Probability Density Functions for Reactive Transport in Porous Media
Abstract
We derive probability density functions for advective transport of a contaminant that undergoes a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase. This allows us to quantify uncertainty associated with spatially varying reaction rate constants, for both linear and nonlinear kinetic rate laws. While standard techniques for uncertainty quantification in groundwater hydrology (e.g., Monte Carlo simulations and moment equations) typically yield only concentration's mean and variance, the proposed approach leads to its full probabilistic description. This allows one to compute so-called rare event (distribution tails), which are required in modern probabilistic risk analyses. We also compute an effective (apparent, upscaled) kinetic rate constant, a parameter that enters transport equations governing the spatio- temporal evolution of mean concentration. We demonstrate the effective kinetic rate of nonlinear reactions is time dependent. This behavior provides a possible explanation for the observed discrepancy between laboratory measured rate constants on uniform grain sizes and field measurements may in part be caused by the heterogeneous distribution of grain sizes in natural systems.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2008
- Bibcode:
- 2008AGUFM.H24B..01T
- Keywords:
-
- 1009 Geochemical modeling (3610;
- 8410);
- 1832 Groundwater transport;
- 1873 Uncertainty assessment (3275)