Physical Simulation of Gas–Liquid Mass Transfer Behavior in Oxygen Bottom Blowing Copper Furnace

Abstract

In order to improve the internal chemical reaction efficiency of oxygen bottom blowing copper smelting furnace, the efficient separation and flow control device and technology of matte and slag in oxygen bottom blowing copper smelting furnace were put forward. A physical model was established to investigate the effects of the insertion depth of the retaining wall, the horizontal distances, the gas flow rate, and the diameter of the deflector holes on the gas–liquid mass transfer behavior in the molten bath and the gas utilization rate. The results show that the gas–liquid mass transfer rate and the gas utilization rate will decrease with the increase in the depth when the insertion depth of the retaining wall is more than 0.054 m. The horizontal distance is 1.18 m, and the area of the whole reaction zone is suitable. The absence of diversion holes is conducive to smelting. The gas flow rate of 3.0 Nm³/h is beneficial to the gas–liquid mass transfer behavior and the gas utilization rate.

1. Introduction

Oxygen bottom blowing copper smelter technology has significant advantages, such as low energy consumption, high operation flexibility, good product quality, green and high efficiency [1,2]. The oxygen bottom blowing copper smelting furnace mainly comprises two parts, one part is a reaction zone in which oxygen enters a molten bath through an oxygen lance to carry out temperature rise smelting and slagging on copper matte. The other part is the sedimental zone, where the separation of the molten metal and slag is promoted [1]. In actual production, in order to improve the reaction efficiency, the oxygen supply rate and the effect of stirring the molten bath are often enhanced by blowing a large amount of oxygen in the reaction zone, but this will also hinder the effect of slag-metal separation in the subsequent sedimental zone. In order to improve the above disadvantages, the internal structure of the oxygen bottom blowing copper smelting furnace needs to be improved.

In order to improve the reaction efficiency and mixing effect, scholars have studied the gas–liquid mass transfer behavior and inside structure inside the oxygen bottom blowing copper smelting furnace through numerical simulation [3,4,5,6,7,8,9,10] and the water model [11,12,13,14,15,16]. In the aspect of numerical simulation, Tingting Lu [3] took the large-scale oxygen bottom blowing copper smelting furnace as the research object, and proposed the asymmetric gas flowing technology to solve the problems of uneven melt stirring and gas flow coalescence in the furnace. Zhenyang Zhang [4] established a three-dimensional gas–liquid two-phase flow model for simulation study in order to improve the reaction rate inside the oxygen bottom blowing copper smelting furnace and optimize the structure of the oxygen lance. Xueyi Guo [5] established two oxygen lance seat parameters through CFD numerical analysis to study the influence on the flow characteristics of the molten bath. Qinmang Wang [6] constructed a thermodynamic model of an oxygen bottom blowing copper smelting furnace to study and analyze the content and proportion of elements in the furnace. Baocheng Jiang [7] established a simplified model based on a large oxygen-bottom blowing copper smelting furnace and studied the effects of slag layer thickness, injection flow, and oxygen lance angle on molten bath stirring. Xintao Su [8] finally completed the “ dynamic balance “ of gas-slag-matte three-phase mixing by using the VOF coupling double-side-blown multiphase flow model. Pin Shao [9] used the Eulerian-Eulerian model to simulate the gas–liquid two-phase flow in the oxygen bottom blowing copper smelting furnace, and studied the simulation of the influence of double-row oxygen lance nozzles with different gas flow rate angles on the gas–liquid two-phase flow and gas content in the bath. Hoang, Q.N. [10] explored the influence of gas flow rate, Q, oil (slag) thickness, h, and oil (slag) viscosity on mass transfer behavior by establishing a numerical simulation model of mass transfer and mixing behavior in three-phase gas stirring ladle. In the aspect of water model, Shui Lang [11,12,13] used a laboratory-scale water model of oxygen bottom blowing copper smelting furnace to use an oil–water double-phased to investigate the impact of industry-adjustable variables on bath mixing time, including lower layer thickness, gas flow rate, upper layer thickness, and upper layer viscosity. He also used the water model to study the characteristics of longitudinal waves on the surface of a molten bath during smelting and to investigate the features of the waves formed on the bath surface. Dongxing Wang [14] established a 1/5 scale physical slice model for the oxygen bottom blowing copper smelting furnace and used PIV measurement technology to study the flow field, gas flow rates, and oxygen lance installation angle at different molten bath depths in the furnace. Yanting Liu [15] established an oxygen-enriched side-blown water model to study the effects of different gas flow rate, immersion depths, and downward angles of nozzles on gas–liquid two-phase flow. Fuyong Su [16] designed a hydraulic experimental system through a water model, conducted a hydraulic experimental study on the formation of mushroom heads in the oxygen bottom blowing copper smelting furnace, and analyzed the formation process of mushroom heads in the oxygen bottom blowing copper smelting furnace.

