(403k) Three-Phase Equilibrium Computations for Hydrocarbon-Water Mixtures

Thermal compositional simulation requires phase equilibrium calculations for three phases. The use of pre-computed equilibrium ratios (K-values) has long been justified on the basis of efficiency. However, this method may not appropriately represent thermal recovery mechanisms. A full EOS-approach is more rigorous, though prohibitively costly.

The development of efficient and robust phase equilibrium algorithms has been motivated by the study of miscible enhanced oil recovery (EOR) mechanisms, whereby CO₂and/or intermediate components are used to improve displacement efficiency. For this reason, existing protocols for hydrocarbon phase equilibrium computations are geared towards identification of multiple hydrocarbon liquid phases and achieving convergence in the near critical region. The aqueous phase is treated as inanimate. In thermal recovery processes the injection of steam results in water-hydrocarbon interactions at elevated temperatures. Representation of phase behavior for hydrocarbon-water mixtures in a non-isothermal context gives rise to a unique set of challenges, owing to the polarity of the water molecule and resulting non-ideal behavior. In this research we address two difficulties pertinent to thermal compositional reservoir simulation: (i) Phase stability analysis with a minimum number of initial estimates for phase equilibrium ratios; (ii) Numerical approaches to phase split calculations in the presence of trace components.

Phase stability testing is deceptively difficult for hydrocarbon-water mixtures. Three-phase regions are often 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 the Wilson correlation, its inverse and compositions dominated by each of the N_c components present. For hydrocarbon-water mixtures, far 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 govern our selection of trial phase compositions. Below the 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 initiate 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 dramatically reduced. 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 Newton’s method. However, in a non-isothermal setting the presence of trace amounts of hydrocarbons in the aqueous phase can produce very ill-conditioned Jacobian matrices 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 formulation is formulated to take advantage of the sparsity of the binary interaction parameter matrix. We demonstrate for the first time the efficacy of a reduced variables formulation for phase split calculations in which trace components appear.

We present our protocol for hydrocarbon-water phase equilibrium computations through comprehensive testing of characterized fluids from the literature. We showcase several examples, including the 5-component mixture of Luo & Barrufet (2005), 5-component mixture of Brantferger (1991), and the 8-component mixture of Lapene et al. (2010). Through our approach to efficient phase stability testing and phase split calculations we are able to accurately resolve phase boundaries. We expect this research to have implications for phase split computations in a non-isothermal setting (isenthalpic, isentropic). In addition, this work is an important step toward fortifying the coupling of phase equilibrium calculations and the transport equations in thermal compositional simulation.