A generalized solution for transient radial flow in hierarchical multifractal fractured aquifers
Résumé
An analytical solution in the Laplace domain is derived for modeling anomalous pressure diffusion during pumping tests in aquifer displaying hierarchical fractal fracture networks. The proposed solution generalizes all of the analytical models for fractal flow published previously by combining multifractal diffusion and nested multiporosity with transient exchanges, interface skin effects, and well storage effect. Solutions are derived for fracture-delimited blocks with planar, cylindrical, and spherical shapes, as well as with any fractional dimensional shapes. Any combinations of these shapes can be defined in order to model a large range of situations. Within each permeability level, the fractal properties of the fracture network can be specified and the fractal dimension can be distinct from the shape dimension of the block.
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