Applied research on the numerical simulation of Cu and Cd transport laws in a metal mining area

With the continuous progress of industrialized production in China,¹ the development of minerals has promoted economic development, but at the same time, mineral development has also caused serious environmental problems.² Mine wastelands formed by the constant development of minerals take up large amounts of land, cause damage to the local ecological environment, and lead to environmental pollution.³ Mining causes serious pollution to the surrounding ecological environment. Mine waste piled in an open environment will enter the soil, water, and atmosphere with surface runoff, which can be promoted by various reasons leading to serious heavy metal pollution problems.^4,5 Once heavy metal ions enter the soil, they will accumulate and irreversibly remain in the soil for decades because bacteria, micro-organisms, and fungi in the environment cannot readily degrade these heavy metal ions;⁶ subsequent human agricultural activities and the cumulative absorption effect of crops themselves cause direct or indirect transport to humans through the food chain, ultimately causing damage to human organs.⁷ 

The seriousness of environmental pollution by heavy metals in mining areas has been widely acknowledged by researchers at home and abroad. Many research studies have been carried out on heavy metal pollution in the soil in mining areas. Domestic and foreign research on heavy metal pollution in mining areas mainly focuses on the following: determining the content of heavy metals in the soil around mining areas and the study of chemical forms,⁸ the study of ecological risk assessments of soil heavy metal pollution,⁹ research on soil heavy metal enrichment characteristics around mining areas,¹⁰ soil heavy metal pollution behavior and distribution characteristics in mining areas,¹¹ soil heavy metal migration and transformation research,¹² and soil heavy metal pollution ecological restoration research.¹³ Among these studies, there are many studies on the ecological risk assessment, ecological restoration, content, and enrichment characteristics of heavy metals in soils in mining areas. However, there are few studies of the migration and transformation of heavy metals in soil and numerical simulations thereof. In 2014, Han et al.¹⁴ first studied the migration characteristics of heavy metals in soil and the reasons affecting their migration; in 2018, Zhan et al.¹⁵ introduced the idea of a layered soil pillar model and studied two groups according to the migration laws of heavy metal ions in layered soils; in 2018, Jiao et al.¹⁶ first used COMSOL porous media and groundwater flow modules to simulate the unsaturated soil water flow, built a coupled transport model, adopted a different coefficient estimation method, and analyzed the results of the migration simulation; in 2018, Xin and Zhan¹⁷ used the COMSOL software to simulate the migration law of different heavy metal ions and studied multicomponent heavy metal ions in multiple layers to assess the law of migration in the soil and its impact on the surrounding environment. However, most studies on heavy metals in mining areas have focused on the heavy metal migration laws and their concentration changes in the soil. There are relatively few theoretical studies combining heavy metal migration laws and numerical simulations.

Combining the migration law of heavy metals with numerical simulation research is of great significance for understanding the distribution and migration characteristics of soil heavy metals in mining areas, as well as the continuous use and effective management of mining areas, and provides a certain scientific basis for remediating soil ecological risks in mining areas.¹⁸ Aimed at assessing the current status of soil pollution in the mining area of Leiyang City, Hunan Province, this paper first uses a Geographic Information System (GIS) to collect soil in the mining area¹⁹ and then uses a layered soil column model and the COMSOL software to simulate the movement of pollutants in the soil. Finally, the heavy metals Cd and Cu in the soil of the mining area are analyzed experimentally.

The determination of the heavy metal contents was divided into the following steps:

1. To determine the total content, a proper amount of a treated sample of soil was placed in a digestion tank and digested with HCl–HF–HNO3–HClO4. After the reaction was completed, a nitric acid solution was added, and the remaining residue was put in a volumetric flask after complete reaction. Then, after measuring the volume and filtering, the residue was determined by atomic absorption spectrometry.²⁰ 

2. To determine the content of the exchangeable state, the soil sample and deionized water were mixed in a certain ratio, and the pH was adjusted to 7 by adding a magnesium chloride solution. After shaking at 25 °C with an oscillator and centrifuging, the clear surface solution was taken to measure the exchangeable state.²¹ 

3. To determine the content of the carbonate-bound form, the residue from the exchangeable state was measured after mixing with a sodium acetate solution. The pH was adjusted to 5, and the surface supernatant was taken to determine the carbonate form after continuous shaking and centrifugation.

