Abstract
The traditional advection–dispersion–reaction equation (ADRE) often meets difficulty in simulating diffusion-controlled reactive transport, because the grid-based ADRE with a laboratory-measured reaction rate overpredicts pore-scale mixing and the product concentration. In this study, we chose bimolecular reactive transport (A\(\,+\,\)B\(\,\rightarrow \,\)AB) in porous media as an example and developed a fully implicit Galerkin finite-element method with Picard’s linearization scheme for solving the ADRE considering incomplete mixing at pore scale (IM-ADRE) based on a continuum approximation by Sanchez-Vila et al. (Water Resour Res 46:W12510, 2010). Sensitivity analysis showed that the IM-ADRE model was most sensitive to the parameter “m,” which was the power index of time used to control the decline rate of the time-dependent kinetic reaction term considering effects of incomplete mixing at pore scale. We used the IM-ADRE model to interpret the column experiment reported by Raje and Kapoor (Environ Sci Technol 34(7):1234–1239, 2000), which studied bimolecular reactive transport of aniline (AN) +1,2-naphthoquinone-4-sulfonic acid (NQS)\(\rightarrow \)1,2-naphthoquinone-4-aminobenzene (NQAB) in porous media. Previous studies found that the discrepancy between the simulated and observed peak product concentrations was as large as 55 % by the traditional ADRE, while the discrepancy was reduced to 5 % by the IM-ADRE model. We further conducted new reactive transport column experiments with NQS and AN to systematically understand the nature of bimolecular reactive transport in porous media and further check the validity of the IM-ADRE model. Our experiments differed from previous ones in two aspects. First, we used two different realistic porous media with six different flow velocities while previous experiments mostly involved artificial media such as glass beads under two similar flow velocities. Second, our experiment used a column (with the length of 100 cm) relatively longer than that (18 cm) in Raje and Kapoor (2000), and thus, the boundary effect of the column was minimized, and the time dependence of the effective reaction term could be further checked rigorously. Our study reveals that the IM-ADRE is a feasible tool in quantifying reactive transport at a travel distance up to 100 cm, further validating the effective, time-dependent rate coefficient proposed empirically by Sanchez-Vila et al. (2010).
Similar content being viewed by others
References
Berkowitz, B., Cortis, A., Dentz, M., Scher, H.: Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44(2), 1–39 (2006)
Benson, D.A., Meerschaert, M.M.: Simulation of chemical reaction via particle tracking: diffusion-limited versus thermodynamic rate-limited regimes. Water Resour. Res. 44, W12202 (2008). doi:10.1029/2008WR007111
Bolster, D., Benson, D.A., Le Borgne, T., Dentz, M.: Anomalous mixing and reaction induced by superdiffusive nonlocal transport. Phys. Rev. E 82, 021119 (2010)
Bolster, D., de Anna, P., Benson, D.A., Tartakovsky, A.M.: Incomplete mixing and reactions with fractional dispersion. Adv. Water Resour. 37, 86–93 (2012)
Cao, Y., Gillespie, L., Petzold, D.: Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems. J. Comput. Phys. 206, 395–411 (2005)
Dentz, M., Gouze, P., Carrera, J.: Effective non-local reaction kinetics for transport in physically and chemically heterogeneous media. J. Contam. Hydrol. 120–121, 222–236 (2011)
Ding, D., Benson, D.A., Paster, A., Bolster, D.: Modeling bimolecular reactions and transport in porous media via particle tracking. Adv. Water Resour. 53, 56–65 (2013)
Edery, Y., Scher, H., Berkowitz, B.: Modeling bimolecular reactions and transport in porous media. Geophys. Res. Lett. 36, L02407 (2009)
Eschenbach, T.G.: Spiderplots versus tornado diagrams for sensitivity analysis. Interfaces 22(6), 44–46 (1992)
Fabriol, R., Sauty, J.P., Ouzounian, G.: Coupling geochemistry with a particle tracking transport model. J. Contam. Hydrol. 13, 117–129 (1993)
