Introduction Gas hydrates are crystalline ice-like compounds composed of water and natural gas. Until recently studieson hydrates were directed toward preventing their formationin natural gas pipelines. The apparent discovery of natural gas hydrates in arctic regions, and under these a floor, has generated interest in their study as apotential source of clean energy. Hydrates also have been discovered in oil-beating reservoirs. In such reservoirs, the presence of hydrates is important not only as a potential source of free gas, but also in the way they affect oil production. Hydrates will block reservoir poresand will selectively remove high-vapor-pressure components such as methane, thus increasing oil viscosity and reducing the driving force for oil production. The existence of hydrates in the earth, therefore, has diverse implications. Recent estimates indicate that as much as 10(18) m3 of natural gas could exist as in-situhydrates. While there is no certainty that hydrated gascan be produced economically, the potential of thisresource clearly demands evaluation. This paper examines the potential for recovering gasfrom naturally occurring hydrates. Factors to be considered in such a study arelocation of the hydratefields,purity of hydrates in the reservoir,types of media in which hydrates form,thermodynamic conditions of temperature, pressure, and composition, andthermal properties of the reservoir. Based on these considerations, calculations were made to determine the energy needed to dissociate hydrates and the amount of gas recovered per gmol of hydrate dissociated. Nature of Gas Hydrates Two strictures of gas hydrates called structures 1 and 2 are known to form from mixtures of water and light gases. Each of these structures has two approximatelyspherical cavities of different diameters (Table 1). Not all the cavities need be occupied by gas molecules toproduce a stable hydrate, but a completely unoccupied lattice phase is metastable and does not exist. The thermodynanmic behavior of gas hydrates isillustrated by the phase diagram for methane/propane/water hydrate-forming mixtures(Fig. 1). A gas of anyindicated composition will form hydrates at pressure/ temperature points above the corresponding curve. Below the curve, hydrates will decompose, high pressure and low temperature favor hydrate formation. The enthalpy of formation of gas hydrates from waterand free gas can be approximated by a modification ofthe Clapeyron equation. dlnpH =Z RT2 -----...............................(1)Diss dT The derivative dlnp/dT is the slope of the semilogarithmic p - T graph shown in Fig. 1. Calculation of the enthalpy of formation is important because it gives the energy required to dissociate the hydrates. The hydrates that form in the earth are likely to be Structure 1 hydrates only when pure methane is present. Structure 2 hydrates generally will form in the presence of even small quantities of heavier gas constituents, suchas propane. The amount of gas in the hydrate does notgenerally depend on the structure; Structure 1 has one cavity for every five and three-fourths water molecules and structure 2 has a cavity for every five and two-thirds water molecules. Occupation of all the cavities of either structure results in a maximum gas concentration, 15%, in the hydrate phase. Table 2 shows the calculated composition of the hydrate that would be in equilibrium witha natural gas containing 97% methane, 2% ethane and 1 % propane. As this table indicates, the hydrate phase gas composition depends on the formation temperature. JPT P. 1127^

Temperature associated with the logitudinal thermal velocities overshoots for M1 > (9/5)½ for monatomic gases. The overshoot and the location of the maximum temperature are functions of M1.

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The non-linear Boltzmann equation has been solved for shock waves in a gas of elastic spheres. The solutions were made possible by the use of Nordsieck's Monte Carlo method of evaluation of the collision integral in the equation. Accurate solutions were obtained by the same method for the whole range of upstream Mach numbers M^ from 1.1 to 10 even though the corresponding degree of departure from equilibrium varies by a factor greater than 1000. Many characteristics of the internal structure of the shock waves have been calcu lated from the solutions and compared with Navier-Stokes, Mott-Smith and Krook descriptions which, except for low Mach numbers, are not based upon the Boltz mann equation itself. Among our conclusions are the following: 1. The reciprocal shock thickness is in agreement with that of the 2 Mott-Smith shock (u-moment) from M^ of 2.5 to 8. The density profile is asymmetric with an upstream relaxation rate (measured as density change per mean free path) approximately twice as large as the downstream value for weak shocks and equal to the downstream value for strong shocks. 2. The temperature density relation is in agreement with that of the Navier-Stokes shocks for the lower Mach numbers in the range of 1"1 to 1.56. The Boltzmann reciprocal shock thickness is smaller than the Navier-Stokes value at this range of Mach number because the viscosity-temperature relation computed is not constant as predicted by the linearized theory. 2 3. The velocity moments of the distribution function are, like the Mott-Smith shock, approximately linear with respect to the number density; however, the deviations from linearity are statistically significant. The four functionals of the distribution function discussed show maxima within the shock. 4. The entropy is a good approximation to the Boltzmann function for all M^. The solutions obtained satisfy the Boltzmann theorem for all Mach numbers. The increase in total temperature within the shock is small, but the increase is significantly different from zero. 5. The ratio of total heat flux q to (associated with the longi tudinal degree of freedom) correlates well with local Mach number for all M^ in accord with a relation derived by Baganoff and Nathenson. The Chapman-Enskog linearized theory predicts that the ratio is constant. The (effective) transport coefficients are larger than the Chapman-Enskog equivalents by as much as a factor of three at the mid-shock position. 6. At M 1=4, and for 40% of velocity bins, the distribution function is different from the corresponding Mott-Smith value by more than three times the 90% confidence limit. The rms value of the percent difference, in distribu tion function is 15% for this Mach number. The halfwidth and several other characteristics of the function Jfdw^dvz differ from that of the Chapman-Enskog first iterate, and many of the deviations are in agreement with an experiment by Muntz and Harnett. 7. The ratio of the collision integral (found from our solution of the Boltzmann equation) to that calculated from Mott-Smit...

The nonlinear Boltzmann equation has been solved for shock waves in a Max-wellian gas for eight upstream Mach numbers M1 ranging from 1·1 to 10. The numerical solutions were obtained by using Nordsieck's method, which was revised for use with the differential cross-section corresponding to an intermolecular force potential following an inverse fifth-power law. The accuracy of the calculations of microscopic and macroscopic properties for this collision law is comparable with that for elastic spheres published earlier (Hicks, Yen & Reilly 1972).We have made comparisons of the detailed characteristics of the internal shock structure in a Maxwellian gas with those in a gas of elastic spheres. The purpose of this comparative study is to find the shock properties that are sensitive as well as those which are insensitive to the change in collision law and to find effective ways to study them.The variation of thermodynamic and transport properties of interest with respect to density and to each other was found to depend only weakly on the change in collision law. The principal effect on the macroscopic shock structure due to the change in intermolecular potential is in the spatial variation of the macroscopic properties. The spatial variation of macroscopic properties may be determined accurately from the corresponding moments of the collision integral, especially in the upstream and downstream wings of the shock wave. The results for the velocity distribution function exhibit the microscopic shock characteristics influenced by a difference in intermolecular collisions, in particular the departure from equilibrium in the upstream wing of the shock and the relaxation towards equilibrium in the downstream wing. The departure of several characteristics of weak shock waves from those of the Chapman-Enskog linearized theory and the Navier-Stokes shock is also insensitive to the change in collision law. The deviation of the half-width of the function ∫fdvyduz from the Chapman-Enskog first iterate at M1 = 1·59 is in agreement with an experiment (Muntz & Harnett 1969).