Accurate prediction of thermophysical properties is an essential requirement for optimum design and operation of most process equipment involved in petroleum production, transportation, and processing. Equipment failure is often directly attributed to lack of accurate design data. Methods of fluid property prediction can be divided into three main categories, namely the Corresponding States Theory (CST), Equation of State (EOS) model, and Activity Coefficient Model (ACM). The EOS approach is most popularly used for natural gas systems due to its applicability at high pressures for both liquid and vapor phases.

Probably the most successful cubic equation of state for natural gas property calculation is the one proposed by Peng and Robinson (PR)1. However, Peng-Robinson EOS assumes a fixed value of critical compressibility factor and, as a result, the predicted densities of the saturated liquids and the predicted critical volumes differ considerably from experimental values. Patel and Teja (PT)2 introduced a substance dependent critical compressibility factor that allowed them to more accurately reproduce the experimental saturated liquid volume at a particular temperature.

The present work is an extension of that of Patel and Teja. The modified Patel and Teja's EOS improves the prediction of liquid phase density and vapor liquid equilibrium. A comprehensive assessment of the modified equation-of-state is conducted through performance comparison with the more popular equations of state. For saturated liquid volume predictions, the improved equation of state yields 33% and 11% improvement over PR and PT EOS, respectively. For vaporization equilibrium ratio predictions, 36% improvement over PR and 67% improvement over PT EOS are observed.


Equations of state provide a most efficient and simple means of expressing various thermodynamic functions in terms of PVT data. The importance and necessity of an accurate EOS is reflected by the appearance of many such equations in the literature. Publications on EOS are so numerous that, Reid3 stated, "It is a full time job just to maintain familiarity with the publications in this field". In 1980/81 year alone, Reid counted 885 papers dealing with the use of EOS. In spite of this high rate of research activities in the area, universally accurate equation of state is still lacking, thus necessitating continued research.

With better liquid density prediction as a main goal, particularly in the vicinity of the critical region, Peng and Robinson1 developed the following expression:

  • Equation 1

where a, b and a have the same significance as they have in the Soave-Redlich-Kwong4 (SRK) equation. For parameter c, they took two criteria into account. First, the experimental values of hydrocarbon critical compressibility factor lies between 0.24–0.30, and the EOS should be capable of reproducing a close value to those. Second, the experimental (b/vc) ratio is around 0.26 and EOS should reproduce this value. Keeping these constraints, Peng and Robinson found that the optimized integer value of parameter c should be equal to 2. As a result, Peng-Robinson EOS produces a compressibility factor of 0.307 and (b/vc) of 0.253. Later it was established that instead of optimizing Zc and (b/vc) to constant values, one can increase the number of parameters of EOS, and thus be able to produce variable values of Zc and (b/vc). For 2-parameter equations of states, the only constraint equations used are the criticality conditions. A 3-parameter equation of state utilizes either the critical compressibility factor or the co-volume definitions as an additional constraint to criticality conditions. For a 4-parameter equation of state both of these definitions together with the criticality conditions are used.

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