The deposition of particles through the system is quantitatively expressed by a single parameter: the deposition efficiency in the porous bed, whose theoretical reference lies in the classical colloid filtration theory (CFT), which further subdivides the process of deposition in the three distinct mechanisms by which particles can reach the solid grain: Brownian diffusion, steric interception, and gravitational sedimentation. It has to be noted that the most important parameter affecting these three mechanisms (and the only common amongst them) is particle size.
Theoretical works based on the CFT studying particle deposition at the pore-scale suffer a big disadvantage: mainly, they either consider a single unit-cell comprised of a single grain, thus ignoring the effect of packing randomness to macroscale fluid flow behaviour, or are limited to very simple particle shapes, thus neglecting the effects of the grains surface roughness (and thus, increased surface area) on mass transport. Moreover, no comprehensive pore-scale study of the influence of the geometrical features of the porous medium on particle removal mechanisms is still available, whereas indeed both the packed bed porosity and tortuosity have been shown to have a marked influence on particle deposition efficiency. Last but not least deposition involving a population of particles characterized by a particle size distribution has not been studied before. More strikingly, while aggregation kernels for solid particles in fluid flows for use in population balance modelling are available, no work has yet approached the search for a macroscopic formulation of these kernels which also took account of the porous medium geometric features.
In order to satisfy these needs, our novel approach relies on the construction of an array of 3D realistic models using the open-source code Blender, which allows for a fast and robust modelling of packings of arbitrary grain size distribution and grain shape. Having obtained the geometrical models of the porous media considered, flow field and particle transport were then investigated using a finite-volume CFD code (OpenFoam). The Navier-Stokes equations were solved for the flow and an Eulerian approach was used for particle transport, considering both uniform and non-uniform particle size distributions. Figure 1 qualitatively shows a result of the performed particle deposition simulations, and depicts the particle removal process. This methodology allowed us to perform a comprehensive study of all the relevant geometric and fluid dynamic variabilities at the pore-scale and obtain, in each case considered, an estimate of the particle deposition efficiency.
Another important innovation in our work is the introduction of the population balance equation, whose solution is dealt with using the Quadrature Method of Moments (QMOM). This approach allowed us to consider the evolution of a non-uniformly distributed population of particles which remains unexplored in the current state of the art regarding particle deposition simulation at the pore-scale and, as mentioned, will allow for a description of aggregation phenomena at the macroscopic scale. The mentioned case of nano-sized zerovalent iron injection for groundwater remediation will serve well as illustration of the importance of this improvement. Due to magnetic and Van der Waals interactions these particles are prone to aggregation, forming clusters of varying size. These same aggregates, subject to high shear forces in zones of increased fluid velocity (i.e.: pore throats), will then break; these two effects combined will result in a temporal and spatial evolution of the particle size distribution, which greatly affects the particle deposition efficiency in the porous medium for each of the three aforementioned deposition mechanisms, heavily influenced as they are by particle size.
The effects of these innovations are made apparent by the results of this work, which clearly show how the standard CFT theory fails to correctly describe particle deposition in realistic, random, packed beds (as it can clearly be seen in Fig.2) and how both particle transport profiles and deposition efficiencies differ a great deal between uniform particle distributions and non-uniform ones.
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