Modeling high-pressure phase equilibria of coalbed gases/water mixtures with the Peng–Robinson equation of state

Reservoir simulations for enhanced coalbed methane recovery and CO2 sequestration require an equation of state (EOS) model that can provide accurate predictions of vapor–liquid equilibria (VLE) of mixtures of coalbed gases (methane, nitrogen and carbon dioxide) with water at high-pressures and near-critical temperatures. An EOS should be capable of providing rapid and accurate estimates of phase equilibrium for gas + water mixtures under the conditions encountered in coalbed reservoir work. Although more complex equations of state may be used, the computational efficiency of cubic equations of state offers a distinct advantage for reservoir simulation purposes. Therefore, in this work, we utilized the Peng–Robinson equation of state (PR EOS) to model the high-pressure phase equilibria of coalbed gas + water mixtures, then developed expressions for the binary interaction parameters as functions of temperature for each of the important binary systems methane + water, nitrogen + water and carbon dioxide + water. For this purpose, an expanded database was assembled that contains vapor–liquid equilibrium measurements for the three binary mixtures. Several case studies were conducted to investigate both the correlative and predictive capabilities of the PR EOS. The PR EOS was found to be capable of describing the phase equilibria of these systems over the range of conditions encountered in coalbed reservoirs; however, the level of precision varies with the degree of complexity used in representing the interaction parameters in the mixing rules. Overall, an absolute average percentage deviation (%AAD) ranging from 0.3 to 1.7 was obtained for the liquid-phase compositions of the gas for the three binary systems when two system-specific interaction parameters were used. Expressions were developed to account for the temperature dependence of the binary interaction parameters. Using these expressions, the liquid-phase compositions for the three systems can be predicted within about 3–6%AAD, which is within three times the experimental errors in the measurements used in the analysis. The predictions for the vapor-phase composition of water, however, were less accurate (in terms of %AAD) due to the low values of the mole fraction of water in the vapor phase, where small errors in composition could lead to large percentage errors.