4. To determine the content of the Fe–Mn oxide form, an acetate solution with ammonium dihydrochloride was added to the residue from the carbonate form, and after intermittent shaking and centrifugation, the surface supernatant was taken to determine the Fe–Mn oxide form.

5. To measure the content of the organic fraction, the residue from the Fe–Mn oxide form was shaken intermittently with nitric acid and hydrogen peroxide, and then, an acetate solution with ammonium acetate was added. After continuous shaking and centrifugation, the surface supernatant was collected and used to determine the organic fraction.

6. For the determination of the content of the residual state, all the digested solution was taken.

The measured experimental data after integrating and processing were used to analyze the simulation results, which is shown in Table I.

To collect soil from the mining area in Leiyang City, 3 sampling areas were randomly selected in the mining area, and 4 sampling points were set in each area; there were 12 sampling points in total. Soil from the 0 cm–30 cm surface layer was collected, and all soil was cleaned of impurities and sieved after grinding. The treated samples of soil were subjected to the quartile method after mixing. Then, the collected soil was put into a transparent bag for storage.²² 

Heavy metal migration in soil is complicated. It is affected by the soil type, soil layer, and role of soil, and heavy metals in soil penetrate to the deep soil layer through convection transport, dispersion, adsorption, and volatilization. In this paper, the COMSOL software was used to simulate and predict the migration and evolution of Cu and Cd ions in soil.²³ 

The movement of pollutants in the soil is similar to the movement of groundwater, and Darcy’s law is usually expressed in a differential form for unsteady flow or heterogeneous soil, that is, the equation for pollutant migration can be expressed as²⁴ 

In the formula, Q_x is the seepage discharge per unit time (ml/s), K_x is the permeation coefficient (cm/s), and A is the infiltrated area (cm²).

Convection refers to a series of changes in the movement of pollutants in soil along with the movement of water and solute transport in which pollutants in soil follow the flow of fluids through the pores of the soil. The equation can be expressed as²⁵ 

In the formula, J_x is the convective flux of the pollutant [mol/(m² s)], q_x is the water flux (m/s), and c is the concentration of the pollutant (mol/m³) or (kg/m³).

Diffusion refers to the transport caused by the movement of ions or molecules; even if there is no movement of the medium,²⁶ diffusion causes pollutants to move from high-concentration areas to low-concentration areas. It can be expressed by Fick’s law,²⁷ 

In the formula, dm_x/dt is the rate of diffusion (amount per unit time) and D is the diffusion coefficient (m²/s).

The COMSOL software was used to simulate the movement of pollutants in the soil; first, Computer Aided Design (CAD) was used to design the model of the soil column,²⁸ then, the COMSOL software was used to create the starting point for the source of heavy metal pollution,²⁹ and finally, the COMSOL software was used to simulate the change in pollutant concentration with time.³⁰ 

First, we show the soil column model. The soil in the sampling area is sandy loam. Assuming the depth of the studied soil area is 30 cm, heavy metal pollutants in the soil can be regarded as a solute in a homogeneous medium according to the law of migration.³¹ What the experiment explores is the migration of Cu and Cd. Therefore, the model can be displayed as a plane. The entire design layout is shown in Fig. 1.

The experimental soil column model was a transparent plastic bucket; its depth and width was 35cm and 30 respectively. To simulate the outdoor soil environment, 2 cm of dust was added to the top of the bucket, and sand and gravel were used to simulate the surface soil of the mining area. Sprayed water simulated rainwater in the outdoor environment. At the bottom of the bucket, a circle of cotton gauze was added and replaced regularly to balance the water flow in and out. The sample soil was divided into three layers: 0 cm–10 cm, 10 cm–20 cm, and 20 cm–30 cm. A sampling point for each layer was placed on the right side of the sidewall, and three sampling points were set. The sampling pipes were hard plastic tubes, and the sampling tubes were inserted into the soil near the center.

