caa a22 4500 463163400 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s11242-006-9032-0 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9032-0 Permeability up-scaling using Haar Wavelets [Elektronische Daten] [Vera Pancaldi, Kim Christensen, Peter King] In the context of flow in porous media, up-scaling is the coarsening of a geological model and it is at the core of water resources research and reservoir simulation. An ideal up-scaling procedure preserves heterogeneities at different length-scales but reduces the computational costs required by dynamic simulations. A number of up-scaling procedures have been proposed. We present a block renormalization algorithm using Haar wavelets which provide a representation of data based on averages and fluctuations. In this work, absolute permeability will be discussed for single-phase incompressible creeping flow in the Darcy regime, leading to a finite difference diffusion type equation for pressure. By transforming the terms in the flow equation, given by Darcy's law, and assuming that the change in scale does not imply a change in governing physical principles, a new equation is obtained, identical in form to the original. Haar wavelets allow us to relate the pressures to their averages and apply the transformation to the entire equation, exploiting their orthonormal property, thus providing values for the coarse permeabilities. Focusing on the mean-field approximation leads to an up-scaling where the solution to the coarse scale problem well approximates the averaged fine scale pressure profile. Springer Science+Business Media B.V., 2006 Up-scaling nationallicence Real-space Renormalization nationallicence Haar Wavelets nationallicence Pancaldi Vera Department of Earth Science and Engineering, South Kensington Campus, Imperial College, SW7 2AZ, London, UK aut Christensen Kim Department of Physics, South Kensington Campus, Imperial College, SW7 2AZ, London, UK aut King Peter Department of Earth Science and Engineering, South Kensington Campus, Imperial College, SW7 2AZ, London, UK aut Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 395-412 0169-3913 67:3<395 2007 67 11242 https://doi.org/10.1007/s11242-006-9032-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9032-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pancaldi Vera Department of Earth Science and Engineering, South Kensington Campus, Imperial College, SW7 2AZ, London, UK aut NATIONALLICENCE 700 1- Christensen Kim Department of Physics, South Kensington Campus, Imperial College, SW7 2AZ, London, UK aut NATIONALLICENCE 700 1- King Peter Department of Earth Science and Engineering, South Kensington Campus, Imperial College, SW7 2AZ, London, UK aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 395-412 0169-3913 67:3<395 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer