Optimization of the Wastewater Treatment Process Using Kinetic Equations for Nitrification Processes

Abstract

The primary objective of the present study is to evaluate the effect of conglomerate microorganisms on nitrification in activated sludge. The present study compares this process with activated-sludge technology to explore the variables that influence the complex biochemical processes taking place in bioreactors. The research under consideration involves monitoring the effectiveness of optimizing the wastewater treatment process using kinetic modeling for the nitrification and denitrification processes. The system is designed to simulate various operating scenarios and adjust process parameters in real time. The nitrification rate demonstrates a 99.03% performance, while the denitrification rate ranges from 19.08% to 91.01%. A substantial correlation has been demonstrated between this variable and the temperature of the treated wastewater. This provides the possibility of accurately assessing the ammonium oxidation potential. Furthermore, kinetic equations facilitate the estimation of parameters that are not typically measured, yet are essential for optimizing operational parameters (e.g., dissolved oxygen levels in the aeration tank, sludge dosage, and influent flow rate). This estimation is crucial for enhancing the effectiveness of the process and attaining the desired or anticipated outcomes. This validation underscores the efficacy of the technology, thereby establishing a foundational framework for subsequent research endeavors. These research efforts are directed towards providing decision-makers and stakeholders with actionable insights. The validation underscores the significance of optimized practices in the context of water resource protection. Moreover, it signifies a substantial advancement in the instrumentation of wastewater treatment plants.

1. Introduction

The present research endeavors to enhance the nitrification process in activated sludge comprising conglomerated microorganisms at the Alexandria Municipality wastewater treatment facility. A rigorous mathematical approach was employed to determine the nitrification efficiency of the activated-sludge system. This approach entailed the utilization of a kinetic model in conjunction with equilibrium mass balance, a methodical process that enabled the accurate calculation of relevant parameters [1,2]. The enhanced nitrification/denitrification biological treatment process for municipal wastewater is characterized by its autonomy from external infusion. It has been observed that this phenomenon is characterized by the presence of conglomerated biofilm flocs, which appear to serve the purpose of augmenting the concentration of microorganisms. This augmentation is thought to be facilitated by the introduction of an internal carbon source into the intracochlear space. The phenomenon under investigation is attributed to the lysis and hydrolysis of microbial cells within the bacterial cavity. With the support of the flocs, these microorganisms form an anaerobic environment [3,4].

Conventional activated-sludge methodologies have been predominantly employed for the treatment of urban and municipal wastewater until this point. It has become essential to optimize existing wastewater treatment plants with innovative technologies for nitrification/denitrification processes involving floc conglomerations of microorganisms in activated sludge to ensure the safety of human health and the environment. Improperly treated wastewater can cause water pollution, affecting ecosystems and resources [5,6,7]. By implementing solutions to optimize the treatment process, contamination of drinking water sources can be prevented, and water resources can be conserved [8,9]. Optimization of the wastewater treatment process also helps to reduce the negative impact on biodiversity, ensuring a healthier environment for all life forms. Thus, a sustainable approach to wastewater treatment not only protects the environment but also supports the development of a healthy ecosystem [10,11,12,13].

The developed/studied model has the capacity to serve as a substitute for knowledge of the hydraulic residence time, substrate concentration in the influent layer, thickness of the stationary liquid layer, minimum substrate concentration necessary for biofilm growth, and kinetic constants. This allows for calculation of substrate and biomass concentrations in the effluent layer [14,15,16]. Once the biomass concentration is estimated, other values such as the feed/biomass ratio and sludge mass loss can be derived. In addition, the proportion of active biofilm to total biomass can be determined, as well as the percentage of substrate used by any culture [17,18,19]. The main novelty of this research lies in the use of kinetic equations to facilitate the estimation of parameters that are not routinely measured but are essential for optimizing operational parameters (e.g., dissolved oxygen level, sludge dosage in aeration tanks, and influent flow rate). This estimation is crucial for increasing the efficiency of the nitrification/denitrification process and achieving the desired or anticipated results. The estimation of these parameters is performed in real time, based on a dynamic model that accounts for the behavior of microorganisms within conglomerated flocs. Unlike ASMs (activated-sludge models), which rely on fixed parameter sets and standardized assumptions, our model introduces an adaptive component that enables the optimization of biological processes according to operational conditions and environmental factors (e.g., temperature).

Moreover, our study highlights the specific role of conglomerated microbial flocs, which significantly contribute to the efficiency of nitrification and denitrification processes by generating an internal carbon source. This aspect is rarely addressed explicitly in traditional ASMs (activated-sludge models). The ASM1/2/3 models have provided a solid foundation for understanding biological processes in wastewater treatment plants, but they are limited by their static nature and reliance on simplifying assumptions. The model proposed in this study does not aim to replace the ASMs, but rather, to complement them with a dynamic, real-time applicable approach that integrates biological particularities observed in conglomerated microbial flocs, enables the optimization of operational parameters without direct measurements, and responds more effectively to the real variability in wastewater treatment systems.

2. Materials and Methods

2.1. Description of the Wastewater Treatment Plant Under Study and Monitored Parameters

Wastewater reaching the treatment plant through collectors is composed of both domestic wastewater and industrial water. In the case of separate sewage networks, it may also include rainwater, depending on the type of network. When there is a single system of collectors that transports all types of water generated by the population, it is called a combined sewage network [20,21,22].

