Analytical model for fully three-dimensional radial dispersion in a finite-thickness aquifer

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Analytical solutions for contaminant transport in a non-uniform flow filed are very difficult and relatively rare in subsurface hydrology. The difficulty is because of the fact that velocity vector in the non-uniform flow field is space-dependent rather than constant. In this study, an analytical model is presented for describing the three-dimensional contaminant transport from an area source in a radial flow field which is a simplest case of the non-uniform flow. The development of the analytical model is achieved by coupling the power series technique, the Laplace transform and the two finite Fourier cosine transform. The developed analytical model is examined by comparing with the Laplace transform finite difference (LTFD) solution. Excellent agreements between the developed analytical model and the numerical model certificate the accuracy of the developed model. The developed model can evaluate solution for Peclet number up to 100. Moreover, the mathematical behaviours of the developed solution are also studied. More specifically, a hypothetical convergent flow tracer test is considered as an illustrative example to demonstrate the three-dimensional concentration distribution in a radial flow field. The developed model can serve as benchmark to check the more comprehensive three-dimensional numerical solutions describing non-uniform flow contaminant transport.

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