DEVELOPMENT OF A MATHEMATICAL MODEL OF A MOLYBDENITE LEACHING PROCESS by Geoffrey Joseph Parsons B.Sc.(Tech.) with merit, Univ. of New South Wales, Australia, 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 Metallurgical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1978 © Geoffrey Joseph Parsons, 1978 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 - i -ABSTRACT A mathematical model has been developed for the more critical 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 pilot- or commercial-scale plant. Simulation of leaching is based on mass balancing with determination of reaction rates from the individual components of the'rate equations. The rate of leaching of molybdenite is 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 is based on a combination of theory and empiricism while the flotation model is derived from the simple first-order rate equation. The simulation is still subject to some uncertainty since verification is not possible at this stage of process development. However, the model effectively accounts for the complex system - ii -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 all considered. - iii -TABLE OF CONTENTS Page ABSTRACT .. .. .. '.. .. i TABLE OF CONTENTS a O «. O oo oo oo co o o. a a o • «• on » • oo • 9 o • * • iiJL LIST OF TABLES 00 * e <>« oo «* oo «• <> © o » »o «• •« <. * •» * <> <>« vxi LXST OF FIGURES e *> eo ©« o» & • oo o« • ° <>» •« •••• »« •» »» »• • • vixi ACKNOWLEDGEMENTS ..... .. . .- xi Chapter 1 INTRODUCTION . . '.. .. 1 1.1 General .. .. .. .. 1 1.2 Model Classification .. 3 I 1.3 The Process .. .. . 5 1.4 Process Chemistry . ..11 i. 1.4.1 Leach Chemistry . . ..11 1.4.2 Precipitation Chemistry .. ..18 1.4.3 Solution Purification Chemistry . „ .„ ..21 1.4.4 Acid Regeneration Chemistry ..22 1.5 Scope of Model .. ». .» .. .. . = .. ... .. 23 •1.6 Source and Supply of Molybdenum .. ..26 1.7 Economic Situation of Molybdenum ..32 1.8 Current Methods for Processing Molybdenite Concentrates 34 1.9 Advantages of Nitric Acid Leach Process .. .. ..40 - iv -Chapter Page l.l'O Nitric Acid Leaching of Sulphides 42 1.10.1 Molybdenum Sulphide -.. .. ., 43 1.10.2 Copper Sulphides .... 45 1.10.3 Nickel Sulphides .. 47 1.11 Modelling in Hydrometallurgy .. .. 50 1.11.1 Leaching .. .. .. .. .. .. 51 1.12 Modelling of Other Unit Operations in Leach Circuit 58 1.12.1 Grinding 51.12.2 Flotation 60 2 BASIS OF LEACHING MODEL .. . . .. 63 2.1 Modelling by Mass Balances .. .. 63 2.2 Rates of Reaction 65 1 2.2.1 Analysis of Terms 66 X 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 oe a* o o a m • • mo oo « a o • 83 3.3.2 Determination of Area Factor Relation ship 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 .. .. ». 100 4.5 Filter .. .. 104.6 Regrind . .. . .. 101 4.7 Stream Splitter .. .. .... .. .. .. = 103 4.8 Flotation *. 104 4.9 Recycle Combinaton 106 4.10 Input/Output Routines 107 5 MODEL EVALUATION AND DISCUSSION .. .. 108 5.1 Stability and Convergence .. HO 5.2 Model Results H6 — ~ 5.2.1 New Solids Flow Rate 116 i 5.2.2 Initial Acid Strength 121 5.2.3 Solution Flow Rate .. .. .. 125 I 5.2.4 Leach Temperature <•. • - I32 5.2.5 Partial Bypassing of Flotation ...... 136 5.2.6 Leach Vessel Volume .. .. .. 139 5.2.7 Number of Leaching Stages .. .. 143 5.2.8 Grinding .. .. 146 6 CONCLUSIONS .. - - 15° 7 RECOMMENDATIONS 153 REFERENCES • 154 APPENDICES A Consumption of Molybdenum by Category 159 - vi -Page B Experimental Results .. .. ... • .. .. 160 C Source Listing of Computer Program .. 162 D Other Specific Parameters Used in Model 181 - vii -LIST OF TABLES Table Page VI I Concentrations of Mo . Remaining in Various Solutions, (g/1 MoVI) .. .. 16 II Important Molybdenum Minerals and Composition .» .. 27 III Molybdenite: Mineralogical Data ...... 27 IV Metal Content Ranges of Molybdenum Ores 29 V 1976 Molybdenum Production of Leading Countries .. 32 VI Copper Penalties in Molybdenite Concentrate .... 34 VII Concentrate Analyses and Sizings 79 VIII _ Size Reduction Steps in Normal Milling Operations . 101 IX Standard Condition for Leach Process , .. 109 i X Extraction from Total Input Solids on each Pass for Different New Solids Flow Rates. (%) .. .. 121 i XI Extraction from Total Input Solids on each Pass for Different Initial Nitric 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 ...... 7 Endako molybdenite concentrate (600 x) 10 Precipitated molybdic oxide hemihydrate (MoO^-^l^O) (^00 9 o o o oo oo o • o « oo oo »• oo •« • * •« oo oo 10 Eh-pH relationship for nitric and nitrous species in acid solutions 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 nitric acid as a function of initial sulphuric acid concentration .. .. .. 49 Typical extraction curve .. .... 56 Rate of extraction vs extraction, showing construc tion for staging analysis . . .. . 56 Extraction curves for Gibraltar molybdenite concentrate (a) as received (b) wet ground one hour in laboratory pebble mill 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) 60-75% extraction (4000 x) . 72 - ix -Page Approximate dimensional characteristics of four molybdenite concentrates 74 Surface area vs fraction leached for initial equal masses of spheres of one unit radius and two units ITcldlUS • o 09 00 so so 00 e o • » o • ••<«• OB • » *• 77 Surface area vs time for initial equal masses of spheres of one unit radius and two units radius .. 77 Experimental apparatus „ 80 Log initial reaction rate vs log initial HNO3 for Brenda +325 mesh molybdenite concentrate 85 Leaching rate and area factor vs fraction leached for Endako molybdenite concentrate 87 Model block diagram . .. 91 Computer model flowsheet . .. .. .. ..92 Solids recycle ratio vs new solids flow rate .. .. 117 Total input pulp density, operating area factors and operating nitric acid concentrations vs new solids flow rate .. .. 119 Gain in solution molybdenum concentration vs new solids flow rate 120 Solids recycle ratio vs initial nitric acid concentration .. .. . 122 Total input pulp density, operating area factors and operating nitric acid concentrations vs initial nitric acid concentration .. 124 Insol content of leach residue, reflotation con centrate and recycle solids vs initial nitric acid concentration 126 Solids recycle ratio vs solution flow rate 129 - X -Figure Page 30 Total input pulp density, operating area factors and operating nitric acid concentrations vs solution flow rate 130 31 Gain in solution molybdenum concentration vs solution flow rate .; .. .. .. 131 32 Solids recycle ratio vs leach temperature .. .. 133 33 Total input pulp density and operating area factors vs leach temperature .... .. 135 34 Insol content of leach residue, reflotation con centrate and recycle solids vs fraction bypassing flotation 137 35 Solids recycle ratio 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 . 142 38 Solids recycle ratio vs number of leach stages. ^ Constant stage volume 144 39 Recycle area factor vs fraction leached for different values of b^ • • • • 40 Recycle area factor vs fraction leached for different grinding mill sizes 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 is 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 is often quite complex. However, the expansion in computer facilities has enabled the formulation of numerous types of mathe matical 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 in a predictive capacity, or interactively with the process to attain efficient control. Once the* model is sufficiently well developed to establish reliability it 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 initial 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 initially formulated. This may result in an unrealistic model but provides a basis for analysis of deficiencies and for construction of more realistic 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 is, process properties at any particular location may vary as a function of time. i The dynamic simulation may be more versatile but it is more difficult 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 is in 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 statistical models - which rely on analysis of experimental or operating data. Completely empirical models rely on the determination (or fitting) of operating relationships in terms of measurable variables for the actual plant units. Although the fitting of relationships is based on statistical 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 in their operational behaviour due to subtle differences in 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 in 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 in a series of monthly reports with the tentative design for a 10 ton per day plant outlined in report No. 12 [3,4]. The possibility for such a process had been demonstrated in earlier unpublished work at U.B.C. by Peters and Vizsolyi [5]. The process flowsheet was modified slightly for the modelling study, as shown in Figure 1. It must still be considered that this flowsheet design is not necessarily the optimum that could be used for the process. However, it is this flowsheet which is modelled with the objective of determining the potential of the nitric acid leaching i • process with a recycle solids stream. The flowsheet is based on the required operations so that there is some flexibility 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 in creased nitric acid consumption within the leaching vessels. The HN03 Make-up jHN03Regen. HN03 Recycle MoSg Concentrates NO Gas Oil Removal MoS2 Recycle Cocurrent Staged Leaching S H Pregnant Solution .Wash n Regrind Ground-Limestone Sulphate Rejection Recycle Ground Limestone {Recovery of^ 1 Rhenium j Purge Impurity Purge $CaSQ>2H20 Refloat "T Silicious Residues -Dehydration] 350°C lhr| Mo03 (High Purity) |CaCQ3 CaS04.2H20 Fe(OH)3 Cu(OH)2 etc Figure 1„ Process flowsheet used for modelling study. - 8 -combined solids are then subjected to cocurrent multistaged leaching with nitric 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 is well mixed in any leach stage either by mechanical means in agitator vessels or by NO lifting gas in pachuca vessels. _ _ The slurry exiting the final leaching stage is filtered and washed, with the filtrate 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 is designed to reject a considerable -ap portion of the insoluble content into a low molybdenum tailing. The refloated concentrate is then passed back to the leach after filtra tion and deoiling. (ii) Precipitation Section The pregnant solution is heated to about 80°C to precipitate molybdenum as MoO^-^l^O. The precipitate is in a fibrous form and is thus quite readily filtered. Scanning electron microscope photo graphs of typical molybdenite concentrate and the molybdic oxide hemihydrate product are shown in Figures 2 and 3. MoO^ is produced by_relatively low temperature calcination of the hemihydrate. (iii) Solution Purification L Before recycling, the solution must be purified by partial elimination of impurities built up in the leach. The major aqueous by-product of the leach is the sulphate ion. This can be reduced to low levels by the addition of calcium ions in some form to pre cipitate gypsum (CaSO^-^B^O). The soluble impurities, particularly iron and copper, are not removed by the purification step. To eliminate these a portion of the low sulphate solution is purged and treated separately. The purged and purified solution is then recycled to the sulphate rejection step. Rhenium may also be recovered Figure 2. Endako molybdenite concentrate (600x) - 11 -from the purge recycle solution. (iv) Acid Regeneration Nitric acid is regenerated by conventional methods using nitric 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 is consider ably enhanced but the simultaneous precipitation of MoO^-^l^O becomes appreciable. Precipitation of molybdenum in the leach must be avoided as it is not recovered from the leach residue. The overall reaction can be represented by the following balance : MoS2 .