The flux of methane, jcH4 is the flow rate per unit area, in moles per second per m2 of sediment section, and is proportional to the gradient in the concentration of methane in solution in the pore water. The concentration must be expressed here in moles per cubic meter. The diffusion coefficient D* is lower than the diffusion coefficient through bulk water because of the tortuosity of the flow paths through the sediment (Clennell 1997). Iversen and Jorgensen (1993) give values for the D* for methane in unconsolidated marine sediments ranging from 10"8 to 10"9 mV1. Values for consolidated mudrocks can be as low as 10"13 mV (Schlomer and Krooss 1997). According to Hunt, (1997):
"Diffusion acts to disperse rather than concentrate gas and is an exceedingly slow process."
Diffusion is very inefficient at transporting gas over long distances, because the concentration gradients are small. However, diffusion is omnipresent in systems that are out of chemical and thermal equilibrium.
When the pore water is moving it is appropriate to consider dispersion, which includes the effect of mesoscale to macroscale fluctuations in the velocity field as well as random thermal molecular motions that constitute molecular diffusion. Together these effects combine into an effective dispersion coefficient, with the same dimensions as D*, i.e. m2s"' (cf. Xu and Ruppel 1999). If the fluid advection rate is very small, then the dispersion coefficient is of the same order as D*, however, on larger scale of observation the effective dispersivity can be much greater, particularly if flow makes use of fractures.
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