Benedict, Webb and Rubin

Another class of equations, known as extended virial equations, was introduced by Benedict, Webb, and Rubin [/. Chem. Phys. 8 334-345 (1940) 10 747-758 (1942)]. This equation contains eight parameters, all functions of composition. It and its modifications, despite their complexity, find application in the petroleum and natural gas industries for light hydrocarbons and a few other commonly encountered gases [see Lee and Kesler, AIChE/., 21 510A527 (1975)]. 

Lastly I would like to consider the Beattie-Bridgeman equation and its offspring the Benedict, Webb, and Rubin equation which start with the VDW equation and replace 1/(V — Nb) by (V + Nb)/V2. Several additional parameters are introduced. However, the above replacement is so meaningless at high densities that I cannot bring myself to comment further on this family of empirical equations. 

Much more sophisticated is the form known as the BWR-EOS, proposed by Benedict, Webb and Rubin (1940) . This model represents a more complex dependency of pressure as function of volume ... 

Equation (4-26) was developed by Hougen and Watson. More recently, Mehra, Brown, and Thodos utUized it to determine /C-values for binary hydrocarbon systems up to and including the true mixtiu-e critical point. Equation (4-27) has received considerable attention. Applications of importance are given by Benedict, Webb, and Rubin Starling and Han " and Soave. Two unsymmetrical formulations are ... 

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. 

A number of investigators have developed equations similar or identical to some discussed herein. Among these workers are Beattie [1, 2], Dokoupil et al. [3], Robin [5], Ewald et al. [6, 7], Rowlinson and Richardson [9], Benedict, Webb, and Rubin [10], Prausnitz [11] and Hydrocarbon Research, Inc. [12], Several of these investigators have compared their equations to low temperature, high pressure binary equilibrium data. 

The virial equation of state given by eq 5.1 applies to gases and has been discussed in Chapter 3. The composition dependence for the second and third virial coefficients are obtained from statistical mechanics and given by eqs 5.3 and 5.4. Consequently, the virial equation has formed the basis for the development of other semi-empirical equations of state capable of correlating both (p, V, T) and phase behaviour some approaches are discussed in Chapter 12. One example of this form of equation is the Benedict, Webb and Rubin (known by the acronym BWR) equation of state given by ... 

In 1940, Benedict, Webb, and Rubin published their formulation both in terms of pressure and in the residual Helmholtz energy. However, the formulation in pressure was considered the original formulation, and the Helmholtz energy formulation was rarely used because the ideal gas contribution was missing. The first equation of state that was formulated exclusively in terms of the Helmholtz energy a was published in 1969 by Keenan et al for water and steam. The equation is given in specific quantities by... 

Multiparameter equations of state and their mixing rules. The Benedict Webb and Rubin equation [22] is a well-known example of an equation of the first type. According to this equation... 

Naturally, I am very pleased to note that others have extended the accuracy and range of our tables and equations with consideration of more recent experimental results. Of particularly broad importance is the 1975 paper by Lee and Kessler (17) which presents both improved tables and analytical equations for all of the major functions Including vapor pressures, volumetric properties, enthalpies, entropies, fugacities, and heat capacities. Their equation is an extension of that of Benedict, Webb, and Rubin now containing twelve parameters. They considered more recent experimental data as well as a number of papers which had already extended my earlier work in particular areas. I refer to their bibliography (17) for most of this more detailed work, but I do want to note the improved equation of Tsonopoulos (18) for the second virial coefficient. This equation deals also with effects of electrical polarity. 

The same equation of state is then employed to get both the numerator and denominator in this expression using standard thermodynamic relationships. The work of Benedict, Webb and Rubin (.6), of Starling (.2) > and the series of Exxon papers (Lin et al., ( ) Lin and Hopke,( ))—all on various forms-of the BWR, Soave, and Peng-Robinson equations of state are examples of the use of one equation of state to perform the whole calculation. It should be added that the original developments in this area treated the fL /x term in the numerator as a separate entity and multiplied the final answer by l/ir for consistency. Most contemporary approaches relate both numerator and denominator to equations of state via the fugacity coefficient route, the only difference in liquid and vapor being the density and the equation constants obtained from the respective mixing rules. 

One of the oldest, but still used, non-cubic equations of state is that proposed by Benedict, Webb and Rubin (1940 1942 1951). It contains eight parameters that are determined from experimental data. Parameter values for several compounds are given by Reid et al. 

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