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11: Cubic EOS and Their Behavior III

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    Learning Objectives

    • Module Goal: To demonstrate thermodynamic quantification using modern cubic EOS.
    • Module Objective: To assess the relative merit of applying the most common EOS.

    • 11.1: Peng-Robinson EOS (1976)
      The Peng-Robinson EOS has become the most popular equation of state for natural gas systems in the petroleum industry.  A slightly better performance around critical conditions makes the PR EOS somewhat better suited to gas/condensate systems.
    • 11.2: Comparative Assessment of RK, SRK, and PR EOS
      Over the years, these EOS have been tested, and some comparisons can be made. As an engineer, you have to be able to decide which EOS best fits your purposes.
    • 11.3: Critical Compressibility as a Measure of Goodness of an EOS
      The fact of the matter is, as a consequence of the Corresponding States Principle, all cubic EOS predict a “unique” and “universal” value of Z at the critical point, regardless of the substance. None of the equations of state we have studied is capable of predicting a value similar to experimental values. The “best” job is done by PR EOS, which provides the “closest” match to the real values observed for most substances. This illustrates why the PR EOS performs somewhat better near critical cond
    • 11.4: Advantages of Using Cubic Equations of State
      All cubic equations of state have their foundation in vdW EOS. The use of cubic equations of state has become widespread because of their advantages: (1) Simplicity of application, (2) Only a few parameters need to be determined, and (3) Low computational overhead is required to implement them. This was a critical issue, particularly in the early stages of computers; it is not really anymore. Nevertheless, this feature is still a “plus.”
    • 11.5: Solution Techniques for Cubic Expressions and Root Finding
      Even though cubic equations of state are explicit in pressure, pressure is not the common unknown to be calculated in the typical problem. In the most common problem, pressure and temperature are known and we want either molar volume (or its reciprocal, molar density) or compressibility factor (the most likely case). Therefore, we are faced very often with the need to solve for the roots of a cubic expression. Here we present a number of approaches that may be followed.
    • 11.6: Action Item

    11: Cubic EOS and Their Behavior III is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Michael Adewumi (John A. Dutton: e-Education Institute) via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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