Pore Network Modeling of Nanoparticle Dispersion in Porous Media

Understanding the processes that give rise to hydrodynamic dispersion of nanoparticles in porous media is important not only for assessing the risk from their accidental release in subsurface environments, but also for the design of nanoremediation strategies.  Pore network models offer distinct advantages over continuum models, including the ability to account for the distribution of pore-scale velocities, as well as other phenomena that occur at the pore scale and are dependent on the interaction between nanoparticles and the local geometry of the pore space (hindered diffusion, size exclusion, etc.). Adopting a Eulerian approach, we formulate here a pore network model in OpenPNM, and present simulations of nanoparticle transport in a fully-saturated column packed with spherical beads. The pore network which is extracted from a voxel image of the simulated sphere pack is found to accurately represent the permeability, tortuosity and capillary properties of a real column of glass beads. The resulting pore network model is used to investigate an aspect of nanoparticle transport that has so far received limited attention, namely the possible effect of nanoparticle size on dispersivity. To this end, the longitudinal dispersion coefficient is determined by simulating transient advection and diffusion in the pore network, introducing either a pulse or step-change injection, and then fitting analytical solutions to the resulting elution curve.  It is found that nanoparticle size influences the dispersion coefficient or the effective particle velocity only when the ratio of particle to bead (solid grain) size is sufficiently high (greater than about 0.01). Under such conditions, the nanoparticles experience an earlier breakthrough due to the velocity profile exclusion. Hindered diffusion is found to play a significant role only when the Peclet number is less than 10.  In the absence of such effects, the simulations provide a priori predictions of the longitudinal dispersion coefficient in agreement with a large body of literature data.