Stochastic model for filtration by porous materials

Abstract

The transport of colloids in porous media is governed by deposition on solid surfaces and porescale flow variability. Classical approaches, like the colloid filtration theory (CFT), do not capture the behaviors observed experimentally, such as non-exponential steady state deposition profiles and heavy tailed arrival time distributions. In the framework of CFT a key assumption is that the colloid attachment rate k is constant and empirically estimated by a posteriori macroscopic data fitting. We propose a stochastic model that explicitly accounts for variability of the pore-scale transport and attachment properties. Colloidal motion is modeled as a sequence of displacements whose velocity and extension are statistically distributed. Colloidal depositions are modeled as random events whose statistics are determined by flow velocity, pore size and attachment rate. The resulting deposition profiles are in general non-exponential and can be predicted based on the disorder distributions.

Trait-specific dispersal of bacteria in heterogeneous porous environments: from pore to porous medium scale

“…We adopted a recently published model that accounts for the fundamental mechanisms driving colloid filtration by porous systems, by explicitly taking into account the variability of particle transport and attachment rate, which describes the individual attachment events per unit of time [37]. This physical model is similar to pore-network models that represent the flow through the entire porous system as that through a network of connected tubes (pipes): each pore is a tube of given radius and is characterized by a given velocity and connectivity.…”

“…Furthermore, we directly observed how the presence of a resident biofilm on grain surfaces affects the dispersal of motile and non-motile cells. We coupled observations at the micro-and macro-scales with a recently proposed stochastic model [37] that takes into account both the physical heterogeneity and transport dynamics within a continuous time random walk (CTRW) framework. This novel approach allowed us to shed new light on the bacterial dispersal behaviour and its consequences for ecological processes in porous environments.…”

Multiscale dynamics of colloidal deposition and erosion in porous media

“…While in many cases this approach provides a useful way to model colloidal transport and deposition, it often does not reliably predict experimentally observed deposition profiles without the use of additional fitting parameters, reflecting the combined influence of many different factors on particle transport and deposition (37)(38)(39). To shed further light on this problem, various computational schemes are being developed, generating intriguing predictions of particle deposition and erosion (40)(41)(42)(43)(44)(45)(46). However, in the absence of experimental studies connecting the dynamics of colloidal deposition and erosion at the pore scale to flow and transport at the scale of the overall porous medium, accurate prediction or control of particle transport and deposition remains elusive.…”

The Complexity of Porous Media Flow Characterized in a Microfluidic Model Based on Confocal Laser Scanning Microscopy and Micro-PIV

“…Notice that the work by Morales et al utilized 68 µm diameter spheres, a size which effectively rules out diffusion. It does nicely fit in a very elegant line of work that studies Lagrangian (i.e., particle trajectories, so effectively streamlines) stochastics (Bijeljic et al 2004;Dentz et al 2016Dentz et al , 2018Puyguiraud et al 2019), and even including absorption/desorption (Miele et al 2019). The work by Bijeljic stands out because of the use of pore-network models.…”

“…Streamline routing is no longer included when the stochastic Lagrangian velocity distribution is derived from a stochastic description of the pore space (Dentz et al 2018). Nevertheless, the CTRW approach appears to work well for colloidal particles (Morales et al 2017;Miele et al 2019). Proving the current form of CTRW to be suitable for molecular solutes would be the next step.…”