Effective Stress Law for the Permeability and Pore Volume Change of Clayey Sandstones

Abstract

AbstractThe influence of confining and pore pressures on permeability and pore volume change was studied in two clayey sandstones. The coupling effect is characterized by the effective stress coefficients κ and β, respectively. Hydrostatic compression of a porous rock typically involves an initial nonlinear stage of elastic crack closure and a subsequent linear stage of pore deformation. To elucidate the influence of microcracks on the behavior, we measured the effective stress coefficients in these two stages separately. Our data show that the coefficients κ for permeability of both clayey sandstones are uniformly greater than 1, in agreement with published data and theoretical prediction for a microscopically inhomogeneous assemblage. Our data show that the presence of microcracks may homogenize the pore space, as reflected by a significantly lower κ value during the initial stage of nonlinear compression. We obtained some of the first measurements of the effective stress coefficient β for pore volume change in sandstones, which show values close to but uniformly less than 1. Synthesizing our sandstone data, recently published data on limestones, and theoretical analyses, we propose to define in the β‐κ space two fundamentally different regimes for the effective stress behavior. A comparison of our data with Berryman's model, the clay shell model, and clay particle model indicates apparent discrepancies, which we propose to resolve with a dual equivalent‐channel model based on the spatial partitioning of clayey and clay‐free pore volumes.