Analytical description of colloid behavior in single fractures under irreversible deposition

OBJECTIVES: Irreversible colloid deposition in groundwater-saturated fractures is typically modeled using a lumped deposition coefficient (κ) that reflects the system physiochemical conditions. A mathematical relationship between this coefficient and the physicochemical conditions controlling deposition has not yet been defined in the literature; thus, κ is typically fitted using experimental observations. This research develops, for the first time, an analytical relationship between κ and the fraction of colloids retained in single fractures (F_r). This relationship could be subsequently integrated with available models relating F_r to the system's physicochemical properties to develop an explicit mathematical relationship between κ and these properties. METHOD: The F_r-κ analytical relationship was developed through conceptualizing irreversible deposition as first-order decay, as both lead to permanent mass loss, and coupling this with the advection-dispersion equation. The model estimates of colloid deposition were compared to observations from laboratory-scale colloid tracer experiments. A variance-based global sensitivity analysis was applied to identify the parameters controlling deposition. FINDINGS: The analytical relationship efficiently replicated the experimental observations, and the global sensitivity analysis revealed that colloid deposition variability is controlled by fracture length, aperture size, and deposition coefficient; this supports the accepted understanding that colloid deposition is controlled by the system's physicochemical properties.