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where i is either water or carbon dioxide for the system in consideration. Using the equilibrium composition of the hydrate (i.e. also taking into account the equilibrium filling fraction) the density as well the free energies and enthalpies of the hydrate are available. From this the corresponding entropies can be calculated. We use molecular dynamics simulations to estimate interfacial tensions (Kvamme & Kuznetsova (2000)) for the different interfaces involved. In summary the variation of RH from zero and upwards directly gives the corresponding fluxes for phase transition from CO2-enriched seawater over to hydrate.

The use of equations (12) - (20) for other phase transitions involved is quite analogue. Chemical potential of ice as function of temperature is estimated by Kvamme & Tanaka (1995) and is tabulated in a form that is easy to use. According to the predictions from these equations the hydrate formation flux rate from saturated seawater solution is a very slow process. An example is given in fig. 2.

In estimation of hydrate melting it is assumed that the melted carbon dioxide gets instantly diluted to background concentration of carbon dioxide. Except for extremely small hydrate particles this is reasonable since we consider hydrate particles that are continuously sinking in a gravity field through seawater with a background concentration of carbon dioxide. Although this concentration will vary somewhat we have used a constant value of 2000 μmoles/kg for this concentration. Within these assumptions and the theory above a hydrate particle equal to a quarter mm will melt in 8 seconds. Larger particles will have a larger letting flux but the very low chemical potential of carbon dioxide diluted to 2000 μmoles/kg results in a diverging exponent in equation (18) for larger particles.

Formation of a stable ice shell is the critical issue in the COSMOS concept. In fig, 3 we plot estimated flux as function of particle size.

 

V. DISCUSSION AND CONCLUSIONS

 

The formation of hydrate from carbon dioxide dissolved in seawater has recently been discussed by Kvamme (2000). Even though these results are predictions the thermodynamic models have been verified separately. The activity coefficient model reproduces experimental solubility for the range of pressures discussed. pH of the seawater is also reproduced well for the diluted solutions. The hydrate model has been compared with experimental data in a paper by Kvamme & Tanaka (1995). According to this we might expect a small shift in the estimated equilibrium conditions. The kinetic estimates presented here are theoretical predictions and will need experimental verification. According to these estimates approaches involving sinking hydrate particles are questionable due to the significant driving force for melting related to the low chemical potential of carbon dioxide in average seawater background concentration. If the cost related to conversion is low this might be an alternative to other ocean sequestration techniques and deposition of carbon dioxide enriched seawater.

Deposition of very cold large carbon dioxide droplets depends on a very rapid ice formation. The estimates presented here indicates that the kinetics of this phase transition might be too slow. A thin film of hydrate will form rapidly and strictly speaking we also have to take into consideration the kinetics of the phase transition between hydrate and ice. But once a thin ice layer is formed the rate determining kinetics for further ice growth is the ice/seawater freezing process. This situation could potentially be improved if a portion of the carbon dioxide were converted to hydrate prior to deposition through the pipeline. Experimental work along this line is in progress. Due to page limitations we have not presented the results for ice melting kinetics here but these estimates indicate the melting rate for ice at 3, 5 and even 7 degrees Celsius is very low.

 

 

 

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