Dimensionless Dynamic Model for the Simulation of Microalgae Biomass Production in Compact Photobioreactors

Photobioreactors simulation is currently the subject of scientific research in many countries due to interest in biofuel production. One challenge in the assessment of photobioreactors behavior is the lack of information about algae growth properties. In this paper, a dimensionless mathematical model is introduced for assessing the transient microalgae growth, O2, CO2 concentrations and temperature as function of light intensity. An equation to calculate the growth rate independently of algae specie is introduced. Photobioreactor geometry is considered as well. The equipment was discretized in space by the volume element method, VEM. Balances of energy and species together with thermodynamics, heat transfer and chemistry empirical and theoretical correlations are applied to each volume element. The resulting system of ordinary differential equations with respect to time is capable of delivering temperatures and concentrations as functions of space and time, even with a coarse mesh. The numerical results are capable of predicting the transient and steady state photobioreactor biomass production with low computational time. The results are dimensionless and they represents the behavior of any equipment build with functional and physical characteristics similar to the system analyzed by the model. As a result, the model is expected to be a useful tool for simulation, design, and optimization of photobioreactors.