In a set of water injection, imbibition and drying tests on the Obourg Chalk, relaxation processes induced by variations in water saturation were continuously recorded at a constant ultrasonic frequency, with a peak in attenuation concomitant to a velocity increase from a lower to an upper bound. This behavior is well described by standard viscoelastic models, considering a continuously changing relaxation frequency which at water saturation above 80% matches the frequency of our ultrasonic pulse generator. Using a patchy saturation model, we show that the heterogeneity in fluid distribution is responsible for this relaxation phenomenon which could be observed at the ultrasonic frequency, thanks to the very fine scale of the rock microstructure combining low permeability and high porosity. We believe that our detailed data set can feed new models or help improve existing ones for a better understanding of wave-induced fluid flow processes in reservoir rocks.