Cadmium Depth Separation Method in Polymetallic Sulfate Solution: Flow-Electric Field Enhanced Cementation Combined with M5640 Extraction

Abstract

An efficient and controllable process for separating copper and cadmium was required to be developed due to the high cost of the long separation process of copper cadmium slag generated from the zinc smelting process. Therefore, a new process for the application and deep separation of copper and cadmium was developed by combining the Circulating Flow Electric (CFE) cadmium cement method and the 2-hydroxy-5-nonyl formaldehyde oxime (M5640) copper extract method. The process firstly removed copper ions utilizing M5640 and obtained a primary purification solution, followed by CFE method to extract cadmium in depth. The effects of extractant volume fraction, pH, Oil phase/Aqueous phase (O/A) ratio and reaction time on the removal of copper ions were investigated. The results showed that the removal of copper was above 97%, while the removal of zinc and cadmium was below 1.6%, respectively, proved that the selectivity of M5640 for copper was significantly higher than that for metals such as cadmium and zinc. The characterization results indicate that the oxygen on the hydroxyl group and the nitrogen on the oxime group co-ligated with the copper ions and subsequently formed chelated extracts. That was the mechanism of the copper ion purification by M5640. Furthermore, the extraction of high purity cadmium was carried out in the extraction residual liquid. A novel method of cadmium removal enhanced by coupling an electric field with a circulating flow field was developed and applied to the cement cadmium from sulfate solutions. The optimal process conditions of the method were explored, which were further fitted into statistical equations and optimized by response surface analysis. Since the fitted theoretical results were close to the experimental results, the optimization was considered as effective. The optimized experimental parameters were 6.23 mL/s of flow rate, 48.14 mA/cm² of current density, 2.25 of pH, and 0.93 of anode/cathode area ratio, respectively. Next, the extraction electrical efficiency, purity and its weight distribution in the cell of cadmium sponge under different flow fields were calculated and measured. The results were analyzed to prove the existence of an optimal interval for the distribution of cadmium under high-speed flow field.

1. Introduction

Cadmium is widely used in the battery, electroplating, electronics, paint and printing industries [1]. Although the application of cadmium is more widespread, but its use is still constantly restricted due to its high toxicity [2]. Cadmium pollution mainly originates from its production and use process, such as the smelting of zinc and other metals and the use of batteries. Among them, the recovery of cadmium associated with zinc smelting is the main source of cadmium production in China, so the zinc smelting industry has become the most important source of cadmium pollution in the non-ferrous metal industry. About 75% of the world’s refined cadmium supply is currently recovered from zinc refinery by-products in recycling facilities [3]. Among these recoveries, more than 85% of the cadmium is recovered using a classical two-stage process. That is, the copper-cadmium residue is leached with zinc sulfate to form a liquid and then removed with zinc powder cement [4,5,6]. The challenging problem in this field is that the conventional cementation cadmium extraction method suffers from the defective problem of zinc encapsulation by cadmium, resulting in high zinc consumption, incomplete removal of cadmium, and low purity of harvested cadmium sponge. Moreover, some of the cadmium sponge can be floated, causing difficulties in separation and recovery [7].

Numerous researchers have attempted to efficiently separate cadmium from copper-cadmium slag of zinc smelting [8]. The conventional industrial process exploits the difference in solubility of copper-cadmium-zinc in dilute sulfuric acid to obtain a cadmium-rich leach solution. However, the actual leaching of copper-cadmium slag is carried out, and the cadmium-rich solution obtained will still have a high amount of copper ions in it [9]. These copper ions will reduce the purity of the sponge cadmium extracted by zinc powder cementation. Thus, it is necessary to perform a corresponding pretreatment to remove excessive copper before cementing cadmium. Precipitation, extraction, and electrowinning are the most commonly used techniques for copper removal today. The extraction method is superior for separating copper from the polymetallic solution extra deeply among them [10,11,12,13]. Oximes, β-diketones, and ternary amines are several copper extractants commonly used in the current industrial process of wet smelting, among which oxime extractants are widely used due to their wider adaptability and lower cost [14,15,16].

Researchers have tried methods to improve the efficiency of Zn-Cd cementation in various solutions. Some of the research optimized the cementation efficiency by changing the particle size and morphology of zinc metal [17,18] to obtain higher purified cadmium sponge. Another aspect of the research approach is to expand the contact area of zinc-cadmium powder in the reaction system by optimizing the stirring or extending the reaction time to improve the purity of sponge cadmium [19,20,21]. Notably, some studies have shown that it is feasible to optimize the zinc-cadmium cementation process by using a variety of physical external fields. The results also showed that the purity of the cadmium sponge was significantly improved while minimizing undesirable side effects.

