Groundwater Flux, Travel Time, and Radionuclide Transport
Authors: Chesnut Dwayne A. 
Published: April 2011

Inflow measurements at Stripa and in other underground openings in Sweden, as well as observations elsewhere in mines and tunnels, reveal that there is generally an extremely broad distribution of groundwater flux in fractured rock. Non-sorbing and sorbing tracer tests typically show similar variability in groundwater travel time (GWTT) and tracer transport.

In the U.S. Nuclear Waste Program, Nuclear Regulatory Commission regulations require the GWTT from the disturbed zone to the accessible environment to exceed 1000 years. The regulations seem to envision a rather uniform and narrow distribution of travel time, with perhaps a few identifiable “fast pathways” contained within the rock mass surrounding a potential repository. The premise is that most of these features could be mapped during site characterization, and that regions of the potential repository host rock containing such features could be avoided during waste emplacement.

However, both field experience and theoretical studies in recent years provide strong evidence that groundwater flux, GWTT, and aqueous transport of dissolved substances exhibit extremely heterogeneous behavior, even in intact porous media and in fractured rock regions between major features. These phenomena are all dominated by the spatial distribution of permeability within the rock mass of interest. The permeability distribution is often approximately log-normal, with a natural log standard deviation, σ. For unfractured porous rock, σ typically ranges from about 0.6 to about 1.2 for field-scale investigations, and for fractured permeable media, it frequently exceeds 2. Values of σ smaller than 0.6 may be observed in small field-scale projects when the macroscopic flow regime is essentially linear within very uniform sediments and in laboratory displacement experitments.

With some additional assumptions, a log-normal permeability distribution implies that groundwater flux, GWTT, and the transport of radionuclides from a potential repository are also log-normal. To first order, the appropriate value of σ describing these distributions is the same as the value for the permeability distribution. This allows σ to be estimated from a large number of hydraulic or pneumatic packer tests within the fractured rock mass of interest.

We define a groundwater transport function (GWTF) for the rate of radioactivity release to the accessible environment (AE) at time t resulting from the release of a pulse of unit activity at time 0. The GWTF depends on the mean groundwater travel time, tw, and σ, as well as the retardation factor and decay constant. As σ increases from 0 (a hypothetical completely homogeneous system), the radioactivity breakthrough at early time increases from 0 to 100%. This behavior is consistent with our intuitive notions of “fast transport pathways” in heterogeneous systems, and σ is thus seen to be a parameter for quantifying the effects of heterogeneity.

Convolution of the GWTF with a time-dependent release function for the Engineered Barrier System (EBS) is easily performed numerically, resulting in the rate of release to the AE as a function of time, which can then be integrated numerically to calculate the cumulative release as a function of time. The convolution approach clearly separates the effects of uncertainty and heterogeneity on repository performance and is extremely useful for sensitivity analyses. An example calculation shows the combinations of σ and tw required for compliance with total system release standards.

Since the effect of heterogeneity is captured by a single parameter in a deterministic calculation, uncertainty can be investigated separately by Monte Carlo sampling from distributions of such parameters as σ, tw and source term strength, allowing (in the future) specific and scientifically meaningful goals to be defined for both site characterization and design.

Finally, we emphasize that this approach, in its present form, does not include thermal effects. These effects may dominate both the EBS failure rate and hydrogeochemical behavior, including radionuclide transport, for most of the compliance period and beyond. It cannot be used directly to support any particular thermal loading strategy.