## 1 Introduction  
Tight sandstone gas, as an unconventional natural gas resource, has garnered considerable attention due to its abundant reserves. In China, significant deposits of tight sandstone gas are mainly found in the Sichuan Basin, the Ordos Basin, and the Tarim Basin [1, 2]. The unique geological conditions in these areas have resulted in tight gas reserves that are even more abundant than those of conventional natural gas [3, 4, 5]. Take the Shujiahe Formation reservoir in Rongchang District as an example. While tight sandstone gas reserves are substantial and hold great potential for development, the denseness of the formations typically leads to high fracture pressures, which present challenges for current wellhead pressure control equipment to effectively tap into these reservoirs [6, 7]. As exploration and development of unconventional oil and gas resources reach greater depths, this issue becomes increasingly prominent [8, 9]. Consequently, reducing the crack initiation pressure in reservoirs is one of the main factors to consider for large-scale exploitation of tight sandstone gas fields. Currently, supercritical CO\({}_{2}\) fracturing [10] is a promising waterless fracturing technique that holds potential for developing unconventional oil and gas reservoirs, as it can reduce water consumption, mitigate reservoir and environmental pollution, lower rock initial pressure, and also achieve partial carbon sequestration. Studies have demonstrated that acid treatment, while reducing the fracture pressure of reservoirs, can also enhance the physical properties of the reservoirs [11]  
[PERSON] et al. [12] analyzed the effects of acid concentration, acid dosage, and acid reaction time on hydraulic fracture heterogeneity and fracture extension. The results show that the main factor affecting fracture extension was acid concentration followed by acid dosage, and the effect of acid reaction time was minimal. [PERSON] [13] studied the initiation and extension characteristics of fractures under different fracturing methods through physical and numerical simulations. They found that acid pressure effectively reduced the pressure of crack initiation and extension, and that the use of thickeners slowed the acid-rock reaction and increased the transmission distance of the acid [14]: Compared with acid pressure, the combined action of thickener and acid pressure made the crack initiation and extension more obvious, leading to more micro-cracks around the main crack. [PERSON] et al. [15] used the discontinuous deformation analysis (DDA) method to study the effect of dissolution on the shear behavior of rock cracks. This research provides an effective tool for the micro-quantification of hydrochemical damage. Acid treatment destroys the rock's frame structure and intergranular cementation [16; 17], changes the internal stress, and reduces the stress required for crack extension. This leads to the enhancement of subcritical crack extension and a reduction in rock strength [18; 19]. [PERSON] et al. [20] analyzed the physical characteristics of loose sandstone reservoirs under lower supercritical CO2 pressure and discovered that supercritical CO2 under low pressure conditions reduced the permeability of sandstone reservoirs. [PERSON] et al. [21] studied sandstone after soaking in supercritical CO2 for different lengths of time, which had a significant weakening effect on the mechanical properties of the top sandstone. Research indicates that pore structure plays a significant role in the dissolution of rock minerals and changes in porosity [22]. Changes in microstructure are strongly influenced by the distribution of minerals. In addition, the physical properties of the reservoir are determined by the pore structure and microcracks [23], which are abundant in loose sandstones, so it is necessary to study the pore structure and microstructure quantitatively.