# Wastewater Treatment System Optimization for Sustainable Operation of the SHARON–Anammox Process under Varying Carbon/Nitrogen Loadings

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}/NH

_{4}) ratio. This study aimed to implement a set of control strategies in a WWTP model BSM2-SHAMX, combining PN in a single reactor system for high-activity ammonia removal over nitrite (SHARON) to an Anammox reactor, using proportional–integrative–derivative (PID) control and model predictive control (MPC) in a cascade. For correct coupling, the PN should maintain an output NO

_{2}/NH

_{4}ratio between 1 and 1.3, suitable for the Anammox process. In the cascade controller feedback loop, the primary control loop controls the NO

_{2}/NH

_{4}ratio through the DO concentration from the secondary control loop, which guarantees better effluent nitrogen removal. The performance of the plant was assessed by evaluating the control strategies with different influent carbon/nitrogen (C/N) loadings. The study results showed that the MPC controllers provided better results, with an improvement of 36% in the operational cost compared to the base case with a cost around 26,000 EUR/d, and better nitrogen removal surpassing 90% removal, 10% more than the base case.

## 1. Introduction

_{2}/NH

_{4}ratio, and temperature conditions, for maintaining the microorganisms activity in the treatment process [12].

_{2}/NH

_{4}ratio as the influent to the Anammox process [24]. An optimal and low C/N ratio, for nitrogen removal, has the potential to completely convert ammonium to nitrogen gas (N

_{2}) in ammonium-rich wastewater [1,5,25,26]. The NO

_{2}/NH

_{4}ratio is an underlying condition for the correct operation of the Anammox process. Given that the effluent from the anaerobic digester should be able to oxidize half of the ammonium to nitrite, an adequate product mixture from the partial nitritation process can be obtained by manipulating the NO

_{2}/NH

_{4}ratio, which affects the nitrogen removal efficiency in the Anammox process by reducing nitrate production in the deammonification process [12]. A NO

_{2}/NH

_{4}ratio of around 1 to 1.3 prevents the oxidation of nitrite to nitrate, influencing the bacterial growth needed [1,24,27]. Thus, the conditions needed to achieve the correct NO

_{2}/NH

_{4}ratio in the operation of the deammonification process need to be thoroughly analyzed. This work proposes the use of cascade controllers to evaluate the optimal operation of the deammonification process and maximize nitrogen removal.

## 2. Materials and Methods

#### 2.1. Problem Statement

_{2}/NH

_{4}ratio, which can be difficult to achieve naturally in WWTP reject water. Therefore, cascade controllers can be integrated into the system to achieve that ratio and improve the plant’s overall nitrogen removal.

- The data include the influent flowrate and the flowrate of the components, such as nitrate, ammonia, and oxygen, as well as the sludge concentration, among others in form of model input data such as nitrite, C/N ratio, solids, particulate matter, etc. All of these are required for the model.
- The processes of a simple biological treatment are given in the WWTP model as one primary clarifier, five biological reactors, one secondary clarifier, one AD, one SHARON, and one Anammox reactor.

#### 2.2. Proposed Method

#### 2.3. BSM2-SHAMX Model

#### 2.4. MPC State Space Model

_{P}. The control moves over a control horizon to estimate the optimal trajectory for a defined optimization criterion. Thus, only the first move of the optimal sequence is applied to the plant; after that, the state estimated is corrected with the measured output at the present sampling instant. That process is then repeated at sampling time k + 1 using the present state x(k + 1) [30,31]. Overall, MPC consists of the RHP and the optimization for choosing the best sequence of control actions in the time horizon. The optimization comprises the optimization model, an internal MPC model, and its optimization solver [32]. For the control process, the state-space model (SSM) is established assuming the current state x(k), control input u(k), disturbance input d(k), and output y(k) (Equations (1) and (2)) [30,31].

