# Sustainable Optimization for Wastewater Treatment System Using PSF-HS

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

^{3}/day is first treated with two operations of settling and biological oxidation to eliminate organic material. However, these treatments are not enough to satisfy the water quality standard of 5 ppm (or 5 mg/L) dissolved oxygen (DO) during summertime, which was set by regulation agencies for maintaining aquatic life. Thus, the city is forced to construct additional treatment systems to enhance the effluent quality.

^{3}m

^{3}/day); (2) wastewater amount treated by filtration operations (${Q}_{2}$ 10

^{3}m

^{3}/day); (3) wastewater amount treated by nitrification operations (${Q}_{3}$ 10

^{3}m

^{3}/day); (4) wastewater amount treated by both nitrification and filtration operations (${Q}_{4}$ 10

^{3}m

^{3}/day); and (5) wastewater amount diverted for irrigation and fertilization (${Q}_{5}$ 10

^{3}m

^{3}/day). Table 1 shows the effluent quality after each treatment.

^{3}/day, river DO is 8.0 ppm, river CBOD is 2.0 ppm, and river NBOD is 5.0 ppm, ${C}_{0}$, ${B}_{0}$, and ${N}_{0}$ become as follows:

## 3. Optimization Formulation

^{3}/year), which consists of capital costs (first term in right hand side) and operation and maintenance (O and M) costs (second term), is expressed as follow:

^{3}/year), which consists of capital costs and O and M costs, is expressed as follow:

^{3}/year), which consists of capital cost of transmission pipe, capital cost of the storage system, O and M costs of the storage system, capital cost of irrigation system, O and M costs of the irrigation system, and net benefit of crop farming (crop sales minus land rent), is expressed as follow:

^{3}/day; the constraint in Equation (26) represents that the amount for nitrification should be greater than, or equal to, that for both nitrification and filtration; the constraint in Equation (27) represents that any individual amount cannot exceed the total amount as a non-negative value; the constraint in Equation (28) represents that DO concentration at any point ($x$ km downstream from the discharged point) should be greater than or equal to 5 ppm as regulated. In reality, we cannot test all the points because the number of them is astronomical. Thus, we instead test eight points with an even interval (5 km or 10 km) as previous studies did, which contain the DO sag curve; and the constraint in Equation (29) represents that the nitrate-nitrogen concentration ${c}_{n}$ should be less than, or equal to, 10 ppm as in Equation (2) and the total nitrogen amount should be greater than, or equal to, the crop nitrogen requirement as in Equation (3).

## 4. Parameter-Setting-Free Harmony Search

## 5. Computation Results

^{3}/year) and the average solution of 302.4 ($10

^{3}/year). Meanwhile, with worse parameters (HMCR = 0.5, PAR = 0.5, iterations = 10,000, and 10 runs), it found the best solution of 308.2 ($10

^{3}/year) and the average solution of 312.7 ($10

^{3}/year).

^{3}/year) and the average solution of 207.87 ($10

^{3}/year). PSF-HS successfully produced the solutions without demanding the tedious algorithm parameter setting process. Table 2 shows the computational results of 10 runs from PSF-HS.

^{3}/year) of PSF-HS with the solution vector (${Q}_{1}$ = 0.2; ${Q}_{2}$ = 0.7; ${Q}_{3}$ = 39.1; ${Q}_{4}$ = 34.6; ${Q}_{5}$ = 0.0; $r$ = 6.5) satisfies the minimum DO requirement constraint (DO ≥ 5 ppm) specified in Equation (28) at all river reaches, the maximal nitrate-nitrogen concentration constraint (0.0 ppm ≤ 10 ppm) specified in Equation (2), and the minimal nitrogen requirement constraint specified in Equation (3) (170.04 kg/ha ≥ 170 kg/ha). Figure 2 shows DO sag curve of the best solution ($175.18 × 10

^{3}/year), which satisfies the minimal DO constraint.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

$A$ | irrigated area (ha or 10 ^{4} m^{2}) |

$B$ | carbonaceous biochemical oxygen demand (CBOD) at distance $x$ (ppm) |

${B}_{0}$ | river CBOD right after discharge |

$C(x)$ | dissolved oxygen at a distance $x$ (ppm) |

${C}_{0}$ | river DO right after discharge |

${C}_{ft}$ | filtration cost |

${C}_{ir}$ | irrigation cost |

${C}_{nt}$ | nitrification cost |

${C}_{s}$ | saturation DO (8.0 ppm in this study) |

${c}_{n}$ | nitrate-nitrogen concentration (ppm) in the percolation (≤10 ppm in this study) |

$ct(\cdot )$ | count function |

$ET$ | evapotranspiration amount (cm) during the irrigation period |

HM | harmony memory (solution pool) |

HMCR | harmony memory considering rate (0 ≤ HMCR ≤ 1) |

HMS | harmony memory size (number of solution vectors in HM) |

${k}_{1}$ | rate constants (0.35/day in this study) |

${k}_{2}$ | reaeration rate (0.5/day in this study) |

${k}_{n}$ | rate constants (0.2/day in this study) |

$N$ | nitrogenous biochemical oxygen demand (NBOD) at distance $x$ (ppm) |

${N}_{0}$ | river NBOD right after discharge |

$NC$ | crop nitrogen uptake amount (170 kg/ha in this study) |

$n$ | nitrogen concentration of the diverted amount ${Q}_{5}$ (20 ppm in this study) |

