We have developed a new model for compressible clathrates that extends the well-known van der Waals and Platteeuw model. The new model is derived by dispensing with the assumption of constant cages radii in the partition function level, resulting in new thermodynamically consistent expressions relating thermodynamic properties of the hydrate phase and the empty lattice isochoric reference. One set of additional parameters to the clathrate modeling framework is introduced, consisting of a scaling factor for each cage radius relative to the edge length of the unit cell. No additional guest-dependent empirical parameters are required. The model exhibits two features not previously reported in the literature: (i) a pressure shift between the clathrate being described and the empty lattice isochoric reference, and (ii) differences in the edge length of the unit cell and in the cages radii for different guest species at the same temperature and pressure, as a consequence of the sorption of guests. We also propose a test for thermodynamic consistency at high pressure, based on the multicomponent and multiphase Clapeyron equation. Using this test, we show that the proposed model solves an inconsistency issue observed in phase equilibrium calculations with some of the compressible clathrate models currently in use. We have performed parameter optimization for methane, ethane, and xenon in sI hydrates. Two sets of results are presented: 3-phase equilibrium conditions; and lattice size versus temperature or pressure for each of these substances, along with available experimental data.

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 (β-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 β-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.

Diverse engineering fields request flash calculations like isothermal flash, isenthalpic flash, and isentropic flash. They can be cast as minimization of a thermodynamic state-function and solved by Michelsen’s Q-function approach. Flash calculations for open systems, i.e. systems where chemical potentials are specified instead of the mole numbers for some components, also belong to this scope. By analyzing the construction of Q-functions through Legendre transforms, we extend this approach to the flash for open systems in the absence or presence of chemical reactions, resulting in general formulations for various specifications. For systems without reactions, the classical framework using mole numbers as independent variables is employed; for those with reactions, the modified-RAND framework is employed. We present examples for open systems at constant temperature and pressure. Using the Q-function minimization, we can solve multicomponent non-reactive or reactive systems at a specified chemical potential with quadratic convergence over a wide range of conditions.