Divergence of Solutions to Solute Transport Moment Equations
We provide explicit solutions to one-dimensional moment equations for solute transport in random porous media using asymptotic perturbation expansions up through fourth order in standard deviation of log hydraulic conductivity. From these solutions, we demonstrate the source of the multi-modal behavior previously observed in more complex flow and transport simulations; namely, oscillatory terms that increase with the variance of velocity (or of log conductivity) and time. We show that over time higher-order moments become less accurate than second-order moments. Moreover, we show that the complete asymptotic series solution diverges for any value of log conductivity variance after sufficient time, using an analytical bound and assuming Gaussian-distributed velocity. This bound depends on the zero-order mean velocity, correlation length, and properties of the initial data. We find that the bound is also a good approximation when applied to our solutions of moment equations for a non-Gaussian velocity distribution.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 940982
- Report Number(s):
- PNNL-SA-59036; KJ0101010
- Journal Information:
- Geophysical Research Letters, 35(15):30-34, Art. no.: L15401, Journal Name: Geophysical Research Letters, 35(15):30-34, Art. no.: L15401 Journal Issue: 15 Vol. 35; ISSN GPRLAJ; ISSN 0094-8276
- Country of Publication:
- United States
- Language:
- English
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