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The use of standard numerical schemes to solve nonlinear advective-dispersive equations for the estimation of parameters is CPU-time consuming and hence not desirable for routine use. An efficient scheme using a novel mixing cell approach has been used to estimate parameter values by nonlinear least-squares fitting for nonlinear adsorption of a single solute species coupled with one- dimensional transport. A problem with gradient methods of nonlinear least-squares fitting is that they are prone to determine best-fit parameters corresponding to local minima rather than the global minimum. As is well known, this problem can be avoided by judicious selection of the