Optimized structural parameters and heat extraction capacity of a mixing device for constant pressure CO2 mineralization using alkaline waste

Alkaline waste such as calcium carbide slag is an ideal material for mineralizing CO2 and promoting atmospheric carbon reduction. In this study, the structural parameters of a mixing device and a thermal extraction method for the high-efficiency mineralization of CO2 using alkaline waste were optimized. First, the influence of structural parameters was studied by means of numerical simulation, and it was found that when the length–diameter ratio, blade angle, spacing, and diameter of the mixing device were 3, 15, 6 cm, and 14 cm respectively, 2.14 t CO2 can be mineralized within 1 h. The amount of heat extracted from mineralization of 1 t CO2 reached 189.60 MJ. In addition, the winding configuration of the heat pipe, which is beneficial for extracting more reaction heat, was optimal, and a model of the relationship between the heat pipe outlet water temperature and flow velocity at the outlet of the heat pipe was established. This study provides theoretical guidance for the field application of alkaline waste for high-efficiency mineralization of CO2, which can accelerate the realization of peak CO2 emissions and carbon neutrality.


Introduction
Mixing technology is widely used in the desalination of seawater, chemical and metallurgical processing, and other industrial processes (Mauro et al. 2010;Li and Xu 2017). With the increasing industrial demand for ethylene production and coal and iron resource mining, a large amount of alkaline waste is produced, such as calcium carbide slag and fly ash (Miao et al. 2022;Wu et al. 2021a). At the same time, many of the alkaline components in these wastes can mineralize and sequester large amounts of CO 2 (Mayoral et al. 2013;Yang et al. 2019;Wang et al. 2021). A mixing device that can ensure that the alkaline waste mineralizes and absorbs a large amount of CO 2 and that can efficiently extract a large amount of reaction heat can accelerate the realization of peak CO 2 emissions and carbon neutrality (Nazari et al. 2018a;Pan et al. 2020).
Improving the efficiency of the mixing device is imperative for the efficient mineralization of CO 2 using alkaline waste, where the structural parameters of the mixing device are known to affect its efficiency (Geng et al. 2021). Methods of achieving efficient mass and heat transfer in mixing devices have been widely studied in scholastic settings. For example, Moradkhani et al. (2017) studied the influence of five impeller structures and three different aeration flow rates on the mass transfer coefficient based on the "k-ε" Reynoldsaveraged Navier-Stokes (RANS) model. They found that a stirring speed of 300-800 rpm provided the most effective rate of oxygen mass transfer in a two-phase distribution bioreactor. Tatterson and Morrison (1987). studied the length-diameter ratio of the agitator in a mixing device and found that when the length-diameter ratio was greater than 4, the hydrodynamics of the fluid near the blade was close to solid rotation. Ranade and Joshi (1989) studied the influence of the blade inclination on the flow pattern in a mixing device and determined that the blade inclination has a Responsible Editor: Guilherme L. Dotto significant effect on the flow characteristics. Ameur (2016) found that the stirring power increases with an increase in the blade inclination angle. Wu et al. (2021b) studied the heat transfer performance of a rotating fluidized bed using the Euler-Lagrangian hybrid method. It was found that the heat transfer coefficient of the bed wall increased by 20% when the blade inclination angle was changed from 45 to 12°.
Kumaresan and Joshi (2016) obtained a higher average shear rate, average normal stress, and turbulent kinetic energy of a downflow impeller by studying the influence of the blade inclination angle on the power. Zuo et al. (2020) studied the effect of different blade numbers on the mixing efficiency of an agitator using the discrete element method and found that increasing the blade number can promote the mixing efficiency. Bao et al. (2020) used the discrete element method to study the effect of the impeller structure on particle flow and mixing. The results showed that the mixing efficiency and axial diffusion coefficient increased with an increase in the blade diameter.
We found by reviewing the literature that heat pipes are widely used in the field of heat exchange. Many scholars have studied the effect of heat pipe structure parameters on the efficiency of heat exchange. For example, Jouhara et al. (2017) manufactured and tested a flat heat pipe heat exchanger with a heat recovery rate of about 5 kW and verified through experiments that the heat recovery rate was basically consistent with the theoretical value. Deng et al. (2020) used heat pipe to recycle underground heat resources, and the heat extracted is used to heat water for regional heating. Nazari et al. (2018b) added surfactant into pure water to improve the thermal performance of pulsating heat pipe. Ramezanizadeh et al. (2019) carried out a lot of research on the heat transfer performance of pulsating heat pipe by adding different materials to water. The results show that pulsating heat pipe has superior heat transfer performance when applied to cooling equipment and heat exchanger, and the maximum heat transfer performance can reach 100%.
Different from previous studies (Yuan et al. 2022), this paper mainly studies the effect of mixing devices with different structural parameters on thermal extraction efficiency. In addition, heat extraction by the heat pipe using different winding configurations is studied. The heat extraction ability of the heat pipe at different fluid velocities is analyzed. Despite numerous studies on the structural parameters of mixing devices, there are few studies of the influence of the length-diameter ratio, blade inclination angle, blade diameter, and blade spacing on the reaction heat transfer and heat transfer efficiency. In order to realize high efficiency and maximize the mineralization and storage of CO 2 using waste, it is urgent to develop a device for the rapid mineralization of CO 2 . Therefore, in this study, the influence of various factors, including the length-diameter ratio of the mixing device, inclination angle, spacing, and diameter of the blades, on the degree of CO 2 mineralization using carbide slag (where the mineralization degree refers to the ratio of the mass of carbide slag participating in the CO 2 mineralization reaction to the total mass of carbide slag filled into the mixing device) and reaction heat extraction during the mineralization process is investigated through experiments and numerical simulations. The relationship between the heat pipe outlet water temperature and fluid velocity at the outlet of the heat pipe is analyzed by numerical simulation.
This research is of great significance for the early realization of peak CO 2 emissions and carbon neutrality and enhances the extraction and utilization of reaction heat during the mineralization process. In the "Mechanism of CO 2 mineralization and mathematical model" section, the mechanism of CO 2 mineralization with carbide slag is analyzed, and a mathematical model of CO 2 mineralization with carbide slag slurry under constant pressure is established and verified. In the "Numerical simulation of CO 2 mineralization process in mixing device" section, a mixing device model with different structural parameters is established and the effects of different structural parameters on the degree of mineralization and reaction heat extraction under constantpressure and continuous-feed conditions are studied by numerical simulation. A model of the relationship between the heat pipe outlet water temperature and flow velocity at the outlet of the heat pipe is established.

