Abstract:

The accurate description of transport of charged chemical species
through porous media needs to include electrostatic interactions. While
solute transport models have pursued the incorporation of electrostatic
coupling effects, efforts have been primarily focused on Eulerian
formulations of transport. Particle-based models provide an alternative
approach with known advantages for simulating solute transport in porous
media. However, electrostatic coupling effects are generally not
considered, hence limiting the applicability of particle-based
formulations to problems of multispecies ionic solute transport. This
work presents a Random Walk Particle Tracking (RWPT) formulation that
incorporates electrostatic coupling effects while calculating the
displacement of solute particles. The formulation is based on an
equivalent Fokker–Planck form of the Nernst–Planck-based transport
equation that allows to determine the nonlinear transport coefficients
that effectively incorporate electrostatic coupling in the particles’
displacements. The simulation approach is generalized, enabling the use
of the RWPT method for simulating problems of multispecies ionic solute
transport through homogeneous and heterogeneous porous media. Numerical
simulations making use of the proposed formulation are benchmarked at
different scales with experimental data and with known Eulerian
solutions to problems of transport with electrostatic coupling, with
results supporting the validity of the particle-based simulation approach.