+• 6HN03 -»• H2>fo04 •+ 2H2S04 + 6N0 (1) - 12 -Equation (1) represents an overall balance only and does not neces sarily describe the correct form of all the species present. Although the initial unused nitric acid may contain nitrogen essentially in 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 nitric 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 com ponent 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; in fact, its concentration would be limited to that at which its oxidation potential just equals that of the residual nitric 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 initial reduction product in nitric acid solutions by reaction (2). HN03 . + 2H+ + 2e~ -»•' HN02 + H20 (2) - 13 -I l.5j—"T r~ -i—•— 1 r Figure 4. Eh-pH relationship for nitric and nitrous species in acid solutions. Basis- one mole/litre in solution and one atmosphere pressure. The electrons In Equation (2) are supplied by oxidation of the mineral. The nitrous acid will tend to equilibrate with nitric acid and nitric oxide gas by the reversible reaction of Equation (3) 3HN0 HN03 + 2N0 + H20 (3) The nitrous acid could react by Equation (4) with the electrons again supplied by oxidation of the mineral. The-nitric oxide produced by Equation (4) would enhance the stability of nitrous acid by pushing reaction (3) to the left although this would ultimately be determined by the total pressure in the system, assuming that nitric oxide is the only gas component other than water vapour. reactive sulphide oxidant [7]. It is however, only an ionization product of HN02 due to the presence of a strong acid (ie. an^ H_S0, in this case), as shown in Equation 4(a) HN0„ + H+ +• e NO + H20 (4) The nitrosyl ion (NO , .) has been suggested as a highly HN02 +. H+ NO + 4(a) -«-- 15 -Thus, any special reactivity of the NO ion would show up at strong acidities and high HN02 concentrations, as when nitrogen dioxide is sparged directly into the system. The overall balance of Equation (1) represents the dissolved molybdenum as molybdic acid (H^MoO^) but its exact form in solution is 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 2-is present in solution as the molybdate anion (MoO^ ). 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 moly-2+ bdenyl cation (M0O2 ) or its 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. The effects of acidity and temperature are clearly demonstrated. 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 it is likely that the molybdenum would - 16 -dissolve in a cationic form and remain in this form throughout the leach despite the consumption of nitric acid. Acid conditions are maintained to an extent by the production of sulphuric acid as Table I CONCENTRATIONS OF MoVI REMAINING IN VI VARIOUS SOLUTIONS* g/1 Mo Concentration HN03 HNO3/H2SO4 IN 2N 3N 4N JSNAN IJ2NAN IN/IN 24 hrs/24°C 1.1 52.1 95. 5 121 0 1. 4 78.7 79.0 48-hrs/24°C - . 90. 0 - -96 hrs/24°C - - 75. 7 - - -2 hrs/55°C - - 9. 9 - - -4 hrs/55°C - - 8. 1 - - -24 hrs/55°C 0.5 1.6 3. 4 4 9 0. 7 * 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 * After saturating with reagent grade H9Mo0 indicated in reaction (1). 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 is demonstrated by hydrogen ion requirement in the formation of the molybdenyl cation. (Equation 5) Other base-metal sulphides are leached by nitric acid but only chalcopyrite and pyrite are considered in this study as these were the major sulphide impurities in the concentrates studied. They are considered to leach by the overall stoichiometry of the following equations. 2+ (5) -> -> 3Cu + 3Fe + 6H2S04 + 10H20 + 17N0 (6) FeS„ + 5HN0- + 3H+ -> Fe 3+ + 2H-S0. +• 2H_0 + 5N0 2 4 2 (7) Initially all the sulphur may not be oxidized to sulphate as shown by Equations (6) and (7). The non-sulphate sulphur is present as elemen tal sulphur; the yield of which depends on the mineral, nitric acid - 18 -strength, temperature and time of contact, Of the two minerals con sidered only chalcopyrite can have an appreciable initial yield of elemental sulphur. Sulphur may dissolve directly by Equation (8) S* + 2HN03 -> H2SQ4 + 2N0 (8) Molybdenite, particularly as a by-product from copper porphyries can contain significant quantities of rhenium. Since rhenium is in solid solution in the molybdenite crystals it dissolves quantitatively with molybdenum during the leach. —1.4.2- Precipitation Chemistry The pregnant solution from the leach is supersaturated with molybdenum since the kinetics of KoO^'H^O precipitation are immeasur ably slow at operating temperature. At temperatures in excess of about 40°C the rate of precipitation becomes appreciable with close to com plete possible precipitation occurring within 2 hours at 80°C (see Table I). Complete precipitation of the contained molybdenum is not possible since there is a finite solubility in the acid solutions. This solubility will be at a minimum at the isoelectric point and will - 19 -increase with changes in pH. The rate jat which the solubility changes with pH will be dependent on the particular cations or anions in solution. The following equations and Figure 5 illustrate 2+ -this point when considering only M0O2 AN<^ ®*0U>4 as the ionic species, 2+ For precipitation from M0O2 *n s°luti°n tne reaction is: Mo022+ + 1^0 ^ -> MoOyJ^O +. 2H+ (9) Given an equilibrium constant for this reaction the equilibrium solubility is expressed by Equation (10) log[-Mo092+] = - log K- - 2pH (10) For precipitation from HMoO^ in solution the reaction is: HMo04 + H+ ^ MoO^t^O + ^0 (11) The corresponding solubility relationship for an equilibrium constant K2 is then: log[HMoOA~] = - log K2 + pH (12) The solubility will 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: H2S04 + CaC03 + H20 -> CaS04'2H20 + C02 (13) H 2S04 + Ca(N03)2 + 2H20 -*• CaS04'2H20 + 2HN03 (14) Elimination of sulphate is 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: H2Mo04 + Ca2+ ^ -> CaMo04 + 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 is 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 utilise the high calcium content. The rhenium present in the leach liquor is unaffected by the precipitation or purification steps and is 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 nitric acid content of the recycled, purified solution must be regenerated for further leaching. Acid regeneration is achieved by oxidizing the nitric oxide evolved from the leach to form nitrogen dioxide which is then absorbed into the recycle solution as nitric acid. The following equations describe the overall reactions taking place. Oxidation of nitric oxide: 2N0 + 02 •* 2N02 (16) - 23 -Absorption of nitrogen dioxide: 3N0o + Ho0 -»• 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] it was evident that leaching of molybdenite in nitric acid is relatively slow compared to other similar systems. A typical batch extraction curve for a moly bdenite concentrate at an initial total pulp density of 126 g/litre of solution and 4 molar nitric 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, initial pulp density 126 grams/litre solution, initial 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 is 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, con sistent 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 critical units in the cycle such as filtration, 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 nitric acid regeneration which made accurate mass balancing of the nitric acid impossible. This phenomenon was shown by a high pulp density test in which more molybdenum was dissolved then could be accounted for by the stoichio-metry of Equation (1). I 1.6 Source and Supply of Molybdenum Molybdenite is 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 lists 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) Fe2°3*3MO(V 8H2° Powellite CaMoO, (up to 10% W) Wulfenite PbMoO, The mineralogical properties of the dominant mineral, molybdenite are given in Table III [12] . : Table III MOLYBDENITE: MINERALOGICAL DATA Crystal System ; Hexagonal Common Form ; Massive, scales, granules Cleavage ; Perfect basal-flexible laminae Colour : Lead-grey Streak : Greenish lead-grey Lustre : Metallic, opaque Tenacity : Sectile Hardness : 1.-1.5 Specific Gravity : 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 its hydrophobic properties and hence its natural floatability. This is not as dominant at the plate edges since at these locations both sulphur and molybdenum atoms are exposed to the environment and result in greater reactivity in aqueous solutions. The sources and recovery of molybdenum have been outlined in 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 in 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 all the known resources of molybdenum fall into one of the first three categories with porphyries being the most important. - 29 -Of the current recoverable world reserves of 4.5 x 10* kg roughly one half is found in primary molybdenum porphyries where molybdenite is the only economic mineral. The remainder is found mostly as a secondary mineral in copper porphyries and is mined as a by-product [17]. Although this source represents a major supply of molybdenum it is tied to the production of the major component and hence is subject to conditions of the copper market. Only in a very few cases is the molybdenum mined as a co-product where the value of molybdenum recovered is similar to the value of the copper. Small quantities of molybdenum have also been recovered from tungsten and uranium ores. Typical analysis ranges of the major ore types currently mined are outlined-in Table IV. Table IV METAL CONTENT RANGES OF MOLYBDENUM ORES Primary molybdenum porphyries Copper porphyries 0.05 - 0.5% MoS2 0.01 - 0.05 MoS2 0.4 - 1.8% Cu Despite the uniformity of mineral type the metallurgical 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 mill 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 pro perties. Although molybdenite is relatively stable to oxidation some surface alteration can occur in the more oxidized upper zones of"ore bodies. The formation of molybdate minerals on the surface of molybdenite results in 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 is 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 is floated while the copper mineralization is depressed. - 31 -Usually many cleaner flotation stages are required to produce an acceptable concentrate. However, further chemical treatment is often required to reduce impurity contents to satisfactory levels. This aspect is discussed in 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 it is 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 wnile primary sources usually 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 is 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 in Table V. - 32 -Table V 1976 MOLYBDENUM PRODUCTION OF LEADING COUNTRIES (106 KG CONTAINED Mo) United States Canada Chile These three countries are estimated to contain 75% of known world reserves. Small but significant production is 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^) bas been relatively consistent in terms of constant dollars [19]. The price in 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 50 14 9.5 - 33 -the current recession in many metal markets the molybdenum demand is expected to grow at a rate of 6 to 7 percent per annum due to its specialized application, mainly in alloy steels. The future supply and conditions of supply will partly be dependent upon the supply/demand situation. At present world pro duction is increasing and has further potential for increasing. However, in 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 critical with final product purity maintained within the limits 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 in sulphide concentrate (fob mine) there is considerable incentive for improved recoveries from ores. This is particularly so for by-product molybdenite where present recoveries may be quite low. With the roasted oxide selling price at $US 4.31 per pound ($US 9.49/kg) of contained molybdenum [20] it is imperative the treatment losses be kept to very low levels because of the small added value in 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 in excess of 0.1% in concentrate. Table VI lists 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 is a maximum content of 0.05 percent. Gangue impurities have a greater influence on the molybdenum grade since they are usually present in 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 is usually not of great importance since this element is 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 is required to be less than 0.1% for use in steels. In one operation this is reduced by leaching the molybdenite concentrate in hydrochloric acid for 6 to 8 hours [21]. By maintaining a slurry pH of 2.5 the CaO content is reduced from 0.5 to 0.05 percent. In some cases copper may be leached by sodium cyanide. However, this reagent is only effective in leaching secondary copper minerals such as chalcoite and covellite and is ineffective with chalcopyrite. Examples of this procedure in 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 in two Chilean operations [15]. This leachant has also been used on the roasted product. The copper content, as chalcopyrite, can be significantly reduced by a hot chloride leach [22,23,24]. This is also effective in lowering the lead (as galena) and calcium contents. Current practice 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) is reduced to less than 0.05 percent. Another process designed to remove lead [25] involves a 16 hour leach at 85°C in 5% HC1. i' Most molybdenite roasting is accomplished by multiple hearth roasting although other means such as rotary reverberatory furnaces or fluid-bed roasters have been used. The process is semi-autogenous in that the reaction is exothermic although additional heat.is often required for initiation of the reaction and to ensure completion of desulphurization. With multiple-hearth roasting the solids are fed in at the top while air is admitted in a controlled manner on most hearths. Air flow manipulation is important to temperature control in roasting, a necessary aspect considering the - 37 -volatility of molybdic oxide and the 'stickiness' problems that can occur in 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 air flows result in lower temperatures from the diluting effect of excess air. 