# Cost Optimization of Wastewater and Septage Treatment Process

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{5}): 82%, chemical oxygen demand (COD): 82%, suspended solids (SS) 91%, total nitrogen (TN): 47%, total Kjeldahl nitrogen (TKN): 71%, ammonia nitrogen (NH

_{4}-N): 70%, total phosphorus (TP): 79%. The research was conducted over a 12-month period using a pilot-scale installation built in one of the municipal WWTP in north-eastern Poland. The SS-VF bed with a 5 m

^{2}surface area and 0.65 m depth was planted with Phragmines australis. The bed consisted of three layers: 0.15 m stones, 0.35 m gravel and 0.15 m sand. The results of research carried out under other conditions and by means of different systems were described by Tan et al. [20] and Bui et al. [21].

## 2. Mathematical Modeling

_{r}[26,27]:

_{r}—expected annual cost (PLN/year), I—investment outlays (PLN), r—discount rate (year

^{−1}), s—depreciation rate (year

^{−1}), K

_{a}—annual operating costs (without depreciation) (PLN/year).

_{1}, the quantity Q

_{1}is directed to the biological section of a municipal WWTP.

_{2}and quantity Q

_{2}is fed into the biological section of a WWTP. There, the mixture of septage (Q

_{1}, S

_{1}) and wastewater (Q

_{2}, S

_{2}) undergoes a treatment process with efficiency η

_{2}, allowing to reduce the concentration of pollutants in wastewater discharged into the receiver (Q

_{1}+ Q

_{2}) to the maximum permissible level (S

_{p}).

_{1}, the amount of Q

_{1}is directed to the biological treatment. The part of that total septage quantity (Q

_{1}· q = Q

_{1′}) is input into the SS-VF bed, where it is pretreated with efficiency η

_{1}. The rest of the septage {(1 − q) · Q

_{1})} is transferred directly into to the biological section of a WWTP. The optimization task is to determine the optimal coefficient of septage stream distribution q = Q

_{1′}/Q

_{1}. For technological reasons, the same septage should be directed to the biological section of a WWTP and excluded from optimization. This is important in the case of large WWTPs, for which a high efficiency of nutrient removal requires addition of an external carbon source [28]. Organic compounds contained in septage may provide an external carbon source for the denitrification process.

_{2}and quantity Q

_{2}) it is transferred into the biological section of the WWTP. There, the mixture of septage (Q

_{1}, S

_{1}) and wastewater (Q

_{2}, S

_{2}) undergoes a treatment process with efficiency η

_{2}, allowing to reduce the concentration of pollutants in wastewater discharged into the receiver (Q

_{1}+ Q

_{2}) to the maximum permissible level (S

_{p}).

## 3. Results

- (1)
- Optimization criterion:

_{1}—expected annual cost of septage pre-treatment in SS-VF bed (PLN/year)

_{2}—expected annual cost of treatment in the biological section of a WWTP (PLN/year).

- (2)
- Decision variables:

- (3)
- Objective function:

_{1}) and the function of the annual cost of treatment in the biological section of a WWTP (K

_{2}):

_{1}—septage flow (m

^{3}/year),

_{2}—wastewater flow (m

^{3}/year),

_{1}—effectiveness of septage pre-treatment in SS-VF bed (–),

_{2}—effectiveness of treatment in the biological section of a WWTP (–),

_{01},α

_{1},γ

_{1}—power regression coefficients of the cost function of septage pre-treatment in SS-VF (–),

_{02},α

_{2},γ

_{2}—power regression coefficients of the cost function of treatment in the biological section of a WWTP (–).

_{0}, α, γ are determined on the basis of real sample data obtained from WWTPs operators. For this purpose, it is necessary to obtain data concerning the expected annual cost of treatment (K

_{r}) and the effectiveness (η) of at least four WWTPs. To determine the power regression coefficients a computer program “Modeling of wastewater treatment costs” was developed (Figure 4) (programmer Malinowski P).

- (4)
- Constraints:

_{1}), (L

_{2}) and (L

_{3}) cannot be greater than the permitted discharged load (L

_{p}):

_{1}—pollution load in septage treated in the SS-VF bed and in the biological section of a WWTP (kg/year),

_{2}—pollution load in septage excluding SS-VF bed (kg/year),

_{3}—pollution load in treated wastewater (kg/year),

_{p}—permissible input pollution load into a receiver (kg/year).

_{1}, Q

_{2,}η

_{1,}η

_{2}—S/A

_{1}—pollutant concentration in septage (g/m

^{3}),

_{2}—pollutant concentration in wastewater (g/m

^{3}),

_{p}—maximum permissible level of the pollutants concentration in wastewater discharged into the receiver (g/m

^{3}).

