Weitao Sun

Comparison of P-wave attenuation models of wave-induced flow

ABSTRACT Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with Whites and Johnsons models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.

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

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.

Wave Propagation and Attenuation in Heterogeneous Reservoir Rocks

In order to investigate wave propagation in heterogeneous reservoir rocks, the equations of wave motion in a fluid-saturated double-porosity medium are derived based on Biot’s theory of poroelasticity and a generalization of Rayleigh’s theory of fluid collapse to the porous case, namely the Biot–Rayleigh Theory. The theory assumes a porous inclusion embedded in a porous host medium. Two cases are considered based on the Biot–Rayleigh equations, namely a double-porosity solid saturated with a single fluid and a single-porosity solid saturated with two immiscible fluids. The fluid kinetic energy of the spherical inclusions contributes to the local-flow kinetic energy and dissipation function. The local fluid-flow velocity fields inside and outside the inclusions are derived, leading to the kinetic energy function and dissipation function, rederived on the basis of the Biot–Rayleigh theory. Examples comparing the wave-propagation theories and experimental measurements are given for different types of rocks and fluids. By considering ultrasonic measurements on reservoir rocks that are partially saturated with oil and brine, the fluid substitution effects are studied in the analysis with Biot’s poroelasticity.