# Systematic Design, Optimization, and Sustainability Assessment for Generation of Efficient Wastewater Treatment Networks

^{*}

## Abstract

**:**

^{3}, while that for the pharmaceutical WWT is 3.44 USD/m

^{3}. With the treatment of WW, there is a reduction of over 90% ecological burden based on the SPI metric.

## 1. Introduction

_{5}reduction maximization, and wastewater reuse volume maximization using the genetic algorithm for the solution of the nonlinear optimization problem. Bozkurt et al. (2009) [14] used a more generic process model to develop a superstructure-based optimization methodology for WWT. Ku-Pineda and Tan (2006) [15] used the sustainable process index (SPI) as a means of measuring the environmental impact. However, in their work, they only concentrated on the retrofitting of WWNs. Optimizing the cost of treatment as well as sustainability assessment has been given some attention in recent years [5]. However, few studies focus on sustainability assessment using ecological footprints. Therefore, this work uses a superstructure-based approach to minimize the cost of WWT through an MINLP formulation and optimization, as well as employs the sustainable process index (SPI), which is an ecological footprint indicator, as the sustainability assessment metric.

#### 1.1. Stages and Categories in WW Treatment

#### 1.2. WW Treatment Technologies

#### 1.2.1. Pretreatment Technologies

#### 1.2.2. Primary Treatment Technologies

#### 1.2.3. Secondary Treatment Technologies

#### 1.2.4. Tertiary Treatment Technologies

#### 1.3. WW Contaminants and Their Classification

#### 1.4. WW Treatment Using Superstructure and Optimization Approach

#### 1.5. Sustainability Assessment

## 2. Methodology

#### 2.1. Model Building

#### 2.2. Generation of Superstructure and Optimization Technique

#### 2.3. Sustainability Assessment Using the Sustainable Process Index (SPI) Methodology

_{P}is the area needed to dissipate the products sustainably into the ecosystem.

_{R}takes into account the area needed to provide both renewable and non-renewable raw materials. Equation (2) gives the area needed for renewable raw material production, A

_{RR}.

_{RR}(kg/y), in this case, is WW. The annual yield of rainfall, y

_{RR}(kg/m

^{2}y), is estimated using average precipitation rate (from the year 2009 to 2019) data from the United States’ National Oceanic and Atmospheric Administration (NOAA) website [86]. This value is 0.8105 m/y (31.91 in/y). The precipitation rate is multiplied by the density of water and a seeping ratio of 0.3 to give a value of 243.2 kg/m

^{2}y. The area needed to supply non-renewable raw material, as shown by Equation (3), is estimated by using the energy demand to supply one kilogram of the material in question, and the mean industrial energy supply. F

_{RN}(kg/y) is the flow rate of the non-renewable raw material used in the WW treatment. E

_{D,RN}(kWh/kg), which is the energy demand, is estimated using Equation (4). C

_{N}(USD/kg) is the price of the material excluding taxes, while C

_{E}(USD/kWh) is the price of one kilowatt-hour of energy. The annual non-renewable raw material yield is given by y

_{RN}(kWh/m

^{2}y).

_{E}takes into account the area needed to provide energy for the WWT. In estimating this area, any energy carrier, such as coal, oil, and biomass, is treated as a raw material. Equation (5) is used to estimate the area needed to provide energy for the process. F

_{E}(kWh/y) is the energy used in the process, and y

_{E}(kWh/m

^{2}y) is the energy yield. Narodoslawsky and Krotscheck (1995) [80], gave a value of 43 kWh/m

^{2}y for electricity.

_{I}depicts the area needed to provide direct and indirect installation. Direct installation includes the area needed to install the various technologies, while the indirect area accounts for the area needed for other installations, such as pipelines and valves. The direct installation area is derived from the optimization problem. Similar to using the energy demand in estimating the area needed for non-renewable raw material, Equation (6) estimates the area needed for indirect installation. E

_{D,II}(kWh/y) is the energy demand while y

_{I}(kWh/m

^{2}y) is the energy yield.

_{C}is the cross-sectional area of the technologies and A

_{II}is the indirect area.

_{I}(USD) is the cost of the installation, while LS (y) is the life span of the process. The ‘other cost’ category is used for C

_{I}, with plant life of 30 years assumed for LS.

_{S}is the area needed to accommodate the number of workers or staff at the treatment plant. The total number of workers, N

_{S}(cap/y), and the staff yield, y

_{S}(cap/m

^{2}y), are used to estimate the staff area, as shown by Equation (8).

