A MATHEMATICAL MODEL OF THE NICKEL CONVERTER

Transcription

1 A MATHEMATICAL MODEL OF THE NICKEL CONVERTER ANDREW KEVIN KYLLO B.A.Sc, The University of British Columbia, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES METALS AND MATERIALS ENGINEERING We accept this thesis as conforming to the required standard i THE UNIVERSITY OF BRITISH COLUMBIA January 1989 Andrew Kevin Kyllo, 1989

2 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 or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without permission. my written Department of The University of British Columbia Vancouver, Canada Date i r :\ m<\ DE-6 (2/88)

3 ABSTRACT A mathematical model of the nickel converter has been developed based on the assumption that the converting reactions pass through a finite series of equilibrium steps. The model predicts the bath temperature and the composition of the three phases present. Detailed data collected during in-plant trials are used to test the validity of the model predictions. The model is found to give relatively accurate predictions for the first blows of a converting charge, but overpredicts both temperature and iron removal during the last blows. The errors in the last blows are expected to be caused by the converting reactions coming under liquid phase mass transport control. An analysis of some of the more important variables in a converter operation indicates that, according to the assumption of equilibrium, there is very little that can be done to chemically improve the converting process. ii

4 TABLE OF CONTENTS Abstract ii Table of Contents iii List of Tables vi List of Figures viii Nomenclature xi Acknowledgement xii 1.0 Introduction Literature Review Converter Modelling Converter Operation Impurity Distribution Thermodynamics of the Condensed Phases Matte Thermodynamics Slag Thermodynamics Objectives Model Development Introduction Heat Balance Compositional Calculations Model Operation 45 iii

5 5.0 Model Validation General Mass Balance Modelling of Plant Trials Discussion Sensitivity Analysis Model Operating Parameters Converter Operating Parameters Converter Inputs Thermodynamic Data Other Variables Validity of the Equilibrium Assumption Analysis of Nickel Converter Operation Varying Matte Composition Converting High Grade Mattes Converting Sulphur Deficient Mattes Iron and Sulphur Elimination Oxygen in Matte Effect of Carbon Addition Operating Efficiency Conclusions and Further Work Bibliography Appendix 134 iv

6 10.1 Plant Trials In] ection Equipment 136 v.

7 LIST OF TABLES Table II-I Reported activity coefficients of nickel oxide in 19 slags Table IV-I Converter dimensions and refractory data 27 Table IV-II Integrated values of C P. for use in equation 4.9.(64] 29 Table LV-III Heat of formation values used in equation 4.13.[64] 31 Table rv-iv Values of constants used to calculate heat capacity. [64] 34 Table IV-V Constituents of the phases in the converter. 36 Table TV-VI Equilibrium equations used in the compositional calculations 38 Table IV-VII Mass balance equations used in the compositional calculations 39 Table IV-VIII Free energy equations for the reactions used in the mass balance model.[9,44,64] 41 Table IV-IX Activity coefficients of the non-gaseous constituents 42 Table IV-X Standard assays (weight %).[66] 44 Table V-I Details of charges modelled 54 Table V-II Details of fitting carried out 56 Table V-III Comparison of model predicted matte compositions with assays taken at the end of the stated blow 64 vi

8 Table V-LV Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 98, May Table V-V Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 105, May Table V-VI Comparison of model predicted slag compositions with assays taken at the end oftineblow, (weight fraction), #3 converter Charge 106, May Table V-VII Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 107, May Table V-VIII Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 108, May Table V-IX Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 109, May Table V-X Flux assays for charges 105 to 109, May 1988, (weight fraction) 71 Table VI-I Standard charge used in sensitivity analysis. 73 Table VI-II Variables tested in sensitivity analysis 74 Table VI-III Scrap compositions used in the sensitivity analysis 75 Table VI-IV Units of measurement of converter inputs and outputs with approximate conversion factors used in the model 75 Table VII-I Compositions of mattes used in analysis (weight fraction) 105 vii

9 LIST OF FIGURES Figure 1.1 Schematic flow diagram of nickel smelting routes.11] 2 Figure 4.1 Flow chart of the converter model 47 Figure 5.2 Iron in matte versus matte grade, comparison of model predictions with plant average data 50 Figure 5.3 Schematic showing the limiting converting path in the iron-nickel-sulphur system. [2] 51 Figure 5.4 Comparison of model predicted bath temperature with plant data, #3 converter Charge 98, May Figure 5.5 Comparison of model predicted bath temperature with plant data, #3 converter Charge 105, May Figure 5.6 Comparison of model predicted bath temperature with plant data, #3 converter Charge 106, May Figure 5.7 Comparison of model predicted bath temperature with plant data, #3 converter Charge 107, May Figure 5.8 Comparison of model predicted bath temperature with plant data, #3 converter Charge 108, May Figure 5.9 Comparison of model predicted bath temperature with plant data, #3 converter Charge 109, May Figure 6.1 The effect of time step on model predicted bath temperature and weight fraction iron in matte 77 Figure 6.2 Effect of oxygen efficiency on model predicted bath temperature and weight fraction iron in matte 79 viii

10 Figure 6.3 Effect of bath emissivity on model predicted bath temperature and weight fraction iron in matte. 80 Figure 6.4 Effect of refractory thickness on model predicted bath temperature and weight fraction iron in matte 83 Figure 6.5 Effect of water in flux on model predicted bath temperature and weight fraction iron in matte 85 Figure 6.6 Effect of water in scrap on model predicted bath temperature and weight fraction iron in matte 86 Figure 6.7 Effect of weight of matte charged on model predicted bath temperature and weight fraction iron in matte 88 Figure 6.8 Effect of scrap composition on model predicted bath temperature and weight fraction iron in matte 89 Figure 6.9 Effect of NiS activity coefficient on model predicted bath temperature and weight fraction iron in matte 92 Figure 6.10 Effect of NiS activity coefficient on model predicted weight fractions of nickel and sulphur in matte. 93 Figure 6.11 Effect of initial temperature on model predicted bath temperature and weight fraction iron in matte 96 Figure 6.12 Effect of air rate on model predicted bath temperature and weight fraction iron in matte 97 Figure 6.13 Effect of oxygen enrichment on model predicted bath temperature and weight fraction iron in matte 99 Figure 6.14 Effect of oxygen enrichment on model predicted sulphur dioxide content of the off-gas 100 Figure 6.15 View of the inside back wall of a converter showing colour variation between matte and slag 102 ix

11 Figure 7.1 Effect of using high grade matte on model predicted bath temperature and weight fraction iron in matte 107 Figure 7.2 Effect of using high grade sulphur deficient matte on model predicted bath temperature and weight fraction iron in matte 109 Figure 7.3 Effect of using high grade sulphur deficient matte on model predicted partial pressure of sulphur dioxide Ill Figure 7.4 Effect of initial bath temperature on the relative rates of iron and sulphur elimination 113 Figure 7.5 Effect of oxygen enrichment on the relative rates of iron and sulphur elimination 114 Figure 7.6 Effect of matte type on the relative rates of iron and sulphur elimination 115 Figure 7.7 Variation of iron-to-sulphur ratio with weight percent iron in matte. Regression line from model simulation of plant trials, points from plant data 117 Figure 7.8 Oxygen in matte versus matte grade 120 Figure 7.9 Effect of carbon addition at 15 kg min" 1 on model predicted bath temperature and weight fraction iron in matte 122 Figure 7.10 Effect of carbon addition at 15 kg min" 1 on model predicted nickel in the slag and partial pressure of sulphur dioxide 123 Figure Al Schematic layout of coke injection system x

12 NOMENCLATURE subscripts A Area (m) 2 acc Accumulation a,b,c,d Constants B Bath C P Specific heat (Jkg^K 1 ) c Converter e a Heat balance tolerence cb Converter barrel e 2 Compositional calculation tolerence ce con k Thermal conductivity (Wm^K" 1 ) ext External Converter endwall Consumption L Length (m) G Gas phase M Moles H Hood m Molecular weight (g mol" 1 ) int Internal q Heat loss (kj) M Matte phase R Radius (m) m Mouth T Temperature (K) 0 Old t Time (min) P Phase W Weight (kg) rad Radiation w Interaction parameter rea Reaction X Mole fraction ref Refractory X Thickness (m) SI Slag phase AH f Heat of formation To Total y e Activity coefficient Bath emissivity P Density (kgm 3 ) a Stephan-Boltzman constant (Wm 2 K 4 ) xi

13 ACKNOWLEDGEMENT I would like to acknowledge the financial support for this project from Inco Ltd., as well as personal support from the Cy and Emerald Keyes Foundation. For their assistance during the plant trials I would like to thank the staff of the Copper Cliff smelter, in particular Dave Hall, Ron Falcioni, Ahmed Vahed, and Sam Marcusen. I would also like to thank Dr. Greg Richards for guidance, and my wife for proof-reading and patience. xii

