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# Benedict-Webb-Rubin equation

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

## 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