The commonly used Gassmann equations for fluid substitution of rocks tend to under-predict the velocities for higher frequencies, such as ultrasonic measurements. This discrepancy is often ascribed to wave-induced fluid flow (WIFF) effects such as Biot and squirt flow. Biot's theory attempts to explain wavelength-scale pressure differences whereas squirt flow tries to account for the pressure gradients arising from the heterogeneous pore space. In this work, we combine the two theories by exchanging the dry moduli in the theory of Biot with frequency-dependent dry moduli containing saturated compliant pores with small aspect ratios, which describe the effect of squirt flow. The resulting Biot-squirt flow model is then tested against ultrasonic velocity measurements for Westerley Granite and Navajo Sandstone. We also compare the model to the theory of Biot and Gassmann. Our model is in relative good agreement with the saturated velocity data for both P- and S-waves, whereas Biot and Gassmann tends to under-predict the velocities. Thus the grain-scale fluid effects are shown to be important to explain the dispersion for the two rock types.
Presentation Date: Monday, September 25, 2017
Start Time: 2:15 PM
Location: 351D
Presentation Type: ORAL
