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Advection-dispersion-reaction equations are widely used to simulate heat and mass transport problems in science and engineering. Analytical and semi-analytical solutions to such problems are highly desirable but are currently limited to a single type of source. This limitation poses significant challenges to the interaction analysis between different types of sources and the accurate inversion of the actual source zone. In this paper, We developed a two-dimensional analytical model for solute transport in a finite domain subject to both internal point sources and boundary sources. The solution approach applies Laplace transform combined with finite Fourier transform and variable substitution to obtain the generalized semi-analytical solution. An instantaneous point source system, together with Dirichlet and Robin inlet boundary, is selected to investigate the solute transport behavior in a more realistic scenario. Results reveal that the transport system with point source and Dirichlet boundary source has the largest predicted concentration. The selection of inlet boundaries for the migration prediction model with low-permeability media (small Péclet number) or highly reactive solute (large Damköhler number) is of great importance, especially when performing long-term predictions.

Solute transport, Advection-dispersion-reaction equation, Analytical solution, Point source, Boundary source