Citation: | Bing-qing Lu, Yong Zhang, Hong-guang Sun, Chun-miao Zheng. 2018: Lagrangian simulation of multi-step and rate-limited chemical reactions in multi-dimensional porous media. Water Science and Engineering, 11(2): 101-113. doi: 10.1016/j.wse.2018.07.006 |
Andrews, S.S, Bray, D., 2004. Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Physical Biology, 1(3–4), 137–151. https://doi.org/10.1088/1478-3967/1/3/001.
|
Barnard, J.M., 2017. Simulation of mixing-limited reactions using a continuum approach. Advances in Water Resources, 104(6), 15–22. https://doi.org/10.1016/j.advwatres.2017.03.012.
|
Benson, D.A., Meerschaert, M.M., 2008. Simulation of chemical reaction via particle tracking: Diffusion-limited versus thermodynamic rate-limited regimes. Water Resources Research, 44(12), W12202. https://doi.org/10.1029/2008WR007111.
|
Benson, D.A., Aquino, T., Bolster, D., Engdahl, N., Henri, C.V., Fernàndez-Garcia, D., 2017. A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms. Advances in Water Resources, 99, 15–37. https://doi.org/10.1016/j.advwatres.2016.11.003.
|
Berkowitz, B., Cortis, A., Dentz, M., Scher, H., 2006. Modeling non-Fickian transport on geological formations as a continuous time random walk. Review of Geophysics, 44, RG2003, https://doi.org/10.1029/2005RG000178.
|
Bolster, D., Benson, D.A., Singha, K., 2017. Upscaling chemical reactions in multicontinuum systems: When might time fractional equations work? Chaos, Solitons & Fractals, 102, 414–425. https://doi.org/10.1016/j.chaos.2017.04.028.
|
Cirpka, O.A., 2002. Choice of dispersion coefficients in reactive transport calculations on smoothed fields. Journal of Contaminant Hydrology, 58(3), 261–282. https://doi.org/10.1016/S0169-7722(02)00039-6.
|
Cirpka, O.A., Valocchi, A.J., 2016. Debates-stochastic subsurface hydrology from theory to practice: Does stochastic subsurface hydrology help solving practical problems of contaminant hydrogeology? Water Resources Research, 52(12), 9218–9227. https://doi.org/10.1002/2016WR019087.
|
Dentz, M., Borgne, T.L., Englert, A., Bijeljic, B., 2011. Mixing, spreading and reaction in heterogeneous media: A brief review. Journal of Contaminant Hydrology, 120–121, 1–17. https://doi.org/10.1016/j.jconhyd.2010.05.002.
|
Ding, D., Benson, D.A., Paster, A., Bolster, D., 2013. Modeling bimolecular reactions and transport in porous media via particle tracking. Advances in Water Resources, 53, 56–65. https://doi.org/10.1016/j.advwatres.2012.11.001.
|
Edery, Y., Scher, H., Berkowitz, B., 2009. Modeling bimolecular reactions and transport in porous media. Geophysical Research Letters, 36(2), L02407. https://doi.org/10.1029/2008GL036381.
|
Edery, Y., Scher, H., Berkowitz, B., 2010. Particle tracking model of bimolecular reactive transport in porous media. Water Resources Research, 46(7), W07524. https://doi.org/10.1029/2009WR009017.
|
Engdahl, N.B., Benson, D.A., Bolster, D., 2017. Lagrangian simulation of mixing and reactions in complex geochemical systems. Water Resources Research, 53(4), 3513-3522. https://doi.org/10.1002/2017WR020362.
|
Erban, R., Chapman, S.J., 2009. Stochastic modeling of reaction-diffusion processes: Algorithms for bimolecular reactions. Physical Biology, 6(4), 046001. https://doi.org/10.1088/1478-3975/6/4/046001.
|
Gillespie, D.T., 1977. Exact stochastic simulation of coupled chemical react ions. The Journal of Physical Chemistry, 81(25), 2340–2361. https://doi.org/10.1021/j100540a008.
|
Gillespie, D.T., 2009. A diffusional bimolecular propensity function. Journal of Chemical Physics, 131(16), 164109. https://doi.org/10.1063/1.3253798.
|
Gramling, C.M., Harvey, C.F., Meigs, L.C., 2002. Reactive transport in porous media: A comparison of model prediction with laboratory visualization. Environmental Science & Technology, 36(11), 2508–2514. https://doi.org/10.1021/es0157144.
|
Ham, P.A.S., Schotting, R.J., Prommer, H., Davis, G.B., 2004. Effects of hydrodynamic dispersion on plume lengths for instantaneous bimolecular reactions. Advances in Water Resources, 27(8), 803–813. https://doi.org/10.1016/j.advwatres.2004.05.008.
|
Hattne, J., Fange, D., Elf, J., 2005. Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics, 21(12), 2923–2924. https://doi.org/10.1093/bioinformatics/bti431.
|
Isaacson, S.A., Peskin, C.S., 2006. Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations. SIAM Journal on Scientific Computing, 28(1), 47–74. https://doi.org/10.1137/040605060.
|
Kang, K., Redner, S., 1984. Scaling approach for the kinetics of recombination processes. Physical Review Letters, 52(12), 955–958. https://doi.org/10.1103/PhysRevLett.52.955.
|
Kang, K., Redner, S., 1985. Fluctuation-dominated kinetics in diffusion-controlled reactions. Physical Review A: Atomic, Molecular and Optical Physics, 32(1), 435–447. https://doi.org/10.1103/PhysRevA.32.435.
