Redlich-Kwong empirical

Redlich-Kwong Equation. The Redlich-Kwong equation, which was proposed in 1949 [5], has been found to reproduce experimental P-V-T data for gases just as well as several equations that use more than two empirical constants and better than other two-parameter equations [6]. It has the form... 

Halback H. E. and Chatterjee N. D. (1982). An empirical Redlich-Kwong-type equation state for water to 1000°C and 200 kbar. Contrib. Mineral Petrol, 79 337-345. 

Equation of state research has returned recently to the spirit of van der Waals, that is, cubic equations with two constants. Many equations of this form have been proposed.13 Two popularly accepted equations of state in the petroleum industry, Redlich-Kwong and Peng-Robinson, are cubic equations with two empirical constants. These equations have been used widely to calculate physical properties and vapor-liquid equilibria of hydrocarbon mixtures. 

The Chao-Seader and the Grayson-Streed methods are very similar in that they both use the same mathematical models for each phase. For the vapor, the Redlich-Kwong equation of state is used. This two-parameter generalized pressure-volume-temperature (P-V-T) expression is very convenient because only the critical constants of the mixture components are required for applications. For the liquid phase, both methods used the regular solution theory of Scatchard and Hildebrand (26) for the activity coefficient plus an empirical relationship for the reference liquid fugacity coefficient. Chao-Seader and Grayson-Streed derived different constants for these two liquid equations, however. 

The application of cubic equations of state to mixtures requires expression of the equation-of-state parameters as functions of composition. No exact theory like that for the virial coefficients prescribes this composition dependence, and empirical mixing rules provide approximate relationships. The mixing rules that have found general favor for the Redlich/Kwong equation are ... 

Reid, Prausnitz, and Poling (see footnote 1) discuss other important cubic equations of state including the Redlich-Kwong, Soave-Redlich-Kwong (SRK). and Peng-Robinson equations. These equations are empirical but have proved remarkably robust in describing a wide variety of systems. Here we will use the SRK expression to illustrate the general characteristics of cubic equations of state. 

This work proposed the use of the Predictive Soave-Redlich-Kwong (PSRK) model to describe the phase equilibria in the flash distillation, using modified molecular parameters r and q for ethanol. In this way, the PSRK equation of state becomes more empirical, but keeps the predictive capabilities of the model. Furthermore, the introduction of new molecular parameters r and in the UNIFAC model gives more accurate predictions for the concentration of the congener in the gas phase for binary and ternary systems. 

Unlike the van der Waals and Redlich-Kwong equations, which are cubics in density, this mRK equation is fifth-order. It is not unusual that improvements in accuracy are accompanied by increases in algebraic complexity here the complexity occurs because we have combined a theoretically reliable repulsive term with an empirically proven attractive term. 

Enthalpy and entropy of gases at low pressure can be calculated accurately from the Soave-Redlich-Kwong, Peng-Robinson or Patel-Teja equations of state at moderate and high pressure the Peng-Robinson or Patel-Teja equations of state are recommended. On the other hand, for liquid phase enthalpy and entropy none of the cubic equations of state can provide precise results. Empirical correlations, such as that proposed by Lee-Kesler, are much more precise. 

If an equation of state is to be used for the calculation, it is often better to introduce the fugacity coefficient This is particularly important if there is no expression for the Gibbs energy as in the case of empirical cubic equations of state like Soave-Redlich-Kwong and Peng-Robinson. In usual thermodynamics the fugacity coefficient may be calculated from... 

No chemical engineer has ever relied on directly measured values for all the thermodynamic properties he uses. It is one of the great virtues of classical thermodynamics (indeed, it has been said that it is its only virtue ( )) that it allows us to calculate one physical or chemical property from another, for example, a latent heat of evaporation from the change of vapour pressure with temperature. Less obvious, but almost equally secure calculations can be made by fitting measured values to an empirical equation and calculating other properties by a subsequent manipulation of that equation. Thus we can fit the pressure of a gas to a Redlich-Kwong (RK) or Benedict-Webb-Rubin (BWR) equation, from which the other properties such as changes of enthalpy and entropy are then derived. Similarly we fit activity coefficients to Wilson s equation and calculate K-values. 

In thermodynamics, the pressure-volume-temperature relationship of real gases is described by the equation of state. There are several semitheoretical or empirical equations, such as Redlich-Kwong, Soave-Redlich-Kwong, and the Benedict-Webb-Rubin equations,... 

To illustrate how an empirical equation may be used to calculate fugacity coefficients, we use the equation of Redlich and Kwong (R2), which generally gives satisfactory results for nonpolar fluids. This equation is... 

The five-constant equation of Beattie and Bridgeman, the eight-constant equation of Benedict, Webb, and Rubin (B-W-R), and the two-constant equation of Redlich and Kwong (R-K), are empirical relationships applicable over a wide range of pressure. The R-K equation is particularly attractive because it contains only two constants and these can be determined directly from the critical temperature and critical pressure Pc-Furthermore, the R-K equation has an accuracy that compares quite favorably with more complex equations of state and if has the ability to approximate the liquid region, as is illustrated in the following example. The two-constant van der Waals equation can fail badly in this respect. 

The vdW EOS is not very good at representing experimental PvT data, but it has had a profound influence on thermodynamics. Fairly simple, totally empirical modifications of it by Redlich and Kwong, Soave, and Peng and Robinson are very widely used in vapor-liquid equilibrium calculations, as discussed in Chapter 10 and Appendix F. Furthermore, it led to the principle of corresponding states, discussed below, which is very useful. 

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