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 oils followed by partial oxidation to moly bdenum dioxide (MoC^) which on further roasting is converted to MoO^. During roasting rhenium is volatilized as heptoxide (I^O^) which enables recovery by gas scrubbing (at < 80°C) if sufficient quantities are present. As with all 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 in 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 overall plant investment [28]. In many cases environmental considerations require that the emission of sulphur in the off gases be reduced to acceptably low levels. This is achieved by wet scrubbing and neutralization with lime [21,29] or by manufacture of sulphuric acid. The technical molybdic oxide produced by roasting can be used directly as additions to alloy steelmaking or may be briquetted with a pitch binder for the same purpose. The technical oxide is also the usual starting material for production of other molybdenum products. The principal process routes and final products are shown in 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 metallic molybdenum. A number of hydrometallurgical processes for treatment of molybdenite concentrate have been proposed including leaching in hypochlorite solutions, under oxygen pressure in alkaline solutions and with nitric acid. To date most have not been developed past the pilot stage. Apparently one commercial operation in the U.S.S.R. uses a nitric acid process to decompose molybdenite but details were not available [30]. Direct additions to steelmaking MoS2 Concentrate Purify (Si02) MoS2 Lubricants Roasting Technical Mo0„ Alloy steels -Powder -Briquets -FeMo Glass Ceramics Fertilizer Electric furnace sublimation Pure Mo0„ +NaOH-+ Sodium molybdate Chemicals Pigments Fertilizer +NH. Oft* Ammonium molybdate Chemicals Catalysts Extrusion Rolling Arc-cast ingots < > Bars Rods Sheet Electric furnace reduction Metal powder Press Sinter(H ) Work Honferrous alloys Rods Wire Sheet Figure 7. Molybdenum production flowsheet, (condensed from reference [16] ) - 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, it may suffer from a number of limitations: (i) Purity of oxide is 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 nitric 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 reject ion 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 nitro gen. In-plant environmental safety can be enhanced by operating the leach vessels under a slight negative pressure to avoid accidental leakage. Although the nitrogen in the system moves essentially in 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 is currently available. The potential for the process ultimately depends on economics. It is not the object of this study to undertake an economic evaluation but rather a metallurgical evaluation. However, the viability of the • process may be influenced by the prices of the feed and product, ie. -if impurity penalties are significant and if a premium price is - 42 -received for high purity oxide. 1.10 Nitric-Acid Leaching of Sulphides Nitric acid has been considered as an oxidant for sulphide ores and concentrates since early in the 20th century but commercial application has been virtually non-existent. The studies to date have concentrated predominantly on sulphides of copper although those of nickel and molybdenum have received some attention. The oxidizing power of nitric acid also provides incentive for its use in place of other aqueous oxidants. Nitric acid may also be used in a "catalyst" capacity with small additions made to other leaching agents. However, significant oxygen pressure may be required to at least partially, regenerate the nitric acid in-situ. A general study of the reaction of nitric acid on a number of sulphides was reported by Bjorling and Kolta in 1964 [31]. They examined the behaviour of pyrite, pyrrhotite, chalcopyrite, sphalerite, galena and molybdenite with nitric acid under various conditions. The examination of molybdenite was not extremely detailed although some of the potential for such a system was recognized. A somewhat general process utilizing nitric acid has been - 43 -proposed by Posel et al for the leaching of transition metals from iron bearing sulphide ores [32,33]. The leach system is 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 is removed by precipitation, under pressure and elevated temperatures if necessary. 1.10.1 Molybdenum Sulphide _ The behaviour of molybdenite in nitric acid has been studied by Zelikman et al [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 nitric acid is increased by the injection of oxygen to regenerate nitric and nitrous acids.. A stagewise decomposition flowsheet is proposed by Zelikman which involves additional intermediate leaching with ammonium hydroxide. Smirnov et al [35] performed laboratory-scale studies on the oxidation of molybdenite in nitric 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 is quoted as 20-26 Kcal/ mole indicating that the reaction is chemically controlled unless, precipitation hinders reagent access to the mineral surface. Nitric acid oxidation studies were also conducted by Fedulov et al [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 nitric acid oxidation of molybdenite has been developed by Noranda Mines Ltd-. [37} The basis of the process is the oxidative leaching and precipitation in the one vessel. The conditions applied ensure reasonable reaction rates with elimination of soluble impurities. i However insoluble impurities such as silica, alumina and any pre cipitated gypsum would remain with the molybdenum product. With sufficiently high temperatures and pressures a dehydrated molybenum oxide is produced in the leach rather than the hydrated form. A bleed stream is also required for sulphate removal following recovery of residual nitrate, molybdenum and rhenium. Nitric acid is also used to purify roasted calcines con taining residual sulphur [38]. As well as lowering the sulphur content the level of metallic impurities is also decreased. - 45 -1.10.2 Copper Sulphides A number of studies on the nitric acid leaching of copper sulphides have been conducted in recent years although the strategies of the possible processes differ in some aspects. Prater et al [39,40] developed a flowsheet for nitric 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 nitric 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 nitric 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 al have proposed a nitric acid process for treatment of chalcopyrite [42]. The concentrate is leached in a sulphuric acid nitric 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 is precipitated as goethite leaving a solution of sufficient purity for copper electro-winning. 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 al [43] with process improvements detailed by Davies et al [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, if present, is dissolved - 47 -and may be recovered by liquid ion exchange but this applies to relatively low concentrations, below the saturation limit. An economic evaluation shows the process to be more viable for relatively small operations where pyrometallurgical costs per unit of production would be extremely high. The suggested improvements to the process involve the use of a two-stage leach with direct injection of NC>2 gas regenerated from the nitric oxide evolved. Besides increased leach reactor performance the reduced equipment requirements enhance the economic position of the process. Acidified nitrate solutions have also been suggested as a possible reagent for in-situ leaching of copper ores [44], The presence of nitrates would enhance the conventional in-situ acid leaching rates. 1.10.3 Nickel Sulphides Habashi also presented a study on the extraction of nickel, copper and elemental sulphur from a low-grade, pyrrhotite-pentlandite concentrate [45]. Under suitable conditions of acid concentration, and temperature high batch recoveries of nickel and copper could 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 nitric 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 con centration of 1.97 moles/litre. j- Bjorling and Mulak investigated the dissolution of synthetic millerite (NiS) in nitric acid [47], and determined the process to be chemically controlled. Nickel extractions increased with temperature and nitric acid concentration and almost complete sulphur dissolution was achieved with nitric acid concentrations in excess of 2 molar. A pilot-scale study of a nitric 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 nitric acid as a function of initial sulphuric acid concentration. [46] - 50 -the basis of the subsequent processing is purification and denitrifi-cation prior to electrolysis. Purification is achieved by hydrolysis for iron, IL^S precipitation for copper and zinc and nickel hydroxide or sodium hypo-chlorite additions for cobalt removal. Nitrate elimi nation is accomplished by crystallization of nickel sulphate or by precipitation of basic nickel carbonate, 1.11 Modelling in Hydrometallurgy With the increasing emphasis on hydrometallurgy in recent years there has been greater interest in 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 will 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 is relatively small and only the final distributions are important is generally of minor significance in 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 is rate controlling unless reagent access is 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 first applies to leaching of high grade materials such as concentrates 52 -where a high proportion of the input solids mass is leached. The second case applies to low grade material where only a small fraction . of the mass of solids is leached from an essentially inert matrix. A-popular approach to the modelling of the leaching of particles con taining disseminated leachable mineral in an inert matrix is the shrinking core assumption. The reaction front is considered to be quite narrow and gradually proceeds toward the centre of the particle. The particles may be considered spherical or allowances made for non-sphericity, pore structure and nonuniform mineralization or exposure [50]. A similar approach is 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 pro gression of the leaching front may smooth out the "roughness", particu larly if the process is isotropic. Bjorling [42] utilized a grain-age term based on the diminution of a characteristic dimension of the particle to account for the change in surface area. It can be seen then, that the description of leaching kinetics can be quite complicated, with variation in reaction control, ranges in particle size and mineral distribution. One simplified approach is 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 is 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 - K Cn W (18) where 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 ^ all in appropriate units. This is a very simplified approach which accounts for the change in surface area only by the change in weight concentration of the species. ^ n 2/3 r = K C 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 strictly accurate if the leaching particles are equi-sized spheres but the method may be useful for approximations. (3) r = K C W (20) where K includes the variable activation energy The parameters included in the activation energy term must be determined by statistical analysis of experimental data. (4) r - K Cn A (21) where A = surface area for reaction J The^variation in area term must be accounted for in some manner. As mentioned previously the shrinking sphere, with or without adjustment factors is often used. An empirical method accounting for the change in area is considered later in 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. However analysis by this method is somewhat restrictive. - 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 in 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 is 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]. The method is shown in Figures 9 and 10. The quantity of component dissolved, Q, in a batch test is obtained as a function of time, t, as in Figure 9. This extraction curve is analysed by practical or mathematical means and the slope, , is plotted against Q as shown in Figure 10. A line of slope equal to the inverse 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 is 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 trial and error basis for a particular stage configuration, Since this analysis is based only on the amount of material dissolved it is only suitable for the same initial 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 is 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 is ex pressed in Equation (22) for a leaching reaction v C = v Cq + r V (22) where v = solution volumetric flow rate C = concentration of component in outlet solution CQ = initial concentration of component in input solution r = rate of reaction per unit volume V = volume of vessel - 58 -Again, the difficulty is 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 it may have to be taken into account. For perfect backmixing the RTD is given by: E(t) = 3 e_t/t (23) t where t = time t = nominal residence time 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 is satisfactory for first order reactions since the rates are then independent of concentration. For non first order reactions the situation is considerably more complex. Detailed analysis of the chemical engineering principles involved are given in the references [1,2,56,57,58,59]. 