Modelling of Leaching of Molybdenum in Slag

Jean-Paul Veas

University of Concepción

Stockholm, April 2005


Abstract

Leaching experiments of molybdenum from slag were carried out in laboratory at the Concepción University. These experiments were modelled and the results compared with the experimental data. Several reactions occur during the dissolution of the slag by the acid. For sake of simplicity, the reaction of sulphuric acid with oxide of Iron (III) was considered as representative of the system. The model assumed that the dissolution rate varies with the pH of the solution and the surface area of the particles, which decrease with time. Some simple cases are solved by applying analytical solutions. For more complicate situation, numerical solutions were employed by using the software MATLAB.

Heap leaching of slag is also modelled. The heap is irrigated with sulphuric acid. In this case, the variation of the metal concentration in the solution, of the proton concentration, and the concentration of metal in the slag no reacted are considered. The differential equations were solved by using the software FEMLAB.

The experimental showed that the particle size has a large impact on the dissolution rate of the slag. However, the impact of the pH seems to be very small. A reasonable agreement is obtained between the experimental results and the simulations.


Table of Contents

Abstract 2

Contents 3

Introduction 5

Characterisation of the slag 6

Experimental part 7

Modelling used in the simulations 9

Modelling of the laboratory experiments 9

Leaching model with constant reaction rate 9

Reaction rate in function of particle size and acid concentration 10

Model to be solved by numerical methods 13

Dissolution of slag in a heap irrigates with sulphuric acid 14

Results and Discussion of the Experiments. 15

Experiment A 15

Experiment B 20

Simulation of heap leaching for slag. 22

Conclusions. 25

References 25

APPENDIX 26


Introduction

Chile is the major producer of molybdenum in the world (Reference: Statistics of Copper and Other Minerals 1994-2003). The main mineral ores is the molybdenite. In those deposits the molybdenite is, in general, associated to copper ores. Different processes are used to separate the molybdenum of the cooper and other metals.

When the minerals are separated and refined by pyrometallurgy, slag is generated. The slag formed contents still interesting percentages of some metals (e.g., copper, molybdenum, irons, etc), which may do its recovery economically attractive. Therefore, it is important to study the properties of the slag and investigate the separation methods that could be applied. This could give a commercial value to the slag.

At the department of Metallurgy of University of Concepción, the recovery of metals from the slag has been studied for several years. At present, a pilot plant is working to extract address the extraction of metals from the slag and increase its commercial value. Slag originated at the northern of Chile is used in the plant.

This present the results of simulations performed of experiments carried out in the plant of University of Concepción. Dynamical model are developed and different programs (tools) are used (e.g., Matlab, Phreeqc, Femlab).


Characterisation of the slag

Some properties of the slag are present below (Ref: Rory-report). Table 1 shows the composition of a slag from Caletones (slow cooling). The density of the slag is shown in Table 2.

Table 1: Slag composition

Elements / Concentration, %
Cu / 1.1
Fe / 43.4
Mo / 0.3
Si / 15.2

Table 2: Slag Density

Components / Density / Units
Slag / 5000 / kg/m3

Some data used in this report are also shown. Table 3 shows the particle size used in the simulations equivalent to the respective size expressed as mesh N (Perry and Green, 1984). The densities of the sulphuric acid solution at ambient temperature (Perry and Green, 1997) are also shown, Table 4.

Table 3. Total surface area of the solid

Mesh N / Assumed radius,
mm / Total Surface Area in 200 g of slag, m2
100%-200 / 0.037 / 3.24
100%-75 / 0.100 / 1.20
-35+100 / 0.2845 / 0.42
-10+20 / 1.2605 / 0.095

Table 4: Sulphuric acid solution densities ambient temperature

Sulphuric acid solution (%) / Densities (kg/m3)
1.25 / 1009
2.5 / 1016
5.0 / 1032
10 / 1066
15 / 1103


Experimental part

The experimental part was carried out in the pilot plant at the University of Concepción (Ref: Rory-report). A short summary of the experimental conditions and the results are shown.

Two sets of experiments were performed. In the first set (A), the influence of the size of the particle in the mineral recovery was addressed. The second one (B) shows the influence of different concentration of acid at the beginning on the recovery of mineral.

The experimental conditions used in the experiments are shown in Table 5. The experimental results, iron recovery as a function of time, are shown in Figures 1 and 2.

Table 5: Experimental conditions used in the experiments

Data
Temperature, C / 18
Agitation, rpm / 500
Liquid volume, (l) / 1
Ratio (liquid/solid), l/kg / 5
Experiment A
Volume of solution, l / 1.0
Concentration of acid, g/l / 25
Radius size, m / 0.000037 – 0.00126
Experiment B
Radius size, m / 0.000037
Concentration of acid, g/l / 12.5 - 150

Figure 1. Iron recovery for different particles sizes (Experiment A) with an acid concentration of 0.26 M.

Figure 2. Iron recovery for different acid concentration (Experiment B) with a particle radius 0.037 mm.

Modelling used in the simulations

Regarding the reaction of the sulphuric acid with the slag, there are several minerals in the slag that may react with the sulphuric acid. But, due to the high concentration of Fe in the slag, only the reactions between the sulphuric acid and iron are considered. The dissolution of the other minerals (e.g., molybdenum) is calculated assuming the dissolution of the minerals takes place in congruent form.

There are also several iron minerals that may react with the sulphuric acid, but for sake of simplicity, only the reaction with is considered

In the simulations, models of different degree of complexity are used. In the first set of modelling, the batch experiments carried out in the laboratory are modelled. Two cases are modelled:

§  Reaction rate constant. This model may be used at the initial period, when the initial conditions do not have changed too much.

