Stochastic analysis of early tracer arrival in a segmented fracture pathway

Abstract

Abstract. 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. IntroductionGeological isolation of radioactive waste relies on stable, low-permeability rock as an important barrier to the release of radionuclides to the biosphere. Transport in these lowpermeability rock barriers occurs mainly by advection through interconnected networks of fractures but is slowed by microscopic processes that act to retain particles in the surrounding rock. As particles are swept along by water flowing in the rock fractures, they can diffuse into the stagnant (or relatively slowly moving) water in the pore space of surrounding rocks where they may sorb onto mineral grains. These microscopic retention mechanisms act together to retard the downstream movement in a nonlinear fashion. As part of ongoing safety assessments of proposed waste isolation facilities, it is necessary to have quantitative predictions for the time required for radionuclides to migrate through the rock barriers, taking into account advection and retention processes.Transport in fractured rock is further complicated by uncertainty in the transport pathways, as it is usually not possible to have direct observations of subsurface features. The best that could be hoped for in a typical application is to know the statistics of fracture attributes, such as aperture and length. This uncertainty requires that radionuclide migration, and the related issue of waste repository performance assessment, be addressed in a probabilistic framework. In a previous paper

Hydrodynamic control of tracer retention in heterogeneous rock fractures

“…The actual problems of tracer transport and retention in fracture rock require a transition from a single fracture to a fracture network. Analytical results have been provided in this direction [ Painter et al , 1998; Painter and Cvetkovic , 2001]; however, their applicability under field conditions has yet to be established, presumably using numerical discrete fracture network simulations. Thus further simulation studies are needed where heterogeneity on at least two scales is accounted for (within fractures and between fractures), and simple estimators (bounds) are identified under a varying range of boundary conditions and network heterogeneity.…”

U, Th, Eu and colloid mobility in a granite fracture under near-natural flow conditions

“…However, in longer flow field experiments (4.9 m) with decreased linear flow velocity (1 m h −1 ) a significant peak retardation and peak height reduction for the reactive radionuclides could be observed, which [21] interpreted by a sorption and matrix diffusion dominated transport process with less relevant transport through highly transmissive zones. Stochastic analysis could show that the expected peak arrival time strongly depends on the bulk retention parameter η B [22]. This dimensionless parameter η B is thereby defined as:…”

Stochastic simulation of radionuclide migration in discretely fractured rock near the Äspö Hard Rock Laboratory

“… Cvetkovic et al [1999] were the first to account for effects of flow dynamics on tracer retention in single heterogeneous fractures, introducing a random (Lagrangian) variable β [T/L]. Analytical results on the β statistics for fracture networks were provided by Painter et al [1998] and Painter and Cvetkovic [2001] by extending the channel concept of Neretnieks [1980]. Results on the statistics of β in fracture networks where flow dynamics is resolved, were presented by Painter et al [2002] using generic DFN simulations.…”