Cost-performance trade-off analysis of physicochemical phosphorus removal systems for wastewater treatment: A bi-objective optimization approach

Florencia Caro; Diego Rossit; Claudia Santiviago; Jimena Ferreira; Sergio Nesmachnow; Florencia Caro; Diego Rossit; Claudia Santiviago; Jimena Ferreira; Sergio Nesmachnow

doi:10.3934/mbe.2026006

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 1: 124-147. doi: 10.3934/mbe.2026006

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Cost-performance trade-off analysis of physicochemical phosphorus removal systems for wastewater treatment: A bi-objective optimization approach

1.
Biotechnological Processes for the Environment Group, Faculty of Engineering, Universidad de la República, Montevideo, Uruguay, 11300
2.
Department of Engineering, INMABB, Universidad Nacional del Sur (UNS)-CONICET, Bahía Blanca, Argentina, 8000
3.
Chemical & Process Systems Engineering Group, Faculty of Engineering, Universidad de la República, Montevideo, Uruguay, 11300
4.
Heterogeneous Computing Laboratory, Faculty of Engineering, Universidad de la República, Montevideo, Uruguay, 11300
5.
Universidad de la República, Uruguay

Received: 29 July 2025 Revised: 22 October 2025 Accepted: 07 November 2025 Published: 02 December 2025

In an increasingly competitive world, industries face growing pressure to improve efficiency while meeting strict environmental and social standards. Wastewater treatment plants (WWTPs) play a key role in reducing the environmental impact of water use across industrial, agricultural, and domestic activities. This study presents a bi-objective optimization framework to support chemical dosing decisions in physicochemical phosphorus removal (PPR) systems. Using an edible-oil WWTP as a case study, two common metal salts (aluminum sulfate and ferric chloride) are compared, considering operational cost and phosphorus removal efficiency as conflicting objectives. Polynomial surrogate models enabled the integration of BioWin PPR models into the optimization problem, and the weighted sum and $ \varepsilon $-constraint methods were used to estimate the Pareto fronts, yielding complementary solutions. The proposed framework provides a practical decision-support tool for WWTPs by revealing cost–performance trade-offs. Results show that costs escalate disproportionately: reducing effluent P from 3.0 to 1.0 mg−P/L increased costs by 114% with aluminum sulfate and 355% with ferric chloride. The framework is adaptable to different PPR systems and influent conditions.
- Bi-objective optimization,
- physicochemical phosphorus removal,
- chemical costs,
- chemical dosing strategies,
- wastewater treatment,
- Industry 5.0
Citation: Florencia Caro, Diego Rossit, Claudia Santiviago, Jimena Ferreira, Sergio Nesmachnow. Cost-performance trade-off analysis of physicochemical phosphorus removal systems for wastewater treatment: A bi-objective optimization approach[J]. Mathematical Biosciences and Engineering, 2026, 23(1): 124-147. doi: 10.3934/mbe.2026006

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Abstract

In an increasingly competitive world, industries face growing pressure to improve efficiency while meeting strict environmental and social standards. Wastewater treatment plants (WWTPs) play a key role in reducing the environmental impact of water use across industrial, agricultural, and domestic activities. This study presents a bi-objective optimization framework to support chemical dosing decisions in physicochemical phosphorus removal (PPR) systems. Using an edible-oil WWTP as a case study, two common metal salts (aluminum sulfate and ferric chloride) are compared, considering operational cost and phosphorus removal efficiency as conflicting objectives. Polynomial surrogate models enabled the integration of BioWin PPR models into the optimization problem, and the weighted sum and $ \varepsilon $-constraint methods were used to estimate the Pareto fronts, yielding complementary solutions. The proposed framework provides a practical decision-support tool for WWTPs by revealing cost–performance trade-offs. Results show that costs escalate disproportionately: reducing effluent P from 3.0 to 1.0 mg−P/L increased costs by 114% with aluminum sulfate and 355% with ferric chloride. The framework is adaptable to different PPR systems and influent conditions.

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