Abstract
We present a cumulative density function (CDF) method for the probabilistic analysis of d-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified large-eddy-diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a (d + 1) dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advective dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.
Original language | English (US) |
---|---|
Pages (from-to) | 180-212 |
Number of pages | 33 |
Journal | SIAM-ASA Journal on Uncertainty Quantification |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - 2018 |
Externally published | Yes |
Keywords
- Cumulative density function method
- LED closure
- Probability density function method
- Reactive transport
- Stochastic advection-reaction equation
- Uncertainty quantification
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Discrete Mathematics and Combinatorics
- Applied Mathematics