Thus far, the above scholars have made important contributions to improving the reaction efficiency and mixing effect of oxygen bottom blowing copper smelting furnace. In the water model, there are many studies on improving the mixing effect and reducing the mixing time, but there is a lack of further research and analysis on the effect of changing the internal structure on the gas–liquid mass transfer efficiency. The existence of the retaining wall device is beneficial to the acceleration of the chemical reaction in the molten bath and the promotion of the collision between reactants, effectively improving the slag-gold separation efficiency and the recovery rate of valuable metals. The presence of the retaining wall has an impact on the smelting efficiency within the molten bath, so further analysis is needed. In this paper, the physical experiment method is used, and the 1:9.3 water model of the oxygen bottom blowing copper smelting furnace is established to carry out the related variable experiment. On this basis, the effects of different insertion depth, horizontal distance, gas flow rate, and deflector hole diameter of the retaining wall on the gas–liquid mass transfer efficiency in the furnace are studied and analyzed, and the bottom blown parameters, the quasi-number equation, and the optimized layout of the retaining wall are proposed.

2. Materials and Methods

2.1. Experimental Setup and Design Parameters

This study is no longer based on the original oxygen bottom blowing copper smelting furnace, but introduces a new retaining wall device to carry out innovative research. The gas–liquid mass transfer efficiency of the oxygen bottom blowing copper smelting furnace can be effectively improved by changing the insertion depth of the retaining wall, the horizontal distance, the diameter of the diversion hole, the gas flow rate, and other factors, so that the smelting efficiency is improved. In the existing research, due to the appearance of the retaining wall, the slag-metal separation efficiency inside the oxygen bottom blowing copper smelting furnace is also significantly improved.

This study is based on the geometric similarity and dynamic similarity of the water model, mainly to use the physical model to reflect the gas–liquid mass transfer rate in the actual oxygen bottom blowing copper smelting furnace. The CO₂-NaOH-H₂O system is used as the experimental water environment in this study. This method is based on the application of Yan Liu [17] study on the volumetric mass transfer coefficient and gas utilization rate in the study of bubble micronization and dispersion in a new type of mechanically agitated jet refining device. The model has been used as experimental equipment by scholars in related fields, and the experimentability of the water model is of high value [18]. Based on the research of scholars, it is found that both the water model experiment and the actual oxygen bottom blowing copper smelting furnace process belong to the gas–liquid mass transfer process, and the control link is the interphase mass transfer. The mass transfer reaction in the actual bath can be reflected by the related study of CO₂ and NaOH in the water model. The schematic diagram of oxygen bottom blowing copper smelting furnace (including retaining wall) in industry is shown in Figure 1. In Figure 1, L is the horizontal distance of the retaining wall; H is the insertion depth. In this experiment, a special 1:9.3 oxygen bottom blowing copper smelting furnace water model for the laboratory is used as the experimental platform, Figure 2 straight cylinder nozzle 18, diameter 3.2 mm; magnetic electrochemical analysis instrument; and magnetic pH composite electrode are used to monitor that change range of the pH value in the experimental process; the high-pressure CO₂ gas is connected with a gas flow meter after passing through a pressure reducing valve by a gas cylinder, and the flow rate of the CO₂ gas is controlled.

2.1.1. Establishment of Physical Model

Geometric similarity:

In this study, the water model is composed of plexiglass, and all dimensions are scaled down to the actual metallurgical reactor, and the data were similar. In the research process, if the metallurgical reactor under actual conditions is used, it will consume a lot of manpower and material resources, and it cannot guarantee the success of the experiment at one time, so the use of a water model is helpful to the experiment and saves a lot of resources. Water model and condition model size ratio Table 1.

Dynamics similarity:

Dynamic similarity can reduce the risk of the experiment and improve the accuracy and reliability of the experiment. In this study, it is sufficient to ensure that the Reynolds number (Re) and the modified Froude number (Fr′) of the water model are equal to the condition model. Because the fluid is mainly affected by pressure and gravity in the process of oxygen bottom blowing copper smelting, the modified Froude number (Fr′) is used as the similarity criterion, and the Fr′ of the water model is required to be equal to that of the prototype under actual conditions.

(1)$F{r}^{\prime }={\displaystyle \frac{{\rho }_g\cdot u^2}{{\rho }_1\cdot \mathrm{g}\cdot H}}$

where u is the characteristic velocity, m/s; ρ_g is the gas density, kg/m³; ρ₁ is the liquid density, kg/m³; H is the bath depth, cm.

