Benedict, Webb and Rubin equation

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. 

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... 

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)]. 

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... 

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. 

Other pressure—volume—temperature (PVT) relationships may be found in the Hterature ie, Benedict, Webb, Rubin equations of state (4—7) the Benedict, Webb, Rubin, Starling equation of state (8) the Redlich equation of state (9) and the Redlich-Kwong equation of state (10). 

Cubic equations, although simple and able to provide semiquantitative descriptions of real fluid behavior, are not generally useful for accurate representation of volumetric data over wide ranges of T and P. For such appHcations, more comprehensive expressions with large numbers of adjustable parameters are needed. 7h.e simplest of these are the extended virial equations, exemplified by the eight-constant Benedict-Webb-Rubin (BWR) equation of state (13) ... 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

The existing equations of state (i.e., Benedict-Webb-Rubin (BWR), Soave-Redlich-Kwang, and Peng-Robinson) have some practical limitations. The equations of state developed by the University of Illinois... 

Benedict, Manson, Webb, George B., and Rubin, Louis C., An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Then Mixtures, Chemical Engineering Progress, Vol. 47, No. 8, August, 195 I pp. 419-422. 

Presently, sophisticated computer programs are available based on properties published by various scientific organizations. These programs are normally based upon the equations of state derived by Benedict Webb-Rubin [4] and Starling [5] for use with hydrocarbons. Modifit i-... 

The need for methods of accurately describing the thermodynamic behavior of natural and synthetic gas systems has been well established. Of the numerous equations of state available, three--the Soave-Redlich-Kwong (SRK) (19), the Peng-Robinson (PR) (18) and the Starling version of the Benedict-Webb-Rubin (BWRS) (13, 20)--have satisfied this need for many hydrocarbon systems. These equations can be readily extended to describe the behavior of synthetic gas systems. At least two of the equations (SRK and PR) have been further extended to describe the thermodynamic properties of water-light hydrocarbon systems. 

Benedict equation of etate phys chem An empirical equation relating pressures, temperatures, and volumes for gases and gas mixtures superseded by the Benedict-Webb-Rubin equation of state. ben-3,dikt i kwa-zhsn 3v stat ... 

The van der Waals equation is not a particularly accurate tool for prediction of compressibility Z, but it is the first theory to illuminate the nature of the attractive and repulsive forces that lead to departure from the perfect gas law. There are many more accurate equations of state that use more parameters, including the Benedict-Webb-Rubin equation, the Redlich-Kwong equation, and the Peng-Robinson equation. The compressibility factor can also be expanded into the virial form... 

PREDICTIONS BY CORRELATIONS 1 81 And the Benedict-Webb-Rubin equation has many more parameters ... 

Equations of state (detonation and expin), listing of Abel, Allan, Beattie-Bridgeman, Becker, Becker-Kistiakowsky-Wilson, Benedict-Webb-Rubin, Berthelot, Boltzman, Brinkley-Wilson, Caldirola Paterson, Callendar,... 

Other researchers examined the deviations of the Benedict-Webb-Rubin constants with pressure, temperature, and molar volume.12 Equations with as many as 20 empirical constants were developed. Although... 

Other forms of the virial equation of state have been developed for specific compounds and mixtures. For example, the Benedict-Webb-Rubin (BWR) equation, which has eight empirical constants, has been used extensively for light hydrocarbons and other nonpolar gases. Perry s Chemical Engineers Handbook (see footnote 2) describes the BWR equation of state and gives the eight constants for a number of gases on pp. 3-270 to 3-272. 

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