Incomplete mixing and reactions with fractional dispersion

Advances in Water Resources

Volumn 37, Issue , 2012, Pages 86-93

  Bolster, Diogo ^a   de Anna, Pietro ^b   Benson, David A ^c   Tartakovsky, Alexandre M ^d  

^a University of Notre Dame   (United States)

^b UNIVERSITÉ DE RENNES 1   (France)

^c Department of Geology and Geological Engineering   (United States)

^d PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

Author keywords

Fractional dispersion; Incomplete mixing; Reactions

Indexed keywords

ADVECTION-DISPERSION EQUATION; ANOMALOUS TRANSPORT; BIMOLECULAR REACTION; FRACTIONAL DISPERSIONS; FRACTIONAL ORDER; PARTICLE-BASED SIMULATION; RANDOM WALK; RATE OF REACTION; REACTIONS;

TECHNOLOGY; WATER RESOURCES;

DISPERSIONS;

ADVECTION; ANALYTICAL FRAMEWORK; COMPUTER SIMULATION; DISPERSION; STOCHASTICITY; THERMODYNAMICS;

EID: 84855271496     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2011.11.005     Document Type: Article

References (47)

1. De Anna P., Le Borgne T., Dentz M., Bolster D., Davy P. Anomalous kinetics in diffusion limited reactions linked to non-Gaussian concentration PDF. J Chem Phys 2011, 135:174104.
2. Benson D.A., Meerschaert M.M. Simulation of chemical reaction via particle tracking: diffusion-limited versus thermodynamic rate-limited regimes. Water Resour Res 2008, 44:W12201. 10.1029/2008WR007111.
3. Berkowitz B., Cortis A., Dentz M., Scher H. Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev Geophys 2006, 44:RG2003.
4. Bolster D., Dentz M., Le Borgne T. Hyper mixing in shear flow. Water Resour Res 2011, 47:W09602. 10.1029/2011WR010737.
5. Bolster D., Valdes-Parada F.J., Le Borgne T., Dentz M., Carrera J. Mixing in confined stratified aquifers. J Contam Hydrol 2011, 120-121:P198-21. 10.1016/j.jconhyd.2010.02.003.
6. Bolster D., Benson D.A., LeBorgne T., Dentz M. Anomalous mixing and reaction induced by superdiffusive nonlocal transport. Phys Rev E 2010, 82:021119. 10.1103/PhysRevE.82.021119.
7. Bolster D., Dentz M., Carrera J. Effective two-phase flow in heterogeneous media under temporal pressure fluctuations. Water Resour Res 2009, 45:W05408.
8. Bradley D., Tucker G., Benson D. Fractional dispersion in a sand bed river. J Geophys Res F Earth Surf 2010, 115:F00A09. 10.1029/2009JF001268.
9. Chiogna G., Cirpka O.A., Gratwohl P., Rolle M. Transverse mixing of conservative and reactive tracers in porous media: quantification through the concepts of flux-related and critical dilution indices. Water Resour Res 2011, 47:W02505.
10. Cirpka O.A., de Barros F.P.J., Chiogna G., Rolle M., Nowak W. Stochastic flux-related analysis of transverse mixing in two-dimensional heterogeneous porous media. Water Resour Res 2011, 47:W06515.
11. Cushman J.H., Ginn T.R. Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Transport Porous Med 1993, 13:123-138.
12. Cushman-Roisin B. Beyond eddy diffusivity: an alternative model for turbulent dispersion. Environ Fluid Mech 2008, 8:543-549.
13. Dentz M., Bolster D. Distribution versus correlation-induced anomalous transport in quenched random velocity fields. Phys Rev Lett 2010, 105:244301.
14. Dentz M., LeBorgne T., Englert A., Bijeljic B. Mixing, spreading and reaction in heterogeneous media: a brief review. J Contam Hydrol 2011, 120-121:1-17.
15. Dentz M., Tartakovsky D.M. Delay mechanisms of non-Fickian transport in heterogeneous media. Geophys Res Lett 2006, 33(16):L16406.
16. Donado L.D., Sánchez-Vila X., Dentz M., Carrera J., Bolster D. Multicomponent reactive transport in multicontinuum media. Water Resour Res 2009, 45:W11402.
17. Edery Y., Scher H., Berkowitz B. Modeling bimolecular reactions and transport in porous media. Geophys Res Lett 2009, 35:L02407.
18. Fiori A., Jankovic I. Can we determine the transverse macrodispersivity by using the method of moments. Adv Water Resour 2005, 28(6):589-599.
19. Furbish D., Childs E., Haff P., Schmeeckle M. Rain splash of soil grains as a stochastic advection-dispersion process, with implications for desert plant-soil interactions and land-surface evolution. J Geophys Res 2009, 114:F00A03.
20. Gillespie D.T. The chemical Langevin equation. J Chem Phys 2000, 113(1):297-306.
21. Gnedenko B.V., Kolmogorov A.N. Limit distributions for sums of independent random variables 1954, Addison-Wesley, [Translated from Russian].