Mechanism of CO 2 mineralization and mathematical model
The total reaction during CO 2 absorption by the carbide slag slurry can be expressed as Eq. (1) (Meng et al. 2022;Liu et al. 2021): Figure 1 shows a schematic of the instantaneous mass transfer near the gas-slurry interface of the carbide slag slurry When the pH is greater than 11, reactions (1) are expected to occur at a high rate (Gupta and Fan, 2002). Therefore, the process of CO 2 absorption by calcium carbide slag slurry can be replaced by reaction (1) (Rigopoulos and Jones, 2003).
The validity of the mathematical model used in this paper has been verified in the previously published articles (Yuan et al. 2022). In this mathematical model, turbulence, component transport and other models are used to realize the chemical reaction and the source phase is established to ensure that the CO 2 inside the mixing device is in a constant pressure state. This mathematical model is independent of the structural parameters of the mixing device (Heydarifard et al. 2020;Liu et al. 2020;Malakhov et al. 2020, and it is feasible to apply the mathematical model to the study of the structural parameters of the mixing device on the mineralization degree and the extraction temperature of the heat pipe (Wu et al. 2018;Xuan et al. 2016). The maximum error between the numerical simulation results and the experimental results is less than 10%, which shows that the mathematical model is effective in simulating the CO 2 mineralization process of carbide slag. Therefore, next, the CO 2 mineralization process of mixing devices with different structural parameters is studied.

Numerical simulation of CO 2 mineralization using calcium carbide slag and optimum process parameters
The mass transfer and heat pipe outlet water temperature for CO 2 mineralization with calcium carbide slag were studied by controlling the length-to-diameter ratio (A), blade inclination angle (B), blade spacing (C), and blade diameter (D) in the device. The numerical simulation was carried out by designing orthogonal experiments, and the gradient was divided, as shown in Table 1. The 3D physical model of the mixing device centered on (0,0,0) was established using Solidworks software (Fig. 2). The model includes a slurry inlet and outlet, a CO 2 source phase, and a heat pipe (screw thread spacing of 10 cm); the function of the middle heat pipe in the mixing device is to extract the reaction heat released by the mineralization reaction, so as to reduce the heat loss and the mineralization cost. The data from domestic and foreign studies on the degree of mineralization promoted by different factors were summarized, from which the rotational speed, pressure, solid-liquid ratio, and slurry   The length-diameter ratio, blade angle, spacing, and diameter of the mixing device are 1.5-3, 15-45°, 3-6 cm, and 11-14 cm, respectively, and were equally divided into four gradients for orthogonal numerical simulation. The gradient was divided as shown in Table 1.
The degree of mineralization and the heat pipe outlet water temperature were calculated when the mass of the CaCO 3 outlet was stable. Sixteen groups of mineralization degree data and heat pipe outlet water temperature were obtained by orthogonal simulation, as shown in Table 2.
The range of R j reflects the influence of this factor on the degree of mineralization or temperature rise. The greater the R j value, the greater the influence of this factor on the results. As can be seen from Table 2, for the degree of mineralization, R 1 follows the order A > D > B > C. For the heat pipe outlet water temperature, R 2 follows the order A > D > C > B. Therefore, factor A has the greatest influence on both the degree of mineralization and the heat pipe outlet water temperature.
Combined with the data in Tables 3 and 4, the analysis of variance shows that when the mineralization degree is an objective function (Wu et al. 2020), the F ratio for factors A, B, and D (3.54, 0.08, and 0.37, respectively) is greater Table 2 Mineralization degree and water temperature after orthogonal simulation Note: A is the mineralization degree, and T is the water temperature. Kij represents the average mineralization degree and outlet temperature rise corresponding to level I in column j. R j stands for k max −K min in column j

