Effect of Pore Collapse and Grain Crushing on the Frequency Dependence of Elastic Wave Velocities in a Porous Sandstone
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ORIGINAL PAPER
Effect of Pore Collapse and Grain Crushing on the Frequency Dependence of Elastic Wave Velocities in a Porous Sandstone Chao Sun1,2 · Jan V. M. Borgomano2 · Jérôme Fortin2 · ShangXu Wang1 Received: 3 February 2020 / Accepted: 22 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A saturated Bleurswiller sandstone, of 25% porosity, was compacted by increasing the confining pressure over the critical pressure P* which characterizes the onset of pore collapse and grain crushing. The frequency-dependence of Young’s moduli were measured before and after the compaction using forced-oscillation method in a triaxial cell. For the intact and compacted samples, we observed one dispersive transition within the seismic band (0.01–100 Hz). The dispersion is consistent with crack-to-pore squirt flow, making the transition from the relaxed to the unrelaxed fluid-flow regime. The induced compaction shifted the critical frequency of the squirt-flow dispersion towards higher frequencies, thus moving it out of the seismic band and allowing Biot-Gassmann to fully apply. This result is a consequence of an increase in the crack aspect ratio after compaction. In addition, the dispersion of elastic modulus after compaction increases from about 25 to 30%, related to the increase of crack fraction. Keywords Young’s modulus · Dispersion · Attenuation · Compaction · Squirt-flow · Forced-oscillations List of symbols E Young’s modulus EAl The Young’s modulus of the aluminum reference 𝜀al The axial-strain of the aluminum reference 𝜀ax The axial-strain of the sample 𝜀vol Volumetric strain Q−1 Young’s attenuation E 𝜑al The axial-strain phase of the aluminum reference 𝜑ax The axial-strain phase of the sample 𝜅 Permeability Φ Porosity 𝜉 Aspect ratio K Bulk modulus G Shear modulus
* Chao Sun [email protected] * ShangXu Wang [email protected] 1
State Key Laboratory of Petroleum Resources and Prospecting, Key Laboratory of Geophysical Prospecting, China University of Petroleum, Beijing, CNPC, ChangPing, Beijing 102249, China
Laboratoire de Géologie, Ecole Normale Supérieure/CNRS, UMR8538, PSL Research University, 75005 Paris, France
2
K0 Bulk modulus of dry matrix (crack- and porosity-free) G0 Shear modulus of dry matrix (crack- and porosity-free) fc Critical frequency of the dispersion 𝜂 Viscosity of fluid ΔPc Confining pressure Kd Drained bulk modulus Gd Drained shear modulus
1 Introduction The frequency-dependence of the elastic moduli observed in previous experiments (e.g., Batzle et al. 2006; Borgomano et al. 2017; Chapman et al. 2016; Mikhaltsevitch et al. 2016; Pimienta et al. 2015a, b; Sun et al. 2017) are of great interest for seismic interpretation, as they investigate the difference of elastic properties between the field surveys (seismic 1–100 Hz, and logs, ~ 10 kHz) and conventional laboratory measurements (ultrasonic, 1 MHz). These differences are related to the dispersion of the elastic properties and may be influenced by many factors. In saturated ro
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