Static and Dynamic Bulk Moduli of Deepwater Reservoir Sands: Influence of Pressure and Fluid Saturation

The static bulk modulus of unconsolidated sands is essential for predicting the in situ effective pressure to reduce drilling risks in deepwater reservoirs; however, the dynamic bulk modulus is often more broadly available from seismic or well logging data. Therefore, it is tempting to investigate the relationship between static and dynamic bulk moduli. We perform a series of ultrasonic velocity measurements on 21 deepwater reservoir sands from the Gulf of Mexico (GoM) to study the static and dynamic bulk moduli simultaneously. Both room-dry and brine-saturated ultrasonic velocities are measured under hydrostatic stress conditions to derive the dynamic bulk moduli. Under brine-saturated conditions, if the pore pressure is kept constant, the pore volume change with the confining pressure can be monitored accurately by a digital pump, which is subsequently used to estimate the static bulk modulus. The experimental results suggest that both the static and dynamic bulk moduli decrease upon pressure unloading. The pressure-dependent bulk moduli are modeled using the Hertz-Mindlin contact theory at the critical porosity and combined with the modified Hashin-Shtrikman lower bound for other porosities. The results suggest that the theoretical estimates can serve as the lower bound for the dynamic bulk modulus and the upper bound for the static bulk modulus. Under room-dry conditions, the static-to-dynamic modulus ratio decreases from a value approaching 0.8 to approximately 0.25 with decreasing differential pressure. Moreover, the effects of brine saturation on the relationship between the static and dynamic moduli are investigated using Gassmann’s equation. The brine saturation substantially reduces the difference between the static and dynamic bulk moduli, making the static-to-dynamic modulus ratio approach unity, which may be relevant to the in situ reservoir rock properties.