(2)$u={\displaystyle \frac{4Q}{\pi \cdot d^2}}$

where Q is the gas volume flow, Nm³/s; d is the diameter of oxygen lance, m.

Substitute (2) to (1), one obtains:

(3)$F{\mathrm{r}}^{\prime }={\displaystyle \frac{1.624{\rho }_g\cdot Q}{\pi \cdot d^2}}$

2.1.2. Selection of Experimental Parameters

Insertion depth:

The height of the molten bath is 0.16 m, so the insertion depth ranges from 0 m~0.16 m. In this experiment, the insertion depths of 0 m, 0.018 m, 0.036 m, 0.054 m, and 0.072 m are selected as variables.

Horizontal distance:

The horizontal distance should be selected near the end of the reaction zone, and the front of the sedimentation zone is the best. The horizontal distance ranges from 1.04 to 1.36 m from the leftmost end of the oxygen bottom blowing copper smelting furnace. The horizontal distances of 1.11 m, 1.18 m, and 1.25 m are selected as variables in this experiment.

Gas flow rate:

The ratio of the air supply in the water model to the actual air supply is:

(4)$Q^{″}=Q^{\prime }\sqrt{{\left({\displaystyle \frac{1}{\lambda }}\right)}^5\cdot {\displaystyle \frac{{\rho }_1^{″}}{{\rho }_1^{\prime }}}\cdot {\displaystyle \frac{{\rho }_g^{\prime }}{{\rho }_g^{″}}}}$

where Q″ is the model gas flow; Q′ is the actual gas flow; ρ₁″ is the model liquid density; ρ₁′ is the actual liquid density; ρ_g″ is the model gas phase density; ρ_g′ is the actual gas phase density; λ is the model ratio.

Through the research, the mass transfer rate can be greatly improved by the way of bottom gas supply [19]. Through the calculation and the setting of industrial gas flow rate at the present stage, it is concluded that the gas flow range of the water model in this experiment is 2~20 Nm³/h. Therefore, parameters 2.1 Nm³/h, 3.0 Nm³/h, 3.9 Nm³/h, 4.8 Nm³/h, and 5.7 Nm³/h are selected. In order to be able to carry out the next experiment, the units are converted to 35 L/min, 50 L/min, 65 L/min, 80 L/min, and 95 L/min. However, m³/h is still used as the blowing flow unit in the drawing.

Diversion hole diameters:

The diversion hole diameter range shall be determined under the condition that the whole structure of the retaining wall is not damaged and the diameter of 0–10 cm is acceptable. Because the maximum insertion depth of the retaining wall in this experiment is 7.2 cm, the diameter of the diversion hole is selected as 0 cm, 2 cm, 4 cm, and 6 cm. The specific method is to make a circle in the middle area of the retaining wall immersed in the liquid surface of the molten bath and remove the area of the required diversion hole. The schematic diagram of the diversion hole is shown in Figure 3.

Oxygen lance angle:

According to the asymmetric blowing principle proposed by Tingting Lu [3], the asymmetric blowing mode is beneficial to the stirring of the bath. In the process of bottom gas blowing in the ladle, it is also found that the method of double gas blowing is more conducive to the mixing in the molten bath [20]. Therefore, in this experiment, the included angles of the two rows of oxygen lances are arranged at 0° and 14°, and each row has 9 oxygen lances, totaling 18. In the design of the water model, there are three rows of oxygen lances, and the included angles are 14°, 0°, and −14°, respectively. Therefore, the included angles of the oxygen lances in this experiment are arranged at 0° and 14°. The specific arrangement is shown in Figure 4.

Oxygen lance diameter:

According to Table 1, the water model is designed according to the ratio of 1:9.3, so the diameter of the oxygen lance of the water model is 32 mm. The diameter of the water model oxygen lance is shown in Figure 5.

Setting of NaOH parameters:

The CO₂-NaOH-H₂O system is used in this experiment. First, the water model is injected into H₂O at a height of 0.16 m, and the mass of NaOH alkenol needed to prepare the aqueous solution with pH 12 is calculated. After calculation, the mass of NaOH sub-enol is 32.68 g ± 2 g.

The scientific selection of experimental data is conducive to the conduct of the experiment and increases the probability of success of the experiment. The reasonable choice of the parameters can increase the persuasion of the experimental data. It is the preparation for analyzing the mass transfer rate of CO₂ in NaOH solution by changing the layout of the retaining wall. After the parameters are specifically selected, we get the specific experimental variables, Table 2. L is the horizontal distance of the retaining wall; H is the insertion depth. Q is the gas flow rate. D is the diversion hole diameter.

