# Enhancing Tank Leaching Efficiency through Electrokinetic Remediation: A Laboratory and Numerical Modeling Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}, aligning closely with the measured value of 192.5 mol/m

^{3}. These results indicate that the electrokinetic process can significantly enhance copper recovery efficiency in tank leaching processes and curtail environmental side effects. Overall, this study provides valuable insights into the benefits of using the electrokinetic process to remediate leaching residue and improve the efficiency of industrial processes.

## 1. Introduction

^{−9}to 1.36 × 10

^{−9}m

^{2}/V·s. The highest efficiency in water extraction was achieved by applying a voltage gradient of 1 V/cm over a period of 24 h.

## 2. Materials and Methods

^{−3}kg/L) remains trapped in the pregnant leach solution (PLS). Investigating the quantity and mechanism of copper transport from the anode to the cathode, as well as studying the extraction of soil pore water, are crucial for both environmental and economic analyses.

#### 2.1. Physical Model Geometry

^{3}was considered as the pulp storage pond, which is open at the top (Figure 2).

#### 2.2. Chemical Materials

#### 2.3. Electrokinetic System

#### 2.4. Copper Cation Transport

#### 2.5. Modeling

#### 2.5.1. Model Solution

^{2}/s), c is the concentration (SI unit: mol/m

^{3}), z represents the tracer’s charge number, F is the Faraday’s constant (SI unit: C/mol), and $u$ denotes the average linear velocity (SI unit: m/s). The mobility, u

_{m}(SI unit: mol·m

^{2}/(J·s)), is given by the Nernst–Einstein equation:

_{1}(anode surface)

^{2}), n is the normal velocity component, and V represents the potential (SI unit: V). The boundary conditions for Equation (1), as the final mass-transport equation, are insulating except at the inlet and the outlet boundaries where flux condition was specified to set the diffusion and advection terms to the flux through the boundaries to zero:

_{top}denotes the peak concentration, x

_{m}represents the position of the peak along the x-axis, and p

_{w}equals the base width of the peak [32,33,34].

#### 2.5.2. Simulation of Electrokinetic Process

^{3}and a water content of 17.73 × 10

^{−3}, representing realistic conditions. It was postulated that the soil’s deformability under these compaction conditions was negligible. Electrodes were positioned in Parts 1 and 3, with the anode in Part 1 and the cathode in Part 3. The electrodes’ thickness was assumed to be 1 cm, consistent with real-world conditions. Table 8 displays the soil’s hydraulic parameters, with Ø representing porosity, Ρ denoting bulk density, and EC signifying electrical conductivity. Table 9 lists diffusion coefficients and charges for cations such as Cu

^{+2}.

_{1}is the pressure head at point 1, h

_{2}represents the pressure head at point 2, and L signifies the length of the system’s column. The hydraulic conductivity is calculated from the grain size using the following equation [37]:

_{10}is the particle size for which 10% of the material is finer, and the uniformity coefficient ${C}_{U}$ is defined as the ratio between d

_{60}and d

_{10}:

^{3}), and ${\u2206x}_{i}$ indicates the disparity between the measured and predicted concentrations.

## 3. Results and Discussion

#### 3.1. Experiment

#### 3.2. Modeling

^{3}in the anode part, 165 mol/m

^{3}in the middle part, and 135 mol/m

^{3}in the cathode part (Figure 9a). Table 11 presents the maximum percentage error in predicting the copper concentration at various measurement points over time [39].

^{3}on the first day of the test. This indicates the transportation of copper from the anode to the cathode side. The anode part exhibited the minimum copper concentration, while the maximum concentration was evident near the cathode across all segments. Figure 9c, representing the second day of the test, shows a decrease in copper concentration near the anode and an increase near the cathode, highlighting the continued movement of copper cations in the system. Figure 9d–f depicts the 8th, 14th, and last days of the test, respectively. The simulated copper concentrations align well with the laboratory measurements. A comparison between the experimental measurements and numerical modeling for the anode and cathode parts is presented in Figure 10a and Figure 10b, respectively.

^{3}to above 220 mol/m

^{3}after 20 days. Also, in the same period of time, it decreased from 137.5 mol/m

^{3}to less than 70 mol/m

^{3}on the anode side. These results show that the electrokinetic process can significantly increase copper transport and its recovery efficiency in the tank leaching process.

## 4. Conclusions and Future Prospects

^{3}. Experimental data indicated an actual concentration of 192.5 mol/m

^{3}in the solution extracted from the cathode part, which aligns well with the model’s predictions. It is important to emphasize that while these results underscore the potential for scaling up the electrokinetic process, further research is required to confirm its wider applicability.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Arrangement of the tanks for mixing pulps and draining to the ponds with a gradient of 5% at Nasim mine. The tank’s length and diameter were 3 and 3.5 m, respectively.

**Figure 2.**The plexiglass with dimensions of 0.25 × 0.40 × 1 m

^{3}was used as the pulp storage pond.

