We present a numerical method for estimating the stiffness-to-porosity relationships for evolving microstructures of Fontainebleau sandstone. The proposed study is linked to geological storage of CO 2 and focuses on long-term and far field conditions, when the progressive degradation of the porous matrix can be assumed to be homogeneous at the sample scale. The method is based on microstructure sampling with respect to morphological descriptors extracted from microtomography. First, an efficient method of generation of accurate numerical media is proposed. The method is based on grain deposit, compaction and diagenesis and allows to reproduce user-defined morphological parameters. Second, two simple numerical models that mimic chemical degradation of porous aquifers are presented. Effective elastic properties are estimated within the framework of periodic homogenization and finite element approach. A fixed-point method on a self-consisted outer layer allows to consider non-periodic representative volume elements. Accurate predictions of elastic properties over a wide range of porosity are obtained. The overall evolutions of elastic behaviour due to the increase of porosity are in excellent agreement both, with experimental data and the results obtained by Arns et al. [1].