10.4122/1.1000000265
Frih, Najla
Najla
Frih
najla-frih@lamsin.rnu.tn
Roberts, Jean
Jean
Roberts
jean.roberts@inria.fr
Saada, Ali
Ali
Saada
ali.saada@ipein.rnu.tn
Frih, Najla
Najla
Frih
najla-frih@lamsin.rnu.tn
Modeling Forchheimer fractures as interfaces
XVI International Conference on Computational Methods in Water Resources
2006
2006
Modeling flow and transport of contaminants in porous media is made difficult by the
presence of heterogenieties in the characteristics of the medium occurring at scales
quite different from those describing the average characteristics of the medium. One
particular instance of this phenomena is the occurrence of fractures in the medium,
regions very small in width but very important for modeling flow because of their
much higher (or possibly much lower ) permeability. Fine networks of interconnected
fractures occurring with some degree of regularity are often taken into account by
double porosity models. Here however we are concerned with larger fractures or
faults of known location that need to be included specifically in the model. In
earlier works, a model was introduced in which the fracture was treated as a lower
dimensional domain, as an interface between two subdomains, and domain decomposition
techniques with nonlocal interface conditions were used to solve the equations. The
porous medium was divided into subdomains with some of the interfaces representing
fractures. At these fracture interfaces, the flux continuity condition was replaced
by an equation representing Darcy flow along the interface.
When the flow in the fracture is sufficiently rapid however, inertial effects need
to be taken into account, and Forchheimer's law describes the flow in the fracture
more accurately than does Darcy's law. The object of this presentation is to extend
the above model to the case in which the flow along the fracture is governed by
Forchheimer's law. As Forchheimer's law is given by a nonlinear equation, this model
is more complex. It is derived by averaging across the fracture under the assumption
that the flow in the direction normal to the fracture is less important than in
directions tangential to the fracture. Domain decomposition type techniques can
still be used as the nonlinearities involve only the interface unknowns. A
quasi-Newton method can then be used to solve the resulting nonlinear problem on the
interfaces. In this presentation the numerical model will be derived and numerical
results will be presented.