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Development of a mathematical model of a molybdenite leaching process Parsons, Geoffrey Joseph 1978

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DEVELOPMENT OF A MATHEMATICAL MODEL OF A MOLYBDENITE LEACHING PROCESS by Geoffrey Joseph Parsons B.Sc.(Tech.) with merit, Univ. of New South Wales, A u s t r a l i a , 1973  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of M e t a l l u r g i c a l Engineering  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1978  ©  Geoffrey Joseph Parsons, 1978  In  presenting  this  an a d v a n c e d  degree  the  shall  I  Library  f u r t h e r agree  for  scholarly  by h i s of  this  written  thesis at  the U n i v e r s i t y  make  that  it  purposes  for  freely  permission may  representatives. thesis  in p a r t i a l  is  financial  of  British  by  for  gain  Columbia  shall  the  that  not  requirements  Columbia,  I  agree  r e f e r e n c e and copying  t h e Head o f  understood  Department  2075 Wesbrook Place Vancouver, Canada V6T 1W5  British  for extensive  permission.  The U n i v e r s i t y  of  available  be g r a n t e d  It  fulfilment of  of  or  that  study.  this  thesis  my D e p a r t m e n t  copying  for  or  publication  be a l l o w e d w i t h o u t  my  - i-  ABSTRACT  A mathematical model has been developed for the more c r i t i c a l section of a proposed molybdenite/nitric acid leaching process.  The model accounts for the unit operations of leaching,  grinding and flotation, with the leaching simulation involving the most rigorous formulation.  The accuracy of the model could not be  evaluated at this stage owing to the lack of an operating p i l o t - or commercial-scale plant.  Simulation of leaching i s based on mass balancing with determination  of reaction rates from the individual components of  the'rate equations.  The rate of leaching of molybdenite i s accounted  for as a function of solution reactivity, active surface area per reference weight, pulp density and temperature.  The leaching of  contained pyrite and chalcopyrite are similarly accounted for but in a more simplified manner. The grinding model i s based on a combination of theory and empiricism while the flotation model i s derived from the simple first-order rate equation.  The simulation i s s t i l l subject to some uncertainty since verification i s not possible at this stage of process development. However, the model effectively accounts for the complex system  - i i -  involving a solids recycle stream.  The effects of new solids flow  and analysis, leachant flow and strength, leaching temperature, partial flotation bypass, leaching vessel size and number, grinding mill size, number and size of flotation cells are a l l considered.  - iii -  TABLE OF CONTENTS Page ABSTRACT  .. .. ..  TABLE OF CONTENTS LIST OF TABLES  0 0  '..  ..  i  a O «. O o o o o o o c o o o. a a o • «• on » • o o • 9 o • * • iiJL * e <>« o o « * o o « • <> © o » » o «• •« <. * •» * < > <>«  vxi  LXST OF FIGURES e *> e o © « o » & • o o o « • ° <>» •« •••• »« •» »» »• • • v i x i ACKNOWLEDGEMENTS  ..... ..  .. .- x i  Chapter 1  INTRODUCTION . . 1.1  General ..  '.. .. 1 ..  .. .. 1  1.2 Model Classification I  1.3 The Process  ..  3  .. ..  ..  1.4 Process Chemistry  5  .. ..11  i.  1.5 •1.6  1.4.1  Leach Chemistry .  .. ..11  1.4.2  Precipitation Chemistry  .. ..18  1.4.3  Solution Purification Chemistry  1.4.4  Acid Regeneration Chemistry  Scope of Model  . „ .„ ..21 ..22  .. ». .» .. .. . = .. ...  Source and Supply of Molybdenum  .. ..26  1.7 Economic Situation of Molybdenum 1.8 Current Methods for Processing Molybdenite Concentrates 1.9  Advantages of Nitric Acid Leach Process  .. 23  ..32 34  .. .. ..40  - iv -  Chapter  Page l.l'O  Nitric Acid Leaching of Sulphides  42  1.10.1 Molybdenum Sulphide -.. .. .,  43  1.10.2  Copper Sulphides  1.10.3 Nickel Sulphides  .... 45 ..  1.11 Modelling i n Hydrometallurgy 1.11.1 Leaching .. ..  ..  47 .. .. ..  50 ..  .. 51  1.12 Modelling of Other Unit Operations in Leach Circuit  2  1.12.1 Grinding  58  1.12.2  60  Flotation  BASIS OF LEACHING MODEL  .. . . .. 63  2.1 Modelling by Mass Balances 2.2 1  X  58  .. .. 63  Rates of Reaction  65  2.2.1 Analysis of Terms  66  EXPERIMENTATION  ..  ». . • 78  3.1 Apparatus  .. .. .. .. . • •» •. •. •» • • • • • • 78  3.2  Chemical Analysis  .. 81  3.3  Experimentation and Analysis  .. ..  ..  .. 83  3.3.1 Reaction Order with Respect to Nitric A.CXd o • o e o e a * o o a m • • mo o o « a  o•  83  3.3.2 Determination of Area Factor Relationship for Endako Molybdenite Concentrate. 84 4  FORMULATION OF MODEL  ..  ..  90  4.1 Recycle Estimates .. ... .. .. .. ..  93  4.2 Concentrate Mixer  94  4.3 Leaching  95  - V -  Chapter  Page. 4.4 Leach Balance 4.5 F i l t e r  .. .. ».  100  .. ..  100  4.6 Regrind  5  .. .. .  4.7  Stream S p l i t t e r  4.8  Flotation  .. 101  .. .. .... .. .. ..  = 103 *.  104  4.9 Recycle Combinaton  106  4.10 Input/Output Routines  107  MODEL EVALUATION AND DISCUSSION  .. .. 108  5.1 S t a b i l i t y and Convergence  ..  5.2 Model Results —  ~  i  HO H6  5.2.1 New Solids Flow Rate  116  5.2.2  I n i t i a l Acid Strength  121  5.2.3  Solution Flow Rate  .. .. .. 125  I  5.2.4 Leach Temperature  <•. • - I  5.2.5 P a r t i a l Bypassing of Flotation  ......  5.2.6 Leach Vessel Volume  .. .. .. 139  5.2.7 Number of Leaching Stages 5.2.8 6  3  CONCLUSIONS  Grinding  .. ..  ..  7 RECOMMENDATIONS REFERENCES  ..  ..  136  143 146  -  -  15° 153  •  1 5 4  APPENDICES A  2  Consumption of Molybdenum by Category  159  - vi -  Page B  Experimental Results  .. .. ...  C  Source Listing of Computer Program  D  Other Specific Parameters Used in Model  • .. .. 160 .. 162 181  - vii -  LIST OF TABLES  Table  Page VI Concentrations of Mo . Remaining i n Various  I  Solutions, (g/1 Mo ) .. ..  16  VI  II  Important Molybdenum Minerals and Composition .» .. 27  III  Molybdenite: Mineralogical Data  IV  Metal Content Ranges of Molybdenum Ores  V  IX i  X i  29  1976 Molybdenum Production of Leading Countries  VI VII VIII  ...... 27  Copper Penalties i n Molybdenite Concentrate _  .. 32  ....  34  Concentrate Analyses SizingsM i l l i n g Operations . 101 79 Size Reduction Steps and i n Normal Standard Condition for Leach Process  , .. 109  Extraction from Total Input Solids on each Pass for Different New Solids Flow Rates. (%) .. .. 121  XI  Extraction from Total Input Solids on each Pass f o r Different I n i t i a l N i t r i c Acid Concentrations. (%).. 127  XII  Extraction from Total Input Solids on each Pass for Different Solution Flow Rates. (%) .. .. .. -.. .. 132  XIII  Extraction from Total Input Solids on each Pass for Different Leach Temperatures. (%) .. 134  XIV  Extraction from Total Input Solids on each Pass for Different Number of Stages. (%) 143  XV  Solids Recycle Ratio as a Function of Number of Stages (Constant Total Volume)  145  - viii -  LIST OF FIGURES  Page Process flowsheet used for modelling study . . . . . . Endako molybdenite concentrate (600 x)  7 10  Precipitated molybdic oxide hemihydrate (MoO^-^l^O) (^00 o o oo oo o • « oo »• oo •« • * •« o o oo 10 9 o  o  o o  Eh-pH relationship for n i t r i c in acid solutions  and nitrous species 13  Solubility of molybdenum vs pH in acid solutions .. 20 Batch extraction curve for Gibraltar molybdenite concentrate .. .. .. 24 Molybdenum production flowsheet  .. .. 39  Extraction of nickel,cobalt and copper from pentlandite by n i t r i c acid as a function of i n i t i a l sulphuric acid concentration .. .. .. 49 Typical extraction curve  ..  .... 56  Rate of extraction vs extraction, showing construction for staging analysis . . .. .. 56 Extraction curves for Gibraltar molybdenite concentrate (a) as received (b) wet ground one hour i n laboratory pebble m i l l  67  Leaching rate of molybdenite concentrate as a function of time for (a) as received (b) wet ground one hour .. 68 Molybdenite concentrates (a) Brenda +325 mesh (160 x) (b) Brenda -400 mesh (160 x) (c) Gibraltar (325 x) (d) Gibraltar (1600 x) 70 Leach residues (a) Gibraltar, 3 days (2000 x) (b) 6075% extraction (4000 x) . 72  - ix -  Page Approximate dimensional characteristics of four molybdenite concentrates  74  Surface area vs fraction leached for i n i t i a l equal masses of spheres of one unit radius and two units ITcldlUS  •  o  0 9  0 0  s o  s o  e  0 0  o  •  »  o  •  •  •  <  «  •  O B  •  »  Surface area vs time for i n i t i a l equal masses of spheres of one unit radius and two units radius  * •  . . 77  „  Experimental apparatus  77  80  Log i n i t i a l reaction rate vs log i n i t i a l HNO3 for Brenda +325 mesh molybdenite concentrate  85  Leaching rate and area factor vs fraction leached 87  for Endako molybdenite concentrate Model block diagram Computer model flowsheet  . .  .. 91  .. .. .. ..92  Solids recycle ratio vs new solids flow rate  .. .. 117  Total input pulp density, operating area factors and operating n i t r i c acid concentrations vs new solids flow rate .. .. 119 Gain in solution molybdenum concentration vs new solids flow rate 120 Solids recycle ratio vs i n i t i a l n i t r i c acid concentration .. .. ..  122  Total input pulp density, operating area factors and operating n i t r i c acid concentrations vs i n i t i a l n i t r i c acid concentration ..  124  Insol content of leach residue, reflotation concentrate and recycle solids vs i n i t i a l n i t r i c acid concentration  126  Solids recycle ratio vs solution flow rate  129  - X -  Figure 30  Page Total input pulp density, operating area factors and operating n i t r i c acid concentrations vs solution flow rate  130  31  Gain i n solution molybdenum concentration vs solution flow rate .; .. .. ..  131  32  Solids recycle ratio vs leach temperature  33  Total input pulp density and operating area factors vs leach temperature .... .. 135  34  Insol content of leach residue, reflotation concentrate and recycle solids vs fraction bypassing flotation  137  35  Solids recycle r a t i o vs fraction bypassing flotation ..  138  36  Solids recycle ratio vs leach vessel volume .. ..  140  37  Total input pulp density and operating area factors vs leach vessel volume  .. ..  133  . 142  38 ^  Solids recycle ratio vs number of leach stages. Constant stage volume  39  Recycle area factor vs fraction leached for different values of b^ •• ••  40  Recycle area factor vs fraction leached for different grinding m i l l sizes  144  148  - xi -  ACKNOWLEDGEMENT S  I extend my gratitude to both my supervisors, Dr. Ernie Peters and Dr. J. Keith Brimacombe, for their assistance and advice throughout my period at U.B.C. I also wish to thank those members of the Departments of Mineral Engineering and Chemical Engineering as well as other members, both staff and students, of the Department of Metallurgical Engineering for their time and help.  The financial support of the National Research Council of Canada i s greatly appreciated.  I am also grateful to both Brenda  Mines Ltd. and Canex Placer Ltd. for supplying the molybdenite concentrates necessary for the experimental portion of this study. i  "So You want to be a Metallurgist!  - 1-  CHAPTER 1  INTRODUCTION  1.1  General  The complete quantitative description of an industrial process i s often quite complex.  However, the expansion i n computer  f a c i l i t i e s has enabled the formulation of numerous types of mathematical models which can contain much of this complexity and provide a reasonably realistic analysis.  Computerized  mathematical  models provide an economical means for design or for simulation of processes and may be used either i n a predictive capacity, or interactively with the process to attain efficient control.  Once  the* model i s sufficiently well developed to establish r e l i a b i l i t y i t may be used with confidence to determine the consequences of changes in operating variables without risking the expense of pilot- or plant-scale experiments.  Mathematical models are developed to varying degrees of sophistication depending on the state of knowledge of the process and the i n i t i a l aims for the formulation, The development may be restricted by the accuracy with which the influencing variables  - 2 -  can be measured thus resulting in a range of models from relatively simple simulations with numerous broad assumptions to more complex descriptions which account for many process variables.  The process of model building generally follows a stepwise development as outlined by Himmelblau [ 1 ] . A highly idealized, and hence simplified, mathematical description is i n i t i a l l y formulated. This may result in an unrealistic model but provides a basis for analysis of deficiencies and for construction of more r e a l i s t i c models.  _  _ The purpose of this study was to establish a metallurgical  simulation model for a proposed molybdenite/nitric acid leaching process.  The approach to formulation was dictated by the fact that  no industrial-scale or pilot-scale plant was in existence.  Hence  the model was based on available theory, laboratory experimentation, analogies to other systems and plausible assumptions where information was lacking.  The section of the process modelled in the study involved a number of unit operations.  Varying degrees of emphasis were placed  on the modelling of these different units with the ultimate aim of formulating a satisfactory computer simulation within reasonable limits.  1.2  Model Classification  Mathematical models may be classified into two types on a time basis: 1.  Steady state - where the process properties are time  invariant at any particular location and accumulation terms are equal to zero.  This applies to uniform operations after the effects  of parameter variations or fluctuations have come to consistent levels. 2.  Dynamic - where the model describes the changing state  of the system.  That i s , process properties at any particular location  may vary as a function of time. i  The dynamic simulation may be more versatile but i t i s more d i f f i c u l t and hence more costly to develop.  Its formulation therefore  requires greater justification than for a steady-state simulation. Often the development of a steady-state model precedes the development of the dynamic model in accordance with the stepwise construction of more realistic simulations.  At this stage of development of the molybdenite/nitric acid leach only a steady state model is required for the prediction of plant behaviour under steady operating conditions.  Dynamic modelling  -  4  -  may be considered when a commercial plant i s i n operation.  Mathematical models may also be broadly classified into two extremes on the basis of the method of formulation: 1.  Fundamental or mechanistic models - which are based  on known or assumed mechanisms for the process.  This enables a  relatively complete characterization but may require considerable time and effort to develop.  Since there is a reasonable understanding  of the mechanisms involved these models may be applicable over wide ranges of operations, provided that there are no changes in mechanism. Although based on fundamentals, numerous industrial models of this type require empirical or semi-empirical corrections to achieve satisfactory agreement between predicted and practical results. 2.  Empirical or s t a t i s t i c a l models - which rely on analysis  of experimental or operating data. on the determination  Completely empirical models rely  (or fitting) of operating relationships i n terms  of measurable variables for the actual plant units. Although the f i t t i n g of relationships i s based on s t a t i s t i c a l analysis the form of the equations may be influenced by some fundamental at practical knowledge of the process.  This form of simulation may be a simpler and less  expensive approach particularly where the governing theories have not been developed to a sufficient degree.  As a consequence of the method  of formulation empirical models are generally applicable only over the  the ranges of operating variables within which the model was determined. The resulting relationships are usually valid only for the process units on which they were determined.  Even units superficially of the same  size and configuration may vary i n their operational behaviour due to subtle differences i n construction and operation.  Himmelblau  [1»2] considers a third category termed population-  balance models which include residence-time  distributions and other age  distributions.  In the case of the molybdenite leaching process the lack of an-operating plant prevents the construction of a purely empirical model with equation coefficients determined from the results of plant experimentation.  For leaching, the lack of established theory and  t  the nature of this heterogeneous process prevents the formulation of a purely fundamental model. A similar argument applies to the other unit operations i n the leach cycle.  As a consequence, this process  was simulated by a combination of empirical relationships determined experimentally or by analogy and by some fundamentals such as chemical reaction theory. 1.3  The Process  The proposed hydrometallurgical process for the production  - 6 -  of high grade molybdic oxide from molybdenite concentrates was based on a twelve month period of research during 1974-75 at U.B.C. by E. Peters and A. Vizsolyi.  The experimental program and results  were presented i n a series of monthly reports with the tentative design for a 10 ton per day plant outlined i n report No. 12 [3,4]. The possibility for such a process had been demonstrated i n earlier unpublished work at U.B.C. by Peters and Vizsolyi [5].  The process flowsheet was modified slightly for the modelling study, as shown i n Figure 1.  It must s t i l l be considered that this  flowsheet design i s not necessarily the optimum that could be used for the process.  However, i t i s this flowsheet which i s modelled with the  objective of determining the potential of the nitric acid leaching i • process with a recycle solids stream. The flowsheet i s based on the required operations so that there i s some f l e x i b i l i t y on the choice of actual units to perform these functions.  The complete process can be described as follows:  (i)  Leach Section  Both the new and refloated concentrates are treated for the removal of the flotation oils to prevent potential frothing and i n creased n i t r i c acid consumption within the leaching vessels.  The  MoSg HN0 Make-up  Concentrates  3  Oil  MoS  Removal  2  Recycle  NO Gas jHN0 Regen. 3  Cocurrent Staged Leaching  S Pregnant Solution  HN0 Recycle  .Wash  H  Refloat  n Regrind  " T  3  Silicious Residues GroundLimestone  -  Sulphate Rejection  Dehydration] 350°C lhr|  Recycle Ground Limestone {Recovery of^ Rhenium j  Mo0 Purge Impurity Purge  3  (High Purity)  $CaSQ>2H 0 2  1  |CaCQ  Fe(OH)  Figure 1„ Process flowsheet used for modelling study.  CaS04.2H 0  3  2  3  Cu(OH)  2  etc  - 8 -  combined solids are then subjected to cocurrent multistaged  leaching  with n i t r i c acid at temperatures not exceeding about 40°C. Although counter-current leaching would maintain a maximum driving force for molybdenum dissolution cocurrent leaching has been considered for the model to eliminate repeated phase separations required by the former method. Also, the recycling of unleached solids avoids the criterion of attaining high degrees of extraction on a single pass through a leaching train.  The slurry i s well mixed in any leach  stage either by mechanical means in agitator vessels or by NO l i f t i n g gas in pachuca vessels.  _  _ The slurry exiting the final leaching stage is filtered  and washed, with the f i l t r a t e passing on to the precipitation section. The filtered solids are repulped and fed to a continuous grinding mill to^reactivate the partially leached solids by creating new active surface area.  The reactivated solids are then split with a portion  passing directly back to the leach train after filtering and the remainder passing on to the flotation section.  In reality some form  of classifying stream splitter may be more advantageous, possibly in a closed loop configuration in the flowsheet.  However, the aim in  this section was to determine the level of insoluble elimination in order to maintain satisfactory insoluble levels within the leach.  The reflotation section i s designed to reject a considerable  -ap-  p o r t i o n o f the i n s o l u b l e c o n t e n t i n t o a low molybdenum  tailing.  r e f l o a t e d c o n c e n t r a t e i s then passed back t o the l e a c h a f t e r  The  filtra-  t i o n and d e o i l i n g .  (ii)  Precipitation  Section  The pregnant s o l u t i o n i s heated to about 80°C t o p r e c i p i t a t e molybdenum as MoO^-^l^O.  The p r e c i p i t a t e i s i n a f i b r o u s form and  i s thus q u i t e r e a d i l y f i l t e r e d .  Scanning e l e c t r o n m i c r o s c o p e  photo-  graphs o f t y p i c a l m o l y b d e n i t e c o n c e n t r a t e and the molybdic o x i d e hemihydrate  p r o d u c t a r e shown i n F i g u r e s 2 and 3.  MoO^  i s produced  b y _ r e l a t i v e l y low temperature c a l c i n a t i o n o f t h e hemihydrate.  (iii)  Solution  Purification  L  B e f o r e r e c y c l i n g , t h e s o l u t i o n must be p u r i f i e d b y p a r t i a l e l i m i n a t i o n of i m p u r i t i e s b u i l t up i n t h e l e a c h .  The major aqueous  b y - p r o d u c t o f t h e l e a c h i s t h e s u l p h a t e i o n . T h i s can be r e d u c e d t o low l e v e l s by t h e a d d i t i o n of c a l c i u m i o n s i n some form t o p r e c i p i t a t e gypsum  (CaSO^-^B^O).  The s o l u b l e i m p u r i t i e s ,  particularly  i r o n and copper, a r e n o t removed by t h e p u r i f i c a t i o n s t e p .  To  e l i m i n a t e t h e s e a p o r t i o n o f t h e low s u l p h a t e s o l u t i o n i s purged and t r e a t e d s e p a r a t e l y .  The purged and p u r i f i e d s o l u t i o n i s then  r e c y c l e d to the s u l p h a t e r e j e c t i o n s t e p .  Rhenium may a l s o be r e c o v e r e d  Figure 2. Endako molybdenite (600x)  concentrate  - 11 -  from the purge recycle solution.  (iv)  Acid Regeneration  Nitric acid i s regenerated by conventional methods using n i t r i c oxide from the leaching reactions together with oxygen and recycle solution.  1.4  Process Chemistry  1.4.1  Leach Chemistry  Nitric acid can disolve molybdenum from molybdenite at slow to moderate rates at temperatures not exceeding about 40°C. At temperatures greater than 40°C the rate of leaching i s considerably enhanced but the simultaneous precipitation of MoO^-^l^O becomes appreciable.  Precipitation of molybdenum i n the leach must be avoided  as i t i s not recovered from the leach residue.  The overall reaction can be represented by the following balance :  MoS .