Contaminant advection and spreading in a fractured permeable formation: Part 2. Numerical simulation

Birkhölzer, Jens; Rubin, Hillel; Daniels, H.; Rouve, G.

doi:10.1016/0022-1694(93)90164-5

Cited by 26 publications

(2 citation statements)

References 6 publications

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“…Our study aims at demonstrating that the CTRW framework not only can substitute for dual‐continuum approaches, but is generally applicable to fractured porous formations over a wide range of matrix permeabilities. We do this by first conducting numerical tracer experiments in discrete fracture‐matrix systems [ Berkowitz et al , 1988; Birkholzer et al , 1993a, 1993b; Birkholzer and Rouve , 1994; Rubin et al , 1996]. These simulations are assumed to represent the “correct” system behavior.…”

Section: Introductionmentioning

confidence: 99%

Continuous time random walk analysis of solute transport in fractured porous media

Cortis

Birkhölzer

2008

Water Resources Research

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[1] The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable inter-connected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the ''correct'' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains.

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Section: Introductionmentioning

confidence: 99%

Continuous time random walk analysis of solute transport in fractured porous media

Cortis

Birkhölzer

2008

Water Resources Research

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“…In such models, retention in the rock matrix is accounted for by defining two interacting continua, one for the fractures and a second for the rock matrix. The rock matrix is modeled as either a second flow system [Pruess and Narasimhan, 1985;Berkowitz et al, 1988;Birkholzer et al, 1993] or as a nonflowing reservoir accessible through diffusive mass exchange [Foster, 1975;Gtisak and Pickens, 1980;Neretnieks, 1980;Bibby, 1981]. Prediction uncertainty can be addressed in continuum models by making the effective medium properties a random space function.…”

Section: Introductionmentioning

confidence: 99%

Stochastic analysis of early tracer arrival in a segmented fracture pathway

Painter¹,

Cvetković²

2001

Water Resources Research

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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

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