1.12 Modelling of other Unit Operations in Leach Circuit 1.12.1 Grinding - 59 -With the current flowsheet it is envisaged that ball milling will be used to reactivate the leach residue. The object of grinding simulation is usually to determine the product size distribution as a function of feed size distribution and mill parameters. By necessity, the modelling of grinding is extremely empirical and involves a large series of calculations to account for the complete particle size range. A kinetic model may be used for ball milling based on the following first order assumption [60]. d W. — = - K. W. (24) dt i i where W^ = amount of material in size range i K_ = breakage constant d W. —;— - rate of breakage from size range i dt The complete analysis is based on the assumption of perfect backmixing, a condition which is reasonable for ball milling. Another method for grinding simulation is the matrix model which involves a combination of classification, selection for breakage and breakage matrices to determine output size distributions [61]. - 60 -A number of theoretical relations have been proposed to describe size reduction. The one which applies more closely to fine grinding is that of Rittinger. d E = - (25) where 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 mill, the rest reporting as heat and sound. i 1.32.2 Flotation It has been found that flotation often closely follows the simple first order relationship of Equation 26 [61]. r = K W (26) where r = rate of flotat ion - 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 in retaining the desired mineral. The complete characterization of all influencing variables is not possible. How ever, the range of some of these variables in practice may be suffi ciently small that they can be assumed constant for approximations of circuit behaviour. On the basis of Equation (26) and backmixed flotation cells it can be shown that the recovery of floatable mineral is [63]: R a , K.,Q (27) 1 1 + K 9 K } where R^ = recovery from 1st cell 9 = cell retention time This can be extended to recovery from the cell in series: - 62 -Hence the total recovery from a simple series set of flotation cells is the summation of the individual'cell recoveries. R = E(R- + R0 + R ) (29) J- / n - 1 - (1 + K 6)"" (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 this Chapter introduces the approach to the formulation of the leaching model while complete details are presented in 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 practical and versatile method for simulation of leaching. For the steady state conditions considered the mass balance is most simply described by Equation (31). 0 = I ± R (31) where 0 = rate of output I = rate of input R = total rate of generation (+) or consumption (-) - 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 is 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 nullify the effects for a non first 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 con centrate consisting of non-uniform particles is based on equation (21) MOLYBDENITE: . r = K Cn A (21) Two other sulphide minerals are considered since they con sume nitric 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) is used. PYRITE, CHALCOPYRITE: r = K C W2/3 (19a) For lack of information the reactions for both these minerals are considered to be first order with respect to C. - 66 -It is 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 mill 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 it cannot be claimed that this analysis is accurate it still demonstrates the point that in a partially closed or bounded system the finer material will initially leach faster but will eventually leach at a slower rate due to depletion of solids and consumption of active reagent. However the net extraction will still 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 60 t (hr) 80 Figure 11. Extraction curves for Gibraltar molybdenite concentrate (a) as received (b) wet ground one hour in laboratory pebble mill. 49.9%Mo, initial pulp density 112 grams/litre solution, initial 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. - 69 -(2) C In the earlier discussion it was shown that the exact mechanism for leaching of sulphides by nitric acid may be quite com plex. On the basis of empiricism then, the term C was taken as the "nitric acid" concentration in molar units since it could be measured and had a determinable influence on the rate of reaction. (3) n Having decided to use the nitric acid concentration as the reactant in solution the reaction order had to be determined by experiments using standard procedures. (4) A This defines the surface area of particles on which the chemical reaction occurs. It is 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 is described by summation over all 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 in surface area of a molybdenite particle is also com plicated by the following factors: (i) Initial definition of A is not adequate since it cannot be determined accurately. (ii) Anisotropy of leaching, Leaching is 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 difficult 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 is that the single particle basis is illogical 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 it 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) Gibralter concentrate leached 3 days,Initial pulp density 168 g/1 solution,initial 4M HN03> 64% extraction. (2000x). (b) MoS concentrate leached to 60-75% extraction. (4000x). - 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 is also shown. This is not conclusive evidence since the ratio will be influenced not only by the degree of grinding but also the morphology of the mineral in the ore. However it does demonstrate the complexity involved in evaluating the reactive surface, area. The problem is overcome by the following strategy using the results from batch"experimentation. Equation (21) is normalized as: r = K' Cn A (32) where A' = A - area factor For batch or continuous cocurrent leaching then: r = K' C at t = 0 (33) since A' 1 The functional form of A' versus fraction leached (area decay curve) can be determined by curve fitting of appropriate experimental data. - 74 -Figure 15. Approximate dimensional characteristics of four molybdenite concentrates. - 75 -This then defines the area factor in a term independent of time. If A' is determined on a per unit weight of solid basis then an additional term has to be introduced to account for the pulp density and its change in the practical system. r = K' Cn A' P' (34) where P = 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' = r e (35) where E^ = activation energy R = gas constant T = absolute temperature 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 con sidered separately throughout the leach. Although bulk analysis - 76 -and initial area factor could be easily calculated by a weighted average, the properties subsequent to commencement of leaching are much more difficult if 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 is replotted in Figure 17 as surface area versus time. The total surface area for a 50 wt % initial 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 -0 LO FRACTION LEACHED -—— Figure 16. Surface area vs. fraction leached for initial equal masses of spheres of one unit radius and two units radius. Constant leaching environment„' \£Owf% MIXTURE \ Y \ TIME Figure 17. Surface area vs. time for initial equal masses of spheres one unit radius and two units radius. Constant leaching environment. of - 78 -CHAPTER 3 EXPERIMENTATION The previous Chapter outlining 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, literature or by analogy were furnished by designed experiments. Most experiments involved relatively short term tests in which the effects of changing variables could be neglected or averaged. The molybdenite concentrates used in the test work were supplied by Endako Mines Division of Canex Placer Ltd. (Sept. 1977) and.Brenda Mines Ltd. (Sept. 1977) both located in British Columbia. Both concentrates were direct flotation products which had not been subjected to the purification leaches practised at each of the plants. Chemical analyses and sizings for these two concentrates are listed in Table VII. 3.1 Apparatus The experimental apparatus is depicted in Figure 18. The leaching reactions were conducted in a standard 500 ml filtering flask - 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* 38.36* sio2 8.0** -INS0L - 1.59 Sizing 5% + 19 microns 44% + 9 microns 56% - 9 microns (^99% - 325#) (^72% - 325#) * by calculation on basis of MoS,,, FeS2, CuFeS ** 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 in the water bath surrounding the re action 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 dis placed through an overflow. Before most leaching tests were performed the solution in the reaction flask was bubbled with argon and then nitric oxide produced in a gas generator by sodium nitrite and sulphuric acid. Bubbling with argon eliminated most of the air from the system while bubbling with nitric oxide attempted to duplicate the continuous system which is saturated with this gas. It was impossible to avoid some air 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 in molybdenum concentration could be readily detected by atomic absorption techniques whereas changes in solids content was more difficult to determine and less reliable. A Perkin Elmer Model 306 Atomic Absorption Spectrophotometer was used for the analyses. Standard solutions for molybdenum, as outlined in the operating manual, required slightly alkaline conditions. Since the leach solutions were acid and contained iron the treatment with alkali could result in hydroxide precipitation, thus necessitating filtration. 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 stan dards gave low results. Molybdenum is known to suffer from interfering ions in 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 start ing leach acid which already contained nitric and sulphuric acids, and dissolved iron. Testing also showed that molybdenum absorbance was relatively insensitive to nitric acid over ranges of interest in 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 initial 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 initial rate of reaction was determined for different initial nitric 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 it 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 in solution concentrations. Since the area of reaction is essentially constant for these reactions the area may be included within the rate constant so that the rate equation becomes pseudo-homogeneous. r = K'[HN03]n (36) Therefore the plot of log r versus log [HNO^] has a slope equal to the reaction order as shown in Figure 19. The slope is evaluated at 1.84 for the filled points. Due to the limited experimentation the; reaction order is taken as 2.0 for the model calculations. I The two high points at lMtHNO^] are neglected in 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 initial reaction rate vs. log initial HNO^ for Brenda +325 mesh molybdenite concentrate. - 86 -the reactive surface area of the molybdenite changed as leaching progressed. Since the leaching rate is directly proportional to the active surface area the relative change in 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 in 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]. 