_{P}is the area needed to dissipate the exit product stream from the process into the environmental compartments air, water, and soil. The dissipation is related to the rate of natural regeneration of the environmental compartment. The area needed to dissipate the products is evaluated using the rate of renewal of compartment c (R

_{C}kg/m

^{2}y), the allowable concentration of substance m into the compartment c (C

_{m,C}, kg

_{m}/kg), and the product flow, F

_{m,C}(kg

_{m}/y), of substance m into compartment c. The rate of compost regeneration depicts the rate of soil regeneration. The rate of soil renewal in the United States averages 0.00022 m/y. Assuming the soil is loamy with a 50% pore space, the bulk density is 1300 kg/m

^{3}. Multiplying the density by the rate of soil renewal gives a R

_{soil}value of 0.2926 kg/m

^{2}y. The precipitation rate and seeping ratio used for estimating the yield of water in Equation (2) was used for the rate of regeneration of the water compartment. This value corresponds to the renewable resource yield, y

_{RR}. Shown by Equations (9)–(12) are the equations for calculating the area for dissipation, where A

_{Pc}is the flow of substance m in compartment c, and A

_{PS,c}is the flow of substance m from stream s into compartment c.

#### 2.4. Framework for Optimal Design Evaluation

## 3. Results and Discussions

#### 3.1. Municipal (Regional) Case Study

^{3}, with an equipment purchase cost of USD 48,787. That for the sedimentation unit is 35.43 m

^{2}with a purchase cost of USD 65,122. The adsorption unit has a capacity of 24.31 m

^{3}with a purchase cost of USD 46,522, while the bleaching process has a capacity of 190.45 m

^{3}with an equipment purchase cost of USD 52,377. The purchase cost was annualized for a 30-year plant life. Since the concentration of the solids for the municipal WW is high, the process first selected a primary stage to remove the appreciable amount of the solid contaminants.

^{3}. Out of this cost, the total operating cost (material cost, consumable cost, labor cost, utility cost, and other costs) of WW treated is 1.65 USD/m

^{3}. Table 4 gives a summary of the second and third best treatment networks.

#### 3.2. Pharmaceutical WW Case Study

^{3}/h of WW, and the treatment is for irrigation purposes.

^{2}, with a purchase cost of USD 130,330. This was the highest contributor to the total purchase cost. The mass of flocculants required is 215,464 kg/y, while that for granular activated carbon (GAC) is 280,207 kg/y. The only material cost associated with the pharmaceutical WWT is flocculants cost. Filtration and adsorption contributed to the total cost of consumables. The primary stage dominates the labor cost with a percentage contribution of 30.5%.

^{3}, while that of the operating cost for the treatment process is 3.16 USD/m

^{3}. Table 8 presents a summary of the second and third best treatment networks for this case study.

## 4. Conclusions

^{3}/h, the cost of WWT for municipal WW supersedes the pharmaceutical WW by ~44%. This is because they both have different contaminant characterization and concentrations. Moreover, different technologies were selected at the primary stage treatment process. Based on the sustainability analysis, WWT for reuse proved a better alternative to direct disposal into the environment.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Availability of Code

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**Figure 2.**Stage-wise WWT and some typical technologies. Technologies are classified based on their efficiencies, driving force for separation, and type of contaminant removal.

**Figure 3.**Overall superstructure for WW treatment. The treatment technologies are flocculation (Flc), sedimentation (Sdm), filtration (Ftt), adsorption (Ads), activated sludge (Asl), rotating biological containers (Rbc), disinfection (Dis), membrane bioreactor (Mbrt), advanced oxidation processes (Aop), bleaching (Blc), and membrane processes (Mbr). Bypass (Byp 1,2,3,4) streams become active if a stage does not apply to the treatment process.

**Figure 4.**Optimal path selected for municipal WWT through GAMS. Flocculation (Flc), sedimentation (Sdm), adsorption (Ads), and bleaching (Blc) are the selected technologies. The tertiary stage contributes a percentage of 45.03% to the total cost, followed by the pretreatment, secondary, and primary stages, respectively.

**Figure 5.**Percentage stage-wise cost for municipal WWT. TC is the total treatment cost. It can be noted that the material cost contributes the highest cost to the total treatment cost. Therefore, other alternatives can be used to lower the cost contribution of the materials.

