Utilização de linguagem Python para modelagem e simulação do Modelo de Silva e Cerqueira no tratamento de efluentes por microalgas

Abstract

The excessive presence of nutrients such as nitrogen and phosphorus in water bodies is a current target of environmental concern, using microalgae to remove these nutrients appears as a promising alternative to wastewater treatment. The application of computational tools allows the development of algorithms that evaluate the behaviour and optimize the effectiveness of this removal through process modelling and simulation. The present study sought to determine the kinetic modelling of microalgal growth through the classic Monod model and the Silva and Cerqueira model, solving the characteristic kinetic constants and allowing the bioprocesses modelling and simulation by microalgae. Literature data were used for two studies, in the first one the removal of nutrients (contaminants) by Chlorella sp. for effluent from a combined anaerobic digestion (CAD) and an anaerobic digestion effluent from a primary settling tank (PS). In the second study, the removal of nutrients from an urban effluent was evaluated by a mix of microalgae (Chlorella vulgaris, Scenedesmus obliquus and Chlamydomonas reinhardtii). The adopted algorithm proved to be adequate in both studies. To solve the proposed problem, the PSO (Particle Swarm Optimization) algorithm was implemented in Spyder software (an open-source integrated development environment for programming in Python), and the PYSWARMS research toolkit was used for optimization (library). The model parameters were estimated by minimizing the sum of the calculated square errors and to evaluate the deviation of the simulated curve and of the experimental points, the concept of model predictive error (MPE – Model Predictive Error) was used (%). For the removal of contaminants, the equation of n-order proved to be more suitable with intermediate order between 1st and 2nd being used (ie, 1 < n < 2) and with constant 0 < k < 0.2, obtaining MPE between 15 -28% similar to that seen in literature. Using the Monod Model, the algorithm was able to determine μmax and Ks that were shown in the intervals: 0 < μmax < 4 day-1 and 0 < Ks < 50 mg/L with MPE between 15-28%. These constants could be applied in the Silva and Cerqueira model and were used to evaluate the delimitation of m and p, which are specific constants of this model. In fact, this model proved to be very sensitive to these constants, managing to define an interval for convergence: 0 < p < 0.5 and 0 < m < 2, obtaining for the same data tested in Monod an MPE between 4 -15% for Silva and Cerqueira (significantly lower). m and p showed a significant influence on the magnitude and curvature of the microalgal growth curve. The results showed that there was a good adjustment of microalgae growth and that it is possible to associate several contaminants with the cellular growth of microalgae.