_{1}, B

_{2}, C, D

_{1}, and D

_{2}are the respective coefficient matrices. The output y(k + 1) of the next step is estimated from the iteration of Equations (1) and (2), as presented in Equation (3).

_{P}) (Equations (4)–(10)). From Equations (4) and (5), the SSM establishes relationships among the system output, current state, control input, and disturbances from which the system behavior for the next steps can be predicted.

_{NH,AMX}) in the AMX reactor is the controlled variable, and the manipulated variable is the DO (S

_{O,SH}) from the SH reactor. The linear model matrices A, B, C, and D are determined by minimizing the error between the process measurements and the simulated model outputs, which are estimated using the MPC toolbox in MATLAB R2016a. In this work, the following matrices represent the MPC model (Equations (11)–(14)):

#### 2.5. Sensitivity Analysis of BSM2-SHAMX

#### 2.6. Control Strategy Modeling and Evaluation

#### 2.6.1. Implementation of the Control Strategies

_{O,SH}) by manipulating the oxygen transfer coefficient in the SH reactor (K

_{L}a

_{,SH}). C2 uses an NH

_{4}controller on the Anammox process to regulate the NH

_{4}concentration going into the main stream of the system. The controlled variable is the ammonia concentration in the AMX reactor (S

_{NH,AMX}), and the manipulated variable is the S

_{O,SH}. C3 proposes a cascade control comprising PI-PI controllers. S

_{NH,AMX}is the controlled variable in the primary control loop, and the manipulated variables are S

_{O,SH}in the primary control loop and k

_{L}a

_{,SH}in the secondary control loop. This control scheme aims to control the deammonification process to reduce the plant’s final nitrogen concentration.

^{3}/d, with an average COD of 592.53 mg/L. Those data simulate the wastewater flowrate with daily and seasonal variations, from which dry weather data were adopted. The data from [4] were adopted for a period of 153 days, with an average influent flowrate of 16,730 m

^{3}/d, average ammonia concentration of 24.42 mg/L, average nitrite concentration of 121.2 mg/L, and average nitrate concentration of 337.9 mg/L.

#### 2.6.2. Control Performance Indices

_{4}) flowrate in kWh/d, ${p}_{gas,C{H}_{4}}$ is the methane gas pressure in bar, and ${P}_{gas}$ is the gas pressure considering CO

_{2}, H

_{2}, and H

_{2}O in bar. More details on the performance evaluation indices are presented in Section 1.3 of Supplementary Materials.

#### 2.6.3. Resource Recovery Evaluation

## 3. Results and Discussion

#### 3.1. Sensitivity Analysis

_{L}a

_{5}) and the volume of the third reactor. Figure 4b,c show the correlations between the parameters and the effluent nitrate and ammonia concentrations, respectively. In Figure 4b, the parameters of importance for the nitrate effluent concentration are the waste flowrate and the volume of the primary clarifier. Similarly, for the ammonia effluent concentration, the most influential parameters are the volume of the first reactor, the waste flowrate, and the volume of the primary clarifier (Figure 4c).

#### 3.2. Control Performance

_{2}/NH

_{4}ratio, which later influences the primary MPC control loop to maintain the NH

_{4}concentration, enhancing the plant’s nitrogen removal. The OC in C5 was reduced by 36.73%, representing a total of 9596.71 EUR/d, an important improvement in plant operations.

_{2}/NH

_{4}ratio helps achieve good nitrogen removal in the Anammox process by decreasing nitrate production. C5 presents the lowest OC in part through lower SP, which stems from the lower TSS in the system. On the other hand, the highest OC among the control strategies was with C3 and C4 for all influent variations. However, the increase compared to C0 is small. Efficient nitrogen removal and efficient operational costs are achieved with all the control strategies because the controlled variables include the DO concentration in the SHARON reactor and the ammonia concentration in the Anammox reactor. Those variables directly influence nitrogen removal in WWTPs, affecting the microorganisms in the sludge and the denitrification process in the main line.