§  Reaction rate is a function of the particle size and the acid concentration. This model could be applied over long times.

In the second set of simulations a hypothetical heap with slag is modelled, where the acid is irrigated on the top the heap.

Modelling of the laboratory experiments

In order to simplify the simulations some assumptions are done. The following assumptions were done,

§  The composition of the slag is uniform.

§  The dissolution occurs on the surface of the particle.

§  The congruent dissolution of the minerals takes place. The metals are dissolved in proportion to its composition.

§  The solution with the minerals are well-stirred.

§  All the particles have the same size.

Leaching model with constant reaction rate

In this case the reaction rate is assumed to be constant. This model may be applied at the initial period when the particle size (i.e., the specific surface) and the acid concentration in the solution do not have changed too much. The results also indicate the maximum reaction rate, since with reaction rate decreases with the time due mainly to the reduction of the concentration of the acid. The differential equation describing the concentration of the metal ion in the solution may be written as,

(1)

Where is the volume of the solution (m3), C the metal concentration (mol/m3), t the time (s) and the reaction rate (mol/s), which is constant and calculated for the initial conditions.

The reaction rate is constant with time and its value is calculated using the conditions (particle size and acid concentration) at the start of the experiment. The dependence of the reaction rate with the concentration of the acid is poorly known. In this simulation is assumed that the reaction rate is proportional to the concentration of protons in the solution.

(2)

Where is the total surface area of the particles at the start of the experiment (m2), is the composition of metal in the slag, is the acid concentration at the experiment start (mol/m3), and k is a reaction rate constant (m/s).

The Equation (1) may be integrated directly using that the solution was initially free of solute (metal ion)

(3)

Then the integration yields

(4)

The total surface area of the particles at the start of the experiment, , is determined as

(5)

Reaction rate in function of particle size and acid concentration

In this case the reaction rate is considered to be function of the proton concentration and the particle size. The latter determines the contact surface between the acid solution and the material in the particle. The differential equation describing the concentration in the solution may then be written as,

(6)

is the total surface area of the particles (m2), which decreases with time. It is determined by the particle radius, (m) and the number of particles in the solid, . It is assumed that the number of particles is constant during the experiment. The radius of the particles decreases with time due to the dissolution reaction.

(7)

The number of particles is determined by the volume of the solid, (m3) and the radius of the particles, (m) at the start of the experiment.

(8)

Introducing Equation (8) in (7) and reorganizing, we total surface area during the experiment is obtained.

(9)

Finally, the ratio between the radii may be expressed as the ratio between the mass of solid during the experiment, (mol) and the mass at the start, (mol)

(10)

Now, a relation between solid mass and the concentration of the sulphuric acid is needed. At the start of the experiment the mass of solid equals its initial value and no metal is dissolved in the solution. At the end of the experiment the solid has been completely dissolved and the concentration of the solution will be

(11)

Since that this relationship is linear, we can write

(12)

Introducing Equation (12) in Equation (10), the total surface area is expressed as a function of the concentration of the metal ion in the solution.

(13)

Regarding the concentration of protons in the solution, this decreases when the concentration of metal ions in the solution increases.

(14)

Where f is the stoichiometric factor for the dissolution reaction

(15)

Introducing Equations (13) and (14) in Equation (6), the differential equation for the concentration of the metals ions in the solution is obtained,

(16)

The analytical integration of this equation is apparently not possible. Equation (16) is solved for two special cases. One is the case where the concentration of the acid is assumed to be constant and the other where the particle size is assumed to be constant.

The first case, constant acid concentration, could be applicable when the consumption of acid is not important (small stoichiometric coefficient f) compared with the variation of the particle radius or when acid is continuously added. The equation for the concentration of the metal ion in the solution is then

(17)

This equation may be directly integrated using that the concentration of the solution is zero at initial time (C(t=0) = 0) as initial condition

(18)

The second case, constant particle size, could be applicable when the consumption of acid is important (large stoichiometric coefficient f) compared with the variation of the particle radius. The differential equation for the concentration of the metal ion in the solution is then

(19)

This equation may also be directly integrated

(20)

Model to be solved by numerical methods

Equation (16) may be however integrated numerically using e.g., Runge-Kutta. However, in practical cases, the dependence between the variables and parameters may be more complicated and difficult to visualise. In order to give transparency to the equations and allow that modifications and improvements may easily be made, the Equation (16) is writen using three differential equations: for the concentration of the metal ion in the solution, concentration of acid in the solution, and for the mass of metal that has not reacted.

Equation for the concentration of the metal ion in the solution

(21)

Equation for the concentration of the acid in the solution

(22)

Equation for the amount the metal that has not reacted

(23)

Where H is the concentration of protons (mol/m3) in the solution, m is the mass of metal (mol) to be dissolved. The reaction rate , varies with the particle size (specific surface area) and the pH of the solution,

(24)

There are several tools that may be used to solve these differential equations. The equations were integrated by using the Runge-Kutta method. Software MATLAB was used.

Dissolution of slag in a heap irrigates with sulphuric acid

In this case, the slag is deposited forming a heap of a given height. Solution of sulphuric acid is irrigated on the top of the heap. For sake of simplicity, it is assumed that the height of the heap is practically constant. This means that when the metals are dissolved, the size of the particle is maintained constant; no gangue is consumed by the acid. This assumption will be discussed later. In this case, we have a variation of the concentration of the acid in the solution and the particle size. They vary in time and along the bed.