Dispersion of a continuously injected, nonlinearly adsorbing solute in chemically or physically heterogeneous porous formations

In this paper we consider transport of a nonlinearly adsorbing solute in a two-dimensional porous medium. The solute is continuously injected along a line source with a size equal to the transverse dimension of the domain. Adsorption is described by the Freundlich isotherm. The domain is assumed to be spatially variable and variation of hydraulic conductivity and adsorption coefficient is considered separately. Solute transport is solved by a mixed Eulerian-Lagrangian method. It is shown that nonlinear adsorption adds an extra requirement of taking into account pore scale dispersion while using Eulerian-Lagrangian solution methods. Solute dispersion is characterized in terms of spatial moments, where the pdf is the derivative of the transversely averaged concentration field. Results of numerical calculations are obtained for nonlinear and linear adsorption. It is shown that for large displacements an increase of pore scale dispersion leads to a decrease of average front spreading in case of nonlinear adsorption. The nonlinearity of adsorption opposes the local spreading in the longitudinal direction, whereas transverse spreading decreases the average front spreading. For larger displacements the front variance increases linearly with time. If transverse mixing is of the order of magnitude of the scale of heterogeneity, the front variance approaches a constant value, i.e a traveling wave becomes apparent.