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| Titel |
Non-Darcian effects in a rough fracture using lattice-Bolztmann methods |
| VerfasserIn |
Amélie Neuville, Eirik G. Flekkøy, Renaud Toussaint, Jean Schmittbuhl |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250056760
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| Zusammenfassung |
| Some natural fractures may be considered, at first order, as flat. However, looking at the
influence of the fracture morphology in a geothermal background, it was shown that the
complexity of the fracture topography changes the hydro-thermal flows which occurs when a
cold fluid is injected into a hot fractured bedrock [1]. This was shown under lubrication
approximations, which assumes that the fracture morphology varies in a smooth way,
by solving Stokes equation and a bidimensional (integrated over the thickness)
advection-diffusion equation. However, some features which are observed in the real world,
like fluid recirculation, and time-dependent temperature at the pumping well, cannot be
explained with this model.
We therefore wish to go beyond this lubrication assumption and be able to observe non
Darcy effects, which may happen due to highly variable morphology of the fluid-rock
interface.
Lattice-Boltzmann methods appear to be very suitable to implement this problem. Indeed,
as the algorithms require only local operations, they can handle very well complex
boundaries. We develop an algorithm which is based on two coupled lattice Boltzmann
methods, allowing us to solve both the advective mass transport and the conducto-advective
heat transport. No term are discarded in this solving: Navier-Stokes and the full
advection-diffusion equations are solved in three dimensions in the fluid and solid. This
allows us to observe how both the velocity and the temperature evolves with time and space,
also possibly under a time variable pressure gradient. We investigate the effect of
recirculation around sharp asperities and wedges along the fracture over the mass and heat
transport. We observe that the velocity profile is far from a quadratic profile in the
surrounding of sharp asperities: cold fluid may be first trapped into such zones showing a low
velocity, and released later.
Note that this approach could also be used in any field requiring advection-diffusion
solving, like the evolution of the concentration of a solute. By using suitable boundary
conditions, it is also possible to implement fracture morphology evolution, for instance by
considering chemical dissolution at the interface between fluid and rock.
[1] Neuville, A., Toussaint, R., and Schmittbuhl, J. (2010). Hydro-thermal flows in a
self-affine rough fracture. Physical Review E, 82, 036317. |
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