An advanced general dominant eigenvalue method of accelerating successive substitution during flash calculation for compositional reservoir model

Abstract

The efficiency and accuracy of phase equilibrium calculations are essential in compositional reservoir models. Usually, a significant part of the computational effort in compositional reservoir simulations is spent on phase equilibrium calculations. The nonlinear nature of phase equilibrium calculations requires an iterative solution procedure. Although the successive substitution method (SSM) is robust and simple to implement, it suffers from slow convergence, especially near the critical point of the mixture. The general dominant eigenvalue method (GDEM) has been widely used to accelerate SSM, but its stability and efficiency deteriorate as the temperature and pressure approach the critical point. This paper proposes a modified form of GDEM to improve its performance in the near-critical region. The modifications have two aspects. First, the liquid phase fraction in the mixture is added as a variable when performing GDEM acceleration, improving both stability and efficiency. The second modification is a post-calibration step imposed to replace the conventional criterion, which is applied before triggering GDEM. With the help of the postcalibration step, the stability of the modified GDEM is ensured, and more importantly, the calculation efficiency can be improved. Numerical tests of three hydrocarbon mixtures, including different numbers of components, show that the stability of the modified GDEM is almost the same as SSM and that its calculation efficiency is much higher than SSM and the conventional GDEM.