Application of the θ-method to a telegraphic model of fluid flow in a dual-porosity medium

In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose numerical treatment outcomes in a tri-diagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions.Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor semianalytic solutions are available.

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Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

Herrera-Hernández

Aguilar-Madera

Hernández

et al. 2018

Comp. Appl. Math.

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Application of the θ-method to a telegraphic model of fluid flow in a dual-porosity medium

Cited by 1 publication

References 48 publications

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

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