+• 6HN0 2  3  -»•  H >fo0 2  4  •+ 2H S0 2  4  +  6N0  (1)  - 12 -  Equation (1) represents an overall balance only and does not necessarily describe the correct form of a l l the species present. Although the i n i t i a l unused n i t r i c acid may contain nitrogen essentially i n the form of nitrate ion the recycle solution or solution after reaction has proceeded may contain other nitrogen species such as the nitrite ion.  The mechanism of reaction may therefore be quite complex. It  is possible that other nitrogen species may be more reactive to the mineral than the nitrates.  Figure 4 shows the Eh - pH relationship  for the n i t r i c and nitrous species under acid conditions. The slightly higher oxidizing potential of the nitrites over the nitrates result from the diagram being drawn for "standard states", ie. soluble component concentrations of one mole/litre and gas component pressures of one atmosphere.  It would not be thermodynamically possible for  the concentration of nitrous acid to build up to one mole/litre; i n fact, i t s concentration would be limited to that at which i t s oxidation potential just equals that of the residual n i t r i c acid.  A possible sequence of leaching involving nitrous acid as the main reactive component for molybdenum dissolution can be outlined [6].  Nitrous acid may be formed as an i n i t i a l reduction product i n  n i t r i c acid solutions by reaction (2).  HN0 . + 3  2H  +  +  2e~  -»•' HN0  2  + H0 2  (2)  - 13 -  I l.5j—"T  r~  -i—•—  1  r  Figure 4. Eh-pH relationship f o r n i t r i c and nitrous species i n acid solutions. Basis- one mole/litre i n solution and one atmosphere pressure.  The electrons In Equation (2) are supplied by oxidation of the mineral. The nitrous acid w i l l tend to equilibrate with n i t r i c acid and n i t r i c oxide gas by the reversible reaction of Equation (3)  3HN0  HN0  3  +  2N0 +  H0  (3)  2  The nitrous acid could react by Equation (4) with the electrons again supplied by oxidation of the mineral.  HN0„  + H  +  +• e  NO +  H0  (4)  2  The-nitric oxide produced by Equation (4) would enhance the stability of nitrous acid by pushing reaction (3) to the l e f t although this would ultimately be determined by the total pressure in the system, assuming that n i t r i c oxide i s the only gas component other than water vapour.  The nitrosyl ion (NO ,  .) has been suggested as a highly  reactive sulphide oxidant [7]. It i s however, only an ionization product of HN0 due to the presence of a strong acid (ie. 2  H_S0,  a n  ^  in this case), as shown in Equation 4(a)  HN0  2  +. H  +  -«-  + NO  4(a)  - 15 -  Thus, any special reactivity of the NO  ion would show up at strong  acidities and high HN0 concentrations, as when nitrogen dioxide i s 2  sparged directly into the system.  The overall balance of Equation (1) represents the dissolved molybdenum as molybdic acid (H^MoO^) but i t s exact form in solution i s uncertain.  The precise ionic form is also a function of pH.  Above a  pH of about 6 (ie. outside the range of this process) the molybdenum is present in solution as the molybdate anion (MoO^  2-  ).  With increasing  acid strength the molybdenum is predominantly present in other anionic — 6— forms such as bimolybdate (HMoO^ ) and paramolybdate (MO7O24 )•  At  acidities- exceeding the isoelectric point at a pH of 0.9 the molybdenum is in the form of cations with the most likely specie being the moly2+  bdenyl cation  (M0O2  ) or i t s polymers [8].  The complex ion  [(M0O2)  2+  (Mo0^) ^] x  has also been suggested as the ionic form in strongly  acid solutions [9]. The high solubilities of molybdenum attained under certain conditions are an indication that polymerization does occur. Table I shows the solubilities of molybdenum in various acid solutions as a function of time and temperature. temperature are clearly demonstrated.  The effects of acidity and The results indicate that  although precipitation can occur from saturated solutions at room temperature the kinetics of this process are extremely slow. Under the conditions of leaching i t i s likely that the molybdenum would  - 16 -  dissolve i n a cationic form and remain in this form throughout the leach despite the consumption of n i t r i c acid.  Acid conditions are  maintained to an extent by the production of sulphuric acid as  Table I CONCENTRATIONS OF Mo  VI  REMAINING IN VI  VARIOUS SOLUTIONS* g/1 Mo HN0  Concentration IN  24 hrs/24°C  1.1  HNO3/H2SO4  3  2N  3N  4N  52.1  95. 5  121 0  90. 0  -  -  JSNAN  IJ2NAN  1. 4  78.7  IN/IN  79.0  48-hrs/24°C  -.  96 hrs/24°C  -  -  75. 7  -  -  -  2 hrs/55°C  -  -  9.9  -  -  -  4 hrs/55°C  -  -  8.1  -  -  -  0.5  1.6  3. 4  4  5.3  7.7  2 hrs/80°C  -  -  3. 8  -  -  -  4 hrs/80°C  -  -  2  7  -  -  -  24 hrs/80°C  0.5  1.4  2 0  2 .6  0. 5  2.7  7.2  24 hrs/boiling  0.5  1.2  1  8  2 3  0. 5  1.7  6.5  24 hrs/55°C  *  9  0. 7  *  After saturating with reagent grade H Mo0  indicated i n reaction ( 1 ) .  9  The acidity relationship becomes more  -  17 -  complicated when considering the degree of dissociation of the acid radicals and the form of molybdenum produced on dissolution. The latter point i s demonstrated by hydrogen ion requirement i n the formation of the molybdenyl cation.  (Equation 5)  2+  ->  (5)  Other base-metal sulphides are leached by n i t r i c acid but only chalcopyrite and pyrite are considered i n this study as these were the major sulphide impurities i n the concentrates studied. They are considered to leach by the overall stoichiometry of the following equations.  -> 3Cu  FeS„  +  5HN0-  +  +  3Fe  3H  +  +  ->  6H S0 2  Fe  3+  4  +  +  10H 0 2  +  17N0  2H-S0. +• 2H_0 2 4 2  (6)  +  5N0 (7)  I n i t i a l l y a l l the sulphur may not be oxidized to sulphate as shown by Equations (6) and (7). The non-sulphate sulphur i s present as element a l sulphur; the yield of which depends on the mineral, n i t r i c acid  - 18 -  strength, temperature and time of contact,  Of the two minerals con-  sidered only chalcopyrite can have an appreciable i n i t i a l yield of elemental sulphur.  Sulphur may dissolve directly by Equation (8)  S* +  2HN0  3  ->  H SQ 2  4  +  2N0  (8)  Molybdenite, particularly as a by-product from copper porphyries can contain significant quantities of rhenium.  Since  rhenium i s i n solid solution i n the molybdenite crystals i t dissolves quantitatively with molybdenum during the leach.  —1.4.2- Precipitation Chemistry  The pregnant solution from the leach i s supersaturated with molybdenum since the kinetics of KoO^'H^O precipitation are immeasurably slow at operating temperature.  At temperatures i n excess of about  40°C the rate of precipitation becomes appreciable with close to complete possible precipitation occurring within 2 hours at 80°C (see Table I ) .  Complete precipitation of the contained molybdenum i s not possible since there i s a finite solubility i n the acid solutions. This solubility w i l l be at a minimum at the isoelectric point and w i l l  - 19 -  increase with changes i n pH.  The rate jat which the solubility  changes with pH w i l l be dependent on the particular cations or anions in solution.  The following equations and Figure 5 illustrate -  2+  this point when considering only M 0 O 2 2+ For precipitation from M 0 O 2 * °l i° n s  Mo0  2+ 2  +  1^0  ^ ->  Given an equilibrium constant  u t  A  n  N  <  t  ^ ®* n  e  MoOyJ^O  0 U >  4  a  s the ionic species,  reaction i s :  +. 2H  +  (9)  for this reaction the equilibrium  solubility i s expressed by Equation (10)  log[-Mo0 ] 2+  9  = - log K-  -  2pH  (10)  For precipitation from HMoO^ i n solution the reaction i s :  HMo0  4  + H  ^  +  MoO^t^O  + ^ 0  (11)  The corresponding solubility relationship for an equilibrium constant K2 i s then:  log[HMoO ~] = - log K A  2  +  pH  (12)  The solubility w i l l always decrease with increasing pH for  - 20 -  \ \  •  Figure 5. Solubility of molybdenum vs. pH in acid solutions.  - 21 -  cationic molybdenum and Increase with increasing pH for anionic forms.  From the point of view of maximum precipitation the solution pH should be near that for the minimum solubility.  This would lead to  a minimum recirculating load of dissolved molybdenum but may not result in optimum leaching conditions.  1.4.3  Solution Purification Chemistry  Sulphate rejection to low levels is achieved by the addition of calcium ions to precipitate gypsum. Two equations are shown for adding calcium as limestone or externally produced calcium nitrate:  H S0  4  +  CaC0  H S0  4  +  Ca(N0 )  2  2  +  3  3  H0  ->  2  CaS0 '2H 0 4  2  +  + 2H 0 -*• CaS0 '2H 0 +  2  2  4  2  C0  (13)  2  2HN0  3  (14)  Elimination of sulphate i s not taken to completion since the high levels of calcium ion in solution would lead to molybdenum losses to the precipitate by the following overall reaction:  H Mo0 2  4  +  Ca  2 +  ^ ->  CaMo0  4  +  2H  +  (15)  - 22 -  To prevent the continual build up of impurities such as iron and copper in the recycle acid a minor portion of the solution exiting the sulphate rejection step i s purged for further treatment. The purge treatment involves overliming to the extent that the soluble metallic impurities are precipitated as hydroxides along with the gypsum formed from the residual sulphate.  The remaining solution is  separated from the solids and recycled to the sulphate rejection stage to u t i l i s e the high calcium content.  The rhenium present in the leach liquor is unaffected by the precipitation or purification steps and i s hence continuously  recycled.  This would allow a build up of a suitable rhenium concentration to allow possible recovery by solvent extraction or ion exchange [10,11]. t  1.4.4  Acid Regeneration Chemistry  The n i t r i c acid content of the recycled, purified solution must be regenerated for further leaching.  Acid regeneration i s  achieved by oxidizing the n i t r i c oxide evolved from the leach to form nitrogen dioxide which i s then absorbed into the recycle solution as n i t r i c acid.  The following equations describe the overall reactions  taking place. Oxidation of n i t r i c oxide: 2N0  +  0  2  •*  2N0  2  (16)  - 23 -  Absorption of nitrogen dioxide: 3N0  o  +  H0  -»•  o  2HN0„  + NO  (17)  The complete absorption chemistry is more complicated than Equation (17) suggests, consisting of a number of steps involving intermediate species.  However, the detailed process need not be  considered here.  1.5  Scope of Model  From the prior studies of the process [4] i t was evident that leaching of molybdenite i n n i t r i c acid i s relatively slow compared to other similar systems.  A typical batch extraction curve for a moly-  bdenite concentrate at an i n i t i a l total pulp density of 126 g/litre of solution and 4 molar n i t r i c acid concentration, shown in Figure 6, illustrates this aspect.  High degrees of extraction cannot be obtained  within reasonable time periods since the rate of dissolution becomes prohibitively slow after relatively low levels of extraction. An economic design requires sufficiently high rates of extraction while maintaining high recoveries of valuable product.  This leads to the  following design strategies: 1. Maximize reaction rates by operating at high pulp densities while accepting low degrees of extraction for a single  - 24 -  100  RETENTION  (hrs)  Figure 6,, Batch extraction curve for Gibraltar molybdenite concentrate. 49.9%Mo, i n i t i a l pulp density 126 grams/litre solution, i n i t i a l 4M HN0„, ambient temperature, atmospheric exposure. [4]  - 25 -  pass through the leach. 2.  Reactivate the leach residue by regrinding and partially  eliminate the insoluble gangue by reflotation before recycling to the leach.  Examination of the overall flowsheet shows that the leaching section i s the rate limiting step in the overall process.  The kinetics  of the other unit operations are considerably faster than those of importance in the leach.  Hence any modelling effort should be con-  centrated on simulating the leaching section with the aim of maximizing the mass transfer of molybdenum from the solids to the solution, consistent with operations of the other sections of the process. j  Since the leaching section involves a recycle solids stream i  the unit operations associated with that stream were also modelled. Greater emphasis was placed on the leach simulation with more simplified models being used for the regrind and reflotation units.  Less c r i t i c a l  units in the cycle such as f i l t r a t i o n , washing and stream splitting were considered to operate ideally so that 100% efficiencies and negligible kinetic effects are assumed.  The limitations in available data for such a process that has not yet been developed on a pilot or commercial scale hinders  -26 -  accurate simulation. Although considerable laboratory data was generated during the previous work [4],the experiments were not conducted with the intention of formulating a kinetic model of the process.  This work demonstrated ,the feasibility of the process and  allowed an overall approximation to possible plant behaviour for a particular flowsheet configuration.  The use of the previous data  in this kinetic simulation was also restricted by the fact that most of the previous experiments were conducted with atmospheric exposure.  This allowed partial in-situ n i t r i c acid regeneration  which made accurate mass balancing of the n i t r i c acid impossible. This phenomenon was shown by a high pulp density test i n which more molybdenum was dissolved then could be accounted for by the stoichiometry of Equation (1). I  1.6  Source and Supply of Molybdenum  Molybdenite i s by far the most abundant molybdenum mineral and the only one presently of commercial importance.  A small number  of other molybdenum minerals do exist, some of which have contributed minor amounts to production figures in the past. Table II l i s t s the chemical composition of a few of the molybdenum minerals. On an atomic scale molybdenite has a three-layered structure of a S-Mo-S form with strong covalent bonds between the sulphur and molybdenum  - 27 -  Table II IMPORTANT MOLYBDENUM MINERALS AND COMPOSITION  Molybdenite  M0S2  Molybdite (or Ferrimolybdite)  F e  2°3*  3 M O (  V 2° 8 H  Powellite  CaMoO, (up to 10% W)  Wulfenite  PbMoO,  The mineralogical properties of the dominant mineral, molybdenite are given i n Table III [12] .  :  Table III MOLYBDENITE: MINERALOGICAL DATA  Crystal System  ;  Hexagonal  Common Form  ;  Massive, scales, granules  ;  Perfect basal-flexible laminae  Cleavage Colour  Lead-grey  :  Streak  :  Greenish lead-grey  Lustre  :  Metallic, opaque  Tenacity Hardness Specific Gravity  Sectile  :  :  1.-1.5  :  4.7-4.8  - 28 -  atoms. The cleavage properties of molybdenite arise from the weak bonding between these S-Mo-S groups.  The exposure of sulphur atoms  on the plate surface give the mineral i t s hydrophobic properties and hence i t s natural f l o a t a b i l i t y .  This i s not as dominant at the plate  edges since at these locations both sulphur and molybdenum atoms are exposed to the environment and result i n greater reactivity i n aqueous solutions.  The sources and recovery of molybdenum have been outlined i n a number of publications by Sutulov [13,14,151. These references cover many aspects of the molybdenum-bearing deposits, their milling behaviourand conversion technology as well as the sources and recovery of rhenium.  \  Molybdenite may be found i n a number of geological environ-  ments as follows [16]: 1.  Porphyries including stockwork and breccia pipes  2.  Contact metamorphic zones  3.  Quartz veins  4.  Pegmatites  5.  Sedimentary deposits  Nearly a l l the known resources of molybdenum f a l l into one of the f i r s t three categories with porphyries being the most important.  -  29 -  Of the current recoverable world reserves of 4 . 5 x 10* kg roughly one half i s found i n primary molybdenum porphyries where molybdenite  i s the only economic mineral.  The remainder i s found  mostly as a secondary mineral i n copper porphyries and i s mined as a by-product  [17].  Although t h i s source represents a major supply  of molybdenum i t i s t i e d to the production of the major component and hence i s subject to conditions of the copper market.  Only i n a  very few cases i s the molybdenum mined as a co-product where the value of molybdenum recovered i s s i m i l a r to the value of the copper.  Small  quantities of molybdenum have also been recovered from tungsten and uranium ores.  T y p i c a l analysis ranges of the major ore types currently  mined are o u t l i n e d - i n Table IV.  Table IV METAL CONTENT RANGES OF MOLYBDENUM ORES  Primary molybdenum porphyries  0.05 - 0.5% MoS  Copper porphyries  0.01 - 0.05 MoS  2  2  0.4 - 1.8% Cu  Despite the uniformity of mineral type the m e t a l l u r g i c a l behaviour of molybdenum deposits varies quite widely.  Recoveries  - 30 -  depend on the physical form of the molybdenite, the associated mineralisation and degree of oxidation.  The m i l l recoveries from  primary deposits can be quite high, in the order of 80 to 90 percent whereas recoveries from copper porphyries can range from as high as 75 percent to less than 25 percent.  Molybdenum morphology can vary from well crystallized with a large plate surface to edge surface ratio and hence good floatability to poorly crystallized forms with poor flotation properties.  Although molybdenite i s relatively stable to oxidation  some surface alteration can occur i n the more oxidized  upper zones  of"ore bodies. The formation of molybdate minerals on the surface of molybdenite results i n poorer milling recoveries.  The lower recoveries of molybdenite from copper porphyries results from the complicated mineralogy and the more extensive milling requirements. The usual associated sulphides are pyrite and chalcopyrite although some deposits contain high contents of secondary copper minerals such as chalcocite.  Molybdenum i s not  only lost to the tailings stream but to the copper concentrate stream as well.  With emphasis placed on the recovery of the dominant  component, copper, the recovery of molybdenum in the bulk flotation concentrate may suffer.  This compounds the losses involved in the  selective flotation where generally molybdenite i s floated while the copper mineralization i s depressed.  - 31 -  Usually many cleaner flotation stages are required to produce an acceptable concentrate.  However, further chemical  treatment i s often required to reduce impurity contents to satisfactory levels.  This aspect i s discussed i n Section 1.8.  The Russian philosophy differs from that of the West. The larger Russian plants produce a low grade concentrate, with associated higher recovery, and hydrometallurgically purify the roasted oxide.  Although molybdenite represents the only source of rhenium i t i s only recoverable from molybdenite extracted from porphyry coppers.  The rhenium contents from by-product molybdenite usually  range from 200 to 2000 ppm of ^0^2 i l e primary sources usually w n  contain less than 80 ppm of M0S2•  At current prices this can be an  attractive economic by-product but overall recoveries are very low, in the order of 30%.  Geographically molybdenite production i s concentrated in very few countries with the United States by far the most dominant. The 1976 production for the three leading non-communist producers is listed i n Table V.  - 32 -  Table V 1976 MOLYBDENUM PRODUCTION OF LEADING COUNTRIES (10 KG CONTAINED Mo) 6  United States  50  Canada  14  Chile  9.5  These three countries are estimated to contain 75% of known world reserves.  Small but significant production i s accounted for by  U.-S.S.R.- and the People's Republic of China.  In the early 1970's  very minor production was also reported from Peru, Japan, Bulgaria, Norway, Australia, South Korea and Mexico.  1.7  Economic Situation of Molybdenum  Over the last twenty years the price of molybdenum (as MoO^) [19].  bas been relatively consistent in terms of constant dollars The price i n current dollars has risen considerably since  1973 so that the present price is favourable in terms of the increased production costs and the effects of inflation.  The pricing stability  arises in part from the localization of supply with the domination of a few large suppliers,particularly Amax, Inc. of the U.S.  Despite  - 33 -  the current recession i n many metal markets the molybdenum demand i s expected to grow at a rate of 6 to 7 percent per annum due to i t s specialized application, mainly i n alloy steels.  The future supply and conditions of supply w i l l partly be dependent upon the supply/demand situation.  At present world pro-  duction i s increasing and has further potential for increasing. However, i n periods of short supply some speculation does occur with premium prices being paid for alternative sources.  In such times  the purity requirements of the molybdenite concentrate become less c r i t i c a l with f i n a l product purity maintained within the l i m i t s by some form of leaching or by blending with high grade material.  At the current North American price of $US 4.01 per pound j.  of contained molybdenum i n sulphide concentrate (fob mine) there i s considerable incentive for improved recoveries from ores. This i s p a r t i c u l a r l y so for by-product molybdenite where present recoveries may be quite low.  With the roasted oxide s e l l i n g price at $US  4.31  per pound ($US 9.49/kg) of contained molybdenum [20] i t i s imperative the treatment losses be kept to very low levels because of the small added value i n relation to the material value.  - 34 -  1.8  Current Methods for Processing Molybdenite Concentrates  Most molybdenite concentrate undergoes roasting to tnolybdic oxide (MoO^) although the overall process from molybdenite concentrate to final product may vary according to impurity contents and ultimate use.  Penalties are usually charged to concentrate producers for  impurity contents above specified minimum levels.  In most cases  standard penalties are applied to copper contents i n excess of 0.1% in concentrate.  Table VI l i s t s the penalty scale for copper current  in February, 1978.  Table VI COPPER PENALTIES IN MOLYBDENITE CONCENTRATE  % Cu  Penalty c/lb Mo  0.1 - 0.6  5  0.61 - 0.80  6  0.81 - 1.00  7  1.01 - 1.20  10  1.21 - 1.40  13  1.41 - 1.50  15  Penalties exist for other impurities such as lead and bismuth but  - 35 -  these occur more rarely and are usually determined on an individual basis.  The usual limit for these impurities i s a maximum content of  0.05 percent.  Gangue impurities have a greater influence on the  molybdenum grade since they are usually present i n greater proportions. These can be controlled to a large degree by the flotation practice by ensuring that the molybdenite content exceeds the minimum 85 percent M0S2.  