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A direct method for the identification of the permeability field based on flux assimilation by a discrete analog of Darcy's law

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Author: Zijl, W.
Type:article
Date:2004
Institution: Nederlands Instituut voor Toegepaste Geowetenschappen TNO
Source:Transport in Porous Media, 1, 56, 87-112
Identifier: 237851
doi: doi:10.1023/B:TIPM.0000018405.22085.99
Keywords: Geosciences · Discrete Darcy's law · Edge-based vector potentials · Flux assimilation · Inverse modeling · Mechanical permeability · Pressure effects · Vectors · Flux assimilation method · Flux density · Inverse models · Porous materials · Darcy law · permeability · porous medium

Abstract

Inverse models to determine the permeability are generally based on existing forward models for the pressure. The permeabilities are adapted in such a way that the calculated pressures match the specified pressures in a number of points. To assimilate a priori knowledge about the flux, we introduce the 'flux assimilation method', which is based on the 'vector potential-pressure formulation' of Darcy's law. Thanks to an unconventional discretization technique - the 'edge-based face element method' - not only the specified pressures, but also specified information about the flux density can easily be assimilated. A relatively simple, but insightful analytical example illustrates the potential of this method. © 2004 Kluwer Academic Publishers.