- (5)
- Constraints of decision variables: q (0; 1 − κ)

- (6)
- Model solution algorithm:

**Stage 1**: Optimization concentrated on η

_{2}

_{2}is sought in which the expected annual cost of treatment in the biological section of a WWTP will be the lowest, i.e.,

_{2}, therefore its minimum possible value resulting from legal requirements concerning the pollutants concentration in wastewater discharged into the receiver should be included, i.e.,

**Stage 2:**Optimization concentrated on the decision variable q

_{2}determined in step 1 will depend on the decision variable q, i.e.,

- (7)
- Computer program:

_{i}) for each variable q

_{i}= iε, assuming the discretization of decision variable q with the step ε = 10

^{−6}, where i = 0, 1, 2, ..., (1/ε). It then selects the value of q

_{i}for which the cost reaches the minimum value. In the next step, the value of η

_{2}is calculated according to previous equations.

- (8)
- Verification of the optimization model and interpretation of the optimization results:

_{5}concentrations and the cost function coefficient.

## 4. Discussion—Verification of the Optimization Model

_{5}load were provided by WWTPs operators.

#### 4.1. Example One

_{5}load contained therein is 12% of the WWTP total load. The input data are shown in Figure 5. The results of optimization are presented in Figure 6.

_{2}) in the BOD

_{5}index from 90.9% to 89.9% (Figure 6a). Figure 6b summarizes the dependence of costs (K

_{1}, K

_{2}, K) on the value of the decision variable (q). As the value of the decision variable (q) increases, the annual cost of septage pre-treatment in the SS-VF bed (K

_{1}) increases (Figure 6c), and the cost of treatment in the biological section of WWTP (K

_{2}) decreases (Figure 6d) together with the total cost of treatment (K) (Figure 6e). Comparison of costs in variant zero and in alternative variant is presented in Table 1.

#### 4.2. Example Two

_{5}load contained therein is 57% of the WWTP total load. The input data are shown in Figure 7. The results of optimization are presented in Figure 8.

_{2}) in the BOD

_{5}index from 94.5% to 89.5% (Figure 8a). Figure 8b summarizes the dependence of costs (K

_{1}, K

_{2}, K) on the value of the decision variable (q). As the value of the decision variable (q) increases, the annual cost of septage pre-treatment in the SS-VF bed (K

_{1}) increases (Figure 8c), and the cost of treatment in the biological section of WWTP (K

_{2}) decreases (Figure 8d) together with the total cost of treatment (K) (Figure 8e). Comparison of costs in variant zero and in alternative variant is presented in Table 2.

#### 4.3. Example Three

_{5}load contained therein is 3% of the total load of the WWTP. The input data are shown in Figure 9. The results of optimization are presented in Figure 10.

_{2}) in the BOD

_{5}index from 90.2% to 90.1% (Figure 10a). Figure 10b summarizes the dependence of costs (K

_{1}, K

_{2}, K) on the value of the decision variable (q). As the value of the decision variable (q) increases, the annual cost of septage pre-treatment in the SS-VF bed (K

_{1}) increases (Figure 10c), and the cost of treatment in the biological section of WWTP (K

_{2}) decreases (Figure 10d). The total cost of treatment (K) is the lowest at q = 0.43 (Figure 10e). Comparison of costs in variant zero and in alternative variant is presented in Table 3.