The iron content of concentrates i s usually not of great  importance since this element i s not detrimental to the major use for the products.  Pretreatment of the concentrate before roasting may be required depending on the intended use of the final product. (see Appendix A).  High limestone contents lead to high residual sulphur  in the roaster calcine by formation of stable calcium compounds. The sulphur content of oxide i s required to be less than 0.1% for use i n steels.  In one operation this i s reduced by leaching the molybdenite  concentrate i n hydrochloric acid for 6 to 8 hours [21]. By maintaining a slurry pH of 2.5 the CaO content i s reduced from 0.5 to 0.05 percent.  In some cases copper may be leached by sodium cyanide. However, this reagent i s only effective i n leaching secondary copper minerals such as chalcoite and covellite and i s ineffective with chalcopyrite.  Examples of this procedure i n literature quote a  - 36 -  lowering of copper content from 2 percent to less than 0.5 percent at one U.S. operation and attainment of less than 0.2 percent copper i n two Chilean operations [15]. on the roasted product.  This leachant has also been used  The copper content, as chalcopyrite, can  be s i g n i f i c a n t l y reduced by a hot chloride leach [22,23,24].  This  i s also e f f e c t i v e i n lowering the lead (as galena) and calcium contents.  Current p r a c t i c e involves approximately a 30 minute leach  at 110°C with additions of ferrous chloride, sodium chloride and chlorine.  The process can lower the copper content from an average  0.34 percent to less the 0.07 percent while lead when present (up to 2.0 percent) i s reduced to l e s s than 0.05 percent.  Another  process designed to remove lead [25] involves a 16 hour leach a t 85°C i n 5% HC1.  i'  Most molybdenite roasting i s accomplished by multiple hearth roasting although other means such as rotary reverberatory furnaces or fluid-bed roasters have been used.  The process i s  semi-autogenous i n that the reaction i s exothermic although a d d i t i o n a l heat.is often required f o r i n i t i a t i o n of the reaction and to ensure completion of desulphurization. With multiple-hearth roasting the s o l i d s are fed i n at the top while a i r i s admitted i n a controlled manner on most hearths. temperature  A i r flow manipulation i s important to  control i n roasting, a necessary aspect considering the  - 37 -  v o l a t i l i t y of molybdic oxide and the 'stickiness' problems that can occur i n the furnace.  Increasing the air flow from low levels  results in higher hearth temperatures due to greater rates of reaction.  This increases to a maximum where-after higher a i r flows  result i n lower temperatures from the diluting effect of excess a i r . Cooling with excess air can be detrimental to SC>2 scrubbling since this practice dilutes the flue gas.  Adequate temperature control  may be achieved by shaft cooling and use of water sprays in the hearth space [26].  The roasting sequence involves the volatilization and combustion of flotation o i l s followed by partial oxidation to molybdenum dioxide (MoC^) which on further roasting i s converted to MoO^.  During roasting rhenium i s volatilized as heptoxide (I^O^)  which enables recovery by gas scrubbing (at < 80°C) i f sufficient quantities are present.  As with a l l sulphide pyrometallurgical processes dust laden sulphur-bearing gases are produced.  The dust must be collected by  some means such as multiclones and electrostatic precipitators to avoid excessive losses and to protect the environment.  Dust burdens  in the gas may be i n the order of 10-15% of the charge and may even fluctuate to higher levels [27].  The cost of the dust-collection  - 38 -  equipment can represent up to 20 to 30 percent of the o v e r a l l plant investment  [28].  In many cases environmental considerations require  that the emission of sulphur i n the o f f gases be reduced to acceptably low l e v e l s .  This i s achieved by wet scrubbing and n e u t r a l i z a t i o n with  lime [21,29] or by manufacture of sulphuric a c i d .  The technical molybdic oxide produced by roasting can be used d i r e c t l y as additions to a l l o y steelmaking or may be briquetted with a p i t c h binder f o r the same purpose.  The technical oxide i s  also the usual s t a r t i n g material f o r production of other molybdenum products.  The p r i n c i p a l process routes and f i n a l products are shown  i n Figure 7 [16]. As can be seen the oxide may be processed by chemical means or by sublimation to obtain high purity chemical forms and electric  furnace reduction or hydrogen reduction to produce m e t a l l i c  molybdenum.  A number of hydrometallurgical processes f o r treatment of molybdenite  concentrate have been proposed  including leaching i n  hypochlorite solutions, under oxygen pressure i n a l k a l i n e solutions and with n i t r i c a c i d . the p i l o t stage.  To date most have not been developed past  Apparently one commercial operation i n the U.S.S.R.  uses a n i t r i c acid process to decompose molybdenite but d e t a i l s were not a v a i l a b l e [30].  Direct additions to steelmaking  MoS  2  Concentrate  Purify (Si0 ) 2  MoS  2  Lubricants  Roasting  Technical Mo0„  Alloy steels -Powder -Briquets -FeMo  Glass Ceramics Fertilizer  E l e c t r i c furnace sublimation  +NaOH-+ Sodium molybdate  Chemicals Pigments Fertilizer  Pure Mo0„  E l e c t r i c furnace reduction  Extrusion Rolling  Arc-cast ingots  Metal powder  Press Sinter(H ) Work  <>  Bars Rods Sheet  Honferrous alloys  Rods Wire Sheet  Figure 7. Molybdenum production flowsheet, (condensed from reference [16] )  +NH. Oft* Ammonium molybdate  Chemicals Catalysts  - 40 -  1.9  Advantages of the Nitric Acid Leach Process  Conventional roasting represents a relatively simple single major step process for production of technical grade molybdic oxide. However, i t may suffer from a number of limitations: (i)  Purity of oxide i s subject to purity of concentrate feed.  (ii)  High grade products require additional treatment by sublimation or hydrometallurgy.  (iii)  Roasting produces dusty, sulphur-bearing off-gases which must be cleaned for reasons of economy and environmental protection,  i  (iv) Rhenium recovery may be low.  I  The proposed low temperature n i t r i c acid leach offers a number of advantages as follows: (i)  Production of high grade material directly by leaching and precipitation (99.9% purity) as shown by laboratory experimentation.  (ii)  Potential to treat off-grade concentrates and obtain a satisfactory product.  The limits of this aspect have  yet to be experimentally established but on a commercial scale may be dependent on plant operating conditions.  - 41 -  This enables the possibility of producing lower grade flotation concentrates with associated higher recoveries which would then lead to higher overall molybdenum recoveries. (iii)  Elimination of smelter gas handling problems by rejection of sulphur as gypsum,  (iv)  Higher possible recovery of rhenium.  The nitric-acid leach process must also consider environmental aspects particularly with respect to emissions of toxic oxides of nitrogen.  In-plant environmental safety can be enhanced by operating the  leach vessels under a slight negative pressure to avoid accidental leakage.  Although the nitrogen i n the system moves essentially i n  a closed cycle a small bleed stream may be necessary to eliminate other nitrogen oxides.  Catalytic conversion of nitrogen oxides to harmless  forms would be required before emission to the atmosphere but this technology i s currently available.  The potential for the process ultimately depends on economics. It i s not the object of this study to undertake an economic evaluation but rather a metallurgical evaluation. However, the v i a b i l i t y of the • process may be influenced by the prices of the feed and product, ie. - i f impurity penalties are significant and i f a premium price i s  - 42 -  received f o r high p u r i t y oxide.  1.10  N i t r i c - A c i d Leaching of Sulphides  N i t r i c acid has been considered as an oxidant f o r sulphide ores and concentrates since early i n the 20th century but commercial a p p l i c a t i o n has been v i r t u a l l y non-existent. have concentrated predominantly  The studies to date  on sulphides of copper although  those  of n i c k e l and molybdenum have received some attention. The o x i d i z i n g power of n i t r i c acid also provides incentive f o r i t s use i n place of other aqueous oxidants.  N i t r i c acid may also be used i n a " c a t a l y s t "  capacity with small additions made to other leaching agents. s i g n i f i c a n t oxygen pressure may  However,  be required to at least p a r t i a l l y ,  regenerate the n i t r i c acid i n - s i t u .  A general study of the reaction of n i t r i c acid on a number of sulphides was reported by B j o r l i n g and Kolta i n 1964  [31].  They  examined the behaviour of p y r i t e , p y r r h o t i t e , chalcopyrite, s p h a l e r i t e , galena and molybdenite with n i t r i c acid under various conditions. examination of molybdenite was not extremely detailed although some of the p o t e n t i a l for such a system was  recognized.  A somewhat general process u t i l i z i n g n i t r i c acid has been  The  - 43 -  proposed by Posel et a l for the leaching of transition metals from iron bearing sulphide ores [32,33].  The leach system i s based on  an elevated temperature, pressurized reactor with recovery of copper nickel, zinc and silver as well as other precious metals and sulphur by various means including solvent extraction and electrowinning. The dissolved iron i s removed by precipitation, under pressure and elevated temperatures i f necessary.  1.10.1 Molybdenum Sulphide  _  The behaviour of molybdenite in n i t r i c acid has been studied  by Zelikman et a l [30,34].  They demonstrated the leach/precipitation  behaviour within the same vessel as a function of time, temperature and acid concentration.  Oxidation curves at 20 and 80°C and a solution  curve at 80°C show the expected behaviour.  The utilization of n i t r i c  acid i s increased by the injection of oxygen to regenerate n i t r i c and nitrous acids.. A stagewise decomposition flowsheet is proposed by Zelikman which involves additional intermediate leaching with ammonium hydroxide.  Smirnov et a l [35] performed laboratory-scale studies on the oxidation of molybdenite i n n i t r i c acid at 80°C in the presence of relatively large quantities of particular impurities or additives.  - 44 -  The rate of leaching was increased by direct injection of nitrogen dioxide.  The apparent activation energy i s quoted as 20-26 Kcal/  mole indicating that the reaction i s chemically controlled unless, precipitation hinders reagent access to the mineral surface.  Nitric acid oxidation studies were also conducted by Fedulov et a l [36].  The oxidation rate was shown to increase rapidly  over 40-70°C but was slowed by diffusion once precipitation commenced.  A high-temperature, high-pressure  process for the n i t r i c  acid oxidation of molybdenite has been developed by Noranda Mines Ltd-. [37} The basis of the process i s the oxidative leaching and precipitation i n the one vessel.  The conditions applied ensure  reasonable reaction rates with elimination of soluble impurities. i  However insoluble impurities such as s i l i c a , alumina and any precipitated gypsum would remain with the molybdenum product.  With  sufficiently high temperatures and pressures a dehydrated molybenum oxide i s produced i n the leach rather than the hydrated form. A bleed stream i s also required for sulphate removal following recovery of residual nitrate, molybdenum and rhenium. Nitric acid i s also used to purify roasted calcines containing residual sulphur [38].  As well as lowering the sulphur  content the level of metallic impurities i s also decreased.  - 45 -  1.10.2 Copper Sulphides  A number of studies on the n i t r i c acid leaching of copper sulphides have been conducted in recent years although the strategies of the possible processes differ i n some aspects.  Prater et a l [39,40]  developed a flowsheet for n i t r i c acid leaching of copper concentrate which involved residue recycle with upgrading by flotation and regrinding (with new feed).  Test work showed the elemental sulphur yield to be  dependent on acid conditions, temperature and the mineralogy. When n i t r i c acid is present in excess any increase in acidity or temperature results in lower elemental sulphur yields.  Elemental sulphur is con-  sidered as a more desirable form for subsequent disposal. Dissolved sulphur is precipitated by lime in a separate step.  Under suitable  conditions the iron is precipitated as a jarosite rather than a less easily filtered hydroxide.  The dissolved copper is recovered by solvent  extraction and electrowinning.  Habashi [47] investigated the recoveries of copper and elemental sulphur under varying conditions of acid concentration, temperature, pressure and time of contact.  These laboratory tests  showed the increasing copper extraction rates with increasing n i t r i c acid concentration, temperature and time of contact.  The  elemental  sulphur yields were more complex, showing a maximum in most cases,  - 46 -  which did not exceed 50 percent.  The elemental sulphur yield could  be increased slightly by prior heat treatment of the chalcopyrite. Under conditions of high temperature and pressure the iron remains in the leach residue as an oxide.  More recently Bjorling et a l have proposed a n i t r i c acid process for treatment of chalcopyrite [42].  The concentrate i s leached  in a sulphuric acid n i t r i c acid mixture at elevated temperatures with recovery of copper and iron sulphates by crystallization.  To separate  the iron and copper the crystals are dissolved in water and oxidized in an autoclave at elevated temperatures.  The iron i s precipitated  as goethite leaving a solution of sufficient purity for copper electrowinning.  This process also enables the recovery of zinc by solvent  extraction from the leach liquor as well as recovering an iron compound of sufficient purity for recovery.  The paper also presents a brief  economic analysis.  A rather detailed study based on a continuous, integrated semi-pilot plant operation has been presented by Brennecke et a l [43] with process improvements detailed by Davies et a l [7].  The process  is based on a high-temperature, countercurrent leach with eventual copper recovery by electrowinning after removal of residual nitrogen, iron as jarosite and selenium.  Molybdenum, i f present, i s dissolved  - 47 -  and  may be r e c o v e r e d  by l i q u i d  r e l a t i v e l y low c o n c e n t r a t i o n s ,  i o n exchange but t h i s a p p l i e s t o below the s a t u r a t i o n l i m i t .  An  economic e v a l u a t i o n shows t h e p r o c e s s to be more v i a b l e f o r r e l a t i v e l y small operations of production  The  where p y r o m e t a l l u r g i c a l c o s t s p e r u n i t  would be e x t r e m e l y  high.  suggested improvements t o the p r o c e s s i n v o l v e t h e use  of a two-stage l e a c h w i t h d i r e c t i n j e c t i o n o f NC>2 gas r e g e n e r a t e d from t h e n i t r i c  oxide evolved.  Besides increased  leach  reactor  performance t h e reduced equipment requirements enhance t h e economic p o s i t i o n of the process.  A c i d i f i e d n i t r a t e s o l u t i o n s have a l s o been suggested as a p o s s i b l e reagent f o r i n - s i t u l e a c h i n g of copper o r e s [44], p r e s e n c e of n i t r a t e s would enhance the c o n v e n t i o n a l leaching  The  in-situ acid  rates.  1.10.3 N i c k e l  Sulphides  H a b a s h i a l s o p r e s e n t e d a study on the e x t r a c t i o n o f n i c k e l , copper and e l e m e n t a l sulphur concentrate and  [45].  from a low-grade, p y r r h o t i t e - p e n t l a n d i t e  Under s u i t a b l e c o n d i t i o n s  of a c i d  concentration,  temperature h i g h b a t c h r e c o v e r i e s o f n i c k e l and copper c o u l d be  - 48 -  attained in relatively short times.  The effects of the sulphuric-nitric system on a pentlandite concentrate was investigated on a laboratory scale by Ouellet et al [46].  They studied the influences of time, temperature, sulphuric  and n i t r i c acid concentrations and pulp density on the extractions of nickel, cobalt and copper.  This system was determined to be  diffusion controlled by the formation of a film of elemental sulphur and basic ferric sulphate on the mineral surface.  The plot of Fig. 8  demonstrates the slight effect of sulphuric acid concentration over the_ range 0 - 1.0 moles/litre on extraction for a nitric acid concentration of 1.97 moles/litre.  j-  Bjorling and Mulak investigated the dissolution of synthetic  millerite (NiS) i n n i t r i c acid [47], and determined the process to be chemically controlled. Nickel extractions increased with temperature and n i t r i c acid concentration and almost complete sulphur dissolution was achieved with n i t r i c acid concentrations in excess of 2 molar.  A pilot-scale study of a n i t r i c acid process for treatment of high-grade nickel matte or a nickel-cobalt sulphide precipitate has been described [48].  The feed is leached in nitric acid at  atmospheric pressure and 90°C.  Several flowsheets are presented but  - 49 -  Figure 8. Extraction of nickel, cobalt and copper from pentlandite by n i t r i c acid as a function of i n i t i a l sulphuric acid concentration. [46]  - 50 -  the basis of the subsequent processing i s purification and d e n i t r i f i cation prior to electrolysis.  Purification i s achieved by hydrolysis  for iron, IL^S precipitation for copper and zinc and nickel hydroxide or sodium hypo-chlorite additions for cobalt removal. Nitrate elimination i s accomplished by crystallization of nickel sulphate or by precipitation of basic nickel carbonate,  1.11  Modelling i n Hydrometallurgy  With the increasing emphasis on hydrometallurgy  i n recent  years there has been greater interest i n the modelling of such processes. Often, due to the proprietary nature of the work, the details of the modelling are not published but may be referred to as existing.  However,  the approaches of a number of hydrometallurgical modelling studies have been published.  Owing to the scope of this work, hydrometallurgical modelling w i l l be discussed only with respect to leaching.  Simulation of leaching  involves the analysis of the kinetics of the system generally involving irreversible reactions under steady state or unsteady state conditions. Equilibrium modelling, where the transient period i s relatively small and only the final distributions are important i s generally of minor significance i n leaching.  - 51 -  1.11.1 Leaching  The metallurgical description of leaching process can be considered on two scales: (1)  Micro-scale which involves a characterization of the  chemical processes or boundary-layer mass-transfer kinetics occurring in these heterogeneous reactions. (2)  Macro-scale which describes the physical distribution  of the system and which influences the rates of the chemical reactions.  Usually the rate of reaction is controlled by the chemical processes which occur on the particle surfaces or by mass transfer of species to the reacting surfaces.  In rare cases the dispersion of  oxidant, such as dissolved oxygen, may be the rate limiting step. At the usual temperatures of operation in hydrometallurgy the chemical surface reaction i s rate controlling unless reagent access i s hindered by unleached solid or precipitated material.  This latter phenomenon  can lead to mixed control with the chemical reaction as the rate controlling step for low degrees of extraction while mass transfer becomes the rate-limiting factor when diffusion cannot maintain an adequate reagent supply [49].  Two extremes of leaching practice can be considered.  The  f i r s t applies to leaching of high grade materials such as concentrates  52 -  where a high proportion of the input solids mass i s leached. The second case applies to low grade material where only a small fraction . of the mass of solids i s leached from an essentially inert matrix. Apopular approach to the modelling of the leaching of particles containing disseminated leachable mineral i n an inert matrix i s the shrinking core assumption.  The reaction front i s considered to be  quite narrow and gradually proceeds toward the centre of the particle. The particles may be considered spherical or allowances made for nonsphericity, pore structure and nonuniform mineralization or exposure [50].  A similar approach i s often used for leaching of particles  which leach completely or almost completely to soluble products. The par-ticles- are assumed spherical with or without appropriate correction factors and simply shrink as the reaction proceeds.  Although the  particles are almost certainly non-spherical before leaching, the progression of the leaching front may smooth out the "roughness", particul a r l y i f the process i s isotropic.  Bjorling [42] utilized a grain-age term  based on the diminution of a characteristic dimension of the particle to account for the change i n surface area.  It can be seen then, that the description of leaching kinetics can be quite complicated, with variation i n reaction control, ranges i n particle size and mineral distribution.  One simplified approach i s to  group the rate-limiting effects into a variable activation energy term [51].  As the reactive mineral becomes more inaccessible or more refractory  - 53 -  the activation energy i s increased to account for the change in reaction rate.  For a chemically-controlled reaction then, the rate may be classified by relations of increasing complexity. (1) r  where  -  K  W  n C  (18)  r  =  rate of reaction  K  =  rate constant  C  =  concentration of leaching reagent  W  =  weight or mole concentration of reactive mineral  n  =  reaction order w.r.t. C ^  a l l in appropriate units.  This i s a very simplified approach which accounts for the change in surface area only by the change in weight concentration of the species. ^  n r  = K C  2/3 W  / J  (19)  This is of more representative than Equation (18) since the exponent of W expresses the surface area to volume ratio.  The method  - 54 -  is s t r i c t l y accurate i f the leaching particles are equi-sized spheres but the method may be useful for approximations. (3)  r  where  K  =  K  C W  (20)  includes the variable activation energy  The parameters included i n the activation energy term must be determined by s t a t i s t i c a l analysis of experimental data. (4) r where A  =  -  K C  n  A  (21)  surface area for reaction  J  The^variation i n area term must be accounted for i n some manner. As mentioned previously the shrinking sphere, with or without adjustment factors i s often used.  