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Equation of State Primer - Historical Development of the Cubic EOS to Present Day Forms

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Course Credit: 0.15 CEU, 1.5 PDH

The development of the van der Waals (VDW) cubic equation of state (EOS) more than century ago was a watershed moment in the prediction of volumetric, thermodynamic and phase equilibrium properties of fluids. A brief account of the historical contributions to EOS development prior to VDW is offered. The equation proposed by Johannes Diderik van der Waals in his celebrated thesis presented in 1873 at the University of Leiden is then analyzed. A chronological walk through of the most important developments in cubic EOS from the early 1900s to present is summarized. The application of cubic EOS to mixtures and the development of mixing rules are briefly described. Finally, a critical discussion of various EOS parameters including model parameters, characterization parameters, and tuning parameters is presented.

While the VDW EOS provided a description of real gases and the transition to condensed liquid phase, its accuracy suffered beyond simple gases like helium or methane. Today’s current form of cubic EOSs with multiple adjustable parameters could suffer a similar fate when applied “out-of -the-box” to complex mixtures at high-pressures, such as encountered with reservoir fluids.

The proper use of EOS in production measurement and allocation applications is currently being addressed in the development of API MPMS Ch. 20.4 – Phase Behavior Application in Upstream Measurement (of which the author was the founding chair and is now a working group member). The upstream production applications include allocation, multiphase flow meter and virtual flow meter configuration, and assurance of PVT properties derived from surface samples.

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Course Chapters

  • 1Equation of State Primer - Historical Development of the Cubic EOS to Present Day Forms - Chapter 1
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Earn credits by completing this course0.15 CEU credit1.5 PDH credits


Amin AminAmin joined Belsim Engineering in 2018 after 32 years with Schlumberger, where he held operations and management positions in field operations, strategic marketing, and R&D, and 6 Years of engineering consulting specializing in multiphase, wetgas, VFM, production allocation systems, and Data Validation and Reconciliation modeling.

He is an active member of the API Committee on Production Measurement and Allocation (CPMA), Program Chair of SPE Flow Measurement Technical Section (FMTS), and member of ASME PTC DVR Control and Quality Improvement of Process Data.

Amin has Diplôme De Maîtrise from Université de Nice, a Master of Engineering from Supélec-Paris, and a Master of Petroleum Engineering from Heriot-Watt University-Edinburgh. He holds an Executive MBA from the Sloan School of Management-MIT Boston.
Dr. Robbie Lansangan