Eliminating the negative effects on the environment is an important goal in wastewater treatment. One important tool for achieving this goal is wastewater analysis [23]. Wastewater treatment plants are usually located on the outskirts of populated centers. They are sets of installations whose main function is to reduce pollutants in domestic wastewater to acceptable limits for discharge into the aquatic environment [24,25]. The primary function of the municipal wastewater treatment plant is to reduce the physical, chemical, bacteriological, and biological characteristics of pollutants in wastewater, ensuring that they meet quality standards for discharge into the outfall.

The following conventional water quality parameters are analyzed and monitored in the wastewater treatment process: fecal coliform bacteria, total organic carbon (TOC), total nitrogen, chemical oxygen demand (COD), phosphorus, biochemical oxygen demand (BOD), and total dissolved solids (TDS). The degree of purification of each parameter depends on the purification technology used. Through the mechanical and biological purification stage, BOD is reduced by 90–95% and TDS by 90–95%, and fecal coliform bacteria are removed with high efficiency (92–99.9%), but removal of phosphorus is 10–20%, total nitrogen is 15–25%, and that of heavy metals is 24–82% [26,27].

Wastewater treatment processes are organized into distinct operational lines depending on the size of the pollutants to be treated. There are usually two main operational lines: the water line, which focuses on wastewater treatment, and the sludge line, which focuses on managing the solids (sludge) generated during treatment [28,29,30]. The present study was conducted on a medium-sized treatment plant that serves an area with a population of approximately 75,000 PE (person equivalent). Figure 1 is a schematic of the studied wastewater treatment plant, showing how municipal wastewater is processed, starting from the moment the raw wastewater enters the plant through the gravity collector, to the discharge point (outfall), where the treated effluent is discharged into the aquatic environment. The water treatment process consists primarily of pretreatment and secondary treatment stages, which include anoxic and aerobic phases.

2.2. Description of the Operational Flow of the Wastewater Treatment Plant Under Study

The raw wastewater is conveyed to the treatment facility via the gravity collector. This stage entails preliminary treatment, which involves the retention of floating objects and the removal of both large and small particles through screening (sieving). Additionally, this stage includes the removal of fats and oils through the fat removal system (grease separator). Following the preliminary treatment of the primary objects, the water continues in its technological progression, undergoing a secondary treatment phase that entails the extraction of residual dissolved and suspended organic matter. This takes place in the area of the aeration basins. The procedure implemented at the treatment plant under study involves activated-sludge technology and prolonged aeration [31,32,33]. At this stage, the treatment procedure in the technological flow involves combining the anoxic phase, in which the blowers are stopped so as not to supply oxygen to the system (favoring the elimination of nitrates), with an aerobic phase in which the blowers are in operation to supply the necessary oxygen to the aerobic microorganisms responsible for the decomposition of organic matter [34,35,36].

At this stage, the analyzed facility carries out biological treatments to reduce the chemical (mineral and organic) and bacteriological impurities contained in the wastewater below certain limits. This ensures that the wastewater does not harm the aquatic environment into which it is discharged nor endanger the users of the water [37,38]. It should be noted that municipal wastewater treatment processes are largely similar to those that occur during surface water self-purification, except that they are coordinated by specialized personnel, monitored by automatic systems, and carried out in modern facilities at a much higher speed. The installations/set of installations for wastewater treatment are designed to intensify and favor the processes whose main function is to reduce waste to acceptable limits, allowing discharge into a body of water (Vedea River outfall) [39,40]. During the wastewater treatment process, part of the sludge generated from the bottom of the secondary settling tanks (secondary sludge) of the wastewater treatment plant is collected through the scraper bridge mixing procedure and transmitted to be recirculated in the biological reactors and become part of the bioconcentrate (active biomass) [41,42,43]. At the same time, the excess sludge is pumped through pipes to the sludge line for treatment (dewatering procedure). To facilitate further handling and processing, the sludge is subjected to a gravity thickening process by centrifugation, in which the solids concentration is increased. After the dehydration procedure is completed, laboratory samples are taken from the sludge, which is temporarily stored in a sludge depot within the treatment plant until final transfer for various uses, such as agricultural fertilizer (only during certain periods of the year) or to the incinerator if heavy metal contents are exceeded [44,45,46].

2.3. Description of the Nitrification/Denitrification Processes of the Wastewater Treatment Plant Under Study

The main concern should be to improve the aeration processes, as these processes play a significant role in the energy consumption of these plants. By using advanced technology, such as oxygen transfer aeration systems, plants can ensure that oxygen is supplied more efficiently, which in turn will reduce the energy needs associated with the treatment processes [47,48,49].

The technological process involving the biological film occurs through the intense stripping of air produced by the blower. The air is moved through a series of pipes to a static bed, which is then used as a submerged biofilter compartment in the treatment apparatus. This part is made up of well-organized polymer structures with a fairly developed surface, as shown in Figure 2.

The special shapes of the polymer help the biological film (active biomass) to form and grow, which makes it easier for the body to break down organic substances and the nitrification process. The diffusion of the substance dictates the location of the nitrate reduction process, which occurs within the internal layer in the presence of oxygen deficiency. The filter block is equipped with a discrete, intensive air aeration system. This system is employed to dislodge the developed biological film (active biomass) [50,51,52].

The slow, noisy movement of the water in the fine bubble area after it has been aerated causes the biological film to separate from the surface. This process leads to the formation of conglomerate flocs of microflora, as illustrated in Figure 3 [53,54].

