This paper studied the bifurcation phenomena that can occur in a continuous bioreactor for lipid-rich biomass production using Rhodococcus opacus that feeds on refinery wastewater. An unstructured model of the bioreactor was developed based on experimentally validated studies reported in the literature. The analysis of the unsteady-state model was carried out both analytically and through numerical simulations. It was shown that the inhibition effect of the biomass growth rate can lead to the occurrence of static bistability in the model. Periodic behavior was also found for some range of model parameters. The effect of model parameters on the productivity of the bioreactor was also investigated. The analysis carried out in this paper allowed for the detection of unsafe operating regions in the bioreactor which, would help in the attenuation of these operational problems in the early stage of process design.