Stochastic analysis of early tracer arrival in a segmented fracture pathway

A stochastic model for transport and retention in fractured rock is proposed as an alternative to more elaborate numerical simulations. Contaminants are transported by advection through a series of n rock fractures. The microscopic processes of matrix diffusion and sorption act together to retain contaminants in the host rock. The transport pathway is characterized by large-scale fluctuations in the advection velocity caused by spatial variability in the fracture attributes along the pathway. The moments of the time of arrival of an initial solute pulse are related in a generic way to the joint distribution of fracture aperture and length. These moments are controlled primarily by a dimensionless retention parameter that incorporates all the deterministic model parameters and by correlation between fracture length and aperture. The results show that a systematic bias in the predicted contaminant transport can be introduced by neglecting spatial variability in fracture attributes. The relative contributions of fracture-to-fracture variability and within-fracture variability are also explored. The proposed stochastic methodology can be merged with relatively simple numerical simulations to broaden the applicability.