A practical approach to ensure the stability and convergence of the solutions to black-oil model used in basin modelling. (17th October 2011)

• Record Type: Journal Article
• Authors: Shi, Guang-Ren
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 2:Number 4(2011)
• Page Start: 405
• Page End: 421
• Publication Date: 2011-10-17
• Subjects: 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; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

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.