Interpreting correlations in stress-dependent permeability, porosity, and compressibility of rocks: A viewpoint from finite strain theory

Abstract

Characteristics of stress-dependent properties of rocks are commonly described by empirical laws. It is crucial to establish a universal law that connects rock properties with stress. The present study focuses on exploring the correlations among permeability, porosity, and compressibility observed in experiments. To achieve this, we propose a novel finite strain-based dual-component (FS-DC) model, grounded in the finite strain theory within the framework of continuum mechanics. The FS-DC model decomposes the original problem into the rock matrix and micro-pores/cracks components. The deformation gradient tensor is utilized to derive the constitutive relations. One of the novelties is that the stress-dependent variables are calculated in the current configuration, in contrast to the reference configuration used in small deformation theory. The model has only a few number of parameters, each with specific physical interpretations. It can be reduced to existing models with appropriate simplifications. Then, model performance is examined against experimental data, including permeability, porosity, compressibility, volumetric strain and specific storage. It proves that the variations of these properties are effectively described by the proposed model. Further analysis reveals the effect of pores/cracks parameters. The validity of the FS-DC model is examined across a broad range of pressures. The results show that rock properties at high confining pressures ($>$300 MPa) differ from those observed under relatively low pressures ($<$200 MPa). This disparity can be attributed to inelastic behaviors of micro-structure, wherein the rock skeleton undergoes permanent deformation and breakage.