14 1 INTRODUCTION 1 INTRODUCTION There are three different routes used in the pyrometallurgical processing of nickel sulphide concentrates. The converting step is present in each route as the final stage before matte separation or refining. The composition of the feed to the converter will depend on the smelting furnace used, as well as on the original concentrate composition. Each of the processing routes is comprised of three unit operations.il] A schematic layout of each route is given in figure 1.1, although there are operating differences between sites using the same basic route. The main difference between routes is in the choice of the smelting furnace used. If a reverberatory furnace, as at Inco's Copper Cliff operation, or an electric furnace, as at Inco's Thompson operation, is used the first stage is roasting. This is carried out either in a multiple-hearth or fluidized-bed roaster. The roasting stage drives off a large proportion of the sulphur from the concentrate. This is caused by the oxidation of iron sulphide to magnetite. The off-gas from fluid bed roasters is often sent to an acid plant, but the sulphur concentration in the off-gas from multiple hearth roasters is not usually high enough for this. 1

15 1 INTRODUCTION REVERBERATORY FURNACE e.g. Inco - Copper Cliff Concentrate + Flux calcine c matte 1 Bessemer matte to further processing Multiple Hearth Roasters Reverberatory Furnace Converter ELECTRIC FURNACE e.g. Inco - Thompson Falconbridge.[Concentrate + Flux calcine 1 1 Bessemer matte to further processing Fluidized Bed Roasters Electric Furnace Converter FLASH FURNACE e.g. Western Mining BCL Dry concentrate + Flux + Fuel matte Bessemer matte to further processing Rotary Dryer Flash Furnace Converter Figure 1.1 Schematic flow diagram of nickel smelting routes.[1] 2

16 1 INTRODUCTION The roasted concentrate is fed to either the reverberatory furnace or the electric furnace for the smelting stage. In this stage the magnetite formed in roasting is removed in the slag, primarily by the reaction 3Fe FeS -> lofeo +S0 2 - l - l thus further removing iron sulphide from the matte. The matte produced in the electric furnace usually contains much less sulphur than mattes from either the reverberatory or flash furnaces, due to the more reducing nature of the electric furnace. If a flash furnace is used for smelting concentrates, as, for example, by Western Mining at Kalgoorlie or by B.C.L. in Botswana, the first stage is drying the concentrate. In this stage the concentrate is also mixed with flux and fuel. The more oxidizing conditions prevalent in the flash furnace tend to produce a higher grade matte than the reverberatory or electric furnaces. Therefore, the composition of the matte fed to the converter varies widely between nickel smelters. The converting process is primarily the selective oxidation of iron from the matte. The heat for the process is provided by the reactions involved, and is generally more than is required to make up for heat losses. Cold materials are added to regulate the temperature, and siliceous flux is added to form a fayalite 3

17 1 INTRODUCTION slag. The end product is a low iron, copper-nickel sulphide matte known as Bessemer matte. The amount of copper in the matte depends on the initial copper level in the concentrate, and in some operations is negligible. Bessemer matte may also contain cobalt and precious metals which can be recovered in the refining stage. The production of nickel metal from Bessemer matte by continued blowing of air, as used for copper production, is only thermodynamically possible at temperatures which are above the safe operating temperature of a standard converter. [2] Nickel converting is a batch operation consisting of a series of charging, blowing and skimming steps. Each complete cycle is known as a 'charge', with each charge being divided into a number of 'blows'. The nature of the process is such that no two charges will be the same. The composition of the input materials changes between charges and throughout each charge. The air rate to the converter also varies during the blow. At the beginning of the charge the converter will usually contain i some semi-solid 'mush'. This is the final slag from the previous charge which was too.viscous to be skimmed. Mush composition varies over a wide range, but generally has a relatively high nickel content. The 4

18 1 INTRODUCTION amount of mush in the converter is not known, but can be estimated from the weight of flux and scrap added to the last blow of the previous charge. The amount of matte initially charged depends on the size of the converter, and to some extent on matte availability. Often some form of cold scrap is added before the first blow. There is no specific time length for any blow, as in most cases the converter is blown until the temperature reaches a specified value. The converter is then taken off stack. A short settling time is allowed before skimming the slag to remove some of the matte which is entrained in the slag. Following skimming, more matte, and possibly scrap, is charged and blowing is recommenced. Flux is usually added immediately following the start of each blow. The amount of flux added is dependent on the size of the converter, but is roughly calculated to achieve a specified silica content in the slag at the end of the blow. The charge-blow-skim cycle is repeated a variable number of times until the iron content of the matte has been reduced to below a specified value, usually five to ten weight percent. In the last two or three blows matte is not usually added, to allow the iron content to drop sufficiently. In the last blow a large amount of cold charge and flux is often added, which makes up most of the mush. 5

19 1 INTRODUCTION Nickel converting, then, is a complex process involving many variables. The qualitative effects of most of these variables are relatively well known, but not necessarily understood. The quantitative effects can only be estimated from historical data. In order to aid in the overall understanding of the converting process a mathematical model of the nickel converter has been developed. 6

20 2.1.1 Converter Operation 2 LITERATURE REVIEW 2.1 Converter Modelling Of the mathematical models published to date which consider the converting process, only two consider the particular chemistry of the nickel converter. The majority of models of converting deal with the distribution of impurities between matte, metal, and slag in the copper converter. Three models attempt to reproduce the overall material balances during the copper converting operation, and of these only one attempts to reproduce the heat balance as well Converter Operation One of the models which considers the converting of nickel mattes calculates only the instantaneous oxidation path in the ternary iron-nickel-sulphur system[2] in equilibrium with a fayalite slag with fixed iron-to-silica ratio. As such it cannot properly be considered a model of the converter. However, it can be used to make some predictions about the operation of the converter, and the effect of some of the variables on the oxidation path. In particular this model introduces the concept of the 'limiting converting path'. This is a compositional path which the converter follows after initially correcting for any sulphur excess or deficiency. The path is dependent on the temperature of the bath, as well as some of the other converting variables, especially those relating to the oxygen content of the gas. 7

21 2.1.1 Converter Operation The second model which considers nickel converting is an empirical model developed at Falconbridge Limited.[3] The compositional variations of the bath are calculated based on curves fitted to plant data. The heat balance is calculated only at the end of each blow. Considering the empirical nature of the model, its predicted results are remarkably accurate. None of the empirical correlations involve a dependence on temperature, suggesting that the converting operation is not particularly sensitive to temperature variations. The model originated by Nagamori and Mackey,[4,5] and further developed by Nagamori and Chaubal,[6-8] concerns the Noranda continuous converting process. This model only calculates the equilibrium composition at a given temperature, partial pressure of sulphur dioxide, magnetite activity, and, in the case of matte-making, matte grade. It does not attempt to model the entire process. Some aspects of the model, however, may be of some interest. The idea of suspension coefficients to allow for mechanical entrapment of matte in slag is introduced.[4] These are numbers which are calculated from assays of matte and slag samples collected from the Noranda Process, and can be used to determine the amount of matte trapped in the slag and vice versa. The suspension coefficients for the nickel converter, however, will be different from those for the Noranda Process, because they are dependent on the slag viscosity, 8

22 2.1.1 Converter Operation composition, temperature, and the degree of mixing in the converter. As the first three of these factors vary considerably during a blow this concept would be difficult to apply to the nickel converter. Nickel is an impurity in the Noranda Process, and so is considered as such in the model.[5] The form of nickel sulphide used, Ni 2 S, was introduced in an earlier discussion of the thermodynamics of continuous converting. [9] This form allows the model[5] to consider the so called 'sulphur deficient' mattes often found in nickel converting. The free energy of formation of Ni 2 S is also given, allowing for its use in the present model. The other model which assumes a constant temperature appears to be more a demonstration of a possible use for the Solgasmix program than a bone jide model. [10] A more recent extension of this model using a modification of Solgasmix has been written to simulate an injection concentrate smelting technique.! 11] It does not include a heat balance as the process is assumed to be isothermal. Experiments were carried out to determine how good the model was in predicting the behaviour of three different concentrates. For the more complex concentrates the model predictions were poor, but were somewhat better for the less complex sulphides. The third model, developed by Goto, has been gradually improved upon over the last fifteen years, most recently being applied to the 9

