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 fracture-matrix 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 (ρ) were examined. The results showed that a functional relation was established to describe the k-ρ relationship. The k-ρ relationship is influenced by scale and matrix porosity. When the matrix porosity is 0.004, k-ρ 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-ρ 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.