Yang et al. [22] proposed a consolidation technique called electric-enhanced cementation for cadmium extraction, which is a clean and efficient method that can be used to extract cadmium from cadmium-containing solutions by electric-enhanced cement. However, subsequent studies found that “floating sponge cadmium” was easily produced during the process of cementation with electro-enhanced. Since a large amount of “floating sponge cadmium” will cover the anode and cathode plates, it may cause electrode short-circuiting in the later phase of the electric-enhanced cementation reaction. Nan et al. [23] then tried a new method namely by using ultrasonic external field to avoid the generation of floating sponge cadmium for the purpose of optimizing the reaction. In addition, other researchers have also achieved better results by changing the constant current electric field to a pulsed electric field to facilitate the reaction.

Collectively, the currently available methods focus on reducing zinc consumption while maximizing the cementation rate of cadmium but pose additional problems, such as more complex operational steps and higher energy consumption [24,25,26]. As an improved method, electric field-enhanced cementation makes the operation more uncomplicated, but there are still issues. Such as the collection difficulties brought on by the floating cadmium sponge and the increased equipment costs brought on by the external solid field that was superimposed. These restrictions can be overcome by modifying and coupling the existing physical fields.

In light of the above discussion, it is obvious that coupling extra physical fields into the zinc-cadmium cementing electric field is an effective technique to solve the zinc-cadmium mixture. The flow field condition is the most cost-effective and straightforward external field condition to acquire. The flow field changes during the electrolysis process, on the one hand, allows the moving electrolyte to make an improved homogeneity of the concentration and temperature distribution, which is advantageous to the progress of electrolysis. On the other hand, the coupling of the flow field may aggravate the separation of metal zinc and cadmium sponge, forming a new cementing activity point on the zinc surface to further improve current efficiency. Thus, maintaining the stability of the flow field within the electrolytic cell may have a beneficial effect on current efficiency enhancement. Based on this, the primary objective of this work is to construct a system that provides a circulating flow field that will further facilitate the separation and extraction of cadmium sponge based on electric-enhanced cementation to improve the extraction rate of cadmium sponge and promote the settling and efficient collection of cadmium sponge.

2. Experimental

2.1. Material

The electrolyte used is a cadmium-rich sulfate solution collected from the Shuikoushan zinc smelter of the Zhuzhou Smelter Group, China, as a by-product of the zinc wet smelting process. The composition was analyzed by ICP and listed in

Table 1. The composition of the main metal content of the solution before cadmium extraction in the zinc smelting process (mg L⁻¹).

	Zn	Cd	Cu	Co	Ni
1	25,087	17,363	738.2	217.9	175.89
2	26,376	18,762	819.4	141.6	165.76
3	24,754	16,541	855.9	198.3	177.09
Avg	25,405.67	17,555.33	804.50	185.93	172.91

. it is known that the main metal elements in this sulfate solution are Zn, Cd, Mg, Mn, Fe and small amounts of Cu, Co and Ni.

The large variety of impurities contained in the initial solution led to unfavorable analysis of the interaction of the elements of the reaction. Therefore, a simulated sulfate solution of the original solution was configured using analytically pure cadmium sulfate (3CdSO₄–8H₂O), zinc sulfate, copper sulfate and deionized water. Its specific content was formulated as Cu 804.50 mg L⁻¹,Zn 25,405.67 mg L⁻¹ and Cd 17,555.3 mg L⁻¹.The extractant used for copper removal is AcorgaM5640, an extractant commonly used in the purification of non-ferrous metallurgy. It is a copper extractant with the addition of ester modifier from P50. Its main active ingredient is 2-hydroxy-5-nonyl formaldehyde oxime.

The design of the circulating flow-electric field enhanced cementation device is shown in Figure 1. The device consists of three main systems, including the circulating flow system (system A), and the power electrode system (system B). The cell is made of acid-resistant transparent acrylic glass. The circulating flow system consists of a constant flow pump A1 with a design flow rate of about 1–30 mL⁻¹ and a connection pipe A2 to circulate the electrolyte, which can be controlled by the inflow rate and the total inlet area. The pump input and outlet are connected to a 500 mL electrolyte reservoir A4, which collects the filtered electrolyte from the discharge outlet, mixes it, and then re-enters the cycle. The electrode power system tree used consists mainly of a constant current power supply B1, electrode plates B3 and B4, and a thermostat B2, where a 60 mm × 80 mm × 5 mm zinc plate is used as the anode (97.5% purity) and a 60 mm × 80 mm × 5 mm titanium plate as the cathode (99% purity). Both electrodes have been thoroughly cleaned and polished before the experiment.

2.2. Process

In the study of the effects of the main process parameters on the cadmium extraction effect, the factors were selected by single-factor experiments and their parameters were optimized using statistical methods. The factors examined in the experiments included current density, pH, flow rate, plate spacing, reaction temperature, average current density, and anode plate to cathode plate area ratio. The flow rate, pH and temperature of the electrolyte were adjusted to the target values before the reaction started. In this case, 500 mL of the material solution was added to the reactor. After recording the weight of the test electrode plates separately, they were inserted into the reaction tank and the anode to cathode spacing and area ratio were adjusted, at which point the reaction started.

