General Strategy for Stability Testing and Phase-Split Calculation in Two and Three Phases

Abstract

Efficient and robust phase equilibrium computation has become a prerequisite for successful large-scale compositional reservoir simulation. When knowledge of the number of phases is not available, the ideal strategy for phase-split calculation is the use of stability testing. Stability testing not only establishes whether a given state is stable, but also provides good initial guess for phase-split calculation. In this research, we present a general strategy for two-and three-phase split calculations based on reliable stability testing. Our strategy includes the introduction of systematic initialization of stability testing particularly for liquid/liquid and vapor/liquid/liquid equilibria. Powerful features of the strategy are extensively tested by examples including calculation of complicated phase envelopes of hydrocarbon fluids mixed with CO 2 in single-, two-, and three-phase regions.

Initialization of phase fractions in Rachford–Rice equations for robust and efficient three-phase split calculation

“…This trial phase is selected to represent the third phase. In three-phase split calculation, {K 2P i,y } and {K 2P i,t } are the best initial guess of {K i,y } and {K i,z } [1,2]. ˇ2 P y and zero (the trial phase has infinitesimal amount) are an excellent starting guess of ˇy anď z .…”

“…But our starting guess has a solid foundation, i.e., it is also from two-phase split calculation and two-phase stability testing. The direct Newton method is based on a reliable two-phase stability testing that has been proposed in our recent work [2].…”

“…1 schematically shows the procedure of equilibrium computation for two and three phases. In our recent work, single-phase stability testing, two-phase split calculation, and twophase stability testing are presented for efficiency and robustness [2]. One important aspect of three-phase split calculation, i.e., the initialization of phase fractions, is discussed in this paper.…”

“…(1) and (2) combined with Eq. (3) for the 2C + 2 unknowns, {K i,y }, {K i,z }, ˇy anď z , is a hybrid approach based on the successive substitution iteration (SSI) method followed by the Newton method [2]. The SSI is used to provide a good enough estimate for the Newton method.…”

“…In order to start the SSI, the initial guess of {K i,y }, {K i,z }, ˇy and ˇz is required. The best initial guess of {K i,y } and {K i,z } is directly made from two-phase split calculation and two-phase stability testing [1,2]. The details on how to get the initial guess of y and ˇz robustly and efficiently are provided in this article.…”