Zinc Beneficiation Simulator

CHE445Z

CHEMICAL ENGINEERING PROJECT

Development of a spreadsheet-based simulator for a zinc beneficiation practical

Mineral Processing Research Unit at the University of

Cape Town PREPARED BY: MICHAEL FLETCHER (FLTMIC007) NEIL ROBINSON (RBNNEI002) PREPARED FOR: DR. D.A. DEGLON MR. P. LEKOMA

13 November, 2002

© Copyright 2002

Development of a Spreadsheet Based Zinc Simulator Synopsis

i

Synopsis The hydrometallurgical zinc beneficiation process is studied by third year chemical

engineering students at the Western Cape Mineral Processing Facility in Stellenbosch. Currently, students learn by first researching the zinc beneficiation process and giving a presentation to demonstrate theoretical knowledge gained. They then perform experiments which demonstrate the principles behind the industrial process. It is felt that the theoretical and practical knowledge gained from these tasks is not adequately reconciled.

To combat this problem the process (from milling through to electrowinning) has been successfully modelled using the Microsoft Excel spreadsheet add-on LIMN.

It is proposed that the simulator should be used as an educational tool for the third year students. It is hoped that exposure to the simulator will help students to bridge the gap between their theoretical and practical knowledge.

The simulator successfully shows trends in the process with changes of variables, but does not, and is not intended to predict accurate process values.

The major assumption made for the entire process was that the ore fed to the system consisted of pure ZnS. i.e. no impurities.

The models chosen for each unit operation are: Milling: Standard population balance model, incorporating JKMRC Massive Sulphide

ore appearance function. Cyclone cut based on reduced recovery curve Flotation: 1st order kinetics model, with rate constant estimated using the Jameson

equation Roasting: Mass transfer limited shrinking core model in a fluidised bed Leaching: Thermodynamic equilibrium model Electrowinning: CSTR operating in a semi-batch environment

Several student learning assignments are proposed. They are: A Fresh Feed Exercise An Optimisation Exercise

Expected outcomes from the learning assignments are: Understanding of knock-on effects in a system Appreciation of the sensitivity of unit operations An appreciation of the impact of economic and production factors on optimisation

Development of a Spreadsheet Based Zinc Simulator Table of Contents

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Table of Contents

Synopsis----------------------------------------------------------------------------------------------------i

Table of Contents---------------------------------------------------------------------------------------- ii

List of Figures ------------------------------------------------------------------------------------------ iv

List of Tables -------------------------------------------------------------------------------------------- iv

Nomenclature -------------------------------------------------------------------------------------------- v

1 Introduction ---------------------------------------------------------------------------------------- 1 1.1 Background--------------------------------------------------------------------------------------------2 1.2 Practical Procedure ----------------------------------------------------------------------------------2 1.3 LIMN – The Flowsheet Processor-----------------------------------------------------------------3 1.4 Aims and Objectives ---------------------------------------------------------------------------------4

2 Review of the Hydrometallurgical Route ------------------------------------------------------ 5 2.1 Communition and Flotation------------------------------------------------------------------------6 2.2 RLE (Roasting, Leaching, Electrowinning) Process Review --------------------------------6

2.2.1 Roasting of Zinc Bearing Ore-------------------------------------------------------------------------------6 2.2.2 Leaching -------------------------------------------------------------------------------------------------------7 2.2.3 Electrolysis ----------------------------------------------------------------------------------------------------8

3 Review of Mathematical Models ---------------------------------------------------------------- 9 3.1 Modelling of the Ball Mill------------------------------------------------------------------------- 10

3.1.1 Population Balance Model -------------------------------------------------------------------------------- 10 3.1.2 Modelling the rate of breakage---------------------------------------------------------------------------- 11 3.1.3 A simplified Ball Mill Model ----------------------------------------------------------------------------- 12

3.2 Hydrocyclone Modelling -------------------------------------------------------------------------- 12 3.3 Flotation circuit Modelling ----------------------------------------------------------------------- 15

3.3.1 First order Flotation Kinetics------------------------------------------------------------------------------ 15 3.3.2 Estimation of the First order rate Constant -------------------------------------------------------------- 15 3.3.3 Second order Flotation Kinetics -------------------------------------------------------------------------- 16

3.4 Roasting Models – Kinetic and Thermodynamic -------------------------------------------- 16 3.4.1 Roasting Thermodynamics -------------------------------------------------------------------------------- 16 3.4.2 Bubbling Bed Model --------------------------------------------------------------------------------------- 17 3.4.3 Shrinking Core Model ------------------------------------------------------------------------------------- 18

3.5 Zinc Leaching Models ----------------------------------------------------------------------------- 18 3.5.1 Thermodynamics of Leaching ---------------------------------------------------------------------------- 18 3.5.2 Leaching Kinetics – Mass-Transfer Limited Model --------------------------------------------------- 19 3.5.3 Thermodynamic Equilibrium Model --------------------------------------------------------------------- 20

3.6 Electrowinning Models ---------------------------------------------------------------------------- 20 3.6.1 Single pass reactors----------------------------------------------------------------------------------------- 20 3.6.2 Semi-batch reactors----------------------------------------------------------------------------------------- 21

4 Models Used and Major Assumptions Made-------------------------------------------------22 4.1 The Simulator Appearance----------------------------------------------------------------------- 23 4.2 Ball Mill Model-------------------------------------------------------------------------------------- 23

Development of a Spreadsheet Based Zinc Simulator Table of Contents

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4.2.1 Model Selection--------------------------------------------------------------------------------------------- 23 4.2.2 Assumptions Made ----------------------------------------------------------------------------------------- 24 4.2.3 User Input Variables --------------------------------------------------------------------------------------- 24

4.3 Hydrocyclone model ------------------------------------------------------------------------------- 25 4.3.1 Model Selection--------------------------------------------------------------------------------------------- 25 4.3.2 Assumption Made ------------------------------------------------------------------------------------------ 25 4.3.3 User Input Variables --------------------------------------------------------------------------------------- 25

4.4 Flotation Model ------------------------------------------------------------------------------------- 25 4.4.1 Model Selection--------------------------------------------------------------------------------------------- 25 4.4.2 Assumptions Made ----------------------------------------------------------------------------------------- 26 4.4.3 User Input Variables --------------------------------------------------------------------------------------- 26

4.5 Roasting Models ------------------------------------------------------------------------------------ 26 4.5.1 Thermodynamic Model Selection ------------------------------------------------------------------------ 26 4.5.2 Kinetic and Mass Transfer Model Selection ------------------------------------------------------------ 27 4.5.3 Assumptions------------------------------------------------------------------------------------------------- 27 4.5.4 Roasting Unit User Inputs --------------------------------------------------------------------------------- 27

4.6 Leaching Models------------------------------------------------------------------------------------ 28 4.6.1 Mass Transfer Limited Model ---------------------------------------------------------------------------- 28 4.6.2 Thermodynamic Equilibrium Model --------------------------------------------------------------------- 29 4.6.3 Assumptions------------------------------------------------------------------------------------------------- 29 4.6.4 User Inputs -------------------------------------------------------------------------------------------------- 29

4.7 Electrowinning Models ---------------------------------------------------------------------------- 29 4.7.1 Assumptions Made ----------------------------------------------------------------------------------------- 30 4.7.2 User Inputs -------------------------------------------------------------------------------------------------- 30

5 Results and Discussions -------------------------------------------------------------------------31 5.1 Individual Unit Trends ---------------------------------------------------------------------------- 32

5.1.1 Changing the Ball Mill speed ----------------------------------------------------------------------------- 32 5.1.2 Changing the superficial gas velocity during flotation------------------------------------------------- 33 5.1.3 Changing the acid flowrate through the leaching tank------------------------------------------------- 34 5.1.4 Changing the current used in the Electrowinning cells ------------------------------------------------ 35

5.2 Circuiting Effects ----------------------------------------------------------------------------------- 36 5.2.1 Effect of changing the Fresh Feed to the system ------------------------------------------------------- 36 5.2.2 Effect of changing the Fresh Feed size distribution ---------------------------------------------------- 37

6 Concluding recommendations------------------------------------------------------------------38 6.1 Student Exercises ----------------------------------------------------------------------------------- 39

6.1.1 Assignment 1 – Fresh Feed Exercise--------------------------------------------------------------------- 39 6.1.2 Assignment 2 – Optimisation Exercise ------------------------------------------------------------------ 40

6.2 Possible improvements to the Simulator------------------------------------------------------- 40 6.3 Acknowledgements --------------------------------------------------------------------------------- 41

7 References -----------------------------------------------------------------------------------------42

8 Appendices-----------------------------------------------------------------------------------------45 Supplementary Calculations ------------------------------------------------------------------------------- 45 Method Used to Vary Size Distribution------------------------------------------------------------------ 46 Simulator Spreadsheets ------------------------------------------------------------------------------------- 47

Development of a Spreadsheet Based Zinc Simulator List of Figures

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List of Figures Figure 1.1 Schematic diagram showing student learning----------------------------------------------- 3 Figure 2.1 Example of a typical fluidised bed roaster (From Reuter and Lans, 2001)------------- 6 Figure 2.2 Flow sheet of the leaching process at IMMSA, excluding advanced refining.

(Adapted from information and diagrams by Alfar and Castro, 1998, and Reuter and Lans, 2001) --------------------------------------------------------------------------------------- 7

Figure 3.1 Ball Mill in closed circuit with hydrocyclone-----------------------------------------------12 Figure 3.2 Reduced efficiency curve based on partition curve ---------------------------------------13 Figure 3.3 Partially reacted ZnS particle, illustrating gaseous diffusion in and out of the system.

