This paper aims to study the dispersion phenomena of acoustic waves propagating in a medium composed of a periodic mixture of different poroelastic saturated materials. At mesoscale, each poroelastic saturated material are assumed to be considered by the Biot model. We will present and compare two computational procedures for estimating the effective phase velocities and attenuation of plane waves in the period poroelastic structure at the macroscopic scale. First, wave-based Bloch analysis was employed to derive a finite element formulation which leads to a quadratic complex eigenvalue problem. The equivalent fast/slow compressional as well shear wave modes may be selected by analyzing the computed complex wave numbers. Second, we used the asymptotic homogenization method to derive the effective properties (mass, poroelastic, dynamic permeabilities) which allows us to estimate the effective wave dispersion equation. The polarization of wave modes at the cell level may be reconstructed from macroscopic solution. Numerical results show that both methods could provide well-matched estimations of the effective phase velocities and attenuation within the first Brillouin zone associated with the periodic structure.