Reservoir-Fluid Phase Behavior and Volumetric Prediction With Equations of State (includes associated papers 18400 and 18579 )
Authors: Firoozabadi Abbas 
Published: December 2007

Distinguished Author Series articles are general, descriptiverepresentations that summarize the state of the art in an area of technology bydescribing recent developments for readers who are not specialists in thetopics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and presentspecific details only to illustrate the technology. Purpose: to informthe general readership of recent advances in various areas of petroleumengineering.

Summary.
The use of several cubic equations of state (EOS) in predictingvapor/liquid (VLE) and volumetric behaviour of reservoir-like and realreservoir fluids is discussed, and the difference between these equations isexamined. It is shown that these equations can reliably predict phase behaviorof complex reservoir crude and gas-condensate systems away from the criticaland retrograde regions. The cubic equations that we have examined predictnearly the same K values. The volumetric prediction, however, is different fromone equation to another.

Introduction
Three basic types of computations are required for a reservoir fluid inreservoir engineering: VLE and saturation pressure, volumetric behavior, andthermal and transport properties. Before the mid-1970's, correlations andempirical relationships generally were used for both simple flash calculationsand compositional simulation of reservoir fluid systems. In the last 10 years, EOS have shown surprising capabilities in the computation of the VLE, volumetric, and thermal properties of complex reservoir fluids. Currently, anumber of EOS are used in reservoir engineering calculations. One mainobjective of this paper is to examine the difference (if any) between theseequations. Another objective is to explore their strengths and weaknesses andto re-examine the predictive capability of these equations. This paperaddresses only phase behavior and volumetric property predictions.

EOS Review
An EOS could be defined as an algebraic equation that can describe therelationship between pressure, volume, and temperature for both a puresubstance and a mixture. It may be used to describe gas, liquid, and solidstates. The volumetric behavior of a pure substance and a multicomponentmixture is directly given by the EOS. The VLE is calculated from the EOS by useof the relationship of fugacity to partial molal volume and the equality offugacities of components at equilibrium. There are several families of EOS. Thevan der Waals family enjoys simple cubic form, and most have only twoconstants. Basic parameters for these equations are the critical properties andthe normal boiling point or the vapor pressure. For mixtures containing variousmolecular families, the interaction coefficients between primary constituentsshould be included to account for the degree of compatibility.
The two-constant cubic EOS have proved useful in the VLE computation forcomplex fluid mixtures. However, noncubic EOS with very many constants couldmore precisely represent the PVT data of pure components. As an example, themodified Benedict-Webb-Rubin equation with 11 constants is admittedly moreaccurate than the cubic EOS [such as the Peng-Robinson (PR) EOS] for the PVTdescription of pure substances, but it may be less accurate than thetwo-constant cubic equations for VLE, computation of complex reservoir fluidsystems. Because of the interest in complex reservoir fluid systems, our reviewof the literature will include a handful of the cubic EOS used in estimatingphase behavior and volumetric properties of these systems.
Zudkevitch-Joffe-Redlich-Kwong EOS. In 1970, Zudkevitch and Joffe and Joffeet al., on the basis of the work of Chueh and Prausnitz, assumed the andparameters of the Redlich-Kwong (RK) EOS to be temperature-dependent(seeAppendix A). They determined these two parameters for each pure substance from(1) saturated liquid density, (2) vapor pressure, and (3) equalization of thefugacity of the saturated liquid and vapor phases. Table 1 shows the Omega oaand Omega ob values at different temperatures for propane. At the criticaltemperature and above, these two parameters are assigned constant values of0.4278 and 0.0867, respectively. Therefore, at subcritical temperatures, andare temperature-dependent, while at supercritical temperatures, they aretemperature-independent and equal to their values at Tr=1. Because enthalpy andheat capacities are related to first and second derivatives of and adiscontinuity could exist at Tr= 1, and theZudkevitch-Joffee-Redlich-Kwong(ZJRK) EOS may not be used for enthalpy andheat-capacity calculations around the critical temperature. Zudkevitch and Joffe used a binary interaction coefficient, delta ij. when computing binaryand ternary VLE.