The electrolyte collection was recorded at intervals of every 30 min, while the test phenomena were observed and recorded. The sample electrolyte collected during the reaction was filtered, and the elemental content in the filtrate was detected by ICP. The collected cadmium sponge filtrate was washed with pure water to remove electrolytes to obtain cadmium sponge residue, which was analyzed by ICP, SEM, BEM and XRD to confirm the purity, morphology and phase composition of cadmium sponge. The anode and cathode plates after the reaction were washed and dried and weighed separately and recorded.

3. Results and Discussion

3.1. Copper Removal by M5640

The original sample processed for the study was a polymetallic liquid containing zinc, cadmium, and copper. The direct use of a circulating current field to cement cadmium would significantly reduce the electrical efficiency and the purity of the sponge cadmium. Since the standard potential for copper is −0.337 v close to −0.403 v for cadmium [27,28]. Therefore, an attempt was made to first remove copper from the sample solution utilizing M5640 as the extractant in this section. The effects of reaction time, initial pH of the solution, extractant concentration and Oil phase/Aqueous phase (O/A) comparison on the extraction efficiency of copper were explored. Thus, optimized conditions for copper removal were acquired to obtain a purification electrolyte adapted to the CFE method for cadmium cementation.

3.1.1. Copper Removal Test Utilizing M5640

A set of condition experiments were performed to explore the main factors influencing the extraction of copper removal by M5640, namely volume concentration, O/A ratio, initial pH of the aqueous phase, and reaction time. The volume concentration of M5640 was set to 4–12% with sulfonated kerosene to form 20 mL of organic phase, the original solution of the aqueous phase response results is shown in Figure 2A. In addition, the above extraction conditions were reacted for 20 min to explore the extraction time influence of copper, and the results are shown in Figure 2B. Furthermore, the O/A ratio was adapted to 1:3, 1:2.5, 1:2, 1:1.5, 1:1, 1.5:1, 2:1, 2.5:1, 3:1 to obtain its effect on the copper extraction rate, as shown in Figure 2C. The variation of copper extraction rate at the initial pH 0.1–5 of the aqueous phase was continually explored under the above optimal conditions, respectively. The results are shown in Figure 2D.

According to Figure 2A, the extraction rate of copper increases with the volume concentration of M5640. The extraction rate stops increasing at 6% volume concentration. That is due to the excess volume concentration depleting the remaining copper ions, while the removal of trace residual copper ions is more difficult owing to the more dilute the presence of copper ions in the aqueous phase. According to Figure 2B, the extraction rate of copper remained stable at 91% after 4 min of mixing time. Meanwhile, the extraction rate of M5640 for good cadmium zinc was maintained at less than 1%. It shows that M5640 has a strong selective separation ability for Cu-Zn-Cd. According to Figure 2C, the copper extraction rate increased with the comparison increase. The copper removal rate reached 98.45% when the (O/A) ratio was 1.5:1. As the (O/A) ratio continued to increase, the copper extraction rate not increased significantly anymore. This is mainly caused by increasing the OA ratio appropriately, which improves the capacity of copper ions in the oil phase of M5640. Improving the continuous migration of copper ions from the aqueous phase to the oil phase is beneficial which is favorable to the enrichment of copper ions and the purification of the aqueous phase. Based on Figure 2D, the copper removal rate showed a clear upward trend with the increase of pH and reached a peak and no longer increased [29,30,31]. This is since copper extraction by M5640 in a sulfuric acid medium is a cation exchange process, and its extraction reaction can be expressed as:

Cu²⁺ + 2HR = CuR₂ + 2H+

where: HR corresponds to M5640.

According to the above reaction equation, the high concentration of H+ in the solution is detrimental to extraction [32]. The partition coefficient and extraction rate of metal ions increase as the pH of the aqueous phase increases [33]. At pH = 1.5 or higher, the extraction rate of copper is 94.15%. This is primarily due to the high concentration of H+ in the solution under conditions of low pH, and the competition between H+ and copper ions for extraction becomes the most significant factor. When the pH rises, the concentration of hydrogen ions in the solution falls, which promotes the exchange reaction between copper ions and hydrogen ions in the extractant and is conducive to enhancing the copper extraction rate. When the pH of the solution was 2.0, the copper extraction rate reached 95.61%, and increasing the pH of the solution did not significantly increase the copper extraction rate, indicating that the extraction reaction was close to equilibrium under these conditions. The results indicate that M5640 has an excellent selective separation effect on copper and zinc-cadmium ions in an acidic solution, which is advantageous for subsequent high-purity cadmium cementation.

