Rishi Parashar

On iterative techniques for computing flow in large two-dimensional discrete fracture networks

Computation of flow in discrete fracture networks often involves solving for hydraulic head values at all intersection points of a large number of stochastically generated fractures inside a bounded domain. For large systems, this approach leads to the generation of problems involving highly sparse matrices which must be solved iteratively. Distributions of fracture lengths spanning over several orders of magnitude, and the randomness of fracture orientations and locations, lead to coefficient matrices that are devoid of any regular structure in the sparsity pattern. In addition to the rapid increase in computational effort with increase in the size of the fracture network, the spread in the distribution of fracture parameters, such as length and transmissivity, dramatically influences the convergence behavior of the system of linear equations. An overview of the discrete fracture network (DFN) methodology for computation of flow is presented along with a comparative study of various Krylov subspace iterative methods for the resulting class of sparse matrices. The rate of convergence of the iterative techniques is found to exhibit a systematic pattern with respect to changes in statistical parameters of the stochastically generated fracture networks. Salient features of the observed trends in the convergence pattern are discussed and guidelines for design of DFN algorithms are provided.

Hydrogeologic Characterization of Fractured Rock Masses Intended for Disposal of Radioactive Waste

There are currently 441 nuclear power reactors in operation or under construction distributed over 30 countries (International Atomic Energy Agency, 2011). The global radioactive waste inventory reported as storage in 2008 was approximately 17.6 million cubic meters: 21% short-lived, lowand intermediate-level waste, 77% long-lived, lowand intermediate-level waste and 2% high-level waste (International Atomic Energy Agency, 2011). There is a consensus among most of the scientific community that geologic repositories offer the best solution for the long-term disposal of radioactive waste. In the United States, for example, geologic disposal is considered the only technically feasible, long-term strategy for isolating radioactive waste from the biosphere without active management (Long & Ewing, 2004; National Research Council, 2001; Nuclear Energy Agency, 1999).

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

Prediction of effective transport for mixing driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2D porous medium.