(Adapted from Fogler, 1999) -----------------------------------------------------------------18 Figure 3.4 Simple semi-batch reactor system with continuous or intermittent addition of

reactant (Adapted from Pletcher and Walsh, 1993)---------------------------------------21 Figure 4.1 Schematic layout of the Unit operations used in Zinc Beneficiation ------------------23 Figure 5.1 Graph showing the effect of mill speed on mill product size ---------------------------32 Figure 5.2 Graph showing the effect of volumetric gas flowrate on flotation recovery ---------33 Figure 5.3 Graph showing the effects seen when changing the mass flow rate of acid ----------34 Figure 5.4 Graph showing the effect when the current in the electrowinnig cell is altered -----35 Figure 5.5 Overall process efficiency as a function of fresh feed------------------------------------36 Figure 5.6 Overall process efficiency as a function of the fresh feed size distribution-----------37 Figure 8.1 Chart illustrating effect of shifting particle size distribution to the right --------------46

List of Tables Table 3.1 Table showing the Breakage Appearance Distribution matrix -------------------------10 Table 3.2 Table showing Rajamani and Herbst (1991) variables in hydrocyclone modelling-14 Table 4.1 JKMRC Massive Sulphide ore appearance function -------------------------------------24

Development of a Spreadsheet Based Zinc Simulator Nomenclature

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Nomenclature Symbol Description Units

α Constant parameter representing efficiency

τ residence time s ρb Density of grinding material kg/m3

τb Flotation residence time in the bank hr

τT residence time in mixing tank s A electrode area m2 Ai cross-sectional of particle of size fraction i m2 As cross-sectional area of the particle m2 bij mass fraction of particle of size that appears in size i after breakage φ c Volume fraction of ZnS fraction c(IN, 0) initial concentration of reactant mol.m-3 c(IN, t) concentration of reactant at time t mol.m-3 C1 Fraction of cyclone feed above critical size reporting to underflow C2 Fraction of cyclone feed below critical size reporting to underflow CA0 Concentration of gas mol.m-3 cb concentration in the bulk of the solution mol.dm-3,

mol.m-3 cs concentration at the solid surface mol.dm-3 d25 Particle diameter where 25% of feed reports to underflow µm d50 Cut size µm d50(c) Corrected Cut Size µm d75 Particle diameter where 75% of feed reports to underflow µm db Bubble diameter mm Dc cyclone diameter cm De Diffusivity m2.s-1 di Diameter of particles in size fraction i mm di Discharge rate from mill hr-1 Di inlet diameter cm di,j rate of discharge of particle size i or j hr-1 DM mill diameter m Do vortex finder diameter cm dp Particle diameter mm Du apex diameter cm F Faraday’s constant A.s.mol-1

fi feed of size fraction i t/hr Finsol mass flow rate of insoluble material kg.s-1


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Symbol Description Units

Fsol mass flow rate of soluble material kg.s-1 h distance from bottom of vortex finder to top of underflow orifice cm H mass hold-up in mill (subscript M) tonnes iL mass transport controlled limiting current A JB fractional mill filling with balls Jg Superficial gas velocity m/s k first order rate constant hr-1 kcat specific reaction rate (determined experimentally) kf kinetic rate constant for fast floating fraction hr-1 ki First order reaction constant for flotation of size fraction i hr-1 kL mass transport coefficient m.s-1 km mass transfer coefficient dm.s-1 ko specific rate of breakage constant hr-1 KR a function of mass transfer coefficients, volume of solid particle in

bubbles, clouds and emulsion, and the specific reaction rate

ks kinetic rate constant for slow floating fraction hr-1 L mill length m M solids feed rate of fresh feed (FF) and underflow (UF) ton/hr M Mass of mineral floated ton/hr M0 Mass of mineral originally in the cell ton/hr M0,f mass of fast floating mineral initially in cell ton/hr M0,s mass of slow floating mineral initially in cell ton/hr Mi Mass flow of size fraction i t/hr n Number of cells in the bank n number of electrons dimensionlessn molar flux mol.dm-2 N rotational rate of the mill (fraction of critical) ni mass flux of Zn from size fraction i kg.m-2 P Net power draw kW Pa Probability of attachment Pc Probability of collision Pcoll Probability of collection Pd Probability of detachment pi,j product flow of size fraction i or j t/hr Q Volumetric flow rate of feed slurry m3/hr Q volumetric flowrate m3.s-1 Qpulp volumetric flowrate of slurry m3/hr R the fraction of material above critical size in mill (subscript M), fresh

feed (subscript FF) and underflow (subscript UF)

R constant ratio of mass of solvent per mass of insoluble solids kg/kg R Radius of core at time t m R0 Initial radius m


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Symbol Description Units

rEi specific selction function hr-1

Ri Fractional Recovery of size fraction i ri,j breakage rate of particle size i or j hr-1

S mass flow of pure solvent kg.s-1 S, L density of solids and liquids respectively g/cm3

Si breakage rate of particle size i hr-1 t time s, hr ub velocity of bubble rise m.s-1 V volumetric percentage of solids in the feed % V0 initial volume of particle m3 Vb volume of bulk solution m3 Vcore volume of particle core after time t m3 Vpulp slurry hold-up m3 VR reactor volume m3 x Normalised particle size (d/d50) X conversion, where A denotes species A, single denotes single pass fraction Xout mass soluble material per solute free solvent in underflow kg/kg Y Fraction of Feed appearing in the underflow Yout mass soluble material per mass solute free solvent in overflow kg/kg δ fraction of total bed occupied by bubbles fraction εmf porosity at minimum fluidisation velocity fraction ρs density of solid kg.m-3

Development of a Spreadsheet Based Zinc Simulator Introduction

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1 Introduction

Introduction and Background 1


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1.1 Background The Departments of Chemical Engineering of the University of Cape Town, the University of Stellenbosch and Cape Technikon jointly own and operate the Western Cape Mineral Processing Facility (WCMPF) in Stellenbosch. In 2001, the practical course that 3rd year mineral processing students undertake was reorganised to concentrate on the zinc beneficiation route, more precisely the hydrodynamic route. The course sets out five practicals that the students are to complete and are listed below:

Operation of a Continuous Ball Mill in closed circuit with a Screen Classifier Kinetics of Continuous Flotation [of Zinc Sulphide] Roasting Leaching [and iron removal] Introduction to electrometallurgy principles

These experiments are designed to illustrate the principles of the RLE process (Roast-Leach-Electrowinning) to students, which is the most common process to produce zinc (Reuter and Lans, 2001). The other main route is the pyrometallurgical route which involves pre-treatment (e.g. sintering), concentration (e.g. Waelz kiln process) and production (eg. Imperial Smelting Process). This route of zinc beneficiation is however of little interest in this modelling exercise as it is not studied at the WCMPF. Milling and flotation are common to both routes as they are the accepted means of size reduction and ore concentration in zinc treatment. Of the five practicals that were designed, only four are currently physically conducted by the students. The roasting practical was deemed exceedingly “boring” by students and demonstrators alike in 2001, and has therefore become a paper exercise based only on theory.

1.2 Practical Procedure At the beginning of the second semester, students who are completing the mineral processing practical course are required to give a presentation on zinc beneficiation. A literature pack is distributed for students to obtain references from and the following topics are to be covered in their presentations.

1. Environmental impact, legislation and reasons for recycling 2. Mineralogical origin, properties, applications, production and market performance 3. Hydrometallurgical Zn-Extraction processes 4. Pyrometallurgical Zn-Extraction processes and some new recycling developments

After the presentations, the students are then required to perform all four practicals in no particular order. If one was to schematically represent the way in which students learn, Figure 1.1 would best show the two areas of interest in this thesis. As can be see in Figure 1.1, a students understanding of zinc beneficiation will be derived from theory (Presentations) and


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practice (practicals). This project sets out to simulate the processes that are mimicked by the experiments using purely theoretical models. The use of these models will allow students to experiment with variables that are impossible to change during the allocated practical time. The final model that describes the whole system is to be used as an education tool for the students. It will allow them to see how changing key factors in certain unit operations affects units downstream, and what the impact on the final product is. This will hopefully enhance the learning of students by creating a stronger link between theoretical knowledge and the lessons learnt by completing the practicals. Students will therefore complete their presentations as before, but then before going on to do the practicals, they will be exposed to the simulator. This will enable them to get familiar with how the units are described in theory and what trends they can expect from making changes to input variables. Students will then go onto complete the practicals, hopefully with a better understanding of why certain effects take place.

1.3 LIMN – The Flowsheet Processor LIMN is a spreadsheet based flowsheet processor that is an add-on application for Microsoft® Windows™ Excel software. LIMN has the ability to draw flowsheets quickly and easily with a large selection of built-in icons, as well as the ability to draw one’s own icons. The flowsheet is then coupled with LIMN’s general purpose flowsheet solution engine to make it simple to complete mass balances. Utilising individual sheets to describe unit operations, one can use standard spreadsheet functions to set up process models and solve for the product streams from a particular unit. Macros embedded in the flowsheet enable the units to have inputs and outputs specified (linked to the unit ops sheet) and allow the overall mass balance to be solved iteratively – a task which is cumbersome without LIMN. LIMN is however not a dynamic simulator and only solves for steady state, but still gives a good indication of how certain parameters affect the overall product. LIMN is an additive system, i.e. streams need to be specified in a measurement that can be added and subtracted directly (such as mass). When certain unit ops use non additive measurements (e.g. concentration), one will need to convert the product streams into an additive measurement before they can be used in the flowsheet.

Figure 1.1 Schematic diagram showing student learning

Student Knowledge

Theoretical Knowledge

Practical Knowledge


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1.4 Aims and Objectives Taking all the above into account, the following main points can be used to describe the expected outcomes of this project:

1. The simulator is to be an educational tool that enhances student learning 2. The simulator is designed to predict trends, rather than accurate process values 3. Students using the simulator must be exposed to the effects of changing variables on

individual unit operations as well as the knock-on effect that changes in one unit can have down stream

4. From the results of several simulation runs, students must be able to interpret results from a theoretical and practical viewpoint

5. The simulator inputs and outputs must be clear and easy to use

Development of a Spreadsheet Based Zinc Simulator Review of the Hydrometallurgical Route

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2 Review of the Hydrometallurgical Route The hydrometallurgical route for the beneficiation of zinc begins with communition and flotation. The concentrate from flotation usually proceeds to a refinery for further processing. This processing involves roasting, leaching and electrowinning.

Review of the H

ydrometallurgical Route

2


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2.1 Communition and Flotation The SME Mineral Processing Handbook (1985) gives a concise overview of various Pb-Zn-Cu and Pb-Zn concentrators around the world. Each operation varies slightly in approach, depending on the precise mineralogy of their ore, but the general process can be gleaned from the information easily enough. Initially ore is crushed, often in underground crushers, such as the Brunswick and Buick concentrators. Crushed ore is ground in milling circuits, consisting of primary rod-mills and secondary ball-mills. Generally, the mills are operated in closed circuit with hydrocyclones as the classifiers of choice. Ore that has exited the size reduction stages is floated. Two flotation circuits exist at concentrators – firstly the lead float, tailings of which proceed to the zinc float. In some cases (e.g. Buick) regrinding is employed in the flotation circuits.

2.2 RLE (Roasting, Leaching, Electrowinning) Process Review The RLE process is not the only option available to refine zinc, but it is the most popular (Reuter and Lans, 2001). This section will describe the process in more detail incorporating practices of the zinc refinery of IMMSA in Mexico. This refinery has used the RLE process for over 20 years, and treats the floated concentrate from six mines (Alfaro and Castro, 1998). Thus it is a good case study of an operation in the industry.

2.2.1 Roasting of Zinc Bearing Ore The purpose of roasting is to convert the water insoluble zinc sulphide into soluble zinc oxide. Simultaneously ferrous content in the ore is oxidised. Some of the zinc oxide reacts with iron oxide to form zinc ferrite. Zinc ferrite is not soluble in water and so complicates the leaching stage (Reuter and Lans, 2001). The chemical reactions that occur in the roaster are explicitly stated in Section 3.4.1, on page 16. The IMMSA refinery uses a Lurgi fluidised bed roaster to process an average of 600t/d of zinc concentrate. Roasting temperatures are maintained at around 920°C using water sprays. Energy from the hot flue gas leaving the roaster is

recovered by a boiler. This recovered energy is used to drive the water spray pumps and other utilities. After further gas cleaning, the gas (consisting of 10% to 12% SO2) proceeds to the Sulphuric Acid Plant (Alfar and Castro, 1998).