#### 4.4. Comparison of Examples One to Three

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Sheng, P.; Dong, Y.; Vochozka, M. Analysis of Cost-Effective Methods to Reduce Industrial Wastewater Emissions in China. Water
**2020**, 12, 1600. [Google Scholar] [CrossRef] - Hernandez-Sancho, F.; Molinos-Senante, M.; Sala-Garrido, R. Cost modelling for wastewater treatment processes. Desalination
**2011**, 268, 1–5. [Google Scholar] [CrossRef] - Engin, G.O.; Demir, I. Cost analysis of alternative methods for wastewater handling in small communities. J. Environ. Manag.
**2006**, 79, 357–363. [Google Scholar] [CrossRef] [PubMed] - Boller, M. Small wastewater treatment plants—A challenge to wastewater engineers. Water Sci. Technol.
**1997**, 35, 1–12. [Google Scholar] [CrossRef] - Ignatowicz, K.; Puchlik, M. Rotary biological contactor as alternative for small amount of wastewater treatment. Annu. Set Environ. Prot.
**2011**, 13, 1385–1404. [Google Scholar] - Al-Sa’ed, R.M.Y.; Hithnawi, T.M. Domestic septage characteristic and cotreatment impacts on Albireh Wastewater Treatment Plant efficiency. Diraset Eng. Sci.
**2006**, 33, 187–197. [Google Scholar] - US Environmental Protection Agency. Guide to Septage Treatment and Disposal; EPA Office of Research and Development: Washington, DC, USA, 1994. [Google Scholar]
- Liénard, A.; Payrastre, E. Treatment of sludge from septic tanks in a reed-bed filters pilot system. In Proceedings of the 5th International Conference on Wetland Systems for Water Pollution Control, Vienna, Austria, 15–19 September 1996. [Google Scholar]
- Paing, J.; Voisin, J. Vertical flow constructed wetlands for municipal wastewater and septage treatment in French rural area. Water Sci. Technol.
**2005**, 51, 145–155. [Google Scholar] [CrossRef] [PubMed] - Ingallinella, A.M.; Sanguinetti, G.; Koottatep, T.; Montangero, A.; Strauss, M. The challenge of faecal sludge management in urban areas–strategies, regulations and treatment options. Water Sci. Technol.
**2002**, 46, 285–294. [Google Scholar] [CrossRef] [PubMed] - Kadlec, R.H.; Wallace, S.D. Treatment Wetlands, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2009. [Google Scholar]
- Kołecka, K.; Obarska-Pempkowiak, H.; Gajewska, M. Polish experience in operation of sludge treatment reed beds. Ecol. Eng.
**2018**, 120, 405–410. [Google Scholar] - Jóźwiakowski, K.; Marzec, M.; Kowalczyk-Juśko, A.; Gizińska-Górna, M.; Pytka-Woszczyło, A.; Malik, A.; Listosz, A.; Gajewska, M. 25years of research and experiences about the application of constructed wetlands in south-eastern Poland. Ecol. Eng.
**2019**, 127, 440–453. [Google Scholar] [CrossRef] - Malinowski, P.; Dąbrowski, W. Modeling of Organic Substances and Ammonia Nitrogen Removal in Vertical Flow Constructed Wetlands. J. Ecol. Eng.
**2020**, 21, 231–237. [Google Scholar] [CrossRef] - Kinsley, C.; Crolla, A. Reed Bed Filters to Treat Septage under Canadian Climatic Conditions, AOWMA Annual Conference; Ramada Convention Centre: Edmonton, Alberta, 2013. [Google Scholar]
- Kengne, I.M.; Dodane, P.-H.; Amougou, A.; Koné, D. Vertical–Flow Constructed Wetlands as Sustainable Approach for Feacal Sludge Dewatering in Developing Countries. Desalination
**2009**, 248, 291–297. [Google Scholar] [CrossRef] - Koottatep, T.; Surinkul, N.; Polprasert, C.; Kamal, A.S.M.; Koné, D.; Montangero, A.; Heinss, U.; Strauss, M. Treatment of septage in constructed wetlands in tropical climate: Lessons learnt from seven years of operation. Water Sci. Technol.
**2005**, 51, 119–126. [Google Scholar] [CrossRef] [PubMed] - Koné, D.; Strauss, M. Low-cost options for treating faecal sludge in developing countries–challenges and performance. In Proceedings of the 9th International IWA Specialist Group Conference on Wetlands Systems for Water Pollution Control and to the 6th International IWA Specialist Group Conference on WasteStabilisation Ponds, Avignon, France, 27 September 2004. [Google Scholar]
- Karolinczak, B.; Dąbrowski, W. Effectiveness of septage pre-treatment in vertical flow constructed wetlands. Water Sci. Technol.
**2017**, 76, 2544–2553. [Google Scholar] - Tan, Y.Y.; Tang, F.E.; Saptoro, A.; Khor, E.H. Septage treatment using vertical-flow engineered wetland: A critical review. Chem. Eng. Trans.
**2015**, 45, 1531–1536. [Google Scholar] - Bui, J.J.X.; Tang, F.E.; Tan, Y.Y.; Wong, K.S.; Saptoto, A. Dewatering and Mineralization of Sludge in Vertical Flow Constructed Wetlands: A Review. In Proceedings of the IOP Conference Series: Materials Science and Engineering, International Conference, Sarawak, Malaysia, 26–28 November 2018. [Google Scholar]
- Tyteca, D. Nonlinear programming model of wastewater treatment plant. J. Environ. Eng. Div. Am. Soc. Civ. Eng.
**1981**, 107, 747–766. [Google Scholar] - Gillot, S.; De Clercq, B.; Defour, D.; Simoens, F.; Gernaey, K.; Vanrolleghem, P.A. Optimization of Wastewater Treatment Plant Design and Operation Using Simulation and Cost Analysis. Available online: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.1268&rep=rep1&type=pdf (accessed on 20 September 2020).
- Sid, S.; Volant, A.; Lesage, G.; Heran, M. Cost minimization in a full-scale conventional wastewater treatment plant: Associated costs of biological energy consumption versus sludge production. Water Sci. Technol.
**2017**, 76, 2473–2481. [Google Scholar] [CrossRef][Green Version] - Lange, O. Optimal Decisions. Principles of Programming; PWN: Warsaw, Poland, 1974; pp. 12–14. (In Polish) [Google Scholar]
- Miłaszewski, R. Economic effectiveness of investments in water supply and sewage management and water pollution control. In Materials for Studying Water Supply and Water Pollution Control Economics, 2nd ed.; Cygler, M., Miłaszewski, R., Eds.; Economy and Environment: Białystok, Poland, 2008; pp. 56–64. [Google Scholar]
- Karolinczak, B.; Miłaszewski, R. Application of assessment methods of the economic effectiveness of water supply and sewerage facilities. Annu. Set Environ. Prot.
**2016**, 18, 770–782. (In Polish) [Google Scholar] - Mielcarek, A.; Rodziewicz, J.; Janczukowicz, W.; Struk-Sokołowska, J. The impact of biodegradable carbon sources on nutrients removal in post-denitrification biofilm reactors. Sci. Total Environ.
**2020**, 720, 137377. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**System for wastewater and septage treatment in a municipal wastewater treatment plant (WWTP).

