A wave propagation model with the Biot and the fractional viscoelastic mechanisms
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wave propagation model with the Biot and the fractional viscoelastic mechanisms 1
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Jiaming YANG , Dinghui YANG , Hongwei HAN , Lingyun QIU & Yuanfeng CHENG 1
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Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; 2 Shengli Geophysical Research Institute of SINOPEC, Dongying 257000, China; 3 Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
Received January 2, 2020; revised July 24, 2020; accepted August 3, 2020; published online October 29, 2020
Abstract Energy loss in porous media containing fluids is typically caused by a variety of dynamic mechanisms. In the Biot theory, energy loss only includes the frictional dissipation between the solid phase and the fluid phase, resulting in underestimation of the dispersion and attenuation of the waves in the low frequency range. To develop a dynamic model that can predict the high dispersion and strong attenuation of waves at the seismic band, we introduce viscoelasticity into the Biot model and use fractional derivatives to describe the viscoelastic mechanism, and finally propose a new wave propagation model. Unlike the Biot model, the proposed model includes the intrinsic dissipation of the solid frame. We investigate the effects of the fractional order parameters on the dispersion and attenuation of the P- and S-waves using several numerical experiments. Furthermore, we use several groups of experimental data from different fluid-saturated rocks to testify the validity of the new model. The results demonstrate that the new model provides more accurate predictions of high dispersion and strong attenuation of different waves in the low frequency range. Keywords Citation:
Poroviscoelasticity, Wave propagation, Dispersion and attenuation, Fractional derivative
Yang J, Yang D, Han H, Qiu L, Cheng Y. 2020. A wave propagation model with the Biot and the fractional viscoelastic mechanisms. Science China Earth Sciences, 63, https://doi.org/10.1007/s11430-020-9668-5
1. Introduction Petroleum is one of the most important energy resources for human society, and its exploration has become a research hotspot during the past few decades. Underground geological information is critical in the search for oil reservoirs. One of the most popular methods is the reservoir inversion based on wave propagation models. Therefore, it is of crucial importance to establish an appropriate physical model to simulate the wave propagation in underground porous media. The straightforward wave propagation model is the elastic wave model in isotropic media (Wang et al., 2012). However, the actual media beneath the surface usually consist of the rock frame, fluids and gases
(Nie and Yang, 2008). It leads to complex coupling dynamic mechanisms in this multiphase mixture and the inappropriateness of the assumption of the elasticity. Biot (1956a, 1956b) first established a two-phase wave propagation model that considers the dynamic coupling effects and dissipation mechanisms between the fluid phase and solid phase in porous media. The Bio
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