2.2. Experimental Principles and Procedures

2.2.1. Experimental Principles

Smelting in oxygen bottom blowing copper smelting furnace belongs to high temperature smelting process, and the chemical reaction is rapid. Through the research of scholars, it is found that the key factor limiting the reaction rate is the gas–liquid mass transfer process [21]. The molecular diffusion mass transfer process of CO₂ gas in the liquid phase of NaOH aqueous solution can replace the mass transfer process in the reactive copper smelting furnace [22]. Therefore, in this experiment, the NaOH aqueous solution-CO₂ system is used to simulate the mass transfer process in the smelter process, and the pH value measurement method is used to measure the absorption rate of CO₂ in NaOH aqueous solution [23]. A magnetic pH composite electrode can measure the pH change in the solution in real time and then calculate the CO₂ concentration at this pH value [24].

Determination of mass transfer coefficient:

(5)$\ln \left[\left(C_e-C_t\right)/\left(C_e-C_0\right)\right]=-\left(AK/V\right)t$

where C_e − CO₂ is the equilibrium concentration, 0.049 mol/L; C_t is the value of CO₂ concentration absorbed by the NaOH solution after the experiment has been carried out for t seconds, mol/L; C₀$-$CO₂ is the initial concentration, the value of CO₂ concentration absorbed by the solution at pH 12, mol/L; A is the surface area of gas–liquid reactions in the melt pool.cm²; K-CO₂ is the mass transfer coefficient, cm/s; V-NaOH is the volume of the solution, cm³; t is the chemical reaction time, s.

Determination of CO₂ gas utilization:

(6)$\eta =\left[V\left(C_{{\mathrm{CO}}_{2,\coprod }}-C_{{\mathrm{CO}}_{2,\mathsf{{\rm I}}}}\right)/\mathrm{t}\right]/\left[\left({\rho }_{{\mathrm{CO}}_2}\cdot Q\right)/M\right]$

where V-NaOH is the volume of the solution, cm³; C_CO2,I is the concentration of CO₂ in the solution after reaction t₁ min of reaction, mol/L; C_CO2,II is the concentration of CO₂ in the solution after reaction t₂ min of reaction, mol/L; t is the time difference between t₂ and t₁, and t = t₂ − t₁ > 0, min; ρ_CO2-CO2 is the gas density, 1.977 × 10⁻³ g/cm³; Q-CO₂ is the gas flow rate, L/min; M-CO₂ is the molar mass, g/mol.

2.2.2. Experimental Procedures

The control variable method is used to study the different insertion depth H of the retaining wall, horizontal distance L, gas flow rate Q and diameter D of the diversion hole as experimental variables. The water model is composed of plexiglass and contains with 0.16 m of NaOH solution at pH 12. Double rows of 9-nozzle oxygen lances are used at the bottom, with 0° and 14° alternately distributed, 18 nozzles in total, with a diameter of 3.2 mm. Asymmetric blowing can effectively suppress gas flow and improve stirring uniformity. After passing through a pressure reduction valve and gas flow meter, high-pressure CO₂ gas is connected with an 18-hole oxygen lance shunt device and enters a molten bath from an oxygen lance at that bottom of the water model to react with NaOH aqueous solution. The pH composite electrode is placed at a height of 0.15 m from the oxygen lance, which corresponds to the phase interface between matte and slag in an actual oxygen bottom blowing copper smelting furnace. Before the start of the experiment, the magnetic electrochemical analysis instrument is connected to the computer, and the experiment can be started only after the value is stable, and the pH value inside the molten bath is recorded every 4 s. The pH value in the molten bath began to decrease from 12, and when the pH value decreased to 7, the recording was stopped, and the experiment is ended [25]. Select data in the pH range of 12–8. Due to the fluctuation of CO₂ injection and other reasons, there must be accidental errors in the experimental data, which cannot avoid affecting the experimental results. Each group of experiments is carried out three times, and the average value is taken. The experimental process is shown in Figure 6.

3. Results and Discussion

3.1. Effect of Insertion Depth on Molten Bath

When the depth of the molten bath is 0.16 m, the horizontal distance is 1.18 m, without diversion hole, and the gas flow rate is 3.0 Nm³/h, five kinds of insertion depths of 0 m (without retaining wall), 0.018 m, 0.036 m, 0.054 m, and 0.072 m are studied. During the experiment, the pH meter is used to record the pH data at different insertion depths, and the curve of pH value changing with time is drawn and fitted, as shown in Figure 7. Figure 8 shows the gas–liquid mass transfer coefficient and the CO₂ gas utilization rate at different retaining wall insertion depths.

