Numerical Modeling of Non-Equilibrium Phase Transitions in the Isothermal Compositional Hydrocarbon Flow Simulations
Authors: Bogachev Kirill , Zemtsov Sergey , Milyutin Sergey , Indrupskiy Ilya , Lobanova Olga 
Published: October 2019

Abstract
The paper deals with the problem of numerical simulation of multiphase flow with non-equilibrium phase transitions in the development of hydrocarbon deposits. For the isothermal compositional flow model, a new method is proposed that takes into account the rate of thermodynamic equilibration.
A process is called non-equilibrium if its characteristic duration is equal to or greater than the characteristic time of external conditions changing. In the classical formulation of multiphase flow problems, it is believed that flow processes take place under thermodynamic equilibrium, that is, phase transitions can be considered instantaneous compared to the rate of change of the pressure and composition of the hydrocarbon mixture. In real oil and gas-condensate systems phase transitions proceed in forward and reverse directions with different rates. For example, the dissolution of gas is much slower than the liberation of gas from oil, and so non-equilibrium behavior can strongly influence the simulation results. The role of non-equilibrium behavior increases with the increase of the elementary volume of averaging, that is, with the growth of the mesh size of the dynamic flow model.
For black-oil models, there are extensions to the mathematical formulation that are often used in practice to describe non-equilibrium phase transitions. In most realizations of compositional models, the rate of establishing thermodynamic equilibrium is not taken into account. In some typical cases it may call into question the reliability of the simulation results.
Previously, an approach was proposed to extend the traditional compositional model to account for non-equilibrium thermodynamic processes occurring in the reservoir (Indrupskiy et al., 2017). In the non-equilibrium case, the condition of equality of chemical potentials of the components in the phases was replaced by the condition of relaxation of the difference of chemical potentials to zero as the system tends to the equilibrium state after changing the external parameters (pressure and bulk composition of the mixture). In this paper, an alternative approach is formulated in which it is proposed to limit the rate of change of the distribution ratios (K-values) of the components, so as to take into account the relaxation. The new method has a number of advantages: higher numerical efficiency and stability, the possibility of natural generalization to the thermal compositional model. At the same time, as for the method proposed in (Indrupskiy et al., 2017), it is necessary to change only the algorithms for calculating the vapor-liquid "equilibrium" ("flash"), while the flow equations do not change. It makes possible a relatively simple implementation in existing reservoir simulators.
The proposed method, as well as the method of (Indrupskiy et al., 2017), are implemented in the framework of a fully implicit three-phase three-dimensional compositional flow simulator. The results of real reservoir simulations are presented to demonstrate the need to take into account the non-equilibrium phase transitions. The implementation demonstrates high numerical efficiency.