Analytical solution for a radial advection-dispersion equation including both mechanical dispersion and molecular diffusion for a steady-state flow field in a horizontal aquifer caused by a constant rate injection from a well
September 4th, 2018
Masaatsu Aichi, Kento Akitaya
Received 2018/05/23, Accepted 2018/07/18, Published 2018/09/04
Masaatsu Aichi1), Kento Akitaya1)
1) Department of Environment Systems, Graduate School of Frontier Sciences, The University of Tokyo, Japan
This study presents the analytical solution for a radial advection-dispersion equation for a steady-state flow field in a horizontal aquifer caused by a constant rate injection from a well, including the mechanical dispersion and molecular diffusion terms in addition to the retardation and first-order attenuation under a Robin-type boundary condition at the well. The derived analytical solutions were compared with finely-meshed finite difference solutions in steady-state and periodic steady-state problems with typical parameters. The results suggest that the analytical solution is exactly derived and ready for application. Comparisons with analytical solutions ignoring molecular diffusion suggest that the derived analytical solution should be used when the product of the decay constant and the retardation factor and the ratio of injection rate to diffusion coefficient are small. Comparisons with analytical solutions with Dirichlet-type boundary conditions confirmed that Robin-type boundary conditions should be used to exactly evaluate the concentration profile.
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