_{O}setpoint is close to zero, which resulted in a NO

_{2}/NH

_{4}ratio of 1.15 for a low C/N ratio (Figure 6a), a small decrease to 1 for the intermediate C/N ratio (Figure 6b), and a lower NO

_{2}/NH

_{4}ratio of 0.96 for a high C/N ratio (Figure 6c). Moreover, with C5, the MPC-MPC cascade controller outperformed the other control schemes on nitrogen removal, enhancing the operation of the system.

_{Amm}, X

_{Nit}, X

_{Anammox}, and X

_{Het}at all the influent variation conditions. The biomass concentration did not vary with the different influent conditions. X

_{Amm}showed the highest values of around 0.20 mg/L, which later decreased to zero in the period tested. On the other hand, the highest biomass concentration was for X

_{Anammox}, around 8 mg/L, followed by the X

_{Nit}, showing an increase in Anammox bacteria over ammonia-oxidizing bacteria (AOB) and NOB. The nitrate concentration decreased as the NOB was suppressed, which also influenced the ammonia concentration from SHARON. In general, according to the influent conditions evaluated, the most significant result is that the NO

_{2}/NH

_{4}ratio is somewhat affected, improving when the C/N ratio is intermediate or low but underperforming when it is high. More results from control strategies C1 to C3 are presented in Supplementary Materials.

_{2}/NH

_{4}ratio, and the setpoint for the controller then helps to establish it. Moreover, given that the selection factor is the DO concentration, the influent stream from the AD effluent is treated without modifying the flowrates in the partial nitritation process. In that way, when assuming a negligible nitrite concentration in the SHARON input, the ammonium concentration can be controlled instead of the NO

_{2}/NH

_{4}ratio.

#### 3.3. Resource Recovery Potential

_{4}, influences on the later process of anaerobic digestion, similarly occurs for the C5 where the same variables are controlled under an MPC control type. Methane, as a biogas, is one of the most robust and valuable resources produced by WWTPs. Biogas commonly fails to be exploited for energy generation. At least 70% of methane can generate energy for use in the WWTP itself to reduce the operational cost of the system. In analyzing the effluent nitrogen concentration, which was completely removed in the C4 and C5 systems, it can be seen that the cascade controls outperformed the single-loop controls. Nitrogen removal in WWTPs is fundamental to prevent eutrophication, which can also be reused as fertilizer.

## 4. Conclusions

_{2}/NH

_{4}ratio suitable for the Anammox process. In future work, this study could be extended to include more specific environmental and economic objectives for an integrated analysis of the control strategies proposed. In addition, more varied scenarios considering C/N ratio would be considered in future work, allowing for a more integral study.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Block diagram of the proposed cascade control strategy (C3 to C5). The secondary control loop calculates the dissolved oxygen concentration (S

_{O}) at the set point given, S

_{O,sp}, and tracks the S

_{O}set point by adjusting the k

_{L}a of the system. The primary control loop compensates for the errors in the S

_{O}measurement to attain the desired NO

_{2}/NH

_{4}ratio. The primary and secondary control loops are obtained by the feedback of the S

_{O}and NO

_{2}/NH

_{4}ratio, respectively.

**Figure 3.**COD and N in the different influent variations for C4 and C5. (

**a**) Low C/N ratio: COD and N influent to SH. (

**b**) Intermediate C/N ratio: COD and N influent to SH. (

**c**) High C/N ratio: COD and N influent to SH.

**Figure 4.**Sensitivity results for (

**a**) dissolved oxygen effluent concentration, (

**b**) nitrate effluent concentration, and (

**c**) ammonia effluent concentration. KLa5 and KlaSH are the oxygen transfer coefficient in the fifth and SHARON reactors, respectively; VOL1, VOL3, and VOL_P are the volumes of the first and third reactors and the primary clarifier, respectively; Qr is the sludge return flowrate; Qw is the wastage flowrate.

