Importance of Cost Functions for Biological Treatment of Wastewater

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Sustainable Advanced Technologies for Industrial Pollution Control (ATIPC 2022)

Abstract

The availability of many technological alternatives for the biological treatment of wastewater, ranging from conventional treatment options to advanced technologies, introduces the requirement for scrutiny to select the most appropriate technology for the treatment of wastewater for any specific project. Use of cost function may be an approach to compare the costs of alternatives for the biological treatment of wastewater. It enables better engineering decisions and suitable selection of the appropriate treatment scheme based on parametric criteria, requirement of space, construction cost and annual cost of operation as well as maintenance. The literatures available in the context of selection of appropriate technology for biological treatment of wastewater on the basis of engineering economics and other issues are limited, and in most of the studies, the cost functions for wastewater treatment plants have been derived from region-specific historic cost data collected. The objective of this paper is to highlight the importance of initiatives to develop the cost functions and present a methodology for its development by the application of modelled algorithms for process design as well as cost estimation and the use of different statistical regression techniques. This research initiative is believed to be useful in the planning of new facilities by the stakeholders of assets.

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Abbreviations

ASP:

Activated sludge process

BOD5:

Five-day biochemical oxygen demand

BODu:

Ultimate biochemical oxygen demand

CAPEX :

Total bare construction cost

CMAS:

Complete-mix activated sludge

COD :

Chemical oxygen demand

EA:

Extended aeration

FAB:

Fluidized aerobic bioreactor

MAPE:

Mean absolute percentage error

MBBR:

Moving bed biofilm reactor

MLD:

Million litres per day

MLSS :

Mixed liquor suspended solids

MLVSS:

Mixed liquor volatile suspended solids

NH4-N:

Ammonia nitrogen

NO3-N:

Nitrate nitrogen

ON:

Organic nitrogen

OP:

Oxidation pond

OPEX :

Levelized cost based on energy requirement, operation and maintenance

SBR:

Sequential batch reactor

TKN:

Total Kjeldahl nitrogen

TP:

Total phosphorous

TSS:

Total suspended solids

UASB:

Upflow anaerobic sludge blanket

VSS:

Volatile suspended solids

WSP:

Waste stabilization pond

WWTP :

Wastewater treatment plant

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Acknowledgement

The research for the development of cost functions with reference to space-saving modern technologies available for biological treatment is under progress and is at an advanced stage. I would like to thank all the members of the Environmental Engineering Division, Department of Civil Engineering, Jadavpur University, Kolkata 700032, India, for their support and assistance.

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Appendix I: Medium-range WWTPs with MBBR

Appendix I: Medium-range WWTPs with MBBR

Design summary for moving bed biofilm reactor basins

BOD removal

  

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

  

5

10

15

20

25

30

35

40

45

50

Design parameter

Unit

Value

Value

Value

Value

Value

Value

Value

Value

Value

Value

Average wastewater flow rate

m3/d

5000.00

10000.00

15000.00

20000.00

25000.00

30000.00

35000.00

40000.00

45000.00

50000.00

Influent flow rate to reactor basins

m3/d

5723.75

11447.50

17171.25

22895.00

28618.75

34342.50

40066.25

45790.00

51513.75

57237.50

Average BOD load

kg/d

1198.90

2397.80

3596.70

4795.60

5994.50

7193.40

8392.30

9591.20

10790.10

11989.00

Average TKN load

kg/d

275.25

550.50

825.75

1101.00

1376.25

1651.50

1926.75

2202.00

2477.25

2752.50

Two stages for BOD removal

Number of tanks for stage 1 (for preliminary BOD removal)

Number

2

3

4

4

4

4

6

6

6

6

Volume of each tank for stage 1 (for preliminary BOD removal)

m3

99.91

133.21

149.86

199.82

249.77

299.73

233.12

266.42

299.73

333.03

Concentration of BOD in effluent from stage 1

g/m3

47.13

47.13

47.13

47.13

47.13

47.13

47.13

47.13

47.13

47.13

Number of tanks for stage 2 (for final BOD removal)

Number

2

3

4

4

4

4

6

6

6

6

Volume of each tank for stage 2 (for final BOD removal)

m3

97.74

130.32

146.60

195.47

244.34

293.21

228.05

260.63

293.21

325.79

Concentration of BOD in effluent from stage 2

g/m3

2.98

2.98

2.98

2.98

2.98

2.98

2.98

2.98

2.98

2.98

Design features

MLSS (XMLSS)

g TSS/m3

5000.00

5000.00

5000.00

5000.00

5000.00

5000.00

5000.00

5000.00

5000.00

5000.00

MLVSS (XMLVSS)

