New two‐phase and three‐phase Rachford‐Rice algorithms based on free‐water assumption

Abstract

Based on the free-water assumption that the water-rich liquid phase contains only pure water, we develop two simple free-water Rachford-Rice methods: 1) a two-phase free-water Rachford-Rice method where the phase fractions can be analytically solved; and 2) a three-phase free-water Rachford-Rice method where there is only one unknown in the objective function (i.e. the vapour-phase fraction) that is used for solving the phase fractions. Combining these two Rachford-Rice methods, a new free-water flash algorithm is developed to perform multiphase flash calculations where single-phase equilibria, two-phase equilibria, and three-phase vapour-liquid-aqueous equilibria can be considered. In this free-water flash algorithm, we first test if the mixture is stable; if the mixture is found to be unstable, we directly initiate the three-phase free-water flash. A set of criteria is developed for one to properly switch from a three-phase free-water flash to either a two-phase free-water flash or a conventional two-phase flash, depending on whether a water-rich phase is present in the two-phase equilibrium. We also develop efficient and robust methods for initializing the equilibrium ratios for the two-phase flashes. The negative flash is allowed in the flash calculation algorithms. A number of example calculations are carried out to demonstrate the robustness of the newly developed algorithm. A good agreement can be achieved between the flash results obtained by the new flash algorithm and those obtained by the conventional full three-phase flash algorithm.

Robust Three-Phase Vapor–Liquid–Asphaltene Equilibrium Calculation Algorithm for Isothermal CO2 Flooding Applications

“…If any calculated phase fraction is negative, a two-phase flash calculation needs to be conducted. , If any phase fraction calculated by the two-phase flash calculation is negative, the feed is considered to be stable as one phase. Li and Li proposed that the results yielded by the three-phase flash calculation can provide a knowledge of the present phases in the two-phase equilibrium. Negative flash ,, should be allowed in this method.…”

“…They provided efficient initialization method for equilibrium ratios in their three-phase VLA flash calculation algorithm. Li and Li modified this three-phase flash calculation algorithm as well as the alternative stagewise procedure. By integrating the modified three-phase flash calculation algorithm into the modified alternative stagewise procedure, they developed an efficient and robust three-phase free-water vapor–liquid–aqueous (VLA) equilibrium calculation algorithm .…”

“…Li and Li modified this three-phase flash calculation algorithm as well as the alternative stagewise procedure. By integrating the modified three-phase flash calculation algorithm into the modified alternative stagewise procedure, they developed an efficient and robust three-phase free-water vapor–liquid–aqueous (VLA) equilibrium calculation algorithm . Since the assumption made on the asphaltene phase in the asphaltene precipitation model proposed by Nghiem et al is similar to the free-water assumption, the number of equilibrium ratio sets in the three-phase VLS flash calculation can be also reduced when implementing the asphaltene precipitation model proposed by Nghiem et al Thus, it is possible for us to develop a robust three-phase VLS equilibrium calculation algorithm by taking advantage of the free-solid assumption.…”

Determination of Multiphase Boundaries for Pressure–Temperature (P–T) and Enthalpy–Temperature (H–T) Phase Diagrams of C3H8/CO2/Water/Heavy Oil Systems at High Pressures and Elevated Temperatures

“…Considering the computational efficiency and technical difficulty in performing three-phase flash calculations, the aqueous phase is often neglected in the phase behavior determination of water/solvent(s)/hydrocarbon systems. , As mentioned by Shinta and Firoozabadi, however, the presence of water reduces the three-phase bubble point pressure of water/reservoir-crude oil systems. Moreover, only conducting two-phase vapor–liquid equilibrium calculations may lead to inaccurate quantification of three-phase ALV equilibrium for water/solvent(s)/heavy oil mixtures . Therefore, the water-associated model, which considers the solvent with high solubility in the aqueous phase, is applied in this study to quantify the three-phase ALV phase behavior of C 3 H 8 /CO 2 /water/heavy oil systems at high pressures and elevated temperatures without tuning any parameters for the PR EOS.…”

“…Moreover, only conducting two-phase vapor−liquid equilibrium calculations may lead to inaccurate quantification of three-phase ALV equilibrium for water/solvent(s)/heavy oil mixtures. 59 Therefore, the water-associated model, 19 which considers the solvent with high solubility in the aqueous phase, is applied in this study to quantify the three-phase ALV phase behavior of C 3 H 8 /CO 2 /water/heavy oil systems at high pressures and elevated temperatures without tuning any parameters for the PR EOS. It is worth to note that the solubilities of C 3 H 8 and heavy oil in the aqueous phase are neglected in the waterassociated model as their values are very small in this study.…”