A constitutive model for stress‐induced permeability and porosity evolution of Berea sandstone

Abstract

Many applications in geophysics require good estimates of permeability evolution in response to deformation, pore collapse, dilatancy, and microfracturing. Simulations of the upper crust, oil well completion, and nuclear waste repositories depend upon reliable predictions of changes in rock permeability. For some applications, permeability can affect the strength of rock by influencing the pore pressure and effective stress. For example, the pore pressure during production from an oil bearing formation is controlled by the evolving permeability field. The rock strength, however, depends upon the effective stress which is influenced by the pore pressure. Accurate prediction of possible failure in such formations requires reliable estimates of permeability change. Ideally, such estimates could be obtained by directly simulating the changes in pore space connectivity at the microscale. In practice the system being studied is sufficiently large that constitutive models must be developed which address permeability evolution macroscopically. We develop a model for predicting porosity and permeability changes in Berea sandstone. The model has been kept as simple as possible in order to facilitate incorporation of the model into existing mechanics codes. For this reason we assume the existence of a separate material model capable of predicting the stress‐strain response of the rock. In addition, the model assumes that the original pores and pores created by microfracturing can be treated separately with respect to permeability and porosity evolution. Despite these simplifying assumptions, the model is able to reproduce most of the key features observed in previously reported triaxial experiments performed on Berea sandstone.