23 2.1.1 Converter Operation copper flash smelter. [12-16] The mass balance model was developed first. [12] Assuming that the converter is in thermodynamic equilibrium a set of simultaneous equations was developed and solved using a modified form of the Newton-Raphson technique formulated by Brinkley.[17] The activity coefficients required in these equations were derived from published data and experimental work by the authors. The model considered nine elements and nineteen compounds, to give a representation of the distribution of most of the important minor elements present in copper concentrates in Japanese smelters. The second development was the addition of a heat balance model, to complete the representation of the entire converter. [13] The model applied a heat balance to the converter, using the mass balance calculations to derive a heat generation term. An iterative technique was utilized to calculate the temperature change caused by any net heat production during a given interval. Calculations were carried out over a two minute time step throughout the converting cycle, allowing for charging and skimming. It was claimed that the model was able to predict temperature variations fairly well, [13] but no direct comparison with plant data was published, and ho comparison of matte or slag composition was given. More recent developments of the model have included its extension to cover the copper flash smelter, [15] and the addition of a calculation 10

24 2.1.1 Converter Operation of oxygen consumption using kinetic considerations.[16] It should be noted that this last modification is only valid when the converter is under gas phase transport control, and so may not be valid towards the end of the matte blow and blister blow where the kinetics are likely to be under mixed or liquid phase control. A model has been written to calculate the heat losses from an empty Pierce-Smith converter while standing idle.[18] This model indicated that there is a rapid initial heat loss, particularly in the region of the mouth. An idle time of thirty minutes is calculated to cause a temperature drop of about 200 K at a central tuyere, and about 170 K at an end tuyere. The heat losses calculated by this model will probably be greater than those normally seen in practice, as a converter is rarely empty. The presence of molten material will increase the total heat capacity of the system and, hence, reduce the rate of temperature drop. Although the total heat capacity of the bath is approximately half that of the refractory, Bustos et al[ 18] also determined that only six to eight centimetres of the refractory were thermally active. This means that the total heat capacity of the thermally active refractory will be about the same as that of the bath, so the bath will have a significant effect on the cooling rate. Also, the thermal profiles in the refractory 11

25 2.1.2 Impurity Distribution calculated by Bustos et al[18] indicate that the average temperature drop of the thermally active section of the refractory was about 25 K less than that of the surface after 30 minutes Impurity Distribution The more recent papers on modelling of the Noranda Process are primarily concerned with the distribution and volatilization of impurities.[5-8] In particular, a technique to calculate the relative amounts of impurities, including nickel, lost to the off-gas is formulated. From these calculations it has been concluded that approximately one percent of the nickel is lost to the gas during continuous converting. This result is not directly applicable to the Pierce-Smith converter, but does give a rough indication of the amount of dust formed. An attempt to theoretically model the distribution of impurities between matte and bullion in the copper converter using the Temkin model has been carried out. [19] The model gives good results for some of the impurity elements, but is quite poor for predicting nickel and cobalt distributions. Different choices of the sulphide species used for nickel and cobalt in the Temkin model give widely varying values of the distribution coefficient; values which are both higher and lower than those experimentally measured. This tends to indicate the presence of non-stoichiometric nickel and cobalt compounds. 12

26 2.1.2 Impurity Distribution A different model has been developed to predict the amount of metal loss to the slag in both copper[20] and nickel[9] converting. For copper losses both oxidic and sulphidic dissolution in the slag are considered. During the early stages of converting sulphidic losses to the slag predominate. However, they are not easily quantifiable because it is often difficult to distinguish between entrained and dissolved sulphides. In general, sulphidic losses tend to become more significant when there is over five percent iron in the matte; this covers almost the entire period in conventional converting. Modelling of the continuous converting of copper-nickel mattes indicates that to minimize losses to the slag, the final matte must contain at least five percent iron, otherwise a separate slag cleaning step would be required.[9] It is also expected that the sulphidic loss of nickel would be lower than that of copper. [9] The equilibrium calculations required for the Goto model[12] are quite complex. They include both sulphidic and oxidic copper dissolution, as well as the presence of both wustite and magnetite in the matte. Activity coefficients were available or calculable for most of the constituents of the matte and slag. They were not available, however, for sulphides in the slag, and so were estimated. 13

27 2.1.2 Impurity Distribution The predictions made by this model indicate that the majority of oxygen dissolves in the matte as magnetite. It also calculated that there was a gradual increase in sulphidic copper losses with increasing copper in the matte, but oxidic dissolution increases rapidly above fifty weight percent of copper in matte. In this composition range it is also predicted that the majority of sulphur in the slag will be associated with copper losses. Unfortunately an indication of the variation of the total sulphur in slag is not given. [12] 14

28 2.2.1 Matte Thermodynamics 2.2 Thermodynamics of the Condensed Phases Matte Thermodynamics Extensive experimentation has been carried out on the constituent systems of copper-nickel mattes. Most of this, however, has been directed towards the calculation of phase diagrams, and is of limited use to modelling. Due to the complexity of industrial mattes, thermodynamic experiments on them are of limited usefulness without a fairly extensive knowledge of the subsystems of which they are made up. Thermodynamic work on ternary metal-sulphur systems can be used to find approximate activity coefficients for the less abundant species in the matte. In this way, for example, the activity coefficient of CoS can be approximated as 0.4, while those of metallic Co and Fe are in the ranges and respectively. The wide range for the last two values is due to a large sensitivity to temperature variations. [21] The effect of 'dissolved' oxygen on matte thermodynamics has been found to be significant. It has been calculated that the thermodynamic effect of the oxygen in the matte, when combined with the effect of sulphur in the slag, is sufficient to account for all of the copper reporting to the slag in copper smelting.[22] This, in turn, implies that entrainment may not be an important means of copper loss. There is 15

29 2.2.1 Matte Thermodynamics much disagreeament about the amount of entrainment of matte in slag, but it has been reported that about twenty-five percent of the copper losses in reverberatory slag are due to entrainment. [23,24] This result does, however, appear to go against the findings of slag cleaning experiments in which almost sixty percent of the valuable metal was recovered from the slag by settling alone.[25] It has been determined that dissolved copper is precipitated from slags during cooling, [26] implying that tests carried out at room temperature may overestimate the amount of entrainment. The conditions under which settling tests are carried out may also affect the copper solubility in slag, and hence predict entrainment incorrectly. Analyses of industrial mattes indicate that the oxygen in solidified matte is almost entirely in the form of magnetite, but may have some nickel or copper replacing iron in the compound.[27] The theoretical modelling of industrial mattes is not an easy task. The copper-iron-sulphur system has been found to be reasonably described by the Temkin model[28] or the Flood model[29], but mattes involving nickel become more complex. The associated solution model has now been applied extensively to matte systems.[30-43] This model is based on the three-suffix Margules equation 16

30 2.2.2 Slag Thermodynamics \ n n i = ~ X (yv t j + w Jt )Xj + I (WJJ - Zj=l j=l y=lp=l Z;=lp=l where Wy are interaction parameters accounting for the effect of specie i on specie j. The interaction parameters are functions of temperature of the form w,j --1+B.. 1 T As is evident from the equations a large number of fitting parameters are required. These have been derived from a collection of thermodynamic studies of the various systems. Unfortunately this model has not been expanded sufficiently to allow its use for modelling industrial mattes Slag Thermodynamics The thermodynamics of converter slags have undergone much study, and work up to 1980 has been thoroughly reviewed by Mackey.[44] As far as a heat balance is concerned the most important variable in the slag is the wustite to magnetite ratio. The variation of this ratio with oxygen potential is quite well known from equilibrium considerations. Also of interest is the distribution of the valuable metals between matte and slag. In particular their activities as oxides 17

31 2.2.2 Slag Thermodynamics and sulphides in slag are quite important. Almost all experimental work published to date on the solubility of nickel in slags has ignored the presence of sulphur in the slag, assuming that the solubility of nickel sulphides is small. [45-58] The work of Grimsey and Biswas[44-49] has shown that there is a small amount of metallic nickel dissolution as well as oxidic dissolution. They have also reported that y Ni0 = 2.6 at 1573 K in silica saturated slags, [45] and that the addition of lime to the slag decreases nickel solubility. [47] A more recent analysis of their data indicates that the conclusion of the existence of dissolved metallic nickel may have been due to experimental error. [50] A comparison of the published values of nickel oxide activity coefficients is given in table II-I. It is evident that there is little agreement on the actual value of the nickel oxide activity coefficient, but a range of values can be determined, depending on the slag composition. It is important to note that only one of these studies covered a temperature range common in converting. [52] Converter temperatures rarely rise above about 1530 K. A recent study on copper matte-slag equilibrium has reported that the Herasymenko model of an ionic solution can be successfully applied to both copper matte and fayalite slag. [58] This model is similar to the more well known Temkin model, except that it does not 18

32 2.2.2 Slag Thermodynamics Temperature (K) Slag Conditions Ref Silica 45 saturated CaO in fayalite 46 exp(3980/t-1.62) Silica saturated Silica saturated and unsaturated Silica 52 saturated and unsaturated Fayalite Alumina saturated Alumina saturated 55 Table II-I Reported activity coefficients of nickel oxide in slags