|
Kapoor, V., Gelhar, L.W., Miralles-Wilhelm, F., 1997. Bimolecular second-order reactions in spatially varying flows: Segregation induced scale-dependent transformation rates. Water Resources Research, 33(4), 527–536. https://doi.org/10.1029/96WR03687.
|
Kopelman, R., 1988. Fractal reaction kinetics. Science, 241(4873), 1620–1626. https://doi.org/10.1126/science.241.4873.1620.
|
LaBolle, E.M., Fogg, G.E., Tompson, A.F.B., 1996. Random-walk simulation of transport in heterogeneous porous media: Local mass conservation problem and implementation methods. Water Resources Research, 32(3), 583–593. https://doi.org/10.1029/95WR03528.
|
LaBolle, E.M., Quastel, J., Fogg, G.E., Gravner, J., 2000. Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients. Water Resources Research, 36(3), 651–662. https://doi.org/10.1029/1999WR900224.
|
Luo, J., Dentz, M., Carrera, J., Kitanidis, P., 2008. Effective reaction parameters for mixing controlled reactions in heterogeneous media. Water Resources Research, 44(2), W02416. https://doi.org/10.1029/2006/WR005658.
|
Neuman, S.P., Tartakovsky, D.M., 2009. Perspective on theories of non-Fickian transport in heterogeneous media. Advances in Water Resources, 32(5), 670–780.
|
Oates, P.M., Harvey, C.F., 2006. A colorimetric reaction to quantify fluid mixing. Experiments in Fluids, 41(5), 673–683. https://doi.org/10.1007/s00348-006-0184-z.
|
Paster, A., Bolster, D., Benson, D.A., 2013. Particle tracking and the diffusion-reaction equation. Water Resources Research, 49(1), 1–6. https://doi.org/10.1029/2012WR012444.
|
Pogson, M., Smallwood, R., Qwarnstrom, E., Holcombe, M., 2006. Formal agent-based modelling of intracellular chemical interactions. BioSystems, 85(1), 37–45. https://doi.org/10.1016/j.biosystems.2006.02.004.
|
Raje, D.S., Kapoor, V., 2000. Experimental study of bimolecular reaction kinetics in porous media. Environmental Science & Technology, 34(7), 1234–1239. https://doi.org/10.1021/es9908669.
|
Scheibe, T.D., Tartakovsky, A.M., Tartakovsky, D.M., Redden, G.D., Meakin, P., 2007. Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes. Journal of Physics: Conference Series, 78(1), 012063. https://doi.org/10.1088/1742-6596/78/1/012063.
|
Smoluchowski, M.V., 1918. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Zeitschrift für Physikalische Chemie, 92(1), 129–168. https://doi.org/10.1515/zpch-1918-9209. (in German)
|
Sung, B.J., Yethiraj, A., 2005. Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions. The Journal of Chemical Physics, 123(11), 114503. https://doi.org/10.1063/1.2035081.
|
Tartakovsky, A.M., Tartakovsky, G.D., Scheibe, T.D., 2009. Effects of incomplete mixing on multicomponent reactive transport. Advances in Water Resources, 32(11), 1674–1679. https://doi.org/10.1016/j.advwatres.2009.08.012.
|
Tournier, A.L., Fitzjohn, P.W., Bates, P.A., 2006. Probability-based model of protein-protein interactions on biological timescales. Algorithms for Molecular Biology, 1, 25. https://doi.org/10.1186/1748-7188-1-25.
|
Toussaint, D., Wilczek, F., 1983. Particle-antiparticle annihilation in diffusive motion. The Journal of Chemical Physics, 78, 2642. https://doi.org/10.1063/1.445022.
|
Trautz, M., 1916. Das Gesetz der Reaktionsgeschwindigkeit und der Gleichgewichte in Gasen. Bestätigung der Additivität von Cv‐3/2R. Neue Bestimmung der Integrationskonstanten und der Moleküldurchmesser. Zeitschrift für Anorganische und Allgemeine Chemie, 96(1), 1–28. https://doi.org/10.1002/zaac.19160960102. (in German)
|
Willingham, T.W., Werth, C.J., Valocchi, A.J., 2008. Evaluation of the effects of porous media structure on mixing-controlled reactions using pore-scale modeling and micromodel experiments. Environmental Science & Technology, 42(9), 3185–3193. https://doi.org/10.1021/es7022835.
|
Zhang, Y., Papelis, C., Sun, P.T., Yu, Z.B., 2013. Evaluation and linking of effective parameters in particle-based models and continuum models for mixing-limited bimolecular reactions. Water Resources Research, 49(8), 4845–4865. https://doi.org/10.1002/wrcr.20368.
|
Zhang, Y., Qian, J.Z., Papelis, C., Sun, P.T., Yu, Z.B., 2014. Improved understanding of bimolecular reactions in deceptively simple homogeneous media: From laboratory experiments to Lagrangian quantification. Water Resources Research, 50(2), 1704–1715. https://doi.org/10.1002/2013WR014711.
|
Zhang, Y., Meerschaert, M.M., Baeumer, B., LaBolle, E.M., 2015. Modeling mixed retention and early arrivals in multidimensional heterogeneous media using an explicit Lagrangian scheme. Water Resources Research, 51(8), 6311–6337. https://doi.org/10.1002/2015WR016902.
|
Zhang, Y., Green, C.T., LaBolle, E.M., Neupauer, R.M., Sun, H.G., 2016. Bounded fractional diffusion in geological media: Definition and Lagrangian approximation. Water Resources Research, 52(11), 8561–8577. https://doi.org/10.1002/2016WR019178.
|