Figure 7 and Figure 8 show that the increase in the insertion depth of the retaining wall will accelerate the gas flow rate of pH value, increase the gas–liquid mass transfer coefficient, and improve the utilization rate of CO₂ gas under the condition that the gas flow rate and the horizontal distance of the retaining wall are unchanged. When the insertion depth of the retaining wall is 0.054 m, the chemical reaction rate is the fastest, compared with 0 m, the reaction rate is increased by 31.4%, and the utilization rate of CO₂ is increased by 30.4%; the growth rate is 8.6%. When CO₂ gas first enters the molten pool, the pH value shows no significant changes with different retaining wall insertion depths. With the reaction going on, the retaining wall device begins to play a significant role. At the beginning of the experiment, CO₂ bubbles reacted with NaOH solution at the gas–liquid interface on the left side of the retaining wall and were absorbed, and the degree of reaction did not spread to the vicinity of the retaining wall device. As time goes on, the bubbles gradually diffuse to both sides of the oxygen lance, and the flow in the molten bath promotes the continuous diffusion of NaOH to the gas–liquid interface, and the retaining wall accelerates the reaction. The increase in the depth of the retaining wall enhances the isolation between the reaction zone and the sedimental zone. CO₂ first consumes NaOH in the reaction zone to form a concentration difference, which promotes the transfer of high-concentration solution from the sedimentation zone to the reaction zone. Due to the concentration difference formed by the retaining wall, the concentration of the reactant in the reaction area can be supplemented in time, thereby accelerating the overall chemical reaction rate. The fluid in the reaction zone flows to the sedimental zone under the action of the oxygen lance turbulence and generates a reaction force after contacting the retaining wall, so that the unreacted NaOH is promoted to return to the reaction zone, and the utilization rate of CO₂ is improved. When the insertion depth of the retaining wall is 0.018 m, the isolation degree is insufficient and the effect of the reaction force is poor; at 0.072 m, the circulation space is limited, although the isolation degree is the largest, the transfer of NaOH is blocked, and the utilization rate of CO₂ is reduced. The final analysis shows that the best insertion depth of the retaining wall is 0.054 m to ensure the gas–liquid mass transfer efficiency and the slag-metal separation effect in the actual production process. When the insertion depth is 0.054 m, the linear relationship is the best. The equation is pH = a + b * t, and the adjusted R² is 0.99625, close to 1. The linear equation can be used to prove the linear relationship between pH and t under the condition of changing the insertion depth of the retaining wall and keeping other variables unchanged. The slope represents the speed of mass transfer rate.

3.2. Effect of Horizontal Distance on Molten Bath

When the depth of the molten bath is 0.16 m, the insertion depth of the retaining wall is 0.054 m, without diversion hole, and the gas flow rate is 3.0 Nm³/h, three kinds of horizontal distances of 1.11 m, 1.18 m, and 1.25 m are studied. During the experiment, the pH meter is used to record the pH data at different horizontal distances, and the curve of pH value changing with time is drawn and fitted, as shown in Figure 9. Figure 10 shows the gas–liquid mass transfer coefficient and the CO₂ gas utilization rate at different retaining wall horizontal distances.

Figure 9 and Figure 10 show that the pH value of the solution decreases at the fastest rate, the gas–liquid mass transfer coefficient is the highest, and the CO₂ gas utilization rate is the best when the horizontal distance of the retaining wall is 1.18 m under the condition that the gas flow rate and the insertion depth of the retaining wall are unchanged. Under this condition, the chemical reaction rate is 31.4% higher than that without the retaining wall (0 m), and the utilization rate of CO₂ reaches 30.4%. Because the area of the reaction zone is appropriate at this time, the turbulent kinetic energy generated by the CO₂ gas injected from the bottom oxygen lance effectively stirs the molten bath, promotes the overall flow of NaOH solution, and accelerates the mass transfer between bubbles and the liquid phase. When the chemical reaction is carried out in a suitable reaction area, the collision probability of CO₂ gas in the NaOH solution can be increased, and the chemical reaction rate can be effectively improved. The gas–liquid interface is also increased due to the improvement of turbulent kinetic energy on the stirring effect, which significantly increases the specific surface area of the gas in contact with the liquid phase after bubble breakup. This is obviously one of the ways to improve the efficiency of gas–liquid mass transfer. When the horizontal distance of the retaining wall is 1.11 m, the turbulent kinetic energy is mainly concentrated in the reaction zone due to the reduction in the area of the reaction zone, and the stirring effect on the sedimental zone is poor, and the overall liquid flow is not smooth. Due to the short horizontal distance of the retaining wall, the fluid flowing from the reaction zone to the sedimental zone causes a large scour kinetic energy on the retaining wall, which affects the life of the retaining wall. When the horizontal distance is 1.25 m, the area of the reaction zone increases. However, the turbulent kinetic energy is not enough to fully stir, and the degree of bubble breakage is low, which leads to the decrease in gas–liquid mass transfer rate and the utilization rate of CO₂. In the process of fluid flow, the friction increases, which affects the effect of reaction force, thus reducing the efficiency of gas–liquid mass transfer. When the horizontal distance is 1.18 m, the linear relationship is the best. The equation is pH = a + b * t, and the adjusted R² is 0.99962, close to 1. The linear equation can be used to prove the linear relationship between pH and t under the condition of changing the horizontal distance of the retaining wall and keeping other variables unchanged. The slope represents the speed of the mass transfer rate.