OTM | operation type matrix |

$P$ | precipitation amount (cm) during the irrigation period |

PAR | pitch adjusting rate (0 ≤ PAR ≤ 1) |

${Q}_{1}$ | wastewater amount discharged directly into the river (10 ^{3}m^{3}/day) |

${Q}_{2}$ | wastewater amount treated by filtration operation (10 ^{3}m^{3}/day) |

${Q}_{3}$ | wastewater amount treated by nitrification operation (10 ^{3}m^{3}/day) |

${Q}_{4}$ | wastewater amount treated by both nitrification and filtration operations (10 ^{3}m^{3}/day) |

${Q}_{5}$ | wastewater amount diverted for irrigation and fertilization (10 ^{3}m^{3}/day) |

$r$ | irrigation rate (cm/week) |

$T$ | irrigation period (13 weeks in this study) |

$u$ | river flow velocity (7.9 km/day in this study) |

$x$ | distance from the point of wastewater discharge (km) |

${x}^{New}$ | new harmony (solution vector) |

${x}^{Worst}$ | worst harmony stored in HM |

$\mu $ | integral factor |

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Treatment | Effluent Quality (ppm) | ||
---|---|---|---|

DO | CBOD | NBOD | |

Secondary only (${Q}_{1}$) | 2 | 25 | 54 |

Secondary+Filtration (${Q}_{2}$) | 2 | 13 | 50 |

Secondary+Nitrification (${Q}_{3}-{Q}_{4}$) | 2 | 13 | 10 |

Secondary+Nitrification+Filtration (${Q}_{4}$) | 2 | 7 | 10 |

Run No. | #1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | #9 | #10 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Total Cost (k$/year) | 235.54 | 210.31 | 190.13 | 217.26 | 248.77 | 200.63 | 175.18 | 207.85 | 176.51 | 216.55 | |

${Q}_{1}$ (k ton/day) | 0.16 | 0.28 | 0.19 | 0.45 | 0.34 | 0.34 | 0.19 | 0.87 | 0.12 | 0.30 | |

${Q}_{2}$ (k ton/day) | 0.44 | 0.54 | 1.30 | 0.37 | 0.88 | 0.34 | 0.68 | 0.43 | 0.54 | 0.49 | |

${Q}_{3}$ (k ton/day) | 35.66 | 38.17 | 38.44 | 37.70 | 33.56 | 38.80 | 39.14 | 38.08 | 39.34 | 37.75 | |

${Q}_{4}$ (k ton/day) | 22.49 | 31.78 | 37.49 | 30.77 | 21.38 | 32.67 | 34.64 | 36.41 | 33.53 | 30.27 | |

${Q}_{5}$ (k ton/day) | 3.74 | 1.00 | 0.07 | 1.48 | 5.22 | 0.52 | 0.00 | 0.63 | 0.00 | 1.47 | |

$r$ (cm/week) | 13.07 | 13.07 | 11.75 | 12.96 | 13.07 | 13.07 | 6.54 | 13.07 | 13.07 | 13.07 | |

Crop Nitrogen (≥ 170 kg/ha) | 339.82 | 339.82 | 305.47 | 336.83 | 339.82 | 339.82 | 170.04 | 339.82 | 339.82 | 339.82 | |

Percolation ${c}_{n}$ (≤ 10 ppm) | 9.99 | 9.99 | 8.87 | 9.91 | 9.99 | 9.99 | 0.00 | 9.99 | 9.99 | 9.99 | |

$x$ km (≥ 5 ppm) | 5 | 5.61 | 5.57 | 5.56 | 5.58 | 5.64 | 5.56 | 5.56 | 5.57 | 5.56 | 5.58 |

10 | 5.16 | 5.14 | 5.14 | 5.15 | 5.17 | 5.14 | 5.14 | 5.14 | 5.14 | 5.15 | |

15 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | |

20 | 5.03 | 5.03 | 5.04 | 5.03 | 5.02 | 5.04 | 5.04 | 5.03 | 5.04 | 5.03 | |

25 | 5.16 | 5.17 | 5.18 | 5.17 | 5.15 | 5.18 | 5.18 | 5.17 | 5.18 | 5.17 | |

30 | 5.36 | 5.38 | 5.38 | 5.37 | 5.35 | 5.38 | 5.38 | 5.37 | 5.38 | 5.37 | |

40 | 5.83 | 5.84 | 5.84 | 5.84 | 5.82 | 5.85 | 5.85 | 5.84 | 5.85 | 5.84 | |

50 | 6.29 | 6.29 | 6.29 | 6.29 | 6.27 | 6.30 | 6.30 | 6.29 | 6.30 | 6.29 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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Geem, Z.W.; Kim, J.-H.
Sustainable Optimization for Wastewater Treatment System Using PSF-HS. *Sustainability* **2016**, *8*, 321.
https://doi.org/10.3390/su8040321

**AMA Style**

Geem ZW, Kim J-H.
Sustainable Optimization for Wastewater Treatment System Using PSF-HS. *Sustainability*. 2016; 8(4):321.
https://doi.org/10.3390/su8040321

**Chicago/Turabian Style**

Geem, Zong Woo, and Jin-Hong Kim.
2016. "Sustainable Optimization for Wastewater Treatment System Using PSF-HS" *Sustainability* 8, no. 4: 321.
https://doi.org/10.3390/su8040321