Global sensitivity and uncertainty analysis of a microalgae model for wastewater treatment
Graphical abstract
Introduction
Microalgae-based wastewater treatment represents a promising biological system to treat different wastewater sources in a way that can transform conventional wastewater treatment plants (WWTPs) into water resource recovery facilities (WRRFs) (Seco et al., 2018). Photoautotrophic microalgae use light energy, inorganic carbon and nutrients (inorganic nitrogen and phosphorus) for growth. Solar energy and nutrients are harvested in form of microalgae biomass while inorganic carbon is biofixed. Microalgae-based wastewater treatment can reduce treatment costs, generate clean water and reduce the environmental impact of the process (Seco et al., 2018).
An in-depth knowledge of the processes involved in microalgae metabolism is required to better understand how to operate microalgae-based technologies, how to optimize processes associated, how to improve reactor design and how to select the best control strategies to enhance pollutant removal efficiency. Microalgae and traditional activated sludge systems are intrinsically complex, since both depend on environmental variables such as temperature, pH, substrate availability, etc. However, it should be noted that photoautotrophic microalgae metabolism is not only affected by the environmental factors that influence activated sludge but also by seasonal and daily fluctuations in light intensity (González-Camejo et al., 2018). The correct operation of microalgae-based wastewater treatments thus demands a robust, feasible and efficient tool to forecast the culture development and its compliance with increasingly stringent regulations. Mathematical models can help to study the main processes and variables that influence algal metabolism in different culture media, including municipal wastewater.
An array of mathematical models for predicting microalgae growth has been developed in the last ten years (Costache et al., 2013; Eze et al., 2018; Ndiaye et al., 2018; Ruiz et al., 2013; Solimeno et al., 2015, Solimeno et al., 2017; Wágner et al., 2016). This process cannot be considered a well-characterized system, since some model factors are uncertain and speciation-dependent. The ammonium semi-saturation constant has been reported to range from 0.1 to 31.5 g N m−3 (Aslan and Kapdan, 2006; Solimeno et al., 2017), and is a perfect example of the intrinsic variability and uncertainty of model factors, so that the application of these models requires a great number of assumptions regarding the simplification of biological processes and model factors. These assumptions are sources of uncertainty that could propagate through the model thus generating uncertainty in the model outputs. The resulting uncertainty in the model results could lead to misleading decisions during process design and/or optimization. Hence, performing a global sensitivity and uncertainty analysis (GSA and UA, respectively) would help to deal with these issues by analysing and understanding model performance. GSA involves identifying the most important model factors to be calibrated, while UA entails determining the model output uncertainty derived from uncertain model input factors (Rajabi et al., 2020). GSA and UA should be performed concurrently, as both are essential parts of the model development process in design optimization, reliability analysis, and data-worth analysis (Rajabi et al., 2020). To the best of the authors' knowledge, both GSA and UA have not been performed concurrently in mathematical models for wastewater treatment with microalgae. Therefore, no information is available on the microalgae models' most influential factors and the variability of the uncertainty of model output.
Although, the mechanistic microalgae model proposed by Viruela et al. (2021) was validated using 4 experimental periods, which combine key environmental and operational conditions characteristic of a microalgae-based wastewater treatment, the uncertainty of model parameters could lead to uncertainty propagations on modeling results, reducing its practical application. Thus, this study tends to address data gaps related to uncertainty on microalgae-based wastewater treatment models, based on Viruela et al. (2021), by performing a GSA and UA. The Morris screening method was applied as GSA method to identify the most influential factors of the model, which were calibrated through offline (obtained from experimental assays) and online (variation of model parameters to match model predictions to experimental results) methodologies. For further enhancing the model performance, the calibrated values for the influential factors were dynamically optimized using online data. Model uncertainty was analyzed and quantified from Monte Carlo simulations and three uncertainty coefficients: the p-factor, the r-factor and the Average Relative Interval Length (ARIL). A calibration protocol was also recommended to reduce model uncertainty by means of prioritizing different calibration methodologies.
Hence, this work could be seen as the first study to simultaneously perform GSA and UA in the field of microalgae-based wastewater treatment modeling, while proposing a set of input factors to be calibrated by a given protocol.
Section snippets
The mathematical model
The model used in this work (Viruela et al., 2021) simulated microalgae growth from different phosphorus and nitrogen sources. Regarding phosphorus source, the microalgae had two different metabolic pathways: under phosphorus-replete conditions, microalgae uptake dissolved extracellular phosphate (SPO4) to support their vital metabolic functions and stored part of the excess in form of intracellular polyphosphate (XPP-ALG) while under phosphorus-starved conditions they consumed their XPP-ALG
SNHX output
SNHX concentration decreases due to microalgae uptake for growth and SNH3 stripping. Conversely, SNHX concentration increases due to microalgae lysis and endogenous respiration. Processes 1 (XALG growth on SNHX and SPO4), 3 (XALG growth on SNHX and XPP-ALG), 6 (XALG endogenous respiration), 7 (XALG lysis) and 11 (S[NH3] stripping) in Table 1 therefore affect SNHX concentration.
Fig. 1 gives the sensitivity measurements (μ* and σ) calculated from each input factor on the SNHX output for the 4
Conclusions
This paper presents a GSA, an offline/online calibration, a dynamic optimization, and a UA of a previously proposed and validated microalgae model. Eleven out of 34 influential factor were identified from the GSA. The four factors with the most important overall effect on the three outputs evaluated (SNHX, SPO4 and XALG) were μALG, qXPP, TMAX and IOPT. SNHX and XALG model outputs were influenced by kinetic input factors related to microalgae growth, while SPO4 model output was affected by X
CRediT authorship contribution statement
Stéphanie Aparicio: Analysis, Data curation, Writing-original draft; Rebecca Serna-García: Data curation, Revision and Supervision; Aurora Seco: Revision, Supervision and Funding acquisition; José Ferrer: Revision, Supervision and Funding acquisition; Luis Borrás-Falomir: Revision and Supervision; Ángel Robles: Data curation, Revision and Supervision and Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO, Projects CTM2014-54980-C2-1-R, CTM2014-54980-C2-2-R, CTM2017-86751-C2-1-R and CTM2017-86751-C2-2-R) jointly with the European Regional Development Fund (ERDF), both of which are gratefully acknowledged. It was also supported by the Spanish Ministry of Education, Culture and Sport via a pre-doctoral FPU fellowship to author Stéphanie Aparicio (FPU/15/02595).
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