Permeability variation analysis using the superficial diameter correlation with porosity change

Abstract

Permeability characterization is a major factor for ensuring more environment-friendly operations and economically viable industrial applications related to carbon capture sequestration, hydrocarbon recovery, nuclear waste disposal, and remediation in groundwater. Regardless, the permeability variation caused by changes in formation stress is simply defined as the power-law function of porosity. An alternative formula can be presented using the Kozeny-Carman equation based on hydraulic diameter and tortuosity. However, the hydraulic tortuosity and the Kozeny constant cannot be precisely measured because of the extremely complex and microscale pores. Accordingly, this study considers the Kozeny-Carman equation for presenting the other definable variables and more general correlations for performing permeability variation analyses. Herein, the effective tortuosity and effective and superficial diameters of porous media are deduced adopting the conventional viscous flow theory. Subsequently, the Kozeny-Carman equation is improved by replacing the immeasurable variables with the effective variables. The correlations of all the key geometric variables with permeability variation are investigated via pore-scale simulations based on two types of 20-series porous medium models with a wide range of porosity (13.4%-47.4%) and permeability (0.0073-18.3 Darcy). Herein, several impressive functional aspects of the superficial diameter were discovered with porosity changes, such as quadratic functional correlations, parallel shifts for each flow path, and less sensitive variations in low porosity ranges. Consequently, this study proved that permeability variations can be more precisely and generally estimated using the quadratic correlations of the superficial diameter with porosity changes.