In this study, an extended two-fluid model (TFM) describing the gas-liquid two-phase flow when gas influx occurs and an acoustic model describing sound propagation within section of marine riser are proposed. The TFM and acoustic model are validated by comparison of the simulation results and filed data for pit gain, and the experimental tests on a custom-designed acoustic gas influx equipment respectively. These two models are coupled by the pressure of sound and solved using finite volume method. Moreover, two signal processing methods in acoustic gas influx detection based on Fourier transform (FT) and Hilbert-Huang transform (HHT) are introduced. Fourier spectrums and Hilbert-Huang spectrums of the simulated signals are presented in time-frequency or time-amplitude distributions respectively. The results show that compared with wellhead detection methods (WDM) which detect the variation of parameters such as pit gain, the two acoustic detection methods which are based on FT and HHT are more sensitive, and the sensitivity of the HHT method is the highest. The acoustic detection method based on HHT is effective and reliable to be further employed for well control and gas influx detection. (C) 2018 Elsevier Ltd. All rights reserved.