Velocity-saturation relation in partially saturated rocks: Modelling the effect of injection rate changes

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The relationship between P-wave velocity and fluid saturation in a porous medium 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 using a constant fluid patch size are not able to describe these velocity–saturation relations. Therefore, we incorporate a saturation-dependent patch size function into two models for patchy saturation. This recipe allows us to model observed velocity–saturation relations obtained for different and variable injection rates. The results reveal an increase in patch size with fluid saturation and show a reduction in the patch size for decreasing injection rate. This indicates that there can exist a distinct relation between patch size and injection rate. 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 in the injection rate is expected to boost the importance of capillarity.

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