3 3 313 A i^"^360 r = 4.664 x 10 e (g/litre.sec) (37) where <\> = fraction of M0S2 leached This equation fits the points remarkably well but is unrealistic be tween zero extraction and the first experimental point, as well as for extractions above the final experimental value (^50%). For model - 88 -stability a separate linear relationship with an estimate of the intercept on the ordinate is assumed for the zone adjacent to zei:o extraction. The area factor,A*, is 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 fitting was initially employed although the use of the value from the linear approximation may be more realistic. It is not important though,since the normalizing value is only a reference point and will not influence the final results. Under this scheme the area factor relationship is give by: A' = 0.5003 - 4.586 <f> for" ' 0 <fr ^ 0.0333 (38) and, , .0.3360 A' - e-3*3134 • (39) i for 0.0333 < <(> < 0.5 Having calculated the value of n the effective rate constant K' can be calculated since at t = 0 A' = 1 r = K*[HN03]2 (40) K' = 2.915 x 10"4 (- * M°» )( £ -) mole Mo v sec.mole HNO^ - 89 -and K« = 4.5359 x 1010 ( f Mg ) ( \ PM. o mole Mo sec. mole HNO, using an activation energy of 20 Kcal/mole, This value accounts for the molar concentration of nitric acid and the mass rate of extraction of molybdenum. By similar procedures the rate constants for pyrite and chalcopyrite in Endako concentrate were determined assuming activation energies of 10 Kcal/mole. „ - . _ „ -v, , , c,, in4 , g Fe_w I (mole Fe) >. Fe xn FeS: K' = 1.1516 x 10 (—^ =—) ( =r—vjr^:—) o mole Fe mole HNO^-sec ^ . „ „ „, „ ,,0 i^3 , g Fe w& (mole Fe) Fe in CuFeS0: K = 2.618 x 10 (—^—-—) (- ^———~ ) 2 o mole Fe mole HNO -sec „ -,^3 , e Cu . , £2/^(mole Cu)^"^s CuinCuFeS2: IC - 2.978 x 10 (^—^i- mole HNO -sec > - 90 -CHAPTER 4 FORMULATION OF MODEL The model is constructed on a modular basis with a main control program and separate subroutines for different real and hypothetical operations. The block diagram flowsheet on which the computer model is based is presented in Figure 21 while the flow diagram for the computer program is shown in Figure 22. The model was developed using the computing facilities at U.B.C. Initial work was conducted on an IBM 370/168 while the latter stages involved the use of the Amdahl 470 V/6 - II. Double precision arithmetic was used for the calculations. Initial Assumptions (1) The feed concentrate is relatively uniform with respect to chemical analysis and partical size distribution. This is necessary since the behaviour of the model depends on parameters associated with the feed. Milling operations tend to produce a relatively consistent product despite variations in the mill heads so that a single cali bration of a concentrate should be adequate. (2) Laboratory determined parameters are assumed to apply to - 91 -New reed Solution Tails Figure 21. Model block diagram. Adjust required recycle guesses No Begin i Read input data Convert inpuj units to model units Calculate combined solids mass and analysis Calculate leach output for N stages Calculate other leach values Calculate leach filter distributions Cn l.culnte regrtnding effects Calculate scream splitter d IstributIons Convert model units to output units Calculate m:iHti and flotatIon analysis Calculate combined recycle parameters Print output End I SSM Solve simultaneous algebraic equations I to I Figure 22, Computer model flowsheet. - 93 -industrial scale. This may apply reasonably well to many leaching systems but such extrapolation is less accurate in the case of grinding and to a smaller degree, flotation. realistic estimates have to be made for the parameters associated with this stream in order to commence calculations. On passing through the entire cycle these recycle parameters are calculated and compared to the initial estimates. If the guessed and calculated values are not within a specified tolerance the guesses are adjusted and the calculations redone. The adjustment criterion is 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 first time it does not fall within tolerance. Subsequent new guesses are produced by the following relation 4.1 Recycle Estimates Since there is a solids recycle stream in the flowsheet :k+l " \ (41) where X = estimated value XC = calculated value - 94 -k iteration number R multiplying factor defined by? R = <Xk-Xk-l)/(\-\-l~XCk + XCk-l) (42) Subject to R .4: R max This convergence algorithm is performed by the main program on recycle parameters that are initially out of tolerance or stray out of tolerance due to variations in other parameters. 4.2 Concentrate Mixer 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 first stage. For the purpose of simplifying calculations the pyrite and chalcopyrite in the recycle solids are transferred to the new solids stream. This hypothetical unit combines the new solids and recycle - 95 -4.3 Leaching Assumptions (1) All 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 is assumed constant with variations ~ ~ occurring in density as the reaction proceeds. (5) All 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 Variables v = volumetric flow rate of leach solution i p = density of solution w = mass flow rate of solids X - mass fraction of component in 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 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 for determination of P^ = ratio of current pulp density of recycle solids to experimental pulp density used for determination of ^o KJJJo= rate constant for molybdenum leaching* Kpe= rate constants for iron leaching* K^u= rate constant for copper leaching* <|> = fraction leached LEACH EQUATIONS Component Balances (g/s) I I Liquid (Mo, Fe, Cu, HN03) vpX. -vpX + R - R = 0 (43) x Koog c ' Solids (New Mo, Recycle Mo, Fe, Cu) w. X. - w X + R - R = 0 (44) xioogc \ * based on 1 litre of solution. - 98 -Overall Mass Balances (g/s) Liquid vp. - v po •+ ERg ~ ZRc = 0 (45) Solids (New solids, Recycle Solids) w. - w + IR - ER = 0 (46) l o g c RATE EQUATIONS (New Mo, Recycle Mo, Fe, Cu, HN03) (g/s) - New Mo RNMo = K^[HN03]2 A'P'V (47) where A' is determined by interpolation of experimental results and P' by extrapolation based on a linear relationship between surface area and mass of solids. Recycle Mo KRMO = Vmo3]2 WkW (48) Fe Rpe = K^,e[HN03]W2/3 V (49) In the model this rate is considered in two parts: that from FeS^, and that from CuFeS0. Cu R„ = Kl [HNO„]W2/3 V (50) — Cu Cu J - 99 -HN03 RHN03 = 3'9412RMo + 5'6419RFe + °-6611RCu <51> where the constants are based on the stoichiotnetry of leaching of MoS2> FeS2, CuFeS2e AREA FACTORS (New Mo, Recycle Mo) New Mo A' - e'a2y (52) where a2, a^ are empirically determined constants. Recycle Mo" A^ = b± e~b2b3*R (53) where b^ and b2 are parameters conditioned by the regrinding step and b^ is a constant. The solution of such a set of non-linear and linear equations is a formidable task. Several subroutines are available at U.B.C. to solve these equations but the subroutine SSM (see U.B.C. NLE) was chosen since it was quoted as the most "robust" [67,68], The equations are programmed in the following form: Non-Linear Fx = 0 (54) Linear Ax = B (55) .a3 - 100 -Basically this is a secant method which requires an initial 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 is to calculate final 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 filter subroutine performs the solid/liquid separation on the leached slurry. At present it allows for 100% of the solids - 101 -to pass to the regrind operation but was included for future expansion of the program. The main factor to consider in filtration would be the loss of filtrate in the filter cake rather than loss of solids. 4.6 Regrind The regrind operation not only increases the absolute value of the area factor but also increases the curvature of the remaining composite area decay curve. From Figure 20 it can be seen that the area decay curve approaches linearity after a relatively low degree of leaching. Regrinding would increase the curvature but probably not to the same extent as the initial concentrate. In the process of milling the original ore numerous size reduction steps are involved, all having the potential to produce fines. The size reduction steps are listed in Table VIII. Table VIII SIZE REDUCTION STEPS IN NORMAL MILLING OPERATIONS 1 Primary Crushing 2 Secondary Crushing 3 Tertiary Crushing 4 Rod Milling 5 Ball Milling 6 Regrind Ball Milling (may be more than one regrind mill) - 102 -Particles may bypass or be recycled through some size reduction steps by classifiers operated in closed circuit. Since the regrind step in the current flowsheet involves one single-pass operation before returning to the leach it is probable that the "fines" content is not as great as in the new concentrate. Hence the area factor relationship for the recycle concentrate will differ from that for the new concentrate and is assumed to follow the relationship in 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, grind constant (t "*") k g t mean residence time in grinding mill. g incremental new surface area factor created. But k cannot g be determined directly by experimentation. •'• bl = A'(1 + k' t ) g g (57) since k g = k' A' g where k' is determined experimentally (see Appendix D) - 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 is simply assumed as: b2 - l+k'tg (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 mill to the flotation section or directly back to the leach according to a predetermined ratio. Assumption The stream splitting is 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 first 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 in each cell is only significantly influenced by the flotation of the dominant component (molybdenite). (4) Cell volume is 25% air in pulp during operation [69], ~ (5) A simple series of flotation cells is used with no i pulp recycle. t Nomenclature for Flotation til = fractional mineral recovery from i cell (i=l to n) K = flotation rate constant th = pulp residence time in i cell u = pulp volumetic flow into bank of cells m = mass flow rate of floatable component into cell a = factor which converts mass of floated solids to volume of flotation pulp (50 wt % H?0) V = volume of deaerated pulp in cell. - 105 -The pulp residence time in the first cell based on the tailings flow is: 91 " u-\ <59> Since 0 is variable with cell number the total recovery cannot be obtained from a simple series summation as when 6 is assumed constant. Hence the recovery of M0S2 is determined on a cell-by-cell basis. For the xi"^1 cell: KG n-1 Rn - 1 + K8 (1 " * V (60) n x and' e = -1 (61) n n—l u - am (R + Z R.) n . x 1 V n u - am £ R. x x (62) By substituting Equation (61) into Equation (60) and rearranging: „ n-1 n-1 amR - (u - am £ R. + KV)R + (1 - Z R.)KV = 0 n x n .x x x which is a quadratic equation and can be solved for the root 0 < R^ - 106 -R = n-1 (u - am Z R. + KV) i (u - am Z R. + KV) -i 1 n-1 4am(l - Z R )KV i n 2am (63) Equations (63) and (62) are solved sequentially for each flotation cell with the overall recovery of molybdenite given by the summation of the individual cell recoveries- Then equations of the same form as Equation (60) are used for the recoveries of the other minerals using the cell residence times already established by the molybdenite flotation. 