33 2.2.2 Slag Thermodynamics differentiate between cations and anions in the solution. Using the Herasymenko model the changes in oxidic and sulphidic dissolution of copper in slag can be explained, as well as the effect of adding lime or alumina to the slag. The activity coefficient of copper oxide is usually given in the form y Cu0oy and has a widely accepted value of 3.[44,59] A value of y c^0 equal to 204X c o at 1573 K has also been reported.[60] Values of y Co0 have been reported as 0.66 at 1523 K,[61] and 1.16 at 1573 K.[44] 20

34 3 OBJECTIVES 3 OBJECTIVES The mathematical simulation of an industrial process is a complicated procedure. The actual nature of the process may not be well known, and what is happening inside a reaction vessel is often not easily observed or measured. This is especially the case in pyrometallurgical operations, which by definition require high temperatures. The modelling process is one of making a number of assumptions, creating an initial model based on them, testing their validity, and then refining them to achieve a final product. This project represents the first two stages of this process. The primary objective, then, is the development of a model of the nickel converter, based on one major assumption regarding its operation: it is assumed that during operation the nickel converter passes through a finite series of equilibrium steps. The model is to be developed to simulate both the temperature and compositional variations of the converter during a full charge. Also, it should be able to handle the full range of input matte compositions in use in industry. The purpose of such a model is to obtain a better understanding of the nickel converting process. As such it may also aid in the improvement of converter operations. 21

35 3 OBJECTIVES Checking the validity of the primary assumption, as well as any others made, is a secondary objective. Recommendations for modifications to the model should be made. If the model is considered sufficiently valid some discussion of its predictions and their bearing on the operation of the process should also be presented. 22

36 4.1 Introduction 4 MODEL DEVELOPMENT 4.1 Introduction The main purpose of the computer model is to give a better understanding of the working of the nickel converter. The model should be capable of predicting the effect of changes in operating procedures on the temperature and composition of the contents of the converter. In this way the process can be optimized without carrying out extensive and expensive tests. The model should also provide a basis for comparing what actually happened in any particular test with what would have happened had the test not been carried out. The complexity of industrial processes generally necessitates that a number of assumptions be made in order to simplify the modelling process. The most important assumption which must be made in the case of the converting operation is that the entire system is in both chemical and thermal equilibrium. This assumption has been made in all previous theoretical models of the converting operation, and will be made here also, although with some serious reservations. The assumption that the bath is in equilibrium must be made to allow the compositions of the three phases to be calculated. Ideally kinetic considerations should also be involved, but there is not sufficient data on the kinetics of the matte system to allow this. In addition, the equilibrium model should be tried first because it is the 23

37 4.1 Introduction simplest case. It might be inefficient to develop a kinetic model if the process runs very close to equilibrium. The validity of this assumption will be discussed later. The model is primarily comprised of two intimately linked parts, the heat balance and the compositional calculations. The heat balance is used to calculate the temperature at which the equilibrium components of the compositional calculations are carried out. The change in composition provides the 'generated heat term' required for the heat balance. An iterative procedure is required to obtain a final composition and temperature. 24

38 4.2 Heat Balance 4.2 Heat Balance To calculate the temperature variation of the converter with time, a simple heat balance is carried out. The heat balance considers all of the major heat inputs and outputs to and from the converter. The general formulation is: heat accumulation = heat in - heat out + heat generation - heat consumption The net heat accumulation is calculated over one time step and translated into the temperature change over that time step. The only heat input is the sensible heat of input materials, and in most cases this is zero as ambient temperature is used as a baseline. The heat outputs are the heat losses from the converter. These heat losses come from two sources; radiation losses to the hood or atmosphere, and conduction losses through the walls. Radiation losses are calculated as Values for the bath emissivity, e B, and hood temperature, T H have to be estimated. The values used in the model were.8 and 873 K respectively. The sensitivity of the model to these values will be studied below. 25

39 4.2 Heat Balance The conduction losses are divided into two separate parts; the losses through the end walls, and the losses through the barrel. Assuming a linear temperature profile in the converter walls, losses through the end wall are calculated by Q ce ^ce dx dt.»4.3 with the thermal conductivity expressed as a linear function of temperature[62] k = ^(1 +Jt,T) = 1.08( Jtl(r 4 r) Wm^K" and the end wall area gives Vs-T^+^Wl-Tl) Similarly the heat losses from the barrel are given as <lcb = 2k,L c.4.7 In R:. The converter dimensions along with refractory data are given in table IV-I. Equations 4.6 and 4.7 require that there is no temperature variation with position on either the end walls or the barrel. 26

40 4.2 Heat Balance Converter Length, L c (m) 13.7 Inside Diameter, 2R tat (m) 3.8 Outside Diameter, 2R ext (m) 4.6 Barrel Refractory Thickness, x<, b (m).4 Endwall Refractory Thickness, (m).7 Mouth Area, (m 2 ) 9 Refractory Thermal Conductivity, k[62] 1.08(1+4.5(10" 4 )T) (Wm^K 1 ) Refractory Density, p ref [63] (kgm 3 ) 2930 Refractory Specific Heat, C P J63] (Jkg^K 1 ) 960 Table IV-I Converter dimensions and refractory data. 27

41 4.2 Heat Balance These equations also assume that the rate of heat conduction through the walls is equal to the rate of convective and radiative heat loss from the shell, and represents the total heat loss through the converter walls. The effect of this assumption is expected to be very small, as the heat lost through the walls is approximately one percent of the total heat output during blowing. [13J The heat consumption term is made up of the heats required to raise the charged materials and the injected gas to the bath temperature. The heat required to raise the charged materials and gas to the final temperature is calculated as =?kf ' C p {T)dT y ambient The values of the integral in equation 4.8 are pre-calculated to give a final equation of the form Icon = X Mi 4 V Values of the constants in equation 4.9 are given in table IV-II. As no values for specific heat or heat of formation are published for Ni 2 S, they were estimated assuming that CuJ CuS Ni 2 S NiS and AH f,cu^s AH,.4.10 AH, f.cus AH, f.nis 28

42 4.2 Heat Balance jc p m Jmol" 1 i a, b, qxlo 3 d,xlo' 5 Notes Fe Ni Cu Co FeS T<1468K FeS T>1468K Ni 2 S NiS Cu 2 S CoS Fe FeO NiO Cu T<1509K Cu a O T>1509K CoO s o so N SiQ Table IV-II Integrated values of C P. for use in equation 4.9.(64] 29

43 4.2 Heat Balance The heat generated by reaction is calculated from a comparison of the results of the mass balance calculation with the bath composition at the end of the previous time step. The reaction heat is given by q r ea = mm-m it0 )AH LiiT ] i Values of AH fij are calculated from AHf T - AH f, f CP T B (T)dT + AH. J29S Trans,i As with the heat consumption term, the heat of formation equations are precalculated to give the form d W f>iit = a i + b i T B + c i T> + - Values of the constants in these equations are given in table IV-III. The heat of mixing is assumed to be negligible. This is considered justifiable as it has been found in previous modelling studies to be of the order of 0.5% of the total heat involved.[13] The heat required to raise the internal surface of the refractory to the new bath temperature is given as Ar ref = W refp^~y 30

44 4.2 Heat Balance i b, c,xl0 3 dixlo" Notes 5 Fe Ni Cu Co FeS FeS Ni 2 S NiS Cu 2 S CoS Fe FeO NiO Cu T<1468K T>1468K T<1509K Cu T>1509K CoO s o so Table IV-III Heat of formation values used in equation 4.13.[64] 31

45 4.2 Heat Balance with the weight of the refractory calculated as The heat accumulation over the time step is then calculated as <lacc = Irea ~ 4 ram ~ 4 ce^ ~ 4 d,** <lco n = W B C P AT + -W re Pr AT Where and C P =2ZM i C P W B = XM f m l The new bath temperature can then be calculated as T B = T Bo + B ^ w r +-w r...4.i9 Values of the heat capacities at converting temperatures are calculated from equations of the form c C P, i,t B = ^ + b i T B + 1 B 32

46 4.2 Heat Balance The constants used in these equations are given in table IV-IV. All heat capacities are calculated at the final temperature in each time step. If the absolute value of the temperature change over a single time step is above an arbitrarily set tolerence value, e 1( the heat balance is recalculated using the new temperature. This allows corrections to the temperature dependent variables to be made, which may, in turn, effect the overall temperature change. This process is repeated until the temperature difference between iterations becomes less than e^ The affect of the magnitude of e v will be considered in the sensitivity analysis. 33

