Transport in Porous Media

, Volume 67, Issue 1, pp 135–164 | Cite as

A stochastic model for filtration of particulate suspensions with incomplete pore plugging

  • A. A. ShapiroEmail author
  • P. G. Bedrikovetsky
  • A. Santos
  • O. O. Medvedev
Research Article


A population balance model for particulate suspension transport with capture of particles by porous medium accounting for complete and incomplete plugging of pores by retained particles is derived. The model accounts for pore space accessibility, due to restriction on finite size particle movement through the overall pore space, and for particle flux reduction, due to transport of particles by the fraction of the overall flux. The novel feature of the model is the residual pore conductivity after the particle retention in the pore and the possibility of one pore to capture several particles. A closed system of governing stochastic equations determines the evolution of size distributions for suspended particles and pores. Its averaging results in the closed system of hydrodynamic equations accounting for permeability and porosity reduction due to plugging. The problem of deep bed filtration of a single particle size suspension through a single pore size medium where a pore can be completely plugged by two particles allows for an exact analytical solution. The phenomenological deep bed filtration model follows from the analytical solution.


Deep bed filtration Incomplete plugging Suspension Size distribution Accessibility Stochastic model Averaging 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • A. A. Shapiro
    • 1
    Email author
  • P. G. Bedrikovetsky
    • 2
  • A. Santos
    • 3
  • O. O. Medvedev
    • 1
  1. 1.Department of Chemical EngineeringTechnical University of DenmarkLyngbyDenmark
  2. 2.Petroleum DepartmentState North Fluminense University (UENF/LENEP)Riviera Fluminense, MacaéBrazil
  3. 3.Civil Engineering DepartmentCatholic University do Rio de Janeiro (PUC-RJ/GTEP)Rio de JaneiroBrazil

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