Explicit pressure dependence of the Langmuir adsorption constant in the van der Waals–Platteeuw model for the equilibrium conditions of clathrate hydrates

In this work, we propose a new pressure- and temperature-dependent Langmuir adsorption constant for the modeling of the phase boundary of clathrate hydrates over a wide range of conditions. The proposed Langmuir adsorption constant is designed to produce a reduced free volume available to the encapsulated gas molecules as the pressure increases. We show that the combination of a cubic equation of state and the van der Waals–Platteeuw model with this new Langmuir model can be used to describe various types of three phase coexisting conditions of gas hydrates, from vapor–ice–hydrate equilibrium (VIHE) at low temperatures, to vapor–liquid–hydrate equilibrium (VLHE) at higher temperatures, and to liquid–liquid–hydrate equilibrium (LLHE) at high pressures, using a single set of parameters. The average relative deviations in the equilibrium pressure are found to be 4.57% for 12 pure gas hydrates over a large range of temperatures (148.8–323.9 K) and pressures (5.35 × 102 Pa to 8.27 × 108 Pa). Furthermore, the retrograde behavior observed in CH4, CO2, C3H8, and i-C4H10 pure gas hydrate systems can all be successfully modeled by the change of free volume at high pressures. We believe that this method is useful for many gas hydrates related the multiple three-phase regions.