Modelling of biomethane production from agro-industrial wastewaters with constant biomass: analysis of Gompertz equation

Abstract

Gompertz equation, particularly the modified form is widely used to describe growth and product formation data for various types of dynamical biological systems. In biogas production, it becomes a fashion to use it as an empirical representation of biogas accumulation data although its physical meaning is sometimes obscured. This work outlined the use of Gompertz model and its related extensions in more systematic and meaningful manners. Firstly, these time-derivative rate equations were reformulated using unstructured reasoning which considered the effects of growth or non-growth associated product formation, the net rate of biomass accumulation, and two forms of time-rate derivatives: Schnute postulate and power law extension. Secondly, the solutions from each approach were analysed and discussed against a few represented biogas-time data sets available from our experiments and the literature. Then, the corresponding solutions were used to explain a set of accumulated biogas data obtained from anaerobic digesting experiments and the literature. The corresponding solutions were used to explain a set of accumulated biogas data obtained from anaerobic digesting experiments where the biomass density was essentially constant during each experimental batches. Finally, we attempted to draw relations between time-derivative typed models (Gompertz model and its extensions) with substrate-limiting typed models (Monod and Grue n-order models) and establish criteria to justify the validity of these models in specific cases. The results in our analysis indicated that much more insightful mechanistic understanding of anaerobic digestion could be achieved by combined and systematic analysis of these experimental data using the best model from an extended Gompertz model with the best one from substrate limiting type.