**Figure 3.**Block diagram of the alternative variant of wastewater and septage treatment—optimization issue.

**Figure 5.**Computer program “Cost optimization of wastewater and septage treatment process”, example 1—summary of the input data.

**Figure 6.**Example 1—summary of the dependence of decision variable on: required effectiveness of treatment in biological stage of WWTP (

**a**) and costs K

_{1}, K

_{2}, K (

**b**), cost K

_{1}(

**c**), cost K

_{2}(

**d**) and cost K (

**e**).

**Figure 7.**Computer program “Cost optimization of wastewater and septage treatment process”, example 2—summary of the input data.

**Figure 8.**Example 2—summary of the dependence of decision variable on: required effectiveness of treatment in biological stage of WWTP (

**a**) and costs K

_{1}, K

_{2}, K (

**b**), cost K

_{1}(

**c**), cost K

_{2}(

**d**) and cost K (

**e**).

**Figure 9.**Computer program “Cost optimization of wastewater and septage treatment process”, example 3—summary of the input data.

**Figure 10.**Example 3—summary of the dependence of decision variable on: required effectiveness of treatment in biological stage of WWTP (

**a**) and costs K

_{1}, K

_{2}, K (

**b**), cost K

_{1}(

**c**), cost K

_{2}(

**d**) and cost K (

**e**).

Expected Annual Cost (PLN/Year) | Variant Zero | Alternative Variant |
---|---|---|

Cost of septage pre-treatment in SS-VF bed | - | 2.748 |

Cost of treatment in the biological section of a WWTP | 136.287 | 121.978 |

Total | 136.287 | 124.726 |

Savings in alternative variant | 11.561 (8.5%) |

Expected Annual Cost (PLN/Year) | Variant Zero | Alternative Variant |
---|---|---|

Cost of septage pre-treatment in SS-VF bed | - | 16.485 |

Cost of treatment in the biological section of WWTP | 280.548 | 141.979 |

Total | 280.548 | 158.464 |

Savings in alternative variant | 122.083 (43.5%) |

Expected Annual Cost (PLN/Year) | Variant Zero | Alternative Variant |
---|---|---|

Cost of septage pre-treatment in SS-VF bed | - | 2.597 |

Cost of treatment in the biological section of WWTP | 268.957 | 266.220 |

Total | 268.957 | 268.817 |

Savings in alternative variant | 140 (0.05%) |

Example | Septage Share | Savings in Alternative Variant |
---|---|---|

1. Small WWTP in a rural area | 3% of flow 12% of BOD_{5} load | 8.5% |

2. Small WWTP in a rural area | 23% of flow 57% of BOD_{5} load | 43.5% |

3. WWTP in an urban area | 1% of flow 3% of BOD_{5} load | 0.05% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Karolinczak, B.; Miłaszewski, R.; Dąbrowski, W. Cost Optimization of Wastewater and Septage Treatment Process. *Energies* **2020**, *13*, 6406.
https://doi.org/10.3390/en13236406

**AMA Style**

Karolinczak B, Miłaszewski R, Dąbrowski W. Cost Optimization of Wastewater and Septage Treatment Process. *Energies*. 2020; 13(23):6406.
https://doi.org/10.3390/en13236406

**Chicago/Turabian Style**

Karolinczak, Beata, Rafał Miłaszewski, and Wojciech Dąbrowski. 2020. "Cost Optimization of Wastewater and Septage Treatment Process" *Energies* 13, no. 23: 6406.
https://doi.org/10.3390/en13236406