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 injecte d along a line source with a size equal to the transverse dimension of the domain. Adsorption is described by the Freundlich isotherm. The d omain is assumed to be spatially variable and variation of hydraulic c onductivity and adsorption coefficient is considered separately. Solut e transport is solved by a mixed Eulerian-Lagrangian method. It is sho wn 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 momen ts, where the pdf is the derivative of the transversely averaged conce ntration field. Results of numerical calculations are obtained for non linear and linear adsorption. It is shown that for large displacements an increase of pore scale dispersion leads to a decrease of average f ront spreading in case of nonlinear adsorption. The nonlinearity of ad sorption opposes the local spreading in the longitudinal direction, wh ereas 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 hete rogeneity, the front variance approaches a constant value, i.e. a trav eling wave becomes apparent.