Saturation hysteresis effects on the seismic signatures of partially saturated heterogeneous porous rocks

Abstract

Experimental evidence indicates that the spatial distribution of immiscible pore fluids in partially saturated media depends on the flow history and, thus, exhibits hysteresis effects. To date, most works concerned with modelling the effective seismic properties of partially saturated rocks either disregard these effects or account for them employing oversimplified approaches. This, in turn, can lead to erroneous interpretations of the corresponding seismic signatures. In this work, we present a novel methodology that allows to compute hysteresis effects on seismic attenuation and velocity dispersion due to mesoscopic wave-induced fluid flow in realistic scenarios. For this purpose, we first employ a constitutive model that conceptualizes a porous medium as a bundle of constrictive capillary tubes with a fractal pore-size distribution, which allows to estimate local hydraulic properties and capillary pressure-saturation hysteretic relationships in a heterogeneous rock sample. Then, we use a numerical upscaling procedure based on Biot's poroelasticity theory to compute seismic attenuation and velocity dispersion curves during drainage and imbibition cycles. By combining these procedures, we are able to model, for the first time, key features of the saturation field and of the seismic signatures commonly observed in the laboratory during drainage and imbibition experiments. Our results also show that the pore-scale characteristics of a given porous medium, such as the pore-throat geometry, can greatly influence the hysteresis effects on the seismic signatures.