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). This relationship could be subsequently integrated with available models relating F to the system’s physicochemical properties to develop an explicit mathematical relationship between κ and these properties.
The F-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.
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.