Correlation of Saturation Profiles in Slow Drainage in Porous Media

We study the spatial correlation of one-dimensional (1-D) saturation profiles obtained during slow drainage in porous media, where capillary effects predominate. Using properties of Invasion Percolationin an uncorrelated medium, we compute the correlation structure of the profile. At small values of the lag (but for sufficiently large systems) the profile approaches the structure of the record of a fractional Brownian motion(fBm) with Hurstexponent H=(D-1)/2, where D is the fractal dimension of the percolation cluster. Sufficiently far from percolation, the profile is a white noise. Noise measurements in displacement experiments using an acoustic technique are reported for the 3-D case. The theory is confirmed with 2-D simulations. An apparent mismatch in the 3-D case is attributed to finite-size effects. The approach is generalized to correlated percolation.