The effective stress law for stress-sensitive transversely isotropic rocks

This paper first presents a review of the development of the concept of effective stress, followed by major experimental and theoretical studies carried out to estimate the Biot's coefficient. It then uses the constitutive equations for vertically transverse isotropic (VTI) reservoirs, like coal, derived using the principles of thermodynamics for estimation of the Biot's coefficients in the vertical and horizontal directions. Laboratory data for tests conducted on two coal types retrieved from different geologic settings and geographical locations was used to carry out the modeling and validation exercise. Evidence is presented that values of Biot's coefficient can be greater than one, proposed by Biot to be the limiting value, for sorptive rocks. To address this, the term Biot's coefficient is replaced with “effective stress coefficient”. Finally, this paper discusses the pressure- and stress- dependent behavior of the Biot's coefficient. The results clearly show that the estimated values of Biot's coefficients in both vertical and horizontal directions are different, varying with pressure for methane depletion but remaining constant for helium depletion. At the same time, the nature of Biot's coefficient, re-termed as effective stress coefficient, was found to be greater than unity for methane depletion. As a last step, a conceptual physical model is proposed to explain the pressure-dependent variation of effective stress/Biot's coefficients in terms of the contact area between grains. Based on the findings that the effective stress coefficient decreases with pressure, it is concluded that the effective vertical stress would increase significantly with depletion which, in turn, would result in shear failure and increased permeability.