Title: Stability analysis and applications of the control volume finite element scheme for two phase flow in the petroleum reservoirs

Authors: A. Malek; S. Khodayari-Samghabadi

Addresses: Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran ' Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

Abstract: In this paper, in order to design a useful computational flow simulation for the governing equation of two phase incompressible (water and oil), a robust and efficient scheme is proposed. This hybrid method consisting of IMPES technique for the linearisation, control volume finite element method on hexagonal grids for spatial discretisation, backward Euler method for time discretisation and stable variant (adaptive-simpler-GMRES) of simpler generalised minimum residual technique with incomplete factorisation preconditioners is used to solve the corresponding linear system. Moreover, we proposed the general Courant Friedrich Levy condition for two phase immiscible flow with Von Neumann method. Numerical results for oil pressure, oil and water production rates and water saturation in the injection and production wells are illustrated.

Keywords: two phase immiscible flow; control volume FEM; finite element method; CVFE; implicit pressure; explicit saturation; Von Neumann stability analysis; adaptive-simpler-GMRES; ILU precondition; flow simulation; oil pressure; water saturation; petroleum reservoirs; oil wells.

DOI: 10.1504/PCFD.2014.060139

Progress in Computational Fluid Dynamics, An International Journal, 2014 Vol.14 No.2, pp.107 - 117

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 28 Mar 2014 *

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