Lee-Kesler tables

The Lee/Kesler tables indicate that the state in Part (c) is liquid. 

Although the Lee/Kesler tables, App. E, list values for superheated vapor and subcooled liquid, diey do not provide values at saturation conditions. 

The Lee/Kesler tables are adapted and published by permission from "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," by Byungik Lee and Michael G. Kesler, AIChE J.,21,510-527 (1975). The numbers printed in italic type are liquid-phase properties. 

Problem 7.5 Use the Lee-Kesler tables to calculate the chemical potential of benzene at the following states ... 

First, extensive PVT data are needed for the evaluation of the eight parameters. Such data, as we have mentioned, are available for a few compounds only. A generalized form, developed by Lee and Kesler is available, however. (This form, by the way, has been used for the development of the Lee-Kesler tables used in combination with Pitzer s corresponding states approach.)... 

The Pitzer corresponding states approach, with the Lee-Kesler Tables of Appendix D, and the cubic equations of state of Table 8.3 give reasonable accuracy for nonpolar/weakly polar compounds. 

At higher pressures and for nonpolar compounds, cubic EoS can be used except close to the critical temperature. More reliable results in this region can be obtained with Pitzer s corresponding states approach, combined with the Lee-Kesler Tables, which should be also used at high pressures. [While the Tables cannot be easily adapted for computer use, the generalized BWR EoS, from which these Tables (Appendix D) were developed, can be used for this purpose.]... 

For the volumetric behavior of vapor and gaseous mixtures of hydrocarbons up to moderate pressures, the cubic equations of state discussed in Chapter 10 give reasonable results even with k j = 0. At very high pressures, the Pitzer correlation (with the Lee-Kesler Tables) should be used. 

To find values of enthalpy departure, we can use the Lee-Kesler tables. They have the form ... 

TABLE 1.7 Correlation Terms for the Lee-Kesler Vapor-Pressure Equation... 

Here, xt is the mole fraction of component i, n is the number of components, Tcl and Voi are the critical temperature and volume, and w, is the acentric coefficient for species i. In Eq. (3.21), 7h is the normal boiling point in Kelvin at atmospheric pressure, R = 1.987 cal/(molK), and A77v is in cal/mol. Table 3.2 shows the entropy of vaporization of some binary and ternary azeotropic mixtures obtained from the Lee-Kesler correlation. 

This example uses the Lee-Kesler generalized correlation for the reduced enthalpy estimations (see Tables F5-F8) in a throttling process. The reduced properties lead to enthalpies... 

Although tlie molar volumes of liquids can be calculated by means of generalized cubic equations of state, tire results are often not of Irigh accuracy. However, the Lee/Kesler correlation includes data for subcooled liquids, and Fig. 3.14 illustrates curves for both liquids and gases. Values for both phases are provided in Tables E.l tlrrough E.4. Recall, however, that diis correlation is most suitable for nonpolar and slightly polarfluids. 

TABLE 2-353 Constants for the Two Reference Fluids Used in Lee-Kesler Method ... 

The subscript 0 denotes simple fluids with acentric factor to = 0, and subscript r denotes a reference fluid with acentric factor to,. = 0.3978 from its origin in n-octane. The Lee-Kesler equation constants for Zq and Zy are presented in Table 4.4. The compressibihty factors in Equation (4.239)— Zq, Zy—are at the same [T,.,pJ. This correlation is a three-parameter generahzed correlation that improves the Pitzer correlation to a wider range of states. The lower temperamre bound of the correlation is extended from = 0.8 to 0.3. 

In addition to the equations of state listed in Table 14-9, other useful equations of state have been proposed. In order to cover the whole range of reduced temperatures Tr and reduced pressures Pr of practical interest in hydrocarbon processing, Lee and Kesler39 proposed the use of two equations of state similar in form to the BWR equation of state, one for a simple fluid and one for a reference fluid. The Lee-Kesler correlation also makes use of the acentric factor. 

Table 3.2 presents a selection of the most used thermodynamic options for phase equilibrium with suitable enthalpy and entropy methods. The accuracy of both phase equilibrium and enthalpy/entropy computation must be examined when using EOS models. For example, often a cubic EOS underestimates the enthalpy of vaporisation. In this case other methods are more accurate, as those based on three-parameters corresponding states law (Lee-Kesler, Curl-Pitzer, etc.). Mixtures rich in components with particular behaviour, as or CH, need special methods for accurate simulation. When binary interaction parameters for liquid activity models are absent, the UNI FAC predictive method may be employed. It is worth to note that UNIFAC is suitable only for exploratory purposes, but not for final design. When high non-ideal mixtures are involved at higher pressure then the combination of EOS with liquid activity models is recommended (see Chapter 6). 

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