Figure 2.1 Example of a typical fluidised bed roaster (From Reuter and Lans, 2001)


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An alternative to conventional fluidised-bed roasting is flash roasting, using the TORBED reactor. This technology is best applied to fine powders of a maximum size less than 50 microns. Residence time is in the order of milliseconds (Dodson et al., 1999)

2.2.2 Leaching There are three distinct leaching stages of the calcine product from the roaster. They are Neutral Leaching, Weak Acid Leaching and Hot Acid Leaching. A flow sheet of the process is illustrated in Figure 2.2. The IMMSA has further refining steps where valuable trace metals such as cadmium are recovered (Alfar and Castro, 1998). These refining steps are of no interest for the purposes of this project. The following description of the leaching process is elaborated on by Reuter and Lans (2001), and Alfar and Castro (1998).

Figure 2.2 Flow sheet of the leaching process at IMMSA, excluding advanced refining. (Adapted from information and diagrams by Alfar and Castro, 1998, and Reuter and Lans, 2001)

Calcine Spent Electrolyte

To electrolysis

To iron removal

Spent electrolyte and Concentrated H2SO4

Solid residue

Separation

Separation

Separation

Hot Acid Leach

Weak Acid leach

Neutral Leach


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Calcine from roasting and spent electrolyte is added to a cascade of neutral leaching tanks. These tanks are mixed and sparged with oxygen. The streams are pumped to thickeners. Overflow from the thickeners proceeds to electrowinning, while the underflow goes to the weak acid leach. The weak acid leaching stage is fed by the underflow from the neutral leach stage and the overflow from the hot acid leach. The overflow goes to the iron removal stage where either the jarosite or goethite process is employed to precipitate the iron out of the solution. The overflow from that process then proceeds to electrolysis. Hot acid leaching allows the zinc entrained in the zinc ferrite to be leached. The hot acid leach tanks are fed concentrated sulphuric acid and spent electrolyte. The tanks and agitators require special coatings to prevent corrosion.

2.2.3 Electrolysis At the IMMSA, purified solution from leaching is received in two 1000m3 tanks. It is pumped continuously to forced convection cooling towers. This is mixed with spent electrolyte in the main distribution launder. This combined solution is further cooled in more cooling towers before being distributed amongst the cells. The cell house has 384 concrete cells with paraliners. The cell cleaning cycle is approximately 30 days (Alfar and Castro, 1998). Cathode surface areas for cells range from 1 to 4.5m2, and current density from 280 to 640A/m2 (James et. al., 2000).

Development of a Spreadsheet Based Zinc Simulator Review of Mathematical Models

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3 Review of Mathematical Models This section will cover most of the Mathematical models available to simulate the unit operations. Some are adapted from other applications whilst others are very well documented and commonly used.

Review of M

athematical M

odels 3


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3.1 Modelling of the Ball Mill There are three approaches to describe the main phenomenon that takes place in a ball mill (Yovanovic and Moura, 1993).

The process is represented either chemically or physically using Microphenomenological models;

Statistical models based on regression of a series of experiments that describe only the results and not the process itself;

Models which describe certain macroscopic, physical aspects of the process (macrophenomenological)

3.1.1 Population Balance Model The most widely used models are those of the macrophenomenological type and they can be subdivided into two categories: energetic and kinetic. The more common of these two is the kinetic approach. Here the mill is assumed to be a reactor where the larger particles are reacting to form smaller particles. This model can be described by first order reaction kinetics as seen in Equation 3.1:

( ) ( )tMSdttdM

iii ⋅−= Equation 3.1

where Si is the selection function and represents the rate of breakage. This corresponds to the kinetic constant in first-order chemical reactions (Yovanovic and Moura, 1993). When using this model one also needs to take into account the breakage function (bij) which represents the fraction of larger particles that are reduced and can be found in the next (smaller) size fraction. The breakage function corresponds to the stoichiometric coefficient in a chemical reaction (Yovanovic and Moura, 1993). The Breakage function is commonly found in the form of a normalised matrix and a simple example can be seen in Table 3.1.

Table 3.1 Table showing the Breakage Appearance Distribution matrix

bij Breakage from size 'j'

1 2 3 4 5

1 0 0 0 0 02 0.5 0 0 0 03 0.3 0.5 0 0 04 0.2 0.3 0.5 0 0

Frac

tion

endi

ng

in 'i

'

5 0 0.2 0.5 1 0


11

A simple way to describe the meaning of Table 3.1 is to look at the behaviour of one size fraction. Consider size fraction 1 (j), A one looks down the column one can see that of the particles of this size fraction that are broken, 50% appear in size fraction 2, 30% in size fraction 3, 20% in size fraction 4 and none in size fraction 5. Similarly one can view the breakage distribution of each size fraction. One can look across a row (i) to discover the appearance of material. Therefore, looking at size fraction 4, we can tell that during breakage 20% comes from size fraction 1, 30% from size fraction 2 and 50% from size fraction 3. If it is assumed that the mill is operating at steady state and that there is perfect mixing taking place inside the mill, then Equation 3.2 can be used to solve the mass balance over a particular size fraction (Morrell and Man, 1997).

∑=

−+−=i

ji

i

ij

j

jijii p

dr

pdr

bpf1

0 Equation 3.2

Using this equation, one can solve for the product flow of all the size fractions individually, provided that the rate of breakages of each size fraction is known as well as the breakage function. The discharge of a particular size fraction can be calculated as follows in Equation 3.3:

pulp

pulpi VQ

d = Equation 3.3

If there is no segregation in the mill then all solid particles behave like water and thus di will be a constant for all size fractions (Morrell and Man, 1997). Using Equation 3.3, Equation 3.2 and Table 3.1, one is able to solve for the product flowrate of all size fractions.

3.1.2 Modelling the rate of breakage Morrell and Man (1997) also found that the specific rate of breakage of a size fraction can be related to certain mill properties as described below.

pulp

MBi V

LNDJr

2

∝ Equation 3.4

If the above equation is combined with Equation 3.3 it can be found that the rate of breakage is directly proportional to the net mill power divided by the hold-up in the mill as described in the following equations.

pulpi V

Pr ∝ Equation 3.5


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BbM JLDP ρ3∝ Equation 3.6

Equation 3.5 above has been varified by Herbst et al. (1977) who used milling tests in a 25-, a 38- and a 76-cm ball mill and found the selection functions to be directly proportional to the specific power draw of the mill. Namely;

=

pulp

Eii V

Prr Equation 3.7

where rE

i is the specific selction function and can be calculated using a simple equation that was formulated by Rajamani and Herbst (1991) and is written below.

427.1

21

1

∝ −

dddd

r iiEi Equation 3.8

3.1.3 A simplified Ball Mill Model A more simplified model is put forward by Rajamani and Herbst (1991) to enable slower on-line computers (namely the HP2100) to predict results to a reasonable level of accuracy. The following equation was proposed to predict the closed circuit operation of a ball mill.

( ) MUFFFMMoUFUFFFFFM

M RMMRHkRMRMdtdRH +−−+= Equation 3.9

The simplification that is made here is the combinations of size fractions. This model only looks at a specific size and then looks at what is above it and what is below it. This critical size would in most instances be the same, or very close to, the cut size defined in the cyclone or screen controlling the recycle to the mill. The value of the breakage constant would have to be solved experimentally.

3.2 Hydrocyclone Modelling Most mills run today are done so in a closed circuit (i.e. they have a recycle system) as in Figure 3.1. These recycle streams are first classified before being fed back to the mill. The most common classifier used is a hydrocyclone due to its greater efficiency (Wills, 1988). In order to model the cyclone, one first needs to define the cut size (d50). The cut size, as defined by Wills (1988, pp 358), is the size of a particle

Figure 3.1 Ball Mill in closed circuit with hydrocyclone


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that has an equal chance of going to either the overflow or underflow. Most mathematical models use a corrected cut size (d50(c)) which accounts for the short-circuiting that occurs in the cyclone. Modelling of hydrocyclones is very complex as all parameters involved are interrelated. Plitt (1976) developed an empirical model that enables cyclone performance to be calculated with reasonable accuracy without the need for experimental data (Wills, 1988).

( ) ( ) 5.045.038.071.0

063.021.16.046.0

508.14

LSQhDeDDDd

u

Voic

c −= Equation 3.10

These models are however only useful if the cut size needs to be determined from a specific cyclone size. Another approach to the modelling of a cyclone is to specify a specific cut size and then determine how efficient the cyclone will perform. This is most commonly achieved through the use of a partition curve as seen in Figure 3.2 (Wills, 1988). However it must be noted that Figure 3.2 is in fact a reduced efficiency curve but the curve shape is identical to that of a partition curve. The efficiency of the cyclone can be described by what is called the imperfection (Wills, 1988) is defined by Equation 3.11. This imperfection represents the slope of the partition curve. The closer the slope is to vertical, the more efficient the hydrocyclone (Wills, 1988).

Figure 3.2 Reduced efficiency curve based on partition curve

0.000

0.500

1.000

0.000 1.000 2.000

(d/d50)

Frac

tion

of fe

ed a

ppea

ring

in u

nder

flow

Real

Ideal


14

50

2575

2ddd

I−

= Equation 3.11

The curve seen in Figure 3.2 can be described mathematically by Equation 3.12 (Tarr, 1985). This equation however only takes into account the solids fraction recovery and doesn’t take into account any short-circuiting that may take place in the cyclone. Short-circuiting is the term used to describe the effect of solids that are entrenched in the flow and pass through the cyclone unclassified.

21−+

−= αα

α

eeeY x

x

Equation 3.12

The constant α in Equation 3.12 is a representation of the efficiency and is dependent of the feed material. Equation 3.12 was first used by Yoshioka and Hotta in 1955 (Tarr, 1985) who determined that α falls in the range of 3 to 4 for single stage processes in metallurgical plants. When some washing (short-circuiting) is possible then α may reach 5 or 6. The larger the value of α, the more efficient the cyclone will be. It can be found that α will normally range between 1 and 10 (Tarr, 1985). The approach taken by Rajamani and Herbst (1991) to simplify the ballmill model results in its own accompanying model for the attached hydrocyclone. As mentioned before, the model proposed combines size fractions so that there are only two parts, those above the critical size and those below it. Rajamani and Herbst therefore propose that the classification action be described by two constants, C1 and C2. the dependancy of C1 and C2 on the cut size was foundto be linear and can be described by Equation 3.13 and Equation 3.14

1250111 adaC += Equation 3.13

2250212 adaC += Equation 3.14

The model parameters used by Rajamani and Herbst (1991) were calculated at steady-state experimentation using linear regression and their results can be seen in Table 3.2.

Table 3.2 Table showing Rajamani and Herbst (1991) variables in hydrocyclone modelling

a11 0.0056 a12 1.181 a21 0.0480 a22 -2.029


15

3.3 Flotation circuit Modelling

3.3.1 First order Flotation Kinetics The flotation process is used to concentrate the sphalerite (ZnS) present in the ore. The modelling of a flotation process is very complex, as it is not yet fully understood. Due to this there are a wide variety of models available. The simplest model available is the first order kinetics model (Fichera and Chudacek, 1992) as first proposed by Zuniga, 1935.

