A New Mixing Rule for Petroleum Mixture Compositional Processes
Authors: Young D.X. 
Published: March 2010

Abstract
A new mixing rule of a realistic vector form is proposed. It is used for vapor-liquid equilibrium calculations of petroleum mixtures with the commonly used Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) Equations Of State (EOS). The results are compared with those from the conventional calculations with the same EOS and the original matrix form of mixing rule, and the experiment data obtained for the chosen petroleum mixtures with and without added CO2.
The new vector form of mixing rule is a successful "transform" of the old matrix form of mixing rule based on the idea of component deviation from their pure-state, vapor-liquid equilibrium behavior when they are present in a petroleum mixture. Such transformation will allow us to eliminate binary interaction coefficients with the more practical component deviation coefficients for petroleum mixture phase equilibrium problems encountered in compositional simulation and relevant chemical engineering calculations.
The utilization of the new mixing rule has lead to results with improved computation efficiency, convergence behavior and accuracy for the calculations performed. However, convergence problems cannot be solved completely with the proposed mixing rule as the problem does not stem from there only. Further investigation results in a new critical criterion that has not been satisfied by many EOS, including the PR and SRK EOS, on both analytical and numerical basis for all pure components. Thus, convergence problem has never been really solved no matter how sophisticated mathematical methods have been employed to get the "converged" results.
The new critical criterion is established with a newly developed three term cubic EOS, which can be easily reduced to encompass many two term cubic EOS of similar forms as the PR or SRK EOS. A discussion on the new EOS is given. 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.

Introduction
The PR and SRK EOS have been in use for phase equilibrium calculations for over twenty years since they were published(1,2). However some problems still exist for petroleum mixtures containing more heavy fractions and near critical point conditions or across phase boundaries(3). In some cases, it is even hard to get converged results without considering their accuracy. Because such problems have not been solved with satisfaction, reservoir simulators that use EOS to model reservoir fluid compositional behavior are most likely to inherit the problems. When this happens in simulation, a lot of times, it is not clearly understood. The reason that this is important is because reservoir fluid vapor-liquid equilibrium states reflect its energy and petroleum recovery potential.
Another problem with compositional reservoir simulators that use an EOS model is that the computing time and storage requirement increase sharply with the number of components used for each grid and iteration step, and soon become a restriction in a simulation(4). Even with the new generations of computers, this is still the case.