To describe anaerobic fermentation, many mathematical models have been suggested. A commonly accepted hypothesis in microbial growth is the speed of cellular reproduction, which is proportional to the concentration of cells at that instant. The constant of proportionality between the speed of growth and cell concentration is called cell growth rate, μ. In many occasions, the cell growth rate is considered constant. This leads to conclude that the concentration of cells versus time presents an exponential function. The consideration of this equation provides a good adjustment in the beginning of central phase of the anaerobic fermentation process. However, it moves away from the measurements when there is a limited reproduction due to lack of nutrients and competition between the cells in the environment. This produces a sigmoidal variation in concentration. To find a suitable fit function for all phases of the process, Gompertz proposes a model that considers the cell growth rate as variable. In this chapter, the Gompertz model, kinetic models, transference, and cone models are evaluated. Different adaptations to fit the variables to the obtained values in the experiments have been reviewed.

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Bioethanol production from sugarcane represents an opportunity for urban-agricultural development in small communities of Ecuador. Despite the fact that the industry for bioethanol production from sugarcane in Brazil is fully developed, it is still considered expensive as a small rural business. In order to be able to reduce the costs of monitoring the production process, and avoid the application of expensive sensors, the aim of this research was modeling the kinetics of production of bioethanol based on direct measurements of Brix grades, instead of the concentration of alcohol, during the process of cane juice bio-fermentation with Saccharomyces cerevisiae. This avoids the application of expensive sensors that increase the investment costs. Fermentation experiments with three concentrations of yeast and two temperatures were carried out in a laboratory reactor. In each case Brix grades, amount of ethanol and alcoholic degree were measured. A mathematical model to predict the quality and production of bioethanol was developed from Brix grade measurements, obtaining an adjusted coefficient of determination of 0.97. The model was validated in a pilot plant.

In this work, a new approach to evaluating the amount of residual biomass obtained from orange trees based on normalization of variables is proposed for Bolivar province, Ecuador. So far, several models to quantify the amount of residues obtained from pruning have been proposed from dendrometric and cultivation variables, such as height, crown diameter, stem diameter, area per plant, yield, and age. However, the high dispersion of their values, caused by uncontrolled conditions, gave models with a low-medium coeffi cient of determination. The aim of this work has been to develop several models in order to predict wet available biomass using dimensionless dendrometric parameters from height, diameter and height of the crown, and the stem height. They improved the coeffi cients of determination to 0.94 for the global mathematical model. The drying process of pruned materials has also been analyzed. Residual biomass with 50% initial moisture content was dried outdoors on cement and agricultural soil until it reached constant moisture content. Models used to describe the drying process of agricultural products were employed to fi t the observed data of the drying process of orange tree chips. Among the tested models, the Midili and Page models were those that best fi tted the observed data in the drying process. The information offered by these equations is of vital importance because they help estimate the amount of biomass that is generated in a given area, and the implementation geographic information system (GIS) maps. In addition, logistic algorithms can be applied.

This study aims to evaluate the effects of the co‐digestion of agricultural residues with manure from camelids from the Andean zone. Different combinations of llama manure (LM) and vicuñas (VM) were made with amaranth (AS), quinoa (QS), and wheat (WS) residues. They were fermented using sewage sludge as inoculum. The co‐digestion was evaluated under mesophilic conditions for 40 days. The ratios of volatile substances of substrate / co‐substrate evaluated were 0:100; 25:75; 50:50, 75:25, and 100:0. Two substrate / inoculum ratios (SIR 1:1 and SIR1:2) were also evaluated. The results indicate that the maximum methane accumulation rate is obtained in SIR 1:1 for a VM‐AS ratio (25:75) with 540 mL/g volatile solid (VS). In general, the results did not increase with the increase in inoculum; rather, the tendency to improve methane yield is associated with an increase in the amount of agricultural residues, mainly AS. Regarding the kinetic modeling, the transfer model is the one that best adjusted the predicted values to those observed with an r2 between 0.991 and 0.999, and an RMSE value between 2.06 and 13.62 mL/g (volatile solid) VS. Finally, all the trials presented synergistic effects in their co‐digestion except the digesters formed by LM‐AS, LM‐QS and LM‐WS of SIR 1:2. These presented antagonistic effects in which the addition of the co‐substrate generated competition with the substrates, reducing methane production. © 2021 Society of Chemical Industry and John Wiley & Sons, Ltd