VdWP theory

Robinson begins 30 year hydrate research effort with study of paraffin/olefin hydrates 1963 McKoy and Sinanoglu apply Kihara potential to vdWP theory... 

Kobayashi and coworkers apply vdWP theory to mixtures... 

Parrish and Prausnitz apply vdWP theory to natural gases... 

John and Holder determine effect of higher order coordination shells in vdWP theory... 

Mehta obtains sH data, applied vdWP theory to CH4 + large (>8 A) guest(s)... 

Figure 2. Dissociation pressure of ethane hydrate at 273.15 K. Solid, dashed, and dash-dot lines show the dissociation pressures for the nonspherical guest evaluated by anharmonic and harmonic free energy, for spherical guest molecule evaluated by only harmonic free energy, and for spherical guest according to the original vdWP theory, respectively. The horizontal lines show the chemical potential difference between ice and empty hydrate, dashed harmonic-t-anharmonic, dotted harmonic.

It is assumed in the vdWP theory[12] that (1) the cage structure is not distorted by the incorporation of guest molecules, (2) the partition function is independent of the occupation of other cages, (3) the guest molecule inside a cage moves in the force field created by water molecules fixed at lattice sites and there is no coupling between host and guest molecular motions, and (4) that classical mechanics is adequate to describe these systems. 

In the current study we are mainly interested in describing the gas solubility in pure water, under two-phase equihbrium (H-Lw) conditions. Gases of interest to this study include methane and carbon dioxide, and we report results mainly for the case of methane. To this purpose we couple different published thermodynamic models that are based on (i) the van der Waals-Platteeuw (vdWP) theory [9, 10] from Statistical Thermodynamics to describe three-phase (H-Lw-V) equihbria, (ii) Equations of State (EoS) for fugacity calculations, and (iii) models of gas solubihty in the aqueous phase. The considered approach is described in detail by Tsimpanogiannis et al., [11]. The authors conducted an extensive review of experimental and theoretical studies related to the solubility of gases in the aqueous phase under hydrate equilibrium conditions. Here, we report additional results that were not included in the original publication. 

As discussed in detail by Tsimpanogiannis et al., [11] the correlation of Lu et al., [18] is in very good agreement with the experimental data and the ealculations reported by Tsimpanogiarmis et al., [11] based on the vdWP theory. 

In 1958, van der Waals and Platteenw developed a statistical mechanical theory for predicting the stability region of the clathrate hydrate phase with different guest molecules under different temperature and pressure conditions. The van der Waals-Platteeuw (vdWP) theory is based on the thermodynamic condition of equilibrium between a hydrate phase water/ice ()8) phase and i guest species encapsulated in the hydrate at the phase boundary ... 

The strength of the vdWP theory is its ease of use and the speed with which predictions of the clathrate hydrate phase diagram can be generated. If the scope of validity of this theory is recognized, it can be a valuable tool in the hand of researchers in predicting hydrate stability conditions. 

B. Phase Equilibrium and the vdWP Theory for Mnltiple Occupation at High Pressure... 

C. vdWP Theory with a Reference State of the Fnlly Occupied Cages... 

D. vdWP Theory Under a Limited Amount of a Guest Species Highly Affinitive to Clathrate Hydrate... 

D. Estimation of Stability at High Pressures by the Extension of the vdWP Theory... 

Thermodynamic properties of clathrate hydrates have been calculated by the van der Waals and Platteeuw (vdWP) theory [16]. It has been applied to predicting... 

We will, hereafter, refer exclusively to the latter method based on the vdWP theory and its extensions by removing the assumptions imposed on the original theory. The original vdWP theory relies on the assumptions that firstly each cage... 

The vdWP theory with a set of the independent variables necessarily requires semipermeable membrane to separate water from the guest fluid, hence the pressure Pg of the fluid phase is different in general from the pressure p of the hydrate phase. The appropriate thermodynamic potential is derived in Section II.B. In the light of the phase rule and the experimental conditions, it is desirable to alternate the ensemble to meet the thermodynamic potential F [30,31]. The partition function S is converted into the generalized partition function T as... 

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