Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics.

Abstract

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates v. In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of μ and v on the statistical properties of the velocity V, the spatial average of the local front velocities over a window of lateral size . We have varied from the local scale defined by our spatial resolution up to the lateral system size L. Even though the imposed flow rate is constant, the signals V(t) present very strong fluctuations which evolve systematically with the parameters μ, v, and . We have verified that the non-Gaussian fluctuations of the global velocity V(t) are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by Neff = /c (the ratio of the lateral size of the measuring window to the correlation length c ∼ 1/ √μv). The large correlated excursions of V(t) correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents independent of μ, v, and . Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ξS and maximum durations ξT of global avalanches are not controlled by the same mechanism. While ξS are also determined by /c, like the amplitude fluctuations of V(t), ξT and the temporal correlations of V(t) evolve much more strongly with imposed flow rate v than with fluid viscosity μ. DOI: 10.1103/P