A generalized three-dimensional analytical solute transport model for multiple rectangular first-type sources

A generalized three-dimensional analytical solute transport model with a unidirectional flow held from time- and space-dependent rectangular sources in a bounded homogeneous medium is presented using the first-type (or Dirichlet) source condition at the inlet location of the medium. The partial differential equation for solute transport incorporates terms accounting for advection (or convection), mechanical dispersion, molecular diffusion, linear equilibrium sorption, and first-order decay. Fairly general solutions are presented under unsteady-state and steady-state solute transport conditions for arbitrary source input conditions with the help of Fourier analysis and Laplace transform techniques. Special solutions are given for a single source and two rectangular sources with constant source concentrations. It is shown that some one- and two-dimensional analytical solute transport models published in the literature are exact special cases of the general three-dimensional analytical model. The numerical results of the one rectangular source model are also compared with the results of the model of Huyakorn et al. (1987), with good agreement. The solutions may be used for predicting solute concentrations from partially penetrated solute sources located at any place along a vertical plane perpendicular to the flow direction of groundwater, rivers, and canals. The solutions may also be used for verification of more comprehensive numerical models, and laboratory and field determination of solute transport parameters.