Squirt Dispersion and Attenuation Modeling based on Pore Structure Model

Abstract:

Elastic wave dispersion and attenuation due to squirt flow plays a significant role at ultrasonic, seismic and logging frequencies. Modeling squirt dispersion and attenuation often requires the knowledge of the geometric parameters of the pores, in general, the aspect ratio and porosity of the pores. These parameters are often extracted from the measurements of dry or saturated rocks. In most cases, only one characteristic aspect ratio is obtained by such methods. But the fact is that the rock may have pores of any aspect ratio, and each of the pores may have a contribution to the squirt flow. To take full consideration of various pores in rocks, we infer the complete aspect ratio distribution of pores from the pressure dependency of dry ultrasonic velocities based the pore structure model ([1]). Using effective medium theory, we extract the aspect ratio of the stiff pores from the high-pressure data and then invert the porosity and aspect ratio distributions of micro-cracks from dry velocities. These parameters are substituted into the squirt model ([2]) to predict the saturated velocities at ultrasonic frequencies. Our results show that there is a good agreement for clean sandstones and carbonate samples. But for most heterogeneous carbonate and shaley sandstone samples, the calculated results are not perfectly matched with the measurements. On the whole, however, the agreement is not unexpectedly worse. We also combined the squirt model into the Biot theory to calculate dispersion and attenuation in a full frequency range. It is shown that the squirt flow due to pores of different aspect ratio has different characteristic frequency. The overall effect of these pores results in a more gentle velocity change at intermediate frequencies, as compared to the classical models with only one characteristic aspect ratio. We find that the results calculated by squirt model using the complete aspect ratio distribution of pores has a better correlation with the measured velocity dispersion than those obtained by the classical models. This indicates that the seismic dispersion and attenuation can be interpreted by squirt flow mechanism between pores of different aspect ratio.

Reference

[1] David and Zimmerman, 2012, Journal of Geophysical Research, 117, B07210; [2] Gurevich et al. 2010, Geophysics, 75(6), 109-120.