Influence of pore-scale disorder on viscous fingering during drainage

PACS. 47.20.Gv – Viscous instability. PACS. 47.54.+r – Pattern selection; pattern formation. PACS. 47.55.Mh – Flows through porous media. 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 wf ∝ Ca−1 separates lower scales where the invader’s fractal dimension D 1.83 is identical to capillary fingering, and larger scales where the dimension is found to be D 1.53. 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 v ∝ (∇P)2 relates the average interface growth rate and the local pressure gradient. Viscous-fingering instabilities in immiscible two-fluid flows in porous materials have been intensely studied over the past 50 years [1], both because of their important role in oil recover