Influence of pore-scale disorder on viscous fingering during drainage

¹ Department of Physics, University of Oslo - PO Box 1048 Blindern N-0316 Oslo, Norway
² Institut de Physique du Globe, UMR 7516 5 rue René Descartes, 67084 Strasbourg, France
³ Department of Physics, NTNU Trondheim - N-7491 Trondheim, Norway

Received: 18 April 2005
Accepted: 24 June 2005

Abstract

We study viscous fingering during drainage experiments in linear Hele-Shaw cells filled with a random porous medium. The central zone of the cell is found to be statistically more occupied than the average, and to have a lateral width of 40% of the system width, irrespectively of the capillary number Ca. A crossover length separates lower scales where the invader's fractal dimension is identical to capillary fingering, and larger scales where the dimension is found to be . The lateral width and the large-scale dimension are lower than the results for Diffusion Limited Aggregation, but can be explained in terms of Dielectric Breakdown Model. Indeed, we show that when averaging over the quenched disorder in capillary thresholds, an effective law relates the average interface growth rate and the local pressure gradient.