CO 2 injection into an oil reservoir at low temperature can lead to the formation of three hydrocarbon phases. Key challenges persist in the development of phase equilibrium calculations for three-phase hydrocarbon−CO 2 systems. One challenge is the identification of a third equilibrium phase via stability testing of a two-phase mixture. Stability testing requires initial estimates of phase equilibrium ratios (K-values). Existing methods for estimating K-values for the identification of three-phase behavior are unable to detect the whole three-phase region. In addition, many of the initial K-value estimates are redundant, wherein convergence is to the same composition. In this work, we present systematic procedures for single-phase and two-phase stability testing using optimized sets of initial K-value estimates. We show that two-phase stability testing requires one to test both of the equilibrium phases in the system. We reveal that three-phase hydrocarbon− CO 2 behavior cannot be resolved across the pressure−composition parameter space with existing methods for the estimates of the initial K-value. We introduce a new initial K-value estimate for two-phase stability testing to resolve three-phase behavior. Our approach significantly improves the reliability and reduces the cost of phase stability testing. Reservoir simulation requires fast and reliable algorithms for stability testing and flash calculations. Failure of the phase equilibrium kernel leads to time-step cuts and the potential cessation of the simulator. We have implemented a combined successive substitution, Newton, and trust-region optimization algorithm for both stability testing and multiphase flash calculations. We have also developed a novel optimization algorithm to solve the multiphase Rachford−Rice equations. We present the performance of our phase equilibrium framework using nine characterized fluid systems from the literature. Rigorous testing across a wide parameter space demonstrates the robustness of our framework. We show specific instances of quantification of phase equilibrium in challenging scenarios, including near the stability test limit locus in stability testing and the critical region in multiphase flash calculations. The results in this work address the most prominent difficulties in equation of state modeling of CO 2 flooding. In sum, this work provides the comprehensive detailed algorithms for phase equilibrium calculations for simulation of CO 2 flooding in low-temperature reservoirs.
Thermal compositional simulation requires phase-equilibrium calculations for at least three fluid phases. The use of precomputed equilibrium ratios (K-values) has long been justified on the basis of efficiency. However, this method may not appropriately represent thermal recovery mechanisms. An equation of state (EOS) approach is more rigorous, though prohibitively costly. In thermal recovery processes the injection of steam results in hydrocarbon–water interactions at elevated temperatures. Representation of phase behavior for these systems in a nonisothermal context gives rise to a set of challenges owing to the polarity of the water molecule and resulting nonideal phase behavior. In this research we address two difficulties pertinent to thermal compositional reservoir simulation: (i) robust phase-stability analysis using a predetermined set of initial estimates for phase-equilibrium ratios; (ii) numerical solution of phase-split (flash) calculations in the presence of trace components. Phase-stability testing can be difficult for hydrocarbon–water mixtures. Three-phase regions can be extremely narrow in pressure–temperature space, making the resolution of phase boundaries problematic. The standard approach to phase stability testing for hydrocarbon reservoir fluids entails using a series of initial guesses for the equilibrium ratios based on variations of the Wilson correlation (Wilson, G. M. A modified Redlich-Kwong equation of state, application to general physical data calculations; 65th National AIChE Meeting, Cleveland, OH, 1969) and trial-phase compositions dominated by each of the N c components present. For hydrocarbon–water mixtures, fewer initial guesses are required. We propose a physics-based strategy, sensitive to the distinct behavior of water. We use the steam saturation pressure to guide our selection of trial phase compositions. Below saturated steam pressure, only two sets of equilibrium ratios are required to identify the correct phase state. Above the saturation pressure, we expand our set of initial K-value estimates to account for the appearance of a near pure aqueous phase. The K-values obtained from stability analysis are used to perform two-phase flash computations. Then, the stability of the two-phase mixture is assessed. The phase state of the system following the two-phase flash guides the choice of the next set of K-values. This strategy has two direct benefits. First, the number of trial phases required for stability testing is predetermined. Second, the reliability of the phase-stability tests and the ensuing equilibrium calculations is greatly improved. The solution procedure for phase-split calculations in isothermal compositional simulation is typically a two-stage process that uses successive-substitution in conjunction with the Newton method. However, in a nonisothermal setting the presence of trace amounts of hydrocarbons in the aqueous phase can produce ill-conditioned linearized systems when standard (conventional) variables are used in the Newton loop. We have developed ...
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