Fast Algorithm of Numerical Solutions for Strong Nonlinear Partial Differential Equations

Because of a high mobility ratio in the chemical and gas flooding for oil reservoirs, the problems of numerical dispersion and low calculation efficiency also exist in the common methods, such as IMPES and adaptive implicit methods. Therefore, the original calculation process, “one-step calculation...

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Bibliographic Details
Published in:Advances in Mechanical Engineering 2014-01, Vol.6, p.936490
Main Authors: Liu, Tongjing, Diwu, Pengxiang, Liu, Rui, Jiang, Liwu, Jiang, Baoyi
Format: Article
Language:English
Subjects:
Algorithms
Colleges & universities
Computer simulation
Finite element analysis
Finite volume method
Flooding
IMP
Laboratories
Mathematical models
Natural gas
Numerical analysis
Oil recovery
Petroleum engineering
Reservoirs
Saturation
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Summary:Because of a high mobility ratio in the chemical and gas flooding for oil reservoirs, the problems of numerical dispersion and low calculation efficiency also exist in the common methods, such as IMPES and adaptive implicit methods. Therefore, the original calculation process, “one-step calculation for pressure and multistep calculation for saturation,” was improved by introducing a velocity item and using the fractional flow in a direction to calculate the saturation. Based on these developments, a new algorithm of numerical solution for “one-step calculation for pressure, one-step calculation for velocity, and multi-step calculation for fractional flow and saturation” was obtained, and the convergence condition for the calculation of saturation was also proposed. The simulation result of a typical theoretical model shows that the nonconvergence occurred for about 6,000 times in the conventional algorithm of IMPES, and a high fluctuation was observed in the calculation steps. However, the calculation step of the fast algorithm was stabilized for 0.5 d, indicating that the fast algorithm can avoid the nonconvergence caused by the saturation that was directly calculated by pressure. This has an important reference value in the numerical simulations of chemical and gas flooding for oil reservoirs.
ISSN:1687-8132
1687-8140
1687-8140
1687-8132
DOI:10.1155/2014/936490