## 1 Introduction
Relevant studies have shown that the pressure of CO2 in the reaction system has a positive influence on the mineralization reaction. Increasing the pressure facilitates the diffusion of CO2 in water and promotes its penetration into the pores of porous media for mineralization reactions. However, high pressure has a detrimental effect on carbon acid formation, which hinders mineralization efficiency [16; 17; 18]. The concentration of alkaline ions plays a crucial role in the mineralization reaction between fly ash and CO2, determining the efficiency of the process. Researchers both domestically and internationally have explored various methods to enhance the leaching concentration of alkaline ions in fly ash, aiming to improve the mineralization efficiency. Among these methods, the wet process has emerged as the preferred choice due to its advantages of low energy consumption, cost-effectiveness, and high leaching rate. The primary principle behind this process is to utilize the calcium-based compounds present in fly ash to react with a calcium ion-rich leachate in the presence of CO2, resulting in the formation of calcium carbonate [19; 20; 21; 22]. The wet leaching process typically involves using an acid solution or an ammonium salt solution as the leaching solvent. The external conditions, such as high temperature, high pressure, or microwaves, are often modified during the leaching process to enhance the leaching rate. Subsequently, the pH of the leaching solution is adjusted to remove impurities and obtain calcium. The enriched solution of calcium elements is then subjected to CO2 treatment to facilitate a complete reaction with calcium ions. Finally, the solution is filtered to obtain calcium carbonate. Currently, the main leaching methods include deionized water leaching, acid leaching, and ammonia leaching. Among them, deionized water leaching is one of the earliest wet leaching methods [23]. The ionized water leaching method involves using deionized water as the leaching liquid. This method takes advantage of the solubility of alkaline oxides in fly ash in water. By using only deionized water and fly ash in the reaction system, the occurrence of oxidation reactions caused by the introduction of other impurities can be avoided. Currently, researchers focus on studying various factors that influence the -leading process, such as particle size, leaching time, liquid-to-solid ratio, and reaction temperature. It has been found that the optimal conditions for leaching a fly ash aqueous solution involve using fly ash that has passed through a 280-mesh sieve, maintaining a temperature of 60 \({}^{\circ}\)C, maintaining a liquid-to-solid ratio of 1000, and allowing a reaction time of 72 h. Under these conditions, the leaching rate of calcium can reach 23.81% [24; 25]. In order to enhance the leaching rate of Ca\({}^{2+}\) and expedite mineralization, some researchers have explored the use of ultrasonic waves and microwave radiation during the leaching process [26]. [PERSON] [27] opted for tap water as the leaching solution and incorporated ultrasonic effects to enhance the leaching rate. By conducting a comparative analysis of the calcium ion leaching concentration and leaching rate under ultrasonic and stirring conditions, it was observed that the calcium ion concentration in the leachate after ultrasonic treatment was significantly higher compared to that after the corresponding stirring action. This indicates that ultrasonic waves can effectively promote the leaching of calcium ions. Furthermore, when the calcium ion leaching rate is the same, the ultrasonic treatment time can be significantly shorter than the stirring treatment time. [PERSON] et al. [28] discovered that the presence of silica and other common impurities in solid waste can create a porous layer on the surface of the calcium release material, which hampers the release of calcium. However, this porous layer can be effectively eliminated by utilizing ultrasonic waves.