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Based on fluid flow and rock skeleton elastic deformation during heap leaching process, a deformation-flow coupling model is developed. Regarding a leaching column with 1 m height, solution concentration 1 unit, and the leaching time being 10 days, numerical simulations and indoors experiment are conducted, respectively. Numerical results indicate that volumetric strain and concentration of solvent decrease with bed’s depth increasing; while the concentration of dissolved mineral increases firstly and decreases from a certain position, the peak values of concentration curves move leftward with time. The comparison between experimental results and numerical solutions is given, which shows these two are in agreement on the whole trend.

Solution mining is conceptualized as the removal of dissolved metals from original solid matrix [

The purpose of this work is to apply an elastic deformation model for simulating the column leaching processes and develop the governing equations of coupled flow and deformation behavior with mass transfer. These equations are solved numerically by Comsol Multiphysics. The changeable regularity of volumetric strain and concentration distributions of the solvent and the solute is given. The validation of the mathematical model and numerical analysis is concerned through experiment.

Supposing the solution flows in a deformational and homogeneous porous medium, the basic seepage equation for column leaching is [

Solid elastic deformation equations describing the plain strain deformation state are [

Both H^{+} of solvent and Cu^{2+} of solute are transported by the leaching solution. The couple mass relationship is deduced based on the continuous reaction rates between them.

The equations describing mass transfer in pore during leaching processes are

The chemical reaction rate

Assuming that the absorption on pore surface is linear, balanced, and thermal, the relationship between dissolved term and absorption term is

That is,

Considering the diffusion flux

Substituting (

Regarding a leaching column with 1 m height and solution concentration 1 unit being continually supplied from the top of the column for 10 days, application rate is

Schematic of numerical calculation.

The initial conditions, top boundary conditions, and bottom boundary conditions for the flow, deformation, and mass transfer coupled equations are

During calculation process, initial porosity

Figure

Distribution of volumetric strain in leaching column.

Figure

Spatial and temporal distributions of reagent (a) and dissolved mineral (b).

Solute concentration distribution

Reagent concentration distribution

To verify the numerical simulations, indoors physical experiment is done according to dump leaching in Dexing copper mine, Jiangxi province. The chemical content analysis of ore sample is 0.20% sulphide copper, 0.17% sulphide copper, 0.12% free oxide copper, and 0.072% combined oxide copper. Ore component analysis is conducted by X-Ray Diffractometer M21X and is shown in Table

The chemical analysis of main element contained in ore sample.

Component | Cu | Fe | S | Mo | SiO_{2} |
Al_{2}O_{3} |
CaO | MgO | As |
---|---|---|---|---|---|---|---|---|---|

Percentage (%) | 0.56 | 4.40 | 0.91 | 0.012 | 67.73 | 13.21 | 0.20 | 1.64 | 0.013 |

The maximum diameter of ore particle in dump leaching field in Dexing mine is 800 mm. It is very difficult to carry on experiment according to field situation. What is more, the general apparatus is not large enough to hold such large ore sample, so most theoretical research works are conducted indoors. The inner diameter of the column leaching cylinder used in experiment is 50 mm; it is necessary to crash ore sample to let the diameter be less than 10 mm according to the research conclusions obtained by Bear [

The distribution of ore particle diameter after crashing.

Particle diameter (mm) | <0.1 | 0.1~0.2 | 0.2~0.4 | 0.4~0.7 | 0.7~2 | 2~5 | 5~8 | 8~10 |
---|---|---|---|---|---|---|---|---|

Content (%) | 1.94 | 6.3 | 4.12 | 3.63 | 4.6 | 12.59 | 35.84 | 30.98 |

The samples were bioleached in PVC (5 cm in diameter and 100 cm in height) for 10 days. Solution with a concentration of 1 unit is continually supplied from the top of the column; the application rate is

As shown in Figure

Comparison between calculated result and experimental result of the concentration of copper ions in ore heap.

With respect to the mineral skeleton deformation, a flow and solid elastic model is developed to describe the flow reaction and mass transfer processes in heap leaching.

The model equations are solved by Comsol Multiphysics Software. The distributions of volumetric strain and concentrations of reagent and dissolved mineral are given based on numerical results.

The numerical simulation results show that the straight strain decreases with the bed’s depth increasing; the concentration of the solvent decreases with the bed’s depth increasing; the concentration of dissolved mineral increases firstly and decreases from a certain position: the peak values of the curves move leftward with time.

The numerical results are compared with the experimental results; these two are in agreement on the whole trend, which indicates that the mathematical model, the numerical method, and parameters can describe the multifactor coupled processes in heap leaching.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This project is supported by the Natural Science Fund of China (51104100, 51304076, and 51074013).