An empirical method accounting for the change  in area i s considered later i n this thesis.  Even though the reaction kinetics might not be linear they may, for the purpose of analysis, be considered as linear over small ranges of variation. restrictive.  However analysis by this method i s somewhat  - 55 -  The physical motion of the system must also be considered. Three cases are described: (1)  Static bed of solids with passage of leaching solution  and possibly gas as i n dump, column or in-situ leaching.  A number of  models of these processes have been published [50,52,53,54]. (2)  Leaching where both solids and liquids are in motion,  i.e. agitation leaching (a)  Continuous processes where phases are continually added and withdrawn from the system.  (b)  Batch leaching where the system i s essentially closed during the reaction.  The object of this project is to simulate a continuous, cocurrent, agitation-leaching process.  A graphical approach to predict  continuous cocurrent-process behaviour from laboratory batch-extraction data is described by Jones [55]. 10.  The method i s shown in Figures 9 and  The quantity of component dissolved, Q, in a batch test i s obtained  as a function of time, t, as in Figure 9.  This extraction curve is  analysed by practical or mathematical means and the slope, plotted against Q as shown i n Figure 10. inverse  , is  A line of slope equal to the  of the nominal residence time (9) and passing through the stage  input value of Q on the absicca intersects the stage output value on the curve.  This construction i s continued for as many stages as desired.  Figure 9. Typical extraction curve, j  Q Figure 10. Rate of extraction vs. extraction showing construction for staging analysis.  - 57 -  Alternatively, the extractions can be determined on a t r i a l and error basis for a particular stage configuration,  Since this analysis i s  based only on the amount of material dissolved i t i s only suitable for the same i n i t i a l conditions of feed solids, solution and temperature as in the batch test.  It also only applies to the condition of back-  mixing although this assumption i s reasonable for low reaction rates, long residence times and sufficient agitation.  The general mass balance approach applied to purely backmixed reactors involves a set of component and overall mass balances with rates determined as a function of output concentrations for each vessel.  The simplified form of the solution component balance i s expressed i n Equation (22) for a leaching reaction  v  where  C  = v C  q  + r V  v  =  solution volumetric flow rate  C  =  concentration of component in outlet solution  =  i n i t i a l concentration of component in input solution  r  =  rate of reaction per unit volume  V  =  volume of vessel  C  Q  (22)  - 58 -  Again, the d i f f i c u l t y i s in evaluation of the rate term and accounting for variables which affect r.  If the residence time distribution (RTD) has a significant influence on reactor performance i t may have to be taken into account. For perfect backmixing the RTD i s given by:  E(t)  where  =  3  t  t  =  time  t  =  nominal residence time  e  _ t / t  (23)  For; non-ideal mixing the summation approach may be the most suitable i.e.  ^ summing the reaction for each empirically-determined residence  i  time range.  This procedure i s satisfactory for f i r s t order reactions  since the rates are then independent of concentration. For non f i r s t order reactions the situation i s considerably more complex. Detailed analysis of the chemical engineering principles involved are given i n the references [1,2,56,57,58,59]. 1.12  Modelling of other Unit Operations in Leach Circuit  1.12.1 Grinding  - 59 -  With t h e c u r r e n t  flowsheet i t i s envisaged that b a l l m i l l i n g  w i l l be used t o r e a c t i v a t e the l e a c h r e s i d u e . simulation  The o b j e c t o f g r i n d i n g  i s u s u a l l y t o determine the p r o d u c t s i z e d i s t r i b u t i o n as a  f u n c t i o n of feed  s i z e d i s t r i b u t i o n and m i l l parameters.  the m o d e l l i n g o f g r i n d i n g  By  necessity,  i s e x t r e m e l y e m p i r i c a l and i n v o l v e s a l a r g e  s e r i e s o f c a l c u l a t i o n s t o account f o r the complete p a r t i c l e s i z e range.  A k i n e t i c model may be used f o r b a l l m i l l i n g based on the following f i r s t  o r d e r assumption [ 6 0 ] .  d  W. dt  where  —  =  W^  =  amount of m a t e r i a l  K_  =  breakage c o n s t a n t  d W. —;— dt  - K. W. i  (24)  i  i n s i z e range i  r a t e of breakage from s i z e range i  The complete a n a l y s i s i s based on the assumption o f p e r f e c t b a c k m i x i n g , a c o n d i t i o n which i s r e a s o n a b l e f o r b a l l m i l l i n g .  Another method f o r g r i n d i n g s i m u l a t i o n which i n v o l v e s a c o m b i n a t i o n o f c l a s s i f i c a t i o n ,  i s the m a t r i x model s e l e c t i o n f o r breakage  and breakage m a t r i c e s t o determine output s i z e d i s t r i b u t i o n s [ 6 1 ] .  - 60 -  A number of theoretical relations have been proposed to describe size reduction.  The one which applies more closely to fine  grinding i s that of Rittinger.  d E  where  =  -  (25)  dE  =  unit energy input  C  =  proportionality constant  X  =  size dimension  Rittinger's Law states that the amount of new surface area produced in proportional to the energy input to breakage.  This energy of  breakage, however, represents only a small fraction of the total energy input to a m i l l , the rest reporting as heat and sound. i  1.32.2 Flotation  It has been found that flotation often closely follows the simple f i r s t order relationship of Equation 26 [61].  r  where  r  =  rate of flotat ion  =  K W  (26)  - 61 -  K  =  flotation rate constant  W  =  concentration of floatable component.  The flotation rate constant K may be theoretically dependent to varying degrees on a large number of variables [62].  These variables  include particle size, degree of liberation, air bubble surface area, fraction of bubble surface covered with mineral and the efficiency of the froth i n retaining the desired mineral.  The complete  characterization of a l l influencing variables i s not possible. However, the range of some of these variables i n practice may be s u f f i ciently small that they can be assumed constant for approximations of circuit behaviour.  On the basis of Equation (26) and backmixed flotation cells i t can be shown that the recovery of floatable mineral i s [63]:  R  a  ,  1  where  K  R^  =  recovery from 1st c e l l  9  =  c e l l retention time  This can be extended to recovery from the series:  (27)  .,Q  1+ K 9  K  c e l l in  }  - 62 -  Hence the total recovery from a simple series set of flotation cells is the summation of the individual'cell recoveries.  R  = E(R- + R + 0  J-  -  /  1 - (1 + K 6 ) " "  R )  n  (29)  (30)  - 63 -  CHAPTER 2  BASIS OF THE LEACHING MODEL  The basis of the leaching model had to be established to determine the experimentation  required to provide necessary  data.  Hence t h i s Chapter introduces the approach to the formulation of the leaching model while complete d e t a i l s are presented i n Chapter 4 along with the formulation of the models of the other unit operations.  2.1  Modelling by Mass Balances  Mass balancing was considered the. most p r a c t i c a l and v e r s a t i l e method f o r simulation of leaching.  For the steady state  conditions considered the mass balance i s most simply described by Equation (31).  0 =  where  I  ±  R  0  =  rate of output  I  =  rate of input  R  =  t o t a l rate of generation (+) or consumption (-)  (31)  -  64  -  The mass balances are applied to active components in each phase as well the overall phases.  In the flowsheet considered there are two  solids streams entering the leach.  These are considered as separate  phases throughout the leach train for reasons enunicated later in this chapter.  It has already been shown that the reaction is relatively slow.  Therefore the degree of extraction in any one stage i s not  likely to be very high.  Hence the leaching vessels are considered  to be entirely backmixed regardless of their design.  The  existence  of the recycle solids stream validates, to an extent, the neglecting of any non-ideal residence time distribution (R.TD). For example, a particle which short circuits the leach has a higher probability of re-entering the leach train earlier than a particle which has not short circuited the leach.  However this does not entirely n u l l i f y  the effects for a non f i r s t order reaction.  There are many possible complicating effects but these are neglected, on the basis of negligible influence and the aim of maintaining model simplicity.  These factors include the RTD's  for the solution as well as both solids streams.  As well, the RTD  for the different classes of particle size may vary.  Consideration  of a RTD that is not ideally backmixed leads to a rapid escalation of required computations since each residence time class has to be  -  65  -  considered separately.  2.2  Rates of Reaction  Rates of the chemically-controlled reactions must be defined for finely  divided concentrate in an aqueous medium. Two different  bases are used in this model for the different minerals considered. For molybdenite the characterization of the leaching rate of a concentrate consisting of non-uniform particles is based on equation (21) MOLYBDENITE: .  r  =  K C  n  A  (21)  Two other sulphide minerals are considered since they consume n i t r i c acid and raise the impurity content of the solutions. For the concentrates used the major sulphide impurities accounted for were pyrite and chalcopyrite. Since they are present only in relatively small quantities the simplified description of Equation (19a) i s used. PYRITE, CHALCOPYRITE: r  =  K C W  2/3  For lack of information the reactions for both these minerals are considered to be f i r s t order with respect to C.  (19a)  -  66  -  It i s required not only to determine what the parameters are in these reactions but to account for the changes that may occur in them as the reactions proceed.  The importance of the analysis of both the C and the A terms is shown by a rough analysis of previous experiments (Reports 7 and 8, reference [4]). The extraction curves for as-received concentrate and concentrate that had been wet ground for one hour in a pebble m i l l are plotted in Figure 11.  These points have been  approximately fitted to power curve equations of the form y = a t^. The rates of leaching as a function of time were determined by differentiation and are shown in Figure 12.  Although i t cannot be  claimed that this analysis i s accurate i t s t i l l demonstrates the point that in a partially closed or bounded system the finer material w i l l i n i t i a l l y leach faster but w i l l eventually leach at a slower rate due to depletion of solids and consumption of active reagent. However the net extraction w i l l s t i l l be greater for the finer solids at any particular time up to that for complete extraction.  2.2.1  Analysis of Terms  (1)  r -  rate of leaching per unit volume of solution  - 67 -  GROUND  RICOVED  40 t  (hr)  60  80  Figure 11. Extraction curves for Gibraltar molybdenite concentrate (a) as received (b) wet ground one hour i n laboratory pebble m i l l . 49.9%Mo, i n i t i a l pulp density 112 grams/litre s o l u t i o n , i n i t i a l 4M IINO^, ambient temperature, atmospheric exposure, [4]  _ 68 -  50r  20  40 (hr)  60  80  Figure 12. Leaching rates of Gibraltar molybdenite concentrate (a) as received (b) wet ground one hour. Conditions as in Figure 11.  -  (2)  69 -  C In the earlier discussion i t was shown that the exact  mechanism for leaching of sulphides by n i t r i c acid may be quite complex.  On the basis of empiricism then, the term C was taken as the  " n i t r i c acid" concentration in molar units since i t could be measured and had a determinable influence on the rate of reaction. (3)  n Having decided to use the n i t r i c acid concentration as  the reactant i n solution the reaction order had to be determined by experiments using standard (4)  procedures.  A This defines the surface area of particles on which  the chemical reaction occurs.  It i s common practice to consider a  'uniform' or 'average' particle within the bulk or particle size range for analysis of this term.  Having defined the single particle  the overall behaviour i s described by summation over a l l the particles. The SEM photographs in Figure 13 show an extreme non-uniformity of size and shape characteristic of molybdenite concentrates.  Accounting  for the change i n surface area of a molybdenite particle i s also complicated by the following factors: (i)  I n i t i a l definition of A is not adequate since i t  cannot be determined accurately. (ii)  Anisotropy of leaching,  Leaching i s more active  -  70  -  - 71 -  at the plate edges and defects thus leading to complex effects on A (see Figure 14) (a)  Leaching of plate edges decreases the 'active' area available for leaching since the plate is shrinking.  (b)  Leaching of defects within a plate increases the active surface area since the pits formed enlargen as the reaction proceeds.  (iii)  The plate structure of molybdenite can lead to  phenomona that are d i f f i c u l t to take into account.  The weak bonding  between plates may result in the cleavage of particles, induced by agitation or by NO gas pressure where solution has penetrated between plates. (iv)  The softness of the mineral can lead to severe physical  deformation which would likely influence leaching characteristics.  The conclusion i s that the single particle basis i s i l l o g i c a l for this system.  It would be more advantageous to describe the bulk  properties with respect to A in order to truly describe the average behaviour.  The numerical value of A remains an undefinable term in relation to the active surface area and the manner in which i t changes. An extremely approximate analysis was performed on data from reference [64] where the average particle diameter and surface area per gram  (b)  Figure 14. Leach residues, (a) G i b r a l t e r concentrate leached 3 d a y s , I n i t i a l pulp density 168 g/1 s o l u t i o n , i n i t i a l 4M HN0 64% e x t r a c t i o n . (2000x). (b) MoS concentrate leached to 60-75% e x t r a c t i o n . (4000x). 3>  - 73 -  were determined on four different concentrates by Coulter counter and BET with krypton gas respectively.  Calculations based on disc-  shaped particles and the experimentally determined values show the thickness to diameter ratio to increase as the particle size decreases, (see Figure 15).  The effect on surface areas i s also shown.  This i s  not conclusive evidence since the ratio w i l l be influenced not only by the degree of grinding but also the morphology of the mineral i n the ore.  However i t does demonstrate the complexity involved i n  evaluating the reactive surface, area.  The problem i s overcome by the following strategy using the results from batch"experimentation.  r  where  A  A' =  -  =  Equation (21) i s normalized as:  K' C A n  (32)  area factor  For batch or continuous cocurrent leaching then: r  =  K' C  since A'  at t = 0  (33)  1  The functional form of A' versus fraction leached (area decay curve) can be determined by curve f i t t i n g of appropriate experimental data.  - 74 -  Figure 15. Approximate dimensional characteristics of four molybdenite concentrates.  -  75  -  This then defines the area factor i n a term independent of time. If A' i s determined on a per unit weight of solid basis then an additional term has to be introduced to account for the pulp density and i t s change in the practical system.  r  where  P  =  =  K' C A' P'  (34)  n  ratio of current pulp density to experimental  pulp  density  A linear relationship between active surface area and weight of solids is assumed. To allow for the effects of temperature the Arrhenius factor is introduced into the rate constant term. -E /RT K'  where  =  r e  E^ =  activation energy  R  =  gas constant  T  =  absolute temperature  (35)  For evaluation of the rates of reaction of  M0S2  the two  solids streams entering the leach (new solids and recycle solids) having different analyses and particle size distributions are considered separately throughout the leach.  Although bulk analysis  - 76 -  and i n i t i a l area factor could be easily calculated by a weighted average, the properties subsequent to commencement of leaching are much more d i f f i c u l t i f not impossible to determine. A simple analogy based on leaching of uniform spheres demonstrates this point.  For a  hypothetical constant leaching environment the rate of leaching depends only on the surface area.  The surface areas versus fraction leached  for an equal mass of spheres of 1 unit radius and 2 units radius are shown in Figure 16. Several points of equal leaching time are joined by dashed lines to show how the surface areas vary.  The data i s  replotted i n Figure 17 as surface area versus time.  The total surface  area for a 50 wt % i n i t i a l mixture of each size is also shown. This demonstrates the complexity when considering just two particle sizes and j indicates the problems when considering a continuous range of particle sizes or particle size classes.  - 77 -  LO  0  LEACHED - — — Figure 16. Surface area vs. fraction leached for i n i t i a l equal masses of spheres of one unit radius and two units radius. Constant leaching environment„' FRACTION  \£Owf%  MIXTURE  \  Y \  TIME  Figure 17. Surface area vs. time for i n i t i a l equal masses of spheres of one unit radius and two units radius. Constant leaching environment.  - 78 -  CHAPTER 3  EXPERIMENTATION  The previous Chapter o u t l i n i n g the basis for the model formulation also indicated the type of data that would be required to operate the model.  Data that were not available from the previous  work, l i t e r a t u r e or by analogy were furnished by designed Most experiments  experiments.  involved r e l a t i v e l y short term tests i n which the  e f f e c t s of changing variables could be neglected or averaged.  The molybdenite  concentrates used i n the test work were  supplied by Endako Mines D i v i s i o n of Canex Placer Ltd. (Sept. and.Brenda Mines L t d . (Sept. 1977)  1977)  both located i n B r i t i s h Columbia.  Both concentrates were d i r e c t f l o t a t i o n products which had not been subjected to the p u r i f i c a t i o n leaches practised at each of the plants. Chemical analyses and sizings f o r these two concentrates are l i s t e d i n Table VII.  3.1  Apparatus  The experimental apparatus i s depicted i n Figure 18.  The  leaching reactions were conducted i n a standard 500 ml f i l t e r i n g f l a s k  -  79 -  Table VII CONCENTRATE ANALYSES AND SIZINGS  Analysis  Endako •  Brenda  Mo  54.82%  55.92%  Fe  0.84  0.65  Cu  0.027  0.237  Pb  0.048  0.32  Bi  0.059  S  37.63*  sio  2  INS0L  Sizing  38.36*  8.0**  -  -  1.59  5% + 19 microns 44% + 9 microns 56% - 9 microns (^99% - 325#)  * **  (^72% - 325#)  by calculation on basis of MoS,,, FeS , CuFeS 2  typical value  - 80 -  Figure 18. Experimental apparatus.  - 81 -  at essentially atmospheric pressure.  Temperature was automatically  controlled for most of the tests by a Thermistemp controller using an immersion heater located i n the water bath surrounding the reaction flask.  Temperature within the reaction flask was usually  maintained within ±  0.5°C  of the desired set-point. Agitation was  achieved by magnetic stirring.  The reaction flask was sealed during the reaction to avoid oxygen access and in-situ acid regeneration. The gas produced by the leach was trapped in a gas-collecting tube with the water being displaced through an overflow.  Before most leaching tests were performed the solution i n the reaction flask was bubbled with argon and then n i t r i c oxide produced in a gas generator by sodium n i t r i t e and sulphuric acid.  Bubbling with  argon eliminated most of the air from the system while bubbling with n i t r i c oxide attempted to duplicate the continuous system which i s saturated with this gas.  It was impossible to avoid some a i r access  when opening the flask to introduce the concentrate but the effects of this were considered minimal.  3.2  Chemical Analysis  Solution analysis was chosen to gauge the extent of reaction  - 82 -  since changes i n molybdenum concentration could be readily detected by atomic absorption techniques whereas changes in solids content was more d i f f i c u l t to determine and less reliable.  A Perkin Elmer Model  306 Atomic Absorption Spectrophotometer was used for the analyses.  Standard solutions for molybdenum, as outlined i n the operating manual, required slightly alkaline conditions.  Since the leach solutions  were acid and contained iron the treatment with alkali could result i n hydroxide precipitation, thus necessitating f i l t r a t i o n .  The use of acid  standards was investigated and found to be satisfactory. Acid standards were necessary since the use of acid test solutions and alkaline standards gave low results.  Molybdenum i s known to suffer from interfering ions i n AAS analysis.  Suggested methods for overcoming interferences involved the  additions of large quantities of particular salts such as aluminium chloride and ammonium chloride to the solutions. Additions of ammonium chloride created highly unstable readings on the AAS.  To avoid effects  of interferences the standard solutions were generally made with starting leach acid which already contained n i t r i c and sulphuric acids, and dissolved iron. Testing also showed that molybdenum absorbance was relatively insensitive to n i t r i c acid over ranges of interest i n this work.  - 83 -  Iron and copper atomic absorption analyses were conducted with simple acid standards produced by dissolution of pure metal.  3.3  Experimentation and Analysis  The results of the experimental program, including the i n i t i a l exploratory experimentation, are tabulated in Appendix B. The more important results are analysed and discussed in the remainder of this Section under the appropriate headings.  3.3.1  Reaction Order with Respect to Nitric Acid  To determine the reaction order the i n i t i a l rate of reaction was determined for different i n i t i a l n i t r i c acid concentrations.  