Development of Mass-Conserving Atomistic Mathematical Model for Batch Anaerobic Digestion: Framework and Limitations

A variety of mathematical models have been developed to simulate the biochemical and physico-chemical aspects of the anaerobic digestion (AD) process to treat organic wastes and generate biogas. However, all these models, including the most widely accepted and implemented Anaerobic Digestion Model No.1, remain incapable of adequately representing the material balance of AD and are therefore inherently incapable of material conservation. The absence of robust mass conservation constrains reliable estimates of any kinetic parameters being estimated by regression of empirical data. To address this issue, the present work involved the development of a “framework” for a mass-conserving atomistic mathematical model which is capable of mass conservation, with a relative error in the range of machine precision value and an atom balance with a relative error of ±0.02% whilst obeying the Henry’s law and electroneutrality principle. Implementing the model in an Excel spreadsheet, the study calibrated the model using the empirical data derived from batch studies. Although the model shows high fidelity as assessed via inspection, considering several constraints including the drawbacks of the model and implementation platform, the study also provides a non-exhaustive list of limitations and further scope for development.