A generalized Hooke's law to study the transport properties of rocks

The nonlinear characteristics of the rock transport properties as a function of stress (permeability and electrical conductivity in this study) is closely related to the geometry of the pore space, which consists of stiff pores, cracks and fractures. We consider two behaviors of the pore space, one linear and the other exponential, related to the stiff pores and fractures, respectively, where a generalized Hooke's law describes the relation between stress and strain. Using this theory, we derive relations between porosity, transport properties and effective stress (confining minus pore pressure), which are validated by experimental data of four tight sandstones collected from the Shaximiao Formation of Sichuan Basin, southwest China. The agreement is good. At low effective stresses, the closure of cracks is the main mechanism affecting the transport properties, whose behavior is similar in terms of their parameters. Subsequently, experimental data of six tight sandstones from the Yanchang Formation, collected from the Ordos Basin, west China, are employed to confirm the previous results, indicating that the fluid and electrical current follow the same path in the pore space. In addition, we find that the effect of metallic minerals on the electrical conductivity is more significant than that of clay.