Iuri Soter Viana Segtovich
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Fernando de Azevedo Medeiros
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Frederico Wanderley Tavares
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.