Transport in lattice fracture networks : concentration mean and variance
Author(s)Kang, Peter Kyungchul
Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.
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We study transport in fractured systems using a stochastic particle tracking approach. We represent a fractured system as a two-dimensional lattice network system where the transport velocity in each fracture is a random variable. Our goal is to develop an exact effective macroscopic model for the concentration mean and variance from the microscopic disorder model. Within a Lagrangian transport framework, we derive effective equations for particle transport by coarse graining and ensemble averaging of the local scale Langevin equations. The results show that the mean transport can be captured exactly by an uncoupled continuous time random walk (CTRW) and the variance of the concentration by a novel two-particle CTRW formulation. Information about variance of concentration between realizations is important for understanding predictability. Therefore, ensemble mean together with variance provide critical information for understanding and predicting transport through the lattice network.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 53-55).
DepartmentMassachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.; Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology
Civil and Environmental Engineering.