Effect of scale and matrix porosity on the relationship between permeability and resistivity in fracture-matrix system

Monitoring site permeability distribution by resistivity is an effective method to characterize fracture-matrix system. In this study, a link between permeability and resistivity in a fracture-matrix system was established. Fluid flow and electrical current processes in a random fracture-matrix system were numerical simulated. The fracture-matrix system was generated based on field data from the Three Gorges Project in China. The fracturematrix system with six scales (5 m, 10 m, 15 m, 30 m, 45 m, and 60 m) and three matrix porosities (0.1, 0.01, and 0.004) were created using a Monte Carlo approach. The effects of scale and matrix porosity on the relationship between permeability (k) and resistivity (p) were examined. The results showed that a functional relation was established to describe the k-p relationship. The k-p relationship is influenced by scale and matrix porosity. When the matrix porosity is 0.004, k-p relationship is scale-independent, while the relationship is scale-dependent when the matrix porosity is greater than 0.01. The scale-dependent is more obvious with the increase of porosity. When the scale reaches the representative elementary volume (REV) value, the k-p relationship is matrix-dominated below the critical fracture aperture and fracture-dominated above the critical fracture aperture. The results provide a basis for using resistivity characterize fracture permeability variations and will be helpful to evaluate risks of underground engineering.