For simulating flows in a porous medium, a numerical tool based on the Lattice Boltzmann Method (LBM) is developed with regards to the classical D2Q9 model. A short description of this model is presented. This technique, applied to two-dimensional configurations, indicates its ability to simulate phenomena of heat and mass transfer. The numerical study is extended to estimate physical parameters that characterize porous materials, like the so-called Effective Thermal Conductivity (ETC) which is of our interest in this paper. Obtained results are compared with those which could be found analytically and by theoretical models. Finally, a porous medium is considered to find its ETC.