Group
Factor Result  than that when the heat pipe outlet water temperature is the objective function (3.50, 0.06, and 0.27, respectively). Thus A 4 B 1 D 4 was selected under the objective function of the mineralization degree. When the heat pipe outlet water temperature is the objective function, the F ratio (0.18) of factors A, B, and D is greater than that when the mineralization degree is the objective function (0.02). Therefore, C 4 was selected as the objective function for the heat pipe outlet water temperature. The optimal combination is A 4 B 1 C 4 D 4 , that is, the length-to-diameter ratio of the mixing device is 3, and the angle, spacing, and diameter of the blade are 15°, 6 cm, and 14 cm, respectively, which is the fourth group of sixteen orthogonal simulations.

Analysis of CO 2 mineralization and quantification of heat extraction for mixing device
The length-to-diameter ratio of the mixing device has the greatest influence on the mineralization capacity and the heat pipe outlet water temperature. To a certain extent, increasing the length of the mixing device can increase the contact time between the calcium carbide slag and CO 2 , leading to greater reaction, a longer heat exchange time between the heat pipe, and the high-temperature slurry in the mixing device, and improve heat exchange efficiency. Group 4 of the numerical simulation data was imported into TECPLOT post-processing software, and the nephograms of the CaCO 3 concentration and temperature distribution (after the mass of CaCO 3 at the outlet stabilized) were obtained (Fig. 3). The nephograms of the CaCO 3 concentration and temperature distribution show that the CaCO 3 concentration and temperature were high near the entrance and low near the exit. This is because a large amount of heat is released after the reaction of Ca(OH) 2 and CO 2 to form CaCO 3 , which increases the temperature of the slurry containing CaCO 3 , resulting in a similar CaCO 3 concentration distribution and temperature distribution. Table 2 shows that after the mass of CaCO 3 at the outlet stabilized, the degree of mineralization and the temperature of the outlet reached 78% and 319.21 K, respectively. The calculation indicates that the mixing device with the A 4 B 1 C 4 D 4 structure parameters can mineralize about 2.14 t of CO 2 and consume 4.53 t carbide slag within 1 h, which is equivalent to the CO 2 released by complete combustion of 0.957 t coal. In addition, 2.35 m 3 of water can be heated from 300 to 319.21 K for the mineralization of 1 t CO 2 , where the amount of heat extracted reached 189.60 MJ.

Effect of heat pipe configuration on heat extraction capacity
As shown in Table 2, the simulated mineralization capacity and the heat pipe outlet water temperature were the highest in the fourth group. Therefore, the structural parameters from the fourth group simulation were used; that is, the length-diameter ratio, blade angle, spacing, and diameter of the mixing device were 3, 15, 6, and 14 cm, respectively. The influence of the winding density of the heat pipe on the heat extraction capacity was investigated. The distance between the outlet and the inlet of the heat pipe in the mixing device was 120 cm, which was divided into a, b, and c regions on average, and the pitch of the three areas was changed from 10 to 5 cm to encrypt the heat pipe in the corresponding area, after which the calculation was carried out. The heat pipe outlet water temperatures with different winding densities are shown in Fig. 4. Figure 4 shows that the heat pipe outlet water temperature was highest when the winding density corresponded to a. Combined with Fig. 4b, it can be seen that the reaction heat produced by the reaction of Ca(OH) 2 and CO 2 was mainly concentrated in the area of the mixing device. When the winding number of the heat pipe in this area is increased, the heat exchange time between the water inside the heat pipe and the high-temperature slurry outside the heat pipe can be increased, allowing the water inside the heat pipe to absorb more heat, thus increasing the heat pipe outlet water temperature and improving the heat exchange efficiency. Therefore, the winding configuration of the heat pipe (Fig. 4a) was employed in studying the effect of the flow velocity of the internal liquid on the heat extraction capacity.

