Modeling of enhanced oil recovery applications such as miscible gas injection requires careful consideration of phase equilibria, especially between multiple liquid phases. This paper addresses the problem of phase equilibria when more than two phases are present.
A cubic equation of state approach is used and both Peng-Robinson and Soave-Redlich-Kwong equations of state are Peng-Robinson and Soave-Redlich-Kwong equations of state are considered. Solution methods implemented for finding the roots of the nonlinear system of equations include successive substitution method (SSM), accelerated and stabilized successive substitution method (ASSM), and minimum variable Newton-Raphson (MVNR) method.
In the process of finding interaction coefficients for the mixing parameters a linear optimization routine is used to obtain the first set of constants which pertain to mixture energy of interaction while the second set, which pertain to mixture volume, are held equal to zero. To initialize the optimization search, the first set of interaction coefficients are supplied from the available literature. Randomly generated numbers are then used as scaling factors to obtain additional sets of interaction coefficients in the process of constructing an error matrix. Constraints are determined with the aid of a least squares routine, and by using a revised two-phase procedure, best estimates to the interaction coefficients are obtained. The proposed phase equilibria package is also capable of collapsing a number of components into a pseudo component, which in turn requires less computational work. Furthermore, it is also capable of splitting a C7+ fraction into hypothetical components, which will subsequently give a better phase behavior prediction.
The phase equilibrium prediction progresses in a stepwise manner and during this process, the method of Heidemann and Khalil for critical point determination in multi-component systems is utilized to distinguish the types of the phases.
The phase behavior routine has been tested on various three- or four-phase systems and has been found flexible and satisfactory for phase equilibria prediction of multiple liquid phase mixtures.
Although it is not a common situation, mixtures of the reservoir fluids and the injected gas during a gas miscible process may cause the oil phase to split into two or more coexisting hydrocarbon liquid phases. Also, interaction of the gas phase with the water phase may affect the overall process significantly by the dissolution of gas components in the water phase. Only a limited number of researchers have worked on this particular problem of coexisting liquid phases. Fussell, Mehra et al., and Risnes et al. modeled the aforementioned phase behavior problem by using cubic equations of state.
Cubic equations of state have proved to be effective in the modelling of miscible flooding processes. Because of their simplicity, cubic equations of state, particularly Soave-Redlich-Kwong (Soave's modification of Redlich-Kwong equation of state), have gained considerable popularity in phase behavior predictions, especially in compositional reservoir simulation. predictions, especially in compositional reservoir simulation. One major problem encountered during the application of equations of state to naturally occurring hydrocarbon mixtures is the inadequate description of heavier hydrocarbon components. Obviously, this hindrance reduces the accuracy of the PVT predictions. predictions. P. 399