22. Gooseff M.N., Wondzell S.M., Haggerty R., Anderson J. Comparing transient storage modeling and residence time distribution (RTD) analysis in geomorphically varied reaches in the Lookout Creek basin, Oregon, USA. Adv Water Resour 2003, 26:925-937.
23. Gramling C., Harvey C.F., Meigs L.C. Reactive transport in porous media: a comparison of model prediction with laboratory visualization. Environ Sci Technol 2002, 36:2508-2514.
24. Haggerty R., Gorelick S.M. Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity. Water Resour Res 1995, 31(10):2383-2400.
25. Van Hauwermeiren M, Vose D. A compendium of distributions. [ebook]. Ghent, Belgium: Vose Software; 2009.
26. Kang K., Redner S. Fluctuation dominated kinetics in diffusion-controlled reactions. Phys Rev A 1985, 32:435-447.
27. Le Borgne T, Dentz M, Bolster D, Carrera J, de Dreuzy J-R, Bour O. Persistence of incomplete mixing: a key to anomalous transport. Phys Rev E 2011;84:015301(R).
28. Le Borgne T., Dentz M., Bolster D., Carrera J., de Dreuzy J.-R., Davy P. Non-Fickian mixing: temporal evolution of the scalar dissipation rate in porous media. Adv Water Resour 2010, 33:1468-1475.
29. Luo J., Cirpka O.A. How well do mean breakthrough curves predict mixing-controlled reactive transport?. Water Resour Res 2011, 47:W02520.
30. Monson E, Kopelman R. Nonclassical kinetics of an elementary A+B→C reaction-diffusion system showing effects of a speckled initial reactant distribution and eventual self-segregation. Exp Phys Rev E 2004;69:021103.
31. Meerschaert M.M., Scheffler H.-P. Limit distributions for sums of independent random vectors: heavy tails in theory and practice 2001, Wiley Interscience.
32. Neuman S.P. Lagrangian theory of transport in space-time nonstationary velocity fields: exact nonlocal formalisms by conditional moments and weak approximation. Water Resour Res 1993, 29:633-645.
33. Neuman S.P., Tartakovsky D.M. Perspective on theories of anomalous transport in heterogeneous media. Adv Water Resour 2009, 32:670-680.
34. Neuweiler I., Attinger S., Kinzelbach W., King P. Large scale mixing for immiscible displacement in heterogeneous porous media. Transport Porous Med 2003, 51:287-314.
35. Ovchinnikov A.A., Zeldovich Y.B. Role of density fluctuations in bimolecular reactions. Chem Phys 1978, 28:215-218.
36. Raje D., Kapoor V. Experimental study of bimolecular reaction kinetics in porous media. Environ Sci Technol 2000, 34:1234-1239.
37. Rolle M., Eberhardt C., Chiogna G., Cirpka O.A., Gratwohl P. Enhancement of dilution and transverse reactive mixing in porous media: experiments and model-based interpretation. J Contam Hydrol 2009, 110:130-142.
38. Sánchez-Vila X., Fernández-Garcia D., Guadagnini A. Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation. Water Resour Res 2010, 46:W12510.
39. Sanchez-Vila X., Dentz M., Donado L.D. Transport-controlled reaction rates under local non-equilibrium conditions. Geophys Res Lett 2007, 34:L10404. 10.1029/2007GL029410.
40. Schumer R., Meerschaert M.M., Baeumer B. Fractional advection-dispersion equations for modeling transport at the earth surface. J Geophys Res 2009, 114:F00A07.
41. Tartakovsky AM, de Anna P, Borgne TL, Balter A, Bolster D. Effects of spatial concentration fluctuations on non-linear reactions. Water Resour Res [submitted for publication].
42. Tartakovsky A.M., Tartakovsky D.M., Meakin P. Stochastic Langevin model for flow and transport in porous media. Phys Rev Lett 2008, 101:044502.
43. Tartakovsky A.M., Tartakovsky G.D., Scheibe T.D. Effects of incomplete mixing on multicomponent reactive transport. Adv Water Resour 2009, 32:1674-1679.
44. Toussaint D., Wilczek F. Particle-antiparticle annihilation in diffusive motion. J Chem Phys 1983, 78:2642-2647.
45. Tsallis C., Levy S.V.F., Souza A.M.C., Maynard R. Statistical-mechanical foundation of the ubiquity of the Lévy distributions in Nature. Phys Rev Lett 1996, 77:5442.
46. Werth C.J., Cirpka O.A., Grathwohl P. Enhanced mixing and reaction through flow focusing in heterogeneous porous media. Water Resour Res 2006, 42:W12414. 10.1029/2005WR004511.
47. Willmann M., Carrera J., Sánchez-Vila X., Silva O., Dentz M. Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media. Water Resour Res 2010, 44:W12437.