In this work, a continuum 2D model is proposed to study the interaction at the interface of reactive transport processes in porous media. The analysis of the segregation produced by poor reactant homogenization at the poral scale is addressed by a parametric heuristic model that considers the relative gradient of the reacting species involved in the process. The micro inhomogeneities are incorporated by means of longitudinal and transversal mechanical dispersion coefficients. A two-dimensional continuous model for the bimolecular reactive transport is considered where modelling parameters are estimated numerically from experimental data. A competitive effect between segregation and dispersion is observed that is analyzed by means of numerical experiments. The two-dimensional model reproduces properly both the total mass of the product as well as its increase with the velocity of flow and the inhomogeneity of the advanced front. The methodology used is simple and fast, and the numerical results presented here indicate its effectiveness.
References
[1]
Edery, Y., Guadagnini, A., Scher, H. and Berkowitz, B. (2013) Reactive Transport in Disordered Media: Role of Fluctuations in Interpretation of Laboratory Experiments. Advances in Water Resources, 51, 86-103. https://doi.org/10.1016/j.advwatres.2011.12.008
[2]
Kapoor, V., Gelhar, L.W. and Miralles-Wilhelm, F. (1997) Bimolecular Second-Order Reactions in Spatially Varying Flows: Segregation Induced Scale-Dependent Transformation Rates. Water Resources Research, 33, 527-536. https://doi.org/10.1029/96WR03687
[3]
Kapoor, V., Chad T.J. and Lyn, D.A. (1998) Experimental Study of a Bimolecular Reaction in Poiseuille Flow. Water Resources Research, 34, 1997-2004. https://doi.org/10.1029/98WR01649
[4]
Cirpka, O.A. (2002) Choice of Dispersion Coefficients in Reactive Transport Calculations on Smoothed Fields. Journal of Contaminant Hydrology, 58, 261-282. https://doi.org/10.1016/S0169-7722(02)00039-6
[5]
Oates P. and Harvey C.F. (2007) Upscaling Reactive Transport in Porous Media: Laboratory Visualizations and Stochastic Models. In: AGU Fall Meeting Abstracts, American Geophysical Union, Washington DC, H32D-08.
[6]
Willingham, T.W., Werth, C.J. and 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, 3185-3193. https://doi.org/10.1021/es7022835
[7]
Gramling, C., Harvey, C. and Meigs, L. (2002) Reactive Transport in Porous Media: A Comparison of Model Prediction with Laboratory Visualization. Environmental Science & Technology, 36, 2508-2514. https://doi.org/10.1021/es0157144
[8]
Raje, D.S. and Kapoor, V. (2000) Experimental Study of Bimolecular Reaction Kinetics in Porous Media. Environmental Science & Technology, 34, 1234-1239. https://doi.org/10.1021/es9908669
[9]
Edery, Y., Scher, H. and Berkowitz, B. (2009) Modeling Bimolecular Reactions and Transport in Porous Media. Geophysical Research Letters, 36, L02407. https://doi.org/10.1029/2008GL036381
[10]
Edery, Y., Porta, G.M., Guadagnini, A., Scher, H. and Berkowitz, B. (2016) Characterization of Bimolecular Reactive Transport in Heterogeneous Porous Media. Transport in Porous Media, 115, 291-310. https://doi.org/10.1007/s11242-016-0684-0 https://link.springer.com/article/10.1007/s11242-016-0684-0
[11]
Alhashmi, Z., Blunt, M.J. and Bijeljic, B. (2015) Predictions of Dynamic Changes in Reaction Rates as a Consequence of Incomplete Mixing Using Pore Scale Reactive Transport Modeling on Images of Porous Media. Journal of Contaminant Hydrology, 179, 171-181. https://doi.org/10.1016/j.jconhyd.2015.06.004
