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

TL;DR

This paper introduces a semi-numerical method combining Laplace transform and finite difference schemes to solve a complex fractal telegraphic dual-porosity fluid flow model, enabling stable, accurate solutions at any time.

Contribution

It presents a novel semi-numerical approach that overcomes space discretization limitations for fractal dual-porosity models, ensuring stability and mass conservation.

Findings

Semi-numerical solutions agree well with semi-analytical results.

The method allows computation at any time without stability issues.

Parametric analysis reveals effects of parameters on pressure and flow.

Abstract

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 semi-analytic solutions are available.