Abstract
Most of kinetic models applied to microalgal wastewater treatment are focused on the specific contaminant removal (i.e. correlating a limiting substrate to microbial growth) or considering autotrophic characteristic that cannot be correlated to the mixotrophic/heterotrophic cultivation of these microorganisms, specially treating wastewater. However, to find an integrated kinetic approach using the simultaneous removal of organic carbon, nitrogen and phosphorus (main macronutrients) is difficult considering the different characteristics of the wastewaters, and the high number of kinetic constants associated with complex models. In this sense, this study designed a procedure to apply the kinetic modelling of microalgal growth using both the Monod model and the Silva and Cerqueira model (multiple substrates), estimating the characteristic kinetic constants and simulating the bioprocess by implementation on Python language and using Particle Swarm Optimisation (PSO). For contaminants removal, the n-th order equation proved to be more suitable, with an intermediate order between 1st and 2nd order (i.e. 1 < n < 2) and with a kinetic constant 0 < k < 0.2, obtaining an error between 15 and 28%. Using the Monod model, the algorithm was able to determine μmax and Ks, which were shown in the intervals: 0 < μmax < 4 day−1 and 0 < Ks < 50 mg L−1 with error of 15–25%. In the Silva and Cerqueira model, analysing the delimitation of m and p resulted in the following interval of convergence between 0 < p < 0.5 and 0 < m < 2, obtaining an error between 4 and 17% was obtained (significantly lower than for Monod) and using multiple substrates. The algorithm of the procedure is presented.
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The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request through a material transfer agreement.
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Acknowledgements
C.E.F.S would like to thank the National Council of Research and Technological Development of Brazil (CNPq) (Project numbers: 313195/2019-6, 440070/2019-8, 407274/2018-9 and 312996/2022-5) and Research Support Foundation of Alagoas (Project numbers: E:60030.0000002360/2022 and E:60030.0000000318/2023).
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Lopes, E.W.R., dos Santos Carneiro, W., De Farias Silva, C.E. et al. A procedure to implement kinetic modelling of wastewater treatment by microalgae considering multiple contaminant removal. Energ. Ecol. Environ. 8, 556–569 (2023). https://doi.org/10.1007/s40974-023-00279-4
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DOI: https://doi.org/10.1007/s40974-023-00279-4