To compare the distribution and removal of pollutants in a plane, it is also necessary to study the dispersion along the depth direction and the concentration distribution of pollutants. For comparison, the migration of pollution sources with depth and their dispersion directions were simulated (as shown in Fig. 2). The point source of heavy metal pollutants was located at a depth of 0 cm–5 cm on the soil surface. The X and Y coordinates of the maximum concentration within this range were chosen for investigation. According to the soil column model, the starting point of this heavy metal ion pollutant model was set as (5, 5). Pollutants migrate and change through convection, diffusion, and dispersion. The legend on the right is the concentration distribution with 0 as the origin of the y-axis. Increasing values (1, 2, 3, 4, and 5) show that an area is a highly contaminated area. Conversely, decreasing values (−1, −2, −3, −4, and −5) show that an area is a low-pollution area.

To compare the migration of pollutants over time in a given plane, pollution points were selected in the plane direction from the simulation diagram. The horizontal distance from the pollution source to the current location is displayed in the positive vertical direction, and the concentration changes with time. The flow field is the same, and the main direction of transport is the vertical direction. The concentration distributions of Cu and Cd ions after 5 days, 15 days, and 30 days of infiltration are shown in Figs. 3(a)–3(c). The pollutants clearly have reached steady-state conditions, and it is expected that the heavy metals Cu and Cd in the soil will affect a large soil area for a long time.

Through the soil column simulation model, the outdoor soil environment was simulated (as shown in Fig. 1). Combined with the COMSOL software simulation results [as shown in Figs. 3(a)–3(c)], it can be seen that regarding the migration of heavy metal pollutants in soil over time, with increasing soil depth and time, the seepage flow increases in the range of 0 cm–30 cm with a peak shape. The maximum value is located at a depth of 5 cm, and according to the change in color, the concentration gradually decreases from top to bottom; dark blue indicates the maximum concentration, and red indicates a low concentration. After 5 days, the pollutants migrate from the high-concentration area to the low-concentration area. The peak value of the permeation area mainly appears in the interval of 0 cm–15 cm, and the low-value area is mainly in the range of 25 cm–30 cm. After 15 days, the pollutants migrate from the high-concentration area to the low-concentration area. The peak value of the permeation area mainly appears in the range of 0 cm–20 cm, and the low-value area is mainly in the interval of 25 cm–30 cm. After 30 days, the pollutants migrate from the high-concentration area to the low-concentration area, the peak value mainly appears in the interval of 0 cm–25 cm, and the low-value area is mainly in the range of 25 cm–30 cm. It can be seen that during migration, heavy metal pollutants will gradually infiltrate with increasing time, but their range in the vertical direction is limited. The migration of heavy metal pollutants mainly occurs in the range of 0 cm–30 cm, and their contents are mainly concentrated in this interval.

The surface soil was used to measure the total contents of the heavy metals Cd and Cu, as well as the contents of the ion-exchangeable state, carbonate state, iron/manganese oxide state, organic state, and residual state of heavy metals. The results show (as shown in Fig. 4) that the concentration of each form of Cd and Cu in the mining area reached a high degree of pollution. The concentration of each form of Cu was significantly higher than that of Cd. The total contents of Cd and Cu exceeded the national soil background values (Cd: 0.097 mg/kg, Cu: several times greater, 22.6 mg/kg). Cd and Cu were mainly in the form of residues; the next most prevalent fraction for Cd was the organic state and, for Cu, was the oxide state; and the concentrations of Cd and Cu in the ion-exchangeable state were the lowest. Cd and Cu exist in different forms in the 0 cm–30 cm surface layer of soil.

After 30 days, the soil samples were sampled and analyzed (as shown in Figs. 5 and 6). The migration and accumulation of Cu and Cd in the soil were similar. The common feature is that heavy metals collected on the surface of the soil, where the concentration reached the maximum. As the depth increases, the ability of heavy metals to migrate downward is weakened, so as the soil depth increases, the concentration gradually decreases. In the 0 cm–10 cm layer of soil, the contents of Cu and Cd were the highest; the concentration of Cu was 77.38 mg/kg and the concentration of Cd was 11.22 mg/kg; in the 10 cm–20 cm soil layer, the concentration of Cu was 33.85 mg/kg and the concentration of Cd was 3.42 mg/kg; and in the 20 cm–30 cm soil layer, the contents of Cu and Cd were 12.09 mg/kg and 1.37 mg/kg, respectively. After this time, the concentrations were close to equilibrium.

