We present in this paper a new strategy based on the use of polynomial chaos expansion (PCE) for both global sensitivity analysis and parameter optimization. To limit the number of evaluations of the direct model, we develop a simple and efficient procedure to construct a sparse PCE where only coefficients that have a significant contribution to the variance of the model are retained. Parameter estimation is performed using an adaptive procedure where the intervals of variation of the parameters are progressively reduced using information from sensitivity analysis calculated using the sparse PCE. The strategy is shown to be effective for the parameter estimation of two reactive transport problems: a synthetic reactive transport problem involving the Freundlich sorption isotherm and a field experiment of Valocchi et al. (Water Resources Research 17:1517-1527, 1981) involving nonlinear ion exchange reactions.