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| The '''Benedict–Webb–Rubin equation''' ('''BWR'''), named after [[Manson Benedict]], G. B. Webb, and L. C. Rubin, is an [[equation of state]] used in [[fluid dynamics]]. Working at the research laboratory of [[M. W. Kellogg Limited]], the three researchers rearranged the [[Beattie–Bridgeman model|Beattie-Bridgeman Equation of State]] and increased the number of experimentally determined constants to eight.<ref name=bwr1940>{{citation|last1=Benedict|first1=Manson|last2=Webb|first2=George B.|last3=Rubin|first3=Louis C.|title=An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures: I. Methane, Ethane, Propane, and n-Butane|journal=[[Journal of Chemical Physics]]|volume= 8|number=4|page= 334–345|year=1940|issn=0021-9606|doi=10.1063/1.1750658|bibcode = 1940JChPh...8..334B }}</ref><ref>{{citation|url=http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=th&chap_sec=02.4&page=theory|contribution=The Ideal-gas Equation of State|title=Multimedia Engineering Thermodynamics|last2=Huang|first2=Meirong |first1=Kurt|last2= Gramoll|accessdate=May 16, 2012}}</ref>
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| ==The original BWR equation==
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| :<math>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)</math>
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| ==The BWRS equation of state==
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| A modification of the Benedict–Webb–Rubin equation of state by Professor Kenneth E. Starling of the University of Oklahoma:<ref name=starling>{{citation|title=Fluid Properties for Light Petroleum Systems|last=Starling|first=Kenneth E.|publisher=Gulf Publishing Company|year=1973|isbn=978-0872012936|pages=270}}</ref>
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| :<math>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)</math>
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| :''ρ'' = the [[molar density]].
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| Values of the various parameters for 15 substances can be found in Starling's ''Fluid Properties for Light Petroleum Systems.''.<ref name=starling/>
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| ==The Modified BWR equation (mBWR){{anchor|mbwr}}==
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| A further modification of the Benedict–Webb–Rubin equation of state by Jacobsen and Stewart:<ref name=jacobsen>{{citation|first1=Robert C. |last1=Reid|first2=John M.|last2= Prausnitz|first3=Bruce E.|last3=Poling|title=The Properties of Gases & Liquids| edition=4th |publisher=McGraw-Hill|location=New York|date=April 1987|isbn=978-0070517998|pages=741}}
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| *{{citation|first1=Richard T. |last=Jacobsen|first2=Richard B.|last2=Stewart|title=Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63 K to 2000 K with Pressures to 10,000 Bar|journal= Journal of Physical and Chemical Reference Data|doi=10.1063/1.555785|volume=2|number=4|page=757–922 |year=1973|publisher=[[National Institute of Standards and Technology]]|url=http://www.nist.gov/data/PDFfiles/jpcrd39.pdf|format=pdf|issn=0047-2689|doi=10.1063/1.3253132|bibcode = 1973JPCRD...2..757J }}</ref>
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| :<math>P=\sum_{n=1}^{9}a_n\rho^n+\exp\left(-\gamma\rho^2\right)\sum_{n=10}^{15}a_n\rho^{2n-17}</math>
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| where:
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| :<math>\gamma=1/\rho_c^2</math>
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| <br>
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| The mBWR equation subsequently evolved into a 32 term version (Younglove and Ely, 1987) with numerical parameters determined by fitting the equation to empirical data for a reference fluid.<ref name=younglove>{{citation|last1=Younglove|first1=B. A.|first2= J. F. |last2=Ely|title=Thermophysical Properties of Fluids II Methane, Ethane, Propane, Isobutane, and Normal Butane|journal= Journal of Physical and Chemical Reference Data|issn=0047-2689|doi=10.1063/1.555785|volume=16|page=577|year=1987}}</ref> Other fluids then are described by using reduced variables for temperature and density.<ref>{{citation|url=http://repository.tamu.edu/bitstream/handle/1969.1/1094/etd-tamu-2003B-2003062110-Widi-1.pdf|page=11|title=Variation of Density with Composition for Natural Gas Mixtures in the Supercritical Region |date=August 2003|last=Widia|first=B. S.|format=thesis|publisher=[[Texas A&M University]]}}</ref>
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| ==See also==
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| * [[Real gas]]
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| *{{citation|last1=Benedict|first1=Manson|author1-link=Manson Benedict|last2=Webb|first2=George B.|last3=Rubin|first3=Louis C.|title=Mixtures of Methane, Ethane, Propane and ''n''-Butane|journal=[[Journal of Chemical Physics]]|volume= 10|number=12|page= 747–758|year=1942|issn=0021-9606|doi=10.1063/1.1723658|bibcode = 1942JChPh..10..747B }}
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| *{{citation|last1=Benedict|first1=Manson|last2=Webb|first2=George B.|last3=Rubin|first3=Louis C.|title=An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures. '''Constants for Twelve Hydrocarbons'''| journal=Chemical Engineering Progress (CEP)|volume=47|number=8|page= 419–422 |year=1951}}
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| *{{citation|last1=Benedict|first1=Manson|last2=Webb|first2=George B.|last3=Rubin|first3=Louis C.|title=An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures '''Fugacities and Liquid-Vapor Equilibria'''| journal=Chemical Engineering Progress (CEP)|volume=47|number=9|page= 449–454 |year=1951}}.
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| {{DEFAULTSORT:Benedict-Webb-Rubin equation}}
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| [[Category:Equations of fluid dynamics]]
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| {{fluiddynamics-stub}}
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Ed is what individuals contact me and my wife doesn't like it at all. Credit authorising is how she makes a living. The preferred pastime for him and his children is to perform lacross and he would never give it up. I've usually cherished residing in Kentucky but now I'm considering other choices.
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