Through the soil column experiment and the comparison of the COMSOL numerical simulation and sampling data, the results showed that most of Cu and Cd were stored on the surface of the soil and the concentration peaked in the layer of 0 cm–10 cm. Heavy metals moved through the layer of 10 cm–20 cm by infiltration, diffusion, convection, and so on. At this depth, the concentration showed a sharp decreasing curve and the diffusion of the heavy metals Cu and Cd gradually weakened. When reaching the layer of 20 cm–30 cm, the concentration of the heavy metals Cu and Cd was at a minimum, and the concentration changed gradually. Therefore, the heavy metals Cu and Cd rarely moved down to the deep soil layer. According to these results, the heavy metals Cu and Cd were mainly collected in the soil at ∼0 cm to 20 cm and reached the highest content in the surface soil layer at 0 cm–10 cm.

The soil in the study area was heavily polluted by heavy metals. Multiple deep pits can be dug in the soil of mining areas, and physical adsorbents, biologically active bacteria, and chemical adsorbents can be sequentially put into the deep pits. Then, the deep pits are refilled with soil, the surface of the deep pits after refilling soil is covered by alkaline soil as a regulator, and the ecological restoration of soil in abandoned mines will reach a balance after 6 months–12 months. Physical adsorbents include activated carbon, zeolite, diatomite, and betonies, which have a strong adsorption capacity, high stability, and relatively low processing cost. Biologically active bacteria include yeast and cyanobacteria. Due to the charged characteristics of the cell wall of biologically active bacteria, heavy metals are directly adsorbed on the surface of cells through ion exchange, electrostatic adsorption, complexation, and other reactions, which changes the granularity of the soil and promotes a change in the form of the heavy metals, achieving the treatment of heavy metals in soil. Chemical adsorbents include the chitosan solution. Under static conditions, the chelation adsorption reaction between chitosan and heavy metal ions in the soil will produce a stable compound, significantly improving the acid and alkali resistance of chitosan, thus significantly improving the adsorption performance, and having the advantages of low cost, easy biodegradation, and no secondary pollution. The alkaline soil conditioner is lime. An alkaline environment can be provided by lime in soil. Metal hydroxide precipitates are produced by heavy metal ions and OH− ions in the soil, which are difficult to dissolve, so free heavy metal ions in the soil are removed.

Based on the measured contents of heavy metals in soil obtained through soil column model experiments, outdoor environmental factors were considered in the model and rainwater was simulated by spraying water to fully simulate the migration of pollutants in the soil in a real environment. The results were combined with COMSOL; the two modules of porous media and groundwater flow in the software were used to simulate the migration trajectory of Cd and Cu in the soil and verify the migration law of Cd and Cu in the soil. The research results show that the soil column model combined with the COMSOL software can simulate the transport of heavy metal pollutants. The main conclusions are as follows:

1. By measuring the contents of the heavy metals Cd and Cu in a certain mining area of Leiyang, it is shown that the content of heavy metals in this area exceeds the national soil background value, and both metals exist in the residual state.

2. The COMSOL software shows the color-coded concentration change trend of Cu and Cd in the soil after 5 days, 15 days, and 30 days of migration: as the depth reaches 30 cm, the amount stored in the soil decreases, showing that after time and migration of the heavy metals cadmium and copper in the soil, their concentration will continue to decrease with depth, and most of the content will be enriched in the soil surface; only a small portion of the elements will be at 30 cm. The soil continues to move.

3. The experimental measurement data show that after a certain time of migration of heavy metals, the ion concentration at different depths is different. The content in the 0 cm–10 cm layer is the highest. As the depth increases, the concentration gradually decreases. When the migration front reaches 30 cm, the ion concentration will be reduced and will gradually stabilize.

4. Using physical adsorbents, biologically active bacteria and chemical adsorbents combined with alkaline soil and conditioning agents on the surface reduce soil heavy metals in metal mines, especially the contents of Cd and Cu, effectively solving the problem of heavy metal pollution in soil caused by mining and smelting.

The data that support the findings of this study are available within the article.

This research was funded by the Hunan Provincial Department of Education General Project, Grant No. “19C1744,” and the Hunan Province Science Foundation for Youth Scholars of China fund, Grant No. “2018JJ3510.”

The authors declare no conflict of interest.