47 4.2 Heat Cpjn Jmol -1 i ai bpclo 3 CjXlO- 5 Notes Fe Ni Cu Co FeS T<1468K FeS T>1468K Ni 2 S NiS Cu 2 S CoS Fe FeO NiO Cu a O T<1509K CoO s o so Table IV-IV Values of constants used to calculate heat capacity. [64] 34

48 4.3 Compositional Calculations 4.3 Compositional Calculations Compositional calculations are carried out assuming that the converter is in equilibrium. Using the equilibrium assumption the composition of the three phases can be determined from a knowledge of the amount of each element present and the equilibrium temperature. The model considers eight 'elements' (Fe, Ni, Cu, Co, S 2, 0 2, N 2, and 'Si0 2 '), and twelve compounds in three phases. Nitrogen and 'silica' are considered as inert, and act only as diluents in their respective phases. The 'silica' includes all other components of the slag, which are also considered inert. The constituents of each phase are given in table IV-V. Two nickel sulphides are used in the matte phase to account for the sulphur excesses and deficiencies found during the converting cycle. The specie Ni 2 S is chosen because of its high nickel to sulphur ratio. It should be noted that Ni 3 S 2, which is commonly used to represent nickel sulphides, would be made up of a one-to-one mixture of the two nickel sulphide species used here. The system is formed into a set of twenty-three non-linear simultaneous equations: eleven equilibrium equations, six elemental balances, three molar balances (one for each phase), and an equation relating the activity of magnetite in the matte to the activity of magnetite in the slag. These equations are solved using a 35

49 4.3 Compositional Calculations Phase Matte Slag Gas Elements Fe, Ni, 'sicy N 2, 0 2, Cu, Co s 2 Compounds FeS, FeO, so 2 NiS, Fe 3 0 4, Ni 2 S, NiO, Cu 2 S, Cu 2 0, CoS, CoO Fe Table IV-V Constituents of the phases in the converter. 36

50 4.3 Compositional Calculations "Quasi-Newton" method to give values for the twenty-three unknowns. The equations solved are given in tables IV-VI and IV-VII. Values of the mole fractions, Xj, required for the equilibrium calculations are found from M i,p ~ MpJo The non-linear equation solving routine used was obtained from the program library of the University of British Columbia. [65] It is assumed that all material charged during the time step dissolves immediately. For the equilibrium calculation it is also assumed that all the gas blown or formed during the time step remains in the converter until the end of the time step, when it all exits through the hood. The calculations are carried out at atmospheric pressure. It is necessary that an assumption be made regarding the amount of material lost as dust in the flue, splashing from the mouth and as spillage during pouring. None of these losses can be measured with any accuracy. The amounts however should be sufficiently low so as to be negligible when compared to the overall inaccuracy of the weights of materials charged and removed from the converter. 37

51 4.3 Compositional Calculations Equation Equilibrium 1 FeO+\s 2^>FeS + l -S0 2 equations 2 NiO+\s 2 ->NiS+\S0 2 for 3 Cup +\s 2 -> Ci^S +\so 2 reactions 4 CoO +\s 2^> CoS +\S0 2 5 \s 2 +o 2 ->so 2 6 3FeO+l0 2 -^Fe 3 0 A 7 2Ni+\s 2^>Ni 2 S 8 Fe+\S 2^>FeS 9 2Cu+\s 2^Cu 2 S 10 Co+\s 2^CoS 11 Ni+\S 2^>NiS Magnetite equilibrium a Fe304 ~ a Fe304 Table IV-VI Equilibrium equations used in the compositional calculations. 38

52 4.3 Compositional Calculations Equation Elemental M Fe, T = M FeS + M FeQ + M Fe +3[M F^M + M P^ balance M NiJo = M m + M Ni0 + M Ni + 2M Nh s equations Mcujo = M Cu + 2(M CU2S + M CU20 ) M CO,TO = M CoS +M Co0 M s j 0 = M FeS +M m + M Co + M Ni j +M Cu j + M CoS + M S02 + 2M Si M 0,TO = M Fe0 + M mo + M Cui0 + M Co0 +2(M 02 + M s0 ) +4{ M W u + M F^ Molar M M,TO = M FeS + M NiS + M Ni2S +M Cu2S + M CoS + M F^ balances +M Fe + M Ni + M Cu + M Co within MSl,To = M FeO + M NiO + M ClLp +M Co0 + M Ptfi + phases M G, To = M 02 + M Si + M S o 2 + M N2 Table IV-VII Mass balance equations used in the compositional calculations. 39

53 4.3 Compositional Calculations The equations for calculation of the free energy of the reactions considered are given in table IV-VIII. The activity coefficients of the non-gaseous constituents are calculated from the empirical relations given in table IV-IX. Although many of these equations are derived from experimental data their accuracy is questionable, as they were not derived for the particular system considered here. The experiments were also not carried out on complex systems. Many of the activity coefficients could potentially be considered to be fitting parameters for the model, however only a minor amount of fitting had to be done. If the values or equations used are valid all charges simulated by the model should show a reasonable fit using the same values for the activity coefficients. The values of some activity coefficients had to be estimated based on the values for similar species in copper mattes. The values of the activity coefficients of nickel and copper oxides in slag were fitted to try to bring the predicted slag compositions closer to measured values. The use of the activity coefficients as fitting parameters will be discussed later. The gases involved are assumed to be ideal. A further problem is the characterization of the composition of all of the inputs, many of which do not have reliable assays. For these materials a 'standard' assay based on historical plant data is used. 40

54 4.3 Compositional Calculations Reaction No. AG* (J) (Table IV-VI) IT T T T T T IT T T IT T Table IV-VIII Free energy equations for the reactions used in the mass balance model.[9,44,64] 41

55 4.3 Compositional Calculations Phase i Ji Ref. Matte Fe Ni 15 (1) Cu Co FeS exp((^)ln(.54 + lax Fa ]nx pa +.52X FeS )) 15 Ni 2 S exp((^)-.2) 9(2) NiS 1 (1) Cu 2 S 1 (1) CoS.4 21 Fe exp((^) ( ]n(x c^ + X NiS +X NhS ) 15 +la3(\n(x ClhS +X NiS +X NhS )) (ln(X Cu^+X NiS +X Ni2S )f) Slag FeO exp((^)ln(1.42x F, 0 -.2)) 15 (1) Estimated. (2) Fitted. Fe X^ *^ 12 NiO 4.1 (2) Cu a O.006 (2) CoO Table IV-IX Activity coefficients of the non-gaseous constituents. 42

56 4.3 Compositional Calculations 'Standard* assays used are given in table IV-X. Assays used for the other charged materials are average values over the charge period, but are not expected to change significantly. 43

57 4.3 Compositional Calculations Material Cu Ni Co Fe S O Si0 2 Mush Washout Scrap Transfer matte Table IV-X Standard assays (weight %).[66] 44

58 4.4 Model Operation 4.4 Model Operation The model operates by combining the heat balance and compositional calculations over a set time step. The total amount of each element charged over the entire time step is calculated, together with the oxygen and nitrogen in the air blown over that period. These values are added to the contents of the converter at the end of the previous time step, and the mass balance is calculated. The total change in the amounts of each specie present over the time step is calculated and then reduced by the amount of that specie in the material charged during the time step. The net change is multiplied by the heat of formation of the respective specie at the bath temperature, and the result is summed over all species present to give the heat generated by the reactions (equation 4.11). The heat balance over the time step is then carried out. After the heat balance calculations have converged as detailed above, the overall temperature change over the time step is compared with a tolerance value, e 2. If the temperature change is greater than e 2 the equilibrium calculations are carried out at the new temperature and the heat balance is repeated. This continues until the temperature change between successive calculations of composition becomes less than e 2. The purpose of this is to correct the composition for the change in 45

59 4.4 Model Operation temperature over the time step, which may also change the generated heat. The final temperature and composition for the time step are printed to a file, the time is incremented, and the process is repeated. If the converter is idle during the time step the generated heat is assumed to be zero. The heat balance is calculated normally, but the composition change is not calculated. The effect on the bath temperature of the heat generated by the change of composition during cooling is corrected for during the time step immediately following the idle period. This is necessary because the bath is not at equilibrium with the surrounding atmosphere during idle periods, so the compositional calculations would not be valid. Slag skimming is carried out while the converter is idle. The removal of slag should not affect the overall composition of the slag or matte, nor the temperature of the phases, and so is considered to be a simple subtraction in the model. If, during the analysis of an industrial charge, there is not sufficient slag in the converter model to skim the indicated amount, the model will note this in the output and skim 95% of the total slag present. A flow chart of the program is shown in figure 4.1. The model was run on the University of British Columbia Amdahl V8 mainframe computer, and on an AST Premium 286 personal computer with an 46

60 4.4 Model Operation Read Initial Conditions and Operating Conditions Remove Slag Figure 4.1 Flow chart of the converter model. 47