After the above experimental exploration, the optimized conditions were: time 2 min, volume concentration 10%, pH = 3.0, O/A ratio = 1:1. The composition of the residual solution was tested: Cu²⁺ < 0.1(mg/L), Zn²⁺85.05. After calculation, it can be concluded that the extraction rate of copper is more than 99.83%, while the extraction rate of zinc is less than 1, and the extraction rate of cadmium is less than 1. This can be proved that M5640 can effectively isolate copper in this solution system, which provides the basis for further flow electric field coupled cementation of cadmium.

3.1.2. Extraction Mechanism and Characterization

M5640 is a weakly acidic extractant, which is a copper extractant made of 2-Ethylhexylphosphicmono-2-ethylhexylester(P50) with ester modifier. Its main active ingredient is 2-hydroxy-5-nonyl formaldehyde oxime. It can be dissolved in both aqueous and organic phases, and the solubility in the organic phase is greater than that in the aqueous phase [34].

In order to explore the mechanism of copper extraction process, the infrared spectra of M5640 were characterized before and after the organic phase liquid-liquid extraction of copper, and the results are shown in Figure 3. The main groups in the structure of M5640 are benzene ring, –CH2, –CH3, C=N and –OH. Among them, 1501.02 cm⁻¹ is attributed to the bending vibration peak of -OH on the benzene ring; the C=N absorption peak on the benzene ring skeleton is at 1697.29 cm⁻¹, the C=C vibration peaks are at 1583.66 cm⁻¹ and 1502.11 cm⁻¹. Meanwhile the –CH2 and –CH3 groups usually have two or three absorption peaks at 2990–2800 cm⁻¹, the –OH stretching vibration group usually at 3407.15 cm⁻¹, and 1375.44 cm⁻¹ is the symmetrical deformation absorption peak of –CH3 [35].

Comparing the IR spectra of M5640 and M5640-Cu²⁺ complexes, the analysis revealed that the -OH stretching vibration peak was located at 3407.15 cm⁻¹ and 1497.03 cm⁻¹ was the bending vibration peak of -OH on the benzene ring. After coordination with Cu²⁺, the stretching vibration absorption peak was blue-shifted to 3412.28 cm⁻¹ and the bending vibration of –OH on the benzene ring was red-shifted to 1503.40 cm⁻¹, indicating the involvement of –OH in the coordination reaction [36,37,38]. The study of copper extraction by M5640 showed that the oxygen on the hydroxyl group and the nitrogen on the oxime group in the extractant coordinated with the copper ion to form a chelating extractant complex, and the hydrogen on the oxime group formed an internal hydrogen bond with the hydroxyl group [39].

3.2. Cadmium Cementation Enhanced by Flow-Electric Field Coupling

3.2.1. Determination of the Initial Cd Concentration and Reaction Time

The residual solution obtained after copper removal by extraction in the previous section was used as the test sample in this section. Batch experiments were conducted to explore the baseline conditions for the effective performance of this device, and statistical optimization was performed on this basis. The factors examined during the experiments included current density, pH, flow rate, inter-electrode distance, temperature, current density, and area ratio of anode plate to cathode plate. Furthermore, the main influencing factors were weighted and analyzed by statistical methods on the basis of the obtained single-factor test results.

In these experiments, the reaction time and the limiting concentration of the electrolyte should first be confirmed as the initial setting conditions to ensure that the subsequent reaction conditions are explored within a controlled range. The experiments were performed for 10 h using a simulated electrolyte equipped for the test and the solution concentration was continuously monitored with ICP. The results are displayed in Figure 4. Batch experiments were conducted to explore the conditions underlying the effective performance of the device, and optimization was carried out on this basis. The investigated parameters include current density, pH, flow rate, inter-electrode distance, temperature, current density, and anode plate to cathode plate area ratio.

The first thing to confirm is the reaction time and the limiting concentration of the electrolyte as the initial setting conditions. Subsequent reaction parameters were ensured to be explored within the control range. The simulated electrolyte was used for the experiments, and a continuous 5 h reaction was performed. The electrolyte concentration was monitored continuously by ICP and the cadmium extraction rate was calculated based on the ratio of the actual concentration to the initial concentration. The results are shown in Figure 4.

Since the concentration of electrolyte is not stable in actual industrial applications. Thus, the current test 5 groups of electrolyte were formulated with standard simulated solution concentration of Zn 25.40 g L⁻¹, Cu 0.40 g L⁻¹, Cd 17.55 g L⁻¹ floating ratio of −30%, −15%, 0%, 15%, 30%, respectively. Their specified Cd concentrations were 15.24 g L⁻¹, 21.59 g L⁻¹, 25.40 g L⁻¹, 29.21 g L⁻¹, and 33.02 g L⁻¹, respectively.