3.3. Effect of Deflector Hole Diameter on Molten Bath

When the depth of the molten bath is 0.16 m, the insertion depth of the retaining wall is 0.054 m, the horizontal distance is 1.18 m, and the gas flow rate is 3.0 Nm³/h, four kinds of diversion hole diameters of 0 m, 0.02 m, 0.04 m, and 0.06 m are studied. During the experiment, the pH meter is used to record the pH data at different deflector hole diameters, and the curve of pH value changing with time is drawn and fitted, as shown in Figure 11. Figure 12 shows the gas–liquid mass transfer coefficient and the CO₂ gas utilization rate at different deflector hole diameters.

Figure 11 and Figure 12 show that when the diameter of the diversion hole is 0 cm, the pH value of the solution decreases at the fastest rate, the gas–liquid mass transfer coefficient is the highest, and the CO₂ gas utilization rate is high. With the increase in the diameter of the diversion pore, the rate of pH decline did not show obvious signs of fluctuation, but showed a downward trend due to the increase in the diameter of the diversion pore, and the maximum decline is 18.6%. Gas utilization rate decreased by 3.9%. After analysis, it is concluded that the time to reach the ideal concentration difference between the reaction zone and the sedimental zone will be greatly increased with the gradual increase in the diameter of the diversion hole under the condition that other variables remain unchanged. This situation reduces the efficiency of the transfer from the high concentration zone to the low concentration zone, thereby reducing the gas–liquid mass transfer reaction and the utilization rate of CO₂ gas. At this time, the reactant concentration in the reaction zone cannot be supplemented in time, and with the decrease in the reactant concentration, the overall chemical reaction rate will also decrease due to the increase in the diameter of the diversion hole. The increase in the diameter of the diversion hole has a counterforce on the chemical reaction efficiency and will also increase the erosion at the diversion hole and destroy the overall stability of the retaining wall, so it is not recommended to use the diversion hole. The equation is pH = a + b * t, and the adjusted R² is 0.99515, close to 1. In this case, pH has a good linear relationship with t under the condition of only changing diversion hole diameters and not changing other variables. When the diversion hole diameters are 0 m, the linear relationship is the best.

3.4. Effect of Gas Flow Rate on Molten Bath

When the depth of the molten bath is 0.16 m, the insertion depth of the retaining wall is 0.054 m, the horizontal distance is 1.18 m, and the gas flow rate is 3.0 Nm³/h, without diversion hole, five kinds of gas flow rates of 2.1 Nm³/h, 3.0 Nm³/h, 3.9 Nm³/h, 4.8 Nm³/h, and 5.7 Nm³/h are studied. During the experiment, the pH meter is used to record the pH data at different gas flow rates, and the curve of pH value changing with time is drawn and fitted, as shown in Figure 13. Figure 14 shows the gas–liquid mass transfer coefficient and the CO₂ gas utilization rate at different gas flow rates.

Figure 13 and Figure 14 show that under the condition that the insertion depth and horizontal distance of the retaining wall remain unchanged, with the increase in the gas flow rate, the pH decrease rate shows an obvious acceleration trend, the gas–liquid mass transfer coefficient increases, and the utilization rate of CO₂ gas increases. When the gas flow rate is 3.0 Nm³/h, it is more suitable for the reaction in the furnace and the efficient utilization of resources. Because the increase in gas flow means that more CO₂ gas will enter the molten bath at the same time, resulting in a large number of CO₂ bubbles. The increase in bubbles, on the one hand, increases the stirring effect of gas on the inside of the molten bath. Heat generated from the reaction process is homogenized. On the other hand, it will increase the contact area between bubbles and liquid, and the increase in gas–liquid phase interface will promote the gas–liquid mass transfer reaction. The increase in gas–liquid reaction interface is helpful for gas and liquid to contact more fully, and the chemical reaction rate will increase with the increase in reaction interface area. However, with the continuous increase in gas flow rate, the time for CO₂ bubbles to reach the liquid interface from the bottom is shortened. Because of the short residence time of the bubbles in the solution, CO₂ gas cannot fully diffuse from the bubbles to the liquid phase, resulting in a lot of waste of resources. This is also the reason why the gas–liquid mass transfer efficiency is not significantly improved with the increase in gas flow. However, it also causes a large amount of splashing of the solution. In the actual production process, due to the excessive blowing flow, a large number of melt splashes will block the charging port, endanger the production operation, and affect the continuity of smelting. When the gas flow rate is 3.0 Nm³/h, the linear relationship is the best. The equation is pH = a + b * t, and the adjusted R² is 0.99023, close to 1. There is a good linear relationship between pH and t.

