## 1 Introduction  
Absolute permeability \(k\) plays a crucial role when studying fluid flow in a porous medium during the development of oil and gas reservoirs, the injection of CO\({}_{2}\) into reservoirs for further storage, the migration of contaminants in underground aquifers, and the flow of gases in catalytic systems. It presents the macroscopic characteristics of a porous medium, which depend on its microscopic and macroscopic properties. Absolute permeability is usually measured under laboratory conditions on a limited number of rock samples. In practical applications, specific relationships between \(k\) and other properties of the porous medium are necessary. The Kozeny-Carman (K-C) equation is a widely used relationship which relates \(k\) to the porosity \(\phi\), specific surface area, and tortuosity of a porous medium [1; 2; 3; 4]. However, the K-C equation predicts incorrect \(k\) values for many porous materials [2; 5; 6] and, consequently, various modifications have been developed [3; 4; 7; 8; 9; 10]. The most widely used equations describe the relationship between \(k\) and \(\phi\) (\(k\sim\phi^{n}\)) [11; 12; 13; 14; 15], connected porosity \(\phi_{com}\) (\(k\sim\phi_{com}^{n}\)), and percolation threshold porosity \(\phi_{c}\) (\(k\sim(\phi-\phi_{c})^{n}\)) [16; 17; 18; 19; 20; 21; 4; 6; 21]. In the abovementioned equations, \(n\) is the power exponent. In addition, an equation is used to describe the relationship between \(k\) and \(\phi l^{2}\), where \(l\) is the characteristic length of the porous medium [22; 23; 24; 25; 26]. The equation \(k\sim\phi^{n}\) is often used to describe the evolution of the relationship between permeability and porosity during rock dissolution [11; 12; 13; 14; 15; 27; 28] to predict the increase in \(k\) as \(\phi\) changes. Several experimental studies on carbonate dissolution indicated that the fitting of experimental data using the equation \(k\sim\phi^{n}\) led to significantly higher values of \(n\) compared to \(n=3\) obtained in the K-C equation [12; 13; 15; 27]. High values of \(n\) are explained by the formation of wormholes in rock samples as acid solutions interact with carbonate rocks. Moreover, many authors noted that the values of \(n\) change as the rock dissolves [13; 14; 15; 28; 29]. [PERSON] et al. presented the dependence of the exponent \(n\) on porosity during rock dissolution [29]. [PERSON] et al. first mentioned the idea of using the percolation threshold porosity \(\phi_{c}\) to describe the dependence of permeability on porosity while studying the hot pressing of calcite [7]. Later, this idea was implemented to describe the relationship between permeability and porosity using the equation \(k\sim\left(\phi-\phi_{c}\right)^{n}\) to study fluid flow in spherical packing [4] and the hot pressing of calcite aggregates [6]. This equation better describes the dependence of permeability on porosity at \(\phi\to\phi_{c}\). The percolation threshold porosity \(\phi_{c}\)--is the value of porosity below which the pore network becomes disconnected, and therefore its permeability vanishes. It can be determined from the dependencies \(\phi_{con}\sim(\phi-\phi_{c})^{n}\) and \(k\sim(\phi-\phi_{c})^{n}\). [PERSON] et al. found values of \(\phi_{c}\) and \(n\), correspondingly, equal to \(4\%\) and \(n\approx 2.2\) for calcite aggregates [6], while [PERSON] et al. amounted to these values to be \(3\)-\(9\%\) and \(n\approx 4\), respectively, for spherical packing [4]. Different authors have obtained values of \(\phi_{c}\) for limestone samples \(\phi_{c}=5.9\%\)[17], young sea ice \(\phi_{c}=2.4\%\)[18], natural microgranite \(\phi_{c}=0.85\%\)[19], Fontainebleau sandstone \(\phi_{c}=1.9\%\)[20], fused glass packing, hot-pressed calcite \(\phi_{c}=2.5,\ 3.5,\) and \(4.5\%\), respectively [8], and porous media with randomly placed identical squares \(\phi_{c}=33\%\)[16]. There is also a study in the literature of the relationship between \(k\) and the characteristic length of a porous medium \(l\)[18; 24; 25; 26; 30].