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Dual permeability modeling of fractured media Clemo, Thomas Meldon


Dual permeability is introduced as an approach to modeling flow and transport through fractured media. The approach allows a large reduction in the number of fractures that are represented explicitly in a discrete fracture network. The most important fractures in terms of fluid flow are identified using their physical characteristics. These fractures form a sub-network that divides the entire fracture network into smaller domains. The fractures of the smaller domains are approximated. The approximations do not rely on continuum assumptions. They are determined individually and independently for each small domain, resulting in a parallel structure to the calculations. An exploratory model is developed for steady state fluid flow and solute transport in two dimensional fracture networks and compared to a discrete fracture model that represents all of the fractures explicitly. Individual fractures are represented by finite lines with constant hydraulic transmissivity. Solute transport calculations use particle tracking. The dual permeability model is shown to provide acceptably accurate solutions while reducing the maximum number of simultaneous equations by well over an order of magnitude. The dual permeability approach takes advantage of the hydraulic behavior of highly heterogeneous media. Channeling of flow that develops in such media is used to reduce errors introduced through the sub-continuum approximations. The dual permeability approach works better when the fracture system has a broad range in the scale of fracturing as demonstrated by transport calculations for fracture networks with a high degree of clustering or with a fractal nature. A study of sub-REV fracture networks reveals that averaged flow through fractured media can be represented using tensor notation in much smaller domains than an REV. At these scales, heterogeneity within a fracture domain causes the tensor representation to be asymmetric, unlike the continuum representation of granular porous media. Hydraulic heads within a heterogeneous fracture network do not vary in a smooth fashion. The hydraulic head reflects the distribution of heterogeneity within the domain. The approximations developed for the dual permeability model required that the boundary conditions imposed on the small domains reflect heterogeneity both within the domains and external to them.

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