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A nonlinear dual-porosity model. (English) Zbl 0817.76087
A nonlinear dual-porosity formulation incorporating a quadratic gradient term in the governing flow equation is presented. To avoid solving the simultaneous system of equations, decoupling of fluid pressures in the matrix from the fractures is furnished by assuming a quasi-steady-state flow in the matrix with the pressure difference between matrix and fractures as a primary unknown. The nonlinear fracture flow equation is linearized using the function transformation currently adopted in the nonlinear single-porosity formulation. Analytical solutions are obtained in a radial flow domain using the Hankel transform. Both solution accuracy and efficiency are achieved by using an optimized algorithm when solving the inherent Bessel functions.

MSC:
76S05 Flows in porous media; filtration; seepage
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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