According to the technological flow presented in Figure 4, conglomerated flocs of microorganisms are recirculated upstream of the secondary decanter through recirculation pumps and are subjected to the oxidation process, thereby decreasing dependence on the purification-processing fraction [55,56,57]. The dimensions of the developed and captured flocs range from 1.9 to 15.8 mm in length and from 1.3 to 2.6 mm in diameter. The density of the conglomerates of microorganisms is up to 55 to 57 g/L. Consequently, the concentration of activated sludge in the effluent is approximately 18 to 20 times higher. This proportionally increases the potential for eliminating organic and biogenic substances from treated water [58,59,60].

The process of treating municipal wastewater with simultaneous nitrification/denitrification involves conglomerate flocs of active biomass or biological film. This new process increases the concentration of microorganisms by using an internal carbon source from the intracellular space, so external carbon does not need to be added. When intracellular microorganisms are broken down, flocs form, creating an anaerobic environment [61,62].

One significant benefit of flocs of microorganisms is their ability to form oxic, anoxic, and anaerobic zones due to their substantial size [63]. Furthermore, fermentation and cell lysis, which are examples of anaerobic processes, take place in these central zones due to the absence of oxygen and nitrates. These processes break down complex organic materials into simpler compounds. These simpler compounds can then be used by other microorganisms found in the upper layers. This makes it easier to remove organic and biogenic compounds from wastewater [64,65,66]. Using external carbon sources increases the amount of waste generated during biological treatment and decreases the purification of organic and biogenic substances [67,68].

2.4. The Effectiveness of Wastewater Treatment Process Optimization Using Kinetic Modeling

However, to ensure optimal efficiency in removing organic and biogenic compounds from wastewater, we propose a novel and pragmatic approach for wastewater treatment plant operators in the Municipality of Alexandria. This approach involves a comparative analysis utilizing kinetic modeling and equilibrium mass balance calculations for nitrification processes in traditional treatment systems employing activated-sludge technology [69,70,71]. It has been demonstrated that this method leads to substantial enhancements in the administration and optimization of treatment processes. It can accurately estimate the ammonium oxidation potential that is unique to the treatment plant [72].

In other words, the calculations allow us to estimate the treatment potential for the analyzed plant. In addition, the kinetic equation derived below (4) indicates the parameters that are usually not measured, but which should be additionally determined to adjust the operational parameters (dissolved oxygen in the aeration tank, sludge dose and influent flow rate) in order to intensify the process and achieve the desired or planned results. This equation enables the simulation of various operating scenarios and the adjustment of process parameters to optimize the efficiency of pollutant removal. Simulations facilitate the rapid testing of numerous operating scenarios, without physical interventions in the process, and are thus extremely useful for identifying optimal operating conditions, such as the ideal dissolved oxygen concentration, sludge dose or recirculation speed. Kinetic modeling allows for real-time adjustments, adapting the process to unforeseen changes in operating conditions, such as seasonal variations in the influent composition. The equation below was used to calculate the ammonium oxidation potential in the improved process at the Alexandria Municipality Wastewater Treatment Plant:

$$\begin{array}{c}\mathsf{\rho }\mathrm{N}\mathrm{H}4,\mathrm{s}={\displaystyle \frac{1}{{\mathrm{Y}}_{\mathrm{H}\mathrm{N}4,\mathrm{m}\mathrm{a}\mathrm{x}}}}\mathrm{\mu }\mathrm{N}\mathrm{H}\mathrm{4,20}\complement ,{\mathrm{maxe}}^{\mathrm{x}1\left(\mathrm{t}-20\right)}.\hfill \\ \left({\displaystyle \frac{{\mathrm{S}}_{\mathrm{N}\mathrm{H}4}}{{\mathrm{K}}_{\mathrm{s},\mathrm{N}\mathrm{H}4,\mathrm{A}1}+{\mathrm{S}}_{\mathrm{N}\mathrm{H}4}}}{\displaystyle \frac{{\mathrm{S}}_{\mathrm{N}\mathrm{O}2}}{{\mathrm{K}}_{\mathrm{s},\mathrm{N}02,\mathrm{A}2}+{\mathrm{S}}_{\mathrm{N}\mathrm{O}2}}}{\displaystyle \frac{{\mathrm{S}}_{\mathrm{O}2}}{{\mathrm{K}}_{\mathrm{s},02,\mathrm{A}2}+{\mathrm{S}}_{\mathrm{O}2}}}{\displaystyle \frac{{\mathrm{K}}_{\mathrm{p}\mathrm{H}}}{{\mathrm{K}}_{\mathrm{p}\mathrm{H}1}+{10}^{\mathrm{pH},\mathrm{opt}-\mathrm{pHi}}-1}}-\mathsf{\beta }\right)·{\mathrm{X}}_{\mathrm{B}\mathrm{a}}.\hfill \end{array}$$

(1)

where

✓

$\mathsf{\rho }\mathrm{N}\mathrm{H}4,\mathrm{s}$ represents the oxidation potential of ammonium in the optimized technological flow;

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${\mathrm{Y}}_{\mathrm{H}\mathrm{N}4,\mathrm{m}\mathrm{a}\mathrm{x}}$ is an indicator of the rate at which biomass increases for ammonium-oxidizing bacteria;

