Transport of polydisperse colloid suspensions in a single fracture

Abstract

The transport of variably sized colloids (polydisperse) in a fracture with uniform aperture is investigated by a particle-tracking model that treats colloids as discrete particles with unique transport properties while accounting for either matrix diffusion or irreversible colloid deposition. For the special case of a monodisperse colloid suspension the particle-tracking model is in perfect agreement with predictions based on an existing analytical solution. It is shown that lognormal colloid size distributions exhibit greater spreading than monodisperse suspensions. Increasing the fracture porosity of the solid matrix leads to higher matrix diffusion, which in turn delays particle breakthrough for both the monodisperse and variably sized colloid suspensions. The smallest particles of a distribution are more greatly affected by matrix diffusion whereas the largest particles are transported faster and further along a fracture. Both perfect sink and kinetic colloid deposition onto fracture surfaces are examined. Kinetic deposition accounts for colloid surface exclusion by either a linear or nonlinear blocking function. For both cases the smallest colloid particles tend to preferentially deposit onto the fracture wall. Both matrix diffusion and surface deposition tend to discretize colloid distributions according to particle size so that larger particles are least retarded and smaller particles are more slowly transported. Furthermore, it is shown that the rate of colloid deposition is inversely proportional to the fracture aperture.