A pore geometry-based permeability model for tight rocks and new sight of impact of stress on permeability

The prediction of rock permeability is important in the extraction of oil/gas from tight reservoirs. Permeability is determined by connected pores and their distribution in rocks. The existence of pore can induce stress concentration around pore surface which affects pore strains. In common permeability models, volumetric pore strains are used to quantify the permeability evolution during gas production but pore strain solutions exclude the impact of stress concentration. In this study, the stress concentration around pore surface was considered and corresponding pore surface displacements were calculated. Different from solutions of volumetric pore strain, solutions of stress concentration and pore surface displacement have close relationship with pore geometry. Based on SEM images of tight rocks, the pore shape was assumed as ellipse. An analytical solution for the surface displacement of an ellipse pore was derived and substituted into the permeability definition. Different from common permeability models, this novel permeability model includes pore geometry property. This geometry-based permeability model was verified by experimental data. The comparison between the common model and this geometry-based model was also conducted. The sensitivity study was conducted to investigate impacts of pore geometry and stress variation on permeability evolution. It was illustrated that this geometry-based model is valid and its performance of permeability prediction for tight rocks is better than that of common model. This is because the important factors, such as pore geometry size and stress orientation, are incorporated explicitly. The advantage of this geometry-based model is that the impact of stress orientation (α) on permeability is involved so this geometry-based model is able to predict permeability of reservoirs after hydraulic fracturing where the stress orientation commonly changes.