Corresponding states acentric factor

Hexane, for example, is a component whose properties are well known and follow the principle of corresponding states very closely. The acentric factor recommended by the DIPPR is 0.3046 and is considered by convention not to vary with temperature. 

This method utilizes essentially the concept developed by Fitzer in 1955. According to the principle of three-parameter corresponding states, the compressibility factor z, for a fluid of acentric factor w, is obtained by interpolating between the compressibilities Zj and Z2 for the two fluids having acentric factors w, and (p -... 

The volumetric properties of fluids are represented not only by equations of state but also by generalized correlations. The most popular generalized correlations are based on a three-parameter theorem of corresponding states which asserts that the compressibiHty factor is a universal function of reduced temperature, reduced pressure, and a parameter CO, called the acentric factor ... 

Three Parameter Models. Most fluids deviate from the predicted corresponding states values. Thus the acentric factor, CO, was introduced to account for asymmetry in molecular stmcture (79). The acentric factor is defined as the deviation of reduced vapor pressure from 0.1, measured at a reduced temperature of 0.7. In equation form this becomes ... 

The corresponding states approach suggested by Pitzer et al. requires only the critical temperature and acentric factor of the compound. For a close approximation, an analytical representation of this method proposed by Reid et al. " for 0.6 [Pg.394]

Figure A3.3 compares the experimental (corresponding states) results with the predictions from the van der Waals. modified Berthelot, Dieterici, and Redlich-Kwong equations of state.b The comparison is not so direct for the Soave and Peng-Robinson equations of state, since the reduced equation still includes to, the acentric factor. Figure A3.4 compares the corresponding states line, with the prediction from the Soave equation, using four different values of to. The acentric factors chosen are those for H (o> = —0.218), CH4 (to = 0.011),...

Commonly encountered cubic equations of state are classical, and, of themselves, cannot rationalize IE s on PVT properties. Even so, the physical properties of iso-topomers are nearly the same, and it is likely in some sense they are in corresponding state when their reduced thermodynamic variables are the same that is the point explored in this chapter. By assuming that isotopomers are described by EOS s of identical form, the calculation of PVT isotope effects (i.e. the contribution of quantization) is reduced to a knowledge of critical property IE s (or for an extended EOS, to critical property IE s plus the acentric factor IE). One finds molar density IE s to be well described in terms of the critical property IE s alone (even though proper description of the parent molar densities themselves is impossible without the use of the acentric factor or equivalent), but rationalization of VPIE s requires the introduction of an IE on the acentric factor. 

Figure 13.1a shows reduced vapor pressures and Fig. 13.1b reduced liquid molar densities for the parent isotopomers of the reference compounds. Such data can be fit to acceptable precision with an extended four parameter CS model, for example using a modified Van der Waals equation. In each case the parameters are defined in terms of the three critical properties plus one system specific parameter (e.g. Pitzer acentric factor). Were simple corresponding states theory adequate, the data for all... 

Although use of an equation based on the two-parameter theorem of corresponding states provides far better results in general than the ideal-gas equation, significant deviations from experiment still exist for all but the simple fluids argon, krypton, and xenon. Appreciable improvement results from the introduction of a third corresponding-states parameter, characteristic of molecular structure the most popular such parameter is the acentric factor , introduced by K. S. Pitzer and coworkers.t... 

Acentric factor - useful in corresponding state correlations for thermodynamic and transport properties... 

Vapour pressure is a key property in VLB calculations and is thus an important petroleum property. The most common method for prediction of vapour pressures is the corresponding states method. The method requires knowledge of the critical properties and the acentric factor. For petroleum fractions, the Maxwell-BonnelF method is standard. 

Equations of state, such as the Redhch-Kwong (RK) equation, which expresses Z as a function of T, and P, only, yield two-parameter corresponding-states correlations. The SRK equation and the PR equation, in which the acentric factor CO enters through function aiT, Co) as an additional parameter, yield three-parameter corresponding-states correlations. The numerical assignments for parameters , C, 2, and 9 are given in Table 4-2. Expressions are also given for aiT, CO) for the SRK and PR equations. 

Once this function is determined, it could be applied to any substance, provided its critical constants Pc, T, and V are known. One way of applying this principle is to choose a reference substance for which accurate PVT data are available. The properties of other substances are then related to it, based on the assumption of comparable reduced properties. This straightforward application of the principle is valid for components having similar chemical structure. In order to broaden its applicability to disparate substances, additional characterizing parameters have been introduced, such as shape factors, the acentric factor, and the critical compressibility factor. Another difficulty that must be overcome before the principle of corresponding states can successfully be applied to real fluids is the handling of mixtures. The problem concerns the definitions of Pq P(> and Vc for a mixture. It is evident that mixing rules of some sort need to be formulated. One method that is commonly used follows the Kay s rules (Kay, 1936), which define mixture pseudocritical constants in terms of constituent component critical constants ... 

By applying the corresponding states principle, the deviations of the properties of a substance from those of a simple fluid may be correlated in terms of the acentric factor, as described above for vapor pressures (Equation 1.14). The compressibility factor has also been correlated in terms of the acentric factor in the form of a polynomial... 

