Flash Calculation Using Successive Substitution Accelerated by the General Dominant Eigenvalue Method in Reduced-Variable Space: Comparison and New Insights

Abstract

Summary On the basis of a previously published reduced-variables method, we demonstrate that using these reduced variables can substantially accelerate the conventional successive-substitution iterations in solving two-phase flash (TPF) problems. By applying the general dominant eigenvalue method (GDEM) to the successive-substitution iterations in terms of the reduced variables, we obtained a highly efficient solution for the TPF problem. We refer to this solution as Reduced-GDEM. The Reduced-GDEM algorithm is then extensively compared with more than 10 linear-acceleration and Newton-Raphson (NR)-type algorithms. The initial equilibrium ratio for flash calculation is generated from reliable phase-stability analysis (PSA). We propose a series of indicators to interpret the PSA results. Two new insights were obtained from the speed comparison among various algorithms and the PSA. First, the speed and robustness of the Reduced-GDEM algorithm are of the same level as that of the reduced-variables NR flash algorithm, which has previously been proved to be the fastest flash algorithm. Second, two-side phase-stability-analysis results indicate that the conventional successive-substitution phase-stability algorithm is time consuming (but robust) at pressures and temperatures near the stability-test limit locus in the single-phase region and near the spinodal in the two-phase region.