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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Author:CARINE FAMY <> (Institut Français du Pétrole (I.F.P.))
BERNARD BOURBIAUX <> (Institut Français du Pétrole (I.F.P.))
PATRICK LEMONNIER <> (Institut Français du Pétrole (I.F.P.))
MICHEL QUINTARD <> (Institut de Mécanique des Fluides de Toulouse (I.M.F.T.))
Presenter:CARINE FAMY <> (Institut Français du Pétrole (I.F.P.))
Date: 2006-06-18     Track: Special Sessions     Session: Multiscale methods for flow in porous media

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.  T. Arbogast, J. Douglas Jr and U. Hornung (1990), Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal,. 21(4), 823-836.  P. Landereau, B. Noetinger and M. Quintard (2001), Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems, Advances in Water Resources 24, 863-876  K. Pruess and T.N. Narasimhan (1985), A practical method for modeling fluid and heat flow in fractured porous media, SPE Journal.  J.E. Warren and P.J. Root (1963), The behavior of naturally fractured reservoirs, SPE Journal.