A critical review of biomass kinetics and membrane filtration models for membrane bioreactor systems

Performance modeling of wastewater treatment systems has now become an attractive area of investigation for the design, analysis, and optimization of operations. Membrane bioreactor (MBR) is a complex system, composed of different processes such as biological process as well as membrane filtration process. Various models have been developed over the years to individually describe each of these processes. Activated sludge model no. 1 (ASM1) was introduced in 1987, primarily for the design and operation of the biological wastewater treatment processes for ammonia and organic matter removal. In 1995, ASM2 was proposed capturing the removal of phosphorus from wastewater. Finally in 1999, ASM3 was developed as a more accurate model to correct the deficiencies associated with ASM1. ASMs have been widely employed during the last decade to simulate the bioprocess/biomass kinetics in the MBR systems. To incorporate the membrane fouling phenomenon in the modeling approach as well as to better understand the individual and collective foulants, the ASM approaches were modified in 1989 by introducing a main foulant contributing to the membrane fouling phenomenon, the so-called soluble microbial products (SMP) concept. This represents the inception of the hybrid models. Mechanistic modeling of the MBR filtration process is mainly performed using resistance-in-series (RIS) model as one of the extensively used approaches with different subdivisions of total resistance corresponding to the fouling mechanisms. To further improve the knowledge about the system behavior, a combination of the hybrid models with fouling models (mostly RIS) known as integrated models was developed in 2002. Numerous studies have been subsequently devoted to utilizing the integrated models as a best-case scenario for forecasting the MBR process behavior. Moreover in recent years, connectionist tools such as artificial intelligence (AI) and machine learning (ML) have attracted significant attention as reliable modeling methods to predict complex processes associated with the membrane separation by providing linear and nonlinear relationships between the variables. In this paper, we provide a comprehensive review of the literature associated with biomass kinetics developments as well as membrane filtration modeling. A wide range of the models proposed for system optimization, from empirical/system identification to mechanistic/analytical mathematical models are reviewed in this paper. The challenges