Peng-Robinson polarity

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

Mathias, P. M., and Copeman, T. W., 1983. Extension of Peng-Robinson equation of state to polar fluids and fluid mixtures. Fluid Phase Eq., 13 91-108. 

For computing the enthalpy departures of pure gases and gas mixtures, the equations of state of Sec. 14-2 may be used for both the vapor and liquid phases (1) modified versions of the BWR equation of state, such as the one proposed by Starling, (2) the Soave-Redlich-Kwong, and (3) the Peng-Robinson equation of state. Another method which has been tested extensively and found to give accurate results even for polar gas mixtures is the Yen-Alexander correlation.78... 

It must be emphasized that the generalization of the Peng-Robinson equation-of-state parameters given by Eqs. 6.7-2, 6.7-3, and 6.7-4 is useful only for hydrocarbons and inorganic gases (O2, Na, CO2. etc ). For polar fluids (water, organic acids, alcohols, etc.), this simple generalization is not accurate, especially at low temperatures... 

Elevated pressures for a vapor mixture that contains one or more polar and/or associating compounds Use an equation of state, such as the Peng-Robinson or Soave-Redlich-Kwong equation with the excess Gibbs energy-based mixing rules (see Sec. 9.9) and the appropriate activity coefficient model (see Table 9.11-1). 

Clearly, data regression is needed to obtain a rigorous design for the distillation. Furthermore, in this case, the UNIQUAC equation represents the nonidealities of this polar mixture quite well. When the Peng-Robinson (Reid et al., 1987) equation is used instead, as shown on the multimedia CD-ROM, the data are not represented as well after the data regression is completed. ... 

To model the properties of interfaces of mixtures with polar species, suitable equations of state need to be used in conjunction with the gradient theory. This is more important for mixtures than for pure fluids. For polar and even associating species the APACT has been applied, while for non-polar species like alkanes the Peng-Robinson equation of state has been selected. Calculations show that the interfacial tensions obtained with the former model are in good agreement with the experimental tensions. Even the interfacial tensions of mixtures containing water can be described accurately. 

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. 

All of the cubic equations of state presented so far are generally termed two-parameter equations of state. In this respect, each one of them predicts a constant compressibility factor at the critical point Zc=PcVd T, irrespective of the nature of the compound for van der Waals Zc = 0.375, for Redlich-Kwong and Soave-Redlich-Kwong Zc = 0.333 and for Peng-Robinson Zc = 0.307. The actual values may vary significantly, especially for polar and associating fluids for methane Zc = 0.286, for propane Zc = 0.276, for pentane and benzene Zc = 0.268 and for water Zc = 0.229. To correct for this deficiency, a number of authors have proposed three or four adjustable parameters to the cubic equation of state. The most popular three-parameter cubic equation of state was proposed by Patel and Teja is given by ... 

The modern cubic equations of state provide reliable predictions for pure-component thermodynamic properties at conditions where the substance is a gas, liquid or supercritical. Walas and Valderrama provided a thorough evaluation and recommendations on the use of cubic equation of state for primary and derivative properties. Vapour pressures for non-polar and slightly polar fluids can be calculated precisely from any of the modem cubic equations of state presented above (Soave-Redlich-Kwong, Peng-Robinson or Patel-Teja). The use of a complex funetion for a (such as those proposed by Twu and co-workers ) results in a significant improvement in uncertainty of the predicted values. For associating fluids (such as water and alcohols), a higher-order equation of state with explicit account for association, such as either the Elliott-Suresh-Donohue or CPA equations of state, are preferred. For saturated liquid volumes, a three-parameter cubic equation of state (such as Patel-Teja) should be used, whereas for saturated vapour volumes any modern cubic equation of state can be used. 

The description of hydrocarbon mixture VLB at low and high pressure is of major importance to the oil industry. For such mixtures, any of the modern cubic equations of state (such as Redlich-Kwong, Peng-Robinson or Patel-Teja) provide precise predictions when used with a temperature-independent binary interaction parameter of relatively small value (in most cases in between — 0.1 and 0.1). For the case of non-polar hydrocarbon mixtures of similar size, even kij = Q.Q results in excellent prediction of VLB. 

For the case of polar fluids such as water and methanol, Mathias and Copeman proposed an improved expression for the parameter a compared to the original expression of Peng and Robinson. The new expression is written in terms of the reduced temperature of the polar fluid. 

The accuracy of the PR76 equation is comparable to the one of the SRK equation. Both these models are quite popnilar in the hydrocarbon industry and offer generally a good representation of the fluid phase behaviour of few polar and few associated molecules (paraffins, naphthenes, aromatics, permanent gases and so on). (Robinson Peng, 1978) proposed to slightly modify the expression of the m fimction in order to improve the representation of heavy molecules t such that co cime = 0.491. This model is named PR78 in this chapter. 

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. 

---