Chao-Seader correlation

Solubility Parameters and Liquid Molar Volumes in the Chao-Seader Correlation... 

The correlation of Chao and Seader has been computerized and has been used extensively in the petroleum industry. It provides a useful method for estimating high-pressure vapor-liquid equilibria in hydrocarbon systems over a wide range of temperature, pressure, and composition, and presents a significant improvement over the previously used A -charts first introduced by W. K. Lewis, B. F. Dodge, G. G. Brown, M. Souders, and others (see D6) almost forty years ago. However, the Chao-Seader correlation is unreliable at conditions approaching the critical. Various extensions have been proposed (G2), especially for application at extreme temperatures. 

Chao and Seader assume that the partial molar volumes are independent of composition this assumption is equivalent to saying that at constant temperature and pressure there is no volume change upon mixing the pure liquid components, be they real or hypothetical. The term on the right-hand side of Eq. (46) is assumed to be zero for all temperatures, pressures, and compositions. This assumption is very poor near critical conditions, and is undoubtedly the main reason for the poor performance of the Chao-Seader correlation in the critical region. 

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

The module FLASH simulates the reformer flash separator by using a modified Chao-Seader method. The necessary constants for the Chao-Seader correlation have been developed for the lumped components. The output from this module determines the liquid yield and the composition of recycle gas. 

The case studies were selected to reflect different separation difficulties and different contents of the intermediate component of the quaternary mixtures. The mixtures considered are displayed in Tables 1-2. The mole fraction of 0.05 was shown to be a borderline value for use of side-stream columns for ternary separations (Tedder and Rudd, 1978). The total feed flowrate for all cases was 45.5 kmol/h. Since the feed involves a hydrocarbon mixture, the Chao-Seader correlation was used for the prediction of thermodynamic properties. The design pressure for each sequence was chosen such that all condensers could be operated with cooling water. 

In the Chao-Seader correlation, the fugacity coefficient in the gas mixture is obtained from the Redlich-Kwong eos and is as follows ... 

The resulting Chao-Seader correlation predicts K values of both methane/n-heptane mixtures and propane/isopentane mixtures down to at least = 0.5. 

Coefficients for the Chao-Seader correlation of the liquid fugacity coefficient12... 

Example 5.3. Solve Example 4.4 using the liquid enthalpy equation of Edmister, Persyn, and Erbar, which is based on the Chao-Seader correlation. 

The Chao-Seader correlation is widely used in the petroleum and natural gas industries. Waterman and Frazier describe its use in the design of a wide variety of distillation separations involving light hydrocarbons. Correlations more sophisticated than the C-S correlation can give more accurate results in certain ranges of conditions. However, Lo showed that computing requirements can become excessive and extrapolation more uncertain when more complex equations are utilized. 

Example 7.1 is an application of Table 7.2 to the problem of obtaining outlet compositions and flow rates for an isothermal flash using K-values that are concentration independent and are taken from Fig. 7.5. Example 7.2 involves an isothermal flash using the Chao-Seader correlation for K-values in conjunction with the algorithm of Fig. 7.4f>. 

Use the Naphtali-Sandholm SC method with the Chao-Seader correlation for thermodynamic properties to calculate product compositions, stage temperatures, interstage flow rates and compositions, reboiler duty, and condenser duty for the following distillation specifications. 

Example 5.2. Estimate the K-value of benzene in a solution with propane at 400°F (477.5 K) and 410.3 psia (2.829 MPa) by the Chao-Seader correlation. Experimental compositions of equilibrium phases and the corresponding Jif-values are given by Glanville et al."... 

Repeat Problem 4.19 using the Chao-Seader correlation. 

Partial derivatives of enthalpies and K-values depend upon the particular correlation utilized for these properties and are sometimes simplified by including only the dominant terms. For example, suppose that the Chao-Seader correlation is to be used for X-values. In general. 

Composition-Independent Tabular Properties Chao-Seader Correlation Soave-Redlich-Kwong Correlation... 

Derivatives of properties are needed in the Naphtali-Sandholm SC method. For the Chao-Seader correlation, determine analytical derivatives for... 

A saturated liquid feed at 125 psia contains 200 IbmoIe/hr of 5 mole% /C4, 20mole% nCj, 35mole% iCs, and 40mole% nCs- This feed is to be distilled at 125 psia with a column equipped with a total condenser and partial reboiler. The distillate is to contain 95% of the nC4 in the feed, and the bottoms is to contain 95% of the iCs in the feed. Use the Naphtali-Sandholm SC method, with the Chao-Seader correlations for thermodynamic properties, to determine a suitable design. Twice the minimum number of equilibrium stages, as estimated by the Fenske equation in Chapter 12, should provide a reasonable number of equilibrium stages. 

For the adjusted material balance of Example 15.2, as shown in Fig. 15.9 (but using the Chao-Seader correlation for thermodynamic properties), stream temperatures, enthalpies, and entropies are as follows. 

A simple binary separation of propane from isobutane is used in the numerical example considered in this chapter. The VLE relationships for most hydrocarbon systems are well handled by the Chao-Seader correlation, so we select that package. 

Properties. Propylene is an olefin hydrocarbon that is a gas under ambient conditions bnt is normally stored as a liquid under pressin-e. The physical properties of propylene are given in Table 1. Thermodynamic properties are widely reported in the literature. Vapor-liquid equilibria of mixtures of propylene with other hydrocarbons and hydrogen are accurately represented by correlations for hydrocarbon mixtnres, such as the Chao-Seader correlation. 

As pointed out in the preceding paragraph, some equations, by their very nature, complicate matters. As an additional example, consider the specific limitations of the Chao-Seader correlation and others like it, which allow only about 20% methane in the liquid. In a typical flash problem it is conventional for a first set of K constants to be furnished either by the engineer or initialized by the flash program. These K s immediately lead to vapor and liquid compositions. With these compositions the component fugacltles and liquid activity coefficients are calculated, which in turn lead to a seemingly better set of K s. If the first... 

The Chao-Seader correlation and its many modifications, and the Chueh-Prausnitz correlation are examples of this approach. In the Chao-Seader correlation f and ir are combined as a pure liquid fugacity coefficient, v, so that Eq. (5) has three distinct parts —each requiring a unique equation, as just described. 

Chao-Seader Correlation. Reference was made earlier to the well known and much used Chao-Seader correlation for the prediction of vapor-liquid equilibrium for principally hydrogen-hydrocarbon systems with small amounts of CO2, H2S, O2, N2, etc. The heart of the correlation consists of several equations to represent liquid fugacity. The other two constituents, the Scatchard-Hildebrand equation for activity coefficients and the Redllch-Kwong equation for the vapor-phase nonideality, were already well established. 

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