Effect of Mesh Size on the Kinetics of Two-Phase Flow (Diffusion vs. Advection)
Dear all,
I have a question regarding the mesh size and its impact on diffusion in two-phase flow. I'm curious to know if the mesh size affects the diffusion from element0 to element1. Considering the significantly larger volume of element1 compared to that of element0, we would expect to tolerate more gas dissolution before reaching a certain pressure threshold, potentially leading to desaturation of element1.
Sincerly,
2 replies
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Quick reply:
Within each gridblock, the local thermodynamic equilibrium assumption applies, so your description of what is the impact of element volume on phase change (and the calculation of any state variable) is correct. The main question is whether the equilibrium assumption is justified for the larger element (i.e., the issue is not so much related to the differences in the volumes of two connected elements). It is also not quit clear to me whether you are talking about the diffusion of the components air and water within the two phases, or just "diffusive processes" in general. In any case, discretization indeed affects the onset of phase changes and any other front propagation process (pressure, solutes, heat, etc.), a phenomenon referred to as "numerical dispersion", which (at least theoretically) can be partly compensated for by using effective parameters. See, for example:
Pruess, K., Grid orientation and capillary pressure effects in the simulation of water injection into depleted vapor zones, Geothermics, 20(5/6), 257–277, 1991.
and iTOUGH2 Sample Problem 7 in:
Finsterle, S., iTOUGH2 Sample Problems, Report LBNL-40042, Lawrence Berkeley National Laboratory, Berkeley, Calif., 2016.
Stefan
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Thank you, Stéphane agin, for your insightful responses and the valuable resources you provided.