Other  possible variables were kept as constant as possible by the following conditions. (1)  Use of large particle sizes:  Since the Brenda concen-  trate was the coarser of the two, the +325 mesh fraction of i t was used in these tests. (2)  Termination of experiments at low degrees of extraction  so that the area of reaction only changed by a negligible amount. For the different acid concentrations the tests were terminated after different times to attain similar degrees of extraction.  (3)  Low pulp density tests so that there are only minor  changes i n solution concentrations.  Since the area of reaction i s essentially constant for these reactions the area may be included within the rate constant so that the rate equation becomes pseudo-homogeneous.  r  =  K'[HN0 ]  n  3  (36)  Therefore the plot of log r versus log [HNO^] has a slope equal to the reaction order as shown i n Figure 19. The slope i s evaluated at 1.84 for the f i l l e d points. Due to the limited experimentation the; reaction order i s taken as 2.0 for the model calculations. I  The two high points at lMtHNO^] are neglected i n the analysis since they were long-time tests and possibly subject to particle cleave ging.  The test involving the addition of sulphuric acid demonstrated  a very minor difference from those without sulphuric acid additions.  3.3.2  Determination of Area Factor Relationship for Endako Molybdenite Concentrate  The aim of this series of experiments was to determine how  - 85 -  Figure 19. Log i n i t i a l reaction rate vs. log i n i t i a l HNO^ for Brenda +325 mesh molybdenite concentrate.  - 86 -  the reactive surface area of the molybdenite changed as leaching progressed.  Since the leaching rate i s directly proportional to the  active surface area the relative change i n active surface area could be determined from controlled experiments.  In these experiments the  leaching conditions for each test were maintained constant.  (solution  composition, M0S2 pulp density, temperature) except for the degree to which the input solids had been leached.  The tests were performed i n  series with the residue from one test as the feed solids for the next test.  The measured rates were plotted as a function of the arithmetic  average of the degree leached of the input and output solids. For accuracy the degree of leaching within any particular test was kept relatively low.  The results are plotted in Figure 20.  i  .  The experimental points were fitted to a three parameter  exponential equation using the U.B.C. subroutine LQF [70].  r  =  4.664 x 10  3  e  3 313 A i^"^360  (g/litre.sec) (37)  where  < \ > =  fraction of M0S2 leached  This equation f i t s the points remarkably well but i s unrealistic between zero extraction and the f i r s t experimental point, as well as for extractions above the f i n a l experimental value (^50%).  For model  -  88  -  stability a separate linear relationship with an estimate of the intercept on the ordinate i s assumed for the zone adjacent to zei:o extraction.  The area factor,A*, i s obtained by normalizing the  experimental curve by dividing through by the extrapolated value of the rate at zero extraction.  This value calculated from the curve  f i t t i n g was i n i t i a l l y employed although the use of the value from the linear approximation may be more r e a l i s t i c .  It i s not important  though,since the normalizing value i s only a reference point and w i l l not influence the final results.  Under this scheme the area factor  relationship i s give by: A' for"  =  0.5003  0  '  <fr  -  ^  4 . 5 8 6 <f>  0.0333  (38)  and, , A'  -  e  -  3  .0.3360 *  3  1  3  •  4  (39)  i 0.0333  for  <  <(>  <  0.5  Having calculated the value of n the effective rate constant K' can be calculated since at t = 0 A ' = 1  r  K'  =  =  2.915  K*[HN0 ]  (40)  2  3  x  10"  4  (-  *  M  °»  mole Mo  )( v  £  -)  sec.mole HNO^  - 89 -  and  K« o  =  4.5359 x 1 0  10  (  fg ) ( \ . mole Mo sec. mole HNO, M  P M  using an activation energy of 20 Kcal/mole,  This value accounts for the molar concentration of n i t r i c acid and the mass rate of extraction of molybdenum.  By similar procedures the rate constants for pyrite and chalcopyrite i n Endako concentrate were determined assuming activation energies of 10 Kcal/mole.  „ -. _ „ -, Fe xn FeS: K' = o v  , , ,, 4 , g Fe_ I (mole Fe) >. 1.1516 x 10 (—^ =—) ( =r—vjr^:—) mole Fe mole HNO^-sec c  i n  w  ^ . „ „ Fe i n CuFeS : 2  „ , K = o  „ ,, i ^ 3 , g Fe w & (mole Fe) 2.618 x 10 ( — ^ — - — ) (^———~ ) mole Fe mole HNO -sec  CuinCuFeS :  IC  -  „ -,^3 , e Cu . , £ ^(mole Cu)^"^ 2.978 x 10 ( ^ — ^ i mole HNO -sec >  0  0  2/  2  s  - 90 -  CHAPTER 4  FORMULATION OF MODEL  The model i s constructed on a modular basis with a main control program and separate subroutines f o r d i f f e r e n t r e a l and hypothetical operations.  The block diagram flowsheet on which the  computer model i s based i s presented i n Figure 21 while the flow diagram for the computer program i s shown i n Figure 22.  The model was developed using the computing f a c i l i t i e s at U.B.C.  I n i t i a l work was  conducted on an IBM 370/168 while the l a t t e r  stages involved the use of the Amdahl 470 V/6 - I I . Double p r e c i s i o n arithmetic was used f o r the c a l c u l a t i o n s .  I n i t i a l Assumptions (1)  The feed concentrate i s r e l a t i v e l y uniform with respect  to chemical analysis and p a r t i c a l size d i s t r i b u t i o n .  This i s necessary  since the behaviour of the model depends on parameters associated with the feed.  M i l l i n g operations tend to produce a r e l a t i v e l y consistent  product despite v a r i a t i o n s i n the m i l l heads so that a s i n g l e c a l i bration of a concentrate should be adequate. (2)  Laboratory determined parameters are assumed to apply to  - 91 -  New eed r  Solution  Figure 21. Model block diagram.  Tails  Begin  i  Read input data  Convert inpuj units to model units I  Calculate combined solids mass and analysis  Calculate leach output for N stages  SSM  Solve simultaneous algebraic equations  Calculate other leach values  I Calculate leach filter distributions  to I  Cn l.culnte regrtnding effects Calculate scream splitter d IstributIons  Calculate m:iHti  and  flotatIon analysis  Calculate combined recycle parameters  Adjust required recycle guesses  No  Convert model units to output units  Print output  End  Figure 22, Computer model flowsheet.  -  industrial scale.  93  -  This may apply reasonably well to many leaching  systems but such extrapolation i s less accurate in the case of grinding and to a smaller degree, flotation.  4.1  Recycle Estimates  Since there i s a solids recycle stream in the flowsheet r e a l i s t i c estimates have to be made for the parameters associated with this stream i n order to commence calculations.  On passing  through the entire cycle these recycle parameters are calculated and compared to the i n i t i a l estimates.  If the guessed and calculated  values are not within a specified tolerance the guesses are adjusted and the calculations redone.  The adjustment criterion i s a modified  Wegstein method which uses secant techniques.  Two sets of guessed  and calculated values are required to operate the secant method. The sets are produced by a small perturbation in the guessed variable for the f i r s t time i t does not f a l l within tolerance. Subsequent new guesses are produced by the following relation  k+l  :  where  "  X = estimated value XC =  calculated value  \  (41)  - 94 -  k  iteration number  R  multiplying factor defined by?  R  Subject to  =  < k- k-l X  X  ) / (  \-\-l~  X C  k  +  X C  k-l  )  (42)  R .4: R max  This convergence algorithm is performed by the main program on recycle parameters that are i n i t i a l l y out of tolerance or stray out of tolerance due to variations i n other parameters.  4.2  Concentrate Mixer  This hypothetical unit combines the new solids and recycle solids to determine the bulk analysis of the total feed to the leach train.  In reality new and recycle solids streams would be fed  separately to the leach train with adequate mixing occurring quite rapidly in the f i r s t stage.  For the purpose of simplifying calculations the pyrite and chalcopyrite in the recycle solids are transferred to the new solids stream.  - 95 -  4.3  Leaching  Assumptions (1)  A l l leaching reactors operate at the same temperature, (by controlled cooling)  (2)  Each reactor is backmixed.  (3)  The volume occupied by solids and gas in the slurry is small and relatively constant.  For the model  calculations the solids and gas are considered to occupy 8% of the total slurry volume. (4) ~  ~  Solution volume i s assumed constant with variations occurring in density as the reaction proceeds.  (5)  A l l reacted sulphide is considered to dissolve as sulphate on the basis of the long contact times and the minor concentrations of chalcopyrite.  (6)  Negligible frothing occurs in the reactors.  (7)  Iron and copper are in the form of pyrite and chalcopyrite.  (8)  The leach is operated at approximately atmospheric pressure.  Since the reactors are backmixed the rates of reactions are dependent on the output concentrations of the influencing variables.  - 96 -  Hence the set of equations describing the leach must be solved simultaneously.  A set of eighteen equations, fourteen of which are  non-linear are established to simulate the leaching system.  Nomenclature for Leach Equations  Subscripts i  =  input  o  =  output  R  =  recycle solids  v  =  volumetric flow rate of leach solution  p  = density of solution  w  =  mass flow rate of solids  X  -  mass fraction of component i n phase  V  =  reactor volume  R  =  rate of generation of component in phase per vessel  R  =  rate of consumption of component in phase per vessel  A' =  area factor for new solids relative to standard pulp  Variables  i  density A^ =  area factor for recycle solids relative to standard pulp density  P  ?  =  ratio of current pulp density of new solids to  -  97 -  experimental pulp density used f o r determination of  P^ =  r a t i o of current pulp density of recycle s o l i d s to experimental pulp density used f o r determination o  f  ^o  KJJJ =  rate constant f o r molybdenum leaching*  Kp =  r a t e constants f o r i r o n leaching*  K^ =  rate constant f o r copper leaching*  < | > =  f r a c t i o n leached  o  e  u  LEACH EQUATIONS  Component Balances  (g/s)  I  I  Liquid  vpX.  (Mo, Fe, Cu, HN0 ) 3  x  - v p X o  Solids  w. X. x i  o  K  g  R  -  R c  =  0  (43) '  (New Mo, Recycle Mo, Fe, Cu)  w o  X  o  +  \  *  +  based on 1 l i t r e of s o l u t i o n .  R g  c  R  =  0  (44)  - 98 -  Overall Mass Balances (g/s)  Liquid vp.  Solids  •+  o  ER  -  w + o  ~  g  ZR  c  =  0  (45)  Solids)  IR g  ER c  =  0  (46)  (New Mo, Recycle Mo, Fe, Cu, HN0 ) (g/s) 3  - New Mo  where  v p  (New s o l i d s , Recycle w. l  RATE EQUATIONS  -  R  =  N M o  K^[HN0 ]  (47)  A'P'V  2  3  A' i s determined by i n t e r p o l a t i o n of experimental r e s u l t s and P' by extrapolation  based on a l i n e a r relationship between  surface area and mass of s o l i d s .  R e c  Fe  y  c l e  M  R  o  p e  KRMO  =  V  =  m  o  3  K^, [HN0 ]W e  ]  2/3  3  2  V  Wk  W  ( 4 8 )  (49)  In the model t h i s rate i s considered i n two parts: that from FeS^, and that from CuFeS . 0  Cu —  R„ = Cu  K l [HNO„]W Cu J  2/3  V  (50)  - 99 -  HN0  3  R H N  0  3  =  3  '  Mo  9 4 1 2 R  +  5  '  6 4 1 9 R  Fe  +  °-  6  6  1  1  R  < > 51  C  u  where t h e c o n s t a n t s a r e based on t h e s t o i c h i o t n e t r y o f l e a c h i n g o f MoS  2>  FeS , 2  CuFeS e  AREA FACTORS  2  (New Mo, R e c y c l e  Mo) . 3 a  New Mo  A'  -  e'  where a , a ^ a r e e m p i r i c a l l y determined 2  R e c y c l e Mo" A^  where b ^ and b  2  =  b  ±  e  ~  b  2  b  3  (52)  a 2 y  *  constants.  (53)  R  a r e parameters c o n d i t i o n e d by t h e r e g r i n d i n g s t e p and  b^ i s a constant.  The  s o l u t i o n o f such a s e t of n o n - l i n e a r and l i n e a r  i s a formidable task.  equations  S e v e r a l s u b r o u t i n e s a r e a v a i l a b l e a t U.B.C. t o  s o l v e these e q u a t i o n s b u t t h e s u b r o u t i n e SSM (see U.B.C. NLE) was chosen s i n c e i t was quoted as t h e most " r o b u s t "  [67,68],  The e q u a t i o n s a r e  programmed i n t h e f o l l o w i n g form: Non-Linear Fx  =  0  (54)  Ax  =  B  (55)  Linear  - 100 -  Basically this is a secant method which requires an i n i t i a l set of output guesses to commence computations.  Hence guesses have  to be provided for each leaching stage.  4.4  Leach Balance  The purpose of this subroutine i s to calculate f i n a l stage leach output values that are not determined by the solution of the simultaneous equations.  Values calculated are:  (1)  Total solids flow rate - sum of new and recycle solids.  (2)  Molybdenum content of combined solids.  (3)  Siliceous insoluble content of solids by mass balance  ;  since this component is unaffected by the leach. (4)  Sulphur contents of combined solids and of liquid by  i  stoichiometric balance. (5)  Calculation of the weighted-average area factor of solids exiting the leach.  (6)  Total fraction of molybdenum leached from new and recycle input solids.  4.5  Filter  The f i l t e r subroutine performs the solid/liquid separation on the leached slurry.  At present i t allows for 100% of the solids  - 101 -  to  pass t o the r e g r i n d o p e r a t i o n but was  of  the program.  cake r a t h e r than l o s s of  solids.  Regrind  The of  r e g r i n d o p e r a t i o n not o n l y i n c r e a s e s the a b s o l u t e v a l u e  the a r e a f a c t o r but a l s o i n c r e a s e s the c u r v a t u r e of the  composite  a r e a decay c u r v e .  remaining  From F i g u r e 20 i t can be seen t h a t the  a r e a decay c u r v e approaches l i n e a r i t y a f t e r a r e l a t i v e l y low of  expansion  The main f a c t o r t o c o n s i d e r i n f i l t r a t i o n would be  the l o s s of f i l t r a t e i n the f i l t e r  4.6  included for future  leaching.  R e g r i n d i n g would i n c r e a s e the c u r v a t u r e but  not t o the same e x t e n t as the i n i t i a l  concentrate.  degree  probably  In the p r o c e s s of  m i l l i n g the o r i g i n a l o r e numerous s i z e r e d u c t i o n s t e p s a r e i n v o l v e d , a l l h a v i n g t h e p o t e n t i a l t o produce f i n e s . are l i s t e d  The  s i z e r e d u c t i o n steps  i n Table VIII.  Table VIII SIZE REDUCTION STEPS IN NORMAL MILLING OPERATIONS  1  Primary  Crushing  2  Secondary C r u s h i n g  3  Tertiary  4  Rod  5  Ball  6  Regrind B a l l M i l l i n g regrind mill)  Crushing  Milling Milling (may  be more than  one  - 102 -  Particles may bypass or be recycled through some size reduction steps by classifiers operated i n closed circuit.  Since  the regrind step i n the current flowsheet involves one single-pass operation before returning to the leach i t i s probable that the "fines" content i s not as great as i n the new concentrate.  Hence  the area factor relationship for the recycle concentrate w i l l differ from that for the new concentrate and i s assumed to follow the relationship i n Equation (53). The recycle area parameters are determined as follows:  where A_' =  composite area factor value at leach exit area factor value at grind exit,  k t  g g  grind constant (t "*") mean residence time i n grinding m i l l . incremental new surface area factor created.  But k cannot be determined directly by experimentation. g  •'•  since where  b  k  l  g  =  A'(1 + k' t ) g g  =  k' A' g  k' i s determined experimentally (see Appendix D)  (57)  - 103 -  No information was available on the form of the exponential portion of Equation (53)-  To avoid undue complexity in view of the  uncertainty surrounding this expression the relationship i s simply assumed as: b  2  -  l+k't  g  (58)  and b^ = an appropriate constant which influences the shape of the recycle area decay plot.  4.7  Stream Splitter  _ The stream splitter divides the mass flow from the regrind m i l l to the flotation section or directly back to the leach according to a predetermined ratio.  Assumption  The stream splitting i s assumed to be unbiassed so that the chemical analysis and surface area parameters associated with the two separate streams are the same as those for the reground solids.  - 104 -  4.8  Flotation  Assumptions (1)  Flotation rates are considered as f i r s t order with respect to mineral concentration in the pulp.  (2)  The flotation rates of each mineral are described by separate single rate constants.  (3)  The pulp residence time i n each c e l l i s only significantly influenced by the flotation of the dominant component (molybdenite).  (4) ~  Cell volume i s 25% air i n pulp during operation [69],  (5) A simple series of flotation cells i s used with no  i  pulp recycle.  t  Nomenclature for Flotation  til  K  =  fractional mineral recovery from i  =  flotation rate constant  c e l l (i=l to n)  th =  pulp residence time i n i  cell  u  =  pulp volumetic flow into bank of cells  m  = mass flow rate of floatable component into c e l l  a  =  factor which converts mass of floated solids to volume of flotation pulp (50 wt % H 0) ?  V  = volume of deaerated pulp in c e l l .  - 105 -  The pulp residence time i n the f i r s t c e l l based on the tailings flow i s :  9  1  u - \  "  < > 59  Since 0 i s variable with c e l l number the total recovery cannot be obtained from a simple series summation as when 6 i s assumed constant. Hence the recovery of M0S2 i s determined on a cell-by-cell basis. For the xi"^ c e l l : 1  KG R  n  -  1 + K8  (1  n  n-1  " *x V  (60)  and' e  =  n  -  1  (  6  1  )  n—l u - am (R + Z R.) n . x 1  V n u - am £ R. x x By substituting Equation (61) into Equation (60) and rearranging:  amR  „  n-1 n-1 - (u - am £ R. + KV)R + (1 - Z R.)KV n x n . x x x  (62)  = 0  which i s a quadratic equation and can be solved for the root 0 < R^  - 106 -  n-1 (u - am Z R. + KV) i R  n  (u - am Z i  n-1 R. + KV) - 4am(l - Z R )KV i 1  =  2am (63) Equations (63) and (62) are solved sequentially for each  flotation c e l l with the overall recovery of molybdenite given by the summation of the individual c e l l recoveries- Then equations of the same form as Equation (60) are used for the recoveries of the other minerals using the c e l l residence times already established by the molybdenite flotation.  4.9  Recycle Combination  This hypothetical unit i s used to determine the calculated recycle parameters of mass flow, chemical analysis (5 components) and area factor parameters for comparison to the estimated values. The mass flow and analysis are determined by a mass balance on the solids recycling directly after grinding and those in the reflotation concentrate.  Assumption  The refloated product i s assumed to have the same area factor parameters as the solids which are reground only.  The error introduced  - 107 -  by this simplification i s negligible since there is a very high recovery of molybdenite during reflotation,  4.10  Input/Output Routines  The functions of these routines are: (1)  a.  Convert input units to model units  b.  Convert model units to output units  when convergence of recycle parameters has been successful. (2) ~"  ~  Control converged output printing with additional overall calculations.  - 108 -  CHAPTER 5  MODEL EVALUATION AND DISCUSSION  Although some aspects of the overall model are s t i l l subject to uncertainty the simulation was partially evaluated in the current form.  Complete validation is not possible until a continuous plant i s  constructed although model, v i a b i l i t y could likely be improved with further laboratory experimentation, particularly with respect to grinding and flotation.  Model results were obtained for a moderately-sized plant with the! calibrated Endako concentrate as the plant feed.  Since the system  operates under steady-state conditions the response of most interest was i  the solids recycle ratio.  The recycle ratio would be subject to some  maximum limit depending on the i n i t i a l solids feed rate and the maximum pulp density under which the leach can continue to operate satisfactorily. With any steady-state model caution should be exercised in relating model values to plant values where fluctuations occur.  In a relatively slow  leaching system such as this, fluctuations should occur with low frequency. Attainment of steady state after adjusting some variable should similarly take considerable time.  In interpreting the behaviour of such a system i t should be  - 109  -  remembered that the C and A terms i n Equation (21), describing  the  basic rate r e l a t i o n s h i p , are not purely independent variables. new  The  input values are independent to the extent of possible plant  operations but i n t e r a c t i n a r r i v i n g at the steady state values i n each leaching v e s s e l .  operating  The r e l a t i o n s h i p i s further complicated by  presence of the s o l i d s recycle stream.  The model calculations were based on a chosen standard cond i t i o n and  the e f f e c t s of i n d i v i d u a l l y varying p a r t i c u l a r plant or  process v a r i a b l e s .  The  standard conditions are outlined i n Table IX.  Table IX STANDARD CONDITION OF LEACH PROCESS  Vessels - 2 cocurrent at 120,000 l i t r e s each New  Feed - 10.8  S o l u t i o n - 87.8 - 252.1  tonnes/day Endako M0S2 (as  calibrated)  litres/min. grams H N 0 / l i t r e 3  (4 M)  Leach Temperature - 35°C Approximate Leach Stage Residence Time - 19.5 Grinding M i l l Solids Hold Up - 800  kg  Fraction of Recycle Bypassing F l o t a t i o n F l o t a t i o n C e l l s - 4 x 150  litres  0.5  hr.  the  - 110 -  This choice i s not necessarily an optimum but allows the determination of the influences on the process of particular variables. Trends which result in a decreasing recycle ratio, and hence lower input pulp density, show the potential for increased throughput while s t i l l operating below the maximum allowable pulp density.  For this study a tolerance of 0,25% was used on the recycle parameters, (absolute value of difference of estimated and calculated value divided by the average of the two and multiplied by 100).  This  would lead to a tolerance on the calculated molybdenum extraction versus the steady state extraction of less than about 1.8%.  j  Tolerance error i s the cause of the small scatter i n the  following graphs. i  In these graphs each point represents individual  model determinations.  5.1  Stability and Convergence  Stability The problems of instability arise in the solution of the simultaneous equations describing each leaching stage.  Instability  in such a set of equations becomes more likely as the equations became increasingly complex and non-linear.  This requires greater emphasis  - Ill -  on the choice or calculation of i n i t i a l estimates to commence model runs and to continue calculations until a specified convergence criterion on the recycle stream i s satisfied.  