Developing a porosity-permeability relationship for ellipsoidal grains: A correction shape factor for Kozeny-Carman's equation

Abstract

Rock typing is a process through which reservoir layers are classified into distinct units with similar geological conditions. The Kozeny-Carman's equation is commonly used for rock typing based on the porosity-permeability relationship, but it only considers spherical grains in its calculations which does not give representative results on many occasions. Thus, an attempt was made in this study to develop a new mathematical equation to correct the porosity-permeability relationship in rocks with ellipsoidal grains. To validate this equation, several pore-scale models were analysed using the Discrete Element Method (DEM) where the porosity was calculated under different conditions. The permeability of the pore scale models containing ellipsoidal (spheroidal) grains with different aspect ratios were then determined using the Lattice Boltzmann Method (LBM). This was followed by applying the new equation by incorporating the eccentricity of grains in the correction shape factor of the Kozeny- Carmen's equation. The results obtained indicated that any deviations in the sphericity of the grains (increase or decrease in the aspect ratio) increase the permeability of the model. In other words, the developed pore scale model with the aspect ratio of 1.0 (spherical grains) had the lowest permeability at the same porosity. This could be due to the bridging of pores with the ellipsoidal grains which causes a longer and narrower fluid path. Moreover, the models with the aspect ratio of 0.5 and 2.0 had a similar porosity-permeability correlation which could be linked to their similar packing structure. The new equation was further validated through the literature and numerical studies to ensure its accuracy under different geological conditions.