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To reduce the cost of algal biomass production, mathematical model was developed for the first time to describe microalgae growth, lipid production and glycerin consumption under photoheterotrophic conditions based on logistic, Luedeking–Piret and Luedeking–Piret-like equations. All experiments were conducted in a 2 L batch reactor without considering CO2 effect on algae’s growth and lipid production. Biomass and lipid production increased with glycerin as carbon source and were well described by the logistic and Luedeking–Piret equations respectively. Model predictions were in satisfactory agreement with measured data and the mode of lipid production was growth-associated. Sensitivity analysis was applied to examine the effects of certain important parameters on model performance. Results showed that S0, the initial concentration of glycerin, was the most significant factor for algae growth and lipid production. This model is applicable for prediction of other single cell algal species but model testing is recommended before scaling up the fermentation of process.