61 4.4 Model Operation math co-processor. The running time on both machines varied widely depending on the particular charge. There was little difference between results from the different computers. 48

62 5.1 General Mass Balance 5 MODEL VALIDATION 5.1 General Mass Balance In order to verify that the results of the mass balance calculations were consistent with reality, six charges were simulated and their results compared with published data. In particular, a comparison of the variation of weight fraction iron in matte with the sum of the weight fractions of copper, nickel, and cobalt (matte grade) was made. A regression line calculated using data from five different operations has been published,[1] and figure 5.1 shows a comparison of the model predictions with the published line. The agreement is quite good, but a deviation from the general linearity is seen at lower iron levels. This deviation is mainly due to the invalidity of the use of the regression line at low iron levels. This is illustrated by the fact that the regression line gives zero iron in matte at a matte grade of.75, whereas in practice higher matte grades will still contain between.005 and.01 weight fraction iron. In the region where the model deviates from the regression line there is an increase in the ratio of sulphur to iron removal. To some extent this is caused by increased nickel and cobalt oxidation, but the matte is also becoming more sulphur deficient. 49

63 5.1 General Mass Balance WT FRACTION Cu+Ni+Co Figure 5.1 Iron in matte versus matte grade, comparison of model predictions with plant average data. 50

64 5.1 General Mass Balance AT. % Fe Figure 5.2 Schematic showing the limiting converting path in the iron-nickel-sulphur system.[2]

65 5.1 General Mass Balance Both the linear and non-linear regions of this curve can be explained by Kellogg's limiting oxidation path (figure 5.2).[2] This was calculated as being approximately linear up to about eight atomic percent iron in matte, which corresponds to a weight fraction of iron of approximately.09. At this point it curves to reduce the sulphur content in the matte while changing the iron content slightly. This behaviour is very similar to that predicted by the present model. The model predicts a linear reduction of iron content down to a weight fraction between.08 and.1. At this point the rate of iron removal with respect to matte grade is reduced indicating increased sulphur removal. 52

66 5.2 Modelling of Plant Trials 5.2 Modelling of Plant Trials The model was run for six charges monitored during plant trials at Inco's Copper Cliff smelter (see appendix). Details of the charges are given in table V-I. The charges covered a wide range of operation conditions and provide a fairly rigorous test of the model. Comparisons of the predicted temperatures with those measured in-plant are given in figures All model runs assumed an oxygen efficiency of 95%[66], and used the air-rates measured in-plant. The conformity of the model predictions to the plant data until the last blows indicates that the heat balance portion of the model is valid over most of the charge. This is a further validation of the mass balance. The deviation at the end of a charge may be caused by the rate of oxygen consumption being mass transfer controlled at low iron levels. The dissolution of mush has been simulated by adding an equivalent mass of scrap at a constant rate during part of the first blow. Details of the fitting carried out are given in table V-II. In all cases the initial mush was also present, but this is not expected to have a significant effect on the overall composition, as the amount of scrap added was small and the actual initial weight of mush present is not known. No fitting was required for charge 105 (figure 5.4), as the 53

67 5.2 Modelling of Plant Trials Charge Initial matte contents mush (tonnes) scrap other 10(1) 40(2) Blow 1 Times Blowing (min) Idle No. idle periods Material Flux 2.2 added Matte (tonnes) Scrap Slag skimmed (tonnes) Blow 2 Times Blowing (min) Idle No. idle periods Material Flux added Matte 66(2) (tonnes) Scrap Slag skimmed (tonnes) Blow 3 Times Blowing (min) Idle No. idle periods Material Flux added Matte 22 44(2) (2) (tonnes) Scrap Slag skimmed (tonnes) Table V-I Details of charges modelled. 54

68 5.2 Modelling of Plant Trials Charge Blow 4 Times Blowing (min) Idle No. idle periods Material Flux added Matte 30(2) (tonnes) Scrap Slag skimmed (tonnes) Blow 5 Times Blowing (min) Idle 37, 27 No. idle periods 3 2 Material Flux added Matte 44(2) 44(2) (tonnes) Scrap 10 5 Slag skimmed (tonnes) Blow 6 Times Blowing (min) Idle No. idle periods 1 1 Material Flux added (tonnes) Slag skimmed Matte Scrap (tonnes) (1) Slag (2) Matte transferred from another converter. Table V-I Details of charges modelled (continued). 55

69 5.2 Modelling of Plant Trials Charge Tonnes scrap added to simulate mush dissolution addition rate (tonnes min" 1 ) Table V-II Details of fitting carried out. 56

70 5.2 Modelling of Plant Trials TIME (MINUTES) Figure 5.3 Comparison of model predicted bath temperature with plant data, #3 converter Charge 98, May

71 5.2 Modelling of Plant Trials Figure 5.4 Comparison of model predicted bath temperature with plant data, #3 converter Charge 105, May

72 5.2 Modelling of Plant Trials Figure 5.5 Comparison of model predicted bath temperature with plant data, #3 converter Charge 106, May

73 5.2 Modelling of Plant Trials 1 i r TIME (MINUTES) Figure 5.6 Comparison of model predicted bath temperature with plant data, #3 converter Charge 107, May

74 5.2 Modelling of Plant Trials in m n II 1111 ii ni ii'r i m ii iti mi ii 11 in inniiiiiunn]iittttttrmhiiin miiii 1111 n M M1111 n T r n 11 f 1111 M n TIME (MINUTES) Figure 5.7 Comparison of model predicted bath temperature with plant data, #3 converter Charge 108, May

75 5.2 Modelling of Plant Trials TIME (MINUTES) Figure 5.8 Comparison of model predicted bath temperature with plant data, #3 converter Charge 109, May

76 5.2 Modelling of Plant Trials starting point for the model was the beginning of the second blow and both the matte and slag assays were available for this point. However, initial weights of matte and slag had to be estimated from the operation of the first blow. To further check the validity of the mass balance, the predicted matte and slag compositions can be compared with the assays obtained during the trials. A comparison of the predicted and all measured matte compositions is given in table V-III, and of the skimmed slags in tables V-rV to V-IX. In the slag compositions 'Si0 2 ' includes all of the minor oxides which are not considered in the model. The agreement in the matte compositions is good in most cases, although the predicted sulphur level is too low, possibly due to incorrect activity coefficients of the sulphide species. In particular y NiS and y Cu2 s are probably not equal to one; however, no measured values are available. The wide variation seen in the amount of oxygen in the assayed matte samples appears to indicate that there is no particular relationship between matte grade and matte oxygen content in nickel converters. The model's almost complete inability to predict the oxygen in matte tends to imply that the oxygen is not in equilibrium. However, more information on the nature of the oxygen in matte is required. 63

77 5.2 Modelling of Plant Trials Charge Blow Fe Ni Cu Co S O Model Assay Model Assay Model Assay Model Assay Model Assay Model Assay Model Assay Table V-III Comparison of model predicted matte compositions with assays taken at the end of the stated blow, (weight fraction) 64

78 5.2 Modelling of Plant Trials Slag Fe Ni Cu Co O 'Si0 2 ' 1 Model Assay Model Assay Model Assay Model Assay Table V-IV Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 98, May Slag Fe Ni Cu Co O 'SiCV 2 Model Assay Model Assay Model Assay Model Assay Model Assay Table V-V Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 105, May

79 5.2 Modelling of Plant Trials Slag Fe Ni Cu Co O *SiCV 1 Model Assay Model Assay Model Assay Model Assay Table V-VI Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 106, May

80 5.2 Modelling of Plant Trials Slag Fe Ni Cu Co O 'SiCV 1 Model Assay Model Assay Model Assay Model Assay Model Assay Model Assay Table V-VII Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 107, May

81 5.2 Modelling of Plant Trials Slag Fe Ni Cu Co O Si0 2 ' 1 Model Assay Model Assay Model Assay Table V-VIII Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 108, May Slag Fe Ni Cu Co O 'Si0 2 ' 1 Model Assay Model Assay Model Assay Model Assay Table V-IX Comparison of model predicted slag compositions with assays taken at the end of the blow, (weight fraction), #3 converter Charge 109, May

82 5.2 Modelling of Plant Trials The values of copper, nickel, and cobalt in the slag are not expected to be particularly accurate, as entrainment is not considered in the model. This is because entrainment in converter slags is dependent on a number of parameters which cannot be calculated by the model. Some fitting could be carried out using the activity coefficients of the respective oxide species in the slag, but this approach would not be technically valid. The amount of entrainment is not dependent on thermodynamics, and so cannot be modelled using thermodynamic parameters. Even if a fitted activity coefficient gives a good result for one case it is unlikely to do so for all others. The predicted iron and 'silica' compositions, however, are generally close to the assayed values. The error in the silica content of the slags is usually large for the first blow, reflecting the lack of knowledge of the silica content of the mush. Much of the error in the slag composition can be ascribed to variations in the silica content of the flux. Table V-X shows the assays of the flux taken over five consecutive blows. This indicates that there is a wide variation in the silica content of the flux during any specific charge, and may lead to significant errors in the model predictions. The only major discrepancies in the iron predictions are for the last slag of charge 98 and the last two slags of charge 107. In these cases the predicted iron in the slag is much higher than was measured. This may have been caused by errors in 69