( )kteMM −−= 10 Equation 3.15

Flotation is governed by first order kinetics, and the most common models found in literature are based on this assumption. In industrial practice, cells are commonly found in banks which contain any number of cells in series. Using first order kinetics one can find an expression to describe the recovery obtained at the end of the bank as seen in Equation 3.16, this is a size by size recovery.

nb

i

i

nk

R

+

−=τ1

11 Equation 3.16

The rate constant would in most instances be solved from pilot plant scale batch testing and then scale-up techniques used to design the actual flotation plant. However, for modelling purposes, the rate constant can be determined from theoretical estimates. To do this, microkinetics needs to be investigated and combined with some practical macrokinetics.

3.3.2 Estimation of the First order rate Constant One of the most common methods of describing the first order rate constant is through the Jameson equation (Jameson et al, 1977) and can be seen in Equation 3.17.

b

collg

dPJ

k23

= Equation 3.17

Pcoll is referred to as the probability of collection and takes into account three independent probabilities, namely the probability of collision (Pc), attachment (Pa) and detachment (Pd). The relationship can be seen in Equation 3.18.

( )daccoll PPPP −= 1 Equation 3.18

Many attempts have been made at modelling the probability of collision (Pc) using the bases of hydrodynamic forces as the predominant force. Flint and Howard (1971) solved the Navier Stokes equations numerically to obtain the probability of collision. Using this approach, Reay


16

and Ratcliff (1973) modified the modelling method and obtained an expression for the probability of collection of the form seen in Equation 3.19.

m

b

pcoll d

dP

∝ Equation 3.19

The power (m) in Equation 3.19 is dependent on particle to fluid density and can range between 1 and 2.5. Equation 3.19 can again be modified to give Equation 3.20.

mb

np

coll dd

P = Equation 3.20

Here it must be noted that n ≠ m

3.3.3 Second order Flotation Kinetics There are also many other models that are not first order, the JKMRC (Julius Kruttschnitt Mineral Research Centre) has found that a double distributed parameter model better describes the flotation of sulphides (Thorne et al, 1976). This model uses the assumption that there are two different rate constants, namely slow and fast floaters. This model was first proposed by Kelsall (1961) and then later presented by Frew and Trahar (1981) as Equation 3.21:

( ) ( )tkstk

fsf eMeMM −− −+−= 11 ,0,0 Equation 3.21

This model will however require that the feed composition, in terms of fast and slow floaters, be known. It will also require knowing the rate at which fast and slow material floats and will in most instances be solved using experimentation.

3.4 Roasting Models – Kinetic and Thermodynamic This section is an overview of potential models that could be applied to the simulation of the fluidised-bed roaster unit operation on a zinc refinery.

3.4.1 Roasting Thermodynamics The desired roasting reaction in the RLE (Roast-Leach-Electrowin) process is

ZnS + 3/2O2 → ZnO + SO2 (Reuter and Lans, 2001) Equation 3.22

This reaction is achieved in the temperature range of 900°C to 950°C for a fluidised bed reactor (Graf, 1996). The reaction predominance is also a function of partial pressure of oxygen and sulphur dioxide. The iron content in the ore leads to some undesired side-reactions, namely


17

2FeS + 7/2O2 → Fe2O3 + 2SO2 Equation 3.23

2FeS2 + 11/2O2 → Fe2O3 + 4SO2 Equation 3.24

the oxide products of which combine with ZnO to form zinc ferrite (ZnO.Fe2O3) which creates problems in the leaching operation as the zinc cannot be liberated under normal leaching conditions. (Reuter and Lans, 2001). Which reaction products are formed, and in what quantities is controlled by temperature and partial gas pressure.

3.4.2 Bubbling Bed Model The most comprehensive and detailed fluidised-bed reactor model developed so far is the bubbling bed model of Kunii and Levenspiel (Fogler, 1999). This model is based on the following premise. The reactant gas (air in this case) enters the reactor at the bottom and bubbles up through the bed. Mass transfer occurs as the reactant gas (O2) moves out of the bubble, contacting with the solid particles (ZnS), forming the reactant product (ZnO). Product gas (SO2) moves back into the bubble, and then leaves the reactor via the top of the bed. The major factors affecting conversion for this model are:

1. Rate of mass transfer of products and reactants in and out of the bubble 2. Time for the bubble to pass through the bed 3. Rate of reaction at the particle surface

Unknown variables in this model are plentiful. Following the procedure laid out by Fogler (1999) one calculates fluid mechanics parameters, namely: porosity at minimum fluidisation velocity, minimum fluidisation velocity, velocity of bubble rise and bubble size. These parameters are then used to calculate mass transport coefficients. Armed with these values, reaction rate parameters can be determined by first calculating fraction of bed occupied by bubbles, fraction of bed consisting of wakes, and volumes of solid reactant in the bubbles, clouds, and emulsion. Finally the mass of solid reactant (ZnS) required for a chosen conversion of oxygen to SO2 is defined by Equation 3.25.

XKkuA

WRsol

mfbss

−

−−=

11ln

)1)(1( δερ Equation 3.25

It is important to note that Kunii and Levenspiel derive their model for the purposes of a catalytic fluidised-bed, and not directly for ore roasting. The model as described by Fogler (1999) uses Equation 3.25 to solve for mass of catalyst required for a chosen gas conversion. The model has been directly adapted to roasting purposes, and not derived from scratch. It does not solve for solids conversion which is the factor that is of interest in this case.


18

3.4.3 Shrinking Core Model Blair (1985) states that complete roasting of sulphides to oxides happens very rapidly and proceeds effectively to completion under fluid bed roasting conditions. He goes on to state that this is because of the porous nature of the calcines formed which allow easy penetration of oxygen to the core, and easy diffusion of SO2 from it. Because of the turbulent nature of fluidised beds, it is reasonable to assume that transport of gaseous reactant to the suspended particle surface is not limiting.

In turn, this information leads to an assumption that the kinetics of the reaction can be modelled using a shrinking core model. The shrinking core model applied to ZnS roasting assumes all particles are approximately spherical, and that a layer of ZnO forms around the core of ZnS (that shrinks as it reacts with oxygen). Oxygen diffuses in through the ZnO layer, and SO2 diffuses out. This is more clearly illustrated in Figure 3.3. A derivation of the shrinking core model yields time as a function of the unreacted (core) radius. (Equation 3.26)

+

−=

3

0

2

00

20 231

6 RR

RR

CDRt

Ae

cc φρ Equation 3.26

In the case of this educational tool, roasting time is a known parameter, and thus the cubic equation would be solved for R.

3.5 Zinc Leaching Models Calcine from roasting contains predominantly zinc oxide, about 4 wt% zinc sulphate and several percent zinc ferrite (Gupta and Mukherjee, 1990). No explicit models exist in the literature for leaching of zinc. Thus, one must look to general thermodynamic principles and transport kinetics for possible correlations. Thermodynamics gives one an indication of whether or not the reaction will occur under certain conditions, while kinetics provides information on the rate of the reaction.

3.5.1 Thermodynamics of Leaching The leaching process takes place in two steps. The cold neutral leaching reaction is:

Figure 3.3 Partially reacted ZnS particle, illustrating gaseous diffusion in and out of the system. (Adapted from Fogler, 1999)

R0

O2

SO2R

ZnO layer

ZnS layer


19

ZnO (s) + 2H+(aq) ⇔ Zn2+(aq) + H2O (Hayes, 1985) Equation 3.27

Then to liberate zinc locked up in zinc ferrites, a hot acid leach is used:

ZnO.Fe2O3 + 8H+ ⇔ Zn2+ + 2Fe3+ + 4H2O Equation 3.28

The thermodynamics of Equation 3.27 and that of the zinc-water system is discussed by both Hayes (1985) and Jackson (1986). Regions in which dissolution of zinc takes place are best illustrated by a potential/pH diagram. In the modelled process the region of interest is below a pH of 7 and at a potential of greater than -0.85V (at 25°C, and assuming an activity of 10-3 mol.kg-1). Equation 3.28 is discussed in Zinc College Course Notes (Reuter and Lans, 2001), along with the Goethite process (used to precipitate the iron from solution). It is known that the reaction takes place under these conditions, and assuming the system operates under these conditions, dissolution will take place. Thermodynamics do not give an indication of the rate of reaction.

3.5.2 Leaching Kinetics – Mass-Transfer Limited Model Jackson (1986) states that there are 4 stages in leaching when a gaseous reactant is involved. They are:

1. Transfer of gaseous reactant from gaseous phase into liquid solution 2. Transport of reactant through solution to the solid-liquid interface 3. Reaction at the interface 4. Transport of products from the interface back into the bulk solution

Generally the rate limiting step is transport to the solid-liquid interface. For the purposes of the leaching model this would be assumed to be the case. A leach tank would be well mixed, with fluid velocities high enough to cause the turbulent flow regime. Such conditions eliminate diffusivity as a significant factor in mass transfer, and the traditional understanding of a concentration gradient becomes useless. The introduction of a mass transfer coefficient compensates for these problems (Jackson, 1986). The rate of mass transfer per unit area of surface area is expressed in Equation 3.29.

)( sbm cckdtdn

−= Equation 3.29

km can be estimated using the standard correlations involving the Sherwood number (Sh). Assuming Zn2+ concentration at the particle surface and the mass transfer coefficient remain constant with time, the mass of zinc leached into solution after a chosen time can be determined.


20

3.5.3 Thermodynamic Equilibrium Model Although thermodynamic equilibrium is never achieved in practice, an equilibrium model can be implemented, assuming ideal conditions. Seader and Henley (1998) consider an N-stage countercurrent leaching process. Solids entering the process are classified as soluble and insoluble. Pure liquid solvent fed to the system is assumed to completely dissolve the soluble material, and to be inert with respect to the insoluble material. This model can be adapted for a single tank. The material balance of soluble material around this single tank is:

Fsol = Yout(S – RFinsol) + XoutRFinsol Equation 3.30

At equilibrium, the ratio of mass of soluble material per mass of solute free solvent is equal in the underflow and overflow. i.e.

Xout=Yout Equation 3.31

Substituting Equation 3.31 into Equation 3.30 yields Equation 3.32

SFX sol

out = Equation 3.32

Percentage recovery of soluble material can be expressed by

sol

insolout

FRFSY )(Recovery% −

= Equation 3.33

3.6 Electrowinning Models In modelling the electrowinning process, the electrowinning cells are treated as reactors. There are three classical reactor configurations: simple batch reactor, plug flow reactor and constant stir tank reactor (Pletcher and Walsh, 1993). The simple batch reactor is labour intensive and best suited for small operations (Pletcher and Walsh, 1993). This is not appropriate for this modelling exercise and so will not be further investigated.

3.6.1 Single pass reactors Considering a single pass reactor with a steady volumetric flow rate of electrolyte passing through, the single pass conversion for a plug-flow reactor is expressed as:


21

−−= τ

R

LA V

AkX exp1single Equation 3.34

And for a constant stir tank reactor:

+−=

QAk

XL

A1

11single Equation 3.35

Conversion is limited by mass transport and electrode area, and so it is important to optimise these variables. Pletcher and Walsh (1993) show that the product of kLA can be calculated as:

b

LL nFc

iAk = Equation 3.36

Equation 3.34 and Equation 3.35 are derived by Pletcher and Walsh (1993).