**Figure 5.**Results comparison of EQI, OC, and SP for SH influent with various C/N ratios in (

**a**) C4 and (

**b**) C5.

**Figure 6.**Results for the C5 MPC-MPC cascade controller. (

**a**) Low C/N ratio: NO

_{2}/NH

_{4}output ratio from SH, SO setpoint, and biomass concentration of ammonia-oxidizing biomass (X

_{Amm}), nitrite-oxidizing biomass (X

_{Nit}), anammox biomass (X

_{Anammox}), and heterotrophic biomass (X

_{Het}) from SH. (

**b**) Intermediate C/N ratio: NO

_{2}/NH

_{4}output ratio from SH, SO setpoint, and biomass concentration of X

_{Amm}, X

_{Nit}, X

_{Anammox}, and X

_{Het}from SH. (

**c**) High C/N ratio: NO

_{2}/NH

_{4}output ratio from SH, SO setpoint, and biomass concentration of X

_{Amm}, X

_{Nit}, X

_{Anammox}, and X

_{Het}from SH.

**Figure 7.**Ammonia concentration (S

_{NH,eff}) in the effluent for control strategies C1 to C5 with a low C/N ratio.

Control Strategy | Base Case C0 | C1 | C2 | C3 | C4 | C5 |
---|---|---|---|---|---|---|

Controlled variable | - | SO from SHARON reactor (SO,SH) | SNH from Anammox reactor (SNH,AMX) | SNH from Anammox reactor (SNH,AMX) | SNH from Anammox reactor (SNH,AMX) | SNH from Anammox reactor (SNH,AMX) |

Set point | - | SO,SH = 0.0354 * mg/L | SNH,AMX = 12 * mg/L | SNH,AMX = 12 * mg/L | SNH,AMX = 12 * mg/L | SNH,AMX = 12 * mg/L |

Manipulated variable | - | KLa in SHARON reactor (KLa,SH) | KLa,SH; SO,SH | KLa,SH; SO,SH | KLa,SH; SO,SH | KLa,SH; SO,SH |

Measured variable | - | SO,SH | SNH,AMX | SNH,AMX | SNH,AMX | SNH,AMX |

Control algorithm | - | 1 feedback PI control | 1 feedback PI control | 1 cascade PI-PI control | 1 cascade PI-MPC control | 1 cascade MPC-MPC control |

Proportional gain (Kp) | - | 689.23 | 79.88 | 0.181 | 79.88 | - |

Integral gain (Ti) | - | 1.98 | 3.17 | 3.33 | 3.17 | - |

**Table 2.**Plant performance indices for the two single-loop controllers (C1–C2) and three cascade controllers (C3–C5) compared with the base case (C0).

Influent Variation to SHARON | Control Strategy | Base Case C0 | C1 | C2 | C3 | Improvement (%) | C4 | Improvement (%) | C5 | Improvement (%) |
---|---|---|---|---|---|---|---|---|---|---|

Low C/N ratio (C/N < 1) | EQI (kg of pollutants/d) | 916.53 | 916.49 | 916.50 | 944.08 | −3.01% | 1568.65 | −71.15% | 1568.65 | −71.15% |

OC (EUR/d) | 26,129.97 | 26,129.98 | 26,130.02 | 26,130.02 | 0.00% | 26,130.02 | 0.00% | 16,533.26 | 36.73% | |

SP (kg/d) | 160,544.83 | 160,544.92 | 160,545.13 | 160,545.13 | 0.00% | 160,545.13 | 0.00% | 100,565.38 | 37.36% | |

Intermediate C/N ratio (C/N = 1) | EQI (kg of pollutants/d) | 916.53 | 916.49 | 916.50 | 944.08 | −3.01% | 1568.65 | −71.15% | 1568.62 | −71.15% |

