A permeability evolution model of high-pressure waterflooding with dual-fractal characteristics of mechanical properties and fracture structures

The complexities of evaluating permeability evolution during high-pressure waterflooding and subsequent production are primarily governed by rock mechanical damage and extensive microfracture deformation. In this study, we propose a general permeability evolution model for high-pressure waterflooding that incorporates dual fractal characteristics of mechanical properties and fracture structures. Both fracture aperture distribution and Young’s modulus distribution are described using fractal scaling laws. For a given fractal unit with a specified Young’s modulus, an analytical model is developed to quantify fracture aperture variation during elastic deformation and the failure process based on damage mechanics. The damage-induced reduction in Young’s modulus after failure is further considered in the production stage, and an analytical solution for the fracture-medium permeability is established through double integration within the framework of fractal geometry. A percolation-based effective-medium approximation is employed to calculate matrix–fracture permeability. The effects of fracture-related fractal properties, rock mechanics-related fractal properties, and reservoir properties (porosity, matrix permeability, and minimum Young’s modulus) on matrix–fracture permeability are systematically investigated. The key results demonstrate that matrix–fracture permeability is most strongly influenced by fracture fractal dimension and reservoir properties, particularly porosity, matrix permeability, and minimum Young’s modulus.