A unified permeability and effective stress relationship for porous and fractured reservoir rocks

Abstract

As one of the most important parameters for estimating oil/gas production rate, permeability is sensitive to effective stress which may change significantly with reservoir depletion. Although vast amount of data on permeability–stress correlations have been reported, many of them were proposed based on different situations. This makes it difficult to compare the modeling results of the experimental data and limits the adaption of the findings from one set of testing permeability data to other situations. A unified permeability and effective stress relationship would make it possible to evaluate the permeability behavior under different situations. Recently, the validity of an exponential form permeability correlation to any types of fractured rocks has been confirmed by some of the authors in this paper. In this study, the exponential form model is further extended to describe the permeability change for porous media through theoretical derivation. The unified permeability relationship is then applied to represent the permeability data for a large amount of samples from three typical reservoir rocks, including porous sandstone, idealized fractured coal and randomly fractured shale. The results show that the unified relationship is capable of describing permeability data for both porous and fractured rocks. The distributions of the model parameters are also obtained. This unified relationship provides a benchmark to evaluate the permeability behaviors in different rocks and the modeling results form a practical database for permeability in typical reservoir rocks. The outcome of this work would contribute to many circumstances including interpreting permeability data and making comparison, estimating permeability, coupling into existing reservoir simulators for fluid flow modeling and so on.