In this article, a modeling extension for the description of wave propagation in porous media at low-mid frequencies is introduced. To better characterize the viscous and inertial interactions between the fluid and the structure in this regime, two additional terms described by two parameters α1 and α2 are taken into account in the representation of the dynamic tortuosity in a Laurent-series on frequency. The model limitations are discussed. A sensitivity analysis is performed, showing that the influence of α1 and α2 on the acoustic response of porous media is significant. A general Bayesian inference is then conducted to infer, simultaneously, the posterior probability densities of the model parameters. The proposed method is based on the measurement of waves transmitted by a slab of rigid porous material, using a temporal model for the direct and inverse transmission problem. Bayesian inference results obtained on three different porous materials are presented, which suggests that the two additional parameters are accessible and help reduce systematic errors in the identification of other parameters: porosity, static viscous permeability, static viscous tortuosity, static thermal permeability, and static thermal tortuosity.