Solution and scaling of one-dimensional groundwater-solute flow with large density variations

A scaling analysis and solution of one-dimensional groundwater-solute flow is presented for the steady state case when density is strongly dependent on the concentration. The solution is applicable to one-dimensional vertical or sloping flow with constant head and solute concentrations at the inlet and outlet. The dependent dimensionless variables (density, concentration, equivalent freshwater head, and fluid velocity) are shown to be a function of four dimensionless groups: a Peclet number of diffusion, a Peclet number of dispersion, a buoyancy number, and a density number. In practice, however, the dependent variables are shown to be independent of the density number and only a function of the remaining three dimensionless groups. The results show that the velocity decreases quickly by several orders of magnitude as the Peclet and buoyancy numbers increase. The rapid decrease in velocity occurs when the buoyancy number (defined as the ratio of the buoyancy force to equivalent freshwater driving force) is greater than unity. We further show that aquifers can have substantial velocity reductions even when density variations are not large, whereas aquitards will exhibit relative small velocity reductions independent of density variations. Implications of the velocity reduction to hydrogeologic investigations of nuclear waste disposal sites are discussed.