Analytical Modeling of Nonaqueous Phase Liquid Dissolution with Green's Functions

Abstract

Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Green's Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multi‐dimensional problems. The Green's functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semi‐infinite and infinite media. The GFM is applied to analytically model multi‐dimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first‐, second‐, or third‐type boundary or source input conditions. Away from the source, the first‐ and third‐type condition cannot be expected to represent the exact surface condition. The second‐type condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the third‐type condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport.