Particle method for upscaling transport with retention and in-growth in three-dimensional discrete fracture networks

An important challenge in subsurface hydrology is predictive modeling of tracer transport in sparsely fractured rock. A particular issue relevant for applications is how to accurately account for retention processes that are due to exchange (diffusion-sorption) of tracers between mobile fluid in fractures and immobile fluid in the rock matrix. Typically, tracers are subject to decay processes which may involve chains and in-growth (e.g., for radionuclides and some classes of hydrocarbons). Recently, a comprehensive particle-based methodology for upscaling transport with emphasis on tracer retention has been presented and applied to stochastic 2D discrete fracture networks (Frampton and Cvetkovic 2007, WRR, 43, W10429). Furthermore, a time domain random walk method has also recently been presented that effectively accounts for different exchange mechanisms and in-growth (Painter et al. 2008, WRR, 44, W01406). Now we present further advances in coupling these novel methodologies for solving radionuclide transport, and apply them to realistic 3D fracture networks, based on comprehensive data sets obtained from site characterization of the Laxemar area in south-east Sweden. Site measurements have revealed at least five fracture sets based on statistically significant orientation data, exhibiting power-law behaviour for fracture size and inferred transmissivity distributions. A few equally probable DFN realizations are generated based on these interpretations of the field data, in which advective fluid flow is solved using boundary conditions that mimic natural conditions. Thereafter, many particles are injected and tracked through the system, providing first- passage distributions of particle residence time and of the transport resistance parameter (quantifying the hydrodynamic control of retention). These distributions are then used as a basis for implementing the particle time-domain random walk model for radionuclide transport with retention and in-growth. Also, an analytical approach for upscaling transport is evaluated against DFN particle tracking, indicating reasonable/good agreement. We emphasise the importance of incorporating the transport resistance parameter, and show that the initial part of advective residence time and transport resistance distributions is most important for accurate transport predictions of decaying tracers, while the tail part of these distributions has a minor impact. Finally, the presented methodologies can serve as a basis for further testing and model comparison using alternative particle based theoretical approaches to upscale tracer transport in fractured rock.