**Figure 3.**Condition of the soil after one week of natural drainage, with samples taken from three distinct sections:

**A**,

**B**, and

**C**.

**Figure 7.**The electrodes were placed vertically in the soil to apply the electrokinetic process: (

**a**) anodes and (

**b**) cathodes.

**Figure 9.**The changes in copper concentration in 6 different days of applying the electrokinetic process in the tank leaching. (

**a**) 0 day, (

**b**) 1 day, (

**c**) 2 day, (

**d**) 8 day, (

**e**) 14 day, (

**f**) 20 day.

**Figure 10.**Comparison between the numerical modeling and the laboratory test in (

**a**) Anode and (

**b**) Cathode parts.

**Table 1.**The water content of the soil after natural drainage in the parts shown in Figure 3.

Part | Water Content (%) |
---|---|

A | 13.42 |

B | 21.49 |

C | 53 |

Parameters | Values | Units |
---|---|---|

pH | 3.6 | - |

Eh | 413 | mV |

EC | 10.92 | mS/cm |

**Table 3.**The amount of residual moisture content in the anode place (section A). The applied voltage was 0.4 volt/cm.

Type of Process | Rmc-1 ^{1} (%) | Rmc-14 (%) | Rmc-20 (%) | Rmc-29 (%) | Rmc-34 (%) |
---|---|---|---|---|---|

Leaching with the EK ^{2} process (vertical electrodes) | 13.69 | 10.03 | 8.46 | 6.26 | 4.85 |

Leaching without the EK process | 13.18 | 11.45 | 9.3 | 7.8 | 6.7 |

Leaching with the EK process (horizontal electrodes) | 13.42 | 4.62 | - | - | - |

^{1}Rmc-I: Residual moisture content (%) on the (I)th day;

^{2}Electrokinetic.

**Table 4.**The amount of residual moisture content in section B (Middle part of the soil). The applied voltage was 0.4 volt/cm.

Type of Process | Rmc-1 (%) | Rmc-14 (%) | Rmc-16 (%) | Rmc-20 (%) | Rmc-29 (%) | Rmc-34 (%) |
---|---|---|---|---|---|---|

Leaching with the EK process (vertical electrodes) | 21.38 | 15.96 | 14.9 | 13.64 | 7.94 | 6.71 |

Leaching without the EK process | 21.17 | 19.44 | 19.16 | 18.7 | 17.3 | 16.1 |

Leaching with the EK process (horizontal electrodes) | 21.49 | 12.7 | 7.02 | - | - | - |

**Table 5.**The amount of residual moisture content in section C (Cathode place). The applied voltage was 0.4 volt/cm.

Type of Process | Rmc-1 (%) | Rmc-20 (%) | Rmc-29 (%) | Rmc-34 (%) |
---|---|---|---|---|

Leaching with the EK process (vertical electrodes) | 54.28 | 42 | 30.4 | 22.8 |

Leaching without the EK process | 59.6 | 57.6 | 53.72 | 50.26 |

Leaching with the EK process (horizontal electrodes) | 53 | 14.6 | - | - |

Sample | Cu (%) |
---|---|

Anode part | 0.56 |

Middle part | 0.66 |

Cathode part | 0.54 |

Sample | Cu (%) |
---|---|

Anode part | 0.35 |

Middle part | 0.59 |

Cathode part | 0.77 |

Parameter | Value | Unit |
---|---|---|

Ø_{A, B} | 0.375 | - |

Ø_{c} | 0.333 | - |

Ρ | 1600 | kg.m^{−3} |

EC | 1.092 | S.m^{−1} |

Cation | |z| | D_{i}·10^{−9} [m^{2}s^{−1}] |
---|---|---|

Ag^{+} | 1 | 1.648 |

Al^{+3} | 3 | 0.559 |

Ba^{+2} | 2 | 0.848 |

Be^{+2} | 2 | 0.599 |

Ca^{+2} | 2 | 0.793 |

CaHCO_{3}^{+} | 1 | 0.506 |

Cd^{+2} | 2 | 0.717 |

Co^{+2} | 2 | 0.732 |

Cr^{+3} | 3 | 0.595 |

Cu^{+2} | 2 | 0.733 |

Fe^{+2} | 2 | 0.719 |

Fe^{+3} | 3 | 0.604 |

Equation Number | Parameter | Quantity | Unit |
---|---|---|---|

(8) | ${C}_{U}$ | 6.42 | - |

(9) | E | 0.19 | - |

(10) | g (${C}_{U}$) | 2.28 | - |

(11) | E (${C}_{U}$) | 11,329.39 | - |

(7) | k | 2.22 × 10^{−4} | m/s |

(6) | $i$ | 0.0988 | - |

(5) | $v$ | 2.194 × 10^{−5} | m/s |

(12) | $u$ | 5.85 × 10^{−5} | m/s |

Measuring Point | Anode | Cathode | ||||||
---|---|---|---|---|---|---|---|---|

Time (day) | 1 | 7 | 14 | 20 | 1 | 7 | 15 | 20 |

Maximum error (%) | 0 | 9.4 | 3.45 | 5.26 | 0 | 3.53 | 5.56 | 12.4 |

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**MDPI and ACS Style**

Eftekhari, F.; Doulati Ardejani, F.; Amini, M.; Taherdangkoo, R.; Butscher, C.
Enhancing Tank Leaching Efficiency through Electrokinetic Remediation: A Laboratory and Numerical Modeling Study. *Water* **2023**, *15*, 3923.
https://doi.org/10.3390/w15223923

**AMA Style**

Eftekhari F, Doulati Ardejani F, Amini M, Taherdangkoo R, Butscher C.
Enhancing Tank Leaching Efficiency through Electrokinetic Remediation: A Laboratory and Numerical Modeling Study. *Water*. 2023; 15(22):3923.
https://doi.org/10.3390/w15223923

**Chicago/Turabian Style**

Eftekhari, Farnoush, Faramarz Doulati Ardejani, Mehdi Amini, Reza Taherdangkoo, and Christoph Butscher.
2023. "Enhancing Tank Leaching Efficiency through Electrokinetic Remediation: A Laboratory and Numerical Modeling Study" *Water* 15, no. 22: 3923.
https://doi.org/10.3390/w15223923