A new mixing rule for using with the commonly employed cubic equations of state is proposed. It is applied for petroleum mixture vapor-liquid equilibrium computations, and the results are compared to those from the conventional calculations and the experiment data obtained by recombining the well streams with added carbon dioxide.
The new mixing rule is based on the idea of components deviation from their pure state vapor-liquid equilibrium behavior when they are present in petroleum mixtures, instead of the binary interaction basis for limited binary systems. Its application with the cubic equations of state (EOS) for petroleum mixtures eliminates the use of the binary interaction parameters matrix used for compositional reservoir simulation and chemical engineering calculations.
The utilization of the new vector form mixing rule has lead to significant improvements on the computation efficiency and convergence behavior for our petroleum mixture compositional vapor-liquid equilibrium computations with EOS such as the Soave-Redlich-Kwong EOS and Peng-Robinson EOS. The introduction of the mixing rule with component deviation factors for each real and pseudo-components is flexible, easy to control, and comprehensive for mediating the gaps between the theory and practical engineering problems.
Although the convergence problem is alleviated in our calculations, especially for those cases with high CO2 concentrations, when the mixing rule is applied, the problem cannot be totally solved for a number of reasons. Further investigation results in a new generalized three term cubic EOS which satisfies the newly established critical requirement obtained on both analytical and numerical basis.
The new three term EOS can be reduced to encompass many two term cubic EOS of similar forms, and it has the promising form to be shaped for extended applicable physical conditions for better accuracy and convergence behavior. An explanation and discussion are given on the critical point convergence problem based on the newly developed EOS. With the new EOS, it becomes obvious that the critical convergence problem is not purely a mathematical one, the EOS models themselves may have some inherent restrictions for the phase equilibrium computation schemes to work for complex mixtures when the critical points are approached.
Phase equilibrium computations for petroleum mixtures containing heavy hydrocarbon fractions or near critical point conditions have been regarded as being difficult and mysterious for many years. In some cases, it is even hard to get the converged results without considering their accuracy. Because this problem has not been solved with satisfaction, compositional reservoir simulators that use cubic EOS to model the reservoir fluid phase behavior will most likely to inherit the problem and create confusing. When this kind of problem is encountered in compositional reservoir simulation, a lot of times it will not be clearly understood. The reason that this is important is because reservoir fluid phase conditions reflect the energy level of the reservoir and petroleum recovery potential.
Another problem with compositional reservoir simulators that use an EOS, is that the computing time and storage requirements for a simulation increase sharply with the number of components for each grid and iteration step, and soon become prohibitively large.