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A Collection of Analytical Solutions for the Flash Equilibrium Calculation Problem

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Abstract

We describe an interesting family of closed-form solutions for the flash equilibrium calculation problem. These solutions can be used as benchmark solutions for verification of numerical solvers of the flash equilibrium problem for multicomponent mixtures. To obtain a problem possessing an analytical solution, we consider a special form of the free energy. Although this form of the free energy is artificial, it captures qualitatively several features that are present in the realistic cases too. The procedure is first illustrated on a 1-D two-phase case and is further generalized to multicomponent mixtures in two and more phases, and also to a problem including the capillary pressure effect.

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Notes

  1. If X is an arbitrary subset of \(\mathbb {R}^n\), then any point \(\mathbf x\) from the convex hull of X can be written as a convex combination of at most \(n+1\) points in X, i.e., there exist \(\mathbf{x}_1,\dots ,\mathbf{x}_{n+1}\in X\) and \(\alpha _1,\dots ,\alpha _{n+1}\ge 0\) such that \(\mathbf{x}=\sum \nolimits _{i=1}^{n+1}\alpha _i\mathbf{x}_i\) and \(\sum \nolimits _{i=1}^{n+1}\alpha _i=1\). The proof can be found in Rockafellar (1970).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00, Prague 2, Czech Republic

    Jiří Mikyška

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  1. Jiří Mikyška
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Correspondence to Jiří Mikyška.

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The research has been supported by the Project No. 17-06759S (Investigation of shallow subsurface flow with phase transitions) of the Czech Science Foundation.

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Mikyška, J. A Collection of Analytical Solutions for the Flash Equilibrium Calculation Problem. Transp Porous Med 126, 683–699 (2019). https://doi.org/10.1007/s11242-018-1160-9

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