HR: 10:35h
AN: H12A-02 [Abstracts]
TI: Two-phase flow through fractured porous media
AU: Mourzenko, V V
EM: mourzenk@lcd.ensma.fr
AF: LCD, SP2MI, Futuroscope, 86960, France
AU: Bogdanov, I I
EM: bogdanov@lcd.ensma.fr
AF: LCD, SP2MI, Futuroscope, 86960, France
AU: Thovert, J F
EM: thovert@lcd.ensma.fr
AF: LCD, SP2MI, Futuroscope, 86960, France
AU: * Adler, P M
EM: padler@ccr.jussieu.fr
AF: Sisyphe-UPMC, 4 place Jussieu, Paris, 75252, France
AB:
The prediction of two-phase flows in fractured porous media is a challenging problem, because of the multiple
scales that are involved and of the nonlinearity of the governing equations.
The present work is based on a three-dimensional discrete description of the fracture network and of the
embedding matrix. Any fracture network geometry, any type of boundary condition, and any distribution of the
fracture and matrix properties can be addressed, without simplifying approximations.
First, the mathematical framework for two-phase flow in fractured porous media is provided, including the
transport and the constitutive equations that are eventually reformulated in dimensionless form. Dimensionless
parameters and criteria are also introduced to quantify various physical regimes. In particular, an a priori criterion
for the possibility of upscaling generalized Darcy's equation is devised, which is later confirmed by the numerical
simulations.
Then, the 3D meshing of randomly fractured media is described and the spatial and temporal discretizations of
the equations and the solution algorithm are presented. The illustrative simple example of an array of infinite
parallel fractures is treated analytically in order to provide a direct check of the numerical codes. A generalization
for steady-state two-phase flow of the classical result of Snow for single-phase flow in networks of infinite plane
fractures is given. The simulation of the flow in a closed regularly compartmented reservoir is detailed and
discussed in comparison with homogenized models.
Finally, illustrative cases of complex realistic situations with random fractures embedded in a permeable rock
matrix are presented. The temporal evolution of the local saturations is illustrated and discussed. Then,
systematic results related to the steady-state macroscale phase relative permeabilities are given as functions of
saturation, for typical situations with percolating or nonpercolating fracture networks. The influence of the other
parameters is briefly considered.
Ref:
(1) I. I. Bogdanov, V. V. Mourzenko, J.F. Thovert, P. M. Adler, Phys. Rev.E, 68, 026703-1, 2003.
DE: 1832 Groundwater transport
DE: 1847 Modeling
SC: Hydrology [H]
MN: 2007 Fall Meeting