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Abstract
In this paper, the Chebyshev wavelet method, constructed from the Chebyshev polynomial of the first kind is proposed to numerically simulate the single-phase flow of fluid in a reservoir. The method was used together with the operational matrices of integration which resulted in an algebraic system of equations. The system of equation was solved for the wavelet coefficient and used to construct the solutions. The efficiency and accuracy of the method were demonstrated through error measurements. Both the root mean square and the maximum absolute error analysis used in the study were within significantly close range. The Chebyshev wavelet collocation method subsequently was observed to closely approximate the analytic solution to the single phase flow model quite well.
Highlights
Understanding the dynamics of fluid flow in porous media is undoubtedly a subject interesting to many scientists and engineers due to its applications in many areas of research [1]
In order to determine the appropriate conditions of operations as well as the machinery to use for the How to cite this paper: Amoako-Yirenkyi, P., Awashie, G.E. and Dontwi, I.K. (2016) On the Analysis and Numerical Formulation of Miscible Fluid Flow in Porous Media Using Chebyshev Wavelets Collocation Method
We present the numerical solution of the single-phase flow model given in Equation (1) using the solution (Equation (38)) from Chebyshev wavelet collocation method discussed above and compare with the exact solution given in Equation (39) below: P
Summary
Understanding the dynamics of fluid flow in porous media is undoubtedly a subject interesting to many scientists and engineers due to its applications in many areas of research [1]. (2016) On the Analysis and Numerical Formulation of Miscible Fluid Flow in Porous Media Using Chebyshev Wavelets Collocation Method. Different wavelet families are applied in various papers for solving differential equations, in which the wavelet coefficients are computed based on either the Galerkin or Collocation methods [18] [24]. The Chebyshev wavelets method constructed using the first kind of Chebyshev polynomial is proposed for numerically simulating the single-phase flow of fluids in a reservoir.
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