g VSS/m3

2832.63

2832.63

2832.63

2832.63

2832.63

2832.63

2832.63

2832.63

2832.63

2832.63

F/M

(g BOD/d)/g VSS

1.27

1.27

1.27

1.27

1.27

1.27

1.27

1.27

1.27

1.27

Volumetric BOD loading

(kg BOD/d)/m3

3.61

3.61

3.61

3.61

3.61

3.61

3.61

3.61

3.61

3.61

Total sludge (TSS) purged per day

kg TSS/d

1145.43

2290.86

3436.29

4581.72

5727.15

6872.58

8018.01

9163.44

10308.87

11454.30

Observed yield based on VSS

g bVSS/g bCOD

0.34

0.34

0.34

0.34

0.34

0.34

0.34

0.34

0.34

0.34

 

g bVSS/g BOD

0.55

0.55

0.55

0.55

0.55

0.55

0.55

0.55

0.55

0.55

Observed yield based on TSS

g TSS/g bCOD

0.61

0.61

0.61

0.61

0.61

0.61

0.61

0.61

0.61

0.61

 

g TSS/g BOD

0.97

0.97

0.97

0.97

0.97

0.97

0.97

0.97

0.97

0.97

Overall oxygen demand

kg oxygen/h

45.65

91.31

136.96

182.62

228.27

273.93

319.58

365.24

410.89

456.55

Air flow rate at average wastewater flow rate

m3/min

38.92

77.83

116.75

155.66

194.58

233.50

272.41

311.33

350.24

389.16

RAS recycle ratio

Number

0.69

0.69

0.69

0.69

0.69

0.69

0.69

0.69

0.69

0.69

Quality of effluent

Concentration of BOD of effluent

g/m3

9.99

9.99

9.99

9.99

9.99

9.99

9.99

9.99

9.99

9.99

Concentration of TSS of effluent

g/m3

10.00

10.00

10.00

10.00

10.00

10.00

10.00

10.00

10.00

10.00

Concentration of NH4-N of effluent

g/m3

34.19

34.19

34.19

34.19

34.19

34.19

34.19

34.19

34.19

34.19

Concentration of NO3-N of effluent

g/m3

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

Equipment summary for moving bed biological reactor-based system

BOD removal

  

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

  

