We investigate the benefit of operating the chemostat model with periodic controls for biological water decontamination. We address a first problem of minimizing the average output concentration of pollution under a constraint of the total quantity of water treated over the period, and a second one of maximizing this quantity under a constraint on the average output concentration. We first give conditions on the growth characteristics of microorganisms for which an improvement is possible, compared to steady-state. We then give the global optimal periodic control strategies for the first problem and show a duality between the two problems, which allows to obtain the solutions of the second problem from the first one. Results are illustrated on Monod, Haldane, Hill and Contois kinetics.