✓

$\mathrm{\mu }\mathrm{N}\mathrm{H}4,20\complement ,\mathrm{m}\mathrm{a}\mathrm{x}$ indicates the maximum specific growth rate. It has been determined that the substance in question is effective for ammonium-oxidizing bacteria;

✓

${\mathrm{S}}_{\mathrm{N}\mathrm{H}4}$ shows the amount of N-NH₄ in the water that has been treated at the plant;

✓

${\mathrm{K}}_{\mathrm{s},\mathrm{N}\mathrm{H}4,\mathrm{A}1}$ represents indicates the saturation constant. This constant is equivalent to the N-NH₄ concentration. At this concentration, the specific velocity is reduced to half its maximum value in Aeration Tank 1;

✓

${\mathrm{S}}_{\mathrm{N}\mathrm{O}2}$ indicates the level of nitrated nitrogen present within the aerated sections;

✓

${\mathrm{K}}_{\mathrm{s},\mathrm{NO}2,\mathrm{A}2}$ is the saturation constant, which is the same as the NO₂ concentration where the specific velocity is half of the max value in Aeration Tank 2;

✓

${\mathrm{S}}_{\mathrm{O}2}$ is the amount of dissolved oxygen present in the aerated sections;

✓

${\mathrm{K}}_{\mathrm{s},\mathrm{O}2,\mathrm{A}2}$ represents the O₂ saturation constant for autotrophic nitrifying bacteria, which is numerically equal to the value at which saturation is half the maximum value Aeration Tank 2;

✓

${\mathrm{K}}_{\mathrm{p}\mathrm{H}}$ is the pH constant;

✓

${\mathrm{K}}_{\mathrm{p}\mathrm{H}1}+{10}^{\mathrm{p}\mathrm{H},\mathrm{o}\mathrm{p}\mathrm{t}-\mathrm{p}\mathrm{H}\mathrm{i}}-1$ is the numerical value representing the saturation constant, which is equivalent to the concentration value + ${10}^{\mathrm{p}\mathrm{H},\mathrm{o}\mathrm{p}\mathrm{t}-\mathrm{p}\mathrm{H}\mathrm{i}}-1$;

✓

$\mathsf{\beta }$ represents the mortality rate of the autotrophic bacterial mass;

✓

${\mathrm{X}}_{\mathrm{B}\mathrm{a}}$ represents the active biomass.

We used this equation to determine the nitrification rate in suspended activated-sludge systems using the kinetic model (activated-sludge modeling) and the mass balance equation for water treatment systems with recycling:

$${\mathrm{Q}}_{\mathrm{i}}·{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{i}}-{\mathsf{\rho }}_{\mathrm{N}\mathrm{H}4,\mathrm{S}}·\mathrm{V}={\mathrm{Q}}_{\mathrm{e}}·{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{e}}+{\mathrm{Q}}_{\mathrm{e}\mathrm{x}}·{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{e}\mathrm{x}}$$

(2)

The following are the ammonium nitrogen (N-NH₄) concentrations of the influent, effluent, and excess sludge, respectively: S_NH4i, S_NH4e, and S_NH4ex. All three are measured in grams per cubic meter. Q_i, Q_e, and Q_ex are the influent, effluent, and excess sludge flow rates, respectively. All three are measured in cubic meters per day.

Considering that ${\mathrm{Q}}_{\mathrm{I}}·{\mathrm{Q}}_{\mathrm{e},}{\mathrm{Q}}_{\mathrm{e}\mathrm{x}}=0 \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{Q}}_{\mathrm{e}\mathrm{x}}·{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{e}\mathrm{x}}=0$, the following is obtained:

$${\mathrm{Q}}_{\mathrm{i}}·{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{i}}-{\mathsf{\rho }}_{\mathrm{N}\mathrm{H}4,\mathrm{S}}·\mathrm{V}={\mathrm{Q}}_{\mathrm{e}}·{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{e}} \mathrm{o}\mathrm{r} {\displaystyle \frac{\mathrm{V}}{{\mathrm{Q}}_{\mathrm{i}}}}·{{\mathsf{\rho }}_{\mathrm{N}\mathrm{H}4,\mathrm{S}}=\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{i}}-{\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{e}}$$

(3)

✓

${\displaystyle \frac{\mathrm{V}}{{\mathrm{Q}}_{\mathrm{I}}}}$ is the “hydraulic reaction time,” which is a quantitative metric used to assess the efficiency of the aeration system ${\mathrm{S}}_{\mathrm{N}\mathrm{H}4,\mathrm{e}.}$

The next equation is used to calculate how much oxygen is needed to break down ammonia in the ideal wastewater treatment process:

