(551g) Saturation Point Calculations in Reactive Systems Based on the RAND Method

Saturation point calculation and phase envelope calculation belong to the phase fraction specification (β-specification) according to Michelsen’s classification of phase equilibrium calculation. This type of calculation and the flash-type specification form the two most important types of single-stage phase equilibrium calculation. They are central to various process simulation software. The β-specification problems can be used to construct Txy, Pxy and PT phase diagrams. For ordinary non-reactive mixtures, the algorithms for these two types of calculation are well-developed. For reactive mixtures, there are also various stoichiometric and non-stoichiometric methods for the flash calculation of simultaneous chemical and phase equilibrium (CPE). In contrast, there is a lack of reliable and efficient solution to the β-specification problems for a reactive mixture.

In this work, we have developed a RAND-based algorithm for calculating the saturation points and phase envelope of a reactive mixture. The RAND algorithm was a non-stoichiometric flash algorithm originally conceived for single-phase ideal mixtures at constant temperature and pressure. It was recently extended to real mixtures, and also to other types of flash specifications. We showed here how to modify the RAND-based flash formulation for real mixtures to solve the β-specification problems. We distinguished between two types of phase fraction, 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 are essential to pass 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 typical examples (see the attached figure):

• Pxy diagrams for CO₂ solubility in an NaCl brine with ion speciation considered, which is a vapor-liquid equilibrium (VLE) problem modeled by a γ-φ approach;
• a Txy diagram of the solubility of MgCl₂ salts in water with ion speciation and solid formation reactions considered, which is a solid-liquid equilibrium (SLE) problem modeled by a γ model;
• a PT phase envelope for a reactive mixture involving an alkene hydration reaction, which is a VLE problem modeled by a φ-φ approach; and
• a PT phase envelope for a non-reactive hydrocarbon mixture, which is a VLE problem modeled by a φ-φ