An Analytic Element Method solution for multispecies reactive contaminant transport

A new analytic element approach is presented for steady-state reactive contaminant transport modelling with circular boundaries. Two solute compounds (electron donor and electron acceptor) are assumed to undergo an instantaneous and binary reaction [1] in a uniform flow field, forming a steady plume [2]. Transformations of the advection-dispersion-reaction equation are applied resulting in a reactive contaminant transport system governed by the modified Helmholtz equation. Comprehensive solutions to a single as well as multiple superimposed, interacting circular contaminant (electron donor) source elements are expressed by infinite series expansions of Mathieu functions [3]. The concentration of the electron donor and electron acceptor can be calculated at any point in the domain, while boundary conditions are met approximately, by adjusting the unknown coefficients of the truncated series of Mathieu functions.  Accuracy at the boundary interfaces is increased with an increase of number of terms used in the Mathieu functions series expansion. The potential of this novel approach lies in the flexibility of boundary conditions, while maintaining computational efficiency.

The model is implemented using the Python programming language. Model verification was achieved by evaluating the residual of a central difference scheme, evaluation of the error along the boundary interfaces and a comparison with a simple MODFLOW / MT3DMS model setup. Current development includes expansion of the model to line source elements and discontinuous contaminant sources. Further advancements may be achieved by increasing source shape complexity of contaminant sources by superimposing a large number of elements and introducing remediation actions in the form of interacting electron acceptor elements.

[1]           O. A. Cirpka, Å. Olsson, Q. Ju, Md. A. Rahman, and P. Grathwohl, ‘Determination of Transverse Dispersion Coefficients from Reactive Plume Lengths’, Groundwater, vol. 44, no. 2, pp. 212–221, 2006, doi: 10.1111/j.1745-6584.2005.00124.x.

[2]           R. Liedl, A. J. Valocchi, P. Dietrich, and P. Grathwohl, ‘Finiteness of steady state plumes’, Water Resources Research, vol. 41, Dec. 2005, doi: 10.1029/2005WR004000.

[3]           M. Bakker, ‘Modeling groundwater flow to elliptical lakes and through multi-aquifer elliptical inhomogeneities’, Advances in Water Resources, vol. 27, no. 5, pp. 497–506, May 2004, doi: 10.1016/j.advwatres.2004.02.015.