$$\begin{array}{c}{\mathbf{S}}_{\mathbf{N}\mathbf{H}4,\mathbf{i}}={\displaystyle \frac{\mathbf{V}}{\mathbf{Q}\mathbf{i}}}·{\displaystyle \frac{\mathbf{1}}{{\mathbf{Y}}_{\mathbf{H}\mathbf{N}\mathbf{4},\mathbf{\text{max}}}}}·\mathrm{\mu }\mathbf{N}\mathbf{H}\mathbf{4}\mathbf{,}\mathbf{20}\complement ,{\mathbf{\text{maxe}}}^{\mathbf{x}\mathbf{1}\left(\mathbf{t}-\mathbf{20}\right).}\hfill \\ \left({\displaystyle \frac{{\mathbf{S}}_{\mathbf{N}\mathbf{H}\mathbf{4},\mathbf{e}}}{{\mathbf{K}}_{\mathbf{s},\mathbf{N}\mathbf{H}\mathbf{4},\mathbf{A}}+{\mathbf{S}}_{\mathbf{N}\mathbf{H}\mathbf{4},\mathbf{e}}}}{\displaystyle \frac{{\mathbf{S}}_{\mathbf{O}\mathbf{2}}}{{\mathbf{K}}_{\mathbf{s},\mathbf{O}\mathbf{2},\mathbf{A}}+{\mathbf{S}}_{\mathbf{O}\mathbf{2}}}}{\displaystyle \frac{{\mathbf{K}}_{\mathbf{\text{pH}}}}{{\mathbf{K}}_{\mathbf{\text{pH}}}+{\mathbf{10}}^{\mathbf{\text{pH}},\mathbf{\text{opt}}-\mathbf{\text{pHi}}}-1}}-\mathsf{\beta }\right)·{\mathbf{X}}_{\mathbf{B}\mathbf{a}}+{\mathbf{S}}_{\mathbf{N}\mathbf{H}\mathbf{4},\mathbf{e}}\hfill \end{array}$$

(4)

X_Ba, written as gCCO_Cr/g active biomass, is not something that wastewater treatment facilities monitor. Therefore, the equation used to estimate the ammonium oxidation potential was adapted so that operators can use it. This equation takes into account the constructed and physicochemical parameters that can be monitored during the operation of an activated-sludge treatment facility. Thus, the fraction of active biomass in activated sludge, δ_b = 0.65, was introduced, assuming that 0.28–0.3 represents mineral substances and 0.07–0.9 represents low-active biomass due to bacterial lysis.

The CCO_Cr calculation of active biomass considers the composition expressed by the formula C₅H₇NO₂:

$${\mathit{C}}_{\mathbf{5}}{\mathit{H}}_{\mathbf{7}}{\mathit{N}\mathit{O}}_{\mathbf{2}}+{\mathbf{5}\mathit{O}}_{\mathbf{2}}+{\mathit{H}}^{+}\to {\mathbf{5}\mathit{C}\mathit{O}}_{\mathbf{2}}+{\mathbf{2}\mathit{H}}_{\mathbf{2}}\mathit{O}+{\mathit{N}\mathit{H}}_{\mathbf{4}}^{+}$$

(5)

From Formula (5), it follows that one mole of biomass, with a mass of 112 g, corresponds to 5 moles of oxygen, with a mass of 159 g. Thus, it is deduced that for each gram of active biomass the following are required: 159 g of CCO_Cr/112 g of biomass = 1.41 g CCO_Cr/g biomass. Therefore, 1.41 g CCO_Cr/g biomass · 0.65 = 0.92, which is numerically ≈ 1 g MLSS (Suspended solids with mixed liquids). This parameter, which is not monitored at treatment plants, is called Sludge Dose (expressed in gram units).

3. Results

3.1. Calculation of the Ammonium Oxidation Potential in the Optimized Technological Flow

We calculated estimated the ammonium oxidation potential in the optimized technological flow for each process and substrate using the stoichiometric coefficients and constants from Equation (4). The results are shown in

Table 1. The stoichiometric constants and coefficients for the activated-sludge system in the nitrification process.

Stoichiometric Constants and Coefficients Are Important in Chemistry Because They Help to Determine the Amounts of Reacting Substances Needed for a Chemical Reaction to Occur.	Symbol	Unit of Measurement	Value
Ammonium-oxidizing bacteria clearly demonstrate a high biomass growth rate.
	YNH4,max	g MLSS/gN	0.24
The maximum specific growth rate of ammonium-oxidizing bacteria is a critical metric in microbiology.	µNH4,20C,max	Zi−1	0.8
The saturation constant is numerically equivalent to the N-NH4 concentration when the specific velocity is half of the maximum value, as is the case for the nitrification process.
	Ks,NH4,A	gN-NH4/m3	0.5
The O2 saturation constant for autotrophic nitrifying bacteria is numerically equal to the value at which saturation is half of the maximum value.	Ks,O2,A	gO2/m3	1.00
Constant pH	KpH	-	200
Temperature constant	χ	°C−1	0.08
Fraction of autotrophic bacteria in the active bacterial mass	ηa	-	0.05
The mass fraction of active bacteria in activated sludge is equal to the ratio VSS (volatile suspended solids)/MLSS (the concentration of suspended solids with mixed liquids).	δb	-	0.65
Mortality rate of bacterial population that is autonomous from its food	β	zi−1	0.05

(activated-sludge modeling). The operating and operational parameters of the Alexandria City station were also used, according to

Table 2. Technical operating/functioning parameters of the station under study.

Parameter	Symbol	Unit of Measurement	Value
Volume of aerated compartments
	V	m3	1300
Influent wastewater flow rate in the treatment plant	Qi	m3/zi	1900
N-NH4 concentration in wastewater treatment plant effluent
	SNH4,e	g/m3	variable
Dissolved oxygen concentration in aerated compartments	SO2	gO2/m3	variable
The pH concentration in wastewater from the treatment plant’s influent is measured.	pH	-	variable
Activated sludge is added in suspended matter in aerated compartments.	MLSS	g/m3	1850–2150
Temperature of wastewater undergoing treatment	t	°C	10–26

.