Many estimation techniques are corresponding-states methods, where the properties of the target fluid are scaled to the properties of a well-known fluid. Scaling factors are often based on the critical temperature and pressure and the acentric factor (which in many cases must be estimated). It is essential to recognize that most correlations were developed for certain classes of fluids, making it dangerous to use them for fluids that are very different from those used to develop the correlation. For example, a correlation developed for nonpolar hydrocarbons should not be applied to a polar fluid such as ammonia or methanol. 

At low and moderate pressures, the viscosity of a gas is nearly independent of pressure and can be correlated for engineering purposes as a function of temperatnre only. Eqnations have been proposed based on kinetic theory and on corresponding-states principles these are reviewed in The Properties of Gases and Liquids [15], which also inclndes methods for extending the calculations to higher pressures. Most methods contain molecular parameters that may be fitted to data where available. If data are not available, the parameters can be estimated from better-known quantities such as the critical parameters, acentric factor, and dipole moment. The predictive accuracy for gas viscosities is typically within 5%, at least for the sorts of small- and medinm-sized, mostly organic, molecules used to develop the correlations. 

Pitzer derived a term useful in corresponding state predictions. The acentric factor co is defined in terms of vapor pressure and is designed to account for the nonideal behavior of gases. In essence, it encodes information about the nonspherical shape of molecules. Using published " values of to, Kier has shown an excellent correlation with k and... 

Alternatively, fluid characteristics other than Zc can be used as the additional parameter in the generalization of the simple corresponding-states principle. In fact, since for many substances the critical density, and hence Zc, is known with limited accuracy, if at all, there is some advantage in avoiding the use of Zc-Pitzer has suggested that for nonspherical molecules the acentric factor co be used as the third correlative parameter, where co is defined to be... 

Guggenheim Equations 1 and 2 are in corresponding-states form that is, the reduced-form equations pr(Tr) explicitly contain no material constants and are formally applicable to all substances (in practice, to substances having small nearly spherical molecules, with modest accuracy). The desirable corresponding-states formulation will be retained in the equation presented here in a modified form, by including (as is now usual) the Pitzer-Curl acentric factor w as an explicit material constant ... 

A very effective third constant is the acentric factor introduced by Pitzer et al. It is widely used in thermodynamic correlations based on the theorem of corresponding states. The acentric factor accounts for differences in molecular shape and is defined by the vapor pressure curve as... 

The equation of state uses corresponding states theory to determine the attractive and volume parameters of each species. Therefore, the pure component critical temperature, 7, and critical pressure, are required. The EOS uses a third parameter, viz. Pitzer s acentric factor, (O, (9)... 

Critical temperature and pressure are required and can be estimated from the methods of this section. Vapor pressure is predicted by the methods of the next section. Experimental values should be used if available. The acentric factor is used as a third parameter with Tc and Pc in Pitzer-type corresponding states methods to predict volumetric properties and in cubic equations of state such as the Redlich-Kwong-Soave and Peng-Robinson equations. For simple spherical molecules, the acentric factor is essenti y zero, rising as branching and molecu-... 

If the departure from equation (35) is not too large, it can be treated as a perturbation. The effect of non-central interactions on the second virial coefficient is second order and it is very difficult to distinguish between any of the non-central interactions on the basis of the behaviour of In essence, it is possible to fit the properties of many pure substances to equations based on simple corresponding states and additional terms whose magnitude is proportional to a perturbation parameter that is a measure of the deviation from central forces. One such perturbation parameter is Pitzer s acentric factor. 74,76 another is Rowlinson s In a homologous series the number of carbon atoms in the chain constitutes yet another measure of the perturbation. It can be shown that there is a simple relation between the different factors. ... 

A principle of corresponding states based on three parameters can be enunciated for substances to which the perturbation approach applies all substances that have the same value of the perturbation factor have the same reduced equations of state. For example, the reduced second virial coefficient can be written in terms of the acentric factor ... 

An extension of corresponding states to highly polar substances has been based on the acentric factor correlation. A fourth parameter related to the dipole moment must be introduced. A similar four-parameter description of the virial coefficients of polar fluids and their mixtures has been developed by Halm and Stiel and for mixtures of quadrupolar fluids by Ramaiah and Stiel. ... 

Eg. (2.20) is a two-parameter correlation because it requires two physical properties, critical temperature and critical pressure. To improve the predictive power of the principle of corresponding state while retaining its simplicity, a third parameter is introduced, the acentric factor. It is a dimensionless parameter that is defined according to the equation. 

Noble gases such as Ar, Kr, Xe, and other spherical, nonpolar molecules such as CH4, interact through similar potential that is spherically symmetric and which can be described through a combination of van der Waals attraction and hard-core repulsion. These fluids are called simple. Their acentric factor is zero or nearly zero, and they are described accurately by the two-parameter correlation of corresponding states. A notable exception is the group of quantum gases. He, Ne, and H, whose behavior at low temperatures is dominated by quantum effects. 

---