Phase field modeling of CH 4 hydrate conversion into CO 2 hydrate in the presence of liquid CO 2 w G. Tegze, a L. Gra´na´sy a and B. Kvamme b Received 11th January 2007, Accepted 5th April 2007 First published as an Advance Article on the web 27th April 2007 DOI: 10.1039/b700423k We present phase field simulations to estimate the conversion rate of CH 4 hydrate to CO 2 hydrate in the presence of liquid CO 2 under conditions typical for underwater gas hydrate reservoirs. In the computations, all model parameters are evaluated from physical properties taken from experiment or molecular dynamics simulations. It has been found that hydrate conversion is a diffusion controlled process, as after a short transient, the displacement of the conversion front scales with t 1/2 . Assuming a diffusion coefficient of D s = 1.1  10 11 m 2 s 1 in the hydrate phase, the predicted time dependent conversion rate is in reasonable agreement with results from magnetic resonance imaging experiments. This value of the diffusion coefficient is higher than expected for the bulk hydrate phase, probably due to liquid inclusions remaining in the porous sample used in the experiment. 1. Introduction Natural gas hydrates are crystalline solids built of water cages containing gas molecules (mostly methane). These substances can be found in abundance in the Arctic regions and in marine sediments. The methane hydrate is stable at water depths larger than 300 m, and forms sediment layers hundreds of meters thick. According to conservative estimates, the world- wide amount of carbon in gas hydrates is more than twice that of the carbon in fossil fuels. 1–5 Gas hydrates are regarded as a new abundant energy source, whose exploitation may become economic with increasing oil prices and after developing the appropriate technologies. 1,3–7 Under conditions typical to underwater reservoirs the CO 2 hydrate is more stable than the methane hydrate. 1,3–7 This raises the possibility that via pumping industrial CO 2 into hydrate fields one can gain methane, a process that can make CO 2 deposition econom- ic. 1,6,7 Note, however, that methane is an about 20–25 times more efficient green house gas than CO 2 . 3,8–11 Therefore, safe technologies that can handle the released methane properly need to be developed. It is also important to realize that the methane stored in underwater hydrate reservoirs represents a natural climatic hazard: if released even a small fraction could cause serious climatic changes. 1,3–5,8–11 Therefore, it is a basic interest of humanity to understand the details of methane balance on Earth, including the formation and dissolution of gas hydrates. 3–5 Summarizing, gas hydrate transformations are interesting for the following reasons: 4 (i) Gas hydrates contain methane in abundance that could serve as a new energy source in the future, provided that its economic/environmentally safe exploitation is solved. (ii) Gas hydrate reservoirs, as methane source and sink, represent an essential part of the methane balance on Earth, and may play an important role in climatic changes. Two types of hydrate structures might be involved in the conversion process: Pure methane and pure CO 2 , as well as mixtures of methane and CO 2 , form structure I hydrate. The smallest symmetric unit cell of structure I hydrate is a cubic box of sides 12.01 A ˚ containing 46 water molecules forming 6 large (24 water molecules) and 2 small (20 water molecules) cavities. The conversion of methane hydrate into CO 2 hydrate may thus, in principle, be a solid state transformation. 12 Natural gas mixtures, in turn, may form structure II hydrate if the gas content of propane and butane is sufficiently high. Structure II hydrate has a ratio of 2 : 1 of small (20 water molecules) to large (28 molecules) cavities and will benefit from the extra stabilization of the larger cavities by hydro- carbons up to butanes, or other organic or inorganic molecules of similar size. Conversion of natural gas hydrate structure II into structure I CO 2 hydrate evidently involves a restructuring of the water lattice. Further details of these hydrate structures are available in handbooks. 13 The feasibility of CO 2 depositing techniques described above largely depends on such unknown process character- istics as the rate of hydrate conversion. Multiscale modeling, which combines microscopic and mesoscopic simulations, is expected to provide essential information that could be used in large scale process modeling and designing technology. Recently, multiscale modeling of hydrate formation has been attempted using a combined molecular dynamics (MD) and phase field approach. 14–16 Along these lines, first the thermodynamic properties of the solid and fluid CO 2 –H 2 O have been evaluated on the basis of experimental data and MD simulations, 17 together with the structure of the hydrate– aqueous solution interface. 14–16 This information combined with experimental data for the free energy of the hydrate–aqu- eous solution interface have been used to determine the model parameters of the phase field theory. The phase field theory a Research Institute for Solid State Physics and Optics, H-1525, POB 49 Budapest, Hungary b Department of Physics, University of Bergen, All _ egaten. 55, Bergen, 5007, Norway w The HTML version of this article has been enhanced with colour images. 3104 | Phys. Chem. Chem. Phys., 2007, 9, 3104–3111 This journal is  c the Owner Societies 2007 PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics Published on 27 April 2007. Downloaded by Universitetsbiblioteket I Bergen on 25/09/2014 10:51:24. View Article Online / Journal Homepage / Table of Contents for this issue