As the results can be observed from Figure 4, the final cadmium extraction curves at different initial Cd concentrations were concentrated around 96%. It is not difficult to see that there is no apparent correlation between the final cadmium extraction rate and the initial concentration, but it was evident that the cadmium extraction rate rises more rapidly at higher concentrations. After 3.5 h, the cadmium extraction rate at each concentration is not changing significantly, and by four hours, the cadmium extraction rate has risen to 92.18%. The test was finally stopped when the reaction proceeded to 6 h. The maximum cadmium extraction rate was 95.92% at this time. Setting the test time to 4.5 h was based on time cost and practical application considerations.

3.2.2. Single-Factor Experimental Analysis

In this section, investigated parameters include cathode to anode area ratio, electrode spacing, current density, solution pH, and anode current density. The data of the parameters obtained with the cadmium extraction rate as the dependent variable are compiled and presented in Figure 5.

It can be observed from Figure 5A that the expansion of the anode area improves the cadmium removal efficiency. This value reaches a maximum of 97.68% at a cathode-anode area ratio of 1:4. When the anode current density is a fixed value, an increase in anode plate area implies an increase in current, voltage and zinc consumption. Zinc flakes may be dislodged frequently during the reaction due to excessive current causing excessive zinc consumption. Therefore, the optimal cathode-to-anode area ratio for cadmium removal is 1:3.

Theoretically a lower pH is favorable for the dissolution of the zinc plate surface, exposing new reaction surfaces, accelerating the cementation reaction and increasing the extraction rate of cadmium. However, the hydrogen evolution reaction at the cathode during cadmium extraction reduces the acidity of the solution, which adversely affects the cementation reaction. Moreover, the low pH value can lead to the redissolution of precipitated cadmium. Combined with Figure 5B, the optimal pH was initially set at 1.

It can be found from Figure 5C that the efficiency of cadmium extraction increases with the increase of temperature. Due to the promotion of mass transfer by temperature, the cadmium ions in solution can be rapidly replenished when the cadmium ions on the surface of zinc flakes are consumed. This triggers the continuation of the cementation reaction. Therefore, the optimum temperature for the integrated removal of Cd is 45 °C.

As a result of the test with the electrode spacing as a variable, it is easy to find the trend in Figure 5D that the closer the electrode distance is the higher the extraction efficiency. That is due to the dense electric field lines increase the local current density resulting in higher current efficiency [40,41,42]. However, overly close (<1 cm) electrode distance can trigger short circuit due to the growth of cadmium sponge thus rapidly reducing the electrical efficiency. The combined optimal electrode distance is 1.5 cm.

As the anode current density increases, the cadmium lifting efficiency increases. The increase in current density leads to an increase in the current for the dissolution reaction [43]. Thus, the accelerated dissolution of zinc promotes the deposition of cadmium sponge and thus the exposure of unreacted zinc. Considering that higher anode current density requires higher energy, the optimal current density for cadmium removal is 20 mA/cm².

Based on the above discussion, the parameters initially explored are listed in the

Table 2. The experimental conditions obtained after optimization.

Factor	Electrolyte Flow Rate	Current Density	pH	Cathode/Anode Area Ratio	Plate Spacing	Temperature
value	5.40 mL/s	20 mA/cm2	2	1:3	6 cm	45 °C

.

3.2.3. Current Efficiency and Cadmium Sponge Distribution

The sponge cadmium distributed in different locations was collected at the end of the reaction and was post-processed by washing, drying and weighing. Figure 6 shows the comparison of the post-processed cadmium sponge powder collected at different locations. The weights of these three types of collected sponge cadmium were recorded based on the circulating flow conditions of 5 m/s, 10 m/s, 20 m/s, 30 m/s, 40 m/s and 50 m/s. The residual cadmium concentration of the solution was also determined by ICP and converted to grams of cadmium for inclusion in the calculations.

According to Figure 7, it can be observed that the total Cd sponge increases with the growth of the flow rate, but this value no longer increases significantly when the flow rate exceeds 30 mL/s. It is noteworthy that the amount of cadmium sponge grams that can be collected on the surface of the anode in it gradually decreases with the increase of the flow rate. Correspondingly, the grams of deposited or suspended cadmium sponge increased. This phenomenon also proves that the flow rate increase has a strong effect on the autonomous separation of cadmium sponge from the anode.

It is important to note that the cadmium sponge, which adheres to the remaining anode and is suspended or precipitated within the cell, can all be theoretically considered to come from the anode cementation. since the dense cadmium sponge layer of the cathode hardly ever peels off. The total weight of cadmium sponges other than cathode cadmium sponge can be converted to cadmium sponge weight per unit of anode surface area by dividing by the anode surface area. The corresponding current efficiency can then be estimated from the weight of harvested cadmium sponge, according to the following Equation (1).

$$\eta =\frac{W_1}{W_2}=\frac{W}{\frac{ItM}{nF}}=\frac{nFW}{ItM}$$

(1)

where W₁ is the actual weight; W₂ is the theoretical weight; I is the total current applied and t is the total time of the test.

