Benedict-Webb-Rubin- Starling

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). 

Soave-Redlich-Kwong, Peng-Robinson, Benedict-Webb-Rubin, Starling, Lee-... 

There are many types of EOS with a wide range of complexity. The Redlich-Kwong (RK) EOS is a popular EOS that relies only on critical temperatures and critical pressures of all components to compute equilibrium properties for both liquid and vapor phases. However, the RK EOS does not represent liquid phases accurately and is not widely used, except as a method to compute vapor fugacity coefficients in activity-coefficient approaches. On the other hand, the Benedict-Webb-Rubin-Starling (BWRS) EOS [6] has up to sixteen constants specific for a given component This EOS is quite complex and is generally not used to predict properties of mixture with more than few components. 

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. 

The equation-of-state form used herein is the modified Benedict-Webb-Rubin (MBWR) equation as given by Han and Starling (7). It is reformulated into the form of Equation 26 by expressing the constants appearing linearly in the equation into two parts—one isotropic part and one anisotropic part,... 

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. 

This equation improves the liquid density prediction, but still cannol describe volumetric behavior around the critical point because of fundamental reason that will be discussed later. There are thousands of cubic equations of states, and many noncubic equations. The non cubic equations such as the Benedict-Webb-Rubin equation (1942) ant its modification by Starling (1973) have a large number of constants they describe accurately the volumetric behavior of pure substances But for hydrocarbon mixtures and crude oils, because of mixing rub complexities, they may not be suitable (Katz and Firoozabadi, 1978) Cubic equations with more than two constants also may not improv the volumetric behavior prediction of complex reservoir fluids. In fact most of the cubic equations have the same accuracy for phase-behavio prediction of complex hydrocarbon systems the simpler equation often do better. Therefore, the discussion will be limited to the Peng... 

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]. 

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 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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