The lattice Boltzmann method is employed in conjunction with a Lagrangian particle tracking algorithm to investigate the fate and transport of nanoparticles as they propagate in porous columns that are packed with spherical particles. In this approach, physical phenomena that result in particle retention and remobilization are represented by a probability for adsorption and desorption, respectively. The method is validated with experiments where polymer-stabilized purified multi-walled carbon nanotubes propagate in a column packed with inert glass beads. Comparison of simulation results to the conventional filtration equation leads to the correlation of the simulation input parameters to macroscopically observed parameters, such as adsorption and desorption rate constants. It is found that adsorption and desorption nominal rates do not affect the diffusivity of the nanoparticles significantly (the change in particle diffusivity is less than 4%) and that particles with smaller size, where the Brownian motion is dominant, are retained more than larger particles. The difference in particle recovery for small versus large particles is of up to 36% when the probability for adsorption is as high as 0.01. (c) 2014 Elsevier Ltd. All rights reserved.