This study presents the structure of a mathematical model of the composting process. It sets up a methodology for the presentation of the biological and physic-chemical phenomena involved, making possible to couple biological models developed by different authors to the proposed physical model. This one considers the substrate as a porous media in which the three phases, solid, liquid and gaseous, are present. Mass and energy flows between them are governed by basic transfer laws. The gaseous phase is considered, in the base model, as a completely stirred mixture of oxygen, CO2, ammonia, water vapour and nitrogen, both considered as ideal gases. Its extension to the 1D space incorporates the movement of the gaseous phase due to pressure gradient, the conductive heat transfer in the solid matrix, the convective energy transport, both as sensible and latent heat, and the convective mass transport of gaseous components. The simulations, run with a unique set of physical, stoichiometric and kinetic parameters, for experiments with different substrates, reproduce satisfactorily the main trends observed.