Benedict-Webb-Rubin equation

The Benedict-Webb-Rubin equation (BWR) is an equation of state used in fluid dynamics.

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The original BWR

$P=\rho RT + \left(B_0 RT-A_0 - \frac{C_0}{T^2} \right) \rho^2 + \left(bRT-a\right) \rho^3 + \alpha a \rho^6 + \frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right)$

The BWRS Equation of State

A modification of the Benedict-Webb-Rubin equation of state by Professor Kenneth E. Starling of the University of Oklahoma.

$P=\rho RT + \left(B_0 RT-A_0 - \frac{C_0}{T^2} + \frac{D_0}{T^3} - \frac{E_0}{T^4}\right) \rho^2 + \left(bRT-a-\frac{d}{T}\right) \rho^3 + \alpha\left(a+\frac{d}{T}\right) \rho^6 + \frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right)$

ρ = the molar density

Values of the various parameters for 15 substances can be found in:

K.E. Starling, Fluid Properties for Light Petroleum Systems. Gulf Publishing Company (1973).

References

Benedict, M., Webb, G. B., and Rubin, L. C., "An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures: I. Methane, Ethane, Propane, and n-Butane", J. Chem. Phys., Vol. 8, No.4, pp. 334-345 (1940).

ibid, "II. Mixtures of Methane, Ethane, Propane and n-Butane", J. Chem. Phys., Vol. 10, No. 12, pp. 747 - 758 (1942).
ibid, "III. Constants for Twelve Hydrocarbons", Chem. Eng. Progr., Vol. 47, No. 8, pp. 419-422 (1951).
ibid, "IV. Fugacities and Liquid-Vapor Equilibria", Chem. Engr. Progr., Vol. 47, No. 9, pp. 449-454 (1951).
R.C. Reid, J.M. Prausnitz, B.E. Poling: "The Properties of Gases & Liquids", 4th Ed., McGraw-Hill, New Vork 1987

Category: Equations of fluid dynamics