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A wave propagation model with the Biot and the fractional viscoelastic mechanisms

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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.

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Acknowledgements

The authors thank the Exploration and Development Research Institute of PetroChina Changqing Oilfield Company for providing the experimental data. This work was supported by the National Natural Science Foundation of China (Grant Nos. 91730306 and 41390452) and the Shengli Oilfield Company (Grant No. 30200020-18-ZC0613-0030).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Jiaming Yang & Dinghui Yang

  2. Shengli Geophysical Research Institute of SINOPEC, Dongying, 257000, China

    Hongwei Han & Yuanfeng Cheng

  3. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

    Lingyun Qiu

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  1. Jiaming Yang
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  2. Dinghui Yang
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  3. Hongwei Han
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  4. Lingyun Qiu
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  5. Yuanfeng Cheng
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Correspondence to Dinghui Yang.

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Yang, J., Yang, D., Han, H. et al. A wave propagation model with the Biot and the fractional viscoelastic mechanisms. Sci. China Earth Sci. 64, 364–376 (2021). https://doi.org/10.1007/s11430-020-9668-5

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  • DOI: https://doi.org/10.1007/s11430-020-9668-5

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