The sound field in porous media is affected by fluid flow governed by dynamic permeability. This macroscopic quantity is frequency dependent and can be connected with a relevant pore-scale estimation called the stochastic dynamic permeability (SDP) model. To further investigate the characteristics of the SDP model with different variables related to Biot relaxation frequency and envisage its potential applications in borehole acoustics, the influence of microstructures from a pore-scale image on dynamic permeability is studied. Then, the characteristics of dynamic permeability and a borehole Stoneley wave with different parameters are explored by sensitivity analysis. According to the influences of pore fluid parameters including density and viscosity, the velocity dispersion and attenuation of Stoneley waves in oil, gas and water-bearing formations are calculated. The results show that the dynamic permeability is affected by the microstructure of pores and the Biot relaxation frequency parameters have a crucial influence on the attenuation of the borehole Stoneley wave. Meanwhile, the attenuation coefficient can be used to identify the type of pore fluids. This is verified by an application to in situ acoustic logging data. The work provides a relatively comprehensive understanding of the features of the SDP dynamic permeability and indicates an approach to identify pore fluid by using a borehole Stoneley wave.