A novel analytical model for porosity-permeability relations of argillaceous porous media under stress conditions

Argillaceous rocks, such as sandstones, shales, and mudstones, are widely distributed in nature and constitute approximately 50% of the global sedimentary rocks. They are the conventional reservoir rocks for hydrocarbon resources. To better characterize hydrocarbon resources, it is essential to understand the fundamental physical properties of argillaceous porous media (APM), and one of the most crucial properties is the porosity-permeability relationship (PPR). However, due to the enormous complexity of pore structures in APM, the effects of relevant factors on PPR remains unclear, and the major factors controlling PPR are still open questions. In this work, experimental tests were carried out on 43 artificial argillaceous sandstone samples to evaluate the porosity and permeability relations under stress dependence. An analytical model was then proposed to interpret the experimental results. The analytical solutions are consistent with the experimental data and the simulation results obtained from the Lattice Boltzmann method. It indicates that the derived model can precisely capture the PPR of APM. The analysis results show that the PPR of APM under stress dependence is related to clay volume content, effective stress, initial irreducible water saturation, rock lithology, and pore structure parameters (e.g., the maximum pore radius, the minimum pore radius, pore fractal dimension and tortuosity fractal dimension). These findings can enhance the understanding of the PPR and coupled flow-deformation behavior in APM and set the stages for a proper investigation of PPR in APM.