Failure of the leach-solving subroutine to converge within i t s specified tolerance can be attributed to two general reasons: (1)  Failure of the algorithm by i t s inability to determine  an independent set of directions for the variables.  Hence the guesses  for the stage output were in excessive error. (2)  Convergence of the leach algorithm was not achieved  within the maximum number of internal iterations specified (set at 150). This also indicates bad guessing and may further result in failure by (1) i f a greater number of iterations was specified.  Once computations have commenced stability is enhanced by basing new estimates on previous calculations.  The guess criteria are  outlined as follows where: \ »J  XC, G  = .=  estimated value calculated value  =  guess factor for stage 2 based on stage 1 output  k  =  leaching stage counter  j  =  cycle iteration counter  r  - 112 -  (1)  1st stage output guesses: (a)  I n i t i a l guess for j = 1  (b)  For j > 1 X,  (2)  IC. . ,  . =  (64)  2nd stage output guesses: (a)  I n i t i a l guess for j = 1  X  (b)  2,l  -  G  F  X C  1 1  ( 6 5 )  5  For j > 1 XC  (3)  3rd stage output guesses (a)  I n i t i a l guess for j - 1 2 1 xcf: ' XC  x  3 i s  =  XC  2,1  (67  >  except for rate equations where XC X  3 1 S  M  " xc7*7 1  J  x c  1  where M is taken as 1.5  2,i  ( 6 8 )  - 113 -  "(b)  For  j >1 XC  (4)  4th stage or greater output guesses: (a)  I n i t i a l guess for j = 1 XC  \,i (b) For  .- xcTT^ k-2,j " ^ 1 , 3 :  ( 7 0 )  j>1 XC  \,j  - x Vclr. fj r- rl  • ^-i,i x c  ( 7 1 )  Mathematical instability could also arise within the system of algebraic equations since the solving routine i s unconstrained. In searching for the true values certain variables may cause instabilities or impossibilities i n particular equations as follows: (1) A negative number to a fractional power (2)  Negative concentration or flow rate  In most cases when this condition arises, mathematical and physical stability i s maintained by using an alternate equation where the appropriate term i s set to zero.  In one case stability i s maintained by  setting the term to zero i n the original equation.  Convergence  Convergence of the eight recycle parameters within a specified  - 114 -  tolerance i s required before the complete output i s printed. Convergence i s attained by the previously defined adjustment criterion, but to maintain the leach calculation stability, the step sizes must be less than current c r i t i c a l values.  Since the step size i s relative to the difference between the estimated value and calculated value the approach to convergence would decelerate as the true value i s approached.  Hence the fractional adjust-  ment i s increased as the tolerance becomes smaller with model stability maintained since the absolute variation i s s t i l l small.  It was apparent from the early model work that the mass flow rate of recycle solids created more sensitivity to instability. fori  Therefore,  high calculated tolerance values, the fractional adjustment to this  particular variable i s less than for the others.  For low tolerance values  high fractional adjustments are operative for a l l recycle parameters.  Under this convergence scheme a l l parameters that are not within tolerance are continually adjusted until tolerance i s achieved or the computer run terminated.  Some recycle parameters such as molybdenum and  sulphur contents are quite predictable and experience only small variations. Convergence i s therefore quite rapid for these variables.  The recycle parameters are not entirely independent variables.  - 115 -  Hence variations in one parameter can cause alterations in other parameters.  This can lead to a floating effect on some variables  particularly those that are more highly dependent on each other such as recycle solids flow rate and area factor parameters.  With different  degrees of interdependency and different adjustment factors convergence is approached by at least one variable while the other(s) may 'float'. Once the f i r s t has converged the other(s) begin converging.  For economical convergence the estimates for the recycle parameters should not be grossly in error.  Guesses that are highly i n  error w i l l lead to excessive computation times.  For concentrates containing relatively small amounts of iron and copper the convergence criterion becomes superfluous for these two elements.  Since they are leached to extremely low levels (essentially  zero), tolerance adjustments are not necessary after the recycle values for these two elements have been set to appropriately low levels.  Aborted Runs  Once instability or lack of convergence of the leach subroutines has occurred the computer run i s terminated. Often the printed output can be helpful for subsequent runs since, although failure has occurred, many variables have approached their converged values.  The  -  116  -  terminated values for the f i r s t stage output guesses, the recycle parameters and guess factors i f necessary, except for those in obvious error, can be used for the subsequent run.  The more erroneous values  should be altered slightly in the appropriate direction.  The direction  can be ascertained from a knowledge of the variables involved and the form of the equation in the model (ie. Fx - 0).  To date most errors have been associated with the rate equations. Hence i f model failure does occur success can be achieved with an interactive procedure, often within one or two attempts.  5.2- Model Results...  5.2.1  New Solids Flow Rate  i  This variable determines the production of the leaching process since, at steady state, the input of new feed must be balanced by the extraction of the same amount of material to the appropriate exit streams. The range of the new solids flow rate is subject to constraints of maintaining physical stability of the system, particularly with respect to the maximum operable pulp density within the leach.  Figure 23 demonstrates how the recycle ratio increases at an increasing rate as the new solids feed rate is raised.  The graph w i l l  - 117 -  NEW  SOLIDS  FLOWRATE  (tonnes/day)  Figure 23. Solids recycle ratio vs. new solids flowrate. Other conditions standard.  - 118 -  approach an asymptotic limit as the stoichiometric balance of leachable minerals and n i t r i c acid approaches complete consumption of the n i t r i c acid for steady state conditions.  Under most leaching con-  ditions the maximum pulp density restrictions w i l l likely be encountered before this limit i s reached. The impact of the. greater new solids input and correspondingly greater recycle solids flow rate i s to lower the solution reactivity i n each leaching stage.  This shown in Figure 24  where the n i t r i c acid concentration i n each stage i s plotted as a function of the new solids feed rate.  Figure 24 also shows the variation in other  factors which affect the overall rate of molybdenum extraction to solution. The total input pulp density i s raised as a consequence of increases i n both the new and recycle solids streams.  The operating area factors for  both the new and recycle solids are greater for increased solids input since both are leached to lesser degrees on passing through the leach.  For increased new solids flow rate there i s a greater input of molybdenum to solution. Hence for constant solution flow rate the net gain i n molybdenum concentration i s greater.  This point i s con-  firmed by Figure 25 where the difference between the pregnant solution and recycle solution molybdenum contents i s plotted against new solids feed rate.  The lowering of the percent molybdenum extraction per pass as the new solids feed rate i s increased i s shown in Table X. The  - 119 -  500h  NEW  SOLIDS  FLOWRATE  (tonnes/day)  Figure 24. T o t a l input pulp density, operating area factors and operating n i t r i c acid concentrations vs, new solids flowrate. Other conditions standard.  - 120 -  10  NEW  SOLIDS  31 FLO WR ATE  12 (tonnes/day)  Figure 25. Gain in solution molybdenum concentration vs. new solids flowrate. Other conditions standard,  - 121 -  total input solids signify new and recycle concentrates.  Table X EXTRACTION FROM TOTAL INPUT SOLIDS ON EACH PASS FOR DIFFERENT NEW SOLIDS FLOW RATES(%)  New Solids Flow Rate (tonne/day)  Stage 1  Stage 2  Stage 1+2  10.0  18.2  5.6  23.8  10.5  17.7  5.2  22.8  10.8  17.5  5.0  22.5  11.0  17.2  4.9  22.1  11.5  16.7  4.4  21.1  11.8  16.3  4.1  20.4  12.0  16.0  3.9  19.9  It i s also evident that the proportion of extraction work done by the leach vessels shifts slightly more i n favour of the f i r s t stage.  5.2.2  I n i t i a l Acid Strength  The i n i t i a l acid strength i s similarly subject to stoichiometric restrictions.  Figure 26 shows how the recycle ratio increases  as the i n i t i a l n i t r i c acid concentration is decreased, again approaching  - 122 -  INITIAL  230  250 ~  INITIAL  HNO,  (moles/1)  270  ~  NITRIC ACID (g/l)  290  Figure 26. Solids recycle r a t i o vs. i n i t i a l n i t r i c acid concentration. Other conditions standard.  - 123 -  an asymptotic limit due to depletion of n i t r i c acid under steady operations.  This result indicates the advantage of using as high  an i n i t i a l n i t r i c acid concentration as possible, subject to practical limitations.  As shown earlier, the extent to which molybdenum can be  precipitated from solution i s subject to pH.  On a plant scale there  may be an optimum balance between leaching rate and the recycle of soluble molybdenum for different operating acidity levels.  The  earlier laboratory work on the process did show some slight discolouration of the hemi-hydrate when using high i n i t i a l n i t r i c acid concentrations 6M). The cause and extent of this was not fully determined although product purity was s t i l l high.  With higher i n i t i a l n i t r i c acid concentrations each leaching vessel operates at higher n i t r i c acid levels, as demonstreated by Figure 27.  The increased leaching rates result i n a greater degree of reaction  of the solids and hence operation at lower area factor values.  Figure  27 shows how the operating area factors vary as a function of i n i t i a l n i t r i c acid concentration.  The decrease i n input pulp density as a  function of i n i t i a l n i t r i c acid results from the lower solids recycle. This i s also shown i n Figure 27.  Since the mass flow of new solids and volumetric flow of solution are constant for this series of runs the gain i n solution molybdenum concentration i s consistent at the steady state level. Hence,  -  124 -  • _500r  °">400| 0.Z ZtU — Q  300  0.15  cc o o ft  2 OJOI cc <  1-  < cc UJ CL  o  0.05  160  140  120  o f£  80]  z 601  40  1  230  250 INITIAL  275" NITRIC  ACID  (g/D  Figure 27. Total input pulp density, operating area factors and operating n i t r i c acid concentrations vs. i n i t i a l n i t r i c acid concentration. Other conditions standard.  - 125 -  there i s no increase in the molybdenum content of the pregnant solution to offset the higher solubility limits at pH's less than the isoelectric point.  However, increased input acid levels w i l l allow a greater treat-  ment rate of new molybdenite concentrate thus producing a richer pregnant solution while s t i l l operating below the maximum pulp density.  The greater leaching rates result i n higher operating siliceous insoluble concentrations i n solids throughout a l l phases of the leaching operation.  The operating concentrations for leach residue, reflotation  product and recycle solids are graphed against i n i t i a l n i t r i c acid i n Figure 28. This trend applies to variations i n a l l parameters which lead to increased instantaneous reaction rates.  The percent extractions from total solids input of Table XI naturally show increases as the i n i t i a l n i t r i c acid concentration i s raised.  5.2.3  Solution Flow Rate  The variation of solution flow rate has a similar effect on the solids recycle ratio as changes in i n i t i a l n i t r i c acid concentration. This follows from the stoichiometric balance since a lower solution flow rate of the same acid concentration results in fewer moles of acid  - 126 -  I5i— — —r~ :  :  230  :  —  1  ,~-  250 INITIAL NITRIC  r  270 ACID (g/l)  290  Figure 28. Insol content of leach residue, reflotation concentrate and recycle solids vs. i n i t i a l n i t r i c acid concentration. Other conditions standard.  - 127 -  Table XI EXTRACTION FROM TOTAL INPUT SOLIDS ON EACH PASS FOR DIFFERENT INITIAL NITRIC ACID CONCENTRATIONS(%)  I n i t i a l HN0  y  Stage 1  Stage 2  Stage 1+2  230  15.6  3.9  19.5  235  16.0  4.2  20.2  239.5  16.4  4.5  20.9  245.8  17.0  4.8  21.7  252.1  17.5  5.0  22.5  258.4  17.8  5.2  23.0  264  18.3  5.4  23.7  667.8  18.6  5.6  24.2  275  19.3  6,0  25.2  284  20.0  6.4  26.4  290  20.6  6.6  27.2  (g/D  3  The gain i n percent extraction for the f i r s t stage outweighs the gain in the second stage extraction.  - 128 -  available for the same quantity of solids.  The solids recycle ratio  versus solution flow rate i s graphed in Figure 29.  Again i t can be  seen that the recycle ratio rises to an asymptotic limit as the solution flow rate i s decreased.  The factors influencing the rate of reaction are plotted in Figure 30.  With increasing solution flowrate the solution has less  residence time to react and therefore operates at higher n i t r i c acid levels in each leaching stage.  With higher solution reactivity the  recycle ratio and hence input pulp density are lowered.  The greater  degree of reaction similarly results in operation at lower levels of area factor.  Despite the increased solution reactivity the lower residence time and steady-state operation result in a lower gain in molybdenum concentration in solution, as shown in Figure 31.  The net quantity of  dissolved molybdenum is s t i l l the same since the volume flow of solution is greater.  With similar total acidity the molybdenum precipitated per  l i t r e in subsequent processing w i l l be less but this would be compensated by higher volumetric throughput.  A greater percentage extraction per pass through the leach i s obtained as the solution flow rate i s increased.  The values in Table XII  - 129 -  SOLUTION FLOWRATE (I/min) Figure 29, Solids recycle ratio vs.solution flowrate Other conditions standard.  -130 -  50CM-  SOLUTION  FLOWRATE (I/min)  Figure 30. Total input pulp density, operating area factors and operating n i t r i c acid concentrations vs. solution flowrate. Other conditions standard.  - 131 -  Figure 31. Gain in solution molybdenum concentration vs. solution flowrate. Other conditions standard.  - 132 -  also show only a very slight change in the work distribution between stages with the second stage exhibiting a marginally greater gain i n percent extraction than the f i r s t .  Table XII EXTRACTION FROM TOTAL INPUT SOLIDS ON EACH PASS FOR DIFFERENT SOLUTION FLOW RATES(%)  Solution Flow Rate (£/min)  Stage 1  Stage 2  Stage 1+2  16.2  3.8  20.0  16.6  4.2  20.8  85.0  17.2  4.7  21.9  87.8  17.5  5.0  22.5  95.0  17.9  5.6  23.5  100.0  18.2  6.0  24.1  77.5 80.0 \  5.2.4  y  -  Leach Temperature  As with any thermally-activated process the instantaneous reaction rate increases exponentially with temperature.  As Figure 32  shows, the recycle ratio diminished as the leaching temperature was raised.  Over the temperature range examined there was a slight indi-  cation of curvature in the anticipated direction.  - 133 -  4.0i  TEMPERATURE  l°C)  Figure 32. Solids recycle ratio vs. leach temperature. Other conditions standard.  - 134 -  Figure 33 shows that the input pulp density and operating area factors are at lower levels for higher temperatures-  Any change  in operating n i t r i c acid levels was not significant within the tolerance limits used. With constant new solids and solution input the steady state operations result i n a constant gain in molybdenum concentration in the pregnant solution.  Changes in the leaching temperature result i n a slight alteration i n the distribution of leaching work done by each stage as can be seen i n Table XIII.  "  -  :  i  Table XIII  EXTRACTION FROM TOTAL INPUT SOLIDS ON EACH PASS FOR DIFFERENT LEACH TEMPERATURES(%)  Temp (°C)  Stage 1  Stage 2  Stage 1+2  33  16.6  4.9  21.6  34  17.0  5.0  22.0  35  17.5  5.0  22.5  36  17.8  5.0  22.8  37  18.3  5.1  23.4  38  18.7  5.2  23.9  39  19.2  5.3  24.5  40  19.8  5.4  25.2  - 135 -  Figure 33. T o t a l input pulp density and operating area factors vs, leach temperature. Other conditions standard.  - 136 -  These results show that increasing reactivity by raising the leach temperature leads to a slight increase in the proportion of leaching performed by the f i r s t stage.  5.2.5  Partial Bypassing of Flotation  Since the purpose of reflotation i s to eliminate insoluble gangue the increased bypassing of this step leads to higher operating levels of siliceous minerals i n a l l the solids streams,  The effect of  bypassing on the insol contents of the leach residue, reflotation concentrate and recycle solids is shown in Figure 34.  The insol levels  rise at an increasing rate as the effect of recycling the siliceous components compounds i t s e l f .  i.  At recycle solids insol levels less than that of the new feed there is a negligible effect on the total mass of the recycle flow. However, the solids recycle ratio is significantly increased as the reflotation bypass is raised to levels which result in higher operating insol contents of the solids streams.  This point is shown in Figure 35.  At this stage of development the flotation section only provides an indication of behaviour since the flotation rate constants were essentially estimated.  This does not necessarily detract from the  leaching model since preliminary test work has revealed high recoveries.  - 137 -  5h  11  0  i  0.2  i  0.4  FRACTION  i  0.6  BYPASSING  1  0.8  1  1.0  FLOTATION  Figure 34. Insol content of leach r e s i d u e , r e f l o t a t i o n concentrate and recycle s o l i d s vs. "fraction bypassing f l o t a t i o n . Other conditions standard.  - 138 -  Figure 35. Solids recycle ratio vs. fraction bypassing flotation. Other conditions standard.  - 139 -  A major concern in the flotation section is the mass of molybdenum lost to the t a i l s .  Although the model was not run under optimum  flotation conditions the results show a decreasing loss of molybdenum to the tails as the flotation bypass is increased above about 0.5. The results should be treated with caution, however, since the water flow rate to flotation was not adjusted in accordance with the solid flow rate to maintain similar pulp densities.  Although the model does not account for the analysis of the solids in the effect of grinding this may have some influence.  With  higher degrees of flotation bypass the grinding mill treats material with higtfer concentrations of harder siliceous minerals.  As well as  affecting the grinding of molybdenite this would also lead to increased consumption of grinding media.  5.2.6  Leach Vessel Volume  The effect of the leach vessel volume on the solids recycle ratio is shown for the case of two equi-sized stages in Figure 36. Although the recycle ratio decreases as the vessel size increases the change i s not drastic when considering the range of vessel sizes investigated.  Hence the use of extremely large vessels is not  warranted for the small additional benefits gained.  - 140 -  4.0r—«-  Figure 36. solids recycle ratio vs.leach vessel volume. Other conditions standards  - 141 -  The input pulp density and operating area factors both decrease as the vessel volume is increased. Figure 37.  This can be seen in  The operating n i t r i c acid levels, however, did not show  significant variation under the tolerance limits used.  The net decrease in physical factors which affect the reaction rate i s more than compensated for by the longer residence times which increase in an approximately linear fashion with vessel volume.  The effect of two-stage leaching but with different vessel volumes was briefly investigated.  No difference in recycle ratio was  detected (within the tolerance limits) for leaching with stage 1 at 100,000 l i t r e s and stage 2 at 140,000 l i t r e s .  A slight increase in  recycle ratio to 3.46 was calculated when stage one was set at 80,000 l i t r e s and stage 2 at 160,000. This can only be casually compared to the case for a pure, second-order reaction where a shallow minimum i n total reactor volume for a given degree of reaction occurs where the volume of stage 1 is 70% of stage 2.  The slight possible advantages of using different reactor sizes would therefore not compensate for the additional cost of such a configuration.  - 142 -  Figure 37. Total input pulp density and operating area factors vs. leach vessel volume. Other conditions standard.  - 143 -  5.2.7  Number of Leaching Stages  Figure 38 shows the s o l i d s recycle r a t i o as a function of the number of leaching vessels for.constant vessel volume.  The effect  of "adding" cocurrent stages f o r the standard operating conditions indicate a marked decrease i n r e c y c l e r a t i o from one to two stages with much less improvement from two stages to three.  Additional  staging i n t h i s manner above two or three vessels may not be j u s t i f i e d when considering the increased c a p i t a l costs and molybdenum inventory. Table XIV l i s t s the extraction from the t o t a l input solids f o r one, two and three stages under the same conditions pertaining to Figure 38„  Table XIV EXTRACTION FROM TOTAL INPUT SOLIDS ON EACH PASS FOR DIFFERENT NUMBER OF STAGES (%)*  Stages  Stage 1  Stage 1+2  Stage 3  Stage 1+2+3  1  16.5  -  -  -  -  2  17.5  5.0  22.5  -  -  3  17.8  5.7  23.6  2.8  22.4  For three-stage  *  Stage 2  leaching the d i s t r i b u t i o n of leaching work between stages  constant stage volume  - 144 -  2  I  NUMBER  OF  STAGES  Figure 38. Solids recycle ratio v s . number of leach stage Constant stage volume. Other conditions standard.  - 145 -  one, two and three i s in the ratio 1 : 0,32 : 0.16.  The results of the one-stage simulation did show a small, but detectable, concentration of iron and copper i n the recycle solids.  The effect of multiple staging when considering constant total volume i s shown i n Table XV.  Table XV SOLIDS RECYCLE RATIO AS A FUNCTION OF NUMBER OF STAGES (CONSTANT TOTAL VOLUME)  No. of Stages  Vol. Per Stage(£)  Recycle Ratio  2  120,000  3.35  3  80,000  3,22  4  60,000  3.08  The division of leaching vessel volume into a greater number of stages lowers the solids recycle ratio but the additional expense involved with increased staging may again not be justified.  - 146 -  5.2.8  Grinding  Since the grinding section of the model was the most suspect part some study was conducted on the effects of changing grinding parameters.  With the uncertainty in the exponential portion of Equation  (53) the value of the multiplying factor, b^, was examined over a small range.  The influence of this term on the recycle area factor as a  function of fraction leached i s plotted in Figure 39. calculations a value of 2.0 was chosen for b^;  For the model  Although this choice  cannot be validated at this stage extremely rough calculations on the previous grinding work show the resulting exponential value to be in the appropriate range.  There is no doubt that some error is associated with this section.  However i t i s likely that the error i s not extreme and would  mean rather minor changes in the sizing of relatively small-scale equipment to produce approximately equivalent practical results.  The influence of grinding mill size on the recycle solids area factor relationship is presented in Figure 40.  It can be seen  that the plot i s raised and the curvature is increased as the grinding mill size is increased.  However, the solids recycle ratio becomes  - 147 -  T  I  U,  0  0.1  1  l_  02 FRACTION  1  1  1 1 0.3 0.4 LEACHED  T  1_  05  Figure 39. Recycle area factor vs. fraction leached for different values of b y Standard conditions.  - 148 -  0  •v——  -r~~——*T  0.1  0.2  FRACTION  — i  0.3 0.4 LEACHED  !  T  03  Figure 40. Recycle area factor vs. fraction leached for different grinding mill sizes. Standard conditions. (Grinding m i l l size units -' kilograms solids holdup)  - 149 -  relatively insensitive to grinding mill size for higher m i l l sizes. This i s , at least in part, due to the choice of equation but may also indicate the interactive effects of mineral surface area and reagent concentration in such a partially bounded system.  This section of the model does demonstrate the logical trends but further work i s definitely required to verify the results.  - 150 -  CHAPTER 6  CONCLUSIONS  A steady state mathematical model of a major section of a proposed molybdenite leaching process has been developed from a r e l a t i v e l y l i m i t e d amount of a v a i l a b l e data.  A s i g n i f i c a n t feature  of the leaching model f o r molybdenite i s the bulk empirical determination of the change i n a c t i v e mineral surface area as leaching progresses.  This i s achieved by i n t e r p o l a t i o n and extrapolation from  batch experimentation.  The method avoids vague assumptions on p a r t i c l e  shape, with or without correction f a c t o r s , and also allows f o r other influences such as p a r t i c l e non-uniformity and p a r t i c l e which are extremely d i f f i c u l t to quantify.  cleavaging  The number of mathematical  c a l c u l a t i o n s are also somewhat reduced by elimination of the necessity to consider p a r t i c l e s i z e classes.  In i t s current form the model accounts f o r numerous plant and operating variables as follows: (1)  Number, s i z e and d i s t r i b u t i o n of leaching vessels.  (2)  Size of grinding m i l l .  (3)  Number and size of f l o t a t i o n c e l l s .  (4)  V a r i a t i o n i n new s o l i d s feed rate and analysis.  - 151 -  (5)  Variation in solution flow rate and n i t r i c acid strength.  (6)  Influence of partially bypassing flotation.  (7)  Effect of leaching temperature  The model cannot be considered as complete at this stage since some sections are subject to uncertainty and total verification is not possible at this time.  The main points of uncertainty in the  formulation are listed as: (1)  Accounting for the regrind step, particularly with the exponential part of Equation  —  - (2)  Use-of laboratory-determined  (53). batch grinding data and •  extrapolating to continuous plant-scale operations. (3)  Use of constant, estimated flotation rate constants.  (4)  Approximation of the operating active surface area of solids in the leach based on averaging of effects in batch experimentation and the neglecting of the solids residence time distribution in the leaching model.  Although some aspects of the model require further clarification this current type of formulation should be adequate for future work. At the current stage of process development a more rigorous or thorough, and thus more d i f f i c u l t and expensive model is not justified.  - 152 -  Although no detailed economic study was performed the previous work and the results of this model indicate the feasibility of the process.  However, further evaluation is required to ascertain  the v i a b i l i t y of using the process.  The formulation of a mathematical model does not eliminate the necessity of piloting a process which has not previously been tested on a pilot or commercial scale.  The model can be utilized in  the design of such a plant which can then, in turn, provide v e r i f i cation or indicate required adjustments to the formulation.  ~  ~ Industrial piloting is essential for revealing other  possible unknown influences on the smooth operation of the process. A model, such as this one, i s based on a relatively few number of small-scale observations.  Other factors which could influence the  performance may not be taken directly into account by the model. Some may impose limits on the process but these limits could possibly be determined by separate experimentation.  Another aspect to consider  is the frequency and amplitude of fluctuations that might occur on an industrial scale.  Although this model has been developed for a specific process the basis of formulation may prove useful in evaluation of other similar systems.  This applies particularly to the leach simulation.  - 153 -  CHAPTER 7  RECOMMENDATIONS  Further work i s warranted on this system and may be summarized as follows: (1)  Further evaluation of effects of grinding.  (2)  Experimental studies on reflotation of leached and ground residues.  (3)  Increase model stability, e.g. attempt partial linearization.  (4)  Further test and develop ( i f necessary) the chalcopyrite and pyrite leaching equations.  (5)  Test the model on other molybdenite concentrates.  (6)  Evaluation of hemihydrate precipitation behaviour with a view to optimizing the leach/precipitation system.  (7)  Investigate the effects of pressure on leaching rates.  (8)  Investigate N0 as a substitute for HNO^ in f i r s t 2  stage leaching.  - 154 -  REFERENCES  D.M. Himmelblau and L B . Bischoff: Process Analysis and Simulation - Deterministic Systems, John Wiley & Sons Inc. N.Y. 1968. D. M. Himmelblau: Process Analysis by Statistical Methods, John Wiley & Sons Inc. N.Y. 1970. E. Peters and A. Vizsolyi: Hydrometallurgical Treatment of Molybdenite Concentrates, research proposal, University of British Columbia, 1974. E. Peters and A. Vizsolyi: Hydrometallurgical Treatment of Molybdenum Concentrates, Series of 12 monthly reports provided under contract with Placer Development Ltd., University of British Columbia, Aug. 1974 - June 1975. E. Peters and A. Vizsolyi: Cominco Contract Research, University of British Columbia, 1972. M. Pourbaix^and N. 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Sutulov: Molybdenum and Rhenium Recovery from Porphyry Coppers, University of Concepcidn, Chile, 1970.  15.  A. Sutulov: Copper Porphyries, University of Utah Printing Services, Salt Lake City, Utah, 1974.  16.  A. Kuklis: Molybdenum, preprint from Bulletin 667, U.S. Dept. of Interior, Bureau of Mines, pp. 1-16.  17.  A. Sutulov: World Mining, 1978, Vol. No. 3, pp. 73-75.  18.  J.W. Goth: E/MJ, 1977, Vol. 178, No. 3, pp. 88-92.  19.  J.A. Butterfield and J.A. Ganshorn: Molybdenum Supply and Demand Forecast, presented at CIM Conference of Metallurgists, Vancouver, B.C., Aug. 21-24, 1977.  20.  A. Bouchard and R.F. Johnson: Can. Min. J., 1978, Vol. 99, No.2, pp. 116-118.  21.  D.G. Lindsay: Endako Roasting Practice, presented at CIM Conference of Metallurgists, Vancouver, B.C., Aug. 21-24, 1977.  22.  P.H. Jennings, R.W. Stanley and H.L. Ames: International Symposium on Hydrometallurgy, pp. 868-883, AIME, 1973.  23.  E. Gratch and R. Bradburn: Molybdenite Concentrate Production,at Brenda Mines Ltd., presented at CIM Conference of Metallurgists, Vancouver, B.C., Aug. 21-24, 1977.  24.  Brenda Mines Ltd., Company Brochure.  25.  Anonymous: J.O.M., 1977, Vol. 29, No. 10, pp. 9-12.  26.  L.F. McHugh, J. Godschalk and M. Kuzior: Climax Conversion Practice III, presented at CIM Conference of Metallurgists, Vancouver, B.C., Aug. 21-24, 1977.  27.  G.R. Grimes and G. Witkamp: J.O.M., 1971, Vol. 23, No. 2, pp.17-24.  28.  L. White: E/MJ, 1977, Vol. 178, No. 5, pp. 80-81.  - 156 -  29.  P.A. Butters: Mineral Processing and Extractive Metallurgy; Proc. 9th Comm. Min. and Met. Cong., Vol. 3, IMM, London, 1970.  30.  A.N. Zelikman: Molybdenum, pp. 439, Metallurgiya, Moscow, U.S.S.R., 1970.  31.  G. BjQrling and G.A. Kolta: VII International Mineral Processing Congress, Vol. 1, 1964.  32.  J.G. Posel: U.S. Patent 3,965,239, June 22, 1976.  33.  J.G. Posel, G.P. Williams and N. 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Brennecke et a l : The Nitric Sulfuric Leach Process for Recovery of Copper from Concentrate, presented at AIME 107th Annual Meeting, Denver, Colorado, Feb. 27, 1978.  44.  R.A. Hard: U.S. Patent 3,910,636, Oct. 7, 1975.  - 157 -  45.  F. Habashi: Trans. SME-AIME, 1974, Vol. 254, pp. 228-30.  46.  R. Ouellet, A.E. Torma and J.P. Bolduc: Can. Met. Q., 1975, Vol. 14, No.4, pp. 339-43.  47.  G. Bjorling and W. Mulak: Trans. IMM, 1976, Vol. 85, pp. C98-C101.  48.  P. Fossi, L. Gandon, C. Bozec and J.M. Demarthe: CIM Bull., 1977, Vol. 70, No. 783, pp. 188-97.  49.  B.W. Madsen, M.E. Wadsworth and R.D. Groves: Trans. SME-AIME, 1975, Vol. 258, pp. 69-74.  50.  R.L. Braun, A.E. Lewis and M.E. Wadsworth: Solution Mining Symposium, pp. 295-323, AIME, N.Y., 1974.  51.  M.I. Brittan: Int. J. of Min. Proc., 1975, No. 2, pp. 321-31.  52.  J.A. Harris: Proc. Aust. Inst. Min. and Met., 1969, No. 230, pp. 81-91.  53. R.J. Roman, B.R. Benner, G.W. Becker: Trans. SME-AIME, 1974, - Vol.- 256, pp. .247-52. 54.  L.M. Cathles and J.A. Apps: Met. Trans. B, 1975, Vol. 6B, pp. 617-24.  55.  R.W. Jones: Chem. Eng. Prog. , Jan. 1951, pp. 46-8.  56.  0. Levenspiel: Chemical Reaction Engineering, 2nd Edition, John Wiley & Sons Inc., N.Y., 1972.  57.  K.G. Denbigh and J.C.R. Turner: Chemical Reactor Theory, 2nd edition, Cambridge, 1971.  58.  A. Cooper and G. Jeffreys: Chemical Kinetics and Reactor Design, Prentice-Hall Inc., 1973.  59.  R.H. Perry and C.H. Chilton (eds): Chemical Engineers' Handbook, 5th edition, pp. 4-1 to 4-43, McGraw-Hill Book Co., N.Y., 1973.  60.  A. Mular: Mechanistic and Empirical Modelling of Mineral Processes, Mineral Engineering 575, University of British Columbia.  61.  A. Mular and W.R. Bull (eds): Mineral Process: Their Analysis, Optimization and Control, pp. 168-352, 1969-1973.  - 158 -  62.  R.P. King, E.M. Buchalter: NIM Report No. 1573, Johannesburg, South Africa, Feb. 20, 1974.  63.  N. Arbiter and C C . Harris: Froth Flotation, pp. 215-46, AIME, N.Y., 1962.  64.  I.A. Wilkomersky, A.P. Watkinson and J.K. Brimacombe: Trans. IMM, 1975, Vol. 84, pp. C197-C205.  65.  F.E. Pawlek: Extractive Metallurgy of Copper, Vol. II, pp. 690-705, Hydrometallurgy and Electrowinning, Int. Syrop. AIME, Las Vegas, Nevada.  66.  F.C. Bond: Crushing and Grinding Calculations, Allis-Chalmers Manufacturing Co., Milwaukee, Wiscowsin, 1961.  67.  W.B. Gragg and G.W. Stewart: A Stable Variant of the Secant Method for Solving Non-Linear Equations, Carnegie-Mellon University, Pittsburgh, Pennsylvania, April 1974.  68. C. Moore Lee, U.B.C. NLE. Zeros of Non-Linear Equations, Computing _ Centre, University of British Columbia, Feb., 1977. 69.  I.J.T. Hopkins: Modification of a Copper Flotation Circuit, Dept. ; of Mineral Engineering, University of British Columbia, May, 1975.  70.  J. Streat and C. Moore Lee, U.B.C. Curve: Curve Fitting Techniques, ^ Computing Centre, University of British Columbia, March, 1976.  - 159 -  APPENDIX A CONSUMPTION OF MOLYBDENUM  1976*  BY  CATEGORY  1977(est.) [18]  Alloy Steels  50.7%  49%  Stainless Steels  13.4%  20%  Tool Steels  5.3%  9%  Cast Irons  7.9%  7%  Superalloys and Other Special Alloys  7.6%  3%  Molybdenum Metal  6.6%  3%  Chemicals  7.3%  8%  Other  1.2%  1%  —  *  USBM Statistics - January to September, 1976.  APPENDIX B EXPERIMENTAL RESULTS  Run  Solution  Ll L2 L3 L4 L5 L6  3.94M HN0 3.94M HNO3 3.94M HNO 3 3.94M HNO3 L4 leach solution  Solution V o l . (mi) 128 200 200 250 200 200  3  3.6M HNO3  79 45 32 12.5 59 45  24 35 35.5 35 35 35  0.6847 1.3506 1.4723 0.7099 1.2133 1.2201  1.13 2.50 3.83 3.79 1.71 2.26  126.0 126.0 6C.0  43 45 16 35 30 138.5 11.2 45.8 75.2 105.2 9.6 70.2 130.5 190.4 19.4 30.1 65.2  35.5 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35  1.1976 1.0800 0.3550 1.1800 0.0162 0.0946 0.0095 0.0420 0.0780 0.1253 0.0080 0.0720 0.1460 0.2310 0.0165 0.0150 0.0200  2.32 2.00 1.48 2.25 0.0364 0.0465 0.0565 0.0611 0.0691 0.0795 0.0556 0.0684 0.0746 0.0809 0.0567 0.0332 0.0204  L10  4.0M HNO3  245  12.00 11+325*  49.0.  Lll  5.0M IINO3  250  12.00 15+3250  48.0  L12  5.0M IINO3  250  12.00 B+325/;  48.0  L13 1.14 L15  5.0M IINO3 4.0M IINO3 3.0M IINO3  250 250 250  12.00 11+3251! 12.00 B+3250 12.00 B+325#  48.0 48.0 48.0  B  Brenda  Ave.Leach Rate (EMo/t.sec.xl03)  126.3 126.0 232.4 126.0 126.0 126.0  200 200 250  Endako  Mo Leached (g)  16.16 E 25.30 E 46.48 E 31.50 E 25.30 E 25.20 E  7.4g/*Fe(NO3)3'9H20 3.94M HNO3 3.94H HNO3 3.94M IINO3  -  Ave.Temp.  (s)  L7 L8 1.9  E  Leach Time (rain)  Pulp Density (g.solids/ I. solution)  I n i t i a l Solids  25.20 E 25.2 L4 res 15.00 E  CO  1  APPENDIX  B  (Continued)  Run L16 L17 L18 L19 L20 L21 L22  Solution V o l . (ml)  Solution 1.0M HNO3 2.0M UNO3 6.0M HNO3 1.0M HN03 1.0M UNO3 4.0M HNO3 1.0M H2SO4 4.0M HNO3 3 g/1 Fe3+ 5.2 g/1 S0 " 4.0M HNO3 3 g / l Fe3+ 5.2 g / i SOA 4.0M HN'Oj  250 250 250 250 250 250  I n i t i a l Solids (g) 12.00 12.00 12.00 12.00 .12.00 12.00  B+325tf B+325i? B+325ff B+325tf B+3250 B+325//  Pulp D e n s i t y (g.solids/1.solution)  Leach Time (rain)  Ave.temp. (°C)  Mo Leached (g)  Ave.Leach R a t e (gMo/l.sec.xl03)  48.0 48.0 43.0 48.0 48.0 48.0  481 120.5 13.4 480 90.1 30.1  35 35 35 35 35 35  0.0325 0.0158 0.0145 0.0275 0.0039 0.0138  0.00450 0.00874 . 0.0721 0.00382 0.00289 0.0306  25.00 E  55.6  20.8  35  0.9135  1.627  420  22.85 L22 r e s  54.4  40.5  35  0.9996  0.9794  387  20.80 L23 r e s  53.7  80.2  35  1.2694  0.6817  345.5  18.25 L24 rc-s  52.8  100.9  35  1.2680  0.6062  303.8  15.79 L25 r e s  51.97  109.8  35  0.9789  0.4891  271,5  13. S8 L26 r e s  51,12  119,9  35  0.7U3  0.3642  248,3  12,31 L27 r e s  49,57  179,7  35  0,8060  0,3011  450  2  4  L23  2  L24  3 a/1  Vel*  5.2 g/4 SOA 2  L25  4.0M  HNOT  3 g/1 Fe3+ 5.2 g/1 SO/, 4.0M HNO3 3 g/1 FeJ+ 5.2 g/f. S 0 4 4.0M HNO3 3 g/1 Fe3+ S.2 g/1 S0«24.0M HMO3 2  L26  2 -  L27  L28  3 g/1 Fe3+ 5.2 g/i SO42  E  -  Endako  B  -  Brenda  - 162 -  APPENDIX C  SOURCE LISTING OF COMPUTER PROGRAM  NOMENCLATURE A(M,I) ^COEFFICIENTS OF LINEAR EQUATIONS ACIDN =MOLAR CONCENTRATION OF NITRIC ACID - 163 ARCUCP ^ARRHENIUS FACTOR FOR CU (CUFES2) ARFEPY =AHRHENIUS FACTOR FOR FE (FES2) ARFECP =ARRHENIUS FACTOR FOB FE (CUFES2) ARRMO = ARRHENIUS FACTOR FOE MO (MCS2) B{I) = R.H.S. -OF LINEAR EQUATIONS CSF(K,I) =CALCULATED STAGE FACTORS C S F P I T ( K , I ) C A L C U L A T E D STAGE FACTORS FOR PREVIOUS ITERATION CUDIS =CCPPER DISSOLVED IN LEACH EXTRN =LEACH MO EXTRACTION F(I) =NONLINEAR FUNCTIONS IN LEACH ALGORITHM FC(I) =FLOTATION SATE CONSTANTS FEPDIS =IEON AS FES2 DISSOLVED IN LEACH FLOW = W ATER FLOWRATE INTO FLOTATION CELLS FRACL =FEACTION OF NEW FEED MOS2 LEACHED FRACLfi =FRACTION OF RECYCLE MOS2 LEACHED FTX(I) -REFLOTATION TAILING VARIABLES FX (I) =LEACH FILTER OUTPUT G (I) =GU£SSED OUTPUT FROM STAGE 1 GC{I) =GBIND CONSTANTS GF(I) =GUESS FACTORS FO£ STAGE 2 GFX (I) = REGRIN D TO REFLOAT VARIABLES GX(I) ^GRINDING MILL OUTPUT IT =SPECIFIED NUMBER OF ITERATIONS ITPRNT =PRINTING CONTROLLER J =CYCLE ITERATION COUNTER K -=LEACH STAGE COUNTER KK _ = P R I N T I N 3 VARIABLE - EVERY KK' 'TH ITERATION L(I) -RECYCLE ADJUSTMENT COUNTER LC(I) •= LEACH CONSTANTS LL | =PRINTING CONTROLLER MODIS =MOLYBDENUM DISSOLVED IN LEACH MONEB =NEH MOLYBDENUM INPUT MOREC i =R£CYCLE MOLYBDENUM INPUT , MOTOL =TOLERANCE ON MOLYBDENUM EXTRACTION N =NUMBER OF LEACH STAGES NF =NUMBER OF FLOTATION CELLS PFLOW = PU1P FLOW INTO FLOTATION CELLS PULPD =IHPOT PULP DENSITY TO LEACHING R<I) =RECYCLE VARIABLE MULTIPLIERS RCPYlI) =FLOTATION STAGEWISE CUFES2 RECOVERY RDIV =DIVISOR POR R(1) RECCPY ^FLOTATION RECOVERY OF CUFES2 RECMO = FLGTATION RECOVERY OF MOS2 RECPY =FLOTATION RECOVERY OF FES2 RECRAT = RATIO OF RECYCLE SCLIDS/NES SOLIDS RECSIL =FLCTATION RECOVERY OF SILICEOUS GANGUE RFX(I) = REFLOTATION CONCENTRATE VARIABLES RGX(I) =DIRECT REGRIND TO RECYCLE VARIABLES RMAX =INITIAL INPUT MAXIMUM ADJUSTMENT FACTOR ON RECYCLE RMO(I) =FLOTATION STAGEWISE MCS2 RECOVERY RPY(I) = FLOTATION STAGEWISE FES2 RECOVERY RR(I) =MAXIMUM SPECIFICATION ON R {I) RSIL(I) = FLOT ATION STAGEWISE INSOL RECOVERY HX(I) =SOLIDS RECYCLE ESTIMATES RXC(I) =CALCULATED RECYCLE VARIABLES RXCOLD(I) =PREVIOUS CALCULATED RECYCLE VARIABLES 8  PREVIOUS ESTIMATE OF RECYCLE VARIABLES INPUT RECYCLE PARAMETERS FOR EACH LEACH STAGE STAGEWISE OVERALL MO RECOVERY FBOM NEW FEED PROPORTION OF REGRIND OUTPUT BYPASSING REFLOTATION STAGEWISE OVERALL MO RECOVERY - 4 STAGEWISE OVERALL MO RECOVERY FBOM RECYCLE SOLIDS SULPHUR DISSOLVED IN LEACH STORAGE OF LEACH OUTPUT FOB EACH STAGE LEACH TEMPERATURE TOLERANCE LIMIT ON RECYCLE VARIABLES CALCULATED TOLERANCE ON RECYCLE VARIABLES MEAN RESIDENCE TIME IN GRINDING MILL (SEC) MEAN RESIDENCE TIME IN GRINDING MILL {MIN) INPUT VARIABLES COMBINED INPUT VARIABLES LEACH VESSEL VOLUMES VOLUME OF INDVIDUAL FLOTATION CELLS STORAGE OF INPUT VARIABLES OF CUFES2 TRANSFERRED FROM RECYCLE TO NEW SOLIDS -WGT...O? CU TRANSFERRED FROM RECYCLE TC NEW SOLIDS «GT OF FE{FES2) TRANSFERRED FROM RECYCLE TO NEW SOLIDS HGT. OF FES2 TRANSFERRED FROM RECYCLE TO NEH SOLIDS LEACHING OUTPUT VARIABLES LEACH STAGE OUTPUT SOLID FE CONC. AS FES2 OVERALL LEACH OUTEUT VARIABLES CALCULATED SEPARATELY 1 6  0  Q  ***************************  C C C  STEADY-STATE COMPUTER SIMULATION OF MOLYBDENITE/NITRIC ACID LEACHING PROCESS INVOLVING MULTI-STAGE COCURRENT LEACHING GRINDING AND FLOTATION IMEL.ICIT REAL*8 (A-H,0-Z) ~ ^~ SEAL*8 MONEW,MOREC,LC,MCTCL EXTERNAL FCN DIMENSION X(18),F(1<t),V(13),VV(13} DIMENSION RX (8) , RXX (2) DIMENSION LC(15) ,VOL(9) DIMENSION VL(6) ,XX{7) , FX (7) ,GX{8) *GC{2) ,SGX{6) ,GFX{6) ,SFX (6) DIMENSION FTX{3) „RXC(8) ,FC(4) DIMENSION SNR(9),SRR(9) ,SR (9) DIMENSION SX{9,18) DIMENSION G (18) ,GF(18) ,CSF(9„18) DIMENSION R(8) ,RR{8) ,RXOLD(8) ^RXCOLD{8) „TOLC(8) ,L (8) LOGICAL SRCHA COMMON/AREA1/V* VL,RX,RXX COMMCN/AREA2/MONEW,MOREC„LC COMMON/AREA3/VOL T,K COMMCN/AREA4/X,XX COMMON/AREA5/FX,GX COMMCN/AREA6/GC,SPLIT COMMON/AREA7/RGX GFX COMMON/AREA8/RFX,FTX,RXC COMMON/AREA9/FC CO MMCN/AREA10/VOLFL ,FLOW NF COMMON/AREA11/N,LL,J COMMON/AREA12/SNR,SRR,SB„SX CO MMON/AREA1 3/EXTRN ,RECBAT , PULPD, MOTOI. COMMCN/AREA14/RECMO,RECPY„RECCPY,RECSIL ff  B  ff  ff  CCMMCN/AREA15/TMGRNB  COMMCN/AREA16/FRACL,FRACLR COMMON/AREA17/G,GF COMMON/AREA18/CSF CGMMCN/AHE&19/VV COMMQN/AREA20/ARRMO,ARFECP,ARFEPY,ABCUCP CCMMON/AREA21/SWCHA COMMON/SE$$OM/A(20,22) „B ( 2 0 ) T (22,21) NAMELIST/LISTI/J,TOLC,R,L NAEELIST/LISTRX/RX NAMELIST/LISTV/V KAMELIST/LISTG/G NAMELIST/LISTGF/GF NA MELIST/LISTLC/LC NAMELIST/LISTT/T NA MELIST/LISTGC/GCj, SPLIT NAMELIST/FLOTN/NF,VOLFL, FLOW, FC NAMELIST/LISRXC/RXC NAMELIST/LISCON/TOL,IT,RMAX,ITPRNT,KK READ (5, 102) (V (I) ,1=1 ,13) WRITE (6,500) FORMAT(>0«,'NEW SOLIDS INPUT ) WRITE(6,501) FORMAT ( , * . ') WRITE(6,502) V(1) FORMAT ('NEW SOLIDS FLOWRATE (TONNES/DAY)=',F8,3) WRITE{6,503) FORMAT('0»,'NEW SOLIDS INPUT ANALYSIS (WGTX)») WRITE (6,501) V(2) ,V (3) ,V(4) ,V (5) ,V{6) #  500 501 502 503  8  504  FORMAT ('MO=«,F7.3,2X,»FE=',F7.3,2X »CU=% F 7 . 3 , 2 X „ 1 'INSOL= «„F7.3,2X, S=» , F7. 3) WRITE (6,505) FOBMAT{ 0','INPUT SOLUTION•) -166WRITE (6,506) FORMAT (»+«,» «) WRITE(6,507) V(7) ,V (8) FORMAT ("SOLUTION FLOWRATE (L/MIN) = , F 7 . 2 , 4 X DENSITY (G/L) = ,F8» 2) HRITE(6,508) . FORMAT(*0«,'LEACH SOLUTION ANALYSIS ( G / L ) ) WRITE(6,509) V (9) , V (11) , V (12) ,V (10) ,V (13) FORMAT(«MO= ,F8.3,3X FE= F8.3,3X, CU=',F8.3,3X„•S= ,P8.3,3X„ 1°HN03=«,F8.3) READ(5,102) (RX (I) „ 1= 1,8) REAC{5,102) (LC (I) ,1=1, 15) SHITE(6,1ISTLC) READ(5,102) T WRITE(6„LISTI) FORMAT (8G10. 5) READ(5„100) N FORMAT (11) K=1 CONTINUE IF(K.GT.N) GO TO 302 READ(5,101) NS V , VOLUME FORMAT(I1^9X,G10.1) J=1 VOL (K) = VOLUME WRITE(6,120) K,VOL{K) F O R M A T ( * 0 S T A G E NUMBER ,12 , 5X F1 2. 1, 2X ,» LITRES« ) J=J+1 K=K+1 IF (J.GT.NSV) GO TO 300 GO TC 301 CONTINUE READ(5,102) (G (I) ,1 = 1, 18) WRITE(6,LISTG) READ(5,102) (GF (I) ,1=1 , 18) WRITE (6„LISTGF) BEAD(5,102) (GC (I) ,1=1 ,2) BEAE(5,102) SPLIT WRITE(6,LISTGC) BEAB(5,465) NF READ (5,464) VOLFL,FL053 BEAD(5,464) (FC (I) ,1= 1, 4) WRITE(6,FL0TN) VOIFL=0.75D0*VOLFL FORMAT (11) FORMAT(8G10.4) READ (5, 103) IT FORMAT(12) EEAD(5,102) TOL READ(5,102) RMAX READ (5, 100) ITPRNT REAC(5,100) KK WRITE(6,LISCON) SWCHA=.TRUE. IF (ITPBNT.EQ.0) SWCHA=.FALSE. CALL INPUT DO 290 1=1,13 0  <,  505 506 507 508 509  102 100 300 101 301 120  302  465 464 103  9  0  8  8  C  9  9  9  8  ff  8  0  9  8  -  290  298  292  281  JLD/ -  V¥(I)=V(I) CONTINUE BT=1.9871D0*T ARRMC=DEXP {-LC (5)/RT) ARE ECP= D E X P (-LC (6) /RT) ABFEFY=DEXP (-LC J7)/RT) ARCUCP=DEXP (-LC(8)/RT) MCNEW=V {2) *V (1) DO 298 K=1,N VOL (K) =0.92D0*VOL $K) CONTINUE DO 292 1=1,8 !<I) = 1 CONTINUE RDIV=2.0 DO 2S6 J = 1 „ I T M=J/KK LL=KK*M M O £ E C = B X < 1 ) *RX<2) RXX(1) = BX(1) BXX(2)=BX(2) CALL CONHIX DO 324 K=1,N I P (K. NE. 1) GO TO 282 EO 281 1=8,13 V(I)=V7(I) CCRTINUE  282  CONTINUE CALL LEACH(&299) 324 CONTINUE CALL LEABAL CALL FILTER CALL REGB CALL REGRSP CALL REFLOT CALL RECXC I F ( J . EQ, 1) WRITE ( 6 LISTRX) I F ( L L . L T . J ) GO TO 285 WRITE(6,LISTRX) 285 CONTINUE C TOLERANCE AND ITERATION ADJUSTMENT CALCULATIONS DO 293 1=1,8 R(I)=0.D0 TOLC (I)=DABS (2. DO* (RX(I)-RXC (I) )/(RX |I) *-RXC (I) ) } I F ( T C L C (I) cLT.TOL) GO TO 293 I F (I (I) .M-E. 1) GO TO 295 BXCLD (I) =RX (I) BXCCLD{I) = HXC(I) RX (I) =0 . 9 9 9 D 0 * R X (I) L ( I ) = L ( I ) +1 GC T O 293 295 CONTINUE B (I) = (RX (I) -RXOLD (I) } / (RX (I) -RXC (I) -RXOLD (I) +RXCOLD (I) ) I F ( I . NE.3) GO TO 278 I F (RXC (I) .LT. 1. D-05) R(I)=0.D0 2 78 CCNTINUE I F (I.NE.4) GO TO 277 IF <RXC (I) . LT. 1. D-05) R(I)=0,D0 277 CONTINUE IF ( D A B S {R (I) ) . I T . RMAX) GC TO 294 a  -  279  280  294  293 284  287  286  289 296 291 288  276  299  -  A b l  END  £  JltlO  Bfi(I) = BnAX IF (I.EQ. 1) GO TO 279 IF(TOLC(I).LT.0.05.ANDoTOLC (I).GT.0.0 2) RR(I) = B MAX* RH AX/3.0 IF (TOLC (I) .LT. 0.02) RR (I)=RMAX* (2, 0*RMAX/3. 0) IF (TOLC (I) .LT. 0. 