Influence of elastic crack closure and bedding anisotropy on effective stress behavior of clayey sandstones for permeability and deformation

Hydromechanical properties of porous rock depend on confining and pore pressures, which can be described by corresponding effective stress laws. In a microscopically homogeneous assemblage, the effective stress coefficients for permeability (κ), axial strain (α) and pore volume change (β) are predicted to be equal to or less than unity. Because κ of clayey sandstones are greater than unity, they are considered microscopically inhomogeneous. To our knowledge, there have not been any investigations of the effective stress behavior simultaneously of permeability and deformation in sandstones. We conducted such a study on water-saturated samples of three clayey sandstones over a broad range of confining and pore pressures: Berea and Boise perpendicular to bedding, and Rothbach perpendicular and parallel to bedding. Because hydrostatic compression typically involves an initial nonlinear stage 1 of elastic crack closure and a subsequent linear stage 2 of pore deformation, to investigate how crack closure may impact the behavior we characterized the effective stress coefficients in these two stages separately. Our data show that in stage 2 the coefficients for permeability are greater than 1, which accords with published data. In stage 1, we obtained smaller κ values, which are generally greater than 1, except for the Rothbach sample perpendicular to bedding. The overall conclusion is therefore elastic crack closure in our clayey sandstones results in an enhancement of the effective coefficient κ, and bedding anisotropy in Rothbach sandstone results in an enhancement of κ for flow parallel to bedding.

We obtained some of the first measurements of the effective stress coefficient β for pore volume change in sandstones. Values of β are uniformly less than 1, in contrast to β>1 observed in limestones with dual porosity (Wang et al., 2018). Synthesizing the sandstone and limestone data and theoretical analyses, we propose to define in the β-κ space two fundamentally different regimes for the effective stress behavior: Regime I for microscopically homogeneous rocks with , and Regime II for microscopically inhomogeneous rocks with κ>1. The latter regime may be partitioned further into a Regime IIA represented by clayey sandstones with β<1, and Regime IIB represented by limestones with dual-porosity with β>1.