Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties

Abstract

Equivalent fracture models are widely used for simulations of groundwater exploitation, geothermal reservoir production, and solute transport in groundwater systems. Equivalent permeability has a great impact on such processes. In this study, equivalent permeability distributions are investigated based on a state-of-the-art numerical upscaling method (i.e., the multiple boundary method) for fractured porous rocks. An ensemble of discrete fracture models is created based on power law length distributions. The equivalent permeability is upscaled from discrete fracture models based on the multiple boundary method. The results show that the statistical distributions of equivalent permeability tensor components are highly related to fracture geometry and differ from each other. For the histograms of the equivalent permeability, the shapes of $k_{xx}$ and $k_{yy}$ change from a power law-like distribution to a lognormal-like distribution when the fracture length and the number of fractures increase. For the off-diagonal component $k_{xy}$ , it is a normal-like distribution and its range expands when the fracture length and the number of fractures increase. The mean of diagonal equivalent permeability tensor components increases linearly with the fracture density. The analysis helps in generating stochastic equivalent permeability models in fractured porous rocks and reduces uncertainties when applying equivalent fracture models.