Predictive model of solute transport with reversible adsorption in spatially periodic hierarchical porous media

• A model for adsorbing solute transport in hierarchical porous media.
• Closure equations are numerically solved in a unit cell.
• Prediction results agree with numerical and experimental results.
• The model guides the design of pore geometry to control solute transport.

Solute transport in hierarchical porous media with reversible adsorption is predicted by the volume averaging method. A transient macroscopic advection-diffusion equation is derived to describe the multiscale solute transport problem. The theoretical expression of the dispersion tensor is obtained which is the function of pore-scale velocity profile. Steady closure equations are derived to calculate the dispersion tensor. With the aid of pore-scale simulation in unit cells of the hierarchical porous media, the dispersion tensor can be calculated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns comprised of ordered, porous pillars. It is straightforward to use the model to predict the solute transport behavior in fixed beds packed with particles.