On the failure of upscaling the single-collector efficiency to the transport of colloids in an array of collectors

Defining the removal efficiency of a filter is a key aspect for colloid transport in porous media. Several efforts were devoted to derive accurate correlations for the single-collector removal efficiency, but its upscaling to the entire porous medium is still a challenging topic. A common approach involves the assumption of deposition being independent of the history of transport, that is, the collector efficiency is uniform along the porous medium. However, this approach was shown inadequate under unfavorable deposition conditions. In this work, the authors demonstrate that it is not adequate even in the simplest case of favorable deposition. Computational Fluid Dynamics (CFD) simulations were run in a vertical array of 50 identical spherical collectors. Particle transport was numerically solved by analyzing a broad range of parameters. The results evidenced that when particle deposition is not controlled by Brownian diffusion, nonexponential concentration profiles are retrieved, in contrast with the assumption of uniform efficiency. If sedimentation and interception dominate, the efficiency of the first sphere is significantly higher compared to the others, and then declines along the array down to an asymptotic value. Finally, a correlation for the upscaled removal efficiency of the entire array was derived.