Dynamic bulk and shear moduli due to grain-scale local fluid flow in fluid-saturated cracked poroelastic rocks: Theoretical model |
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| Institution: | 1. Department of Astronautics and Mechanics, Harbin Institute of Technology, P. O. Box 344, Harbin 150001, PR China;2. Department of Civil and Environmental Engineering and Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, U.S.A;1. Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel;2. Department of Civil and Environmental Engineering and Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA;3. Department of Biomedical Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel;1. Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, PR China;2. GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany;3. Guangzhou Center for Gas Hydrate Research, Chinese Academy of Sciences, Guangzhou 510640, PR China;4. Guangdong Province Key Laboratory of New and Renewable Energy Research and Development, Guangzhou 510640, PR China;5. Department for Earth and Environmental Sciences, University of Potsdam, 14476 Potsdam, Germany;1. School of Earth Sciences and Engineering, Hohai University, Nanjing, China;2. Earth Atmospheric, and Planetary Sciences Department, Purdue University, West Lafayette, IN, USA;3. National Institute of Oceanography and Applied Geophysics – OGS, Trieste, Italy;4. SINOPEC Geophysical Research Institute, Nanjing, China |
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| Abstract: | Grain-scale local fluid flow is an important loss mechanism for attenuating waves in cracked fluid-saturated poroelastic rocks. In this study, a dynamic elastic modulus model is developed to quantify local flow effect on wave attenuation and velocity dispersion in porous isotropic rocks. The Eshelby transform technique, inclusion-based effective medium model (the Mori–Tanaka scheme), fluid dynamics and mass conservation principle are combined to analyze pore-fluid pressure relaxation and its influences on overall elastic properties. The derivation gives fully analytic, frequency-dependent effective bulk and shear moduli of a fluid-saturated porous rock. It is shown that the derived bulk and shear moduli rigorously satisfy the Biot-Gassmann relationship of poroelasticity in the low-frequency limit, while they are consistent with isolated-pore effective medium theory in the high-frequency limit. In particular, a simplified model is proposed to quantify the squirt-flow dispersion for frequencies lower than stiff-pore relaxation frequency. The main advantage of the proposed model over previous models is its ability to predict the dispersion due to squirt flow between pores and cracks with distributed aspect ratio instead of flow in a simply conceptual double-porosity structure. Independent input parameters include pore aspect ratio distribution, fluid bulk modulus and viscosity, and bulk and shear moduli of the solid grain. Physical assumptions made in this model include (1) pores are inter-connected and (2) crack thickness is smaller than the viscous skin depth. This study is restricted to linear elastic, well-consolidated granular rocks. |
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| Keywords: | Porous rocks Eshelby transform Squirt flow Wave attenuation Mori–Tanaka Scheme |
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