[12]
Sanchez-Vila, X., Fernández-Garcia, D. And Guadagnini, A. (2010) Interpretation of Column Experiments of Transport of Solutes Undergoing an Irreversible Bimolecular Reaction Using a Continuum Approximation. Water Resources Research, 46, W12510. https://doi.org/10.1029/2010WR009539
[13]
Rubio, A.D., Zalts, A. And El Hasi, C.D. (2008) Numerical Solution of the Advection-Reaction-Diffusion Equation at Different Scales. Environmental Modelling & Software, 23, 90-95. https://doi.org/10.1016/j.envsoft.2007.05.009
[14]
Ginn, T.R. (2018) Modeling Bimolecular Reactive Transport with Mixing-Limitation: Theory and Application to Column Experiments. Water Resources Research, 54, 256-270. https://doi.org/10.1002/2017WR022120
[15]
Gurung, D. and Ginn, T.R. (2020) Mixing Ratios with Age: Application to Preasymptotic One-Dimensional Equilibrium Bimolecular Reactive Transport in Porous Media. Water Resources Research, 56, e2020WR027629. https://doi.org/10.1029/2020WR027629
[16]
Valocchi, A.J., Bolster, D. and Werth, C.J. (2019) Mixing-Limited Reactions in Porous Media. Transport in Porous Media, 130, 157-182. https://doi.org/10.1007/s11242-018-1204-1
[17]
Sole-Mari, G., Bolster, D. and Fernàndez-Garcia, D. (2023) A Closer Look: High-Resolution Pore-Scale Simulations of Solute Transport and Mixing through Porous Media Columns. Transport in Porous Media, 146, 85-111. https://doi.org/10.1007/s11242-021-01721-z
[18]
Porta, G.M., Riva, M. and Guadagnini, A. (2012) Upscaling Solute Transport in Porous Media in the Presence of an Irreversible Bimolecular Reaction. Advances in Water Resources, 35, 151-162. https://doi.org/10.1016/j.advwatres.2011.09.004
[19]
Chiogna, G. and Bellin, A. (2013) Analytical Solution for Reactive Solute Transport Considering Incomplete Mixing within a Reference Elementary Volume. Water Resources Research, 49, 2589-2600. https://doi.org/10.1002/wrcr.20200
[20]
Meeder, J.P. and Nieuwstadt, F.T.M. (2000) Large-Eddy Simulation of the Turbulent Dispersion of a Reactive Plume from a Point Source into a Neutral Atmospheric Boundary Layer. Atmospheric Environment, 34, 3563-3573. https://doi.org/10.1016/S1352-2310(00)00124-2
[21]
Meile, C. and Tuncay, K. (2006) Scale Dependence of Reaction Rates in Porous Media. Advances in Water Resources, 29, 62-71. https://doi.org/10.1016/j.advwatres.2005.05.007
[22]
Cuch, D., Rubio, D. and El Hasi, C.D. (2015) Data Pre-Processing for Parameter Estimation—An Application to a Reactive Bimolecular Transport Model. International Journal of Science, Environment and Technology, 4, 1694-1705.
[23]
Cuch, D.A., El Hasi, C.D., Rubio, D., Urcola, G.C. and Zalts, A. (2009) Modelling Reactive Transport Driven by Scale Dependent Segregation. In: Acosta, J.L. and Camacho, A.F., Eds., Porous Media: Heat and Mass Transfer, Transport and Mechanics: Chapter 1, NOVA Science Publishers, Hauppauge, 1-25.
[24]
Hou, J., Liang, Q., Zhang, H. and Hinkelmann, R. (2015) An Efficient Unstructured MUSCL Scheme for Solving the 2D Shallow Water Equations. Environmental Modelling & Software, 66, 131-152. https://doi.org/10.1016/j.envsoft.2014.12.007
[25]
Wheeler, M.F. and Dawson, C.N. (1987) An Operator-Splitting Method for Advection-Diffusion-Reaction Problems. Technical Report 87-9. Mathematical Sciences Department, Rice University, Houston.
[26]
Bear, J. (1988) Dynamics of Fluids in Porous Media. Dover Publications, Inc., New York.
