Analytical solutions of nonaqueous-phase-liquid dissolution problems associated with radial flow in fluid-saturated porous media

•To derive analytical solutions for NAPL dissolution problems with radial flow.•Three key factors can affect the propagating speed of an NAPL dissolution front.•Three key factors can also affect the location and breakthrough time of an NAPL dissolution front.•The Zhao number can be used to represent the overall hydrodynamic characteristic of a NAPL dissolution system.•Several key factors can also affect the distribution pattern and evolution of the NAPL dissolution front. The removal of nonaqueous phase liquids (NAPLs) from contaminated soils by means of fresh water injection through a rejection well can be treated as a fully coupled problem involving the NAPL dissolution, radial aqueous-phase-liquid flow and dissolved NAPL transport through solute advection and diffusion/dispersion. The governing equations of this coupled problem can be mathematically described by a set of simultaneous partial differential equations with variable coefficients. In the case of the NAPL dissolution ratio (which is defined as the ratio of the equilibrium concentration of the dissolved NAPL to the density of the NAPL) approaching zero, analytical solutions for the NAPL dissolution problem associated with radial aqueous-phase-liquid flow have been derived in this paper. As a direct application example, the derived analytical solutions are used to investigate the fundamental behaviours of the NAPL dissolution problems associated with radial aqueous-phase-liquid flow in the fluid-saturated porous media. The related analytical results have demonstrated that three key factors, namely the dimensionless comprehensive number (which is known as the Zhao number and can be used to represent the overall hydrodynamic characteristic of a NAPL dissolution system), the initial saturation of the residual NAPL and the dimensionless injection well radius, can have significant effects on the dimensionless NAPL dissolution front propagation speed, the dimensionless NAPL dissolution front location and dimensionless breakthrough time of the NAPL dissolution front in the NAPL dissolution system associated with radial aqueous-phase-liquid flow.