We consider an Eulerian-Lagrangian localized adjoint method (ELLAM) applied to nonlinear model equations governing solute transport and sorption in porous media. Solute transport in the aqueous phase is modeled by standard advection and hydrodynamic dispersion, while two types of solid phase are distinguished --- a fraction which achieves equilibrium with the aqueous phase quickly, and another which does not. The rapidly sorbing fraction is modeled using a local equilibrium assumption, while a first-order rate expression...