Combining the results in Figure 7 and Figure 8, several observations and explanations can be given. Firstly, the efficiency of obtaining cadmium sponge current at high flow rate has been significantly increased. The reason for this mainly comes from two aspects is that one is the higher mass transfer rate inside the fluid at high flow rate. Secondly, the thickness δ of the diffusion layer decreases when the flow rate increases, and the anode overpotential decreases [44,45] accordingly. This decrease leads to an increase in the current efficiency of the anode by making the cation reaction easier to perform.

Secondly, the weight of cadmium sponge attached to the anode at high flow rate is less than that at low flow rate, which may be due to some cadmium sheaves being washed into the electrolyte at high flow rate. This part of the scattered cadmium sponge usually comes from the outer layer of the anode, and leads to the increase of the weight of the precipitated and suspended cadmium sponge.

Finally, it is obvious that the total weight data obtained at higher circulation flow rates are larger. However, there is a significant increase in the zinc sponge cadmium content at higher flow rates. This is due to the fact that the high-speed jet promotes the sponge cadmium flaking while resulting in the tearing of the zinc layer. The broken zinc layer enters the sponge cadmium, leading to elevated zinc loss.

3.3. Response Surface Optimization of Coupled Fluid-Electric Field Cementation

3.3.1. Response Surface Method

Since the priority of these experimental parameters affected the reaction and could not be derived from the above experimental and analytical results, it was necessary to quantify the effects of these parameters by the response surface method. The methods used a hypersurface to approximately represent the relationship between the input and output of the existing complex system. The experiments were conducted according to the operating conditions derived from the software, and a second-order model was fitted to the data obtained from the experiments to obtain the quadratic regression equation (containing single, square, and interaction terms). Each effect factor was dominating and interacting effects were explored to determine the most significant effect factor and the most optimal solution [46].

A 4-factor, 3-level experimental design and analysis were conducted using the Box-Behnken design in Design-Expert software, and the detailed experimental factors with level values are shown in the

Table 3. The experimental factors and level controls.

Code	Electrolyte Cycle Rate (mL/s)	Current Density (mA/cm2)	Electrode Area Ratio	pH
−1	1.35	30	0.33	0.5
0	4.05	32.5	0.665	2.25
1	6.75	45	1	4

.

Using the data in Table 3, linear, 2FI, quadratic, and cubic prediction models were developed based on the central composite design principle of the Box-Behnken method. The fit (R²), R²_adj, and R²_pre analyses of these models are presented in

Table 4. The response surface experimental design and result.

Test No.	Electrolyte Cycle Rate (mL/s)	Current Density (mA/cm2)	Electrode Area Ratio	pH	Extraction Rate of Cadmium%
1	5	1.35	0.665	2.25	84.13
2	60	1.35	0.665	2.25	85.26
3	5	6.75	0.665	2.25	88.18
4	60	6.75	0.665	2.25	97.21
5	32.5	4.05	0.33	0.5	88.34
6	32.5	4.05	1	0.5	90.08
7	32.5	4.05	0.33	4	92.13
8	32.5	4.05	1	4	94.65
9	5	4.05	0.665	0.5	85.87
10	60	4.05	0.665	0.5	92.83
11	5	4.05	0.665	4	89.62
12	60	4.05	0.665	4	98.13
13	32.5	1.35	0.33	2.25	84.69
14	32.5	6.75	0.33	2.25	90.98
15	32.5	1.35	1	2.25	84.86
16	32.5	6.75	1	2.25	94.17
17	5	4.05	0.33	2.25	85.65
18	60	4.05	0.33	2.25	92.34
19	5	4.05	1	2.25	87.03
20	60	4.05	1	2.25	93.96
21	32.5	1.35	0.665	0.5	84.37
22	32.5	6.75	0.665	0.5	91.75
23	32.5	1.35	0.665	4	84.83
24	32.5	6.75	0.665	4	97.67
25	32.5	4.05	0.665	2.25	95.59
26	32.5	4.05	0.665	2.25	94.15
27	32.5	4.05	0.665	2.25	95.88
28	32.5	4.05	0.665	2.25	95.38
29	32.5	4.05	0.665	2.25	94.81

. For a good-fitting model, the R² value should be greater than 0.8 while the closer the R² value is to 1. In addition, the closer the R²_adj and R²_pre values are, the more the model’s prediction results match the actual results.

From

Table 5. Comparison of Model Fitting.

