We present a finite element – finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. The advantage of the proposed methodology with respect to other pore-scale modelling approaches is that no simplifications regarding the geometry of the porous space are required and no approximations to the flow equations are introduced. We apply this method in a proof-of-concept study of a digitised Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale transport and diffusion of the adsorbing solute. We also demonstrate how analysis of the pore geometry can be used to identify the locations of oil during the two-phase flow and couple this with the reactive transport modeling to show how this procedure can be used to estimate the potential of the enhanced oil recovery techniques.