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 per ception that they are too cumbersome to derive while their implementation r ests on assumptions that are too restrictive. The Green's function method ( GFM) was applied to facilitate analytical solution of the advection-dispers ion equation (ADE) for solute transport in uniform porous media with steady one- or two-dimensional flow. The GFM conveniently handles different bound ary and initial conditions as well as multi-dimensional problems. Concise e xpressions are possible for the solute concentration with the GFM. This pap er provides a general framework to efficiently formulate analytical solutio ns for many transport problems. Expressions for the longitudinal and transv ersal Green's function are presented that can be inserted in the general ex pression to solve a wide variety of transport problems in infinite, semi-in finite, and finite media. These solutions can be used to elucidate transpor t phenomena, estimate transport parameters, evaluate numerical solution pro cedures and simulate the movement and fate of solutes. An illustration of t he GFM is provided by the analytical modeling of transport from a planar so urce of persistent, long-lasting contamination. Such a source may be used t o represent dissolution from a pool of a non-aqueous phase liquid (NAPL). A nalytical solutions are obtained for a first-, second-, and third-type cond ition in case of a planar source; the third-type condition is due to downwa rd flow or rate-limited dissolution. Several examples are presented to show the effect of source conditions, the sensitivity of NAPL dissolution to tr ansport parameters included in the Damkohler and Peclet numbers, and upstre am dispersion. (C) 2000 Elsevier Science B.V. All rights reserved.