Source	Std. Dev.	R2	R2Adj	R2Pre
Linear	2.74	0.6939	0.6429	0.6001
2FI	2.93	0.7382	0.5928	0.4936
Quadratic	0.88	0.9817	0.9634	0.908	Suggested
Cubic	0.67	0.9954	0.9785	0.7949

, it can be seen that the fitting results of Design-Expert software recommend the use of the quadratic model (Quadratic). The table shows that the R² value of Quadratic is 0.9859, and the R²_adj and R²_pre are 0.9718 and 0.9224, and the value of the difference is less than 0.1. This indicates that the quadratic model has the smallest deviation and better fit than other models. Furthermore, the final equation in terms of actual factors can also be fitted:

y = 64.63326 + 3.52261x₁ + 3.96811x₂ + 29.96296x₃ + 0.072394x₄ + 0.41799x₁x₂ + 0.10235x₁x₃ + 0.83472x₁x₄ + 0.018384x₂x₃ + 0.021167x₃x₄ − 0.81693x₁² − 0.55083x₂² − 23.77441x₃² − 1.64540x₄²

where: y = cadmium removal rate%, x₁ = electrolyte circulation rate, mL/s; x₂ = current density, A/m²; x₃ = electrode area ratio; x₄ = pH.

The distribution of the external studentized residual data points of the above quadratic polynomial regression model is shown in Figure 9. The externally studentized residuals are used to indicate the extent to which the predicted values deviate from the measured values to determine whether the error terms obey a normal distribution [47,48]. As can be seen from Figure 9, the experimental points are evenly distributed, and the distribution of each point of the residuals is almost on the same line, which again verifies that the fitting effect of the model is accurate and reliable.

3.3.2. Analysis of Variance and Parameter Interactions

In addition, an ANOVA is conducted on the fitted model to determine the significance of the effect of the parameters on the response values. The larger the obtained F-value indicates the more significant the influence of the factor on the response value, and the smaller the corresponding P-value the more significant the influence of the factor on the response value as well. The results of the specific analysis can be seen in

Table 6. The analysis of variance.

Source	Sum of Squares	df	Mean Square	F Value	p Value
Model	578.2	14	41.3	53.58	<0.0001	significant
A-Current Density	128.38	1	128.38	166.54	<0.0001
B-cycle rate	223.78	1	223.78	290.29	<0.0001
Electrode area ratio	9.4	1	9.4	12.19	0.0036
D-pH	47.16	1	47.16	61.18	<0.0001
AB	15.6	1	15.6	20.24	0.0005
AC	0.014	1	0.014	0.019	0.8932
AD	0.6	1	0.6	0.78	0.3923
BC	2.28	1	2.28	2.96	0.1075
BD	7.45	1	7.45	9.67	0.0077
CD	0.15	1	0.15	0.2	0.6637
A2	40.6	1	40.6	52.67	<0.0001
B2	104.59	1	104.59	135.68	<0.0001
C2	46.18	1	46.18	59.9	<0.0001
D2	10.04	1	10.04	13.03	0.0028
Residual	10.79	14	0.77
Lack of Fit	8.9	10	0.89	1.88	0.2847	not significant
Pure Error	1.89	4	0.47
Cor Total	588.99	28

, where the F-value of the model is 53.58, p < 0.0001, indicating that the effect of the experimental factors on the response value in the regression model is extremely significant. It proves that the established model is accurate for analysis and prediction of experimental results.

In more details, where the P values of A (pH), B (current density), C (electrode area ratio), and D (circulation rate) are all less than 0.01, which indicates that all four single parameters have an extremely significant effect on the cadmium extraction rate. Among the interaction terms of the factors, only the P values of BD and AB were less than 0.05, indicating that only these three interaction terms had a more significant effect on the cadmium extraction rate. By comparing the magnitude of the F values of each factor, it was found that the degree of influence of the single factors on the cadmium extraction rate was FB = 299.29 > FA = 166.54 > FD = 61.18 > FC = 12.19. This indicates that the order of the degree of influence on the cadmium extraction rate among the interaction terms of each factor was as follows.:

FAB = 20.24 > FBD = 9.6 > FBC = 2.96 > FBC = 1.89 > FAD = 0.78 > FCD = 0.2 > FAC = 0.019

Based on the above results, contour plots and response surface plots can be calculated using the model to create four parameters interacting to affect the cadmium lifting rate, as shown in Figure 10. It is achieved to investigate the influence of the remaining two factors on the response values by fixing two of them. The oval shape in the contour line in the figure indicates a significant interaction of the two factors, while the circle is the opposite. The steeper the slope of the response surface, the greater the influence of the factors on the response value, while the gentler the slope, the opposite.

In the response surface analysis of the interaction of the above four factors, it can be seen that the interaction of Current Density (A) and cycle rate (B) has the greatest effect on the cadmium extraction rate. On the contrary, the interaction of Current Density (A) and Electrode area ratio (C) had the least effect on the cadmium extraction rate. This result is in agreement with the ANOVA analysis. Therefore, in order to control the reaction cost and maximize the cadmium extraction rate within the experimental range, the fitted quadratic model was screened for the optimal operating parameters using Design-Expert software with the following constraints: pH 1–3, cycle rate 20–40 mL/s, Current Density 20–60 mA/cm², Electrode area ratio (A), and electrode area ratio (C). 60 mA/cm², Electrode area ratio1:1–1:3.

