Review of Mathematical Models for the Anaerobic Digestion Process

Abstract

To describe anaerobic fermentation, many mathematical models have been suggested. A commonly accepted hypothesis in microbial growth is the speed of cellular reproduction, which is proportional to the concentration of cells at that instant. The constant of proportionality between the speed of growth and cell concentration is called cell growth rate, μ . In many occasions, the cell growth rate is considered constant. This leads to conclude that the concentration of cells versus time presents an exponential function. The consideration of this equation provides a good adjustment in the beginning of central phase of the anaerobic fermentation process. However, it moves away from the measurements when there is a limited reproduction due to lack of nutrients and competition between the cells in the environment. This produces a sigmoidal variation in concentration. To find a suitable fit function for all phases of the process, Gompertz proposes a model that considers the cell growth rate as variable. In this chapter, the Gompertz model, kinetic models, transference, and cone models are evaluated. Different adaptations to fit the variables to the obtained values in the experiments have been reviewed.