Equation of state PR EOS

For the calculations presented in this paper, we first elected to use three simple cubic equations of state PR-EOS SRK-EOS and RK-EOS. For the pure components, critical properties (Pq, Tq) and Pitzer s acentric factor (ci>) are needed to obtain a and b . Critical properties have been measured for most of the low molecular weight components and are reported by Reid et al. 

This work presents a temperature-dependent volume translated model for Peng-Robinson equation of state (PR EOS) for calculating liquid densities of pure compounds and mixtures in the saturated region. For pure compounds, the average absolute percent deviation (AAPD) were calculated in the reduced temperature range of (0.3-0.99). Similarly for mixtures, the (AAPD) of different binary, ternary and multicomponent mixtures were determined. The AAPD for 29 pure compounds and different mixtures(binary, ternary and multicomponents) were 1.29 and 1.35 respectively. The accuracy of this model was compared well with three well-known liquid density correlations and other earlier volume translated models. 

Further, the fugacity coefficient was calculated as a function of X2, and the value of K2 was obtained from the slope of the curve In 02 against X2 (for additional details see Appendix 2). The calculated values of K2 for the CO2 + naphthalene and CO2 + pyrene systems are plotted in Figure 1. Similar calculations were carried out using the Peng—Robinson (PR) EOS. Good agreement was found between the values of K2 obtained from the two equations of state. 

The optimum binary interaction parameters are shown in Table 111. An example of the results is shown in Figure 1 for the PR-EOS applied to carbon dioxide/methyl oleate at 70 C. Comparing the results of those three simple equations of state, the Redlich-Kwong equation of state gave the poorest prediction. 

Figure 4.4.2. VLE correlations of the carbon dioxide and propane binary system with various approximate EOS-G models. Clockwise from top left HVOS, MHV2, MHV1, and LCVM mixing rules combined with the van Laar excess free-energy model and the PRS V equation of state. Solid lines are model predictions. The points are measured VLE data at 343 K (0, ), 310 iC (A, A) and 277 K (O, ) fix>m the DECHEMA Chemistry Data Series (Gmehling and Onken 1977, Vol. 6, p. 589).

Various EoS/G models have been proposed over the last several years for polymers. These models combine the SRK, the PR equation of state, or the Sako et al. cubic equation of state with FV activity coefficient models such as UNIFAC-FV, Entropic-FV, EH and the ASOG. 

As discussed in the thermodynamics chapter (Chapter 4), an equation of state (EOS) can be used to calculate the fugacities of all components in a mixture. This approach hnds widespread use in the chemical and petroleum rehning industries cubic equations of state are used most often, particularly the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equations. 

The g sni solution models fit low-pressure vapor-liquid equilibrium data for many liquid solutions. These models with fitted parameters are the prime interest to be incorporated into equations of state. To set Equation (4.433) to be equal to these g sm s, the v s in the equation are set to the standard-state pure-liquid volumes of a low-pressure vapor-liquid equilibrium mixture. Novenario et al. [19] calculated the saturated liquid volume for a large number of substances at low pressures with the PR eos and expressed the volume as a multiple of b. 

Any equation of state may be used to generate analytical expressions for residual or departure functions. In the case of PR-EOS the results for enthalpy and entropy are ... 

Bubble pressure found experimentally for a mixture of 50.2% COj and 49.8 % n-butane at 344.2 K is 64.8 bar. Specific volume of saturated liquid is 99.13 cm /mol. The interaction coefficients are Oj (l)/n-butane (2) A,2 = 0.143 for SRK and = 0.133 for PR EOS. Compare bubble point pressure values estimated by the two equations of state, as well as the prediction of the liquid volume, and compare it with the value calculated by Racked equation. The critical data are ... 

The improvement in AT-values does not automatically ensure accuracy of other properties. In this example the estimation of liquid volume is poor for SRK, but acceptable for PR. Without interaction coefficients the prediction of the liquid volume is even better Note that when the volumetric properties are important, as in reservoir engineering, special equation of state or mixing rules should be applied, as Teja-Sandler EOS given in Chapter 5. The same observation holds for the enthalpy of vaporisation, which could be in serious error. Another method for enthalpy/entropy computation should be used, as for example based on the principle of corresponding states. 

EOS is normally either the Soave-Redlich-Kwong (SRK) or the Peng-Robinson (PR). Both are cubic EOSs and hence derivations of the van der Waals EOS, and like most equations of state, they use three pure component parameters per substance and one BIP per binary pair. There are other more complex EOSs (see Table 8.4). EOS models are appropriate for modeling ideal and real gases (even in the supercritical region), hydrocarbon mixtures, and light-gas mixtures. However, they are less reliable when the sizes of the mixture components are significantly different or when the mixture comprises nonideal liquids, especially polar mixtures. 

The cubic equations of state may have four branches in P-v space Examine the PR-EOS given by Eq. (3.6.) A plot of Eq. (3.6) shown ii Fig. 3.7 exhibits three vertical asymptotes ... 

Reservoir-fluids phase behavior and volumetric properties. Reservoir fluids are a complex mixture of thousands of components that exhibit very complex phase behavior. It is, however, surprising that a simple two-constant equation of state such as the PR-EOS can do an excellent job for vapor-liquid equilibria calculations away from the critical region. A discussion of the manner in which the calculations are performed is presented. 

Equation-of-state representation of reservoir-fluids 155 TABLE 3.3 Binary interaction coefficients for the PR-EOS... 

Solution of the association equation of state (AEOS). The incorporation of the association in the PR-EOS results in the following equation ... 

Solution Software such as Mathematica have made life easy for deriving the expressions for derivatives of the equations of state. Earlier, such softwares were not available and apparently Baker and Luks (1980) spent considerable effort to derive the above derivations for the SRK-EOS, although the derivations for this EOS are much simpler than those of the PR-EOS. In the following, the derivatives from Mathematica are presented. 

An equation of state can be used to calculate. (P, T). The expression for the PR-EOS for the calculation of (P, T) is provided by Eq. (3.22) of Chapter 3. Then with A/i, T[, and Ac/jp one can calculate fpure i( P)-order to proceed with the wax-precipitation calculations, one needs to dssume a proper solid model. Currently, there are two types of solid models. One is the solid-solution model, and the other is the multisolid-phase model. These models are presented below. 

Vapor pressure predictions can also be obtained through equations of state. Very good results are obtained for nonpolar compounds with the SRK, PR and vdW-711 EoS discussed here, provided that accurate values for Tg, Pg and [Pg.274]

Cubic Equations of State (EoS) are progressively becoming the main tool for phase equilibria calculations and, even though they are - so far -successful for nonpolar/weakly polar systems only, it will not be long before they can handle polar systems as well. The Soave-Redlich-Kwong (SRK, Soave, 1972) and the PR (Peng and Robinson, 1976) EoS - modifications of the first EoS proposed, that of van der Waals (vdW) - are the most commonly used among them. 

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