Hydrate numbers, n, were directly determined by two methods using a new apparatus, designed to alleviate the occlusion of liquid water in the hydrate crystal and to operate up to 15,000 psi in order to evaluate the pressure dependence of the hydrate composition. Experimental conditions for ethane were 1 18.0 psia at 40.0°F, 119.4 psia at 40.2"F, and 225 psia at 48.9"F. The experimental ethane hydrate numbers were from 7.90 to 8.46 with an average maximum relative uncertainty of &4.24/,. Four sets of experimental conditions were used for methane hydrate: 1030 psia at 5O.O0F, 1032 psia at 50.1 OF, 1901 psia at 59.9"F, and 1902 psia at 60.0"F. The experimental hydrate numbers were from 5.84 to 6.34 with an average maximum relative uncertainty of =t 1 5.6y0. Predictions for n from the solid solution theory of van der Waals and Platteeuw are discussed.

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= density = solution vector for O.D.E. $ Q = Thiele modulus D = spatial region Su bscripts e = equilibrium state o = initial state y z Superscripts * = steady state condition = derivative with respect to y = derivative with respect to zCalculation of fugacities of components in a goseous or liquid solution directly from the corresponding states principle requires an improvement in the pseudo-critical constonts for the mixture. The derivation of the pseudo-criticals must take into account deviations from the simple two parameter corresponding states principle which require additional parameters incorporated into the definition of the pseudo-criticals. I n this work porometers called moleculor shape factors are introduced into the pseudo-criticals. A generalized correlation for these shape factors is presented.Use of the shape factors greatly improves the calculation of vapor-liquid equilibrium ratios for nonpolar hydrocarbon mixtures with large differences in moleculor size and shape. Excellent results are obtained both in the low pressure and in the retrograde region when the pseudo-reduced properties of the vapor and liquid lie within the range of accurately known properties of a reference fluid and the reduced temperatures for each component is greater than opproximotely 0.6.

A new ideal K value is defined which does not depend on the Lewis and Randall ideal solution rule but is derived only from composition dependent pseudo criticals and the corresponding states principle. Properties of the liquid and vapor mixtures are evaluated from either experimentally measured properties of closely related pure substances or from generalized tables of thermodynamic properties. A derivation of an improved pseudocritical expression applicable to liquids which may be approximated by simple spherical molecules is presented. The derivation illustrates the assumptions involved and points the way for a possible extension of the technique to more complex molecules. There are some advantages to this approach. It does not require the troublesome extrapolation of liquid properties into regions where no liquid can exist, a fact which is characteristic of K value calculations from the ideal solution rule. It is especially useful for systems in which an equation of state is not available for all of the components present. It avoids the difficulties in defining combination rules for complicated equations of state. Even for systems including very complex or moderately polar molecules it provides a base for subsequent empirical modification. This base follows the correct isotherm of In K vs. In P up to the actual critical of the system without the difficulties associated with defining a convergence pressure or evaluating the extremely large activity coefficient corrections to the ideal solution rule in the critical region. For mixtures of simple molecules the calculated ideal K value is within about 10% of the experimental value in both the low pressure and in the critical region. The entire calculation may be expressed completely analytically for use on a digital computer and may be coupled with an equilibrium flash calculation so that the ideal K values may be determined from a given overall composition, temperature, and pressure.

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