A comprehensive mathematical modeling method for Chlorella vulgaris (Cv) has been developed to assess the influence of nutrient concentration (total nitrogen TN = 28-207 and total phosphorus TP = 6-8 mg L-1) and irradiation intensity (I = 100-250 mu E) at feed gas CO2 concentrations (C-c,C-g) of 0.04-5%. The model encompasses gas-to-liquid mass transfer, algal uptake of carbon dioxide (C-d), nutrient removal efficiency (RE for TN and TP), and the growth biokinetics of Cv with reference to the specific growth rate mu in d(-1). The model was validated using experimental data on the Cv species growth in an externally illuminated photobioreactor (PBR). The fitted parameters of the model were found to be in good agreement with experimental data obtained over the range of cultivation conditions explored. The mathematical model accurately reproduced the dynamic profiles of the algal biomass and nutrient (TN and TP) concentrations, and light attenuation at different input C-c,C-g values. The proposed model may therefore be used for predicting algal growth and nutrient RE for this algal species, permitting both process optimization and scale-up. (C) 2016 Elsevier Ltd. All rights reserved.