Benedict-Webb-Rubin BWR Equation

Attempts have been made to correlate the BWR parameters in terms of the critical temperature, critical pressure, and acentric factor. The equation is thus reduced essentially to a three-parameter function, not necessarily more accurate than the cubic equations. 

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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) ... 

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. 

Benedict-Webb-Rubin (BWR) equation (see Table 3.2) gives the following for... 

The extended virial equations are made up of a truncated virial series followed by a closure term or terms, hi the Benedict-Webb-Rubin (BWR) Equation (4.177), the closure term is an exponential. 

From above, the propane circulation rate is 5,400 Ib/hr. Again, we estimate enthalpies and entropies from a modified Benedict-Webb-Rubin (BWR) equation of state, which gives... 

No chemical engineer has ever relied on directly measured values for all the thermodynamic properties he uses. It is one of the great virtues of classical thermodynamics (indeed, it has been said that it is its only virtue ( )) that it allows us to calculate one physical or chemical property from another, for example, a latent heat of evaporation from the change of vapour pressure with temperature. Less obvious, but almost equally secure calculations can be made by fitting measured values to an empirical equation and calculating other properties by a subsequent manipulation of that equation. Thus we can fit the pressure of a gas to a Redlich-Kwong (RK) or Benedict-Webb-Rubin (BWR) equation, from which the other properties such as changes of enthalpy and entropy are then derived. Similarly we fit activity coefficients to Wilson s equation and calculate K-values. 

Benedict-Webb-Rubin (BWR) equation of state An extended virial equation of state used to describe the vapour-liquid equilibrium data of various substances in terms of molar density. The equation feamres eight constants for which published data is available for numerous hydrocarbons. The Lee-Kesler equation of state is an extended form of the BWR equation of state. 

Within these restrictions, the average absolute deviation for 1345 data points equals 7.9%, as compared to 7.7% for the Benedict-Webb-Rubin (BWR) equation. The method fails, however, in the convergence region as demonstrated in Figure 14.6. 

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... 

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. 

The original Virial EOS was applicable only to the gas phase. This limitation incited the development of extended forms, as the Benedict-Webb-Rubin (BWR) correlation (equation 5.5). This equation may contain sophisticated terms with a large number of parameters, mostly between 10 and 20, and need substantial experimental data for tuning. The extended Virial-type EOS s have lost much of their interest after the arrival of various cubic EOS in the last decades. Some formulations are still used for special applications, notably in gas processing and liquefaction, as BWR-Lee-Starling (BWR-LS) equation, one of the most accurate for hydrogen rich hydrocarbon mixtures. Note that extended Virial EOS may calculate not only volumetric properties, but also VLE. 

Repeat Example 1.2 by using the Benedict-Webb-Rubin (BWR) and the Patel-Teja (PT) equations of state. Compare the results with those obtained in Example 1,2,... 

Benedict/Webb/Rubin Equation of State The BWR equation of state with Z as the dependent variable is written... 

Cubic equations of state are useful because they are capable of handling both liquids and gases, but they are not the only type of equations that have this feature. The mathematical requirement is that subcritical isotherms must exhibit the characteristic h-shaped portion, with an unstable part between the liquid and vapor branches. This behavior can be reproduced by other equations that are not necessarily cubic in Z. One that is worth mentioning is the Benedict-Webb-Rubin equation (BWR), which has the form. 

Benedict, Webb, Rubin method BWR equation" Equation with 8 constants dependent on mixture concentration. Originally developed for light hydrocarbons, but modified and validity region expanded Benedict, M., Webb, G. B., Rubin, L. C., J Chem. Phys. 8 (1940) 334. Bender, E., Habilitationsschrift, Ruhr-universitat Bochum. Orye, R.V., Ind. Eng. Chem. Des. Dev. 8 (1969) 4, 579. 

Equation (0.3), also called the Benedict-Webb-Rubin equation, contains eight constants and is recommended for the evaluations of thermodynamic properties of little known gaseous freons and their mixtures [0.23, 0.39]. Normally, for the calculations of thermodynamic tables and diagrams, complicated variations of the BWR equation are employed. In Table 1, two modifications of an equation of this type with 11 constants are given. Equation (0.4) was proposed by Morsy [0.42] and Eq. (0.5) by Starling [0.48]. 

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 ... 

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. 

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