The process of gasification is a thermochemical conversion of the organic matter, biomass for example, to syngas that can be converted to biofuel. The pyrolysis of biomass, a key stage of the gasification process, is a volatilization of the porous media that constitutes the biomass under the action of heat. The pyrolysis is characterized by 80% of mass loss. Hence, its modeling is crucial to master the process and therefore design large scale devices. Current studies are based on phenomenological low. The purpose of this work is to elaborate a model on the basis of fundamental laws of physics. The pyrolysis of biomass implies a strong coupling between physico-chemical phenomena and multiscale phenomena that raises many modeling issues. The first difficulty is the complexity of the medium structure which is characterized by a double porosity: porosity at particle scale and porosity at the reactor scale. Moreover, the flow is that of an expandable gas due to the high temperature gradients involved in the process. Finally, the structure of the porous media is modified with time due to the consumption of the biomass particles To model the process, the volume averaging method, a technique of homogenization, is applied to the pore scale equations to obtain a macroscopic description of the phenomena. This upscaling technique allows for avoiding the numerically expensive calculation of fully resolved microstructure. In this study, the variability of the gas density, a crucial issue of the process modelling, is investigated. In the first step, the flow of a compressible fluid through a rigid porous medium is considered. The homogenization leads to an equation of motion that contains two new terms resulting from the fluid compressibility: the first term is an additional pressure proportional to the divergence of the average velocity and the second term is a correction to the total permeability. The degree of compressibility, which is quantified with the Isothermal Compressibility Coefficient, has strong implications on the importance of these terms and hence on the form of the obtained equations. Finally, numerical simulations are carried out to determine the compressibility effect on the total permeability of the porous media. In the second step, compressible flow through a porous media is analysed in terms of the method of volume averaging. The compressibility of the flow is quantified by the Mach number. The macroscopic momentum transport equation corresponds to a Darcy-like model involving an apparent permeability composed of the intrinsic permeability tensor and a correction that involves an intrinsic contribution and a dynamic contribution. The component values of the two permeability tensors are computed by solving the associated closure problems on two dimensional periodic unit cells.