A nonlinear dual-porosity model.

*(English)*Zbl 0817.76087A 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) |

##### Keywords:

solution optimization; analytical model; quadratic gradient term; decoupling; quasi-steady-state flow; matrix; fracture flow equation; radial flow; Hankel transform; Bessel functions
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\textit{M. Bai} et al., Appl. Math. Modelling 18, No. 11, 602--610 (1994; Zbl 0817.76087)

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##### References:

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