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\begin{document}

\title{Saturation Point and Phase Envelope Calculation for Reactive Systems Based on the RAND Formulation}



\author[1]{Fernando de Azevedo Medeiros}%
\author[2]{Erling Halfdan Stenby}%
\author[2]{Wei Yan}%
\affil[1]{Affiliation not available}%
\affil[2]{Center for Energy and Resources Engineering, Department of Chemistry, Technical University of Denmark}%


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  \date{May 27, 2024}


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\begin{abstract}
Analysis of multicomponent reactive systems requires reliable and
accurate equilibrium calculation. There are many stoichiometric or
non-stoichiometric methods to solve the flash-type calculations of a
mixture in chemical and phase equilibrium. In contrast, there is a lack
of robust and efficient methods for another important type of
equilibrium calculation, the saturation point calculation or the
calculation under the phase fraction specification (\selectlanguage{greek}β-\selectlanguage{english}specification),
for a reactive mixture. In this work, we developed RAND-based algorithms
for calculating the saturation points and phase envelope of a reactive
mixture. The RAND formulation is a non-stoichiometric approach recently
extended to non-ideal mixtures for different flash specifications. We
showed here how to modify the RAND-based flash formulation to solve the
\selectlanguage{greek}β-\selectlanguage{english}specification problems. We distinguished between two types of phase
fractions, the one based on components and the one based on elements.
They led to different constraint equations in the formulation.
Furthermore, we introduced element-based partition coefficients, similar
to the equilibrium ratios or K-factors used for non-reactive mixtures.
Use of these new variables is essential to cross the critical point of a
reactive mixture in the phase envelope construction. Since the
formulation developed for reactive mixtures is general, it can also be
reduced and used for the simpler non-reactive mixtures. We showed how
the reduction could be made and how the reduced algorithm served as an
alternative approach to the prevailing phase envelope algorithm of
Michelsen. We illustrated the robustness and efficiency of the proposed
algorithm using four examples: Pxy diagrams for CO2-NaCl brine, a
solid-liquid T xy diagram for MgCl2-water, a PT phase envelope for a
reactive mixture with the alkene hydration reaction, and a PT phase
envelope for a non-reactive hydrocarbon mixture.%
\end{abstract}%



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