Department of Mechanical and Aerospace Engineering

Daniel Tartakovsky › Publications › tartakovsky-2009-probability

D. M. Tartakovsky, M. Dentz and P. C. Lichtner, "Probability density functions for advective-reactive transport in porous media with uncertain reaction rates", *Water Resour. Res.*, vol. 45, doi:10.1029/2008WR007383, pp. W07414, 2009

We derive probability density functions for advective transport of a solute that undergoes a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase. This enables us to quantify uncertainty associated with spatially varying reaction rate constants for both linear and nonlinear kinetic rate laws. While many standard techniques for uncertainty quantification in groundwater hydrology yield only concentration’s mean and variance, the proposed approach leads to its full probabilistic description. This allows one to compute so-called rare events (distribution tails), which are required in modern probabilistic risk analyses. We also compute an effective (apparent and upscaled) kinetic rate constant, a parameter that enters transport equations governing the spatiotemporal evolution of mean concentration. We demonstrate that 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 measurements in natural systems where the grain size distributions are heterogeneous.

@article{tartakovsky-2009-probability,

author = {D. M. Tartakovsky and M. Dentz and P. C. Lichtner},

title = {Probability density functions for advective-reactive transport in porous media with uncertain reaction rates},

year = {2009},

urlpdf = {http://maeresearch.ucsd.edu/Tartakovsky/Papers/tartakovsky-2009-probability.pdf},

journal = {Water Resour. Res.},

volume = {45},

doi = {10.1029/2008WR007383},

pages = {W07414}

}