83 5.2 Modelling of Plant Trials the amount silica in the flux, or iron in the matte charged. Overall, the model appears to give a good representation of both the mass balance and the heat balance for the middle blows. Some fitting is required in the first blow to account for the mush composition, weight, and dissolution. In the final blows the model generally tends to overpredict both the temperature and iron removal. This overprediction is likely to be caused by the converting reactions coming under liquid phase mass transfer control. 70

84 5.2 Modelling of Plant Trials Charge Fe Ni Cu Co S Si Table V-X Flux assays for charges 105 to 109, May 1988, (weight to fraction). 71

85 6.1 Sensitivity Analysis 6 DISCUSSION 6.1 Sensitivity Analysis A sensitivity analysis of the model is required to calculate the effect of errors or uncertanties in the inputs on the overall results. It can also be used to test the effects of some of the less important assumptions, and to give an indication of what are the most important variables controlling the converter. A 'standard' charge was developed based on plant practice to allow direct comparisons between different values of the same variable. Details of this charge are given in table VI-I. It is not as complex as an actual charge, and has a constant air rate. This is so that the effects of the variable being tested are not obscured by other considerations. The variables tested and the values used are given in tables VI-II and VI-III. Table VI-IV shows the units of measurement of the more important inputs and outputs to and from the converter. The effect of changes on both the temperature and bath composition are of interest. The effect on composition will be shown by the weight fraction of iron in the matte, which gives a good indication of the overall matte composition (see figure 5.1). The variation in the slag composition is not as large as in the matte composition, and to a certain extent depends on the iron in the matte. In cases where there is a large variation in the gas composition this variation will also be shown. 72

86 6.1 Sensitivity Analysis Initial Contents Blow Matte Mush Time (min) Idle (min) 110 Tonnes 30 Tonnes Matte (Tonnes) Air Rate 633 Nnr'mln' 1 Scrap Flux (Tonnes) (Tonnes) (1) (1) Mush dissolution simulation. 95% of slag skimmed after blows 1-5. Table VTI Standard charge used in sensitivity analysis. 73

87 6.1 Sensitivity Analysis Variable low base high Time step (min) Heat balance tolerence, e! (K) Composition calculation tolerence, e 2 (K) Oxygen efficiency (%) Emissivity of bath Hood temperature (K) Refractory thickness (m) Shell Temperature (K) Water in scrap (%) Water in flux (%) Tonnes scrap in ladle Tonnes matte in ladle y NiS Initial temperature (K) Air rate (Nm^in 1 ) Oxygen enrichment (%) Table VI-II Variables tested in sensitivity analysis. 74

88 6.1 Sensitivity Analysis Scrap Composition (weight fraction) Fe Ni Cu Co S O 'SiCV Flue dust (base) Concentrate Slag Table VI-III Scrap compositions used in the sensitivity analysis. Input or Output Industrial Unit Unit Equivalent Matte Ladle 22 (10 3 )kg Scrap Ladle (large) 15 (10 3 )kg ti Ladle (small) 10 (10 3 )kg II Tons or belts variable Air Tons/day Nm 3 min 1 Oxygen Tons/day Nm 3 min 1 Flux Tons or belts variable Slag Ladle 20 (10 3 )kg Bessemer matte Tons.9072 (10 3 )kg Table VI-IV Units of measurement of converter inputs and outputs with approximate conversion factors used in the model. 75

89 6.1.1 Model Operating Parameters Model Operating Parameters A number of the model parameters may have some effect on the accuracy of the predictions made. The most important of these is the length of the time step used. In general a shorter time step will give better accuracy, but increases the running time and computing cost. The effect of varying the time step is given in figure 6.1, and is quite small. The change in time step does appear to have a larger effect on the weight fraction of iron in the matte than on the temperature, but the difference is still relatively small. The four minute time step, however, does cause a reduced accuracy in the timing of some inputs which must be at the beginning of a time step. The other two model operating parameters which could have an effect on the model predictions are the heat balance and mass balance temperature tolerences, e x and e 2. Smaller values of these are also likely to give better accuracy, but will increase running time. In this case neither of the tolerence values were found to have a significant effect on the model predictions in the range tested. 76

90 6.1.1 Model Operating Parameters i, TIME (MINUTES) Figure 6.1 The effect of time step on model predicted bath temperature and weight fraction iron in matte. 77

91 6.1.2 Converter Operation Parameters Converter Operation Parameters There are five primary parameters of converter operation which are assumed to be constant for the purposes of modelling. Of these, three may be expected to have a significant effect on the model predictions; the oxygen efficiency, bath emissivity, and converter hood temperature. The oxygen efficiency of a converter, defined as theoretical oxygen requirement *JQQ^actual oxygen used is very rarely 100% and is more often around 95%.[66] Figure 6.2 shows the effect of this difference on bath temperature and iron in matte. The change in both of these predictions is significant. Both iron and sulphur removal are increased by a higher oxygen efficiency due to the increased oxygen available for reaction. The increased amount of reaction also causes higher temperatures. This is approximately proportional to the extra amount of oxygen available. The emissivity of the bath may also have a significant effect on the converter temperature, although radiation losses are much smaller than the heat lost to the gas. Figure 6.3 shows that the effect is not as large as that of oxygen efficiency, but is still significant over a full charge. The variation of composition, however, is seen to be verysmall. This implies that the composition of the bath is relatively independent of temperature over the range shown in figure

92 6.1.2 Converter Operation Parameters 1600 H TIME (MINUTES) Figure 6.2 Effect of oxygen efficiency on model predicted bath temperature and weight fraction iron in matte. 79

93 6.1.2 Converter Operation Parameters 1600 I ' " I " " I " " " I '"""I ' I "I "' I'" ""' "" TIME (MINUTES) Figure 6.3 Effect of bath emissivity on model predicted bath temperature and weight fraction iron in matte. 80

94 6.1.2 Converter Operation Parameters The temperature of the converter hood will also affect the radiation losses from the converter. This effect, however, was found to be insignificant. The two parameters which are expected to have a much smaller effect are the converter shell temperature and the thickness of the refractory lining. Goto determined that heat losses through the converter walls were comparatively small! 13], so factors involving wall losses are not likely to be important. Changing the shell temperature is found to cause little difference in the predictions, but figure 6.4 indicates that, at least initially, the refractory thickness does have some effect. This effect, however, is the opposite of that which would be expected; a thinner refractory lining gives a higher temperature at the end of each blow. A similar result was obtained by Bustos and Sanchez[16] over a single blow in a model of the copper converter. They concluded that there must be increased heat losses through the walls which could not be predicted by the model. A better explanation is that the effect is caused by the increased thermal mass of the refractory at higher wall thicknesses. This requires a larger amount of heat to raise the refractory to the average wall temperature and, hence, will reduce the bath temperature for the same amount of accumulated heat. The rate 81

95 6.1.2 Converter Operation Parameters of heat loss during idle periods and flux addition is larger for thinner linings, as would be expected. Also, the effect over an entire charge is still small. 82

96 6.1.2 Converter Operation Parameters TIME (MINUTES) Figure 6.4 Effect of refractory thickness on model predicted bath temperature and weight fraction iron in matte. 83

97 6.1.3 Converter Inputs Converter Inputs The composition and amounts of materials charged to the converter cannot always be accurately measured, and the results of variations in these may be significant. Both flux and scrap are added at ambient temperature, and may contain some water. The amount of moisture contained in each may vary, and has not been measured. For modelling it was assumed that there was no water in the flux, and 2% moisture in the scrap. The effect of increasing the water in the flux and scrap to 5% is shown in figures 6.5 and 6.6. The increased moisture in the flux has a larger effect than the moisture in the scrap. This is due to the larger increase in water content in the flux. The change in the composition is small in both cases as neither flux nor scrap are significant contributors to the matte. Therefore, small variations in the amount of either added will not have much effect on the overall composition. For similar reasons an increase or decrease of 20% in the weight of scrap charged causes little change in the matte composition. The effect of the same variation on the temperature is not large for a single scrap addition, but becomes significant over a full charge. It is not likely that the weight of scrap added will be consistently high or low however, so the actual effect of this variation will be small. 84