**Figure 6.**Optimal network path and cost distribution for pharmaceutical WWT case study. Selected technologies are flocculation (Flc), filtration (granular) (Ftt), and adsorption (Ads).

**Figure 7.**Percentage distribution of the various cost categories for pharmaceutical WWT case study. Other costs from the primary stage dominated the overall cost of treatment.

**Figure 8.**Sustainable process index (SPI) for the various scenarios. (MWWT = municipal wastewater treatment; DDMWW = direct disposal of municipal wastewater; PWWT = pharmaceutical wastewater treatment; DDPWW = direct disposal of pharmaceutical wastewater).

Contaminant | Concentration | Units |
---|---|---|

Acids/Chlorides | 5 | mg/L |

COD | 68–272 | mg/L |

BOD | 100–400 | mg/L |

Settable Solids | 250–450 | mg/L |

Lead | 30–80 | mg/L |

Zinc | 1 | mg/L |

Nickel | 0.04 | mg/L |

Copper | 40–100 | mg/L |

Specialized Chemicals | <0.5 | µg/L |

Contaminants | Inlet Concentrations (g/m^{3}) | Outlet Specifications (mg/m^{3}) |
---|---|---|

Solids (settleable) | 200 | ≤2 |

Metals (Pb, Cu, Zn, Ni) | 0.1 | ≤0.005 |

Chemicals (acids, chlorides, organics, and inorganics) | 1 | ≤0.001 |

Model Statistics | Values |
---|---|

Equations | 425 |

Variables | 312 |

Discrete Variable | 14 |

Relative Gap | 0.0001 |

Solution Time | 0.188 s |

Solution | USD 1.52 million/y |

Treatment | Treatment Network Pathway | Cost (USD/m^{3} WW) |
---|---|---|

First best (optimal treatment option) | Flc–Sdm–Ads–Blc | 1.92 |

Second best treatment network | Flc–Sdm–Dis–Blc | 5.89 |

Third best treatment network | Flc–Ftt–Dis–Blc | 8.56 |

Contaminants | Concentration (mg/L) |
---|---|

Acetaminophen | 32.5 |

Dextromethorphan HBr | 1.0 |

Guaifenesin | 20.0 |

Phenylephrine HCl | 0.5 |

Contaminants | Entering Stream (g/m^{3}) | Purity Specifications (mg/m^{3}) |
---|---|---|

Solids | 10 | ≤2 |

Metals | 0.01 | ≤0.005 |

Chemicals | 44 | ≤5 |

Pharmaceutical (APIs) | 0.4 | ≤0.02 |

Model Statistics | Values |
---|---|

Equations | 503 |

Variables | 358 |

Discrete Variable | 15 |

Relative Gap | 0.0001 |

Solution Time | 0.125 s |

Solution | USD 2.72 million/y |

**Table 8.**The second and third best treatment options for pharmaceutical WWT. There is a 53.8% increase in the second-best option, and 83.5% increase in the third-best option concerning the optimal treatment option.

Treatment | Treatment Network Pathway | Cost (USD/m^{3} WW) |
---|---|---|

First best (optimal treatment option) | Flc–Ftt–Ads–Byp4 | 3.44 |

Second best treatment network | Flc–Ftt–Dis–Byp4 | 7.45 |

Third best treatment network | Flc–Ftt–Byp3–Blc | 20.80 |

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## Share and Cite

**MDPI and ACS Style**

Aboagye, E.A.; Burnham, S.M.; Dailey, J.; Zia, R.; Tran, C.; Desai, M.; Yenkie, K.M.
Systematic Design, Optimization, and Sustainability Assessment for Generation of Efficient Wastewater Treatment Networks. *Water* **2021**, *13*, 1326.
https://doi.org/10.3390/w13091326

**AMA Style**

Aboagye EA, Burnham SM, Dailey J, Zia R, Tran C, Desai M, Yenkie KM.
Systematic Design, Optimization, and Sustainability Assessment for Generation of Efficient Wastewater Treatment Networks. *Water*. 2021; 13(9):1326.
https://doi.org/10.3390/w13091326

**Chicago/Turabian Style**

Aboagye, Emmanuel A., Sean M. Burnham, James Dailey, Rohan Zia, Carley Tran, Maya Desai, and Kirti M. Yenkie.
2021. "Systematic Design, Optimization, and Sustainability Assessment for Generation of Efficient Wastewater Treatment Networks" *Water* 13, no. 9: 1326.
https://doi.org/10.3390/w13091326