3.6.2 Semi-batch reactors Typical tankhouse configurations are semi-batch (Reuter and Lans, 2001), a schematic of which is shown in Figure 3.4. The equation describing the overall fractional conversion of reactant in a semi-batch reactor at time t, derived from the mass balance on

the system, is (Pletcher and Walsh, 1993):

⋅−−=−= single

)0,(

),( exp11 ATIN

tINA Xt

cc

Xτ

Equation 3.37

Substitute Equation 3.34 or Equation 3.35 into XA

single, depending on whether a PFR or CSTR type model is desired.

Figure 3.4 Simple semi-batch reactor system with continuous or intermittent addition of reactant (Adapted from Pletcher and Walsh, 1993)

Mixing Tank Reactor

Development of a Spreadsheet Based Zinc Simulator Models Used and Major Assumptions Made

22

4 Models Used and Major Assumptions Made The following section will cover the exact way in which each unit was modelled with reference to Section 3. The major assumptions that were made will be listed along with the strengths and weakness of each particular model. All user inputs that can be varied in the simulator will also be mentioned. The Simulator layout can be seen in Figure 4.1 following. Please see the Appendix for print outs of all the spreadsheets used.

Models U

sed and Assum

ptions Made

4


23

4.1 The Simulator Appearance

Figure 4.1 Schematic layout of the Unit operations used in Zinc Beneficiation

4.2 Ball Mill Model

4.2.1 Model Selection The model that was used for the ball mill was the standard population balance, taking into account appearance and breakage (Equation 3.2). The values for the appearance function were taken from the JKRMC’s ball mill model for Massive Sulphide containing lead, zinc and copper. The first column of the appearance function can be seen below in Table 4.1. The additional columns for the matrix were derived from Table 4.1 by moving it down one row per column across. The last size fraction was normalised with respect to 1, to ensure that mass was conserved.


24

Table 4.1 JKMRC Massive Sulphide ore appearance function

Size Fraction Appearance function

1 0 2 0.1081 3 0.1442 4 0.1472 5 0.1253 6 0.1006 7 0.0805 8 0.06444 9 0.05076 10 0.03958 11 0.03103

Below 11 0.10829 The selection function was based on the power draw associated with the mill. It was calculated using a combination of the approach taken by Morell and Man (1997), Equation 3.5 and Equation 3.6, Herbst et al (1977), Equation 3.7, and Rajamani and Herbst (1991), Equation 3.8. These four equations were combined to solve for the selection function at any given mill size. The Simplified model approach taken by Rajamani and Herbst (1991) seen in Section 3.1.3, was not used due to the fact that it was over simplified for the computing power available when using LIMN.

4.2.2 Assumptions Made It was assumed that the appearance function for the mill would remain constant at all

times The constants required to solve the selection function were chosen so that the selection

function was of a similar magnitude to that presented in LIMN (Wiseman, 1999) 75% solids assumed to be fed to mill

4.2.3 User Input Variables Mill fresh feed (will effect downstream units) Fresh feed size distribution Mill dimensions (length and diameter) Mill speed (defined as the fraction of the critical speed) Fractional filling of the mill with balls


25

4.3 Hydrocyclone model

4.3.1 Model Selection The model chosen for the hydrocyclone was that of a reduced efficiency curve as seen in Figure 3.2 and modelled using Equation 3.12. Due to the fact that there are many size fractions, which tell us the maximum and minimum size the particles will lay between, it was decided that an average particle size will be used when solving for d/d50. The average particle size was solved using Equation 4.1 where n represents the size fraction in question.

nnn ddd 1+= Equation 4.1

This model was chosen because of its simplicity and general use in mineral processing applications. The major weakness of this model is that it tells us nothing about the actual cyclone (ie. dimensions). This however is not of major importance as in the practicals the mill is actually in closed circuit with a vibratory screen. This would mean that the most common thing changeable in the practical would be to change the screen size. Changing the screen size is effectively the same as changing the cut size in the cyclone, therefore making this model more appropriate to the students. The value of α in Equation 3.12 was left as a user defined constant. α can possibly range between 1 and 10, but for mineral processing plants, it is best defined between 3 and 6 (Tarr, 1985). The simplified model of Rajamani and Herbst (1991) was not used due to its application being with the simplified ball mill model only.

4.3.2 Assumption Made There is no short-circuiting taken into account Separation is on a dry mass into and out the cyclone Operates perfectly with respect to the partition curve

4.3.3 User Input Variables Cut size that cyclone operates at (d50) Sharpness of the cut (efficiency)

4.4 Flotation Model

4.4.1 Model Selection The model chosen for the flotation circuit was the first order kinetics model most commonly used. The second order kinetics was not used due the fact that in order to use them, one would need to know the composition of the ore with respect to fast and slow floaters. In practice this is normally done through a large amount of test work, or from other plants in the area using similar ore. One of the major assumptions made throughout this project is that the ore fed to the mill, and the system, is pure ZnS. Therefore the grade of the concentrate will not be


26

considered. The practical that is carried out by the students requires them to solve for the kinetic rate constant for four continuous cells in series as a function of particle size. This gave more justification to the use of first order kinetics as it would give students the opportunity to compare the results they obtain in the practical with the results they generate using the simulator. To solve for the rate constant, the Jameson equation (Equation 3.17) was combined with Equation 3.20 (where n=1.5 and m=2) to form Equation 4.2.

3

5.1

23

b

pg

ddJ

k = Equation 4.2

Using Equation 4.2 and Equation 3.16 the mass recoveries of all the size fractions can be obtained and hence the flowrate of concentrate and tailings determined.

4.4.2 Assumptions Made Pure ZnS is feed to the system therefore grade not required First order kinetics based on Jameson equation Fixed bubble size Square cells Average particle diameter assumed similar to that of Section 4.3.1 Fixed percentage solids in feed to bank

4.4.3 User Input Variables Number of cells in bank Dimensions of one cell Volumetric air flowrate Bubble size Fraction solids in feed

4.5 Roasting Models

4.5.1 Thermodynamic Model Selection The first consideration to take in setting up the roasting model is a thermodynamic consideration. How much detail is required for the purposes of this educational tool? In industry it is highly unlikely that the roaster operator will run the roaster at conditions that will allow any product other than ZnO to dominate. Unforeseen occurrences could alter the conditions such that undesired products dominate for a short period of time, but the operator will correct this and so these conditions will never be allowed to reach steady state. It is thus safe to discount thermodynamic effects for the purposes of this educational tool, as long as temperature and partial pressure input to the simulator is kept within acceptable


27

thermodynamic bounds (i.e. conditions in which ZnO predominates as a product).

4.5.2 Kinetic and Mass Transfer Model Selection The bubbling bed model (described in Section 3.4.2) would be the best model to use for a fluidised-bed. Unfortunately the complexity of the model is inhibitive for the purposes of this project. A further problem is that is derived to determine the weight of catalyst required for a certain gas conversion. In the case of the roaster, conversion of gas is irrelevant. The mass conversion of ZnS to ZnO is what is important, and so this model seems inappropriate in its current form. The shrinking core model is a superior choice to the bubbling bed model in these circumstances. A particle size distribution in the roaster is known (the concentrate from flotation), and roasting time can be chosen. Knowing R0 for each size fraction, R at time t can be calculated for each size fraction. The volume of the particles is known, and so mass conversion can be determined. Note that density is constant, so mass conversion can be calculated using volume.

3

030

330

0

0 1

−=

−=

−=

RR

RRR

VVVX core Equation 4.3

The obvious drawback of the shrinking core model is the large number of simplifying assumptions that are required – as listed in Section 4.5.3.

4.5.3 Assumptions The following assumptions and conditions have been applied in order to make the model functional and useful as an educational tool in the short time available.

Shrinking core model is applicable All particles are approximately spherical Reaction is limited by oxygen transport through the outer shell of the particle No mass transfer limitations in the bed of the reactor Ideal gas law is reasonable to determine oxygen concentration at the particle surface Nitrogen partial pressure has no impact on the reaction Sulphur dioxide concentration remains constant at all times Thermodynamic predominance is neglected, as long as partial pressure of oxygen, and

temperatures remain in acceptable ranges Residence times in the millisecond range are acceptable – see Section 2.2.1.

4.5.4 Roasting Unit User Inputs Oxygen partial pressure (does not take nitrogen content of air into account) Reactor temperature Roast retention time


28

4.6 Leaching Models Due to the general assumption that the ore fed to the process consists of pure sphalerite (ZnS), the complications that industry experience with zinc ferrite are avoided. This is a dramatic simplification of the leaching system, eliminating the need for the hot acid leach stage and jarosite precipitation. Thus the unit operation of the leach simulator will consist only of the weak acid stage.

4.6.1 Mass Transfer Limited Model The most detailed model to use is the mass transfer limited model discussed in Section 3.5.2. At first glance, this model seems to be the best choice. It is not to complex to implement, while the only other option – that of thermodynamic equilibrium – is perhaps an oversimplification, especially since industrial leaching operations will never have great enough residence times to reach equilibrium. Unfortunately two complications present themselves when attempting to model the system on a size-by-size basis (the basis on which all previously discussed units have been modelled). Firstly, after roasting the particles are now no longer pure sphalerite. The particle core consists of sphalerite, but the shell is ZnO. Only the ZnO is soluble in water. This problem can be resolved by assuming that the whole particle is ZnO for the purposes of mass transport calculations, and then balancing the mass of ZnS and ZnO at the end of the simulation. The second problem is far more severe and more difficult to resolve. Consider Equation 3.29, the rate of mass flux of the leached component (zinc in this case) into solution. It is only applicable to a single size fraction. To incorporate multiple size fractions, the following procedure is followed: The concentration of zinc in the bulk solution is a sum of the fluxes from each size fraction. i.e.

b

n

iii

b V

Anc

∑== 1

Equation 4.4

Thus, for size fraction i, assuming concentration at the surface is a constant

−=∑=

sb

n

iii

mi c

V

Ank

dtdn 1 Equation 4.5

This model has up to twelve size fractions. This function is impossible to integrate analytically, and so can only be solved numerically. Recall that LIMN operates in the Microsoft Excel spreadsheet environment. Excel does not have any built-in capabilities to solve multiply differential equations. It would be necessary to write a


29

macro in the programming language VBA. Neither Fletcher nor Robinson have any knowledge of VBA and unfortunately time allocated for the project was too short for them to attempt to learn it. As a result, this most promising approach to the leaching model was discarded.

4.6.2 Thermodynamic Equilibrium Model The implemented option was the thermodynamic equilibrium model. Such a model would never be used in totally predictive simulator, but at the conceptual stage of the project, with the mass transfer model seemingly too complex, it appeared to be the only option. All mass fractions were grouped together and a total mass independent of particle size was calculated to enter the leaching unit. Conversion was then calculated following the equations set out in Section 3.5.3. In hindsight, Fletcher and Robinson feel that it might not have been necessary to completely discard the mass transfer model. All size fractions could have been grouped together as in the thermodynamic equilibrium model, and the total mass of the size fractions summed. This assumption would effectively reduce Equation 4.5 back to Equation 3.29. At the conceptual phase of the project Fletcher and Robinson were focussed on delivering a simulator that would operate on a size-by-size basis in every unit operation. Once this model was shown to be unusable in this application, it was completely discarded. Once the decision was made to group size fractions, it did not occur to them to re-examine the possibility that the mass transfer model could be used in this way.

