J. Cent. South Univ. Technol. (2007)06-0838-04 

DOI: 10.1007/s11771-007-0159-0 

Dynamic experiment and numerical simulation of solute transmission in heap leaching processing

LIU Jin-zhi(刘金枝)^{1, 2}, WU Ai-xiang(吴爱祥)¹, YANG Bao-hua(杨保华)³, JIANG Huai-chun(江怀春)¹

(1. School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China；

2. College of Information Technology, Shanghai Fisheries University, Shanghai 200090, China;

3. Department of Electricity and Information Engineering, Hunan International Economics University, Changsha 410205, China)

Abstract: Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c₀＝0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.

Key words: heap leaching; solute transmission; dynamic experiment; numerical solution

1 Introduction

Leaching is defined as the removal of minerals by dissolving them from the solid matrix. Generally, in-situ leaching and heap leaching are adopted, and the later is often used to extract the valuable metals from the low-grade ores with its simple technology, low investment, high efficiency and simple management^[1-3].

The scientific research on heap leaching began from saturated situation that contained a coupled solid-liquid phases process^[4-6], and the convection-diffusion-equation (CDE) could be used to describe the solute transfer in porous media^[7]. When considering the interaction between solute and solid bone, the convection-diffusion equation is combined with the retardarce multiplier R_d.

When the spreading rate is small, according to Peclet principle^[8], solute transmission is mainly resulted from diffusion, and the transmission caused by convection can be omitted. Under this circumstance, we can not only discuss the analytic properties of the equations^[9], but also give the expression of the analytic solution^[10]. On the contrary, if the spreading rate is large, solute transmission is dominated by convection, then the analytic method is only used to discuss some simple or ideal cases, and the numerical method is often used to solve the transmission equations in practical problem^[11].

In this paper, the convection-diffusion equation (CDE) was solved numerically by characteristic difference method, the validity of the model and the accuracy of the parameters were verified through the dynamic experiment of ferrous ion transmission in saturated ore column. The numerical results and measured values were compared.

2 Experimental

2.1 Experimental materials

The experiment was conducted according to dump leaching of copper in Dexing Copper Mine, Jiangxi Province. Since there are always some concomitants contained in ore, they encumber the leaching of aimed mental elements through competing with the aimed minerals to consume reagent or oxidant and decreasing the reagent concentration, which results in reducing leaching reaction speed and leaching rate. So it is necessary to analyze the chemical and mineral ingredient contained in ore. The copper ore sample provided by the mine was tested by the Testing Center of Changsha Institute of Mining and Metallurgy. The checkup results of ore rock, the chemical content analysis and the chemical analysis of main element contained in ore sample are shown in Tables 1-3, respectively.

Table 1 Checkup results of ore rock

Table 2 Chemical contents of ore sample

Table 3 Chemical analysis of main element contained in ore sample(mass fraction, %)

The maximum particle diameter of the ore in dump leaching field in Dexing Mine is 800 mm. It is very difficult to conduct experiment in the actual locale, moreover it is almost impossible for the general apparatus to contain such large ore sample. Therefore, the research work is often carried out indoors. According to the research conclusions obtained by Holt & Gibbs et al, the diameter of the sample for modeling should not be less than five or six times of the maximum diameter of specimen^[12]. The inner diameter of the column leaching cylinder used in experiment was 50 mm, so it is necessary to crash the ore sample to ensure the diameter being less than 10 mm. The distribution of ore particle diameter after crashing is listed in Table 4.

Table 4 Distribution of ore particle diameter after crashing

The analysis of ore diameter was done through griddling method. When the differences between different ore diameters are very large, the logarithm coordinate is often adopted to draw ore diameter curve. The distribution curve of ore diameter is shown in Fig.1.

The porosity and permeability coefficient measured by volumetric method are 0.344 and 2.23×10^{-3 m/s, respectively[13]}.

Fig.1 Distribution of particle size of ore granular media used in experiment

2.2 Experimental installation and procedure

The whole experimental installation is composed of upper(two) and lower water trunks, pipe for filling ore granular media and adjusting valve. The scheme is shown in Fig.2, and the type and specification are listed in Table 5.

Fig.2 Scheme of column leaching test set

1－Upper trunk(filling water); 2－Upper trunk(filling sulfide ferrous solution); 3－Adjusting flux valve; 4－Ore sample;   5－Holes for fetching liquid sample; 6－Lower trunk

Table 5 Type and specification of main apparatus used in experiment

The three stages of the experimental procedure are shown as follows:

The first stage includes filling water and sulfide ferrous solution(c₀＝0.04 mol/L) in upper trunks 1 and 2, weighing ore sample according to the distribution of diameter designed beforehand, filling the ore in column leaching cylinder after mixing evenly, and placing a thin layer of fiber on the bottom and a layer of small glass balls on the top to ensure ore sample not lost and uniform spread respectively.

