Using wavelets to characterize the wettability of porous materials.

Visualization experiments of rate-controlled immiscible displacement of oil by water are performed on a model porous medium of controlled fractional wettability, fabricated by mixing water-wet glass microspheres with strongly oil-wet polytetrafluoroethylene microspheres and packing them between two transparent glass plates. The growth pattern is video recorded and the transient response of the pressure drop across the pore network is measured for various fractions of oil-wet particles. The space-averaged capillary pressure coincides to the pressure drop measured across the porous medium. The oscillating transient signal of the capillary pressure is analyzed with multilevel wavelets to produce the best level wavelet details or best level capillary pressure spectrum (BLCPS) by minimizing the "entropy" of wavelet approximation. Invasion of water in oil-wet areas is reflected in high-frequency and low-amplitude fluctuations of the BLCPS. Correspondingly, invasion of water in water-wet areas is associated with low-frequency and high-amplitude fluctuations of the BLCPS. The displacement growth pattern is reflected in the "energy" and "frequency" of the BLCPS which along with the time-averaged capillary pressure are correlated with two parameters quantifying the spatial variation of wettability over the porous medium: the frontal wettability of the active interface of the fluids before each invasion step and the regional wettability of the area invaded by the displacing fluid.