ABSTRACTQuantitative interpretation of time‐lapse seismic data requires knowledge of the relationship between elastic wave velocities and fluid saturation. This relationship is not unique but depends on the spatial distribution of the fluid in the pore‐space of the rock. In turn, the fluid distribution depends on the injection rate. To study this dependency, forced imbibition experiments with variable injection rates have been performed on an air‐dry limestone sample. Water was injected into a cylindrical sample and was monitored by X‐Ray Computed Tomography and ultrasonic time‐of‐flight measurements across the sample. The measurements show that the P‐wave velocity decreases well before the saturation front approaches the ultrasonic raypath. This decrease is followed by an increase as the saturation front crosses the raypath. The observed patterns of the acoustic response and water saturation as functions of the injection rate are consistent with previous observations on sandstone. The results confirm that the injection rate has significant influence on fluid distribution and the corresponding acoustic response. The complexity of the acoustic response —‐ that is not monotonic with changes in saturation, and which at the same saturation varies between hydrostatic conditions and states of dynamic fluid flow – may have implications for the interpretation of time‐lapse seismic responses.

Waves in patchy-saturated rocks are attenuated through the mechanism of wave-induced pressure diffusion. Previous studies reveal that attenuation and phase-velocity dispersion depend on the fluid patch size and distribution. These patch characteristics in turn can be influenced by capillary forces. The effect of capillarity on wave attenuation in patchy-saturated rocks is not fully understood. We studied the combined effects of wave-induced pressure diffusion and capillarity on acoustic signatures. To do so we made use of the concept of patch membrane stiffness as a macroscopic expression of capillarity. We incorporated the membrane stiffness into the continuous random media model of patchy saturation. The membrane stiffness is associated with a pressure discontinuity at patch interfaces. This pressure discontinuity impedes wave-induced pressure diffusion and, therefore, reduces wave attenuation. Conversely, the phase velocity increases due to additional capillarity reinforcement. We applied this capillarity-extended random media model to interpret velocity-saturation relations (VSR) and attenuation-saturation relations (ASR) retrieved from an ultrasonically monitored core flooding experiment. Because the fluid distribution is approximately known from accompanying computerized tomographic images, all but one required model input parameters can be inferred. The elusive input parameter is a shape factor quantifying the geometric irregularity of the pore channels. We found, however, that the experimental data can be consistently modeled only if the capillarity effect is accounted for. The results suggested that wave-induced fluid-pressure diffusion at mesoscopic patches in conjunction with capillary action can have important implications for interpreting ultrasonic VSR and ASR in patchy-saturated rocks.

Seismic waves propagating in porous rocks saturated with two immiscible fluids can be strongly attenuated. Predicting saturation effects on seismic responses requires a sound understanding of attenuation and velocity dependencies on the fluid distribution. Decoding these effects involves interpreting laboratory experiments, analyzing well-log data, and performing numerical simulations. Despite striking differences among scales, flow regimes, and frequency bands, some aspects of wave attenuation can be explained with a single mechanism — wave-induced pressure diffusion. Different facets of wave-induced pressure diffusion can be revealed across scales.

We provide an overview on recent developments on the acoustics of partially saturated porous rocks. The focus is on the mesoscopic flow induced by seismic waves and leading to wave attenuation and dispersion. At the laboratory scale recent core plug imbibition experiments with simultaneous acquisition of X-ray CT and ultrasonic waveforms allow us to retrieve the saturation dependence of velocities and attenation. Fluid patches and their evolution at the milimetre scale are observed. To model these relations in a consistent manner we invoke the concept of fluid patch membrane stiffness. The latter accounts for the net effect of capillary forces at the macroscale. We further extract the velocity saturation relation from time-lapse sonic logs aquired during CO2 injection into a sandstone formation. It is shown that this velocity-saturation relation can be also modelled using the mesoscopic wave-induced flow effect. Simulation results give further support that mescopic fluid patches on the centimetre scale have a first-order effect on seismic amplitudes provided that the fluid bulk modulus contrast across the patch boundaries is suffiently large. This is typically the case in the presence of a gas phase. We conclude that fluid patches on the milimetre-to-centimetre scale have important implications for attenuation estimates.

ABSTRACTForced imbibition was performed in reservoir sandstone by injecting water into a dry sample. The injection was monitored with X‐ray computed tomography and acoustic acquisition to simultaneously visualize the displacement of the fluid and quantify its presence by calculating saturation and P‐wave velocities.We observed a strong influence when changing the injection rates on the acoustic response. Upon decreasing the injection rate from 5 mL/h to 0.1 mL/h, P‐wave velocities decreased sharply: 100 m/s in 1 h. This behaviour is related to the partially saturated conditions of the sample (76% of saturation) before decreasing the injection rate. The air that is still trapped is free to move due to a decrease of pore pressure that is no longer forced by the higher injection rate. After 1 hour, P‐wave velocities started increasing with small changes in saturation. Stopping injection for 16 hrs decreased saturation by 8% and P‐wave velocities by 100 m/s. Restarting injection at 5 mL/h increased saturation to 76% while P‐wave velocities fluctuated considerably for 2 hrs until they stabilized at 2253 m/s. Through the computed tomography scans we observed a water front advancing through the sample and how its shape changed from a plane to a curve after decreasing the injection rate.

Summary Forced imbibition was performed in a Limestone Savonnieres by injecting water into a dry sample. The injection was monitored with X-ray Computed Tomography (CT) and active ultrasonic measurements so that the time-space distribution of the invading fluid could be simultaneously observed in CT images and quantified through measuring P-wave velocities and water saturation. The CT scans allowed us to observe a water front advancing away from the area of injection and estimate saturation. Through the evolution of P-wave velocities, we observed a strong influence on the acoustic response with the presence of water and with the changing of injection rates. The approaching of the water front to the monitored position decreased P-wave velocities while the saturation increased continuously. The P-wave velocities decrease occurred for a short period of time and was followed by a sharp increase which happens when the fluid front crossed the monitored position. Decreasing injection rate decreased P-wave velocities and saturation. Increasing injection rate, increased P-wave velocities and saturation, sharply and for a short period of time followed by a slight decrease for P-wave velocities and a continuous increase. Our experimental data confirms how sensitive acoustic waves are to the presence of water and that changing injection rates promote considerable fluid distribution that is drastically reflected in the acoustic velocities.