M. Sahimi et Ar. Mehrabi, Percolation and flow in geological formations: upscaling from microscopic to megascopic scales, PHYSICA A, 266(1-4), 1999, pp. 136-152
Modelling transport processes in a disordered system with broadly distribut
ed heterogeneities, such as a field-scale porous medium, is often hampered
by the fact that a very large set of equations (of the order of several mil
lions) has to be solved repeatedly if detailed information about the system
's morphology is available. Solving such a large set is often not practical
. We discuss a novel and very efficient method for scale up of such systems
such that no important information about their characteristics is lost at
any length scale, and at the same time the number of transport equations to
be solved is reduced drastically to a manageable level. The method, which
is applicable to any type of heterogeneous medium, including one with perco
lation disorder, uses a wavelet transformation to coarsen the original fine
-scale description of the system, such that finer resolution is maintained
in regions of high transport properties, whereas coarser property descripti
on is applied to the rest of the system. The computational cost of the meth
od is several orders of magnitude less than those of the most efficient met
hods currently available. The performance of the method is demonstrated by
its application to calculation of the effective flow properties of several
models of field-scale porous media. The method is equally applicable to oth
er disordered media with broadly distributed heterogeneities, such as amorp
hous semiconductors. (C) 1999 Elsevier Science B.V. All rights reserved.