Numerical investigation of pore characteristics in compacted sand layers — Physical interpretation of applicability of Kozeny-Carman equation

Accurate evaluation of permeability in subsurface media is essential for solving problems in various fields, such as environmental and petroleum engineering. This study aims to numerically investigate the pore characteristics of spherical particle beds imitating compacted sandstones for the physical understanding of the permeability change with porosity. In this study, the structures of monodisperse and polydisperse particle beds are simulated and the pore regions are extracted using various numerical methods. The pore characteristics, such as effective porosity, tortuosity, and specific surface area in the bed, are quantified. The permeability is then calculated by substituting them into the Kozeny-Carman equation. The obtained permeability is compared with measurement results from actual sandstones. The respective pore characteristics are also evaluated against findings from previous studies. The role of pore characteristics in influencing permeability is investigated to examine changes in permeability in compacted sandstones. Consequently, the respective pore characteristics are modeled as functions of porosity. The effective porosity and tortuosity obtained from the present analysis matches with experimental results and the physical models developed in previous studies. The specific surface area also agrees with previous experimental results. However, the model developed in previous research does not match the experimental and present numerical results at low porosity. Therefore, we develop a new geometric model for specific surface area under low porosity conditions. Based on the numerical results, we assess the applicability of the original Kozeny-Carman equation to actual sandstones composed of deformed particles and analyze its physical interpretation. The results suggest that the rapid increase in tortuosity and the rapid decrease in specific surface area with decreasing porosity cause the Kozeny-Carman equation to maintain its original form even in compacted sandstones.