Corresponding states principle applications

Utracki, L.A. Roovers, J.E.L. Viscosity and normal stresses of linear and star branched polystyrene solution. I. Application of corresponding states principle to zero-shear viscosities. Macromolecules 1973, 6 (3), 366-372. 

Two types of PVT representation are used in simulation equation of state and corresponding states principle. The equations of state are today the most applied. Particularly advantageous are the cubic equations of state, since they offer a consistent computation of both thermodynamic properties and phase equilibria. However, there is no single equation of state that could predict accurately the properties of all components, from hydrogen and methane up to polar species and polymers. That is why there are many models, each being accurate for a particular application. 

The three-parameter corresponding-state principle is applicable to many substances only for strongly polar or associating substances large deviations between the theoretical and experimental values can occur. 

APPLICATION OF THE CORRESPONDING STATES PRINCIPLE TO MIXTURES OF LOW MOLECULAR WEIGHT GASES AT LOW TEMPERATURES AND ELEVATED PRESSURES... 

An equation of state has been developed by Kosinski and Anderko (2001) for the representation of the phase behavior of high-temperature and supercritical aqueous systems containing salts. They improved the EOS by Anderko and Pitzer (1993a) to enhance the predictive capability of the EOS using the three-parameter corresponding-states principle. The model was successfully apphed to the H2O + NaCl solutions up to 573 K, and correctly predicts the p VTx properties of H2O + KCl solution up to 773 K. This EOS also considerably extended the validity range. The EOS is also applicable to water + nonelectrolyte solutions such as water + methane and water + n-decane systems. 

When the above methods fail, estimation methods become important. Schemes based on the Corresponding-States Principle which are particularly important in this respect are described. In order to demonstrate clearly just when the methods of correlation, the theoretical expressions and estimation techniques are applicable, examples are given of transport-property data representation for systems of different complexity simple monatomic fluids, diatomic fluids, polyatomic fluids (specifically, water and refrigerant R134a), nonreacting mixtures and (dilute) alkali-metal vapors as an example of a reacting mixture. 

While virial coefficients can be calculated from statistical-mechanical formulas, for practical work it is usually more convenient to employ semi-empirical correlations. Most of these correlations are based on the principle of corresponding states and as a result their applicability is limited to normal... 

Eq. 3.70 involves neither R nor the van der Waals constant a and b and is called reduced equation of state. It is a general equation applicable to all substances. It follows from this equation that if two moresubstanceshavethesamereduced temperature and thesamereduced pressure, they have thesamereduced volume. This statement is known as the principle of corresponding states. 

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 ... 

The equation in this form is applicable to any substance, provided the critical constants are known. Correlating data in this manner is one illustration of utilizing the principle of corresponding states. 

Even these extensions of the corresponding-states concept, which are meant to ac- count for molecular structure, cannot be expected to be applicable to fluids with permanent dipoles and quadrupoles. Since molecules with strong permanent dipoles interact differently than molecules without dipoles, or th-an molecules with weak dipoles, one would expect the volumetric equation of state for polar fluids to be a function of the dipole moment. In principle, the corresponding-states concept could be further generalized to include this new parameter, but we will not do so here. Instead, we refer you to the book by Reid, Prausnitz, and Poling for a detailed discussion of the corresponding-states correlations commonly used by engineers. ... 

The principle of corresponding states is a special case of the application of scaling laws. In addition io PVT diagrams, transport properties, surface tension, etc., can be modeled [7,8]. Further applications of scaling laws can be found in Sect. 11.4. 

This is the entire formal structure of classical statistical mechanical perturbation theory. The reader will note how much simpler it is than quantum perturbation theory. But the devil lies in the details. How does one choose the unperturbed potential, y How does one evaluate the first-order perturbation It is quite difficult to compute the quantities in Equation P5 from first principles. Most progress has been made by some clever application of the law of corresponding states. It is not the aim of this chapter to follow this road to solution theory any further. 

The principle of corresponding states is a two-parameter theory and works well only for simple molecules, which are the noble gases and a few nonpolar or very slightly polar ones. Two main approaches have been used in expanding its range of applicability. One is to introduce a third parameter, the most successful being the acentric factor, and the other is based on manipulating the intermolecular potentials. We will mention only the acentric factor. 

However, in view of the present limitations of this method, semiempirical predictions such as those based on an extension of the principle of corresponding states, discussed in Chapter 12, and empirical estimations as described in Chapter 13 will continue to be widely used for their general applicability. 

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