Title: A practical approach to ensure the stability and convergence of the solutions to black-oil model used in basin modelling

Authors: Guang-Ren Shi

Addresses: Research Institute of Petroleum Exploration and Development, 20# Xueyuan Road, Beijing 100083, China

Abstract: Since fluids flow under completely different conditions in basin modelling and reservoir simulation, a modified 3-D three-phase (water, oil, gas) black-oil model for basin modelling has been presented in this paper. The main challenge in solving this model is how to ensure the stability and convergence. To tackle this problem, a practical approach to determine the allowable maximum timestep ?t_max has been proposed. The detailed case study in the Kuqa Depression of the Tarim Basin in western China shows that the simulation results and predictions agree well with field evaluations, which suggests that the key to deal with the problem is to correctly select ?t_max for a given application. In the calculations, we employ some techniques such as the finite volume method based on PEBI (perpendicular and bisection) gridcells, and the fully implicit solution based on the Newton iteration and the ORTHOMIN (orthogonal minimum) algorithm.

Keywords: basin modelling; black oil model; variable ranges; stability; 3-D; three-phase; convergence; allowable maximum timestep; finite volume method; Kuqa Depression; mathematical modelling; numerical optimisation; water; oil; gas.

DOI: 10.1504/IJMMNO.2011.043092

International Journal of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2 No.4, pp.405 - 421

Received: 13 Sep 2010
Accepted: 12 Dec 2010
Published online: 26 Mar 2015 *

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