4.9 Recycle Combination 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 con centrate. Assumption This hypothetical unit is used to determine the calculated The refloated product is assumed to have the same area factor parameters as the solids which are reground only. The error introduced - 107 -by this simplification is negligible since there is a very high re covery 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 still subject to uncertainty the simulation was partially evaluated in the current form. Complete validation is not possible until a continuous plant is constructed although model, viability 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 initial 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 fre quency. Attainment of steady state after adjusting some variable should similarly take considerable time. In interpreting the behaviour of such a system it should be - 109 -remembered that the C and A terms in Equation (21), describing the basic rate relationship, are not purely independent variables. The new input values are independent to the extent of possible plant operations but interact in arriving at the steady state values operating in each leaching vessel. The relationship is further complicated by the presence of the solids recycle stream. The model calculations were based on a chosen standard con dition and the effects of individually varying particular plant or process variables. The standard conditions are outlined in Table IX. Table IX STANDARD CONDITION OF LEACH PROCESS Vessels - 2 cocurrent at 120,000 litres each New Feed - 10.8 tonnes/day Endako M0S2 (as calibrated) Solution- 87.8 litres/min. - 252.1 grams HN03/litre (4 M) Leach Temperature - 35°C Approximate Leach Stage Residence Time - 19.5 hr. Grinding Mill Solids Hold Up - 800 kg Fraction of Recycle Bypassing Flotation - 0.5 Flotation Cells - 4 x 150 litres - 110 -This choice is 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 still 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 is the cause of the small scatter in the following graphs. In these graphs each point represents individual i 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 initial estimates to commence model runs and to continue calculations until a specified convergence criterion on the recycle stream is satisfied. Failure of the leach-solving subroutine to converge within its specified tolerance can be attributed to two general reasons: (1) Failure of the algorithm by its 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) if 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: \ = estimated value »J XC, . = calculated value G = guess factor for stage 2 based on stage 1 output r k = leaching stage counter j = cycle iteration counter - 112 -(1) 1st stage output guesses: (a) Initial guess for j = 1 (b) For j > 1 X, . = IC. . , (64) (2) 2nd stage output guesses: (a) Initial guess for j = 1 X2,l - GF XC151(65) (b) For j > 1 XC (3) 3rd stage output guesses (a) Initial guess for j - 1 XC2 1 x3si = xcf: ' XC2,1 (67> except for rate equations where XC X3S1 M " xc7*7 xc2,i (68) 1 J 1 where M is taken as 1.5 - 113 -"(b) For j > 1 XC (4) 4th stage or greater output guesses: (a) Initial guess for j = 1 XC :k-2,j (b) For j > 1 XC Vl.j-l \,i .- xcTT^ " ^1,3 (70) \,j - xcrfrr • xc^-i,i (71) Mathematical instability could also arise within the system of algebraic equations since the solving routine is unconstrained. In searching for the true values certain variables may cause instabilities or impossibilities in 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 is maintained by using an alternate equation where the appro priate term is set to zero. In one case stability is maintained by setting the term to zero in the original equation. Convergence Convergence of the eight recycle parameters within a specified - 114 -tolerance is required before the complete output is printed. Conver gence is attained by the previously defined adjustment criterion, but to maintain the leach calculation stability, the step sizes must be less than current critical values. Since the step size is relative to the difference between the estimated value and calculated value the approach to convergence would decelerate as the true value is approached. Hence the fractional adjust ment is increased as the tolerance becomes smaller with model stability maintained since the absolute variation is still small. It was apparent from the early model work that the mass flow rate of recycle solids created more sensitivity to instability. Therefore, fori high calculated tolerance values, the fractional adjustment to this particular variable is less than for the others. For low tolerance values high fractional adjustments are operative for all recycle parameters. Under this convergence scheme all parameters that are not within tolerance are continually adjusted until tolerance is achieved or the com puter run terminated. Some recycle parameters such as molybdenum and sulphur contents are quite predictable and experience only small variations. Convergence is 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 first 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 in error will 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 sub routines has occurred the computer run is 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 first stage output guesses, the recycle parameters and guess factors if 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 if model failure does occur success can be achieved with an inter active 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 main taining 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 will - 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 leach-able minerals and nitric acid approaches complete consumption of the nitric acid for steady state conditions. Under most leaching con ditions the maximum pulp density restrictions will likely be encountered before this limit is reached. The impact of the. greater new solids input and correspondingly greater recycle solids flow rate is to lower the solution reactivity in each leaching stage. This shown in Figure 24 where the nitric acid concentration in each stage is 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 is raised as a consequence of increases in 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 is a greater input of molybdenum to solution. Hence for constant solution flow rate the net gain in molybdenum concentration is greater. This point is con firmed by Figure 25 where the difference between the pregnant solution and recycle solution molybdenum contents is plotted against new solids feed rate. The lowering of the percent molybdenum extraction per pass as the new solids feed rate is increased is shown in Table X. The - 119 -500h NEW SOLIDS FLOWRATE (tonnes/day) Figure 24. Total input pulp density, operating area factors and operating nitric acid concentrations vs, new solids flowrate. Other conditions standard. - 120 -10 31 12 NEW SOLIDS FLO WR ATE (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 is also evident that the proportion of extraction work done by the leach vessels shifts slightly more in favour of the first stage. 5.2.2 Initial Acid Strength The initial acid strength is similarly subject to stoichio metric restrictions. Figure 26 shows how the recycle ratio increases as the initial nitric acid concentration is decreased, again approaching - 122 -INITIAL HNO, (moles/1) 230 250 ~ 270 ~ 290 INITIAL NITRIC ACID (g/l) Figure 26. Solids recycle ratio vs. initial nitric acid concentration. Other conditions standard. - 123 -an asymptotic limit due to depletion of nitric acid under steady operations. This result indicates the advantage of using as high an initial nitric acid concentration as possible, subject to practical limitations. As shown earlier, the extent to which molybdenum can be precipitated from solution is 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 discoloura tion of the hemi-hydrate when using high initial nitric acid concentrations 6M). The cause and extent of this was not fully determined although product purity was still high. With higher initial nitric acid concentrations each leaching vessel operates at higher nitric acid levels, as demonstreated by Figure 27. The increased leaching rates result in 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 initial nitric acid concentration. The decrease in input pulp density as a function of initial nitric acid results from the lower solids recycle. This is also shown in Figure 27. Since the mass flow of new solids and volumetric flow of solution are constant for this series of runs the gain in solution molybdenum concentration is 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 601 401 230 250 INITIAL 275" NITRIC ACID (g/D Figure 27. Total input pulp density, operating area factors and operating nitric acid concentrations vs. initial nitric acid concentration. Other conditions standard. - 125 -there is 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 will allow a greater treat ment rate of new molybdenite concentrate thus producing a richer pregnant solution while still operating below the maximum pulp density. The greater leaching rates result in higher operating siliceous insoluble concentrations in solids throughout all phases of the leaching operation. The operating concentrations for leach residue, reflotation product and recycle solids are graphed against initial nitric acid in Figure 28. This trend applies to variations in all parameters which lead to increased instantaneous reaction rates. The percent extractions from total solids input of Table XI naturally show increases as the initial nitric acid concentration is 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 initial nitric 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~ :— 1 ,~- r 230 250 270 290 INITIAL NITRIC ACID (g/l) Figure 28. Insol content of leach residue, reflotation concentrate and recycle solids vs. initial nitric acid concentration. Other conditions standard. - 127 -Table XI EXTRACTION FROM TOTAL INPUT SOLIDS ON EACH PASS FOR DIFFERENT INITIAL NITRIC ACID CONCENTRATIONS(%) Initial HN03 (g/D 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 The gain in percent extraction for the first 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 is graphed in Figure 29. Again it can be seen that the recycle ratio rises to an asymptotic limit as the solution flow rate is 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 nitric 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 still the same since the volume flow of solution is greater. With similar total acidity the molybdenum precipitated per litre in subsequent processing will be less but this would be compensated by higher volumetric throughput. A greater percentage extraction per pass through the leach is obtained as the solution flow rate is 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 nitric 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 in percent extraction than the first. 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 77.5 16.2 3.8 20.0 80.0 y - 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 5.2.4 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 nitric acid levels was not significant within the tolerance limits used. With constant new solids and solution input the steady state operations result in a constant gain in molybdenum concentration in the pregnant solution. Changes in the leaching temperature result in a slight alteration in the distribution of leaching work done by each stage as can be seen in Table XIII. ": - Table XIII i 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. Total 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 first stage. 5.2.5 Partial Bypassing of Flotation Since the purpose of reflotation is to eliminate insoluble gangue the increased bypassing of this step leads to higher operating levels of siliceous minerals in all the solids streams, The effect of bypassing on the insol contents of the leach residue, reflotation con centrate 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 itself. 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 pro vides 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 i i i 1 1 0 0.2 0.4 0.6 0.8 1.0 FRACTION BYPASSING FLOTATION Figure 34. Insol content of leach residue,reflotation concentrate and recycle solids vs. "fraction bypassing flotation. 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 tails. 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 is 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. This can be seen in Figure 37. The operating nitric acid levels, however, did not show significant variation under the tolerance limits used. The net decrease in physical factors which affect the reaction rate is 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 litres and stage 2 at 140,000 litres. A slight increase in recycle ratio to 3.46 was calculated when stage one was set at 80,000 litres 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 in 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 solids recycle ratio as a function of the number of leaching vessels for.constant vessel volume. The effect of "adding" cocurrent stages for the standard operating conditions indicate a marked decrease in recycle ratio from one to two stages with much less improvement from two stages to three. Additional staging in this manner above two or three vessels may not be justified when considering the increased capital costs and molybdenum inventory. Table XIV lists the extraction from the total input solids for 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 2 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 leaching the distribution of leaching work between stages * constant stage volume - 144 -I 2 NUMBER OF STAGES Figure 38. Solids recycle ratio vs. number of leach stage Constant stage volume. Other conditions standard. - 145 -one, two and three is 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 in the recycle solids. The effect of multiple staging when considering constant total volume is shown in 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 para meters. 