Size scale considerations in modelling the electrical conductivity of porous rocks and soils

Abstract

The solid components and pore space of rocks and soils have a spectrum of size scales, ranging from clay platelets and intergranular cracks to vugs and boulder size grains. However, the size scale of structural features rarely, if ever, has been explicitly considered in the modelling of the physical properties of geologic materials. These size scaling effects are investigated in this paper using a model that divides the pore space into microporosity (e.g., intergranular cracks), mesoporosity (e.g., main pore volumes) and macroporosity (e.g., vugs and fractures). The differential effective medium approximation (DEMA) is used to determine the electrical conductivity of the porous medium models. This approximation employs a sequential embedding process that implies progressive size scale increase as it proceeds, allowing the explicit incorporation of size scale relationships that occur in porous media. The modelling results demonstrate that the electrical conductivity of porous rocks and soils are very sensitive to the range of porosity size scales that are present in the material. Thus, component size scale needs to be considered when analyzing electrical conductivity information from laboratory experiments, as well as from borehole and surface geophysical techniques.