MATHEMATICAL MODELING AND SIMULATION OF BATCH REGIME FOR IMMOBILIZED MICROALGAE PHOTOBIOREACTOR FOR EFFLUENT TREATMENT

Abstract

The increase of wastewater follows the expansion of the world population generating a deficit in basic sanitation and in the sewage collection provided. It is widely known that the United Nations (UN) instituted the 2030 Agenda, a plan for the sustainability of the planet, improvement of people's lives and world prosperity. There are 17 Sustainable Development Goals (SDGs) in the 2030 Agenda. We highlight the SDG 6: “Clean water and sanitation”, which is aimed at basic sanitation and access to drinking water. Currently, the treatment system is divided into three stages: primary, secondary and tertiary. In the secondary stage, one makes use of microorganisms to remove organic matter from the medium, such as microalgae or bacteria. Preference has been given to the use of microalgae, classified as microorganisms of rapid cell growth with photoautotrophic capacity. However, the free state physical dimension of a microalgae makes the treatment process more expensive and potentially, impacts the treatment time, thus burdening the treatment. With that in mind, a method of immobilization of microalgae and the elaboration of a photobioreactor for the treatment of effluents was developed. Immobilization is a practice that consists of fixing algae within small spheres, which simplifies the separation methodology of microorganisms from the treated effluent. The immobilizing medium provides mechanical resistance and protects the culture from possible contamination. In order to demonstrate the functionality of the system, as a means of effluent treatment, a mathematical modeling of the effluent treatment was conceived. Fortran was the programming language used to solve nonlinear differential equations through temporal discretization. Runge-Kutta was the numerical method chosen to solve the equations of the model that are based on Monod’s model. Monod’s model predicts the growth parameters during the life cycle determining the amount of substrates and the number of microalgae along the lag phase, log phase and stabilization level. It also expresses the consumption of the substrates. Thus, the model allows the visualization of the biomass growth, consumption of inorganic substances and the treatment time under study.