Modelagem de ordem fracionária aplicada a processos de separação

Abstract

Process modeling is a procedure to represent real problems through equations and among the ways of mathematically describing there is the fractional calculus, that comes up as a suggestion to replace integer­order differential with fractional order. The approach used in this work was the application of fractional order differential equations in the modeling of separation processes present in the Chemical Engineering area. Caputo’s derivative was used to solve the proposed equations and, the processes analyzed were the drying of beans, corn and wheat for different temperatures and initial moisture content, adsorption of glycerol for biodiesel purification at different temperatures and the solid­liquid extraction of antioxidant compounds from corn for different solvent proportions. For both processes, the fractional order model was compared with those that are commonly used. In drying process, the fractional order model was compared with Page and first order models.In drying of beans all the conditions analyzed indicated an adequate fit for the fractional order model; for corn, the data with high content of moisture did not respond properly and for wheat there were also divergences. After the analysis of variance, the generalization of the kinetic parameter of the fractional order model, k, was performed using a mean fractional order, exclusive for each grain. For beans, the equation found was first degree with a method efficiency of 0.9769; for corn the equation obtained was a second degree with method efficiency of 0.9906 and for wheat, were first degree equations, one for wheat without initial humidification and with humidification with method efficiencies of 0.9765 and 0.9418, respectively. For the adsorption of glycerol, the fractional order model was compared with the pseudofirst, pseudo­second and first order models; the fractional order model exhibited an adequate fit with method efficiencies of 0.9603 and 0.9433 for temperatures of 45°C and 60°C, respectively, while the performance of traditional models depends on the mechanisms that control the process. Finally, the extraction of antioxidants compounds was analyzed and compared with the first order and So e MacDonald models; the derivative order values for the fractional order model were close to 1, therefore, the behavior is similar to the first order model and there are indications that diffusion occurs as described by Fick’s law of diffusion.