Modelling of low-frequency acoustic wave propagation in dilute gas-bubbly liquids

Zizhen Wang* (Corresponding Author), Weidong Zhou, Tengfei Shu, Qilong Xue, Rui Zhang, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


A numerical modelling method for the low-frequency (∼102 Hz) acoustic wave propagation in a bubbly fluid with a low gas fraction is developed in this paper. Based on the digital image analysis of the bubbly fluid, the geometrical model of polydisperse bubble populations is created. The developed method is first verified by the Wood's (1955) equation and the Commander & Prosperetti (1989) model. Then the influence of gas fraction, excitation frequency and bubble radius on the acoustic properties of the bubbly fluid is systematically examined. The obtained results confirmed that the velocities and attenuations for different bubble radius distributions are close to those obtained for the monodisperse models. The gas fraction is the key controlling factor of the acoustic velocity, while the influence of the bubble size at low frequencies can be neglected. The velocity dispersion with frequency is about 5% even in Wood's regime and the attenuation increases with a higher gas fraction and excitation frequency, while it decreases with a smaller bubble radius. By estimation of bubble expansion during the migration of gas kick, variation trends of acoustic velocity and attenuation along the wellbore are discussed. This implies that variations of the velocity and attenuation of drilling fluid at low-frequencies during the gas migration can be used for an accurate and earlier gas kick detection than currently used methods.
Original languageEnglish
Article number106979
Number of pages13
JournalInternational Journal of Mechanical Sciences
Early online date3 Dec 2021
Publication statusPublished - 15 Feb 2022

Bibliographical note

This research is supported by the National Natural Science Foundation of China (No.52074328). The collaboration between Wang and Wiercigroch is supported by the NSFC-RS Exchange Project (No. 52011530184). This work is also funded by the Fundamental Research Funds for the Central Universities, China (No.18CX07008A). Wiercigroch would like to also acknowledge the generous financial support by the Russian Science Foundation (Project No. 19–19–00408).


  • Acoustic velocity
  • Attenuation
  • Bubbly fluid
  • Gas kick detection
  • Low-frequency acoustic wave
  • Numerical modelling


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