Biological fixation of CO2 using microalgae is an effective carbon dioxide capture technology. To make this option economically competitive compared to other CO2 capture techniques, a better understanding of its dynamic behavior is required. In this study, data generated using a central composite experimental design (CCD) with varying light intensity, CO2 and phosphate concentration was used to develop a mathematical model that describes the kinetics of algal growth and CO2, phosphate, nitrate and ammonium uptake rate of Chlorella kessleri cultivated in oil sands process water (OSPW). The model considers the uncoupling between nutrients uptake and growth and the possibility of luxurious uptake of nutrients. This nonlinear dynamic model was used to determine the optimal CO2 concentration, phosphate concentration and light intensity for CO2 uptake and algal growth over a period of time in a batch culture using a multi-objective optimization technique to maximize CO2 fixation and algal growth simultaneously. (C) 2015 Elsevier Ltd. All rights reserved.