New permeability model for rocks with elliptical pores based on elastic solution of pore wall displacement

The common permeability model is derived with assumption that the shape of rock pores is circle. It is not consistent with SEM image for tight rocks. In this paper, this assumption was broken to propose a new model. Based on the elasticity theory and complex function method, the elastic solution of surface displacement for elliptical pores was built. Substituting this solution into porosity definition and its relationship with permeability, the new permeability model was proposed and then verified by experimental data. The error rates between experimental data and new model's solution are mainly around 10%. Through sensitivity study, the impacts of some important factors those are missed in common models were discovered by this new model. First, the elliptical pore experiences the uneven displacement along pore surface. It makes pore's shape play an important role in permeability evolution. Secondly, the difference between principle stresses also affects permeability evolution. Lastly, the pore's orientation also significantly affects permeability evolution. After hydraulic fracturing, water flooding and production, the stress value and orientation are often various. The advantage of this new permeability model is that impacts of these variations on permeability can be discovered.