3.5. Factorial Analysis and Derivation of Empirical Formulae

Analyzing and processing the above experimental data, it can be seen that the gas–liquid mass transfer coefficient is mainly related to the insertion depth of the retaining wall H, the horizontal distance L, the diversion hole diameter D, the gas flow rate Q and other factors, and the optimal parameter setting in this experiment is no guide holes. Summarizing the relevant studies on the gas–liquid mass transfer rate by previous scholars, it is found that the gas–liquid mass transfer coefficient AK is related to the diameter of the bottom nozzle d₀, the height of the liquid surface h, the liquid viscosity μ₁, the gas viscosity μ_g, and the diffusion coefficient of the gas in the liquid D_g, and is not an independent variable. The general functional equation is obtained using the analytical method:

(7)$f\left(AK,Q,H,L,v_{{\mathrm{CO}}_2},v_{{\mathrm{H}}_2\mathrm{O}},h\right)=0$

where Q is the gas flow rate Nm³/h; h is the height of the molten bath, m; H is insertion depth, m; L is horizontal distance, m.

In order to obtain an expression for the relationship between the AK gas–liquid mass transfer coefficient and the depth of insertion of the retaining wall, the horizontal distance, and the amount of gas flow rate, the above equation is rewritten as an explicit function:

(8)$AK/\left(h\cdot v_{{\mathrm{H}}_2\mathrm{O}}\right)=f\left(Q/\left(h\cdot v_{{\mathrm{CO}}_2}\right),H/h,L/h\right)$

Because there is a power function relationship between the independent variables within a certain range, the fitting relationship of the empirical law is obtained and derived:

(9)$\ln \left({\displaystyle \frac{AK}{h\cdot v_{{\mathrm{H}}_2\mathrm{O}}}}\right)=\ln a_0+a_1\ln \left({\displaystyle \frac{Q}{h\cdot v_{{\mathrm{CO}}_2}}}\right)+a_2\ln \left({\displaystyle \frac{H}{h}}\right)+a_3\left({\displaystyle \frac{L}{h}}\right)$

where a₀, a₁, a₂, and a₃ are the fitting coefficients of Equation (9).

Take a₁ as an example, and keep the other independent variables unchanged under the change of Q. Equation (9) can be written as:

(10)$\ln \left({\displaystyle \frac{AK}{h\cdot v_{{\mathrm{H}}_2\mathrm{O}}}}\right)=c+a_1\ln \left({\displaystyle \frac{Q}{h\cdot v_{{\mathrm{CO}}_2}}}\right)$

where h = 0.16 m; v_H2O = 1.0 × 10⁻⁶ m²/s; v_CO2 = 7.4 × 10⁻⁶ m²/s.

The value of ln[AK/(h·v_H2O)] is linearly fitted to the relationship of ln[AK/(h·v_CO2)], and the intercept of the fitting equation is a₁ = 0.603. In the same way, a₀ = 5.78 × 10⁻⁴, a₂ = 0.381, a₃ = −2.379.

Combining the predicted results of gas–liquid mass transfer coefficients under each parameter condition, regression analyses are performed to obtain the following empirical equations:

(11)$AK=5.78\times {10}^{-4}\cdot Q^{0.603}\cdot H^{0.381}\cdot L^{-2.379}$

Equation (11) can only be used as a reference for the variables related to the bottom-blowing copper furnace 1:9.3 water model with a 14° angle and a 3.2 mm diameter double-row 9-nozzle oxygen lance. The applicable range of Equation (11) is under the retaining wall mode; the insertion depth is 0.018 m~0.072 m, the horizontal distance is 1.11 m~1.25 m, there is no diversion hole, and the gas flow rate is 2.1 Nm³/h~5.7 Nm³/h. Figure 15 shows the AK gas–liquid mass transfer coefficients calculated from empirical Equation (11) for different gas flow rates. The gas flow rate is plotted as the horizontal coordinate, and the AK gas–liquid mass transfer coefficient is plotted as the vertical coordinate. Comparing the theoretical values with the experimental values, the maximum error is 6.67%, the minimum error is 1.20%, and the average error of 3.94% is within the reasonable range, thus it is instructive for practical operation.