We can see in

Table 3. Adjustment of operational parameters Qi = 1900 m³/day, V = 1300 m³, MLSS (the concentration of suspended solids with mixed liquids) = 1980 g/m³, and ${NH}_4^{+}$ = 1.98 g/m³.

DO/mg/L			t, °C
	10	11	12	13	14	15	16	17
1	19.10	20.64	21.32	22.13	23.09	25.22	27.53	29.02
2	26.23	28.37	30.68	32.19	34.91	37.86	40.05	44.50
3	29.79	31.23	33.87	35.72	38.82	42.17	45.81	48.74
4	31.93	34.54	37.37	40.44	43.76	47.36	50.26	53.49
5	33.36	36.09	39.05	43.25	46.73	49.49	552.57	56.98
DO/mg/L			t, °C
	18	19	20	21	22	23	24	25
1	32.73	35.66	38.83	41.10	43.27	45.99	48.03	53.40
2	49.25	53.30	57.80	62.46	67.61	73.20	79.25	85.80
3	56.01	60.62	65.63	71.05	76.92	83.28	90.17	97.64
4	60.06	65.02	70.39	76.20	82.51	89.33	96.73	104.74
5	62.77	67.95	73.56	79.64	86.23	93.36	5101.09	109.47

Note: DO—dissolved oxygen dose.

that the data are presented in tabular form. In order to arrive at the presented data, the stoichiometric constants and coefficients for the activated-sludge system in the nitrification process were replaced with the parameters specified in Table 1 and the operational parameters for the aforementioned station in Equation (4). The values used were Qi = 1900 m³/day, V = 1300 m³, MLSS (the concentration of suspended solids in the mixed liquor) = 1980 g/m³, and NH₄⁺ = 1.98 g/m³.

The objective of the present study was to estimate the ammonium oxidation potential in the technologically optimized flow of the Alexandria Wastewater Treatment Plant (WWTP). The data presented in (Table 3) were employed for this estimation. According to the existing requirements, the data are calculated for an NH₄⁺ concentration in the effluent of 1.98 mg/L.

3.2. Calculation of Simultaneous Nitrification Efficiency and Denitrification Efficiency Determined Using Kinetic Equations

These data show the maximum amount of ammonium nitrogen in wastewater that can be treated by the activated-sludge method alone. The goal of this study was to show that nitrification and denitrification can occur at the same time in wastewater in a single aerated flow, without needing to separate the oxygen-rich and oxygen-poor zones. To do this, we calculated how well each step performed at different temperatures using these formulas:

$$Ef\%N-{NH}_4=\left(N-{NH}_{4}inf-N-{NH}_{4}elf\right)·100\%/N-{NH}_{4}inf$$

(6)

$$Ef\%N=(N-{NH}_{4}inf-(N-{NH}_{4}elf+{N-NO}_{3}elf+{N-NO}_{2}elf)·100\%/N-{NH}_{4}inf$$

(7)

where

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N-NH₄ inf is an indicator of the ammoniacal nitrogen concentration present in the influent, which is measured and represented here;

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N-NH₄ efl is the ammoniacal nitrogen in the effluent, which serves as a proxy for the concentration of this element in the water. The determination of this measurement is crucial for evaluating the quality of the effluent and for determining the necessary treatment processes;

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N-NO₃ efl is the nitrate nitrogen present in the effluent expressed as a concentration;

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N-NO₂ efl represents the concentration the effluent of nitrate nitrogen;

As shown in

Table 4. Calculation of simultaneous nitrification efficiency and denitrification efficiency, determined using kinetic equations.

No.	Temp.	CODCr Influent	CODCr Effluent.	N-NO3 Effluent	N-NO2 Effluent	N-NH4 Influent	N-NH4 Effluent	Eff N-NH4	Eff N
	°C	gO2/m3	gO2/m3	g/m3	g/m3	g/m3	g/m3	%	%
1	9.01	460	109.03	42.09	6.08	82.05	16.05	80.01	19.08
2	10.02	535.07	118.02	36.05	4.06	65.07	2.25	96.06	33.9
3	15.01	522.06	116.04	42.05	0.049	70.04	0.659	99.01	38.06
4	15.09	556.08	93.01	12.01	0.199	49.05	22.419	95.02	70.02
5	17.03	616.02	99.01	1.657	8.12	103.03	7.91	92.04	82.09
6	17.06	488.03	73.02	16.07	0.109	68.98	0.722	98.09	74.01
7	20.08	493.07	96.06	5.324	0.038	65.03	0.437	99.03	91.01
8	20.04	341.01	29.05	6.03	0.109	61.02	0.625	98.08	88.06
9	25.04	622.05	63.9	13.04	0.455	79.08	0.935	98.08	81.05

, denitrification rates range from 19.08% to 91.01%. This is closely related to the temperature of the wastewater that has been treated. Concomitantly, nitrification reaches a performance of up to 99.03%. Table 4 shows that when there are groups of microorganisms from activated sludge in the technological flow, it improves the denitrification process under constant aeration. This demonstrates that the biological film with flocs is functional.

