Heterogeneous porous media: Fronts and noise

Capillary effects can be important in immiscible flows in heterogeneous media, particularly at low capillary numbers (Ca). We present experiments and simulations of slow drainage in 3-D porous media, either homogeneous and in the presence of buoyancy or heterogeneous and in its absence. An acoustic technique allows for an accurate study of the 3-D fronts and the cross-over region. Our results suggest that both cases can be described by invasion percolation in a gradient. Both front tails scale with the corresponding Bond numbers as σft≈B−47 in agreement with the theory. An analogous scaling for viscous effects is also given. The noise of these fronts are found correlated in the form of a fractional Brownian motion (fBm) of a Hurst exponent H≈.5. At higher Ca, experiments performed in 3-D porous media with sharp changes in permeability, exhibit a saturation profile response closely linked to the permeability variations. This viscous response to heterogeneity provides an opportunity to investigate and determine correlated (even at all scales, i.e. fBm), permeability fields.