Micromechanical approach for electrical resistivity and conductivity of sandstone

• I model the electrical resistivity of sandstone.
• The simulations are compared with the laboratory measurements.
• The results show a strong impact of the microstructure on the macroscopic resistivity.

The objective of this work is to employ the micromechanical approach for the modeling of the electrical resistivity and of the conductivity of sandstone. This type of rock is considered as a mixture of solid mineral and porous space filled fully or partially by conductive water. The Eshelby's solution of a spheroidal inclusion in a homogeneous matrix is employed. The differential effective medium model (DEM) with different concepts of the microstructure is developed for the calculation of the resistivity. The parametric study clarifies the impact of the microscopic parameters on the macroscopic electrical properties. The simulations are compared with the classical empirical and theoretical approaches as well as with the laboratory measurements. The results show a strong impact of the microstructure (the shape of the pore, the presence of non-conductive fluids in the pore space, the connectivity of conductive fluid) on the macroscopic resistivity and conductivity of sandstone. This approach gives a link between the microscopic physical parameters of the rock and the macroscopic electrical parameters such as the cementation exponent and the electrical formation factor.