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 CO ₂ 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.

Direct steam generation (DSG) is a promising technology for introducing solar energy into industrial applications, yet it still faces significant challenges. This work analyzes two critical issues associated with DSG: temperature gradients on the receiver tube wall caused by direct and concentrated radiation and flow instability resulting from the phase transition of the working fluid from liquid–vapor to vapor. These phenomena can reduce the mechanical strength of the receiver tube and lead to sudden pressure increases, deformation, or rupture, which hinder the implementation of DSG in solar thermal plants. To address these challenges, the behavior of a receiver tube composed of copper on the inside and an Al₂O₃ envelope is studied. A 50 MWe hybrid solar thermal plant is proposed for Mulegé, Baja California Sur, Mexico, including a solar field designed to analyze the production of superheated steam during peak solar irradiance hours. The effect of the Cu-Al₂O₃ ratio on the receiver tube is evaluated, with Al₂O₃ serving as a thermal regulator to reduce temperature gradients and mitigate flow instability. This combination of materials improves the receiver tube’s performance, ensuring mechanical stability and enhancing the viability of DSG systems. By reducing temperature gradients and flow instability, DSG-based plants can double thermal efficiency and significantly lower environmental impact by eliminating the need for thermal oils, which require frequent replacement. These findings demonstrate the potential for hybrid solar thermal plants to provide sustainable and efficient solutions for industrial energy needs.

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.

The aim of this work was to use macroscopic equations that model biogas production through co-digestion of cattle waste in a laboratory-scale batch tank bioreactor. When modeling the biogas production, the coefficients, parameters and the description of the generation kinetics are obtained. The model of the volume averaging has shown to be adequate for the representation and scaling of the information in the microscale and it is taken to the macroscale involving effective transport coefficients. This model is used to determine the values of macroscopic diffusion coefficient and the associated coefficients with reaction kinetics of co-digestion cattle waste, as well as the concentration of chemical species involved in biogas production. The Laplace domain model is used to determine the concentration of chemical species, as well as their characteristic generation time in the process. The modified Gompertz equation is used to determine the maximum specific potential and rate of methane. All models show an adequate representation of the experimental data of biogas production for the different experiments. The dependency of one model on another is clearly shown, giving rise to future applications of the models on a pilot or industrial scale by knowing the associated coefficients given by the mathematical models.