OC (EUR/d) | 26,129.97 | 26,129.98 | 26,130.02 | 26,488.35 | −1.37% | 16,533.53 | 36.73% | 16,533.32 | 36.73% | |

SP (kg/d) | 160,544.83 | 160,544.92 | 160,545.13 | 162,784.71 | −1.40% | 100,567.08 | 37.36% | 100,565.76 | 37.36% | |

High C/N ratio (C/N > 1) | EQI (kg of pollutants/d) | 916.53 | 916.49 | 916.50 | 944.08 | −3.01% | 1568.65 | −71.15% | 1568.65 | −71.15% |

OC (EUR/d) | 26,129.97 | 26,129.98 | 26,130.02 | 26,130.02 | 0.00% | 26,130.02 | 0.00% | 16,533.26 | 36.73% | |

SP (kg/d) | 160,544.83 | 160,544.92 | 160,545.13 | 160,545.13 | 0.00% | 160,545.13 | 0.00% | 100,565.41 | 37.36% |

Influent Variation to SHARON | Evaluation Criteria | Control Strategies | |||||
---|---|---|---|---|---|---|---|

Base Case C0 | C1 | C2 | C3 | C4 | C5 | ||

Low C/N ratio (C/N < 1) | Effluent nitrogen concentration (mg/L) | $7.5536\times {10}^{-9}$ | $2.6178\times {10}^{-9}$ | $2.6178\times {10}^{-9}$ | $5.9164\times {10}^{-6}$ | 0.00 | 0.00 |

Sludge production (kg/d) | 160,544.83 | 160,544.92 | 160,545.1 | 162,784.71 | 100,567.52 | 100,565.38 | |

Methane production (kg CH_{4}/d) | 980.17 | 980.48 | 980.47 | 994.22 | 0.00 | 0.00 | |

Intermediate C/N ratio (C/N = 1) | Effluent nitrogen concentration (mg/L) | $1.0641\times {10}^{-6}$ | $2.6178\times {10}^{-9}$ | $2.6178\times {10}^{-9}$ | $5.9164\times {10}^{-6}$ | 0.00 | 0.00 |

Sludge production (kg/d) | 160,544.83 | 160,544.92 | 160,545.1 | 162,784.71 | 100,567.08 | 100,565.76 | |

Methane production (kg CH_{4}/d) | 980.17 | 980.48 | 980.47 | 994.22 | 0.00 | 0.00 | |

High C/N ratio (C/N > 1) | Effluent nitrogen concentration (mg/L) | $7.5536\times {10}^{-9}$ | $2.6178\times {10}^{-9}$ | $2.6178\times {10}^{-9}$ | $5.9164\times {10}^{-6}$ | 0.00 | 0.00 |

Sludge production (kg/d) | 160,544.83 | 160,544.92 | 160,545.1 | 162,784.71 | 100,566.85 | 100,565.41 | |

Methane production (kg CH_{4}/d) | 980.17 | 980.48 | 980.47 | 994.22 | 0.00 | 0.00 |

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## Share and Cite

**MDPI and ACS Style**

Vilela, P.; Nam, K.; Yoo, C.
Wastewater Treatment System Optimization for Sustainable Operation of the SHARON–Anammox Process under Varying Carbon/Nitrogen Loadings. *Water* **2023**, *15*, 4015.
https://doi.org/10.3390/w15224015

**AMA Style**

Vilela P, Nam K, Yoo C.
Wastewater Treatment System Optimization for Sustainable Operation of the SHARON–Anammox Process under Varying Carbon/Nitrogen Loadings. *Water*. 2023; 15(22):4015.
https://doi.org/10.3390/w15224015

**Chicago/Turabian Style**

Vilela, Paulina, Kijeon Nam, and Changkyoo Yoo.
2023. "Wastewater Treatment System Optimization for Sustainable Operation of the SHARON–Anammox Process under Varying Carbon/Nitrogen Loadings" *Water* 15, no. 22: 4015.
https://doi.org/10.3390/w15224015