Multiphase Equilibrium Modeling For CO₂-Hydrocarbon System

CO₂ flooding is an essential and popular technology in EOR,and the application in China has been increasing in recent years.During the CO₂ flooding process at the reservoir condition,the phase behavior of the mixture of the oil and CO₂ could be complex.In addition to the conventional vapor-liquid two-phase equilibrium,a CO₂-rich phase could be formed.For the numerical simulation of this system,,a reliable phase behavior model capable of handling at least three-phase equilibrium calculation should be developed.For the phase equilibrium calculation,the number of phases should be determined a prior at the given condition.In this paper,Gibbs energy analysis based tangent plane distance function is used to test the stability of the equilibrium,which is called the stability analysis test.If the instability is detected,the equilibrium calculation follows with the initial value from the stability testing.Different methods for two-phase and three-phase equilibrium are implemented and compared for several fluid mixtures.Especially for the three-phase equilibrium calculation,various reservoir fluids mixed with CO₂ are selected and large-scale at reservoir temperature calculation are conducted to test the algorithm.In addition to the conventional equilibrium calculation,the calculation of the saturation pressure of the mixture,including independent bubble point and dew point calculation are given.Also,the phase envelope construction and direct calculation of the critical point are introduced.Meanwhile,for the three-phase equilibrium pressure calculations,a reasonable initial value for this algorithm are proposed,which is based on the combination of the stability analysis,equilibrium calculation,and phase identification.Through this initial scheme,the type of the three-phase pressure to be calculation could be controlled.The consecutive construction of the three-phase pressure boundaries relies on the initial value from the Lagrange Interpolation.Through the construction of the flash calculation algorithm based on the PR-Eo S,which is capable to determine up to three-phase system of a CO₂-hydrocarbon system,the phase stability analysis is intuitively essential for this model,and the exact number of phases at equilibrium will influence the final result whether the equilibrium is stable or is at the lowest Gibbs free energy state.The robustness and rapid convergence of the flash calculation will also determine the ability of the flash calculation model.