No 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.

Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo intemperizados en suelos y sedimentos (Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil and sediments)

This work analysed the hydraulic behaviour and treatment efficiency of an upflow baffled septic tank (UBST) through tracer tests and mathematical modelling using the axial dispersion and the tank‐in‐series (TIS) models. The tracer tests were performed under different HRTs (12, 18 and 24 h) and configurations (UBST, UBST with sludge and UBST with sludge and zeolite filter). UBST followed a non‐ideal flow, and configuration modifications, rather than HRT, altered its hydraulic behaviour. Mathematical modelling indicated that the TIS model calculated with mean squared error (φ) described adequately UBST hydraulic behaviour (R2 = 0.9833). Additionally, UBST is recommended to operate under 24 h HRT to reach satisfactory hydraulic and pollutant removal efficiencies. At this HRT, total COD and ammonium removals were 75.1% and 49.3%, respectively, which were better than those obtained without the zeolite (71.2% and 1.8%, respectively). However, it quickly saturated, so it is necessary to deepen the research on this topic.

Down-flow fluidization is an attractive unit operation because it allows having a smooth circulation of the fluid and the solid support material as well as an uninterrupted and controlled operation of the fluid. In addition, since the solid support material is less dense than the fluid, the pump energy consumption required for bed expansion is smaller in comparison with upward fluidization. Momentum transport in fluidized beds is usually modeled by macroscopic models, which are expressed in terms of effective-medium coefficients, by making analogies with transport in porous media. In practice, it is desirable to derive these models and to predict the involved coefficients in a reliable manner. For this reason, in this work we derive a macroscopic model for the hydrodynamics of down-flow fluidization, using the method of volume averaging obtaining a model with the form of Darcy’s law with a correction in the relative velocity of the fluid to the solid. A salient feature of the model is that it allows predicting the apparent permeability coefficient in different geometries, and under different transport conditions. Also, the average model obtained can be used for both types of fluidization, because it is not restricted by the flow direction.