Hydrate limits to gas expansion through a valve

To what pressure may a 0.6 gravity gas at 13.8 MPa (2000 psia) and 311 K (100°F) be expanded without danger of hydrate formation  

6 gravity gas is to be expanded from 10.34 MPa (1500 psia) to 3.45 MPa (500 psia). What is the minimum initial temperature that will permit the expansion without danger of hydrates  

and the statistical thermodynamic method of van der Waals and Platteeuw (1959a) was substituted for the three-phase hydrate line prediction by the gas gravity chart of Katz. 

The distribution coefficient method, often called the A -value method, was conceived by Wilcox et al. (1941) and finalized by Carson and Katz (1942). The best methane, ethane, and propane charts are from the latter reference. Updated charts are presented for carbon dioxide (Unruh and Katz, 1949), hydrogen sulfide (Noaker and Katz, 1954), nitrogen (Jhaveri and Robinson, 1965), isobutane (Wu et al., 1976), and n-butane (Poettmann, 1984), as well as for a method that is a function of hydrate structure (Mann et al., 1989). 

Carson and Katz noted that their experimental hydrate composition changed at different temperatures and pressures in a manner indicative of a solid solution of mixtures, rather than segregated macroscopic quantities of pure hydrocarbons within the hydrate. The concept of a solid solution enabled the notion of the mole fraction of a guest component in the solid phase hydrate mixture, on a water-free basis. Carson and Katz defined a vapor-solid distribution coefficient (KVSi) for each component as 

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