4.6.3 Assumptions Thermodynamic equilibrium is achieved – i.e. ratio of mass of soluble material per mass

of solute free solvent is equal in the underflow and overflow A single leaching tank is used Leaching occurs independently of particle size Zinc will only be leached from ZnO, while ZnS will pass through the system Only concentrated H2SO4 is added to the leach – there is no spent electrolyte

recirculation

4.6.4 User Inputs Acid flowrate

4.7 Electrowinning Models The only consideration left with respect to the choice of electrowinning model is whether to treat the reactor as a plug flow or constant stir tank reactor. All other considerations are discussed in Sections 3.6 and 2.2.3. The advantages and disadvantages of PFRs and CSTRs in industry are well documented elsewhere. The choice simply came down to what most would enhance the students’ learning experiences. In the practicals that the students perform, well mixed batch reactors are used. In industry, it is more likely that a plug flow regime exists within the semi-batch set up since most cathodes are flat plates. Thus the two were combined, and the choice of the model incorporates


30

a CSTR model and the semi-batch set up.

4.7.1 Assumptions Made Operation runs in semi-batch mode, with CSTR model for the cells Bulk zinc concentration of the electrolyte remains constant with time Circulating flow rate in the electrowinning circuit is equal to the exiting flow rate from

leaching No impurities in the electrolyte – thus only zinc plates the cathodes Circuit operates independently of pH

4.7.2 User Inputs Recirculating tank volume Batch operation time Limiting current

Development of a Spreadsheet Based Zinc Simulator Results and Discussions

31

5 Results and Discussions The following section will cover some basic examples of the type of trends that can be generated using the simulator. The examples were chosen based on which variables are easiest to change during the practicals run at the WCMPF.

Results and Discussion

5


32

5.1 Individual Unit Trends

5.1.1 Changing the Ball Mill speed

The trend seen in Figure 5.1 is that which is expected theoretically as well as physically. By increasing the mill speed, the impact velocity and frequency of contact is increased. This results in better breakage and thus smaller particles. For a mill of this size, the optimum speed is reported to be around 72%. As can be seen in Figure 5.1, there is still an increase in the amount of fines being produced above this optimum. The optimum running of a mill is based on the operating costs and efficiency (defined as energy required per mass feed). Increasing the speed above the optimum has very little or no effect on the efficiency (Wills, 1988). Figure 5.1 shows no sign of levelling off at much higher speeds (namely above 1). This however will not happen in reality. The critical speed of the mill will cause all the balls to adhere the sides of the mill and no breakage will take place. The reason for the constant increase seen in the simulator would be due to the directly proportional relationship between the rate of breakage and the mill speed.

Figure 5.1 Graph showing the effect of mill speed on mill product size

58

60

62

64

66

68

70

0.55 0.6 0.65 0.7 0.75 0.8 0.85

Fraction of critical speed

% p

assi

ng 0

.150

mm


33

5.1.2 Changing the superficial gas velocity during flotation

Figure 5.2 shows how the volumetric flow rate of air affects the flotation performance. The general increase in recovery as the flowrate increases is expected and will be seen by the students during their completion of the practical. It must however be noted that this model in the simulator is based on pure sphalerite being feed to the system and so grade of recovery is not an issue. If it were, then one would need to remember that by increasing the flowrate, the froth stability will be altered and the grade may be severely affected. When looking from a purely physical point of view, the changing of the flowrate of air will have a knock-on effect in the flotation cells. It will change the mixing in the cells and will also have an affect in the bubble size. Here it was assumed that bubble size remains at a constant and thus the result seen in Figure 5.2 is a purely theoretical result. It also implies that if you were to continually increase the flowrate of air, the recovery would continually increase to some maximum. However, at some point the air flowrate would be so great that it would physically cause the flotation medium to “spew” out of the top.

Figure 5.2 Graph showing the effect of volumetric gas flowrate on flotation recovery

50.00

52.00

54.00

56.00

58.00

60.00

62.00

64.00

66.00

68.00

70.00

1 1.5 2 2.5 3 3.5 4

Air Flowrate (m3/s)

Rec

over

y (%

)


34

5.1.3 Changing the acid flowrate through the leaching tank

Referring to Figure 5.3 above, it is obvious that the zinc recovery increases steeply at first. Recovery shoots from less than 66% to just under 90% with an increase of acid flowrate of 5tph. The steep curve then levels off and it takes a further increase of 12tph of acid to shift recovery up to 95%. This behaviour is an expected result as recovery can never reach 100%, but will instead tend towards that unachievable figure. Average zinc recoveries in industry are in the region of 88.5% (James et al., 2000). Thus it is clear that the model is performing satisfactorily in terms of recovery results. A recovery of 88.5% is about optimum for this scenario, achieving the best recovery with minimum acid usage. Whether the acid flowrates to the leaching section are reasonable or not is unclear. James and his co-workers (2000) do not report mass flowrates, but rather acid concentration. Also, the effect of air sparging is not accounted for.

Figure 5.3 Graph showing the effects seen when changing the mass flow rate of acid

60.00

65.00

70.00

75.00

80.00

85.00

90.00

95.00

100.00

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5

Flowrate of Acid (ton/hr)

Rec

over

y (%

)


35

5.1.4 Changing the current used in the Electrowinning cells

Current applied to the electrowinning circuit is a major variable. It is the source of greatest expense to the unit operation, and ideally should be kept as low as possible. The other important factor is the length of time that the batch runs for. Keeping batch time constant, and varying current, Figure 5.4 was generated using LIMN. Low current resulting in low operating costs also results in unacceptably poor recovery. Extremely high currents achieve acceptable recovery. Although not illustrated here, the longer it takes to run the batch, the better the recovery will be – but this also means that a lower current will be applied for a longer period of time, also escalating cost. Physically, what occurs in the cells when current density is increased is more electrons are made available to the electrolyte. Thus a greater number of Zn2+ ions can receive electrons during the batch, and thus more zinc is deposited on the cathode.

Figure 5.4 Graph showing the effect when the current in the electrowinnig cell is altered

40

50

60

70

80

90

100

500 1000 1500 2000 2500 3000

Current (A)

Rec

over

y (%

)


36

5.2 Circuiting Effects Following is a description of how the system performs when two of the main overall system inputs are changed. On a mineral processing plant, the most obvious and most possible input change will be in the fresh feed to the plant. The fresh feed is most likely to change in two areas, namely its feed rate and the size distribution of the feed.

5.2.1 Effect of changing the Fresh Feed to the system

By leaving the simulator at a fixed point and changing the initial fresh feed to the system, Figure 5.5 can be drawn up. The overall recovery was based on the mass of zinc leaving the electrowinning plant divided by the elemental zinc entering into the plant (again assumed pure ZnS). This gives an indication of how well the plant is running. The trend seen in Figure 5.5 is exactly as one would expect to see. By increasing the flowrate, the residence times in all of the units are decreased and hence they are less effective. The exception of course is the leaching tank as it was modelled at equilibrium; it is however affected as the leaching acid will remain constant whilst the input will increase. The milling circuit will be the most dramatically affected by the fresh feed increase as its recycle stream will become larger with the cyclone having to remain at the given cut size while the mill produces courser material. Individual units will all react differently and they can each be studied.

Figure 5.5 Overall process efficiency as a function of fresh feed

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

Fresh Feed (tons/hr)

Elem

enta

l Zin

c re

cove

ry (%

)


37

5.2.2 Effect of changing the Fresh Feed size distribution

The physical results of varying the size of the particles fed to the system are illustrated in Figure 5.6. Smaller particles result in better elemental zinc recovery. The reason why this occurs is quite complex, and is a combination of effects from all unit operations. In this model, the leaching and electrowinning models are independent of particle size, so their impact can be discounted. The contribution of the mill to this recovery is simple. The mill breaks particles into smaller particles. If the particles are already small, then the mill does not add much value to the system, and in fact is wasting a great deal of energy. The cost of that energy is high, and so the mill could be doing more harm than good by operating in a system that already has exceptionally fine particles. Flotation is very sensitive to particle size. When particles are too small, they will not float. Thus looking at the system solely from the point of view of the flotation operation, it is surprising that recovery increases with decreasing particle size. However, the roasting circuit counters the flotation circuit. Small particles will practically be completely converted in the roaster. Thus it appears that the improved roaster performance compensates for the drop in flotation performance.

Figure 5.6 Overall process efficiency as a function of the fresh feed size distribution

42.5

43

43.5

44

44.5

45

45.5

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Fraction passing 0.150mm

Elem

enta

l Zin

c R

ecov

ery

Development of a Spreadsheet Based Zinc Simulator Concluding recommendations

38

6 Concluding recommendations The following section will cover some of the possibilities that exist as tasks for students to complete before performing the practicals. It will also reiterate some of the key findings and conclude on the overall project.

Concluding Recomm

endations 6


39

6.1 Student Exercises

6.1.1 Assignment 1 – Fresh Feed Exercise This exercise sets out to investigate the effect that changing the fresh feed has on the rest of the system as that seen and discussed in Section 5.2.1 and Figure 5.5 The following tasks are advised for the students to complete

Adjust the Fresh feed to the system for a set range of variables decided before Whilst running the simulator, take note of the following:

o The mill feed (i.e. the recycling that is taking place) o The overall recovery of the system o The recovery changes in each of the unit operations o Load on each of the units

Propagation of error in the system With these tasks in mind, the students running the simulator will hopefully learn some valuable lessons before they move on to completing the practicals. Some of the key learning outcomes from this assignment are discussed below. Knock-on Effects Hopefully students will be able to see how all the units interact with each other and what the effects of this interaction are. The most noticeable effect in this case would be that of the mill. Here it can be seen that by increasing the mill’s feed and leaving the cyclone at the same cut size, the recycle rate becomes very large. The reason for this lies in the fact that with more feed, the mill is less efficient and will produce courser material. The cyclone will then just continue to send the course material back to the mill and so increase its feed. This could carry on indefinitely and the cause major plant problems. Sensitivity of Unit operations When looking at how the feed rate affects the individual units, it can be seen that some units will react differently to the feed increase or decrease. This will allow students to explore a sensitivity analysis of the unit operations. Knowing how sensitive a unit is, the students will be introduced to the concept of control, and can see which units require a stricter control regime. Mathematical Models When watching how each of the unit operations react with the changing feed rate, the students are forced to look closer at the mathematical basis of the models. This will then hopefully allow them to understand what assumptions were made and how the model actually works. With this in mind it is hoped that when they then move on to do the practicals, they will be able to easily predict what would happen if they were to do something during the practical. This will hopefully also give students grounding so that when they are writing there practical reports, they will have a feel as to what is correct.


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6.1.2 Assignment 2 – Optimisation Exercise This exercise is something that is completely different to what students will experience at the practical level, but will expose them to very necessary skills. This task is broken up into two different types of optimisation; namely that of economic optimisation and that of performance optimisation. For the completion of the economic evaluation and optimisation, the following tasks should be looked into and completed by the student.