0075) RR(I)=0.75 CONTINUE ~ I ? (I.NE.1) GO TO 280 RE (I) = RM AX/REIV IF (TOLC (I) .LT. 0.0075) RR(I)=0.9B0 IF (TOLC (I) , L T . 0 , 0 5 o AN Do TOLC (I) oGToQ.015} fiDIV=1„5 IF (TOLC (1) o LT. 0.015) RDIV=1.0 CONTINUE IF (RR (I) .G.T. 0. 6) BR (I) =0.6 IF (R (I) .LT. 0.) fl(I)=-RR(I) IF (B (I) . GEc 0« ) R(I)=RR(I) CONTINUE RXOLD (I) = BX (I) RXCCLD(I)=RXC(I) BX (I)=BX (I) - (RX (I)-RXC (I) ) *R (I) 1(I)=L(I)+1 CONTINUE I F ( L L . L I . J ) GO TO 284 WRITE(6,LISTI) CONTINUE IF (J.NE. 1) GO TO 286 LSUM=0 DO 287 1=1,8 LSUM=LSUM+L (I) CONTINUE IF(J.EQ.1) BRIT£(6,LISTI) IF (LSUM, EQ. 8) GO TO 288 GO TO 2 96 CONTINUE SUMR=0<,D0 DO 289 1=1,8 SUMR=SUMH*DABS (R (I) ) CONTINUE IF (SUMR.EQ.O.) GO TO 288 CONTINUE DO 291 1=1,8 IF (TOLC (I) . GT. TOL) GO TO 299 CONTINUE CONTINUE WRITE(6,LISTG) WRITE(6,LISTRX) RX (1) = RX{1)/11. 57D0 DO 276 1=2,6 RX (I) = 1 00.D0*RX (I) CONTINUE WRITE(6,LISTRX) WRITE(6,LISTI) CALL OUTPUT CALL OUTPRT CONTINUE WRITE(6,LISTI) WRITE (6,LISHXC) WRITE (6,LISTRX) STOP *****************  SUERCUTINE CONMIX COMEINATION OF NEW AND RECYCLE SOLIDS STREAMS IHE1ICIT BEAL*8 (A-H,0-Z) DIMENSION V (13) ,VL (6) ,BX (8) ,RXX (2) ,VV (6) -169CCMMON/AREA1/V, VL,RX„RXX CCMMCN/AREA19/VV NAMELIST/LISTVL/VL VL (1)=VV (1)+BX (1) DC 180 1=2,6 . VL (I)= (VV (1) *VV (I) +RX {1} *BX (I) ) /VL (1) 180 CONTINUE C TRANSFER ALL FES2 AND CDFES2 IN RECYCLE SOLIDS TO NEW SOLIDS WTBCU=RX (4) *RX (1) WTBFEP=BX (3) *RX (1) -0. 8 790D0*WTRCU WTBPY=2.1482D0*WTRFEP WTBCPY=2.8885D0*WTRCU V (1) = VV (1)*WTBCPY*WTBPY V (2) = VV (2) *VV(1)/V (1) V (3) = (VV{3) *VV (1) +BX (3) *BX (1) ) /V (1) V (4)= (VV (4) *VV (1)+8TBCU)/V{1) V (5)=VV (5) *VV (1)/V(1) V (6)= (VV (6) *VV (1) *0„34 94D0*WTRCPY-S'0<, 5345D0*«TRPY) /V (1) BETDRN END  C  Q  C C  ***** ***************#***  SUEBOUTINE LEACH (*) SUBROUTINE TO SET UP LEACH CONDITIONS FOR EACH STAGE AND CALL SCLVING SUBROUTINE IMPLICIT REAL*8 (A-H,0~Z) REAL*8 HONEB,HOREC,LC EXTERNAL FCN DIMENSION X (18) ,F(14) ,V{13) DIMENSION BX(8)„RXX(2) DIMENSION LC (15) „VOL (9) DIMENSION VL(6) DIMENSION XX(7) DIMENSION SNB (9) ,SRR (9) ,SR (9) DIMENSION G (18) ,GF(18) ,CSF (9, 18) DIMENSION S X ( 9 , 18) ,CSFPIT(9, 18) CCKM0N/ABEA1/V,VL,RX,RXX CCMMCN/ABEA2/MONEW^ MOREC^LC CCMMCN/ABEA3/VOL,T„K CCMM0N/AREA4/X,XX CCMMCN/ABEA11/N,LL,J COMMON/ABEA12/SNB,SRB,SB,SX CCMMCN/AREA16/FRACL,FBACLB COMMON/ABEA17/G,GF CCMMCN/AREA18/CSF CCMMON/SE$$OM/A(20,22) ,B{20) ,Y(22,21)* NAMELIST/LISTX/X JSAMEIIST/LISTF/F IF (K.EQ.1) GO TO 325 V(1)=X(1) V(2)=X(2) V(3)=X(13) V(4)=X(14) V(8)=X(5) V(9)=X(3) V(11)=X(15) V (12) = X (16)  -  JL/U  -  V(13)=X{4) RXX(1) =X (9) RXX (2)=X<10) _ 325 CCMINUE C COEFFICIENTS FOR LINEAR EQUATIONS - 1sOVERALL LIQUID MASS BALANCE C 2:N£B SOLIDS MASS BALANCE 3:R ECYCLE SOLIDS MASS BALANCE C 4:RAT I EQUATIOH-HN03 DO 322 1=1,19 DO 3 23 M= 1, 19A(I,M)=0.DO 3 23 CONTINUE 322 CONTINUE A(1,5)=-V<7) A(1,6)=1.6683D0 A {1,7)=-0„ 4762D0 A(1,12)=1.6683DO A (1, 17)=2*1481D0 A(1,18)=0.9999D0 A(2,1) = 1oD0 A(2,6)=1.6683D0 A (2 ,17) = 2o1481D0 A(2,18)=0.9999D0 A(3,9)=1.D0 A(3,12)=1,6683D0 A(4„6) = 3, 9412D0 A(4,7)=-1.D0 A(4,12)=3.9412 DO A(4,17)=5.6419D0 A (4, 18)=0. 6611D0 B(1)=-V (7) *V (8) B(2)=V (1) B(3)=RXX (1) B(4)=0.D0 I F (K.NE. 1) GO TO 326 DO 350 1=1, 18 Y(I,1)=G (I) 350 CONTINUE GO TO 333 326 CONTINUE I F (K.GT.2) GO TO 352 10 351 1=1,18 Y(I,1)=GF(I)*X(I) 351 CONTINUE GO 10 353 352 CONTINUE IF (J.NE. 1) GO TO 318 I F (K. NE. 3) GO TO 313 CSF (K-1,6)=1.5D0*CSF{K-1 ,6) CSF(K-1,7) = 1.5D0*CSF(K-1„7) CSF(K-1,12)=1.5D0*CSF (K-1, 12) CSF(K-1,17)=1.5D0*CSF(K-1 , 17) CSF (K-1, 18) =1.5D0*CSF(K-T, 18) 313 CONTINUE DO 354 1=1,18 Y(I,1)=CSF(K-1,I)*X(I) 354 CONTINUE GO TO 317 318 CONTINUE 1 ? 0  DO 316 1=1,18  Y ( I , 1) = CSFPIT (K , I) *X (I)  -  316 317 333 353  1/1  -  CONTINUE CONTINUE CONTINUE CONTINUE  - 171 -  DO 327 1=2,15  DO 340 M=1,18 340 Y (M , 1 ) = Y (M, 1) 327 Y <I,I) = Y (I,I)*1.001DO C CALL TC SUBROUTINE TO SOLVE SIMULTANEOUS ALGEERAIC EQUATIONS CALL SSM(X,F,14,4,5.D=Q3,150,FCN,.TRUE.,„TaUE.,.TRUE.,IFAIL,S328) I F ( X ( 1 3 ) • L T . 0 . ) X(13) = 1.D-07 I F ( X ( 1 4 ) L T . 0 . ) X(14) = 1 D-07 IF (K.NE.1) GO TO 335 DO 336 1=1, 18 G(I)=X(I) 336 CONTINUE 335 CONTINUE 328 CONTINUE IF (IFAIL.NE. 0) GO TO 329 DO 330 1=1,18 SX (K,I)=X(I) 330 CONTINUE IF(K.EQ.1) GO TO 355 0  o  DO 356 1=1,18  356  314 315  319 320 355 329 331  321  CSF (K,I)=SX (K,I) /SX (K-1 , 1 ) CONTINUE IF (K.EQ.1) GO TO 315  DO 314 1=1,18 CSFPIT(K,I)=SX (K,I) /SX ( K - 1 , 1 )  CONTINUE CONTINUE IF (K.N E. 2) GO TO 320 DO 319 1=1,18 GF (I) = CSF(K,I) CONTINUE CCNTINUE CONTINUE SNR (K) =100. DO* (MONE0-X ( 1) *X (2) )/MONEW SfiR{K)=10Q„D0*{MQREC-X (9) *X (10) )/MOREC CONTINUE WRITE (6,331) K, IF AIL FOR M A I ( ° 0 L E A C H FAIL CGDE FOR STAGE ( ,11 , ") = , 110) IF<J.EQ«1) WEITE(6,LISTX) IF (LL.LT.J) GO TO 321 WRITE (6 ,LISTX) CCNTINUE I F (IFAILoEQ.0) GO TO 334 IF (J.NE. 1) BRITE(6,LISTX) X(1)=X(1)/11.57D0 X(2)=100.D0*X(2) X(3)=X(5)*X(3) X (4)=X (5)*X(4) X(9)=X(9)/11.57D0 X(10)=100.D0*X(10) X( 13) = 100.DO*X (13) X (14) = 100. D0*X (14) X (15)=X (5) *X (15) X (16)=X (5) *X (16) WRITE (6,LISTX) WE IT E (6 , LISTF) 8  8  RETURN 1 CONTINUE RETOEN ~ ?2 EN=E C ***************************************** SUEBGUTINE FCN (X,F) C SUBROUTINE CONTAINING THE SET OF NCKLINEAR ALGEBRAIC EQUATIONS IMPLICIT REAL*8 (A-H,0~Z) REAL*8 MONEH,JMOREC,LC DIMENSION X(18) ,F(14) ,V(13) DIMENSION RX(8),BXX(2) DIMENSION LC(15) , VOL (9) DIMENSION VL{6) CCMHON/ABEA1/V,VL,RX,RXX CCJ3MCN/AREA2/MONEW, MQREC,LC CCMMCN/AREA3/V01,T,K CCMMCN/AREA16/FRACL,FRACLR CCMMCN/AREA20/ABBMO,ARFECP,ARFEPY,ABCUCP FRACL= (MONEW-X {1) *X (2) ) /MONEW I F (FRACL.LT.O.) FRACL=1oD~09 FRACLR= (MOREC-X (9)*X (10) )/MOREC I F (FBACLB.LT.O.) FRACLR=0„E0 ACIDN=X (4) *X (5)/63. 02DO C LIQUID COMPONENT BALANCES - MO,FE,CU,HN03 F (1) — V (7) *V(8) *V (9) -V (7) *X (5) *X (3) * (X (6) +X (12) ) F (2)=V (7) *V (8) *V (11)-V (7)*X (5)*X (15) + X(17) F (3) =V (7) *V (8) *V (12)-V (7) *X (5) *X (16) *X<1 8} F(4)=V (7) *V (8) *V (13) -V (7}*X (5) *X (4) -X (7) C SOLID COMPONENT BALANCES - MO-NEW,MO-RECYCLE,FE,CU F(5)=V(1) * V ( 2 ) - X ( 1 ) * X ( 2 ) - X ( 6 ) F (6)=RXX (1) *RXX (2) -X (9) *X (10) -X (12) F (7) = V (1) *V (3) -X~( 1) *X (13) -X (1 7) F(8)=V (1) *V (4)-X (1) *X(14)-X{18) C RATE EQUATIONS - MO-NEW^MO-RECYCLE^E^CU I F (X (1) .LE.O.) GO TO 15 F(9)=X (6)-LC(1) *VOL (K) *X{8) *ACIEN**2 1*{1.6683D0*X{2) *X{1)/{LC (15) *V (7) ) ) *ARRMQ I F JX (9) .LToO.) GO TO 17 F (10) =X (12) -LC (1) *VOL (K) *X {11) *ACIDN**2 1*{1,6683D0*X(10)*X (9) / (LC (15) *V (7) ) ) * ARRMO GC TO 18 17 CONTINUE F(10)=X(12)-0=DO 18 CONTINUE XFEPY=X (13)-0.8790D0*X (14) I F (XFEPX.LT.O. j' XF£PY=0„D0 IF (X (14) .LT.O. ) GO TO 13 F(11)=X(17)-LC(2) *ACIDN*VOL (K) *ARFEPY 1*(0.8790D0*X(14) *X ( 1 ) / (55. 85D0*V (7) ) ) ** (2./3.) 2-LC (3) *ACIDN*VOL (K) *ARFECP* (XFEPY*X (1) / ( 5 5 . 85D0*V (7) ) ) ** ( 2 . / 3 . ) F (12)=X (18)-LC(4)*ACIDN*VOL(K)*ARCUCP 1* (X (14) *X (1)/(63.54D0*V (7) ) ) ** (2»/3.) GC TO 14 13 CONTINUE F (11)=X (17)-0. DO 2-LC (3)*ACIDN*VOL (K)*ARFECP* (XFEPY*X (1)/(55. 85D0*V ( 7 ) ) ) * *(2./3.) F(12)=X (18)-0. DO 14 CONTINUE GO TO 16 15 CONTINUE 334  1  19 20  16 C  F { S ) - X (6) -0. DO I F < X ( 9 ) . L T . 0 . ) GO T O 19 F (10)=X (12) - L C { 1 ) * ? O L ( K ) *X(11) *ACIDN**2 1*(1.6683D0*X (10) *X ( 9 ) / ( L C (15) *V (7)) ) *ARRH0 G C T O 20 CONTINUE F(10) = X (12)-0„D0 CONTINUE F(11)=X(17)-G..D0 F(12)=X(18)-0.D0 CCNTINUE SURFACE AREA FACTOR TERMS -• M0S2-NEW,MOS2-BECYCLE I F ( F R A C L L T L C ( 1 3 ) ) GO T O 11 F (13) = X (8) -DEXP ( - L C (9) * ( F R A C L * * L C (10) ) ) G O T O 12 CONTINUE F ( 1 3 ) = X (8) - L C ( 1 1 ) + L C (1 2) * F R A C L CCNTINUE F ( 1 4 ) = X (11) - R X (7) *DEXP (-BX (8) * L C ( U ) *FRACLR) REIUBN END 0  11 12  C  C C  C C C  -173-  0  ******************************************************#****  SUEEOUTINE LEABAL CALCULATION OF VARIABLES NOT DIRECTLY DETERMINED BY THE LEACH EQUATIONS I M P L I C I T BEAL*8 (A-H,0-Z) DIMENSION V (13) „VL{6) ,X (18) ,XX(7) DIMENSION R X ( 8 ) , R X X ( 2 ) LOGICAL SWCHA CGMaCN/AREAI/V^VLyRX^RXX CCMMCN/AREA4/X,XX C0MMCN/AREA21/SWCHA NAMELIST/LISTXX/XX R £ A L * 8 MODIS CALCULATE FINAL STAGE OUTPUT VALUES - 1STOTAL SOLIDS FLOE BATE 2:MC IN SOLIDS 3;SI02 IN SOLIDS U t S IN SOLIDS 5:S IN LIQUID 6: WEIGHTED AVERAGE AREA FACTOR 7:T0TAL FRACTION OF MO LEACHED XX (1)=X (1)+X (9) XX (2)= (X(2) * X ( 1 ) + X ( 1 0 ) * X ( 9 ) ) / X X ( 1 ) XX (3)=VL (5) *VL (1)/XX (1) HCDIS=VL (2) *VL ( 1 ) - X X ( 2 ) *XX (1) CUEIS=VL<4) *VL (1)-X (14) *X (1) I EP DIS= (VL(3) *VL(1) -X (13) *X (1)) -0 „ 8 790D0*CUDIS SULDIS=0.6683D0*MODIS*1.0091D0*CUDIS+1.1481B0*F£PDXS XX ( 4 ) = (VL (6) *VL (1) - S U L E I S ) / X X (1) XX (5)= (V (1Q)*V (8) *V{7) +SULDIS) / {V (7) *X{5) ) XX (6)= (X (8) *X (1) +X(11) *X (9) )/XX < 1) XX<7) = ( V L ( 2 ) * V L ( 1 ) - X X (2) *XX(1) ) / (VL (2) *VL (1)) I F (SWCHA) WBITE (6,LISTXX) JSETURN •  Q  C C  END  *********************************************************** SUBROUTINE FILTER I M E L I C I T REAL*8(A-H,0-Z) DIMENSION X (18) ,XX (7) „FX (7) ,GX (8) CCMMCN/AR£A4/X,XX C0MMCN/ABEA5/FX,GX NAKELIST/LISTFX/FX FILTER - SOLIDS/LIQUID SEPARATION AFTER FINAL LEACHING STAGE 1:T0TAL SOLIDS MASS F L O W 2:MO 3:FE 4 ; C U 5:SI02 6; S 7; A 8  FX- (1) XX (1) FX (2) XX (2) FX (3) X (13) *X (1) /XX (1) FX (4) X(14)*X(1)/XX{1) FX ( 5 ) =XX (3) FX(6)=XX(4) FX(7)=XX(6)  - 174 -  RETURN ENE  C  * *************************************** ******************* SUBROUTINE BEGR C DETERMINE EFFECT OF REGBINDING ON SECYCLE SOLIES C ABEA FACTOE PABAMETEBS IMPLICIT BEAL*8 (A—H,0-2) DIMENSION GC(2) ,FX(7) ,GX(8) CGMMCN/ABEA5/FX,GX C0HMCN/ABEA6/GC,SPLIT CO MMCN/ABEA15/TMGEN D NAMELIST/LISTGX/GX TGEIND=GC (1) /FX { 1) DO 370 1=1,6 GX(I) = FX(I) 370 CCNTINUE GX (7) =FX (7) *<t. D0+GC(2) *TGBIND) GX (8) =1 .DO+GC (2) *TGRINE TMGBND=TGRINE/60.DO RETURN  END C *********************************************************** SUBROUTINE REGRSP C CALCULATE DISTRIBUTION OF SOLIDS MASS FLOWRATE TO REFLOTATION C AND DIRECTLY TO THE LEACH IMPLICIT REAL*8(A-H,0-Z) DIMENSION FX (7) „GX{8) „BGX(6) ,GPX (6) DIMENSION GC(2) CGMMCN/ABEA5/FX„GX COMMON/ABEA6/GC,SPLIT COMMON/ABEA7/BGX,GFX NAMELISI/LISBGX/BGX NAMELIST/LISGFX/GFX EO 380 1=2,6 BGX(I)=FX(I) GFX(I)=FX(I) 3 80 CONTINUE RGX (1) =SPLIT*PX (1) GFX (1)= (1. DO-SPLIT) *FX (1) BEIUEN ENE Q  C C  *  **********************************************************  SUEBOUTINE BEFLOT FLOTATION MODEL TO CALCULATE RECOVERIES, MASS FLOWHATES AND ANALYSES. MOS2, CUFES2, FES2, INSOL IMPLICIT REAL*8 (A-H,0-Z) DIMENSION GFX (6) ,PC (4) ,RM0 (9) „RPY (9) ,RCPY (9) ,RSIL (9) ,RT (9) DIMENSION RFX (6),FTX(3) DIMENSION RGX (6) ,RXC (8) LOGICAL SWCHA C0MMCN/AREA7/RGX,GFX CCMMCN/AREA8/RFX,FTX,RXC COMMCN/AREA9/FC  CGMMCN/ARE A10/VOLFL,FLOW,NF CCMM0N/AREA14/RECMO,BECPY,RECCPY„BECSIL COMMON/AREA21/SWCHA NAMELIST/RECOVS/RECMO^RECPY^RECCPYeRECSIL *" " NAMELIST/FLOTS/RFX NAHE1IS1/TAILS/FTX GFX (2) = 1. 6683D0*GFX (2) *GFX (1) GFX (3) =2.1482D0* (GFX (3) -0. 879 0D0*GFX {4) ) *GFX(1) GFX (4) =2. 8885D0+GFX (4) *GFX (1) GFX (5)=GFX (5) *GFX(1) BECMC=0.D0 FFLCW=FLOW + GFX (1J/4.5D + 03 DO 460 1=1,NF RMO (I)= ( (PFLOW-0. 12128D-02*GFX (2) *RECMO+FC(1) * VOLFL) -DSQBT { (PFLOfl10. 1212 8D-02*GFX (2) *BECMO*FC (1) *VCLFL) **2. D0-0. 4 85 12D-02*GFX 12) * 2 (1 . DO-RECMO) *FC (1)*VOLFL) ) / (0.24256D-02*GFX (2) ) BECMC=BECMO + EMO (I) RT (I)=VOLFL/(PFLOW~0.12128D-02*GFX(2) *RECMO) CONTINUE RECPY=0.D0 CO 461 1=1,NF , fiPY (I) = (FC (2) *RT (I) / (1. DO + FC (2) *RT (I) ) ) * (1. DO-RECPY) HECPY=BECPY+RPY(I) CCNTINOE RECCPY=0.D0 DO 462 1=1,NP RCPY (I) = (FC (3) * f i T ( I ) / ( 1 . D 0 + FC (3) *RT (I) ) ) * ( 1 . DO-RECCPY) BECCPY=BECCPY*RCPY(I) CONTINUE BECSIL=0.DO DO 463 1=1 ,NF RSIX (I)=~(FC (4) * B T ( I ) / ( 1 . B 0 + F C (4) *BT (I) ) ) * (1 .DQ-RECSIL) RECSIL=RECSIL+RSIL(I) CONTINUE RFX (1)=GFX (2) *RECMO+GFX<3) *fiECPY+GFX J 4) *RECCPY+GFX (5) *BECSIL BEX {2) =0. 599 4D0+GFX (2) *BECMO/RFX ( 1) EFXi(3) = (0. 4655D0*GFX (3) *RECPY + 0 3C43D0*GFX(4) *RECCPY) /RFX (1) RFX (4) = (0. 3462D0*GFX (4) * RECCPY) /RFX { 1 ) BFX (5)=GFX (5) *BECSIL/RFX {1) RPX (6)=0.6683D0*RFX (2) +1. 0091 D0*BFX (4) * 1. 1481D0* (BFX (3) -0. 8790D0 1*RFX (4)) FTX (1)=GFX ( 1 ) - R F X ( 1 ) FIX (2)= (0.5994D0*GFX (2)-RFX (2) *RFX{1) )/FTX(1) FTX (3) = (GFX (5) -R FX ( 5) *RFX ( 1 ) ) / F I X (1) I F (SWCHA) WRITE (6 , RECOVS) I F (SWCHA) WRITE{6,PLOTS) I F (SWCHA) WRITE (6,TAILS) BETUEN END 7  460  ;  461  462  463  e  Q  C C  ******************************************  SUBROUTINE RECYC COMBINATION OF REFLOTATION CONCENTRATE AND SOLIDS DIRECTLY RECYCLED FEOM BEGBINDING I M P L I C I T REAL*8(A-H,0-Z) DIMENSION RXC (8) ,RGX(6) ,GX{8) ,RFX(6) , FTX{3) ,FX (7) DIMENSION GFX (6) COMMCN/AEEA5/FX,GX COM MON/ABEA7/RGX,GFX COMMON/AREA8/R FX,FTX,RXC CCMMCN/AREA11/N,LL,J  5  390  391 Q  *  NAMELIST/LISBXC/BXC RXC {1) = BGX (1) + BFX (1) DO 390 1=2,6 RXC {I)= (RGX (1) *RGX(I) *RFX(1)*RFX Jl) )/RXC ( 1) CCNTINUE RXC(7)=GX(7) RXC(8)=GX(8) IF(J.EQ„1) WRITE (6, LISRXC) IF (LL.LT, J) GO TO 391 WRITE(6,LISRXC) CCNTINUE RETURN END  - 176 -  **********************************************************  SUEBOUTINE INPUT C CONVERSION OF INPUT UNITS TO MODEL UNITS IMELICIT REAL*8 (A-H,0-Z) DIMENSION V (13) ,VL{6) ,RX (8) ,RXX (2) DIMENSION GC(2) ,G(18) ,GF(18) ,FC(4) ,VOL{9) CCMM0N/ABEA1/V,VL,RX,BXX COMMCN/ABEA3/VOI,T,K COMMON/ABEA6/GC,SPLIT CC MMCN/ABEA9/FC COMMON/ABEA10/VOLFL,FLOW,NF CO MMC N/ABEA17/G,GF V(1) = 11.57D0*V (1) DC 900 1=2,6 V (I) = V ( I ) / 1 0 0 . DO 900 CONTINUE V (7)=V (7) /60« DO DO _9C2 1=9,13 V (I) = V{I)/V(8) 902 CCNTINUE BX (1) = 11.57D0*BX(1) DO 9C1 1=2,6 RX (I)=BX (I)/100.D0 901 CONTINUE T=T+273 15 . G (1) = 11 „57D0*G (1) G(2)=G{2)/100. DO G(3)=G(3)/G{5) G(4)=G(4)/G(5) G (9) = 11.57D0*G(9) G(10)=G(10)/100.D0 G(13)=G(13)/100„D0 G{14)=G(14)/100„D0 G(15)=G(15)/G(5) G(16)=G|16)/G{5) GC (1) = 1,E03*GC(1) GC (2)=GC<2) /60. DO DO 903 1=1,4 FC (I)=FC(I) /60. DO 903 CONTINUE FLCW=FLOW/60.DO EETURN END C ***************************************** SUEBOUTINE OUTPUT C CONVEBSION OF MODEL UNITS TO OUTPUT UNITS PLUS ADDITIONAL C CALCULATIONS 0  IMPLICIT REAL*8 (A-H,0-Z) RE AL*8 MONEW,MOREC,LC,MOTOL DIMENSION VL(6) ,XX{7) ,FX (7) ,GX(8) ,GC{2) ,RGX (6) ,GFX{6) ,RFX (6) DIMENSION FTX (3) ,RXC (8) ,FC (4) ,LC (15) , VOL (9) ,X(18) DIMENSION SNR(9) ,SRR(9) , SR ( 9) , V (1 3) , V V (1 3) , RX ( 8) ,RXX(2) - 1 7 7 DI MEN SIGN SX (9,18) COMMON/AREA1/V,VL,BX,RXX COMMCN/AJREA2/MONEW„MOREC,LC COMMON/AREA3/V0L,T,K COMMCN/ABEA4/X,XX COMMON/AREA5/FX,GX CCMMCN/ASEA7/RGX,GFX COKMCN/ABEA8/HFX,FTX,RXC COMMCN/AREA11/N,LL,J COMMON/AREA12/SNR SRR,SR,SX CCMMCN/AREA13/EXTRN,RECRAT,PULPD,MOTOL CCMMON/AREA1VHECMO,RECPy,RECCPY,RECSIL COMMCN/AREA19/VV C LEACH CALCULATIONS C S1AGEWISE MO RECOVERIES CO 705 K=1, N TBCIN=MCNEW*MOREC SB (K) = (TMOIN-{ (SX (K,1) *SX (K,2) ) • (SX (K,9) *SX (K, 10) ) ) ) /TMOIN 1*100.DO 705 CONTINUE EXTRN=86.40D-Q2* (SNH (N) *MONEW*SBB |») *HOREC) BECBAT=11.57E0*RX (1)/VV (1) EULED= (1 1.57D0*BX (1) + V V { 1) ) /V V (7) BO 700 K=1,N SX (K,1) =0.8640D-01*SX{K*1) SX (K,2)=100.D0*SX(K,2) SX (K, 3) = SX (K, 3) *SX (K, 5} SX (K,4)=SX(K,4)*SX{K,5) SX (K,9)=0.8640D-01*SX (K*9) SX (K,10) = 100.D0*SX(K„10) SX (K,13)=100.D0*SX(K,13) SX (K, 14) = 100.D0*SX (K,14) SX (K,15)=SX (K, 15) *SX (K,5) SX(K,16)=SX(K,16)*SX(K,5) 700 CONTINUE C LEAEAI CALCULATIONS XX (1) = 0. 8640C-01*XX |1) XX (2)=100.D0*XX{2) XX (3) =100.D0*XX (3) XX (4) =100. D0*XX (4) XX(5)=XX(5)*SX(N,5) XX (7) = 100. D0*XX (7) C FILTER CALCULATIONS FX (1) = 0.8640B-01*FX (1) DC 7C1 1=2,6 FX (I) = 100. DOAFX (I) 701 CONTINUE C REGEINB CALCULATIONS GX (1) =0.86400-01 *GX (1) DO 702 1=2,6 GX(I)=100.D0*GX(I) 702 CONTINUE C REGRIND SPLIT CALCULATIONS BGX (1)=0. 8640D-0 1*RGX (1) GFX (1) = 0. 8640D-01*GFX (1) P  C  R E F L O T A T I O N  C A L C U L A T I O N S  RECMO=100.  D0*R£CMO  R E C P Y = 1 0 0 . D 0 * R E C P Y R E C C P Y = 1 0 0 . D O * R E C C P Y  _  R E C S I L = 1 0 0 . D 0 * R E C S I L R F X (1) = 0 . 8 6 4 0 D - 0 1 * R F X DO  703  RFX (I) 703  = 1 0 0 . D 0 * R F X ( I )  CONTINUE F T X ( 1 )  C  (1)  1=2,6  =  0 . 8 6 4 0 D - 0 1 * F T X ( 1 )  F T X (2) = 1 0 0 .  D 0 * F T X  (2)  FTX  D 0 * F I X  (3)  (3) = 1 0 0 .  MOLYBDENUM  TOLERANCE  C A L C U L A T I O N S  MCNEW=86.40D0*MONEW MOTOL= C  R E C Y C L E RXC DO  ( 1 O . D 0 * F T X { 1 )  COMBINATION  ( 1 ) = 0 . 8 6 4 0 D - 0 1 * S X C ( 1 ) 704  1=2,6  RXC (I) = 1 0 0 . D O * R X C 704  -J-EXTRN-MQN35J)/MONEW  * F T X ( 2 )  C A L C U L A T I O N S  (I)  CONTINUE RETURN I N C S U E E O U T I N E  C  CONTROL  OUTPRT  CONVERGED  I M P L I C I T R E A L * 8  OUTPUT  R E A L * 8  P R I N T I N G  (A-H,0=Z)  MONEW,MOTOL  DIMENSION  X X (7)  DIMENSION  F T X ( 3 )  , F X < 7 )  , GX (8)  , R X C (8)  D I M E N S I O N  SX ( 9 , 1 8 )  DIMENSICN  SNB (9)  DIMENSION  V(13)  , CSP  ,SRR  (9)  , V L ( 6 )  , G C $2) , R G X (6)  , J C ( 4 )  , V O L J 9 )  , G F X J6 )  , X {1 8 ) , L C  , R F X { 6 )  (15)  ( 9 , 1 8 ) ,SR  (9)  , B X (8)  , R X X ( 2 )  COMMCN/AREA1/V,VL,RX,RXX C O M B C N / A R E A 2 / M O N E W , M O R E C , L C COMMCN/AREA3/VOL/T,K C C M M C N / A R E A 4 / X , X X C O M M O N / A R E A 5 / F X , G X C C M M C N / A B E A 7 / B G X , G F X C C M M C N / A R E A 8 / R F X , F T X , R X C C O M M 0 N / A H E A 1 1 / N , L L , J C 0 M M 0 N / A R E A 1 2 / S N R , S R B , S B , S X C C M M C N / A R E A 1 3 / E X T R N , R E C R A T , P U L P D , M O T O L C O M M C N / A R E A 1 4 / R E C M O , R E C P Y , R E C C P Y , R E C S I L COMHCN/AREA15/TMGRND C C M M C N / A R E A 1 8 / C S F W R I T E ( 6 , 8 0 1 ) 801  FOEMAT{ WRITE  807  8  0  ,  8  N F I N A L  8  FORMAT  + * ,  8  FORMAT ('.EXTRACTION F O R M A T ( F O R M A T (  8  I N P U T  55)  FOEMAT(  8  8  ,  F O E MAT I F  {  8  0 * ,  MO  TO  SOLUTION  MOLYBDENUM  (KG/DAY)=  , F 7 .  8  TO  LEACH(KG/DAY) =  8  1)  , F 7 . 1 )  FRACTIONAL  8  TOLERANCE=  * , F 8 . 5 )  RECRAT S O L I D S  8  W R I T E ( 6 , 8 5 1 ) 851  OF  MOLYBDENUM 0  ')  MOTOL  WRITE ( 6 , 8 5 0 ) 8 5 0  OUTPUT')  UONEW  NEW  8  W R I T E ( 6 , 8 855  , 1 1 , ' )  E X T R N  WRITE ( 6 , 8 5 4 ) 854  0  ;  WRITE ( 6 , 8 4 3 ) 843  STAG I {  L E A C H I N G  ( 6 , 8 0 7 )  R E C Y C L E  R A T I O =  8  , F 7 . 3 )  PULPD STAGE  ( P U L P D . L T . 5 5 0 . 0 )  1  INPUT GO  TO  P U L P 852  DENSITY  ( G / L ) ='  , F7 . 2)  1  7  8  -  853 852 802 803  804 805  WHITE (6,853) ECEMAT('WABNING:INPUT PULP DENSITY HIGH ) CGNTINUE - 179 WRITE (6,802) FOEMAT( 0 , LEACH SOLIDS BESIDUE FLOW BATE (TON NES/DA Y) ) WBITE (6, 803) XX (1) , SX (N , 1) ,SX (N , 9) FORMAT ("TOTAL S O L I D S = , F 8 . 3 , » N E B SOLIDS= * , F 8 3 , RECYCLE S C L I D S = , 1F8.3) WRITE(6,804) FORMAT( 0 , TOTAL O U T P U T SOLIDS ANALYSIS (WGT%)') WRITE (6,805) XX (2) , FX (3) , F X (4) ,XX (3) ,XX (4) FORMAT ( MO= ,F7. 3 , 2 X , F _ = , F 7 , 3,2X5, ° C U = , F 7 . 3 , 2 X , I N S O L = ,F7. 3 1,2X, S= ,F7.3) WRITE (6,806) FORMAT ( 0 ,'NEW SOLIDS OUTPUT ANALYSIS (WGT%) •) WBITE{6,808) SX(N,2) FOBMAT{'MO=«,F7o3) WRITE (6,809) FOEflAT('0','RECYCLE SOLIDS OUTPUT ANALYSIS (BGT%) ) WRITE(6,810) SX(N,10) FOE MAT ( MO= , F7. 3) 8  8  808 809 810  8  8  8  0  9  e  8  8  8  9  8  806  8  8  0  8  8  8  8  8  8  8  0  3  8  8  W H I T E (6,839)  839 840 841 842  FGEMAT('0 ,"OUTPUT LEACH SOLUTIGN ) WRITE (6,840) SX(N,5) FORMAT("SOLUTION DENSITY (G/L)= ,F8.2) WRITE(6,841) FOEMAT ( 0 , LEACH SOLUTION ANALYSIS {G/L) ) WBITE (6,842) SX (N,3) ,SX (N, 15) ,SX (N, 16) ,XX (5) ,SX (H,4) FOEMAT( MO= ,F8.3 3X, FE- ,F8.3,3X CU= ,F8.3,3X, S= *F8„3 3X 1 HN03= ,F8.3) WBITZ(6,811) FORliAT { 0 ' , STAGE CUMULATIVE RECOVERIES OF MO <%HO DISSOLVED) ) WBITE(6,813) FORMAT ( 10X, TOTAL ,10X, NEW S O L I D S , 1 OX, RECYCLE SOLIDS') DO 812 K=1,N WRITE(6,814) K,SB (K) ,SNR{K) ,SRfl (K) F O E J a A T ( S T A G E ' , I 1 , 3 X , F 7 3 , 1 0 X , F 7 o 3 , 14X,F7.3) CONTINUE WRITE(6,844) I F ( N . E Q 1 ) G O TO 848 FORMAT( ~ ,"CALCULATED STAGE FACTORS - FOR STAGES 2 TO N ) EO 845 K=2,N WRITE(6,847) K FOBMAT ("STAGE ,11) WRITE(6,849) (CSF (K,I) ,1= 1 , 18) FORMAT(18F5.2) CGNTINUE CONTINUE WRITE(6,815) F O E M A T ( 0 , * R £ G B I N D PARAMETERS ) WBITE(6,816) FORMAT (+ , ______• ) WRITE(6,817) TMGRND FCBMAT( 0','MEAN BESIDENCE TIME IN GRINDING M I L L ( M I N U T E S ) - F 7 „ 2) WRITE(6,818) F O R M A T ( 0 , ' R E C Y C L E AREA FACTOR PARAMETERS') WRITE{6,819) GX(7),GX(8) F O B M A T ( B 1 = , F 8 . 5 , » B2=',F8.5) WRIT£{6,820) FOEMAT('0','STREAM SPLIT - SOLIDS FLOWRATES (TONNES/DAY)') 8  8  8  813  814 812  8  s  8  8  8  9  8  8  B  8  811  8  8  9  8  0  e  g  8  r  8  8  8  8  8  8  8  8  a  !  e  844  847 849 845 848 815 816 817 818 819 820  8  B  8  8  8  8  8  8  8  8  0  8  9  e  8  8  8  8  821 822  WRITE{6,821) RGX (1) ,GFX (1) FORMAT('DIRECT GRIND TO RECYCLE= „F8,3,•GRIND TO FLOTATION= ,F8.3) WRITE (6,822) FORMAT{'0*,'FLOTATION RESULTS ) WRITE (6,823) " " FORMAT ( ' +' „ « ,_. ) BBITE(6,824) FORMAT('0',»MINERAL RECOVERIES {%)•) WRITE(6,825) .RECMO, RECPY,RECCPY,RECSIL FORMAT (' MOS2= , F7. 3, F E S 2 = ' ,F7„ 3 , CUFES2= *, F7. 3,•INSOL=',F7.3) WRITE(6,826) RFX{1) FORMAT{'0 ,'MASS FLOWRATE OF CONCENTRATE (TCNNES/DAY)=',F8»3) WRITE(6,827) FORMAT ( ' 0 , ' FLOTATION CONCENTRATE A N A L Y S I S (WGT%) ) WRITE(6,828) RFX (2) ,HFX (3) ,RFX (4) R F X (5) , RFX (6 ) FORMAT('MO=«,F7.3, FE=» , F 7 3,.'C0=« , F 7 , 3, ' INSOL=«, F 7 . 3,'S= ,F7.3) WRITE(6,829) F T X ( 1 ) FORMAT {'0* ,' MASS FLOWRATE OF FLOTATION T A I L S (TONNES/DAY) = , F8= 3) WBITE(6,830) FORMAT(»0°,'FLOTATION T A I L S ANALYSIS (WGT 56) *) WRITE (6,831) FTX(2) FORMAT(«MO=',F7.3) WRIIE(6,832) FORMAT(*0»,'CALCULATED VALUES FOR RECYCLE SOLIDS') WEITE(6,833) FORMAT ( , _„_ ) WRITE (6,834) RXC(1) F O F M A T ( ' 0 , ' R E C Y C L E SOLIDS MASS FLOWRATE (TONNES/DAY) = *,F8» 3) WRITE (6,835) FORMAT('0','RECYCLE SOLIDS ANALYSIS (WGT%)«) B R I T E ( 6 , 8 3 6 ) RXC(2) ,RXC (3) ,RXC (4) ,BXC J5) ,RXC (6) F'OHMAT ( »MO=* , F 7 . 3 , * FE= ,F7. 3, «C0 = " ,F7„3, «INSOL = F 7 ' . 3 , « S= ,F7 „ 3 ) WRITE(6,837) FORMAT(°0 ,'RECYCLE AREA FACTOR PARAMETERS') WRIT£(6,838) RXC (7) ,RXC (8) S B I T E ( 6 , 8 3 8 ) RX(7),RX<8) POEMAT( B1=» F8.5, B2=',F8.5) DO 856 K=1,N WRITE(6,857) K FOEMAT(*0 p'STAGE{° ^ 1 1 , ' ) X VALUES") DO 858 1=1,18 WRITE(6,859) S X ( K , I ) FORMAT (GT2.5) CONTINUE CONTINUE RETURN END 0  0  8  1 8 0  8 23 824 825 826 827  9  9  S  S  s  8  8  0  828 329 830 831 832 833 834 835 8 36 837 838 857 859 858 856  8  8  D  6  8  iI  :  s  9  9  8  0  ff  8  8  9  - 181 -  APPENDIX D  OTHER SPECIFIC PARAMETERS USED IN MODEL  (1)  k' g  Grind Constant -  -1 0.0570 sec  =  by analysis of Report 7 and 8 data [4] using i n i t i a l calculated rates of reaction.  A'  = area factor for grinding mill input  A"  =  area factor for ground solids  I n i t i a l leach rates  (at 1 min.)  r' a A' it  Ratio: A^ A'  =  k  A' + k t g A'  3.43 A 3.43 A' t g  g =  k' A' g  =  0.0570 A'  »  4.43  - 182 -  (2) Flotation rates constants: MoS  2  =  1.0 min  FeS  2  =  0.5*  CuFeS =  0.5*  Insol  0.10  2  *  =  1  estimates - may be some control depending on desirability recyling FeS~ and CuFeS„.  

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