Modeling and optimization of algae growth

The wastewater from greenhouses has a high amount of mineral contamination and an environmentally-friendly method of removal is to use algae to clean this runoff water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity . The aim of this paper is to develop a model of algae production and use this model to investigate how best to optimize algae farms to satisfy the dual goals of maximizing growth and removing mineral contaminants. With this aim in mind the paper is split into five main sections. In the first a review of the biological literature is undertaken with the aim of determining what factors effect the growth of algae. The second section contains a review of exciting mathematical models from the literature, and for each model a steady-state analysis is performed. Moreover, for each model the strengths and weaknesses are discussed in detail. In the third section, a new two-stage model for algae production is proposed, careful estimation of parameters is undertaken and numerical solutions are presented. In the next section, a new one-dimensional spatial-temporal model is presented, numerically solved and optimization strategies are discussed. Finally, these elements are brought together and recommendations of how to continue are drawn. Keywords: Algae growth, steady-state analysis, parameter estimation, optimization