Attempt to optimise the plant taking these key cost indicators into account o Cost of mill power consumption o Cost of acid required in leaching unit o Cost of electricity usage in the electrowinning unit

What happens to the system if acid is no longer paid for o Is the system overly sensitive to it? o Is it a key saving not having to pay for it?

The second part of the optimisation task would be to optimise one particular unit with respect to performance. Once this is complete, the following could be investigated.

What is the effect of the optimisation on downstream units? Some of the key learning outcomes learnt from this task are discussed below. Introduction to Process Economics Students will be able to see how a plant cost is broken down and will be able to see the sensitivity of the plant to certain variables. This will again stress the importance of control, but from an economic view point. Completing this task will also give students experience in searching for economic indicators. Students will also be able to see the benefits involved when using by-products to reduce costs. The example used here is the use of SO2 from the roaster in an acid plant to produce H2SO4 for the leaching unit. System optimisation versus unit optimisation By optimising one unit and seeing negative downstream effects, the students will be able to see how it may be worth running a unit less efficiently so that the system will run better as a whole. An example of this in the system would be the flotation and roasting setup. The flotation circuit runs better for larger size particles, but the larger size particles will cause a drop in the conversion of the roaster.

6.2 Possible improvements to the Simulator The Zinc Beneficiation Simulator produces satisfactory results and should easily be implemented as a learning tool in its current form. However, Fletcher and Robinson feel that there is some scope to improve the simulator. The following improvements are suggested:


41

Convert the leaching model from thermodynamic equilibrium to mass transfer limited.

This will allow the user greater control over the simulator as the effects of variables such as tank volume, residence time, zinc concentration, leach tank temperature and sulphuric acid concentration can be investigated.

Implement the plug flow model in the electrowinning circuit. This is not to say that the current CSTR model should be discarded – rather both can run simultaneously, and comparative results can be produced

6.3 Acknowledgements We would like to thank the following individuals who were indispensable to the successful completion of this project.

Dr. Dave Deglon for his excellent supervision. A list of everything you did for us would take up many pages – so we won’t kill off any more trees than necessary by including it.

Emile Scheepers of Stellenbosch University who gave us a tour of the WCMPF and was more than happy to answer all of our questions.

Peter Lekoma for arranging permission for us to make use of the UCT Chemical Engineering bakkie to travel to Stellenbosch.

Both Emile and Peter for providing us with the 3rd year student practical reports of the previous couple of years. The reports were extremely useful in getting an idea of what it was that the students actually did.

Development of a Spreadsheet Based Zinc Simulator References

42

7 References Alfaro, P., and Castro, S., 1998, The zinc refinery of IMMSA in San Luis Potosí,

Mexico, in Zinc and Lead Processing, Dutrizac et al. (eds), Canadian Institute of Mining, Metallurgy and Petroleum, pp 71

Blair, J.C., 1985, Fluid Bed Roasting, in SME Mineral

Processing Handbook, Vol. 1, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., New York, pp 12-8

Dodson et al., 1999 Flash roasting of sulphide concentrates – Paper

presented at TMS, available at http://www.torftech.com/publications.htm, last accessed 09/11/2001

Fichera M.A. and Chudacek M.W., 1992 Batch Cell flotation models – A Review, Minerals

Engineering, Vol. 5, No.1, pp. 41-55, Great Britain

Flint L.R. and Howard W.J., 1971 Collision efficiency of small particles with spherical

air bubbles, Chem. Eng. Sci., 26, pp 1155-1168

Fogler, H.S.,1999, Elements of Chemical Reaction Engineering, 3rd

Ed. Prentice Hall International, New Jersey, pp787-789

Frew, J.A., and Trahar, W.J., 1980 Roughing and Cleaning Flotation behaviour and the

Realistic Simulation of Complete Plant Performance, Int. J. Miner. Process., Vol. 9, pp 101-20

Graf, G.G., Zinc, in Ullmann’s Encyclopedia of Industrial

Chemistry, Vol. A28, pp514 Gupta, C.K. and Mukherjee, T.K., 1990, Hydrometallurgy in Extraction Processes, Vol 1,

CRC Press, Boston, pp 18, 62


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Herbst J.A., Rajamani K. and Kinneberg D.J., 1977 ESTIMILL–A program for Grinding Simulation

and parameter estimation with linear models, Metallurgical Engineering Department, University of Utah, Salt Lake City, UT

Jackson, E., 1986 Hydrometallurgical Extraction and Reclamation,

Ellis Horwood Limited, West Sussex, pp 48 James, S.E., Watson, J.L., and Peter, J., 2000, Zinc production - A survey of existing smelters and

refineries, in Lead-Zinc, Dutrizac et al (eds), The Minerals, Metals & Materials Society, pp205 – 225

Jameson G.J., Nam S., and Moo Young M., 1977 Physical factors affecting recovery rates in flotation,

Miner. Sci. Eng., 9:103-118 Kelsall D.F., 1961, Application of probability in the Assessment of

flotation systems, Trans. Instn. Min. Metall., 70, pp. 191-204

Morrel S and Man Y.T., 1997, Using modelling and simulation for the design of full

scale Ball mill Circuits, Minerals Engineering, Vol 10, No 12, pp. 1311 – 1327

Picket et al., 1985 Descriptions of Specific Concentrators, in SME

Mineral Processing Handbook, Vol. 2, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., New York, pg 15-14 to 15-48

Pletcher, D., and Walsh, F.C., 1993 Industrial Electrochemistry, 2nd ed., Blackie

Academic and Professional, Cambridge, pp 96

Plitt L.R., A Mathematical model of the hydrocyclone classifier,

CIM Bull. 69, pp 114 Rajamani K., and Herbst J.A., 1991, Optimal control of a ball mill grinding circuit -I.

Grinding circuit modelling and dynamic simulation, Chemical Engineering Science, Vol 46, No. 3, pp 861-870


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Reay D. and Ratcliff G.A., 1973 Removal of fine particles from water by dispersed air flotation – Effects of bubble size and particle size on collection efficiency. Can. J. Chem. Eng., 51, pp178-185

Reuter, M.A. and Lans, S.C., (eds), 2001 Zinc College Course Notes, Delft University of

Technology, Delft, pp 72 Seader, J.D. and Henley, E.J., 1998 Separation Process Principles, John Wiley &

Sons, Inc., New York, 1998, pp 234 -236 Tarr D.T., 1985, Hydrocyclones, in SME Mineral Processing

Handbook, Volume 1, pp 3D-10 – 3D-23 Thorne G.C., 1976, Modelling of industrial sulphide flotation circuits, in

Flotation – The A.M. Gauding Memorial Volume, Vol. 2, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., chapter 26, 1976, pg 725-750.

Wills B.A., 1988, Mineral Processing Technology: An introduction to

the Practical aspects of Ore treatment and mineral recovery, 4th Edition, Pergamon Press, Great Britian

Wiseman D., 1999 Examples that ship with the LIMN Installation,

File name: mill circuit.xls Yovanovic A.P. and Moura H.P., 1993, A New Macrophenomemological Concept of

Comminution in Ball Mills, XVIII International Mineral Processing Congress, Sydney

Zuniga H.G., 1935, Flotation recovery is an exponential function of its

rate, Boln. Soc. Nac Min., Santiago, 47, pp 83-6

Development of a Spreadsheet Based Zinc Simulator Appendices

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8 Appendices

Supplementary Calculations To determining diffusivity of oxygen through the shell of the particle in the roaster, the following equations were used: Diffusivity for the diffusion of gas pairs of non-polar, nonreacting molecules is:

DAB

BAAB P

MMT

DΩ

+

= 2

21

23 11001858.0

σ

Equation i

Where MA and MB are the molecular weights of A and B respectively; T is absolute temperature (in K); P is absolute pressure (atm); σAB is the “collision diameter” (Ǻ); ΏD is the “collision integral for molecular diffusion (dimensionless). The gases in the roaster are assumed to be air and sulphur dioxide. Thus MA = Mair = 28.84g/gmol; and MB = MSO2 = 64g/gmol Pressure and temperature are chosen by the user.

2BA

ABσσσ +

= Equation ii

σA and σB are constant for a particular gas, and are available in literature. ΏD can be cross-referenced in a table available in literature as it is based on the Lennard-Jones constants. Other required variables in the calculation of the mass transfer through the shell are taken as typical values. The typical values chosen are present in the spreadsheet.


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Method Used to Vary Size Distribution The method by which feed size distribution was varied was to choose a size distribution. This was input into the LIMN spreadsheet. It is unlikely that the chosen size fractions will add up to 1, thus they must first be normalised before proceeding. Once the size distribution is normalised, a simulator run is performed and the percentage of material reporting to the size fractions below 150 microns was noted. Changing the feed size distribution is a matter of shifting the size distribution curve to the left or the right, and then normalising the curve again, before repeating the run Normalisation also has the effect of increasing or decreasing the magnitude of the peak of the bell curve.

Figure 8.1 Chart illustrating effect of shifting particle size distribution to the right

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12

Size Fraction

Mas

s Fr

actio

n

Shifted SpreadOriginal Spread


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Simulator Spreadsheets

User Input OptionsInstructions: Only alter cells highlighted in blue on this sheet

Major results are available on the sheet tagged "Results"Important: Do NOT alter any values on ANY other sheet.

This will lead to unpredicable results

Fresh Feed Distrubution

Size Fraction (#) Size Fraction (mm) Feed rate (tph)

Fraction Passing (in

Feed)1 >0.850 3.00 0.102 0.850 - 0.600 4.80 0.163 0.600 - 0.425 5.40 0.184 0.425 - 0.300 4.80 0.165 0.300 - 0.212 3.00 0.106 0.212 - 0.150 2.40 0.087 0.150 - 0.106 1.80 0.068 0.106 - 0.075 1.50 0.059 0.075 - 0.053 1.50 0.05

10 0.053 - 0.038 0.90 0.0311 0.038 - 0.025 0.60 0.0212 <0.025 0.30 0.01

Total 30.00 1.00

Mill Input Variables Cyclone Input Variables

Mill diameter [m] 3.048 Cut Size [mm] 0.1

Mill length [m] 3.66 Alpha 4

Mill speed fraction of critical 0.72

Fractional filling of mill with balls 0.35

Flotation Input Variables Roaster Input Variables

No. of cells 15 Partial Pressure of Oxygen [atm] 0.8

Volume of one cell [m 3] 2 Temperature [K] 1173

Height of cell [m] 2.9 Roast retention time [s] 0.05

Volumetric air flow rate [m 3/s] 2.5

Bubble size [mm] 1

Fraction solids in feed 0.3

W/L 0.286

Leach Input Variables Electrowinning Input Variables

Solvent flow rate (H2SO4) [t/hr] 10 Recirculating tank volume [m^3] 0.3

Actual value used (taking Smin into account) 10.00 Time to run batch [hr] 120

Stoichiometric requirement: 21.06 Limiting current [A] 2000

Results and Stream Data

Stream Data Other ResultsMilling

Size Number

Size [mm] Fresh Feed Mill Feed Mill

DischargeCyclone

UnderflowCyclone Overflow

Flotation Conc

Flotation Gaunge Roast Product

% Passing Less Than 150 microns from mill

discharge

1 0.850 3 3.45 0.45 0.45 0.00 0.00 0.00 ZnS [tph] 1.35 64.91

2 0.600 4.8 5.90 1.10 1.10 0.00 0.00 0.00 ZnO [tph] 17.48 Flotation

3 0.425 5.4 7.65 2.25 2.25 0.00 0.00 0.00Percentage ZnS

Recovered (floated)

