Reactive transport in porous media: pore-network model approach compared to pore-scale model

Accurate determination of three macroscopic parameters governing reactive transport in porous media, namely, the apparent solute velocity, the dispersion, and the apparent reaction rate, is of key importance for predicting solute migration through reservoir aquifers. Two methods are proposed to calculate these parameters as functions of the Péclet and the Péclet-Dahmköhler numbers. In the first method called the pore-scale model (PSM), the porous medium is discretized by the level set method; the Stokes and convection-diffusion equations with reaction at the wall are solved by a finite-difference scheme. In the second method, called the pore-network model (PNM), the void space of the porous medium is represented by an idealized geometry of pore bodies joined by pore throats; the flow field is computed by solving Kirchhoff's laws and transport calculations are performed in the asymptotic regime where the solute concentration undergoes an exponential evolution with time. Two synthetic geometries of porous media are addressed by using both numerical codes. The first geometry is constructed in order to validate the hypotheses implemented in PNM. PSM is also used for a better understanding of the various reaction patterns observed in the asymptotic regime. Despite the PNM approximations, a very good agreement between the models is obtained, which shows that PNM is an accurate description of reactive transport. PNM, which can address much larger pore volumes than PSM, is used to evaluate the influence of the concentration distribution on macroscopic properties of a large irregular network reconstructed from microtomography images. The role of the dimensionless numbers and of the location and size of the largest pore bodies is highlighted.