3.3.3. Validation of Process Parameter Predictions

In view of the above experimental results, it is inclined to consider that the electrolytic cycle rate and the current density are the most important variables in the cadmium cementation reaction. Thus, three replicate experiments for validation were carried out and the results recorded in

Table 7. The recommended scheme and its prediction results and the experimental results.

No.	Circulating Flow Rate mL/s	Current Density mA/cm2	pH	Electrode Area Ratio	Predicted Extraction Rate%	Actual Extraction Rate%
1	6.227	48.142	3.148	0.93	98.974	98.801
2	4.858	41.005	3.840	0.717	98.454	98.507
3	4.967	56.081	2.896	0.764	98.600	98.713

. It can be well observed that the average cadmium extraction rate has reached 94.69% within 3 h. In comparison with Table 3 it is evident that this is virtually the highest cadmium extraction rate in this research. Hence, these data can be used as the final optimization result.

Based on the above experimental results, we tend to think that among the six sets of interaction conditions, electrolytic cycle rate and current density are the most important ones in the cadmium cementation reaction. From the response surface curve analysis of the four factors, it can be seen that the effects of Current Density (A), cycle rate (B) and pH (C) on the cadmium extraction rate are in the optimal range. Therefore, in considering the cost control and maximizing the cadmium extraction rate within the experimental range, the optimized operational parameters were screened by using Design-Expert software for the fitted quadratic model. The limiting conditions were: A: pH 0.54; B: cycle rate 1.35~6.75; C: Electrode area ratio 0.33~1; D: Current Density 5~60 mA/cm², and the response value was set to maximize the extraction rate of cadmium. The software screened three groups of recommended experimental programs within the constraints, and the predicted and experimental results are shown in Table 7.

As can be seen from Table 7, the measured and predicted values of cadmium extraction rate are basically consistent, which indicates that the quadratic model is relatively reliable for cadmium extraction rate prediction and can well predict the effect of cadmium extraction under different conditions. However, as the reaction process, zinc plate and electric power are the biggest application expenses. Therefore, considering the cadmium extraction efficiency and the actual cost conditions, the best parameters for the cadmium extraction experiment were derived as follows: flow rate 6.23 mL/s; Current Density 48.14 mA/cm²; pH 2.25; Electrode area ratio 0.93.

Conclusively, though the methods mentioned above were analyzed and tested can be effectively employed for cadmium depth separation by utilizing existing conditions. Nonetheless, there are still two limitations: first, the mechanism by which the flow field promotes cadmium consolidation is unclear, requiring further kinetic analysis and discussion. The second is that the configuration modes of the circulating flow field are various, and different configuration conditions may affect the actual energy and zinc consumption, lacking further discussion.

4. Conclusions

An innovative method was proposed for deeply cadmium extraction from polymetallic sulfuric acid system by M5640 copper removal combined with electric field-circulating flow field coupled with enhanced cementation. The process parameters of M5640 extraction copper and electric field-circulating flow field for cadmium extraction were explored separately using single factor test method. Furthermore, the cadmium extraction parameters were also optimized using the response surface statistics method. The separation process of cadmium sponge was verified by SEM analysis of the advantages of the circulating flow field. The results of the study are summarized as follow.

Firstly, the optimal process conditions for the solution were determined by investigating the copper removal efficiency of M5640 with different parameters: 2 min of reaction time, 10% volume fraction, pH = 3.0, and O/A = 1:1. After tertiary extraction, the composition of the extracted solution was evaluated for copper ion content: 0.5 mg L⁻¹. The final removal rate for Cu was 96.8%, for Zn 1.2%, and for Cd 0.8%. It has been demonstrated that the extractant has superior separation between copper, zinc, and cadmium, which can effectively remove copper from the system and provide a reasonable foundation for the subsequent cadmium extraction step.

Afterward, the optimal process conditions for cadmium removal in this solution with field enhancement for 4.5 h were determined by comparing the efficacy of cadmium removal under various process parameters. which were pH 2.25, 45 °C, circulation flow rate of 6.23 mL/s, anode current density of 48.14 mA/cm², and anode/cathode area ratio of 0.93. The optimized removal efficiency of cadmium was 96.8%.

Third, the process parameters were optimized using response surface methodology, and the interaction mechanism between the parameters was confirmed by ANOVA and model fitting. The optimized parameters were validated. The results showed that the single parameter with the strongest influence on the cadmium extraction rate was the circulating flow rate. The most influential interaction parameters were the circulating fluid velocity and the anode current density.