Fernández-Garcia, D., Sanchez-Vila, X., Guadagnini, A.: Reaction rates and effective parameters in stratified aquifers. Adv. Water Resour. 31(10), 1364–1376 (2008)
Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976)
Gramling, C.M., Harvey, C.F., Meigs, L.C.: Reactive transport in porous media: a comparison of model prediction with laboratory visualization. Environ. Sci. Technol. 36(11), 2508–2514 (2002)
Haggerty, R., Harvey, C.F., Freiherr von Schwerin, C., Meigs, L.C.: What controls the apparent timescale of solute mass transfer in aquifers and soils? A comparison of experimental results. Water Resour. Res. 40, W01510 (2004)
Henry, B.I., Langlands, T.A.M., Wearne, S.L.: Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations. Phys. Rev. E 74(3), 031116 (2006)
Jose, S.C., Cirpka, O.A.: Measurement of mixing-controlled reactive transport in homogeneous porous media and its prediction from conservative tracer test data. Environ. Sci. Technol. 38(7), 2089–2096 (2004)
Kapoor, V., Jafvert, C.T., Lyn, D.A.: Experimental study of a bimolecular reaction in Poiseuille flow. Water Resour. Res. 34(8), 1997–2004 (1998)
Katz, G.E., Berkowitz, B., Guadagnini, A., Saaltink, M.W.: Experimental and modeling investigation of multicomponent reactive transport in porous media. J. Contam. Hydrol. 120–121, 21–27 (2011)
Palanichamy, J., Becker, T., Spiller, M., Kongeter, J., Mohan, S.: Multicomponent reaction modelling using a stochastic algorithm. Comput. Vis. Sci. 12(2), 51–61 (2009)
Porta, G.M., Chaynikov, S., Thovert, J.-F., Riva, M., Guadagnini, A., Adler, P.M.: Numerical investigation of pore and continuum scale formulations of bimolecular reactive transport in porous media. Adv. Water Resour. 62, 243–253 (2013)
Qian, J.Z., Zhan, H.B., Chen, Z., Ye, H.: Experimental study of solute transport under non-Darcian flow in a single fracture. J. Hydro. 399, 246–254 (2011)
Raje, D.S., Kapoor, V.: Experimental study of bimolecular reaction kinetics in porous media. Environ. Sci. Technol. 34(7), 1234–1239 (2000)
Romero, A.H., Lacasta, A.M., Sancho, J.M., Lindenberg, K.: Numerical study of A \(+\) 0 reactions with inertia. J. Chem. Phys. 127(17), 174506 (2007)
Sanchez-Vila, X., Fernandez-Garcia, D., Guadagnini, A.: Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers. Math. Geosci. 41, 323351 (2009)
Sanchez-Vila, X., Fernandez-Garcia, D., Guadagnini, A.: Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation. Water Resour. Res. 46, W12510 (2010)
Sim, Y., Chrysikopoulos, C.V.: One-dimensional virus transport in porous media with time-dependent inactivation rate. Water Resour. Res. 32, 2607–2611 (1996)
Sokolov, I.M., Schmidt, M.G.W., Sagues, F.: Reaction–subdiffusion equations. Phys. Rev. E 73(3), 031102 (2006)
Tartakovsky, A.M., Redden, G., Lichtner, P.C., Scheibe, T.D., Meakin, P.: Mixing-induced precipitation: experimental study and multi-scale numerical analysis. Water. Resour. Res. 44, W06S04 (2008)
Zhang, Y., Papelis, C.: Particle-tracking simulation of fractional diffusion–reaction processes. Phys. Rev. E 84, 066704 (2011)
Zhang, Y., Papelis, C., Sun, P.T., Yu, Z.B.: Evaluation and linking of effective parameters in particle-based models and continuum models for mixing-limited bimolecular reactions. Water Resour. Res. 49, 4845–4865 (2013)
Acknowledgments
This study was supported by National Natural Science Foundation of China (Nos. 41372245; 41272251, 41372253). P. Sun is supported by NSF Grant DMS-1418806, and P. Sun also thanks for the support of NSF DMS-0913757. Y. Zhang was funded by the NSF under DMS-1025417 and DMS-1460319. We thank three anonymous reviewers for their constructive comments which helped us to improve the presentation of this work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qian, J., Zhan, H., Zhang, Y. et al. Numerical Simulation and Experimental Study of Bimolecular Reactive Transport in Porous Media. Transp Porous Med 109, 727–746 (2015). https://doi.org/10.1007/s11242-015-0549-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-015-0549-y