98 6.1.3 Converter Inputs H UJ CC cc LU QL 2 U l I WATER IN FLUX 0% 5% o cc z o < cc 0.1 I IH IH I llliiliiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiijiiiiiiinniiiiiiiiiiiiiiiiiiuniiiiiiiiiiu)! TIME (MINUTES) Figure 6.5 Effect of water in flux on model predicted bath temperature and weight fraction iron in matte. 85

99 6.1.3 Converter Inputs Figure 6.6 Effect of water in scrap on model predicted bath temperature and weight fraction iron in matte. 86

100 6.1.3 Converter Inputs The main factors which cause variation of the matte ladle volume, spillage and solidification, would, in general, cause consistently lower values than might be expected. A reduced matte addition has little effect on temperature, but a fairly significant effect on matte composition (figure 6.7). This can be explained by the reduction in the amount of iron charged combined with the same amount of air blown, giving an overall decrease in the amount of iron in the matte. The rate of iron removal is not changed significantly, but the difference in iron added due to the reduced amount of matte charged, (approximately 9% less matte), is sufficient to cause a difference of about.03 weight fraction of iron over the entire charge. Perhaps the most variable, and the least well quantified, of the inputs to the converter is the composition of the scrap. For modelling it was assumed that all scrap added was the same composition, approximating the composition of flue dust. Figure 6.8 shows the effect of changing the 'scrap' composition to either a low-iron concentrate or converter slag, both of which are used as scrap. The difference in temperature between the three scrap compositions is small, and can be explained by differences in their heat capacities. The variation in matte composition, however, is large. The reduced final iron content of the matte for both the slag and the low-iron concentrate cases, is caused by the lower amounts of iron sulphide 87

101 6.1.3 Converter Inputs 1580 ' ' " I"""" I '""1 1 1 I""' '""I "" '"I I"" ' TIME (MINUTES) Figure 6.7 Effect of weight of matte charged on model predicted bath temperature and weight fraction iron in matte. 88

102 6.1.3 Converter Inputs I I I 1 mini [inn i ni mn j iii)iiiii iiu TIME (MINUTES) Figure 6.8 Effect of scrap composition on model predicted bath temperature and weight fraction iron in matte. 89

103 6.1.3 Converter Inputs added with the scrap. The higher iron in the matte seen for the slag case is due to an increase in its magnetite content. This increase is caused by the extra oxygen added iri the slag raising the oxygen potential and, hence, the magnetite activity. Towards the end of a charge there is a large increase in the activity coefficient of magnetite in the matte, which leads to the sudden drop in both the iron and oxygen contents of the matte. It is at this point that the 'slag' line drops below the 'flue dust' line. 90

104 6.1.4 Thermodynamic Data Thermodynamic Data Measured data was not available for some of the activity coefficients involved in the model. In particular the activity coefficients of NiS and Cu 2 S were set at unity. In a previous model of the copper converter! 13] a value of y Cu^ equal to one was successfully employed. This assumption was made primarily because Cu 2 S was the main constituent of the matte. In the present model, however, copper is not the primary component of the matte, and so a significant deviation in activity coefficient may occur due to interactions with other matte components. Variations in the activity coefficient of Cu 2 S were determined to have no significant effect on the bath temperature or composition. This is because the amount of copper oxide present s is negligible, and is the only form of copper present outside of the matte. For there to be any significant effect on the matte there would have to be a large increase in the amount of Cu a O present in the slag, which is not thermodynamically likely at low oxygen potentials. The effect of varying the activity coefficient of NiS was found to have a slight effect on the bath temperature, and a larger effect on the iron in matte (figure 6.9). The cause of the change in matte composition is best seen from the changes in the weight fractions of 91

105 6.1.4 Thermodynamic Data 1580 Figure 6.9 Effect of NiS activity coefficient on model predicted bath temperature and weight fraction iron in matte. 92

106 6.1.4 Thermodynamic Data 0.5 o Z o H O 0.4 H X o LU lt TIIIIII!M1IIIIIIM[ir 0.28 H NIS ACTIVITY COEFFICIENT X Q. _J 5) 0.26 z o O -25 H 0.24 CD LU H 0.21 i rrr n Tin ii 1 irrr>mi i]i turn ii 1 i f rr rr n f rmniti mimimj MI I n i i rirmiiif r rip n< i rjiti n TIME (MINUTES) 502 Figure 6.10 Effect of NiS activity coefficient on model predicted weight fractions of nickel and sulphur in matte. 93

107 6.1.4 Thermodynamic Data nickel and sulphur present. Figure 6.10 shows that decreasing the activity coefficient of NiS causes the weight fractions of both nickel and sulphur to increase. This is caused by the increased amount of nickel as NiS altering the relative amounts of the two nickel sulphides present. The increased amount of NiS present increases the amount of sulphur required in the matte per mole of nickel. This, in turn, reduces the amount of sulphur removed from the matte and, hence, increases the amount of iron removed per mole of oxygen blown. The effects of the variation of NiS activity coefficient, however, are within the accuracy of the compositional predictions of the model. 94

108 6.1.5 Other Variables Other Variables There are three other variables which can have a significant effect I on the operation of the converter. These are all measured with a relatively good accuracy, and so are not considered as possible sources of error in the model. However, they give useful information regarding converter operation and so should be examined. The effect of the initial temperature of the bath is shown in figure It is seen that an initial difference in temperature of 100 K is reduced to about 10 K over the period of a complete charge. This will be caused by the increased heat losses at higher temperatures, and the increased amount of heat required to raise the charged materials to the bath temperature. The difference in iron in matte is almost entirely due to the differences in equilibrium compositions with temperature. The overall iron removal is the same regardless of initial temperature. The effect of the air rate is much more significant, as is shown in figure It is not surprising that increasing the air rate gives increased iron removal and, hence, increased temperature. More air is being introduced into the bath over the same time period, so a greater amount of iron will be oxidized. The reduction in the rate of temperature increase at the end of the case with the highest air-rate (730 Nm 3 /min) is due to the large amount of nickel oxidation which occurs at low iron levels. The heat generated by the oxidation of nickel 95

109 6.1.5 Other Variables rpxtti r>iiinnrr»n)iii imni rrrnt m linrirniii nnii in ir riiiniriritti nniiihitiii frmn TIME (MINUTES) Figure 6.11 Effect of initial temperature on model predicted bath temperature and weight fraction iron in matte. 96

110 6.1.5 Other Variables Figure 6.12 Effect of air rate on model predicted bath temperature and weight fraction iron in matte. 97

111 6.1.5 Other Variables is less than that generated by the oxidation of iron. The figure does indicate the increased production rate possible at higher air rates caused by the increased amount of oxygen added in a given time. A similar, but even larger effect is obtained by an increase in the oxygen content of the blown gas (figure 6.13). In fact, the use of oxygen enrichment to 25% throughout an entire charge would lead to the temperature rising well above the maximum temperature allowed in a standard converter (about 1550 K). There is a large increase in the production rate at higher oxygen levels, which is approximately proportional to the additional oxygen available for reaction. The abrupt end of the 30% enrichment case was caused by a convergence failure in the model at very low iron levels in matte (less than 0.1%). A further advantage of oxygen enrichment is shown in figure Higher oxygen enrichment increases the fraction of sulphur dioxide in the off-gas, and so increases the feasibility of off-gas cleaning. 98

112 6.1.5 Other Variables Figure 6.13 Effect of oxygen enrichment on model predicted bath temperature and weight fraction iron in matte. 99

113 6.1.5 Other Variables Figure 6.14 Effect of oxygen enrichment on model predicted sulphur dioxide content of the off-gas. 100

114 6.2 Validity of the Equilibrium Assumption 6.2 Validity of the Equilibrium Assumption The assumption of equilibrium is usually considered justifiable because of the high oxygen efficiency generally obtained in the converting process. However, towards the end of the cycle the oxygen efficiency is seen to drop[66], indicating that the process becomes kinetically controlled. Also, some converting operations do not achieve a high oxygen efficiency. In one case an average efficiency as low as 55% for an entire cycle has been reported for a copper converter. [69] Finally, it can be observed that the condensed phases in the converter (matte and slag) are at different temperatures. Figure 6.15 shows the inside back wall of a converter after being rotated off the tuyeres, standing idle for approximately five minutes, and then rotated again to skim the slag. A definite colour difference can be seen between the sections of the wall which were in contact with the matte and the slag, indicating a difference in temperature. Five minutes would not be sufficient time to cause this difference, as the converter cools under 10 K over this period. As can be seen in figure 6.15, a layer of solidified slag is quickly formed on the top of the bath which significantly reduces the rate of heat loss from the bath. This means that the matte and slag cannot be in thermal equilibrium and, therefore, invalidates the standard formulation of chemical equilibrium equations which require a single temperature to calculate the 101

115 6.2 Validity of the Equilibrium Assumption 102