In our previous work, macroscopic models for multi-species diffusion/heterogeneous reaction with different diffusion coefficients in porous media were derived from the homogenization technique based on a spectral approach ( Le et al. , Applied Mathematical Modelling, 104 , 666-681, 2022 ). This work aims to analyze numerically the properties of the eigenvalues and eigenfunctions of the spectral problem, the solution of the closure problems and the effective coefficients as a function of key parameters such as the Damkohler number, the ratios of the reaction rates and diffusion coefficients. This provides in-depth understanding of the role of the coefficients involved in the macroscopic models in the whole range of the Damkohler number. Simulation results of the macroscopic equations are compared with direct numerical simulations in unsteady regime, showing a very satisfactory agreement and thus numerically validating the proposed models. (c) 2022 Published by Elsevier Inc.