Relationship Between Permeability and Resistivity of Sheared Rock Fractures: The Role of Tortuosity and Flow Path Percolation

Abstract

Abstract The fluid‐flow properties of fractures have received increasing attention regarding the role of geofluids in the genesis of slow and fast earthquakes and recent advances in geoengineering developments. Geophysical observations are promising tools to remotely estimate crustal permeability changes; however, quantitative interpretations are limited by the rock‐physical models' paucity for fractures. This study investigated changes in permeability, resistivity, and their respective relationships at elevated stress by performing numerical simulations of different fracture models with varying fracture size, roughness, and shear displacement. Numerical results and microscopic flow analysis demonstrate that permeability–resistivity relationships are controlled by percolation and are less dependent on fracture geometric characteristics. Our finding suggests that the permeability evolution of fractures can be formulated with resistivity changes independent of both fracture size and microstructure, the trends of which can be predicted using Archie's exponent. The extension to the electro‐mechanical relationship further derives the potential applications of estimating stress changes.

Keywords

• permeability
• electrical resistivity
• fracture
• Archie
• lattice Boltzmann method
• digital rock physics