Journal Article

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

Tsuji, T., Sawayama, K., Jiang, F., Ishibashi, T.

2023

Overview

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. Plain Language Summary Monitoring the flow of fluids through underground fractures is important for developing earth resources and understanding the generation of both slow and fast earthquakes. This can be realized by observing physical properties underground such as electrical resistivity; however, the relationships between electrical and hydraulic properties are poorly understood because we have limited data on rock fractures. Thus, in this study, we explored changes in the hydraulic and electrical properties of synthetic rock fractures by subjecting them to increasing normal stress and shear displacement while varying the properties of the fracture surface topographies and length scales referring to natural data. We formulated the relationship between electrical resistivity and permeability invariant of fracture size, roughness, shear displacement, and normal stress based on both the theoretical model and empirical Archie's equation. We found that the rigorous relationship is controlled by the local connection of the fluid‐flow paths based on the microscopic flow analysis. The proposed formula can estimate the permeability evolution of fractures using resistivity data and is a better approach compared to porosity estimation because resistivity–porosity relationship can change depending on the tortuosity or connectivity. The extension to the electro‐mechanical relationship also derives the potential applications of estimating changes in pore pressure. Key Points Numerical results clarify the dependencies of fracture size, roughness, shear displacement, and stress on permeability and resistivity Flow path percolation can be correlated with tortuosity, which controls the rigorous resistivity–porosity and –permeability relationships Archie's exponent is constant for a percolated single fracture and can be used for monitoring permeability and pore pressure change

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: Archie / digital rock physics / Earth resources / Earthquakes / Electrical properties / Electrical resistivity / Empirical equations / Estimation / Evolution / Flow paths / Fluid flow / Fluids / fracture / Fracture surfaces / Geoengineering / Hydraulic properties / lattice Boltzmann method / Mathematical models / Microstructure / Normal stress / Numerical simulations / Percolation / Permeability / Physical properties / Pore pressure / Porosity / Rock / Rocks / Roughness / Seismic activity / Shear / Tortuosity