4 0.300 4.8 8.65 3.86 3.85 0.00 0.00 0.00 Leach Product 63.34

5 0.212 3 8.46 5.47 5.46 0.01 0.01 0.00 Zn [tph] 12.78 Roasting

6 0.150 2.4 10.63 8.59 8.23 0.35 0.35 0.00ZnS to ZnO Mass Conversion (%)

7 0.106 1.8 8.38 8.87 6.58 2.29 2.29 0.00 Electrowinning Product 92.84

8 0.075 1.5 4.08 6.61 2.58 4.02 3.97 0.05 Zn [tph] 10.38 Leaching

9 0.053 1.5 2.48 5.54 0.98 4.57 4.27 0.29 Zinc Recoved (%)

10 0.038 0.9 1.27 4.31 0.37 3.94 3.23 0.71 91.01

11 0.025 0.6 0.75 3.46 0.15 3.31 2.09 1.22 Electrowinning

12 <0.025 0.3 0.44 11.36 0.14 11.23 2.61 8.62 Zn Recovery (%)

Solids [t/h] 30.00 62.14 61.86 32.14 29.72 18.83 10.90 81.19

Particle Mass Distributions (tph in each size fraction)

Flowsheet

Mill Simulator

size mm Feed Discharge mill diameter [m] 3.050.850 3.448 0.448 mill length [m] 3.660.600 5.901 1.101 mill speed fraction of critical 0.720.425 7.651 2.251 fractional filling of mill with balls 0.350.300 8.655 3.855 mill feed flow rate (solids) [tph] 62.140.212 8.456 5.468 % solids in mill 0.750.150 10.633 8.586 water flow rate to mill [tph] 20.710.106 8.382 8.872 slurry volume [m^3] 4.010.075 4.082 6.607 slurry density [t/m^3] 2.500.053 2.476 5.541 holdup [tons] 0.010.038 1.269 4.307 residence time in mill [hr] 0.00012090.025 0.750 3.463 discharge rate [hr-1] 8.273 Selection Function

<0.025 0.436 11.362 ball density [kg/m^3] 7380.000 k 0.05Total 62.139 61.862 Power Expression 5.782 pk 0.00003

size mm 0.85 0.6 0.425 0.3 0.212 0.15 0.106 0.075 0.053 0.038 0.025 <0.0250.850 0 0 0 0 0 0 0 0 0 0 0 0 0.071987831 55.420418 6.698808 1 42.3840.600 0.1081 0 0 0 0 0 0 0 0 0 0 0 0.05 38.492907 4.652736 2 28.549850.425 0.1442 0.1081 0 0 0 0 0 0 0 0 0 0 0.030491943 23.474471 2.837419 3 19.306940.300 0.1472 0.1442 0.1081 0 0 0 0 0 0 0 0 0 0.018595172 14.315645 1.730369 4 13.005150.212 0.1253 0.1472 0.1442 0.1081 0 0 0 0 0 0 0 0 0.011321014 8.715575 1.053474 5 8.7713110.150 0.1006 0.1253 0.1472 0.1442 0.1081 0 0 0 0 0 0 0 0.006903994 5.3150963 0.642449 6 5.9241630.106 0.0805 0.1006 0.1253 0.1472 0.1442 0.1081 0 0 0 0 0 0 0.004210324 3.2413523 0.391791 7 3.9955460.075 0.06444 0.0805 0.1006 0.1253 0.1472 0.1442 0.1081 0 0 0 0 0 0.002567619 1.9767026 0.238929 8 2.6986010.053 0.05076 0.06444 0.0805 0.1006 0.1253 0.1472 0.1442 0.1081 0 0 0 0 0.001565834 1.2054701 0.145708 9 1.8200680.038 0.03958 0.05076 0.06444 0.0805 0.1006 0.1253 0.1472 0.1442 0.1081 0 0 0 0.000963974 0.7421229 0.089702 10 1.2478880.025 0.03103 0.03958 0.05076 0.06444 0.0805 0.1006 0.1253 0.1472 0.1442 0.1081 0 0 0.000563929 0.4341454 0.052476 11 0.776055

<0.025 0.10829 0.13932 0.1789 0.22966 0.2941 0.3746 0.4752 0.6005 0.7477 0.8919 1 0 0.00026233 0.2019567 0.024411 12 0.369595

r/d

tph Solids Mill Variables

Selection Function

Breakage Function (Normalised) - JKMRC Model using Massive Sulphide (Pb,Zn,Cu)p

Selection Function

Cyclone Simulator

size mm Feed Underflow Overflow d/d50 fraction feed in underflow0.850 0.448 0.448 0.000 8.500 1.000 0.100 0.850.600 1.101 1.101 0.000 7.141 1.000 4.000 0.7140.425 2.251 2.251 0.000 5.050 1.000 0.5050.300 3.855 3.855 0.000 3.571 1.000 0.3570.212 5.468 5.456 0.012 2.522 0.998 0.2520.150 8.586 8.233 0.353 1.783 0.959 0.1780.106 8.872 6.582 2.290 1.261 0.742 0.1260.075 6.607 2.582 4.025 0.892 0.391 0.0890.053 5.541 0.976 4.566 0.630 0.176 0.0630.038 4.307 0.369 3.938 0.449 0.086 0.0450.025 3.463 0.150 3.313 0.308 0.043 0.031

<0.025 11.362 0.136 11.226 0.125 0.012 0.013Total 61.86 32.14 29.72

alpha

tph Solids Cyclone Model Parameters Average Size (mm)

d50c - cut size [mm]

Flotation Simulatorflotation variables Flotation recovery and rates

Size [mm] k [funny unit] RSolids Mass In

[tons/hr]

Solids in Concentrate

[tons/hr]

Solids in Tailings [tons/hr]

No. of cells 15 0.850 308.567 1.000 0.00 0.00 0.00 0.85Total Residence time [hr] 0.484 0.600 237.628 1.000 0.00 0.00 0.00 0.714volume of one cell [m3] 2 0.425 141.295 1.000 0.00 0.00 0.00 0.505height of cell [m] 3.5 0.300 84.014 1.000 0.00 0.00 0.00 0.357volumetric air flow rate [m3/s] 2.5 0.212 49.867 1.000 0.01 0.01 0.00 0.252cross-sectional area [m2] 0.571429 0.150 29.651 1.000 0.35 0.35 0.00 0.178Superficial Air velocity [m.s-1] 4.375 0.106 17.631 0.999 2.29 2.29 0.00 0.126Superficial Air velocity [m.hr-1] 262.5 0.075 10.483 0.987 4.02 3.97 0.05 0.089Bubble size [mm] 1 0.053 6.233 0.936 4.57 4.27 0.29 0.063fraction solids in feed 0.3 0.038 3.743 0.820 3.94 3.23 0.71 0.045total feed in [m3/hr] 61.92 0.025 2.131 0.631 3.31 2.09 1.22 0.031

<0.025 0.550 0.232 11.23 2.61 8.62 0.01329.72 18.83 10.90

Average Size (mm)

Roasting SimulatorRoasting Variables Size [mm]

Average size [mm]

Average Initial Radius [mm]

Average Initial Radius [m]

Critical Time [s] hours t/tc

Final Radius [m] X

Density of ZnS [kg/m^3] 3000 0.850 0.850 0.425 0.00042500 12.465874 0.003463 0.004011 0.000333862 0.51523157Partial Pressure of Oxygen [atm] 0.8 0.600 0.714 0.357 0.00035707 8.7994404 0.002444 0.005682 0.000277742 0.52939356Temperature [K] 1173 0.425 0.505 0.252 0.00025249 4.3997202 0.001222 0.011364 0.000191308 0.5650099concentration of O2 at surface [kg/m^3] 0.26596343 0.300 0.357 0.179 0.00017854 2.1998601 0.000611 0.022729 0.000130134 0.61274077

0.212 0.252 0.126 0.00012610 1.097342 0.000305 0.045565 8.66672E-05 0.67531019Mair 28.84 0.150 0.178 0.089 0.00008916 0.548671 0.000152 0.091129 5.59098E-05 0.75344494MSO2 64 0.106 0.126 0.063 0.00006305 0.2743355 7.62E-05 0.182259 3.39054E-05 0.8444746sigma (collision diameter) 3.954 0.075 0.089 0.045 0.00004458 0.1371677 3.81E-05 0.364517 1.78269E-05 0.93606111omega (collision integral) 0.8386 0.053 0.063 0.032 0.00003152 0.0685839 1.91E-05 0.729034 1.68068E-05 0.84845474Diffusivity [m^2/s] 0.000127686 0.038 0.045 0.022 0.00002244 0.0347492 9.65E-06 1 0 1

0.025 0.031 0.015 0.00001541 0.0163911 4.55E-06 1 0 1volume fraction of ZnS 1 <0.025 0.0125 0.00625 0.00000625 0.0026959 7.49E-07 1 0 1tortuosity 1.5pellet porosity 0.4constriction factor 0.8Effective Diffusivity 2.72398E-05

cactus 69015218.8

Roast time [s] 0.05

Size [mm] feed [t/hour] product (ZnO) product (ZnS)0.850 0.00 0.00 0.00

. 0.600 0.00 0.00 0.000.425 0.00 0.00 0.000.300 0.00 0.00 0.000.212 0.01 0.01 0.000.150 0.35 0.27 0.090.106 2.29 1.93 0.360.075 3.97 3.72 0.250.053 4.27 3.63 0.650.038 3.23 3.23 0.000.025 2.09 2.09 0.00<0.025 2.61 2.61 0.00

18.83 17.48 1.35

ZnS 1.35ZnO 17.48

Leaching SimulatorLeaching VariablesFa (ZnS) [t/hr] 1.35Fb (ZnO) [t/hr] 17.48

S (H2SO4) [t/hr] 10.00 10.00 stoichiometric requirement 21.05833552R 0.67W (Wash factor) 11.12N (Number of tanks) 1.00Xn 1.75Y1 1.75Weight percent solvent in underflow 40.00Smin 0.90Percent Recovery of soluble material 91.01

mass Zn leaving leach [t/hr] 12.78Mass H2SO4 leaving [t/hr] 9.10total mass flow [t/hr] 21.88Volumetric flow rate of electrolyte [m^3/hr] 21.88concentration of Zn [t/m^3] 0.58concentration of Zn [mol/m^3] 8932.12

Electrowinning SimulatorElectrowinning VariablesVolumetric flow rate in [m^3/hr] 21.88

tank volume [m^3] 0.3residence time of tank [hr] 0.01371time to run batch [hr] 120limiting current [A] 2000n 2Faraday's (F) [A.hr/mol] 2.68E+01c infinity [mol/m^3] 8932.12

kLA 4.18E-03

fractional conversion (Xa) 0.81186

Mass Zn In (tph) 12.78Mass Zn Out (tph) 10.3757

Zinc Beneficiation Simulator

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