The relationship between elastic wave velocities and water saturation in a water/gas reservoir depends strongly on whether saturation is heterogeneous (patchy) or homogeneous. Heterogeneity in saturation may result from lithologic heterogeneity because under conditions of capillary equilibrium, different lithologies within a reservoir can have different saturations, depending on their porosities and permeabilities. We investigate this phenomenon by generating models of a reservoir in which we control the distribution of lithologic units and theoretically determine the corresponding velocity-saturation relationship. We assume a state of capillary equilibrium in the reservoir and determine the saturation level of each region within the reservoir from the corresponding capillary pressure curve for the lithologic unit at that location. The velocities we calculate for these models show that saturation heterogeneity, caused by lithologic variation, can lead to a distinct dependence of velocity on saturation. In a water-gas saturated reservoir, a patchy distribution of the different lithologic units is found to cause P-wave velocity to exhibit a noticeable and almost continuous velocity variation across the entire saturation range. This is in distinct contrast to the response of a homogeneous reservoir where there is only a large change in velocity at water saturations close to 100%.

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