## 1 Introduction  
In membrane biological reactors (MBRs), the conventional activated sludge (CAS) process is combined with filtration on micro- or ultra-porous membranes. Final clarifiers are then replaced by membrane filtration units. The main advantages of the MBR technology include [1; 2; 3; 4; 5]: (i) small footprint (due to both the elimination of sedimentation units and the increase of biomass concentration in the biological reactors); (ii) the complete separation of hydraulic retention time (HRT) and solid retention time (SRT); (iii) lower production of surplus activated sludge (if operated at higher SRT); (iv) the elimination of problems due to the poor sedimentation of activated sludge usually present in CAS; (v) high effluent quality, usually suitable for its reuse in agricultural and industrial sectors. However, the performance and operational costs of MBR systems can be affected by several aspects [6; 7; 8]: maximum and sustainable flows of permeates; adequate preliminary treatments (to remove coarse and abrasive materials); membrane fouling and cleaning strategies; aeration and energy consumption; possible need of wastewater equalization; need of skilled personnel. MBRs have been used for both municipal and industrial wastewater treatment [9]. Today, MBR technology has become an attractive solution also for medium-sized wastewater treatment plants (WWTPs) having capacity between 10,000 and 100,000 PE, mainly due to the significant membrane cost reduction in the last 15 years [4]. Alongside the \"conventional\" MBR process, new technological solutions are being developed. For instance, recent studies evaluated the coupling of membrane with the anaerobic biological reactors (AnMBRs) as an alternative solution to the conventional anaerobic digestion processes. This solution is presumed to reduce the overall energy demand and to facilitate the retention of microorganisms so as to operate with high biomass concentration. The advantage of this solution is related to the reduction in sludge volume and the increase in biogas production. However, the membrane fouling seems to be the main drawback of this process [10]. Another interesting application is the thermophilic aerobic membrane reactor (TAMR), which can be adopted for the treatment of high strength aqueous waste or industrial wastewater [11; 12] and the minimization of sludge production [13; 14]. According to [15], the MBR technology is being currently adopted in more than 5000 WWTPs around the world. The annual growth rate of MBR global market, from 2011 to 2018, is estimated around 15%. In particular, MBR plants are spreading a lot in China [16]. Currently, according to the MBR site [17], large MBR plants in the world (with capacity higher than 100,000 m\({}^{3}\)/day) are 63; more than 60% of these plants are present in China, 16% in USA and 11% in Europe. The spreading of MBR technology has been favoured by the stringent environmental regulations, the reduced use of land and the ease of automation that MBRs provide; moreover, the reduction in both membrane cost and energy consumption and the longer membrane lifespan favoured the growth. In the literature, topics of scientific interest have been deeply investigated. Relevant examples are (i) the studies to understand membrane fouling mechanisms [8]; (ii) the study of factors that could promote the removal of trace pollutants, such as presence of slow growing organisms, grater mass transfer efficiency due to presence of free-living bacteria and small flocs, adsorption and retention of hydrophobic compounds [18; 19; 20; 21]; (iii) the use of advanced modeling for process optimization, in order to simulate greenhouse gas emissions depending on the control strategy adopted [22]; (iv) the comparison among MBR and other technologies based on the evaluation of their impacts and benefits on human health [23; 24].