The Benedict-Webb-Rubin Equation of State

An equation of state that can be extended to reasonably high densities was developed by Benedict et al in 1940. The Benedict-Webb-Rubin equation of 

This equation has eight empirical constants Aq, Bq, Cq, a, b, c, a and y. Values for these constants were reported by Benedict et al for 12 hydrocarbons. The Benedict-Webb-Rubin equation was the first equation of state that used an exponential term in density to extend the capabilities of simple polynomial expansions and is thus considered the ancestor of almost all modern equations of state. 

In 1962, Strobridge extended the BWR equation of state using the form 

The Benedict-Webb-Rubin equation and its simple modifications yield sufficiently precise representation of the thermodynamic surface for typical technical applications in the gas phase and at supercritical states with low and medium densities. However, estimates of energy at liquid or liquid-like supercritical states may be in error by more than 10 %. These simple equations are unable to provide precise estimates for what are called both scientific and advanced technical applications. 

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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. 

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of etate phys chem An empirical equation relating pressures, temperatures, and volumes for gases and gas mixtures superseded by the Benedict-Webb-Rubin equation of state.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 development of mixture rules will be discussed in detail in connection with the Benedict-Webb-Rubin equation of state. 

More recently, Ustinov and coworkers [72, 73] developed a thermodynamic approach based on an equation of state to model the gas adsorption equilibrium over a wide range of pressure. Their model is based on the Bender equation of state, which is a virial-like equation with temperature dependent parameters based on the Benedict-Webb-Rubin equation of state [74]. They employed the model [75, 76] to describe supercritical gas adsorption on activated carbon (Norit Rl) at high temperature, and extended this treatment to subcritical fluid adsorption taking into account the phase transition in elements of the adsorption volume. They argued that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of He expansion at room temperature can lead to erroneous results due to the adsorption of He in narrow micropores of activated carbon. 

CONSTANTS AND MODIFICATIONS OF THE BENEDICT-WEBB-RUBIN EQUATION OF STATE... 

A provisional thermodynamic network has been derived [ ] from spectroscopic and P-F-T data by use of an extension of the Benedict-Webb-Rubin equation of state developed by Strobridge [ ]. The range is 20 to 100°K on isobars from 1 to 340 atm. Older P-F-T data for normal hydrogen were used to extend the range to 300°K at pressures up tb 100 atm. The entire set of computations was repeated to obtain tables at uniform values of British engineering units as well. Users should obtain an errata sheet for all internal energies of... 

Computers have greatly reduced the effort and increased the calculation speed. They easily produce the necessary repetitive evaluations required to satisfy simultaneously the material and heat balances and equilibrium relationships. In computerized calculations, the selection of the equation of state influences the number of calculated theoretical stages required. Each equation of state was developed primarily from a specific data bank that usually was confined to a certain type of compound. As an example, the Benedict-Webb-Rubin equation of state was developed from experimental data on methane through n-heptane [8]. This equation is preferred to generate K values for these light hydrocarbons. The equation of state specified for the calculations should be the one based on data for compotmds most closely resembling those being separated. 

Lin, M.-S., and Naphtali, L. M. Prediction of vapor-liquid equilibria with the Benedict-Webb-Rubin equation of state. A. I. Ch. E. J. 9 (1963) 580. 

Some of the equations of state discussed above are applicable to liquids as well as gases. For example, the Benedict-Webb-Rubin equation of state provides reasonable estimates for most hydrocarbons. The generalized compressibility charts that will be discussed in the next section are based on an extension of this equation of state and can be used for both gas and liquid phases. Alternatively, correlations have been developed explicitly for the liquid phase. For example, the liquid volume at saturation is given by the Rackett equation ... 

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