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This study critically analyses filtration process modeling in membrane bioreactor (MBR) technology. More specifically, the variety of approaches and assumptions considered within a curated selection of resistance-in-series (RIS) filtration models found in the literature is critically assessed. Aimed to move towards good filtration process modeling practices, the basis for establishing a unified framework rooted in the fundamentals of membrane fouling is defined in this work, considering fouling classifications, process dynamics, and underlying processes used by different authors for elucidating membrane fouling phenomena. Systematically analyzing these factors should be considered as a basic step for efficiently comparing the performance of different models. This involves a detailed examination of the processes applied within each model and their interplay with the involved resistances and fouling types. A lack of homogeneity in RIS-based filtration modeling has been observed. To address this, basic guidelines towards good modeling practices are proposed aimed at balancing model accuracy and complexity. Specifically, seven model processes, six resistances, and three subgroups for types of fouling, further divided into four or five categories are proposed to guide the selection of processes and state variables in the model structure. Hence, this study facilitates the understanding of different approaches to be used during the modeling exercise of membrane filtration processes within the MBR field, not only to enhance the comprehensibility of available filtration models, but also to help the comparison, implementation, and adaptation of available models and the comprehensive development of new ones., Competing Interests: 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., (Copyright © 2024 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

A mathematical correlation between biomass kinetic and membrane fouling can improve the understanding and spread of Membrane Bioreactor (MBR) technology, especially in solving the membrane fouling issues. On this behalf, this paper, produced by the International Water Association (IWA) Task Group on Membrane modelling and control, reviews the current state-of-the-art regarding the modelling of kinetic processes of biomass, focusing on modelling production and utilization of soluble microbial products (SMP) and extracellular polymeric substances (EPS). The key findings of this work show that the new conceptual approaches focus on the role of different bacterial groups in the formation and degradation of SMP/EPS. Even though several studies have been published regarding SMP modelling, there still needs to be more information due to the highly complicated SMP nature to facilitate the accurate modelling of membrane fouling. The EPS group has seldom been addressed in the literature, probably due to the knowledge deficiency concerning the triggers for production and degradation pathways in MBR systems, which require further efforts. Finally, the successful model applications showed that proper estimation of SMP and EPS by modelling approaches could optimise membrane fouling, which can influence the MBR energy consumption, operating costs, and greenhouse gas emissions., Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Giorgio Mannina reports was provided by University of Palermo. Giorgio Mannina reports a relationship with University of Palermo that includes: employment., (Copyright © 2023 Elsevier Ltd. All rights reserved.)