**2. The IWA models**

Mathematical modeling of activated sludge systems is an optimal technique for WWTP design and operation, human resource training, and research [10]. Therefore, the International Waster Association (IWA) has developed activated sludge models together with benchmark models for assessing control strategies of the AS process even for a plant-wide context including a primary treatment and sludge digestion [5, 6]. Moreover, due to the advantages to treat and reuse wastewater, membrane bioreactor (MBR) models have gained attention [17]. Therefore, the activated sludge models (ASM), benchmark simulation models (BSM) together with those for membrane bioreactor modeling are briefly discussed below.

### **2.1 Activated sludge models (ASM)**

The activated sludge models were introduced in the 1980s with the core model known as ASM1 [10]. Its main purpose was to assess the activated sludge process utilizing simple relationships to mimic the biokinetics occurring within the bioreactor. It consists of a set of biokinetic rates for biological WW treatment based on Monod-like equations (Eq. (1)) for particulate and soluble compounds or state variables (denoted by *S* and *X*, respectively) [5].

$$\frac{\text{S}}{\text{K} \text{s} + \text{S}} \text{ or } \frac{\text{X}}{\text{K} \text{x} + \text{X}} \tag{1}$$

Since the introduction of the ASM1, many attempts were made to improve the model's capability for reproducing biological nutrient removal. **Table 1** presents a brief overview of the most applied ASM developed by the IWA. Mind other models have been developed, however, only the most applied and those strictly related to biological wastewater treatment were considered. Notice the models have different scopes together with a variation in the number of model parameters. Moreover, it is important to notice the similarity in the overall process among the ASM1 and ASM3 as well as for ASM2d and ASM3 BioP. However, these differ from the state variables to be modeled and their parameters.

For example, the ASM3 was developed to deal with the ASM1 limitations concerning the kinetics for nitrogen and alkalinity of heterotrophic microorganisms [5]. While the ASM2d consists of a modified version of the ASM2 (not included in **Table 1**), as ASM2 does not consider denitrification due to phosphorus accumulating organisms (PAOs), together with the glycogen storage as carbon storage for PAOs [5]. Finally, the ASM3 BioP adds biological phosphorus removal to the ASM3. It differs from ASM2d as it does not include P chemical precipitation (easily implemented), the use of endogenous respiration rates, lower rates for anoxic rates


*C, carbon removal; N, nitrogen removal; P, phosphorus removal.*

*a Fermentable COD fractions state variables.*

### **Table 1.**

*Overview of the activated sludge models.*

(compared to aerobic ones), as well as neglecting fermentation [18], so, influent fractionation becomes simpler.

As the activated sludge models are core models, i.e., this can be subjected to refinements to meet modelers' needs, usually for representing the AS process more accurately. For example, to surpass the limitation of the ASM3 of modeling nitrification in a single-step process (SNH4 ! SNO3), Iacopozzi et al. [19] developed a twostep nitrification process (SNH4 ! SNO2 ! SNO3). Hence, they were able to represent the separation of autotrophic biomass into ammonia and nitrite oxidizers within their model. Other modifications have been made for portraying microbial processes in detail [20–22], including modeling the AS process in an MBR scheme, discussed later.

However, the ASMs (including refinements) were developed for assessing the efficiency of the bioreactor. Consequently, the need for a modeling framework that couples the bioreactor, the secondary clarifier, as well as sludge treatment together with key performance indicators, among other features, result in the development of the benchmarking simulation models.