The objective of this study was to demonstrate the nitrification efficiency of the activated-sludge system. To determine this, we used a kind of mathematics called “kinetic modeling” and kept track of the balance of matter. These calculations were based on a controlled environment with small aggregates of organisms called “glomerated microorganism flocs” in the activated sludge. The results were then compared with the efficiency of the system with only activated sludge. The comparative results of the experimental data are presented in Table 4, both for the enhanced nitrification process in the presence of conglomerate flocs and those calculated for the nitrification efficiency of the system with activated sludge only, based on the formulas below:

$$∆N-{NH}_{4}ex.=N-{NH}_{4}inf-N-{NH}_{4}efl$$

(8)

$$∆N-{NH}_{4}calc.=N-{NH}_{4}infcalc.-N-{NH}_{4}efl$$

(9)

$$∆N-{NH}_4=∆N-{NH}_{4}ex.-∆N-{NH}_{4}calc.$$

(10)

where

✓

N-NH₄ inf calc. is the concentration calculated according to Formula (4) in the influent of ammonium nitrogen;

✓

∆N-NH₄ ex. shows the amount of ammonium nitrogen that was removed through the boosted nitrification process by the activity of the microorganisms in the activated sludge;

✓

∆N-NH₄ calc. is the amount of ammonium nitrogen removed by activated sludge, which represents the nitrification efficiency of the system;

✓

∆N-NH₄ indicates the quantity of ammonium nitrogen that has been extracted from the given sample or system.

This removal is achieved through the utilization of microbial flocs. The process occurs during the station’s continuous flow. As shown in

Table 5. The efficacy of the nitrification process, as determined by its yield, within the context of continuous technological flow.

No.	∆N-NH4exp., g/m3	N-NH4 Influent calc. g/m3	N-NH4 calc. g/m3	N-NH4 g/m3
1	66.01	59.54	43.04	22.98
2	63.45	35.79	33.53	29.93
3	69.75	36.49	35.83	33.93
4*	47.10	45.67	43.26	3.85
5	95.41	75.30	67.40	28.02
6	68.29	40.81	40.09	28.21
7	64.88	32.64	32.3	32.68
8	60.59	41.05	40.43	20.17
9	78.87	70.9	69.87	9.01

, when conglomerated microorganism flocs are present in activated sludge, the nitrification process becomes more efficient. This occurs in a continuous technological flow. This is because of a special layer on the bacteria called a biological film. The nitrification process improves when there numerous microorganisms in the activated sludge, which makes the system work better. We can see this in how it performs better at higher levels of ammonia in the water compared to Sample 4*, which has less ammonia.

To understand each part of the process, we took samples from the influent, the mixed influent, and the recycled sludge from the secondary settling tank. We also took samples from downstream of each of the three aerated compartments, the biofilter unit, the secondary settling tank, and the effluent. Thus, the profile of the concentrations of all elements estimated for the entire technological flow can be constructed.

The nitrification process is manifested by the decrease in the N-NH₄ concentration in all aerated compartments and the biofilter unit, indicated by the ammonium oxidation slope. The denitrification process can be seen through the downward slopes of ammonium oxidation and nitrate reduction (a decrease in N-NO₃ concentration). This occurs because they use carbon, which is necessary for the denitrification process. Carbon is present in the form of CCO_Cr in the initial aeration tank. This process is more noticeable in compartments 2 and 3 at temperatures of 17.6 °C and 20.4 °C, respectively. This occurs because of the breakdown of microorganisms in the anaerobic interfloccular zone, which creates a substrate that is consumed by bacteria. In this case, the wastewater has a carbon source, or CCO_Cr, that has undergone oxidation, as shown in Figure 5.

The above results demonstrate that the nitrification and denitrification processes occur simultaneously, as shown in Figure 6, at the analyzed temperatures along the technological flow, as presented in Table 4. It is posited that this encompasses the influent, in conjunction with the activated sludge collected and reused from the secondary clarifier, each of the three biological reactors, the biofilter block, the post-aeration zone, and the effluent.

3.3. Calculation of Hydraulic Retention Time

We can use the data in tabular form to find the best scenario for the treatment process. This allows us to obtain the optimal parameters while also considering the station’s unique characteristics, like the hydraulic retention time $\theta ={\displaystyle \frac{V}{Qi}}=0.7$ and the wastewater temperature of 20 °C. This information is presented in

Table 6. Application for selecting a suitable scenario to achieve the required results in the treatment process with individual plant characteristics such as hydraulic retention time $\theta ={\displaystyle \frac{V}{Qi}}=0.7$ și and wastewater temperature 20 °C.

Parameter OD/Dose/mg/L			Sludge Dose mg/L
	1800	1900	2000	2100	2200	2300	2400
0.50	27.82	29.28	30.74	32.20	33.66	35.12	36.58
1.00	44.21	46.58	48.94	51.31	53.68	56.05	58.42
1.50	54.04	56.95	59.87	62.78	65.70	68.61	71.53
2.00	60.59	63.87	67.15	70.43	73.71	76.99	80.26
2.50	65.27	68.81	72.35	75.89	79.43	82.97	86.51
3.00	68.78	72.51	76.25	79.98	83.72	87.45	91.19
3.50	71.51	75.40	79.28	83.17	87.05	90.94	994.83

. The table based on Equation (4) can be used to adjust the operational parameters of the treatment plants within the limits of practice and optimize the treatment processes.

According to Equation (4), 3D diagrams (Figure 7) can be constructed for various wastewater temperatures, as well as for different hydraulic retention times. These diagrams allow the presentation of the N-NH₄⁺ values potentially treated to regulatory levels by modifying the operational parameters in a tabular form (Table 6).

