Elastic modeling of seismic wave propagation in partially saturated rocks

SUMMARY The effect of single-phase fluid saturation on a rock’s bulk modulus is well understood using Gassmann’s equation. However when multiple fluids are involved the behaviour is not as well understood. Several fluid mixing averages have been suggested (Voigt, Reuss, Hill), and each apply in certain situations, however it is often not clear which model to select in a specific scenario and in some scenarios none of the models are accurate. The critical factor in deciding which average to use depends on the way the fluids are spatially distributed within the rock. We have applied elastic finite difference computational modelling to many different fluid distribution scenarios and have replicated behaviour described by various theoretical, empirical and lab data results, as well as generating results that span the space between these models. Importantly, our results compare well with observations in lab experiments, without relying on poroelastic or squirt-flow models which require parameters that are difficult to estimate for real reservoirs. Our elastic scattering approach is less computationally expensive than poroelastic modelling and can be more easily applied to actual reservoir rock and fluid distributions. Our results provide us with a powerful new method to analyse and predict the effects of multiple fluids and ‘patchy’ saturation on saturated rock bulk moduli and velocity. They also challenge traditional assumptions about the controlling factors on saturated bulk moduli suggesting it is more dominantly affected by the spatial fluid distribution properties rather than pore-scale fluid flow effects.