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Stochastic model for filtration by porous materials

Filippo Miele1,2, Pietro de Anna2,*, and Marco Dentz1,†

  • 1Spanish National Research Council (IDAEA-CSIC), Barcelona 08034, Spain
  • 2Institut des sciences de la Terre, University of Lausanne, Lausanne 1015, Switzerland

  • *pietro.deanna@unil.ch
  • †marco.dentz@csic.es
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Phys. Rev. Fluids 4, 094101 – Published 10 September, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.094101

Abstract

The transport of colloids in porous media is governed by deposition on solid surfaces and pore-scale flow variability. Classical approaches, like the colloid filtration theory (CFT), do not capture the behaviors observed experimentally, such as nonexponential 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, nonexponential and can be predicted based on the disorder distributions.

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Phys. Rev. Fluids 4, 094101– Published 10 September, 2019
  • Received 25 November 2018
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