Direct Inversion of Permeability
Geert Brouwer
TNO the Netherlands, Utrecht, The Netherlands
By confronting permeability realisations or a priori mappings of the geologist -one at a time -with the measured production data a match for each realisation can be obtained. A conventional simulator can be used to abstract the flow velocities and flow potentials in two forward runs given the correct boundary
conditions
. By reformulating the
potential
gradient across the permeability cell and averaging the velocities from the cell faces we find -by directly applying Darcies law- an anisotropic permeability field. In a few iterations this anisotropy is removed. For one-phase the results look promising. We could derive the a posteriori distribution from 100 realisations (on a 50 by 50 grid) in 15 minutes and as expected find a reduced variance in between the wells. The methodology is applicable for groundwater flow, 2 phase flow, thermal flow.
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AAPG Search and Discover Article #90066©2007 AAPG Hedberg Conference, The Hague, The Netherlands
AAPG Search and Discover Article #90066©2007 AAPG Hedberg Conference, The Hague, The Netherlands