Derivation of an Upscaled Model for Mass Transfer and Reaction for Non-Food Starch Conversion to Bioethanol

Abstract

Abstract In this paper, we derive mathematical models for mass transfer and reaction taking place in first-generation bioreactors to convert non-food starch into bioethanol. Given the hierarchical nature of the system, we identified three scale levels ranging from inside bagasse fibers (the pore scale) where the reaction occurs, up to the bioreactor itself (macroscopic scale) where the various products obtained from this reaction are monitored. We derive a macroscopic model at the reactor scale by systematically upscaling the relevant information from the pore scale using the method of volume averaging. A salient feature of the model is that the effective medium coefficients involved are predicted by solving ancillary closure problems in representative unit cells of the different levels of scale. The predictions of the model in terms of CO2 production as well as cellular growth were validated with a close agreement with available experimental data. This work enhances our understanding of the relevance of transport phenomena taking place at the different scales in a bioreactor and may become an aid in design and operation applications of bioethanol production systems.