Colloid transport through a variable-aperture fracture under unfavorable attachment conditions: Characterization with a continuous time random walk model

Although the effects of fracture aperture variability on colloid advection and dispersion are well understood, how aperture variability affects colloid deposition under unfavorable geochemical conditions remains underexplored. To address this knowledge gap, we simulated 6200 cases of colloid transport in variable-aperture fractures with different magnitudes of fracture aperture variability and correlation lengths. Flows were laminar (Reynolds number < 1) with dispersion-dominated transport (Peclet number < 1) in the simulations. The numerically obtained breakthrough curves (BTCs) reflected non-Fickian transport behavior with power-law tailing where the power-law exponent increased with aperture variability rather than correlation length. Solutions to the advection-dispersion-reaction equation (ADRE) and a continuous time random walk (CTRW) model were fit to the BTCs. The CTRW model faithfully reproduced BTCs that decayed according to a power law, while the ADRE failed to do so. The ensemble mean of the attachment rate (equivalent to the reaction rate in the ADRE) in the CTRW model was correlated to a measurable property (i.e., aperture variability) using a power-law function. This newly established function facilitates accurate prediction of non-Fickian colloid transport using the CTRW model where dynamic attachment and detachment of colloids are considered under unfavorable deposition conditions.