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 x x and k y y 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 x y , 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.
Highlights
Modeling flow and its coupled processes in fractured porous rocks are important for subsurface environmental and energy problems [1, 2], such as solute transport in groundwater or at radioactive waste disposal sites [3,4,5], geothermal energy exploitation [6, 7], gas hydrate stability [8], and coal mine water inflows [9]
Permeability is upscaled from discrete fracture geometry to grid blocks, which reduces the complexity of simulations and makes the equivalent fracture models applicable at the field scale (e.g., [14])
The range of kxy lies between −2 × 10−13 and 2 × 10−13 m2. This is because the diagonal components kxx and kyy should always be positive according to the physical meaning of the permeability in Darcy’s law, whereas the off-diagonal term kxy could be positive or negative which depends on the angle between the axes of the equivalent permeability tensor ellipse and the coordinate axes
Summary
Modeling flow and its coupled processes in fractured porous rocks are important for subsurface environmental and energy problems [1, 2], such as solute transport in groundwater or at radioactive waste disposal sites [3,4,5], geothermal energy exploitation [6, 7], gas hydrate stability [8], and coal mine water inflows [9]. Li et al [40] established analytical expressions for equivalent permeability and fractal aperture distribution based on a multiple fractal modeling considering both the rock matrix and discrete fracture network (i.e., the discrete fracture model). Hardebol et al [42] integrated multiple-scale datasets for generating discrete fracture models Their simulation results show that the equivalent permeability of fractured porous rocks can be two to three orders of magnitude higher than the matrix permeability, which is highly controlled by the connectivity of the fractures. Only a few studies investigate the fracture geometry to equivalent permeability distributions for an equivalent fracture model, which has important implications for creating stochastic permeability fields for fractured porous rocks. The statistical distribution of the equivalent permeability and the correlations between equivalent permeability and the fracture density are analyzed, which quantitatively illustrates how equivalent permeability distributions are influenced by the fracture network geometry
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