Upscaling colloid transport and retention under unfavorable conditions: Linking mass transfer to pore and grain topology

• Published in: Water resources research 2013-09, Vol.49 (9), p.5328-5341
• Main Authors: Johnson, William P., Hilpert, Markus
• Format: Article
• Language: English
• Subjects: colloid; Colloids; extended tailing; filtration; Markov processes; Mass transfer; pore and grain matrix and topology; Retention; secondary energy minimum; Topology; upscaling
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1002/wrcr.20433

We revisit the classic upscaling approach for predicting Darcy‐scale colloid retention based on pore‐scale processes, and explore the implicit assumption that retention is a Markov process. Whereas this assumption holds under favorable attachment conditions, it cannot be assumed to hold under unfavorable conditions due to accumulation of colloids in the near‐surface fluid domain. We develop a novel link between two‐layer mass transfer parameters and the topologies of the pore and collector domains, starting with an elegant outcome of classic colloid filtration theory: that the likelihood of mass transfer from the bulk‐ to the near‐surface fluid domain depends strongly on colloid proximity to the forward flow stagnation axis of each collector (grain). Applying this concept to colloid mass transfer from the near‐surface to the bulk fluid domain yields the conclusion that such mass transfer predominantly occurs at rear‐flow stagnation zones on collector surfaces. We support this concept with experimental proof that the alignment of rear and forward flow stagnation zones influences colloid mass transfer to surfaces. Colloid accumulation in the near‐surface fluid domain under unfavorable conditions may produce extended tailing of colloids during elution in Darcy‐scale studies by: (1) long residence times of colloids in the near‐surface fluid domain; (2) direct propagation of near‐surface colloids from upstream to downstream collectors. The latter generates correlated motion that violates the assumed independence of colloid retention on history of transport. We suggest an approach to upscaling that accounts for the above‐described influences of colloid‐surface interactions and pore/collector domain topology. Key Points Colloid retention upscaling assumes independence on transport history Colloid accumulation near surfaces violates the assumed independence Forward and rear flow stagnation zones govern transfer to/from bulk fluid