Effect of flow rate on thermal extraction ability
In this section, the variation of the heat pipe outlet water temperature at flow velocities of 0.2-4 m/s in the heat pipe (where the flow velocity refers to the flow velocity in the heat pipe) was studied. After locally encrypting the density of the heat pipe, there were 16 turns of the heat tube in the mixing device. To monitor the realtime change in the heat pipe outlet water temperature, four points a (5.24, −60, 30.69), b (0, 50, 21), c (0, −22.5, −21), and d (0, −55, 21) were set up at lap 2, lap 8.5, lap 15, and at the outlet of the heat pipe when the water enters the mixing device. The temperature change at each point was determined after the mass of CaCO 3 at the outlet stabilized. The curve t represents the temporal evolution of water flow from the inlet of the heat pipe to the outlet, and the data in curve b corresponds to T b = 12 K. As shown in Fig. 5, the slope of curve t decreased gradually overall. As the flow velocity increased, the time for water to flow from the heat pipe inlet to the outlet decreased. The time required for heat exchange between water in the heat pipe and hightemperature calcium carbide slag slurry decreased with an increase in the flow velocity, leading to a less pronounced decrease in the heat exchange capacity. Therefore, the temperature of points a, b, c, and d decreased slowly with an increase in the flow velocity, and the extent of the decrease gradually became smaller.
The values A = 6.77, t = 2.67, and y 0 = 315.91 were obtained for the exponential decay by using the Expdecl model (y = A*exp(x/t) + y 0 ) in Origin software to analyze the data in curve a. The functional relationship between the heat pipe outlet water temperature and flow velocity at the outlet of the heat pipe is represented by Eq. (2).
The amount of heat extracted from the water in the heat pipe in 1 h is related to the increase in the heat pipe outlet water temperature. Therefore, the function Q describing the relationship between the amount of heat extracted and the flow velocity can be obtained from Eq. ( 3 ).
Here, r is the radius of the heat pipe, t is time, and c is the specific heat capacity of water (4.2 × 10 3 J/(kg·K)).
From Fig. 6, when the flow velocity is 1 m/s, the heat pipe outlet water temperature is 320.56 K, the heat extraction is (2) T = 6.77 × exp −V H ∕2.67 + 315.91 97.66 MJ, and the water output of the heat pipe is 1.13 m 3 /h; when the flow velocity is 2 m/s, the heat pipe outlet water temperature is 319.11 K, the heat extraction is 181.50 MJ, and the water output of the heat pipe is 2.26 m 3 /h, which can be used as domestic water and can further reduce the cost of mineralization (Niu and Wang, 2012). From comprehensive consideration of the heat pipe outlet water temperature, heat extraction, and water output, 1-2 m/s was selected as an appropriate flow velocity for extracting the reaction heat of the mixing device.

Conclusions
The effects of the length-diameter ratio, blade inclination angle, spacing, and diameter on the CO 2 mineralization degree and extraction of the reaction heat using alkaline waste were studied in constant-pressure and continuous-feed systems through experiments and numerical simulations.
(1) Orthogonal numerical simulation showed that when mineralizing CO 2 in the constant-pressure and continuous-feed systems, the influence of the length-diameter ratio, blade inclination angle, spacing, and diameter on the mineralization degree follows the order: length−diameter ratio of mixing device>blade diameter>blade inclination angle>blade spacing. The influence on the heat pipe outlet water temperature follows the order: length−diameter ratio > blade diameter > blade spacing > blade inclination angle.
(2) When the length-diameter ratio, blade inclination angle, spacing, and diameter of the mixing device are 3, 15°, 6 cm, and 14 cm, respectively, the amount of heat extracted from CO 2 mineralization using alkaline waste calcium carbide slag and a heat pipe is optimal; that is, 2.14 t CO 2 can be mineralized at most in 1 h, and 4.53 t carbide slag is consumed at the same time.
The amount of heat extracted from mineralization of 1 t CO 2 reached 189.60 MJ. The study shows that increasing the length-to-diameter ratio of the blade in the mixing device can further improve the degree of mineralization and the thermal extraction ability. (3) The relationship between the winding mode, flow velocity, and water temperature at the heat pipe outlet was evaluated through numerical simulations, showing that when the left area of the heat pipe was encrypted, more reaction heat could be extracted for utilization. On this basis, a model of the relationship between the water temperature and flow velocity was established. When the flow velocity was 1-2 m/s, the heat extraction reached 97.66-181.50 MJ, which provides a theoretical basis for the application of the reaction heat extraction in the field.