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.

From a basin development point of view: we can estimate rapidly an a posteriori distribution of permeability (conductivity) given an a priori permeability (thermal conductivity) distribution conditioned to boundary conditions expressed in pressure (temperature) and (thermal) flux.

A paper by G. Brouwer, P. Fokker, W. Zijl and F. Wilschut is intended to be submitted to Mathematical Geology.

The testing of this concept for 2-phase, 3D, error modelling, multiple assimilation times is under study.

 

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