Probability density functions for advective-reactive transport with uncertain reaction rates

Water Resources Research

Volumn 45, Issue 7, 2009, Pages

  Tartakovsky, Daniel M ^a   Dentz, Marco ^b   Lichtner, Peter C ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTIVE TRANSPORT; AQUEOUS SOLUTIONS; GRAIN SIZE DISTRIBUTION; GROUND-WATER HYDROLOGY; HETEROGENEOUS CHEMICAL REACTION; KINETIC RATE CONSTANTS; KINETIC RATES; MEAN CONCENTRATIONS; NATURAL SYSTEMS; NONLINEAR KINETICS; NONLINEAR REACTION; PROBABILISTIC DESCRIPTIONS; PROBABILISTIC RISK ANALYSIS; RARE EVENT; REACTIVE TRANSPORT; SOLID-PHASE; SPATIOTEMPORAL EVOLUTION; TIME-DEPENDENT; TRANSPORT EQUATION; UNCERTAINTY QUANTIFICATIONS; UNIFORM GRAIN SIZE;

CHEMICAL REACTIONS; GRAIN SIZE AND SHAPE; GROUNDWATER; HYDROGEOLOGY; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; SAFETY FACTOR;

RATE CONSTANTS;

ADVECTION; AQUEOUS SOLUTION; PROBABILITY DENSITY FUNCTION; REACTION KINETICS; REACTION RATE; RISK ASSESSMENT; SIZE DISTRIBUTION; SPATIAL VARIATION; UNCERTAINTY ANALYSIS;

EID: 69249121603     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2008WR007383     Document Type: Article

References (26)

1. Amir, O., and S. P. Neuman (2001), Gaussian closure of one-dimensional unsaturated flow in randomly heterogeneous soils, Transp. Porous Media, 44(2), 355-383. (Pubitemid 32739599)
2. Amir, O., and S. P. Neuman (2004), Gaussian closure of transient unsaturated flow in random soils, Transp. Porous Media, 54(1), 55-77. (Pubitemid 38149222)
3. Bellin, A., and D. Tonina (2007), Probability density function of non-reactive solute concentration in heterogeneous porous formations, J. Contam. Hydrol., 94, 109-125. (Pubitemid 47505376)
4. Bellin, A., A. Rinaldo, W. J. P. Bosma, S. E. A. T. M. van der Zee, and Y. Rubin (1993), Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations: 1. Analytical solutions, Water Resour. Res., 29(12), 4019-4030. (Pubitemid 2013779)
5. Caroni, E., and V. Fiorotto (2005), Analysis of concentration as sampled in natural aquifers, Transp. Porous Media, 59(1), 19-45. (Pubitemid 40301156)
6. Cirpka, O. A., R. L. Schwede, J. Luo, and M. Dentz (2008), Concentration statistics for mixing-controlled reactive transport in random heterogeneous media, J. Contam. Hydrol., 98, 61-74.
7. Clausnitzer, V., and J. W. Hopmans (1999), Determination of phase-volume fractions from tomographic measurements in two-phase systems, Adv. Water Resour., 22, 577-584. (Pubitemid 29253165)
8. Dagan, G., and P. Indelman (1999), Reactive solute transport inflow between a recharging and a pumping well in a heterogeneous aquifer, Water Resour. Res., 35(12), 3639-3647. (Pubitemid 33594132)
9. Espinoza, C, and A. J. Valocchi (1997), Stochastic analysis of one-dimensional transport of kinetically adsorbing solutes in chemically heterogeneous aquifers, Water Resour. Res., 33(11), 2429-2445. (Pubitemid 27506529)
10. Girimaji, S. S. (1991), Assumed ß-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing, Combust. Sci. Technol, 78, 177-196.
11. Indelman, P. V., and M. I. Shvidler (1985), Averaging of stochastic evolution equations of transport in porous media, Fluid Dyn., 20(5), 775-784, Engl. Transl..
12. Lastoskie, C., K. E. Gubbins, and N. Quirke (1993), Pore size distribution analysis of microporous carbons: A density functional theory approach, J. Phys. Chem., 97(18), 4786-4796.
13. Lichtner, P. C, and D. M. Tartakovsky (2003), Stochastic analysis of effective rate constant for heterogeneous reactions, Stochastic Environ. Res. Risk Assess, 17(6), 419-429.
14. Miralles-Wilhelm, F., and L. W. Gelhar (2000), Stochastic analysis of oxygen-limited biodegradation in heterogeneous aquifers with transient microbial dynamics, J. Contam. Hydrol., 42, 69-97. (Pubitemid 30016088)
15. Neuman, S. P. (1993), Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation, Water Resour. Res., 29(3), 633-645.
16. Reichle, R., W. Kinzelbach, and H. Kinzelbach (1998), Effective parameters in heterogeneous and homogeneous transport models with kinetic sorption, Water Resour. Res., 34(4), 583-594. (Pubitemid 28159440)
17. Risken, H. (1996), The Fokker-Planck Equation, Springer, New York.
18. Rubin, Y. (2003), Applied Stochastic Hydrogeology, Oxford Univ. Press, New York.
19. Shvidler, M, and K. Karasaki (2003), Probability density functions for solute transport in random field, Transp. Porous Media, 50(3), 243-266. (Pubitemid 36225638)
20. Srinivasan, G., D. M. Tartakovsky, B. A. Robinson, and A. B. Aceves (2007), Quantification of uncertainty in geochemical reactions, Water Resour. Res., 43, W12415, doi: 10.1029/2007WR006003. (Pubitemid 351161984)
21. Tartakovsky, A. M., D. M. Tartakovsky, T. D. Scheibe, and P. Meakin (2008), Hybrid simulations of reaction-diffusion systems in porous media, SUM J. Sci. Comput., 30(6), 2799-2816.
22. Tartakovsky, D. M. (2007), Probabilistic risk analysis in subsurface hydrology, Geophys. Res. Lett., 34, L05404, doi: 10.1029/2007GL029245. (Pubitemid 46864509)
23. Tartakovsky, D. M., and A. Guadagnini (2001), Prior mapping for nonlinear flows in random environments, Phys. Rev. E, 64, 035302, doi: 10.1103/PhysRevE.64.035302. (Pubitemid 32935441)
24. Tartakovsky, D. M, A. Guadagnini, and M. Riva (2003), Stochastic averaging of nonlinear flows in heterogeneous porous media, J. Fluid Mech., 492, 41-62. (Pubitemid 37307209)
25. Tuli, A., K. Kosugi, and J. W. Hopmans (2001), Simultaneous scaling of soil water retention and unsaturated hydraulic conductivity functions assuming lognormal pore-size distribution, Adv. Water Resour., 24, 677-688. (Pubitemid 32546288)
26. Winter, C. L., and D. M. Tartakovsky (2008), A reduced complexity model for probabilistic risk assessment of groundwater contamination, Water Resour. Res., 44, W06501, doi: 10.1029/2007WR006599.