Contaminant transport with adsorption and their inverse problems

In Constales et al. (water Resources Res. 39(30), 1303, 2003) dual-well tests are used to reconstruct the flow and dispersion parameters in contaminant transport. A tracer is introduced by the injection well, which is considered to be in steady-state regime with the extraction well. Then, from measurements of the time evolution of the extracted tracer (breakthrough curve) the required model data has been recovered. In Constales et al. (water Resources Res. 39(30), 1303, 2003), a very precise numerical method has been developed for the solution of the direct problem. In Kačur et al. (Comput. Meth. Appl. Mech. Engo. 194(2–5), 479–489, 2005); Remešiková (J. Comp. Appl. Math. 169(1), 101–116, 2004) an extension has been discussed which adds adsorption terms to the model. The inverse problem of determination of sorption isotherms in nonequilibrium mode was solved by a Levenberg–Marquardt iteration method. In the present paper we develop the adjoint system to evaluate the sensitivity of the solution (via the breakthrough curve) on the sorption parameters in equilibrium and nonequilibrium modes. Possible use of the adjoint system in determining the several parameters occuring in the model is a crucial point for iteration methods. The obtained model parameters then can be used in a 3D flow and transport model with adsorption. The numerical experiments we present, justify the used method.