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Original Article | Open Access

Adaptive time-splitting scheme for two-phase flow in heterogeneous porous media

Mohamed F. El–Amin1,2( ), Jisheng Kou3, Shuyu Sun2, Amgad Salama4
College of Engineering, Effat University, Jeddah 21478, Kingdom of Saudi Arabia
Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, P. R. China
Process System Engineering, Produced Water Treatment Laboratory, Faculty of Engineering, University of Regina, Regina, SK, Canada
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Abstract

In the present paper, an adaptive time-splitting scheme is introduced to investigate the problem of two-phase flow in heterogeneous porous media. The pressure and saturation equations are coupled by the capillary pressure which is linearized in terms of saturation. An IMplicit Pressure Explicit Saturation scheme is used to solve the problem under consideration. We use the time schemes for the pressure and saturation equations. The external time interval is divided into two levels, the first level is for the pressure, the second one is for the saturation. This method can reduce the computational cost arisen from the implicit solution of the pressure equation and the rapid changes in saturation. The time-step size for saturation equation is adaptive under computing and satisfying the Courant–Friedrichs–Lewy (CFL <1) condition. In order to show the well performance of the suggested scheme, we introduce a numerical example of a highly heterogeneous porous medium. The adaptive time step-size is shown in graphs as well as the water saturation is shown in contours.

Keywords

two-phase flowporous mediaTime-splittingIMPESreservoir simulation.

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Advances in Geo-Energy Research
Volume 1 Issue 3,
December 2017
Pages 182-189
DOI: 10.26804/ager.2017.03.05
Cite this article:
El–Amin MF, Kou J, Sun S, et al. Adaptive time-splitting scheme for two-phase flow in heterogeneous porous media. Advances in Geo-Energy Research, 2017, 1(3): 182-189. https://doi.org/10.26804/ager.2017.03.05

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Received: 20 November 2017
Revised: 03 December 2017
Accepted: 05 December 2017
Published: 25 December 2017
© The Author(s) 2017

Published with open access at Ausasia Science and Technology Press on behalf of the Division of Porous Flow, Hubei Province Society of Rock Mechanics and Engineering.

This article is distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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