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 is plotted in Figure 39. For the model calculations a value of 2.0 was chosen for b^; 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 it is likely that the error is 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 is raised and the curvature is increased as the grinding mill size is increased. However, the solids recycle ratio becomes - 147 -T 1 1 1 T I U, l_ 1 1 1_ 0 0.1 02 0.3 0.4 05 FRACTION LEACHED Figure 39. Recycle area factor vs. fraction leached for different values of by Standard conditions. - 148 -•v—— -r~~——*T —i ! T 0 0.1 0.2 0.3 0.4 03 FRACTION LEACHED Figure 40. Recycle area factor vs. fraction leached for different grinding mill sizes. Standard conditions. (Grinding mill size units -' kilograms solids holdup) - 149 -relatively insensitive to grinding mill size for higher mill sizes. This is, 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 is 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 relatively limited amount of available data. A significant feature of the leaching model for molybdenite is the bulk empirical deter mination of the change in active mineral surface area as leaching progresses. This is achieved by interpolation and extrapolation from batch experimentation. The method avoids vague assumptions on particle shape, with or without correction factors, and also allows for other influences such as particle non-uniformity and particle cleavaging which are extremely difficult to quantify. The number of mathematical calculations are also somewhat reduced by elimination of the necessity to consider particle size classes. In its current form the model accounts for numerous plant and operating variables as follows: (1) Number, size and distribution of leaching vessels. (2) Size of grinding mill. (3) Number and size of flotation cells. (4) Variation in new solids feed rate and analysis. - 151 -(5) Variation in solution flow rate and nitric 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 (53). — - (2) Use-of laboratory-determined 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 difficult 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 viability 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 verifi 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, is 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 is 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 (if necessary) the chalco-pyrite 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 N02 as a substitute for HNO^ in first-stage leaching. - 154 -REFERENCES D.M. Himmelblau and LB. 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. De Zoubov: Atlas of Electrochemical Equilibria in Aqueous Solutions, Permagon, London, 1966. D.S. Davies, R.E. Lueders, R.A. Spitz and T.C. Fraciewicz: Nitric-Sulfuric Leach Process Improvements, presented at AIME 107th Annual Meeting, Denver, Colorado, Feb. 27, 1978, A.I. Busev: Analytical Chemistry of Molybdenum, Ann Arbor-Humphrey Science Publishers, Ann Arbor, 1969. M.M. Jones, J. Am. Chem. Soc, 1954, 76, 4233. P.E. Churchward and J.B. Rosenbaum: Unit Processes in Hydrometallurgy, Met. Soc. Conf., Vol. 24, pp. 441-52, AIME, Dallas, Texas, 1963. J.Y. Lee, D.H. Reynolds and R.B. Bhappu: Continuous Processing and Process Control, Met. Soc. Conf., Vol. 49, pp. 105-24, Philadelphia, Pennsylvania, 1966. H.H. Read: Rutley's Element of Mineralogy, 25th Edition pp. 459-61, Thomas Murby and Co., London, 1967. - 155 -13. A. Sutulov: Molybdenum Extractive Metallurgy, University of Concepcion, Chile, 1965. 14. A. 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. Nilsen: U.S. Patent 3,966,462, June 29, 1976. 34. A.N. Zelikman, L.V. Belyaevskaya and T.E, Prosenkova: Chem. Abs. 72:81734 d. 35. I.P. Smirnov, V.I. Zyurkalov and N.I, Chuikina: Tsvetn. Metally, 1975, No. 2, pp. 44-45, (Russ.). 36. O.V. Fedulov, B.I. Taranenko, V.D. Ponomarev and L.V. Svechkova: Chem. Abs., 68:32601 n. 37. D.G. Kerfoot and R.W. Stanley: U.S. Patent 3,988,418, Oct. 26, 1976. 38. Zh.G. Gukasyan and R.K. Arustamyan: Prom-St. Arm, 1974, No. 9, pp. 68-70, (Russ.). I 39. J.D. Prater, P.B. Queneau and T.J, Hudson: Trans. SME-AIME, 1973, Vol. 254, pp. 117-22. 40. P.B. Queneau and J.D. Prater: U.S. Patent 3,793,429, Feb. 19, 1974. 41. F. Habashi: Trans. SME-AIME, 1973, Vol. 254, pp. 224-27. 42. G. Bjorling, J. Faldt, E. Lindgren and I. Toromanov: Extractive Metallurgy of Copper, Vol. II, Hydrometallurgy and Electrowinning, Int. Symp. AIME, Las Vegas, Nevada, 1976, 43. H.M. Brennecke et al: 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 CC. 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 BY CATEGORY 1976* 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 Solution Vol. (mi) Initial Solids (s) Pulp Density (g.solids/I.solution) Leach Time (rain) Ave.Temp. CO Mo Leached (g) Ave.Leach Rate (EMo/t.sec.xl03) Ll 3.94M HN03 128 16.16 E 126.3 79 24 0.6847 1.13 L2 3.94M HNO3 200 25.30 E 126.0 45 35 1.3506 2.50 L3 3.94M HNO 3 200 46.48 E 232.4 32 35.5 1.4723 3.83 L4 3.94M HNO3 250 31.50 E 126.0 12.5 35 0.7099 3.79 L5 L4 leach solution 200 25.30 E 126.0 59 35 1.2133 1.71 L6 3.6M HNO3 200 25.20 E 126.0 45 35 1.2201 2.26 7.4g/*Fe(NO3)3'9H20 35.5 1.1976 2.32 L7 3.94M HNO3 200 25.20 E 126.0 43 L8 3.94H HNO3 200 25.2 L4 res 126.0 45 35 1.0800 2.00 1.9 3.94M IINO3 250 15.00 E 6C.0 16 35 0.3550 1.48 35 35 1.1800 2.25 L10 4.0M HNO3 245 12.00 11+325* 49.0. 30 35 0.0162 0.0364 138.5 35 0.0946 0.0465 Lll 5.0M IINO3 250 12.00 15+3250 48.0 11.2 35 0.0095 0.0565 45.8 35 0.0420 0.0611 75.2 35 0.0780 0.0691 105.2 35 0.1253 0.0795 L12 5.0M IINO3 250 12.00 B+325/; 48.0 9.6 35 0.0080 0.0556 70.2 35 0.0720 0.0684 130.5 35 0.1460 0.0746 190.4 35 0.2310 0.0809 L13 5.0M IINO3 250 12.00 11+3251! 48.0 19.4 35 0.0165 0.0567 1.14 4.0M IINO3 250 12.00 B+3250 48.0 30.1 35 0.0150 0.0332 L15 3.0M IINO3 250 12.00 B+325# 48.0 65.2 35 1 0.0200 0.0204 E - Endako B Brenda APPENDIX B (Continued) Run Solution L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26 L27 L28 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 S042" 4.0M HNO3 3 g/l Fe3+ 5.2 g/i SOA2-4.0M HN'Oj 3 a/1 Vel* 5.2 g/4 SOA2-4.0M HNOT 3 g/1 Fe3+ 5.2 g/1 SO/,2-4.0M HNO3 3 g/1 FeJ+ 5.2 g/f. S042-4.0M HNO3 3 g/1 Fe3+ S.2 g/1 S0«2-4.0M HMO3 3 g/1 Fe3+ 5.2 g/i SO42-Solution Vol. (ml) 250 250 250 250 250 250 450 420 387 345.5 303.8 271,5 248,3 Initial Solids (g) 12.00 B+325tf 12.00 B+325i? 12.00 B+325ff 12.00 B+325tf .12.00 B+3250 12.00 B+325// 25.00 E 22.85 L22 res 20.80 L23 res 18.25 L24 rc-s 15.79 L25 res 13. S8 L26 res 12,31 L27 res Pulp Density (g.solids/1.solution) 48.0 48.0 43.0 48.0 48.0 48.0 55.6 54.4 53.7 52.8 51.97 51,12 49,57 Leach Time (rain) 481 120.5 13.4 480 90.1 30.1 20.8 40.5 80.2 100.9 109.8 119,9 179,7 Ave.temp. (°C) 35 35 35 35 35 35 35 35 35 35 35 35 35 Mo Leached (g) 0.0325 0.0158 0.0145 0.0275 0.0039 0.0138 0.9135 0.9996 1.2694 1.2680 0.9789 0.7U3 0,8060 Ave.Leach Rate (gMo/l.sec.xl03) 0.00450 0.00874 . 0.0721 0.00382 0.00289 0.0306 1.627 0.9794 0.6817 0.6062 0.4891 0.3642 0,3011 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 CSFPIT(K,I)CALCULATED 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 _ =PRINTIN3 VARIABLE - EVERY 8 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 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 - 164 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 «GT0 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 Q *************************** C STEADY-STATE COMPUTER SIMULATION OF MOLYBDENITE/NITRIC ACID C LEACHING PROCESS INVOLVING MULTI-STAGE COCURRENT LEACHING ff C 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/VOLBT,K COMMCN/AREA4/X,XX COMMON/AREA5/FX,GX COMMCN/AREA6/GC,SPLIT COMMON/AREA7/RGXff GFX COMMON/AREA8/RFX,FTX,RXC COMMON/AREA9/FC CO MMCN/AREA10/VOLFL ,FLOWffNF 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 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 (20)#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) 500 FORMAT(>0«,'NEW SOLIDS INPUT 8) WRITE(6,501) 501 FORMAT ( , * . ') WRITE(6,502) V(1) 502 FORMAT ('NEW SOLIDS FLOWRATE (TONNES/DAY)=',F8,3) WRITE{6,503) 503 FORMAT('0»,'NEW SOLIDS INPUT ANALYSIS (WGTX)») WRITE (6,501) V(2) ,V (3) ,V(4) ,V (5) ,V{6) 504 FORMAT ('MO=«,F7.3,2X,»FE=',F7.3,2X0 »CU=% F7.3,2X„ 1 'INSOL= «„F7.3,2X, <,S=» , F7. 3) WRITE (6,505) 505 FOBMAT{9 0','INPUT SOLUTION•) -166-WRITE (6,506) 506 FORMAT (»+«,» «) WRITE(6,507) V(7) ,V (8) 507 FORMAT ("SOLUTION FLOWRATE (L/MIN) =0,F7.2,4XC8 DENSITY (G/L) = 8 ,F8» 2) HRITE(6,508) . 508 FORMAT(*0«,'LEACH SOLUTION ANALYSIS (G/L)9) WRITE(6,509) V (9) , V (11) , V (12) ,V (10) ,V (13) 509 FORMAT(«MO=9,F8.3,3Xff9 FE=80F8.3,3X, 8CU=',F8.3,3X„•S=8,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) 102 FORMAT (8G10. 5) READ(5„100) N 100 FORMAT (11) K=1 300 CONTINUE IF(K.GT.N) GO TO 302 READ(5,101) NS V , VOLUME 101 FORMAT(I1^9X,G10.1) J=1 301 VOL (K) = VOLUME WRITE(6,120) K,VOL{K) 120 FORMAT(*0STAGE NUMBER9 ,12 , 5X F1 2. 1, 2X ,» LITRES« ) J=J+1 K=K+1 IF (J.GT.NSV) GO TO 300 GO TC 301 302 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 465 FORMAT (11) 464 FORMAT(8G10.4) READ (5, 103) IT 103 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 - JLD/ -V¥(I)=V(I) 290 CONTINUE BT=1.9871D0*T ARRMC=DEXP {-LC (5)/RT) ARE ECP= DEXP (-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) 298 CONTINUE DO 292 1=1,8 !<I) = 1 292 CONTINUE RDIV=2.0 DO 2S6 J=1„IT M=J/KK LL=KK*M MO£EC=BX<1) *RX<2) RXX(1) = BX(1) BXX(2)=BX(2) CALL CONHIX DO 324 K=1,N IP (K. NE. 1) GO TO 282 EO 281 1=8,13 V(I)=V7(I) 281 CCRTINUE 282 CONTINUE CALL LEACH(&299) 324 CONTINUE CALL LEABAL CALL FILTER CALL REGB CALL REGRSP CALL REFLOT CALL RECXC IF (J. EQ, 1) WRITE (6a LISTRX) IF(LL.LT.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) ) } IF(TCLC (I) cLT.TOL) GO TO 293 IF (I (I) .M-E. 1) GO TO 295 BXCLD (I) =RX (I) BXCCLD{I) = HXC(I) RX (I) =0 . 999D0*RX (I) L(I)=L(I) +1 GC TO 293 295 CONTINUE B (I) = (RX (I) -RXOLD (I) } / (RX (I) -RXC (I) -RXOLD (I) +RXCOLD (I) ) IF (I. NE.3) GO TO 278 IF (RXC (I) .LT. 1. D-05) R(I)=0.D0 2 78 CCNTINUE IF (I.NE.4) GO TO 277 IF <RXC (I) . LT. 1. D-05) R(I)=0,D0 277 CONTINUE IF (DABS {R (I) ) . IT. RMAX) GC TO 294 - 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)=0.75 279 CONTINUE ~ Abl 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) ,LT.0,05o AN Do TOLC (I) oGToQ.015} fiDIV=1„5 IF (TOLC (1) o LT. 0.015) RDIV=1.0 280 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) 294 CONTINUE RXOLD (I) = BX (I) RXCCLD(I)=RXC(I) BX (I)=BX (I) - (RX (I)-RXC (I) ) *R (I) 1(I)=L(I)+1 293 CONTINUE IF(LL.LI.J) GO TO 284 WRITE(6,LISTI) 284 CONTINUE IF (J.NE. 1) GO TO 286 LSUM=0 DO 287 1=1,8 LSUM=LSUM+L (I) 287 CONTINUE IF(J.EQ.1) BRIT£(6,LISTI) IF (LSUM, EQ. 8) GO TO 288 GO TO 2 96 286 CONTINUE SUMR=0<,D0 DO 289 1=1,8 SUMR=SUMH*DABS (R (I) ) 289 CONTINUE IF (SUMR.EQ.O.) GO TO 288 296 CONTINUE DO 291 1=1,8 IF (TOLC (I) . GT. TOL) GO TO 299 291 CONTINUE 288 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) 276 CONTINUE WRITE(6,LISTRX) WRITE(6,LISTI) CALL OUTPUT CALL OUTPRT 299 CONTINUE WRITE(6,LISTI) WRITE (6,LISHXC) WRITE (6,LISTRX) STOP END £ ***************** SUERCUTINE CONMIX C 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) -169-CCMMON/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 Q ***** ***************#*** SUEBOUTINE LEACH (*) C SUBROUTINE TO SET UP LEACH CONDITIONS FOR EACH STAGE AND C 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 SX(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) _ 1?0 325 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, 19-A(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 IF (K.NE. 1) GO TO 326 DO 350 1=1, 18 Y(I,1)=G (I) 350 CONTINUE GO TO 333 326 CONTINUE IF (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 IF (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 DO 316 1=1,18 Y (I, 1) = CSFPIT (K , I) *X (I) - 1/1 -316 CONTINUE 317 CONTINUE 333 CONTINUE - 171 -353 CONTINUE 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) IF(X(13)•LT.0.) X(13) = 1.D-07 IF(X(14)0LT.0.) X(14) = 1oD-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 DO 356 1=1,18 CSF (K,I)=SX (K,I) /SX (K-1 ,1) 356 CONTINUE IF (K.EQ.1) GO TO 315 DO 314 1=1,18 CSFPIT(K,I)=SX (K,I) /SX (K-1,1) 314 CONTINUE 315 CONTINUE IF (K.N E. 2) GO TO 320 DO 319 1=1,18 GF (I) = CSF(K,I) 319 CONTINUE 320 CCNTINUE 355 CONTINUE SNR (K) =100. DO* (MONE0-X ( 1) *X (2) )/MONEW SfiR{K)=10Q„D0*{MQREC-X (9) *X (10) )/MOREC 329 CONTINUE WRITE (6,331) K, IF AIL 331 FOR MAI(°0LEACH FAIL CGDE FOR STAGE (8 ,11 , ") = 8 , 110) IF<J.EQ«1) WEITE(6,LISTX) IF (LL.LT.J) GO TO 321 WRITE (6 ,LISTX) 321 CCNTINUE IF (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) RETURN 1 334 CONTINUE RETOEN ~ 1?