Automatic Fitting of Equations of State for Phase Behavior Matching Available to Purchase

Phase behavior modeling of a reservoir hydrocarbon mixture through an equation-of-state, EOS, is preceded by the adjustment of some of the parameters in the equation so as to reproduce measured PVT data of the mixture. In this paper we propose a methodology for the automatic fitting of EOS parameters for phase behavior matching.

Critical properties of the heaviest, C⁺, fraction are obtained from available correlations and fitting of EOS parameters, $Ωa0$ and $Ωb0$⁠, for CH₄ and C⁺ as well as of the binary interaction coefficient, $δCH4−C+$⁠, are performed according to the following procedure: First, keeping the theoretical values of $Ωa0$ and $Ωb0$⁠, we calculate the interaction coefficient $δCH4−C+$ that matches the saturation pressure of the mixture. In a second step, the parameters $Ωa0$ and $Ωb0$ for the CH₄ and C⁺ fractions are fitted through a non-linear least squares regression technique to match PVT experimental data in the one-phase region. Peculiarities of the system of equations produced by the fitting algorithm are discussed; proper solution techniques are discussed as well.

The above procedure was used to adjust the Peng-Robinson EOS to four reservoir hydrocarbon fluid samples, which include gas condensate. Phase behavior in the two-phase region predicted with the EOS was verified to match PVT laboratory data obtained under flash and differential liberation processes. It was verified that the interaction coefficient, $δCH4−C+$ is the relevant parameter for saturation pressure matching. Analysis of regressed parameters indicate, in all four applications, that relevant parameters in the non-linear regression fitting are $Ωa0$ and $Ωb0$ of the CH₄, fraction.