ACCURATE MODELLING OF MATRIX-FRACTURE TRANSFERS IN FRACTURED POROUS MEDIA THROUGH SUB-GRIDDED DUAL-POROSITY MODELS
Creators: name: FAMY, CARINE
name: BOURBIAUX, BERNARD
name: LEMONNIER, PATRICK
name: QUINTARD, MICHEL
name: FAMY, CARINE
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: Conventional models to represent fractured media are often based on the “dual-
porosity” concept (Warren and Root, 1963). In most simulators, to represent the 
exchange between the fracture and matrix media, we use an approximate pseudo-steady-
state mass exchange formulation resulting from an upscaling of the matrix block-
scale flow (Landereau et al., 2001). This formulation is reasonably predictive for 
single-phase flows, but generally inaccurate for multiphase flows. This is mainly 
due to the impact of non-linearities and the coupling between several physical 
mechanisms, especially capillarity and gravity, that do not yield the same 
homogenised flow behaviour at the matrix block scale. A numerical approach to 
overcome this limitation consists in sub-gridding the matrix blocks (Pruess and 
Narasimhan, 1985), which may be viewed as a mixed model as obtained from 
homogenization theory (Arbogast et al., 1990). However, this method is still unused 
in practical situations because of its high computational cost. This paper describes 
the optimisation of this sub-gridding technique in the capillary imbibition case, by 
taking into account the physical specificities of this mechanism and with a 
criterion of minimal computational cost. Implemented in a conventional flow 
simulator, this technique allows the calculation of very reliable exchange terms 
between matrix blocks and fractures. 
The study of the capillary imbibition mechanism on a single matrix block (possibly 
anisotropic) allows one to create an optimised one-dimensional model. This sub-
gridding methodology has been validated by comparison with reference fine-grid 
simulations, for various rock-fluid properties and anisotropic flow conditions. The 
reference solutions are reproduced very accurately, including the detailed time 
evolution of the matrix-fracture transfer rates. Since the sub-gridding methodology 
provides accurate exchange terms, it has been implemented in a conventional flow 
simulator dedicated to fractured porous media. The sub-gridding methodology improves 
the calculation of matrix-fracture exchanges driven by capillary forces. Moreover, 
matrix and fractures unknowns have been decoupled in order to reduce the 
computational cost. Therefore, short- and long-term flows of water-drive fractured 
media can be reliably predicted. This methodology can be applied to other multiphase 
flow problems solved with an industrial fractured reservoir simulator.
The main technical contributions of this work are the development of an optimised 
method for sub-gridding matrix blocks, and the implementation of this sub-gridding 
methodology into a conventional flow simulator dedicated to fractured media.

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