Modelagem matemática de um sistema de biorreatores

Abstract

Sewage treatment is a subject of public policy. This service, when available to the population, can prevent the transmission of diseases. The mathematical modeling of reactors has proven to be a technical resource that permits the estimation of parameters and that simulates system operations at a reduced cost in relation to the experimental models. The objective of this present work is to simulate the variations of organic matter concentration (BOD) in a system composed of two bioreactors coupled in a series (one anaerobic and the other a wetlands type) as a matter of time. The problem was modeled considering both reactors as a complete mixture, through a system of first order ordinary differential equations, whose boundary conditions are the input and output loads. The reaction rate in both reactors was simulated as a constant function - as suggested by the literature - and variable, considering three types of functions: affine, exponential and logarithmic function. The parameters of the model were obtained by solving the inverse problem through the Network Search Method, based on experimental data available in the literature. The simulations showed that, in spite of the strong dispersion of experimental measures of the BOD caused by non-modeled factors (such as rainfall and temperature), the reaction rates expressed with the affine and logarithmic functions presented a BOD curve which was more compatible with the experimental data, than with the other functions that were tested.