In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.
Resumo: Neste trabalho foi realizado um estudo comparativo entre as metodologias de otimização Gradiente Reduzido Generalizado (GRG) e Algoritmo Genético (AG) para a otimização de processos com múltiplas respostas. Para estimar os parâmetros que minimizam a função objetivo foram utilizadas respostas geradas por planejamento de experimentos de forma aglutinada, as quais foram incorporadas à função objetivo. Os estudos de caso utilizados foram baseados em trabalhos selecionados na literatura e, para cada experimento selecionado, foi realizada a otimização dos valores dos parâmetros do processo utilizando as duas metodologias, o GRG, por meio de uma planilha do Microsoft Excel e o AG utilizando o software Scilab. Foram realizadas 10 replicações e calculada a média dos resultados obtidos. A comparação entre os métodos foi realizada com base em medidas de desempenho, por meio da distância média percentual. O AG apresentou melhores resultados em comparação com o GRG.
Palavras-chave:Otimização. Múltiplas Respostas. Algoritmo Genético. GRG.
Abstract:In this paper we present a comparative study between the Generalized Reduced Gradient (GRG) and Genetic Algorithm (GA) methods to optimize multiple-response processes. Results from experiment design were used to compose the objective function to be minimized. The case studies in this work were selected from literature. A Microsoft Excel spreadsheet was used for parameters optimization using GRG, and the Scilab software was used to GA. Ten replicates were performed and the mean of the results was obtained. To assess the methods was used performance measures based on the mean percentage error. From the performance measures used, the AG showed better results compared to the GRG, indicating that the AG can generate better responses than GRG.
Lasiodiplodan, a (1→6)-β-d-glucan, is an exopolysaccharide with high commercial value and many applications in food, pharmaceuticals, and cosmetics. Current industrial production of β-glucans from crops is mostly by chemical routes generating hazardous and toxic waste. Therefore, alternative sustainable and eco-friendly pathways are highly desirable. Here, we have studied the lasiodiplodan production from sugarcane bagasse (SCB), a major lignocellulosic agricultural residue, by Lasiodiplodia theobromae CCT 3966. Lasiodiplodan accumulated on SCB hydrolysate (carbon source) supplemented with soybean bran or rice bran (nitrogen source) was 16.2 [6.8 × 103 Da] and 22.0 [7.6 × 103 Da] g/L, respectively. Lasiodiplodan showed high purity, low solubility, pseudoplastic behavior and was composed of glucose units. Moreover, the exopolysaccharides were substantially amorphous with moderate thermal stability and similar degradation temperatures. To our knowledge, this is the first report on the highest production of SCB-based lasiodiplodan to date. L. theobromae, as a microbial cell factory, demonstrated the commercial potential for the sustainable production of lasiodiplodan from renewable biomass feedstock.
The most recent rise in demand for bioethanol, due mainly to economic and environmental issues, has required highly productive and efficient processes. In this sense, mathematical models play an important role in the design, optimization, and control of bioreactors for ethanol production. Such bioreactors are generally modeled by a set of first-order ordinary differential equations, which are derived from mass and energy balances over bioreactors. Complementary equations have also been included to describe fermentation kinetics, based on Monod equation with additional terms accounting for inhibition effects linked to the substrate, products, and biomass. In this chapter, a reasonable number of unstructured kinetic models of 1-G ethanol fermentations have been compiled and reviewed. Segregated models, as regards the physiological state of the biomass (cell viability), have also been reviewed, and it was found that some of the analyzed kinetic models are also applied to the modeling of second-generation ethanol production processes.
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