Solute transport modeled with Green's functions with application to persistent solute sources

Analytical models can be valuable tools to investigate solute transport in porous media. The application of analytical solutions is limited by the perception that they are too cumbersome to derive while their implementation rests on assumptions that are too restrictive. The Green's function method (GFM) was applied to facilitate analytical solution of the advection- dispersion equation (ADE) for solute transport in uniform porous media with steady one- or two-dimensional flow. The GFM conveniently handles different boundary and initial conditions as well as multi-dimensional problems. Concise expressions are possible for the solute concentration with the GFM. This paper provides a general framework to efficiently formulate analytical solutions for many transport problems. Expressions for the longitudinal and transversal Green's function are presented that can be inserted in the general expression to solve a wide variety of transport problems in infinite, semi-infinite, and finite media. These solutions can be used to elucidate transport phenomena, estimate transport parameters, evaluate numerical solution procedures and simulate the movement and fate of solutes. An illustration of the GFM is provided by the analytical modeling of transport from a planar source of persistent, long-lasting contamination. Such a source may be used to represent dissolution from a pool of a non-aqueous phase liquid (NAPL). Analytical solutions are obtained for a first-, second-, and third-type condition in case of a planar source; the third-type condition is due to downward flow or rate-limited dissolution. Several examples are presented to show the effect of source conditions, the sensitivity of NAPL dissolution to transport parameters included in the Damkohler and Peclet numbers, and upstream dispersion.