The relationship between P-wave velocity and fluid saturation in saturated porous media is of importance for reservoir rock characterization. Forced imbibition experiments in the laboratory reveal rather complicated velocity-saturation relations including rollover-like patterns induced by injection rate changes. Poroelasticity-theory based patchy saturation models with a constant fluid patch size are not enough to describe these velocity-saturation relations. Therefore, we incorporate a saturation-dependent patch size function into two models for patchy saturation. With this, we can model the observed velocitysaturation relations obtained at different injection rates well. The results indicate that there can exist a distinct relation between patch size and injection rate. Moreover, we assess the relative importance of capillarity on velocity-saturation relations and find that capillarity stiffening impairs the impact of patch size changes. Capillarity stiffening appears to be a plausible explanation when a decrease of the injection rate is expected to boost the importance of capillarity.


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