Hybrid Modeling Approach for Transport in Fractured Rock, 20-9252

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Principal Investigators
Scott L. Painter
Roland R. Benke

Inclusive Dates: 04/01/01 - 03/31/02

Background - Many applications in subsurface hydrology involve the transport of solutes through fractured but otherwise low-permeable rock. This issue is, for example, important in remediation of fractured formations and in understanding the safety of proposed underground repositories for radioactive or chemical waste. The conventional modeling approach to this issue is to use the classical advection-dispersion equation (ADE) to calculate the time and space evolution of radionuclide concentrations. However, field investigations and theoretical studies have demonstrated that solutes may be transported in a nondiffusive manner over considerable distances. This observation has important implications for predictive calculations, and there is a strong need for alternative modeling approaches.

Approach - This project is developing new approaches for using the results of discrete fracture network (DFN) simulations in continuum models. DFN simulation is an alternative to continuum models that involve stochastically generating networks of discrete fractures and then solving for flow and transport in the synthetic network. The DFN approach does not suffer the same limitations as the ADE approach, but it is too demanding of computational resources to be of practical value in many applications. The approach of this project is to extract statistics on particle velocities from DFN simulations of modest size. These velocity statistics capture relevant information about the transport properties of the network and are then used to construct new models that yield particle travel time distributions or time evolution of concentration. Two specific approaches are being explored: a Lagrangian transfer function approach that relies on random walk arguments and a continuum model based on the linear Boltzmann transport equation from the kinetic theory of gases. In both approaches, velocity statistics from the DFN simulations are used to calculate model parameters. The simplified model is then used to extrapolate in a computationally efficient way to different boundary or source conditions or to model domains of different sizes.

Accomplishments - A two-dimensional DFN simulator was developed, tested, and used to generate velocity statistics for a reference case based on a log-normal distribution of fracture lengths and a uniform distribution of fracture orientations. These statistics were successfully used in a random walk model to reproduce the global breakthrough curves for contaminants, thereby partially meeting one of the goals of the project. Several approaches to solving the linear Boltzmann transport equation were also developed and are being tested. A method for extracting the relevant Boltzmann parameters from the DFN simulations was implemented. Comparisons between the DFN and Boltzmann simulations will be made in FY02.

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