Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

Abstract

The thermodynamic stability of clathrate hydrate is calculated under a wide range of temperature and pressure conditions applicable to solar system problems, using a statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data on properties of clathrate hydrates and their components. At low pressure, dissociation pressures and partition functions (Langmuir constants) for CO clathrate (hydrate) have been predicted, using the properties of clathrate containing, as guests, molecules similar to CO. The comparable or higher propensity of CO to incorporate in clathrate relative to N 2 is used to argue for high CO-toN 2 ratios in primordial Titan if N 2 was accreted as clathrate. The relative incorporation of noble gases in clathrate ~rom a solar composition gas at low temperatures is calculated and applied to the case of giant-planet atmospheres and icy satellites. It is argued that nonsolar but well-constrained noble gas abundances will be measured by Galileo in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances in Titan's atmosphere are also predicted under the hypothesis that much of the satellite's methane accreted as clathrate. Double occupancy of clathrate cages by H 2 and CH 4 in contact with a solar composition gas is exaniined, and it is concluded that potentially important amounts of H 2 may have incorporated in satellites as clathrate. The kinetics of clathrate formation is also exaniined, and it is suggested that, under thermodynamically appropriate conditions, essentially complete clathration of water ice could have occurred in high-pressure nebulae around giant planets but probably not in the outer solar nebula; comets probably did not aggregate as clathrate. At moderate pressures, the phase diagram for methane clathrate hydrate in the presence of 15% ammonia (relative to water) is constructed, and application to the early Titan atmospheric composition is described. The high-pressure stability of CH 4 , N 2 , and mixed CHc N 2 clathrate hydrate is calculated; conversion back to water and CH 4 and/ or N 2 fluids or solids is predicted for pressures ~ 12 kilobars (independent of temperature) and temperatures ~ 320 K (independent of pressure). The effect of animonia is to shrink the T-P stability field of clathrate with increasing animonia concentration. These results imply that (1) clathrate is stable throughout the interior of Oberon-and Rhea-sized icy satellites, and (2) clathrate incorporated in the innermost icy regions of Titan would have decomposed, perhaps allowing buoyant methane to rise. Brief speculation on the implications of this conclusion for the origin of surficial methane on Titan is given. A list of suggested experiments and observations to test the theory and its predictions is presented.

Volatile inventories in clathrate hydrates formed in the primordial nebula

“…We calculate here the relative abundances of guests that can be incorporated in H 2 S, Xe, CH 4 comets. 54 Thomas et al 52 did a comprehensive comparison between these two sets Figure 2 represents the mole fraction f (Eq.…”

“…54 Thomas et al 52 did a comprehensive comparison between these two sets Figure 2 represents the mole fraction f (Eq. 5) of volatiles encaged in structure I and structure II clathrates a priori dominated by H 2 S, Xe, CH 4 and CO and formed in the primordial nebula. Interestingly enough, this figure shows that, contrary to H 2 S, Xe and CH 4 , which remain the dominating guest species in the clathrates considered, CO becomes a minor compound in the clathrate that is expected to be dominated by this molecule.…”

“…[4][5][6][7][8] Moreover, it has been suggested that the activity observed in some cometary nuclei results from the dissociation of these crystalline structures. 9 Generally speaking, clathrates probably participated in the formation of planetesimals in the solar system.…”

“…Thus, clathrates may have been accreted in comets, in the forming giant planets and in their surrounding satellite systems. 4,[12][13][14][17][18][19][20][21][22][23][24] During the twentieth century, many theoretical and experimental studies allowed This approach, used today in the industry and in science, has saved substantial experimental efforts for the determination of i) the equilibrium pressure of a clathrate formed from various mixtures and ii) the mole fraction of the different species trapped in the clathrate from a given fluid phase.…”

On the volatile inventory of Titan from isotopic abundances in nitrogen and methane

“…Methane is soluble enough in the liquid that substantial quantities could be stored in the interior inde®nitely. Even in the absence of such an ammonia±water liquid mantle, methane can be stored in the water ice as clathrate hydrate up to pressures of at least 5 kilobars (Lunine and Stevenson, 1985). Molecular nitrogen is not nearly as soluble in water±ammonia liquid or in the clathrate hydrate.…”