# 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

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**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% |

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**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