A semi-analytical solution for simulating contaminant transport subject to chain-decay reactions

• Published in: Journal of contaminant hydrology 2013-01, Vol.144 (1), p.20-45
• Main Authors: Sudicky, Edward A., Hwang, Hyoun-Tae, Illman, Walter A., Wu, Yu-Shu, Kool, Jan B., Huyakorn, Peter
• Format: Article
• Language: English
• Subjects: Biodegradation; Branching decay chain; Earth sciences; Earth, ocean, space; Exact sciences and technology; First-order reactions; Groundwater; Hydrogeology; Hydrology. Hydrogeology; Models, Theoretical; Multi-species; Solute transport; Sorption; Uranium; Water Pollutants, Chemical - analysis; Water Pollutants, Chemical - metabolism; Water Pollution
• ISSN: 0169-7722; 1873-6009
• DOI: 10.1016/j.jconhyd.2012.10.001

We present a set of new, semi-analytical solutions to simulate three-dimensional contaminant transport subject to first-order chain-decay reactions. The aquifer is assumed to be areally semi-infinite, but finite in thickness. The analytical solution can treat the transformation of contaminants into daughter products, leading to decay chains consisting of multiple contaminant species and various reaction pathways. The solution in its current form is capable of accounting for up to seven species and four decay levels. The complex pathways are represented by means of first-order decay and production terms, while branching ratios account for decay stoichiometry. Besides advection, dispersion, bio-chemical or radioactive decay and daughter product formation, the model also accounts for sorption of contaminants on the aquifer solid phase with each species having a different retardation factor. First-type contaminant boundary conditions are utilized at the source (x=0 m) and can be either constant-in-time for each species, or the concentration can be allowed to undergo first-order decay. The solutions are obtained by exponential Fourier, Fourier cosine and Laplace transforms. Limiting forms of the solutions can be obtained in closed form, but we evaluate the general solutions by numerically inverting the analytical solutions in exponential Fourier and Laplace transform spaces. Various cases are generated and the solutions are verified against the HydroGeoSphere numerical model. ► A new semi-analytical solution for 3-dimensional contaminant transport is presented. ► Transport subjected to 1st-order chain-decay reactions with various reaction paths. ► The solution is capable of accounting for 7 species and 4 decay levels. ► The solution accounts for sorption with each species with own retardation factor. ► The solution is verified against the HydroGeoSphere numerical model in 1- and 3-D.