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 IF (FRACL.LT.O.) FRACL=1oD~09 FRACLR= (MOREC-X (9)*X (10) )/MOREC IF (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 IF (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 IF 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) IF (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) /(55. 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 F {S)-X (6) -0. DO IF <X(9).LT.0.) GO TO 19 F (10)=X (12) -LC{1) *?OL(K) *X(11) *ACIDN**2 1*(1.6683D0*X (10) *X (9)/(LC (15) *V (7)) ) *ARRH0 -173-GC TO 20 19 CONTINUE F(10) = X (12)-0„D0 20 CONTINUE F(11)=X(17)-G..D0 F(12)=X(18)-0.D0 16 CCNTINUE C SURFACE AREA FACTOR TERMS -• M0S2-NEW,MOS2-BECYCLE IF(FRACL0LT0LC(13)) GO TO 11 F (13) = X (8) -DEXP (-LC (9) * (FRACL**LC (10) ) ) GO TO 12 1 1 CONTINUE F(13)=X (8) -LC(11) +LC (1 2) *FRACL 12 CCNTINUE F(14)=X (11) -RX (7) *DEXP (-BX (8) *LC(U) *FRACLR) REIUBN END C ******************************************************#**** SUEEOUTINE LEABAL C CALCULATION OF VARIABLES NOT DIRECTLY DETERMINED BY C THE LEACH EQUATIONS IMPLICIT BEAL*8 (A-H,0-Z) DIMENSION V (13) „VL{6) ,X (18) ,XX(7) DIMENSION RX(8),RXX(2) LOGICAL SWCHA CGMaCN/AREAI/V^VLyRX^RXX CCMMCN/AREA4/X,XX C0MMCN/AREA21/SWCHA NAMELIST/LISTXX/XX R£AL*8 MODIS C CALCULATE FINAL STAGE OUTPUT VALUES - 1STOTAL SOLIDS FLOE BATE C 2:MC IN SOLIDS 3;SI02 IN SOLIDS UtS IN SOLIDS 5:S IN LIQUID C 6: WEIGHTED AVERAGE AREA FACTOR 7:T0TAL FRACTION OF MO LEACHED XX (1)=X (1)+X (9) XX (2)= (X(2) *X(1)+X(10)*X (9))/XX(1) XX (3)=VL (5) *VL (1)/XX (1) HCDIS=VL (2) *VL (1)-XX(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) -SULEIS)/XX (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) = (VL(2)*VL(1)-XX (2) *XX(1) ) / (VL (2) *VL (1)) IF (SWCHA) WBITE (6,LISTXX) JSETURN • END Q *********************************************************** SUBROUTINE FILTER IMELICIT 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 C FILTER - SOLIDS/LIQUID SEPARATION AFTER FINAL LEACHING STAGE C 1:T0TAL SOLIDS MASS FLOW 2:MO 3:FE 4;CU 5:SI02 6; S 7; A8 FX- (1) FX (2) FX (3) FX (4) XX (1) XX (2) X (13) *X (1) /XX (1) X(14)*X(1)/XX{1) - 174 -FX (5) =XX (3) FX(6)=XX(4) FX(7)=XX(6) 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 * ********************************************************** SUEBOUTINE BEFLOT C FLOTATION MODEL TO CALCULATE RECOVERIES, MASS FLOWHATES AND C 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 *" 75 " 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 { (PFLOfl-10. 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) 460 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) 461 CCNTINOE RECCPY=0.D0 DO 462 1=1,NP RCPY (I) = (FC (3) *fiT(I)/(1.D0 + FC (3) *RT (I) ) ) * (1. DO-RECCPY) BECCPY=BECCPY*RCPY(I) 462 CONTINUE BECSIL=0.DO DO 463 1=1 ,NF RSIX (I)=~(FC (4) *BT(I)/(1.B0+FC (4) *BT (I) ) ) * (1 .DQ-RECSIL) RECSIL=RECSIL+RSIL(I) 463 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 + 0e 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)-RFX(1) FIX (2)= (0.5994D0*GFX (2)-RFX (2) *RFX{1) )/FTX(1) FTX (3) = (GFX (5) -R FX ( 5) *RFX (1) ) /FIX (1) IF (SWCHA) WRITE (6 , RECOVS) IF (SWCHA) WRITE{6,PLOTS) IF (SWCHA) WRITE (6,TAILS) BETUEN END Q ****************************************** SUBROUTINE RECYC C COMBINATION OF REFLOTATION CONCENTRATE AND SOLIDS DIRECTLY C RECYCLED FEOM BEGBINDING IMPLICIT 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 NAMELIST/LISBXC/BXC RXC {1) = BGX (1) + BFX (1) DO 390 1=2,6 - 176 -RXC {I)= (RGX (1) *RGX(I) *RFX(1)*RFX Jl) )/RXC ( 1) 390 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) 391 CCNTINUE RETURN END Q * ********************************************************** 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)/100. 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+273015 . 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 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) -177-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/SNRP 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) C REFLOTATION CALCULATIONS RECMO=100. D0*R£CMO RECPY=100.D0*RECPY RECCPY=100.DO*RECCPY _ 178 -RECSIL=100.D0*RECSIL RFX (1) = 0. 8640D-01*RFX (1) DO 703 1=2,6 RFX (I) =100.D0*RFX(I) 703 CONTINUE FTX(1) = 0.8640D-01*FTX(1) FTX (2) = 100. D0*FTX (2) FTX (3) = 100. D0*FIX (3) C MOLYBDENUM TOLERANCE CALCULATIONS MCNEW=86.40D0*MONEW MOTOL= (1O.D0*FTX{1) *FTX(2) -J-EXTRN-MQN35J)/MONEW C RECYCLE COMBINATION CALCULATIONS RXC (1)=0.8640D-01*SXC(1) DO 704 1=2,6 RXC (I) =100.DO*RXC (I) 704 CONTINUE RETURN INC SUEEOUTINE OUTPRT C CONTROL CONVERGED OUTPUT PRINTING IMPLICIT REAL*8 (A-H,0=Z) REAL*8 MONEW,MOTOL DIMENSION XX (7) ,FX<7) , GX (8) ,GC $2) ,RGX (6) ,GFX J6 ) ,RFX{6) DIMENSION FTX(3) ,RXC (8) ,JC(4) ,VOLJ9) , X {1 8) ,LC (15) DIMENSION SX (9,18) , CSP (9,18) DIMENSICN SNB (9) ,SRR (9) ,SR (9) DIMENSION V(13) ,VL(6) ,BX (8) ,RXX(2) COMMCN/AREA1/V,VL,RX,RXX COMBCN/AREA2/MONEW,MOREC,LC COMMCN/AREA3/VOL/T,K CCMMCN/AREA4/X,XX COMMON/AREA5/FX,GX CCMMCN/ABEA7/BGX,GFX CCMMCN/AREA8/RFX,FTX,RXC COMM0N/AHEA11/N,LL,J C0MM0N/AREA12/SNR,SRB,SB,SX CCMMCN/AREA13/EXTRN,RECRAT,PULPD,MOTOL COMMCN/AREA14/RECMO,RECPY,RECCPY,RECSIL COMHCN/AREA15/TMGRND CCMMCN/AREA18/CSF WRITE(6,801) N 801 FOEMAT{ 80 8 , 8 FINAL LEACHING STAG I{0,11,') OUTPUT') WRITE (6,807) 807 FORMAT + * , 8 ; ') WRITE (6,843) EXTRN 843 FORMAT ('.EXTRACTION OF MO TO SOLUTION (KG/DAY)= 8 ,F7. 1) WRITE (6,854) UONEW 854 FORMAT(8 NEW INPUT MOLYBDENUM TO LEACH(KG/DAY) = 8,F7.1) WRITE(6,8 55) MOTOL 855 FORMAT(8 MOLYBDENUM FRACTIONAL TOLERANCE= *,F8.5) WRITE (6,850) RECRAT 850 FOEMAT( 80 8 , 8 SOLIDS RECYCLE RATIO=8,F7.3) WRITE(6,851) PULPD 851 FOE MAT {8 0 * , 8 STAGE 1 INPUT PULP DENSITY (G/L) =' , F7 . 2) IF (PULPD.LT.550.0) GO TO 852 WHITE (6,853) 853 ECEMAT('WABNING:INPUT PULP DENSITY HIGH8) 852 CGNTINUE - 179 -WRITE (6,802) 802 FOEMAT( 8 0 8 , 8 LEACH SOLIDS BESIDUE FLOW BATE (TON NES/DA Y) 8) WBITE (6, 803) XX (1) , SX (N , 1) ,SX (N , 9) 803 FORMAT ("TOTAL SOLIDS=8,F8.3,»NEB SOLIDS= * ,F8e 3 ,0 RECYCLE SCLIDS=9, 1F8.3) WRITE(6,804) 804 FORMAT(8 0 8,8 TOTAL OUTPUT SOLIDS ANALYSIS (WGT%)') WRITE (6,805) XX (2) , FX (3) ,FX (4) ,XX (3) ,XX (4) 805 FORMAT (9MO=8 ,F7. 3,2X,0F_=8,F7, 3,2X5, °CU=8,F7.3,2X, 8INSOL=8 ,F7. 3 1,2X,8S=8,F7.3) WRITE (6,806) 806 FORMAT ( 80 8 ,'NEW SOLIDS OUTPUT ANALYSIS (WGT%) 0•) WBITE{6,808) SX(N,2) 808 FOBMAT{'MO=«,F7o3) WRITE (6,809) 809 FOEflAT('0','RECYCLE SOLIDS OUTPUT ANALYSIS (BGT%) 3 ) WRITE(6,810) SX(N,10) 810 FOE MAT ( 8MO=8 , F7. 3) WHITE (6,839) 839 FGEMAT('08,"OUTPUT LEACH SOLUTIGN8) WRITE (6,840) SX(N,5) 840 FORMAT("SOLUTION DENSITY (G/L)=8,F8.2) WRITE(6,841) 841 FOEMAT ( 80 8 ,8 LEACH SOLUTION ANALYSIS {G/L) s) WBITE (6,842) SX (N,3) ,SX (N, 15) ,SX (N, 16) ,XX (5) ,SX (H,4) 842 FOEMAT(8MO=8,F8.3B3X,9FE-8,F8.3,3X0 8CU=8,F8.3,3X,9S=8*F8„3e3Xg 18HN03=8,F8.3) WBITZ(6,811) 811 FORliAT { r0 ' , 8 STAGE CUMULATIVE RECOVERIES OF MO <%HO DISSOLVED) 8) WBITE(6,813) 813 FORMAT ( 10X,8 TOTAL8,10X,8NEW SOLIDS8,1 OX,8 RECYCLE SOLIDS') DO 812 K=1,N WRITE(6,814) K,SB (K) ,SNR{K) ,SRfl (K) 814 FOEJaAT(8STAGE',I1,3X,F7a3,10X,F7o3!, 14X,F7.3) 812 CONTINUE WRITE(6,844) IF (N.EQe1) GO TO 848 844 FORMAT(8~B,"CALCULATED STAGE FACTORS - FOR STAGES 2 TO N8) EO 845 K=2,N WRITE(6,847) K 847 FOBMAT ("STAGE8 ,11) WRITE(6,849) (CSF (K,I) ,1= 1 , 18) 849 FORMAT(18F5.2) 845 CGNTINUE 848 CONTINUE WRITE(6,815) 815 FOEMAT(808,*R£GBIND PARAMETERS8) WBITE(6,816) 816 FORMAT ( 8+ 8 , 8 ______• 0) WRITE(6,817) TMGRND 817 FCBMAT(80','MEAN BESIDENCE TIME IN GRINDING MILL(MINUTES)-9eF7„ 2) WRITE(6,818) 818 FORMAT(808,'RECYCLE AREA FACTOR PARAMETERS') WRITE{6,819) GX(7),GX(8) 819 FOBMAT(8B1=8,F8.5,» B2=',F8.5) WRIT£{6,820) 820 FOEMAT('0','STREAM SPLIT - SOLIDS FLOWRATES (TONNES/DAY)') WRITE{6,821) RGX (1) ,GFX (1) 821 FORMAT('DIRECT GRIND TO RECYCLE= 0„F8,3,•GRIND TO FLOTATION=0,F8.3) WRITE (6,822) 822 FORMAT{'0*,'FLOTATION RESULTS 8) WRITE (6,823) " 180 " 8 23 FORMAT ( ' +' „ « ,_. 9) BBITE(6,824) 824 FORMAT('0',»MINERAL RECOVERIES {%)•) WRITE(6,825) .RECMO, RECPY,RECCPY,RECSIL 825 FORMAT (' MOS2= 9 , F7. 3, SFES2= ' ,F7„ 3 , SCUFES2= *, F7. 3,•INSOL=',F7.3) WRITE(6,826) RFX{1) 826 FORMAT{'0s,'MASS FLOWRATE OF CONCENTRATE (TCNNES/DAY)=',F8»3) WRITE(6,827) 827 FORMAT ( '08 , ' FLOTATION CONCENTRATE ANALYSIS (WGT%)8) WRITE(6,828) RFX (2) ,HFX (3) ,RFX (4) 0RFX (5) , RFX (6 ) 828 FORMAT('MO=«,F7.3, 8 FE=» ,F7D 3,.'C0=« ,F7, 3, ' INSOL=«, F7. 3,'S=8,F7.3) WRITE(6,829) FTX(1) 329 FORMAT {'0* ,' MASS FLOWRATE OF FLOTATION TAILS (TONNES/DAY) = 6 , F8= 3) WBITE(6,830) 830 FORMAT(»0°,'FLOTATION TAILS ANALYSIS (WGT 56) *) WRITE (6,831) FTX(2) 831 FORMAT(«MO=',F7.3) WRIIE(6,832) 832 FORMAT(*0»,'CALCULATED VALUES FOR RECYCLE SOLIDS') WEITE(6,833) 833 FORMAT ( 8 , : _„_iI) WRITE (6,834) RXC(1) 834 FOFMAT('0s,'RECYCLE SOLIDS MASS FLOWRATE (TONNES/DAY) = *,F8» 3) WRITE (6,835) 835 FORMAT('0','RECYCLE SOLIDS ANALYSIS (WGT%)«) BRITE(6,836) RXC(2) ,RXC (3) ,RXC (4) ,BXC J5) ,RXC (6) 8 36 F'OHMAT ( »MO=* ,F7.3, * FE= 9 ,F7. 3, «C0 = " ,F7„3, «INSOL = 8F7'. 3 , « S= 9 ,F7 „ 3 ) WRITE(6,837) 837 FORMAT(°09,'RECYCLE AREA FACTOR PARAMETERS') WRIT£(6,838) RXC (7) ,RXC (8) SBITE(6,838) RX(7),RX<8) 838 POEMAT(8B1=»ffF8.5,0B2=',F8.5) DO 856 K=1,N WRITE(6,857) K 857 FOEMAT(*08p'STAGE{° ^11,') X VALUES") DO 858 1=1,18 WRITE(6,859) SX(K,I) 859 FORMAT (GT2.5) 858 CONTINUE 856 CONTINUE RETURN END - 181 -APPENDIX D OTHER SPECIFIC PARAMETERS USED IN MODEL - by analysis of Report 7 and 8 data [4] using initial calculated rates of reaction. A' = area factor for grinding mill input A" = area factor for ground solids Initial leach rates (at 1 min.) r' a A' (1) Grind Constant k' g = 0.0570 sec -1 it Ratio: A^ A' A' + k t g » 4.43 A' = 3.43 A k 3.43 A' g t g = k' A' g = 0.0570 A' - 182 -(2) Flotation rates constants: MoS2 = 1.0 min 1 FeS2 = 0.5* CuFeS2 = 0.5* Insol = 0.10 * estimates - may be some control depending on desirability recyling FeS~ and CuFeS„.
- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Development of a mathematical model of a molybdenite...
Open Collections
UBC Theses and Dissertations
Featured Collection
UBC Theses and Dissertations
Development of a mathematical model of a molybdenite leaching process Parsons, Geoffrey Joseph 1978
pdf
Page Metadata
Item Metadata
Title | Development of a mathematical model of a molybdenite leaching process |
Creator |
Parsons, Geoffrey Joseph |
Date | 1978 |
Date Issued | 2010-02-26T23:59:45Z |
Description | A mathematical model has been developed for the more critical 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 pilot- or commercial-scale plant. Simulation of leaching is based on mass balancing with determination of reaction rates from the individual components of the rate equations. The rate of leaching of molybdenite is 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 is based on a combination of theory and empiricism while the flotation model is derived from the simple first-order rate equation. The simulation is still subject to some uncertainty since verification is not possible at this stage of process development. However, the model effectively accounts for the complex system 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 all considered. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Collection |
Retrospective Theses and Dissertations, 1919-2007 |
Series | UBC Retrospective Theses Digitization Project |
Date Available | 2010-02-26 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0078749 |
Degree |
Master of Applied Science - MASc |
Program |
Metals and Materials Engineering |
Affiliation |
Applied Science, Faculty of Materials Engineering, Department of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
URI | http://hdl.handle.net/2429/21162 |
Aggregated Source Repository | DSpace |
Download
- Media
- UBC_1978_A7 P37.pdf [ 9.32MB ]
- [if-you-see-this-DO-NOT-CLICK]
- Metadata
- JSON: 1.0078749.json
- JSON-LD: 1.0078749+ld.json
- RDF/XML (Pretty): 1.0078749.xml
- RDF/JSON: 1.0078749+rdf.json
- Turtle: 1.0078749+rdf-turtle.txt
- N-Triples: 1.0078749+rdf-ntriples.txt
- Original Record: 1.0078749 +original-record.json
- Full Text
- 1.0078749.txt
- Citation
- 1.0078749.ris
Full Text
Cite
Citation Scheme:
Usage Statistics
Country | Views | Downloads |
---|---|---|
United States | 10 | 0 |
China | 6 | 11 |
Iran | 5 | 2 |
Russia | 2 | 0 |
India | 1 | 0 |
Ukraine | 1 | 0 |
Mexico | 1 | 0 |
Turkey | 1 | 0 |
City | Views | Downloads |
---|---|---|
Unknown | 8 | 2 |
Ashburn | 7 | 0 |
Shanghai | 2 | 0 |
Tiran | 2 | 0 |
Changsha | 2 | 0 |
Shenzhen | 1 | 11 |
Boardman | 1 | 0 |
Plano | 1 | 0 |
Mountain View | 1 | 0 |
Tunceli | 1 | 0 |
Beijing | 1 | 0 |
{[{ mDataHeader[type] }]} | {[{ month[type] }]} | {[{ tData[type] }]} |
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
async >
</script>
</div>
Our image viewer uses the IIIF 2.0 standard.
To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0078749/manifest