Transport of polydisperse colloids in a saturated fracture with spatially variable aperture

A particle tracking model is developed to simulate the transport of variably sized colloids in a fracture with a spatially variable aperture. The aperture of the fracture is treated as a lognormally distributed random variable. The spatial fluctuations of the aperture are described by an exponential autocovariance function. It is assumed that colloids can sorb onto the fracture walls but may not penetrate the rock matrix. Particle advection is governed by the local fracture velocity and diffusion by the Stokes-Einstein equation. Model simulations for various realizations of aperture fluctuations indicate that lognormal colloid size distributions exhibit greater spreading than monodisperse suspensions. Both sorption and spreading of the polydisperse colloids increase with increasing variance in the particle diameter. It is shown that the largest particles are preferentially transported through the fracture leading to early breakthrough while the smallest particles are preferentially sorbed. Increasing the variance of the aperture fluctuations leads to increased tailing for both monodisperse and variably sized colloid suspensions, while increasing the correlation length of the aperture fluctuations leads to increased spreading.