . 2 C0 5 3.9 00 52.200 51.5C0 104.3 6 10 8.30 104.36 105 . 10 1.04 .36 100.GO 159.90 156.5 2 156.5 2 156 .90 208'. 40 2C8. 68 2 0 8-68 206 .30 208.68 208.80 2 0 8.68 208.30  T a b l e ID Output o f d a t a d e r i v e d on C y c l o s i z e r f r a c t i o n No. 1 at gas mixture  ADS.  PEAK  AREA  198. 6 C 197 .30 "197.20 192.40 187 .20  VOL. ADS..N2  190.34 189 .09 189.00 184.40 179 .41  ( c o n t a i n e d 5% n i t r o g e n )  VOLUME  IN STP  174.41 173.27 173 .18 168.96 164.40  P/PO  0.48347E-01 0.48719E-C1 0.48719E-01 0.48719E-01 0.48719E-C1  P/IVAD S ( PO-P ) )  0.29129E-03 0.2S558E-G3 0.29573E-03 0.3O311E-03 C. 3 U 5 3 E - 0 3  T a b l e ID  (continued -  1)  Output of d a t a d e r i v e d on C y c l o s i z e r f r a c t i o n No. at gas mixture  ADS.  PEAK AREA 2C2.8C 218.00 2C8.5G 2C7. F.C 2 09 .60 2.14. CO 198.00  VOL.  ADS.  219.83 236.31 226 .01 . 225.25 227 .20 2 31.97 214.62  N2  ( c o n t a i n e d 15%  1  nitrogen)  VOLUME IN STP  P/PO  201.78 216.91 207.45 206.76 2 0 8.55 2 12.93 197.00  0 . 15061 r. 15061 o . 15061 0. 15003 0. 150C3 0 . 15003 0. 15003  P/(VADS{PO-P}) 0 .87372E-03 0.81744E-03 0.85469E-03 0.8 5 371E-0 3 0.84638E-03 0.82897F-03 • 0.89597E-03  T a b l e ID  (continued - 2)  Output o f d a t a d e r i v e d on C y c l o s i z e r f r a c t i o n No. 1 at gas mixture  ADS.  y  PEAK  AREA  3 4 5 . SC. 347 .20 360.SO 342.30 3 67 .20 353.9C 357.70  VOL.  ADS.  252.14 2 53.09 26 3 .00 249.51 26 7.66 257.97 2 60.7 4  N2  ( c o n t a i n e d 25% n i t r o g e n )  VOLUME  IN  232.06 232.93 242 .06 2 29.6 5 246.35 2 3 7 .43 239.96  STP  P/PO  0 .23863 0.23863 0.238 63 0.23863 0.23715 0 .2 3 6 5 6 0.236 56  P/(VADS(PO-P))  0 .13506E-02 0.1345 5 E - 0 2 0. 1 2 9 4 8 E - 0 2 .0 . 13648 E-02 0. 1 2 6 1 9 E - 0 2 C 13051E-02 0.12912E-02  22  Table 2 D e t e r m i n a t i o n of s p e c i f i c  s u r f a c e a r e a o f C y c l o s i z e r f r a c t i o n No. 1  INTER MFC I A T E E S T I M A T E S CF PARAMETERS, SUM OF SQUARES 0.0 0.17639F-C4 CO . •G.12C55E-G7 0 .4C585E-04 0. 5 3 7 6 C E - C ? FINAL ESTIMATES 0.40584F-04  CF  PARAMETERS 0, 5 3 7 6 I E - 0 2  SUM OF SQUARES E S T I M A T E S CF ROOT 0 . 53 326 E S T I M A T E S OF ROOT 0 . 142QCE-C4 VALUES  OF  P/PO  C.23863 C.23 86 2 0.23863 0. 2 3 8 6 3 0 . 2 3 7 15 0 . 23656 C.2365 6 0. 150 6 1 C. 15061 C . 15C61 0 . 15003 C. 1 5 C C 3 0.15003 C. 15 0 0 3 . 0.48 3 4 7E-C1. 0.48 7 19E-0 1 C.48719E-01 C.46719E-0 1 0 .48719E-0 1 WEIGHT  OF  SAMPLE  0.13230  C. 1 2 0 5 5 E - 0 7 MEAN SQUARE S T A T I S T I C A L ERROR IN THE PARAMETERS 3 .0900 MEAN SQUARE TOTAL ERROR IN THE 'PARAMETERS 0 . 82285E-04 E . E . T .-COORDINATES P/[VADS(PO-P) ) FITTED P/(VACS(PO-P)) 0 .13506E-02 0. 1 3 4 5 5 E - C 2 0 . 12548E-C2 0.13648E-02 0.12619E-C2 0 . 130 5 I t - C 2 0.12512E-C2 C.87872E-G3 0.81744E-03 0.85469E-03 0 .8527 I E - C 3 0.846 33E-03 0.82897E-C3 0 .895 9 7 E - 0 3 0. 2 9 T 2 9 E - C 3 0 .295 5 8 E - C 3 0 .295731-02 0.30Cl1E-C3 0 . 3 I 153E-C3 MCNOLAYER 18 4.62  0.13235E-02 C. 13 2 3 5 E - 0 2 C. 12 2 3 5 E - C 2 0.13235E-0 2 C..13 1 5 5 E - C 2 C.13123E-C2 0.13123E-02 C.85C27E-C3 0.35027E-03 0.85027E-C3 C.64715E-03 0. 84 7 1 5 E - 0 3 C.64715E-C3 C.64715E-03 G.30050E-G3 C.2C25CE-C2 0.3025CE-C3 0.30250E-C3 C.2C25CE-C3  CAP A C I T Y  SPECIFIC 6 . G746  S U R F A C E AREA  

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