## 4 Discussion
The \(R^{2}\) value of 0.27 indicates that about 27% of the variation in tortuosity can be correlated with average throat size. Larger throat sizes can reduce the complexity of fluid flow paths, thereby reducing the flow length and resulting in lower tortuosity values. The average throat size has a significant impact on effective porosity, permeability, and tortuosity, with larger throat sizes tending to increase the effective porosity and permeability but reduce tortuosity. Although the \(R^{2}\) values were not very high (0.19-0.28), they indicate that average throat size influences these rock properties. Additionally, the relationship between the average throat size and permeability, effective porosity, and tortuosity shows a non-linear relationship. The consistent observation that permeability values from [PERSON]'s law are higher than those from the Kozeny-Carman model can be explained by the differences in their underlying assumptions and how they account for pore structure complexity. The Kozeny-Carman model assumes a homogeneous, isotropic pore structure with uniform grain sizes, leading to an underestimation of permeability in real-world systems where pore networks are heterogeneous and irregular. This model simplifies the geometry and connectivity of the pores, neglecting the complex flow paths and channeling that occur in natural porous media. In contrast, [PERSON]'s law is an empirical relationship that directly relates flow rate to permeability, without assuming specific pore geometries. As a result, it better captures the effects of varying pore sizes, tortuosity, and connectivity, which are common in heterogeneous systems. This flexibility allows [PERSON]'s law to reflect the actual flow behavior more accurately, leading to higher permeability estimates compared to the more idealized Kozeny-Carman model. The difference in the level of asymmetry in the distribution indicates that the asymmetry of the Kozeny-Carman Equation is higher compared with the asymmetry level in the LBM permeability data. However, although the asymmetry level in the LBM permeability distribution is lower, it does not mean that the LBM permeability is better. In some previous studies on permeability [34], the resulting distribution is log-normal, so the permeability distribution of the Kozeny-Carman model is more representative compared with the LBMdistribution. Nevertheless, this does not mean that the permeability measurement using the LBM in this study is incorrect, as other studies have mentioned that alternative permeability distribution forms a gamma distribution. Moreover, the calculation using the Kozeny-Carman Equation requires the porous rock conditions to be ideal since it is performed through mathematical calculations, unlike the actual conditions of porous media, which have more complex parameters. Overall, the relationships between porosity, permeability, and tortuosity derived from our simulations can be directly applied to enhanced oil recovery (EOR) processes, where optimizing fluid injection and extraction strategies is crucial. Additionally, these results have applications in groundwater hydrology, adding in the prediction of aquifer behavior and contaminant transport. Moreover, the insights gained from our study can contribute to the design of advanced porous materials, such as filters and catalysts, where precise control over flow properties is essential.