A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow
Résumé
Modeling natural Discrete Fracture Networks (DFN) receives more and more attention in applied geosciences, from oil and gas industry, geothermal recovery. The fractures may be either natural, or artificial in case of weil stimulation . Accounting for the flow inside the fracture network , and accounting for the transfers between the matrix and the fractures, with the same level of accuracy is an important issue for calibrating the wells architecture and for setting up optimal resources recovery strategies. Recently, we proposed an original method allowing to model transient pressure diffusion in the fracture network only. The matrix was assumed to be impervious. A systematic approximation scheme was built, allowing to model the initial DFN by a set of N unknowns located at the intersection between fractures. The higher N, the higher the accuracy of the model. The lowest order approximation N = 1 appears under the form of solving a transient problem in a resistorjcapacitor network, a so-called pipe network. Its topology is the same as the network of geometrical intersections between fractures. In this paper, we generalize this approach in order to account for flux es from matrix to fractures. We show that in the case of weil separated time scales between matrix and fractures, the preceding model need only to be slightly modified in order to incorporate these fluxes . The additional knowl-edge of the so called matrix to fracture transfer function allows to modify the mass matrix that becomes a time convolution operator. This is reminiscent of existing space averaged transient dual porosity models.
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