4. Conclusions

The effect of variables related to the retaining wall device on the gas–liquid mass transfer behavior inside bottom-blown copper furnaces is described by developing a 1:9.3 water model. The effects of this retaining wall device on the efficiency of chemical reactions in the furnace at different insertion depths, horizontal distances, diameters of double guide holes, and gas flow rates are investigated, and empirical formulas are obtained. The results showed that:

1. The inclusion of the retaining wall device promotes the chemical reaction, accelerates the gas–liquid mass transfer efficiency, and improves the CO₂ gas utilization rate. With the retaining wall inserted at a depth of 0.054 m, a horizontal distance of 1.18 m, gas flow rate is 3.0 Nm³/h, and no diversion hole, the chemical reaction efficiency is increased by 31.4% compared with that without the retaining wall, and the gas–liquid mass transfer efficiency is the highest, with a CO₂ gas utilization rate of 30.4%.

2. The empirical formula for the AK volumetric mass transfer coefficient is derived after extensive experiments and calculations:

   $AK=5.78\times {10}^{-4}\cdot Q^{0.603}\cdot H^{0.381}\cdot L^{-2.379}$

The maximum error is only 6.78%, the minimum error is 1.2%, the average error is not large, and it has a certain reference value for the actual industrial production.

Author Contributions

Study design, Z.Z.; experiment, Z.Z.; validation, Z.Z.; date analysis, Z.Z.; figures, Z.Z.; writing—original draft preparation, Z.Z.; Conceptualization, P.S.; methodology, P.S.; Literature, S.S.; software, S.S.; date processing, S.S.; All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The datasets presented in this article are not readily available because the data are part of an ongoing study. Requests to access the datasets should be directed to [[email protected]].

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Oxygen bottom blowing copper smelting furnace (including retaining wall).

Figure 2. Water model of bottom-blown melting furnace.

Figure 3. The schematic diagram of the diversion hole.

Figure 4. Arrangement mode of oxygen lance.

Figure 5. The diameter of the water model oxygen lance.

Figure 6. Experimental process. 1—CO2 gas (Anshan, China); 2—Main regulating valve (Zhejiang Baihui Pneumatic Components Co., Ltd., Zhejiang, China); 3—Gas flow meter (SIARGO, Santa Clara, CA, USA); 4—Air supply pipe (Yueqing Tianxu Electric Co., Ltd., Yueqing, China); 5—pH composite electrode (INASE Scientific Instrument Co., Ltd., Shanghai, China); 6—Electrochemical Analyzer (INASE Scientific Instrument Co., Ltd., Shanghai, China); 7—Computer (Lenovo, Beijing, China); 8—Water model (Colourful plexiglass, Shenyang, China).

Figure 7. Plot of pH over time at different retaining wall insertion depths.

Figure 8. Gas–liquid mass transfer coefficient and CO2 gas utilization rate at different retaining wall insertion depths.

Figure 9. Plot of pH value over time at different retaining wall horizontal distances.

Figure 10. Gas–liquid mass transfer coefficient and CO2 gas utilization rate at different horizontal distances of retaining walls.

Figure 11. Plot of pH value over time at different deflector hole diameters.

Figure 12. Gas–liquid mass transfer coefficient and CO2 gas utilization rate at different deflector hole diameters.

Figure 13. Plot of pH over time with different gas flow rates.

Figure 14. Gas–liquid mass transfer coefficient and CO2 gas utilization rate at different gas flow rates.

Figure 15. Comparison between the theoretical and experimental values of the gas–liquid mass transfer coefficient under different gas flow rates.

Table 1

Dimensions of water model and operating parameters.

Parameter	Water Model Value	Condition Model
Bath lengths/m	1.691	15.718
Bath height/m	0.160	1.5
Bath diameter/m	0.381	3.535
Number of oxygen lance	18	9/18
Diameter of oxygen lance/mm	3.2	30
Working medium	0.01% NaOH (Anshan, China)	Copper matte

Table 2

Experimental variables.

Project	H, mm	L, mm	D, mm	Q, Nm3/h
H	0	1180	0	3.0
	18	1180	0	3.0
	36	1180	0	3.0
	54	1180	0	3.0
	72	1180	0	3.0
L	54	1110	0	3.0
	54	1180	0	3.0
	54	1250	0	3.0
Q	54	1180	0	2.1
	54	1180	0	3.0
	54	1180	0	3.9
	54	1180	0	4.8
	54	1180	0	5.7
D	54	1180	0	3.0
	54	1180	20	3.0
	54	1180	40	3.0
	54	1180	60	3.0

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