The dissolved oxygen (DO) levels in the aeration tanks ranged from 0.5 milligrams per liter (mg/L) to 3.5 mg/L. Maintaining a concentration of more than 3.5 mg/L in aeration tanks results in elevated electric energy consumption due to the operation of blowers at maximum capacity. This, in turn, necessitates the installation of additional blowers, which is not a viable operational solution. Consequently, the air flow rate and the blowers’ capacity to maintain processes in the aerated compartments are constrained during the design phase to within the limits of 2.0–2.5 mg/L. The sludge dose varies from 1800 mg/L to 2400 mg/L. A higher dose can lead to disruption of the sedimentation process in the secondary clarifiers and cause instability of the entire treatment process by uncontrolled discharge of activated sludge from the system.

The temperature of the wastewater is a variable external factor, fluctuating seasonally between 8 °C and 31 °C in the Alexandria Municipality Wastewater Treatment Plant. This temperature variation is essential in the ammonium oxidation process as it affects the sensitivity of the development of autotrophic bacteria responsible for nitrification. According to legislation and other international regulations [73], ammonium oxidation or nitrogen removal processes are regulated only for temperatures higher than 11–16 °C. In this study, the wastewater temperature varied between 12 and 31 °C, with steps of 2 °C.

The hydraulic retention time, denoted by $\theta ={\displaystyle \frac{V}{Q}}$, is a crucial parameter in the analysis. The quantity V, measured in cubic meters, signifies the constructed volume of the aeration basins at the designated station. Q_i, expressed in cubic meters per day, denotes the effective flow rate of the influent at the station, as measured by a designated flowmeter. This parameter, which is a characteristic of the facility design, can range from 0.2–0.3 to 0.9–1.0.

The proportion of autotrophic nitrifying bacteria in a mixed activated-sludge culture is influenced by the C/N ratio, where C is biodegradable carbon and N is total nitrogen. By analyzing the physicochemical parameters of the studied treatment plant, the average C/N ratio for domestic water is found to be 4–5. As the ratio increases, the fraction of bacteria decreases, and vice versa (

Table 7. The present study investigates the relationship between the proportion of autotrophic nitrifying bacteria in a mixed culture of activated sludge and the C/N ratio.

C/N Ratio	Autotrophic Bacteria Fraction ηa	C/N Ratio	Autotrophic Bacteria Fraction ηa
0.5	0.35	5	0.054
1	0.21	6	0.043
2	0.12	7	0.037
3	0.083	8	0.033
4	0.064	9	0.029

). The following text provides a comprehensive overview of this. A value of 0.04 was employed for the fraction of autotrophic nitrifying bacteria in the mixed culture of activated sludge, as determined by the C/N ratio of 4–5. For other C/N ratios, the fraction of autotrophic bacteria, η_a, can be determined using the data provided in Table 7.

The data in the tables correspond to a retention time of $\theta ={\displaystyle \frac{V}{Q}}=0.7$. Given that the factor θ in the equation is a linear correction factor, the data in the tables can also be used for other values of θ of the individual characteristic parameters for the station.

4. Discussion

After completing the study and evaluating such a complex system encompassing a wide range of processes, including carbon oxidation, nitrification, and denitrification, in a single stage, it is clear that a substantial investment of time and resources would be required to operate a facility (the studied treatment plant) under all possible conditions. The availability of such a model as the one presented here, which includes rate equations for the processes involved, allows operators to explore a wide range of system configurations, inputs, and operational strategies through simulation. Once parameter values have been calibrated for a given wastewater, the operator can use a model to eliminate inefficient configurations and to choose those alternative system configurations that are most likely to be economical. For a given system flow scheme, there are several options for unit sizes that will result in the desired degree of treatment.

Achieving these treatment targets will reduce water pollution and conserve biodiversity. Energy savings will be possible by optimizing treatment processes, using kinetic modeling for nitrification/denitrification processes and adjusting process parameters in real time, which will lead to significant reductions in the operational costs of treatment plants and bring notable economic benefits. For example, the energy savings achieved can be reinvested in other wastewater treatment plant development projects or in improving community infrastructure (collection networks).

5. Conclusions

In conclusion, the implementation of a wastewater treatment process that uses kinetic modeling to optimize the nitrification process in the presence of conglomerate microorganisms in activated sludge is expected to generate substantial social and economic benefits.

This approach provides the possibility of accurately assessing the ammonium oxidation potential. In addition, kinetic equations facilitate the estimation of parameters that are not usually measured but are essential for optimizing operational parameters (e.g., dissolved oxygen levels in the aeration tank, sludge dosage, and influent flow rate). The nitrification rate demonstrates a performance of 99.03%, while the denitrification rate ranges from 19.08% to 91.01%. A substantial correlation has been demonstrated between this variable and the temperature of the treated wastewater. This process will improve the quality of life and health of the population and increase the efficiency of wastewater treatment, contributing to the sustainable development of the region.

Wastewater treatment plant operators must use advanced strategies to manage nitrification processes, and one such strategy is the use of kinetic modeling equations. This method provides a valuable tool for improving the quality of treated water and for complying with legal requirements. The innovative solution developed and applied in this research improves the operation of biological wastewater treatment plants by integrating kinetic equations for nitrification processes into classic treatment systems based on activated-sludge technology. The developed technology contributes efficiently and sustainably to reducing the biogenic impact, mitigating the eutrophication of aquatic ecosystems.