화학공학소재연구정보센터
Industrial & Engineering Chemistry Research, Vol.58, No.32, 14954-14974, 2019
Three-Phase Equilibrium Computations for Hydrocarbon-Water Mixtures Using a Reduced Variables Method
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 a reduced order model for three-phase split calculations that allows us to circumvent these numerical difficulties. The reduced method is formulated to take advantage of the sparsity of the binary interaction parameter matrix. For the first time, we demonstrate the efficacy of a reduced-variables formulation for phase-split calculations involving trace components. We present our protocol for hydrocarbon-water phase-equilibrium computations through comprehensive testing of characterized fluids from the literature. Through our approach to robust phase-stability testing and phase-split calculations, we are able to consistently resolve phase boundaries.