Spatiotemporal modelling of dark fermentation in an acidogenic fixed-bed reactor: an experimental validation

The increasing demand for sustainable energy and value-added products has driven the development of technologies for biowaste valorization, fostering advancements in model development to enhance process understanding and optimization. Nevertheless, significant challenges remain in modelling heterogeneous systems, such as fixed-bed anaerobic fermenters, particularly due to their inherent complexity and the associated numerical difficulties. This study presents a spatiotemporal model describing the heterogeneous dark fermentation of glucose, a monosaccharide typically found in high concentrations in sugar-rich wastewaters, in an anaerobic fixed-bed reactor divided into three zones: influent, bed, and effluent. Using partial differential equations (PDE) solved via the Method of Lines, the model effectively captured glucose degradation (RMSE = 0.332) and the production of key metabolites - volatile fatty acids, lactic acid, ethanol, and hydrogen - both throughout the operational time and along the reactor length (Overall RMSE = 0.207). The results confirmed the heterogeneous distribution of biomass attachment within the reactor, with higher concentrations at the base of the reactor. This work highlights the importance of explicitly accounting for heterogeneity when modelling certain types of high-rate fermenters, a physically meaningful spatiotemporal framework capable of representing spatial transport–reaction interactions that cannot be captured by conventional homogeneous models. Moreover, the application of mathematical techniques to solve heterogeneous models enhances their potential for industrial application and supports future scalability.