Transport in Porous Media

, Volume 122, Issue 3, pp 745–759 | Cite as

Numerical Simulations of the Migration of Fine Particles Through Porous Media

  • Qingjian Li
  • Valentina Prigiobbe


The migration of fine particles (or fines) in an oil formation may cause its damage and decrease the well production rate, as several experimental and modeling studies have shown. The major challenge in the description of fines transport is the prediction of the location where particles are blocked. Classical mathematical models consider the fines as a solute and neglect the mechanism that couples fines transport and the fluid flow, without capturing therefore the single particle motion and blockage. Recent observations carried out using microfluidic systems to observe fines migration have shown limitations on tracing particles and on the analysis of the forces acting, e.g., on a single particle. This could be overcome with simulations using a new numerical approach. In this paper, a numerical model comprising lattice Boltzmann method, immersed boundary method, and discrete element method is presented. The model was developed to study fines migration in porous media at the pore scale. By considering the two-way coupling between the liquid and the solid phase (i.e., the particle), the model is able to capture particle motion in the porous medium and the effect of the particle transport on the fluid flow. Simulation results show that the fines migration is determined by the size of the particles as well as by the structure of the porous medium. Particle blockage alters the preferential flow path and decreases the permeability of the porous medium while increasing the swept area and the oil recovery. Moreover, simulations show that the increase of the pressure drop can displace blocked particles in the porous medium throats and allow restoring the initial permeability.


Direct numerical simulation Fines migration Fluid–solid two-phase flow Lattice Boltzmann method Pore-scale modeling 

List of symbols

\(\alpha \)

The direction


The discrete velocity vector

\(\varvec{F}_{\mathrm{f}\text {--}\mathrm{p}}\)

Hydrodynamic force from the fluid to the particle

\(\varvec{F}_{\mathrm{p}\text {--}\mathrm{p}}\)

Collision force between particles

\(\varvec{F}_{\mathrm{w}\text {--}\mathrm{p}}\)

Collision force between a particle and the wall

\(\varvec{T}_{\mathrm{f}\text {--}\mathrm{p}}\)

Torque acting on the particle


The migration velocity of the particle


The angular velocity of the particle


The grid node position

\(\delta _\mathrm{t}\)

The time step

\(\omega _i\)

The weight coefficient

\(\rho _\mathrm{f}\)

The density of fluid

\(\rho _\mathrm{s}\)

The density of solid phase

\(\tau \)

The relaxation time

\(\zeta \)

The safe zone


The lattice sound speed


The force scale


The Dirac delta function


The stiffness parameter

\(F_{\alpha }\)

The external force term

\(f_{\alpha }\)

The distribution function

\(f_{\alpha }^{(\mathrm{eq})}\)

The equilibrium distribution function


The gravity acceleration


The force density


The mass of the ith-particle


The radii of the ith-particle



This work is supported by the Innovation & Entrepreneurial Fellowship Program at Stevens Institute of Technology and the ACS-PRF fund under the Grant Number PRF# 57739-DNI9. The authors would like to thank Dr. Xiaodong Niu at Shantou University (China) for his technical support during the coding of the model presented in this paper. The authors thank the reviewers for their useful comments that allow to improve the quality of the manuscript.

Supplementary material

11242_2018_1024_MOESM1_ESM.pdf (17.1 mb)
Supplementary material 1 (pdf 17466 KB)


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil, Environmental, and Ocean EngineeringStevens Institute of TechnologyHobokenUSA

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