(604k) Economic Optimization of Lipid Production in Microalgae Bioreactor Using Nonlinear Programming

Economic feasibility of biodiesel production from microalgae cultivation can be guaranteed by increasing the lipid production and minimizing nutrients consumption. A microalgae growth model can be used to mathematically calculate the feeding strategy to achieve these goals. This work is based on an existing heterotrophic microalgae (Auxenochlorella protothecoides) fed-batch model[1] which is developed to predict the microalgae growth and oil production. Microalgae grows on two nutrients, glucose and glycine, and the growth and lipid production can be manipulated by different feeding strategies. In addition, the mathematical model has highly nonlinear and time varying parameters such as growth, nitrogen uptake and oil production rates[2].

In this work, mathematical model of heterotrophic growth of microalgae is used to maximize lipid production. The most expensive feed stock in this model is glucose and the economic performance of the bio-reactor can be calculated based on glucose consumption and lipid production. The objective function is defined as the rate of lipid production per use of glucose feed rate. Maximizing this objective function with respect to feeding flow rates and also process time will maximize the economic profitability of microalgae bioreactor. The highly nonlinear rate functions and the constraints on the states and inputs make the conventional optimization tools too slow or not applicable. The optimization problem is formulated as a constrained nonlinear program and solved using Ipopt solver[3]. Ipopt is an open source software package for large-scale nonlinear optimization and the nonlinear program is formulated and passed to Ipopt through AMPL[4] interface. Finally, a feeding strategy is designed to maximize the lipid productivity of microalgae and keep the economic performance at the maximum possible value.

References:

[1] H. De la Hoz Siegler, A. Ben-Zvi, R.E. Burrell, W.C. McCaffrey, The dynamics of heterotrophic algal cultures, Bioresource Technology 102, 2011, 5764-5774

[2] H. De la Hoz Siegler, R.E. Burrell, W.C. McCaffrey, A. Ben-Zvi, Optimization of microalgal pro- ductivity using an adaptive, non-linear model based strategy, Bioresource Technology, 104, 2012, 537-546

[3] A. Wachter and L. T. Biegler, On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), 2006, pp. 25-57

[4] R. Fourer, D. Gay, and B. Kernighan, AMPL: A Mathematical Programming Language, Duxbury Press; Second edition, 2002