A New Modification of Cubic EOS Improves Prediction of Gas Condensate Phase Behavior
Authors: Shtepani E.R. , Weinhardt B.E. , Potsch K.T. 
Published: December 2007

Abstract
The phase and volumetric behavior of fluid systems can be predicted using cubic equations of state (EOS), e.g. SRKEOS (Soave-Redlich-Kwong) or PREOS (Peng-Robinson). In case of the investigated gas condensate systems, all predictions did not coincide with the laboratory data. By a general correction of the attraction parameter a, the coincidence of SRKEOS- and PREOS-based predictions with the laboratory data could be satisfactorily improved.

Introduction
The prediction of phase and volumetric behavior of hydrocarbon systems - including also nonhydrocarbon components - is of certain importance for many applications in chemical and reservoir engineering. In particular, the compositional simulation of a gas condensate reservoir, with the objective of optimizing its development and performance, requires accurate predictions if the simulation results are to be reliable.
Cubic equations of state (EOS) have become the most popular basis of the prediction of phase and volumetric behavior of fluid systems. Among them, the EOS proposed by Redlich and Kwong (RKEOS) has assumed a special rank. Its modification by Soave (SRKEOS) is most widely used though it continues to yield poor liquid density data.
Petroleum engineering applications also often rely on the EOS proposed by Peng and Robinson (PREOS). PREOS is comparable to SRKEOS in simplicity and form. Peng and Robinson reported that PREOS-based prediction of liquid densities is improved compared with the SRKEOS-based results.
A cubic equation of state expresses the pressure as the sum of two terms which are the repulsion pressure PR and the attraction pressure PA. A simple EOS, e.g. SRKEOS or PREOS, can be generally formulated by
(1)
The parameters a and b in Eq. 1 are defined by a molecular view of the system. The term (V - nb) considers the reduction of the space for thermal movement due to the own volume of the molecules. The intermolecular attraction slightly reduces the momentum with which the molecules try to leave the bulk and, consequently, the pressure. This reduction in pressure may be expressed by the term
While the parameter b is usually treated as being independent of the temperature, a dimensionless scaling factor is used to describe the temperature dependence of the attraction parameter a. The scaling factor has been regarded as a function of the reduced temperature as in RKEOS and, additionally, also as a function of the acentric factor as in SRKEOS and PREOS.
Additionally, empirical binary interaction coefficients have become considered in a mixing rule that must be applied in order to calculate the parameter a in the case of a multicomponent system. However, it has become obvious that the lack of prediction accuracy cannot solely be attributed to an imperfection in the mixing rule. It must be partly ascribed to the EOS's lack of accuracy in considering the influence of the nature of the molecules as well as the role of the temperature. Consequently, Soave as well as Peng and Robinson recommendated further refinement of their scaling factor.
Especially the phase behavior prediction of gas condensate systems are especially poor due to the significant fraction of low molecular-weight components. P. 459