The Droop model is a classical model used to describe substrate limitation in cultures of microalgae in photobioreactors. In this study, we address the questions of structural identifiability as well as practical identifiability. Optimal experiment design based on the M-criterion is used to determine a small set of experiments that would allow an accurate estimation of the model parameters. Direct and cross-validation results are presented and discussed in the framework of a simulation study. As a result, all parameters are found to be structurally identifiable and two continuous experiments are proposed that target either the estimation of the maximum substrate uptake rate and maximum growth rate, or the half saturation constant of the uptake rate, respectively.