Contamination of a well in a uniform background flow |
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| Authors: | C J van der Hoek |
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| Institution: | (1) Dept. of Mathematics, Agricultural University, Dreijenlaan 4, 6703 HA Wageningen, The Netherlands |
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| Abstract: | In this paper we describe the transport of pollution in groundwater in the neighbourhood of a well in a uniform background flow. We compute the rate at which contaminated particles reach the well as a function of the place of the source of pollution. The motion of a particle in a dispersive flow is seen as a random walk process. The Fokker-Planck equation for the random motion of a particle is transformed using the complex potential for the advective flow field. The resulting equation is solved asymptotically after a stretching transformation. Finally, the analytical solution is compared with results from Monte Carlo simulations with the random walk model. The method can be extended to arbitrary flow fields. Then by a numerical coordinate transformation the analytical results can still be employed. |
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| Keywords: | Hydrodynamic dispersion Fokker-Planck equation backward equation boundary layer complex potential function fraction of contaminated particles that enter a well |
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