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Villards Rule:The dissociable (hydrate) compounds, that form through the unification of water with different gases

and that are only stable in the solid form, all crystallize regularly and have the same constitution that

can be expressed by the formula M + 6H2O, where M designates a molecule of the respective gas

Note that if a guest fills all of both cavities in sI and sII, the hydration number would be 5.75 and5.67, respectively,

so a value of 6 allows for the possibility of empty cages, and is frequently taken as a goodapproximation to the hydration number for methane hydrates.

However, Villards Rule is not a good approximation for components that only fill the large cavityof either sI (e.g., ethane) or sII (e.g., propane).

Using the Clapeyron equation

This method was originally proposed by de Forcrand Heat of fusion of ice is known so n can be calculated by dividing H3 by heat of fusion of ice The de Forcrand method has been found to be much more accurate than Villards Rule.

Hydration numbers by the Miller and Strong method

applicable when simple hydrates were formed from a solution with an inhibitor, such as a salt. The thermodynamic reaction equilibrium constant K, is only a function of temperature. At a given temperature, if an inhibitor such as a salt is present, the activity of the water

decreases and the activity of the gas must increase in order to maintain a constant product K

n may be obtained from a measurement of the increase of the hydrate pressure with aninhibitor present at a given temperature.

Assumptions involved in the Miller and Strong method

1) The occupation of the hydrate does not change over the region of pressure and temperatureconsidered.

2) The equilibrium constant K does not change when the inhibitor is added to the aqueous fluid,but it is only a function of temperature.

3) The activity of the hydrate phase is constant at a given temperature regardless of the otherphases present.

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4) The vapor presence of any component other than the hydrate former may be neglected,including any water or inhibitor present in the liquid.

5) The aqueous phase without inhibitor is pure water.

Wilms and van Haute (1973) presented the mathematically correct version of the Miller and Strong

method, which eliminates some of the assumptions, together with the statistical thermodynamic

method of the following chapter.

Wilms and van Haute suggest the Miller and Strong equations to be a special case of a more rigorous

method.