## 1 Introduction  
The study of the influence of the microstructure of porous materials on multiphase flow is a key topic of modern oil and gas and geological science. In the context of the constant development of oil and gas production and the need for efficient methods of capturing and sequestrating CO\({}_{2}\), the study of the pore structure of carbonate rocks during the injection of acid solutions becomes especially relevant. Carbonate rocks are not only a key factor in the oil industry but can also contribute to environmental sustainability by capturing and sequestrating CO\({}_{2}\). To achieve more accurate modeling results and gain a better understanding of flow mechanisms in porous media, researchers are utilizing modern research methods. One such method is X-ray micro-computed tomography (uCT), which allows for the generation of high-resolution 3D models of the pore structure. These models, in turn, serve as the foundation for analyzing the behavior of fluids in porous media using various modeling techniques [1, 2, 3]. One of the key factors in the study of carbonate rocks is the analysis of changes in their pore structure under the influence of various acidic solutions, as this can significantly impact their transport properties [4, 5]. Measurements of absolute and relative phase permeabilities play a crucial role in determining the efficiency of displacing one fluid (oilor gas) with another fluid (water or other agents) and in utilizing the pore structure of carbonate rocks for CO\({}_{2}\) sequestration [4; 6; 7; 8]. For a deeper understanding of these processes, researchers use modern modeling techniques for the computation of micro and macro parameters of porous medium. One such technique is fluid flow simulation based on pore network modeling, which allows for the analysis of fluid flow behavior in porous media at the pore scale [9; 10; 11; 12]. Confirmation of the importance of these studies can be found in research that utilizes 3D pore models of samples and numerical modeling to investigate the influence of pore geometry on fluid flow in porous media. These results demonstrate that even minor changes in the sizes and shapes of pores can have a significant impact on flow efficiency [13; 14; 15; 16; 17]. Furthermore, studies on the effects of acid injection on the structure and properties of porous materials, as well as on the relationship between permeability and pore size, highlight the importance of considering the pore structure when analyzing fluid flow in a porous media [18; 19]. This is also supported by research demonstrating the influence of pore geometric parameters on fluid flow processes [20; 21]. [PERSON] and [PERSON] investigated the influence of rock mineral dissolution on multiphase flow characteristics in two distinct carbonate rocks with varying pore structures [4]. They conducted experimental tests involving the dissolution of 0.5% of the mineral volume within rock cores using a temperature-controlled acidic solution. This dissolution process significantly affected the pore structure, leading to changes in relative permeability and residual trapping. The impact of rock matrix dissolution is heavily reliant on changes in the underlying pore structure. If variations in the pore structure can be observed or estimated through modeling, it should be possible to predict the effects on multiphase flow properties. One of the key points during the injection of solutions into rock samples is the wettability change of the rocks, which can lead to more efficient oil displacement. [PERSON] et al. indicated that wettability alterations occurred during low-salinity water flooding [22]. According to that study, wettability alteration from a more oil-wetting to a more water-wetting condition has been obtained as one of the most notable effects of low-salinity water flooding. An important mechanism for wettability alteration in carbonate rocks is mineral dissolution.