The second stage includes saturating the ore sample by soakage method, that is, opening the left valve, spreading with water, and observing the solution surface. Ore column becomes saturated once the solution surface reaches the top of ore sample.

The last stage includes adjusting spreading rate: q=1.44×10^{-4 m3}/(m²?s), closing left valve and opening right valve to fill sulfide ferrous solution. The whole eluviating process lasts for 2.5 h. During the process of filling sulfide ferrous solution, solution samples are fetched from the three holes on side every other certain time so as to test the concentration of ferrous ions.

3 Mathematical simulation

The scalar equation for the ferrous ions concentration c at time t is:

          (1)

where  R_d is the retardarce multiplier, D_L is dispersion coefficient of ferrous ions in liquid, u is flowing velocity, Q is the source/sink term, and x is the distance from the top of the heap. In porous media flow, the flowing velocity is proportional to the spreading rate: u=q/n.

Initial condition:

c(x,0)=0               (2)

Boundary conditions:

            (3)

When u is much larger than D_L, Eqn.(1) is a convection-diffusion equation dominated by convection. Actually, we often meet the convection-diffusion equation dominated by convection in mechanics, physics, and other areas. According to the classification, it belongs to parabolic type(unsteady case) or elliptic type(steady case). Due to the domination of convection, it also bears the basic features of hyperbolic type. Therefore, it is necessary to develop the numerical method to reflect the characteristic properties of hyperbolic equations with high accuracy, good stability, and suitable to small diffusion coefficient. The characteristic difference method can meet these requirements^[14]. When the convection-diffusion equation is discreted by characteristic difference method, the second-order term (diffusion term) is approximated with second-order center difference, and the first-order term(convection term and the derivative with respect to time) is substituted with difference afterward.

According to initial condition and boundary conditions, the equation is discreted by finite characteristic difference method, and the set of closed difference equations is solved through the program written in Visual Fortran5.0 language. The parameters chosen during calculation are as follows: D_L=4.48×10^{-6 m2}/s (determined by experiment), R_d=4.488, u=4.186×10^{-4 m/s, Q=0.}

4 Results and discussion

As shown in Fig.3, the calculated results and measured values of the concentration of ferrous ion at different times are consistent on the whole trend at three fetching points, which indicates that the mathematical model, the numerical method and parameters can describe the transmission process of ferrous ion in saturated ore column.

The case at the point near inlet(x=13 cm) matches better, while at the other two positions, there are some differences between calculated results and measured values. The main reason is that there exists sorption between medium and ions when the solution transfers in ore heap. At the point near inlet, the influence is comparatively small with the time that sorption reaches saturated state being shorter and vanishes more quickly. While at the farther point, the case is contrary, sorption requires longer time to reach saturated state and the corresponding influence becomes greater. In addition to sorption, there are some other phenomena occurring during the solution flowing in ore column, such as immobile effect etc. However, all these factors are just simplified through retardarce multiplier in model calculation which arises some errors. What’s more, the difference at the point near inlet is obviously smaller than the ones at the other two places.

We can also see the changeable regularity of ferrous ions concentration with respect to time. In the initial period of spreading, the concentration near the inlet increases gradually, and reaches the peak value     0.04 mmol/L, with the time going on, the peak of concentration moves upward, when the concentration at the outlet reaches 0.04mmol/L, which means the concentration at every place inside the ore column keeps the same, and is the same as the initial concentration.

Fig.3 Comparison between calculated results and experimental results of concentration of ferrous ions in ore heap

(a) x=13 cm; (b) x=50 cm; (c) x=87 cm

5 Conclusions

1) Based on the dynamic experiment indoors, the transmission of ferrous ion in saturated ore column is simulated by the convection-diffusion equation. The numerical results and measured values are compared and they are consistent on the whole trend, which shows that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore column.

2) However, there also exist some scarcities, the transmission in ore column is influenced by many factors. But only some main factors can be considered when building the model and it is impossible to consider all factors, which results in some differences between the calculated results and measured values. So it is necessary to do further research work on modeling.

3) The leaching rate is the comprehensive result influenced by many factors, and it relates to the physical and chemical properties of ore and heap. The research work conducted in this paper is very useful to analyze and discuss the factors influencing the leaching rate, so as to control the leaching reactive rate reasonably and ensure the uniform leaching.

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(Edited by YANG Hua)

Received date: 2007-03-02; Accepted date: 2007-04-18

Corresponding author: LIU Jin-zhi, PhD; Tel: +86-731-2656845; E-mail: liu0619@mail.csu.edu.cn