Numerical solution of the advection-reaction-diffusion equation at different scales

Solving the transport equation for bimolecular reactive processes in porous media involves several difficulties. The mathematical characteristics of the equation depend on the governing process, for example, when time scales for advection t"A, reaction t"R and diffusion t"D have different orders of magnitude. On the other hand, this equation is based on a continuum model, disregarding inhomogeneities that happen at poral level just where reactions take place. To deal with these problems a different way of modeling the advection-reaction-diffusion process is proposed. Based on the Damkohler number an algorithm has been developed to solve the problem for both slow and fast reactions. Spatial segregation of reactants can be incorporated improving the results.

[1]  L. Gelhar,et al.  Bimolecular second‐order reactions in spatially varying flows: Segregation induced scale‐dependent transformation rates , 1997 .

[2]  Neil Gershenfeld,et al.  The nature of mathematical modeling , 1998 .

[3]  Peter Engesgaard,et al.  Pesticide transport in an aerobic aquifer with variable pH--modeling of a field scale injection experiment. , 2005, Journal of contaminant hydrology.

[4]  J. Šimůnek,et al.  Multi-process herbicide transport in structured soil columns: experiments and model analysis. , 2006, Journal of contaminant hydrology.

[5]  Behzad Ataie-Ashtiani.  MODSharp: Regional-scale numerical model for quantifying groundwater flux and contaminant discharge into the coastal zone , 2007, Environ. Model. Softw..

[6]  D. A. Barry,et al.  Three-dimensional model for multi-component reactive transport with variable density groundwater flow , 2006, Environ. Model. Softw..

[7]  Mary F. Wheeler,et al.  An Operator-Splitting Method for Advection-Diffusion-Reaction Problems , 1987 .

[8]  Behzad Ataie-Ashtiani,et al.  Numerical errors of explicit finite difference approximation for two-dimensional solute transport equation with linear sorption , 2005, Environ. Model. Softw..

[9]  James S. Bonner,et al.  Simulation of constituent transport using a reduced 3D constituent transport model (CTM) driven by HF Radar: Model application and error analysis , 2007, Environ. Model. Softw..

[10]  Michael S. McLachlan,et al.  CoZMo-POP 2 - A fugacity-based dynamic multi-compartmental mass balance model of the fate of persistent organic pollutants , 2006, Environ. Model. Softw..

[11]  Albert J. Valocchi,et al.  Accuracy of operator splitting for advection‐dispersion‐reaction problems , 1992 .

[12]  Vivek Kapoor,et al.  Experimental study of bimolecular reaction kinetics in porous media. , 2000 .

[13]  Kagan Tuncay,et al.  Scale dependence of reaction rates in porous media , 2006 .

[14]  Peter R Jørgensen,et al.  Transport and reduction of nitrate in clayey till underneath forest and arable land. , 2004, Journal of contaminant hydrology.

[15]  Hristo V. Kojouharov,et al.  Nonstandard Eulerian-Lagrangian methods for multi-dimensional reactive transport problems , 2004 .

[16]  L. K. Deeks,et al.  Full title page pp iii Transport of conservative and reactive tracers through a naturally structured upland podzol field lysimeter , 2005 .

[17]  Hristo V. Kojouharov,et al.  Generalized Nonstandard Numerical Methods for Nonlinear Advection-Diffusion-Reaction Equations , 2003, LSSC.

[18]  C. Harvey,et al.  Reactive transport in porous media: a comparison of model prediction with laboratory visualization. , 2002, Environmental science & technology.

[19]  Michael Rode,et al.  Modelling nitrate transport and turnover in a lowland catchment system , 2006 .

[20]  Bruce E. Logan,et al.  Environmental Transport Processes , 1998 .

[21]  Erdal Cokca.  A computer program for the analysis of 1-D contaminant migration through a soil layer , 2003, Environ. Model. Softw..

[22]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[23]  S. K. Kamra,et al.  Quantitative indices to characterize the extent of preferential flow in soils , 2005, Environ. Model. Softw..

[24]  Roger A. Falconer,et al.  Flow and solute fluxes in integrated wetland and coastal systems , 2007, Environ. Model. Softw..

[25]  Dennis A. Lyn,et al.  Experimental study of a bimolecular reaction in Poiseuille Flow , 1998 .