5

10

15

20

25

30

35

40

45

50

Description

Unit

Value

Value

Value

Value

Value

Value

Value

Value

Value

Value

Primary clarifiers

Number of primary clarifiers

Number

2

2

2

2

2

2

2

4

4

4

Diameter of each primary clarifier

m

10.00

13.50

16.60

19.10

21.40

23.40

25.30

19.10

20.30

21.40

Side water depth of each primary clarifier

m

4.00

4.00

4.00

4.00

4.00

4.00

4.00

4.00

4.00

4.00

Primary clarifier sludge sump

Number of sludge sumps

Number

1

1

1

1

1

1

1

1

1

1

Length of each sludge sump

m

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

Width of each sludge sump

m

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

Depth of each sludge sump

m

3.10

3.10

3.10

3.10

3.10

3.10

3.10

3.10

3.10

3.10

Primary clarifier sludge transfer pumps & pump-house

Number of pump-houses

Number

1

1

1

1

1

1

1

1

1

1

Total number of pumps provided in each pump-house

Number

2

2

2

2

2

2

2

2

2

2

Design capacity for each pump

m3/h

10.00

10.00

10.00

10.00

20.00

20.00

20.00

20.00

30.00

30.00

Head to be developed by each pump

mlc

20.00

20.00

20.00

20.00

20.00

20.00

20.00

20.00

20.00

20.00

Stage 1 of double-stage BOD removal reaction basins & accessories

Number of reactor basins

Number

2

3

4

4

4

4

6

6

6

6

Length of each reactor basin

m

5.50

6.30

6.70

7.70

8.60

9.40

8.30

8.90

9.40

10.00

Width of each reactor basin

m

4.60

5.30

5.60

6.50

7.20

7.90

7.00

7.50

7.90

8.40

Depth of each reactor basin

m

4.57

4.57

4.57

4.57

4.57

4.57

4.57

4.57

4.57

4.57

Stage 2 of double-stage BOD removal reaction basins & accessories

Number of reactor basins

Number

2

3

4

4

4

4

6

6

6

6

Length of each reactor basin

m

5.30

6.10

6.50

7.40

8.40

9.20

8.10

8.60

9.20

9.60

Width of each reactor basin

m

4.60

5.30

5.60

6.50

7.20

7.90

7.00

7.50

7.90

8.40

Depth of each reactor basin

m

4.57

4.57

4.57

4.57

4.57

4.57

4.57

4.57

4.57

4.57

Secondary clarifiers

Number of secondary clarifiers

Number

2

2

2

2

2

2

4

4

4

4

Diameter of each secondary clarifier

m

20.90

28.10

34.50

39.80

44.50

48.70

37.20

39.80

42.20

44.50

Side water depth of each secondary clarifier

m

4.50

4.50

4.50

4.50

4.50

4.50

4.50

4.50

4.50

4.50

Secondary clarifier sludge sump

Number of sludge sumps

Number

1

1

1

1

1

1

1

2

2

2

Length of each sludge sump

m

10.99

21.98

32.97

43.97

54.96

65.95

76.94

43.97

49.46

54.96

Width of each sludge sump

m

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

6.10

Depth of each sludge sump

m

3.10

3.10

3.10

3.10

3.10

3.10

3.10

3.10

3.10

3.10

Secondary clarifier sludge transfer pumps & pump-house

Number of pump-houses

Number

1

1

1

1

1

1

1

1

1

1

Total number of pumps provided in each pump-house

Number

2

2

2

2

2

2

2

2

2

2

Design capacity for each pump

m3/h

170.00

340.00

510.00

680.00

840.00

1010.00

1180.00

1350.00

1510.00

1680.00

Head to be developed by each pump

mlc

20.00

20.00

20.00

20.00

20.00

20.00

20.00

20.00

20.00

20.00

Estimated cost summary for moving bed biological reactor-based system

BOD removal

  

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

  

5

10

15

20

25

30

35

40

45

50

Description

Unit

Value

Value

Value

Value

Value

Value

Value

Value

Value

Value

Primary clarifiers

Total bare construction cost (CAPEX)

Crore ₹

1.05

1.40

1.71

1.97

2.22

2.44

2.65

3.95

4.20

4.44

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of primary clarifiers (OPEX)

Crore ₹

0.31

0.38

0.47

0.54

0.61

0.67

0.73

0.89

0.95

1.01

Overall cost inclusive of CAPEX & OPEX

Crore ₹

1.36

1.77

2.18

2.51

2.83

3.11

3.38

4.84

5.16

5.45

Primary clarifier sludge sump

Total bare construction cost (CAPEX)

Crore ₹

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of primary clarifier sludge sump (OPEX)

Crore ₹

0.14

0.14

0.14

0.14

0.14

0.14

0.14

0.14

0.14

0.14

Overall cost inclusive of CAPEX & OPEX

Crore ₹

0.19

0.19

0.19

0.19

0.19

0.19

0.19

0.19

0.19

0.19

Primary clarifier sludge transfer pumps & pump-house

Total bare construction cost (CAPEX)

Crore ₹

0.67

0.67

0.67

0.67

0.70

0.70

0.70

0.70

0.73

0.73

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of primary clarifier sludge transfer pumps & pump-house (OPEX)

Crore ₹

0.21

0.21

0.21

0.21

0.25

0.25

0.25

0.25

0.28

0.28

Overall cost inclusive of CAPEX & OPEX

Crore ₹

0.87

0.87

0.87

0.87

0.95

0.95

0.95

0.95

1.01

1.01

Stage 1 of double-stage BOD removal reaction basins & accessories

Total bare construction cost (CAPEX)

Crore ₹

0.51

0.95

1.50

1.90

2.31

2.71

3.24

3.60

3.95

4.30

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of stage 1 of double-stage BOD removal reaction basins & accessories (OPEX)

Crore ₹

2.58

4.81

7.05

9.23

11.41

13.56

15.74

17.87

20.00

22.12

Overall cost inclusive of CAPEX & OPEX

Crore ₹

3.09

5.75

8.56

11.13

13.72

16.27

18.98

21.48

23.95

26.42

Stage 2 of double-stage BOD removal reaction basins & accessories

Total bare construction cost (CAPEX)

Crore ₹

0.32

0.54

0.86

1.02

1.19

1.35

1.64

1.79

1.96

2.11

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of stage 2 of double-stage BOD removal reaction basins & accessories (OPEX)

Crore ₹

0.10

0.14

0.20

0.22

0.25

0.27

0.31

0.33

0.35

0.37

Overall cost inclusive of CAPEX & OPEX

Crore ₹

0.42

0.68

1.06

1.25

1.44

1.62

1.95

2.12

2.30

2.48

Blowers and blower-building

Total bare construction cost (CAPEX)

Crore ₹

2.13

3.03

3.75

4.38

4.94

5.35

5.82

6.27

6.69

7.09

Secondary clarifiers

Total bare construction cost (CAPEX)

Crore ₹

2.21

3.04

3.85

4.56

5.25

5.89

8.41

9.13

9.82

10.49

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of secondary clarifiers (OPEX)

Crore ₹

0.60

0.83

1.04

1.24

1.42

1.59

1.94

2.10

2.26

2.41

Overall cost inclusive of CAPEX & OPEX

Crore ₹

2.81

3.87

4.89

5.81

6.67

7.48

10.35

11.23

12.07

12.90

Secondary clarifier sludge sump

Total bare construction cost (CAPEX)

Crore ₹

0.08

0.13

0.18

0.24

0.29

0.34

0.40

0.42

0.47

0.52

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of secondary clarifier sludge sump (OPEX)

Crore ₹

0.14

0.16

0.19

0.21

0.24

0.27

0.30

0.32

0.35

0.37

Overall cost inclusive of CAPEX & OPEX

Crore ₹

0.22

0.29

0.37

0.45

0.53

0.61

0.70

0.74

0.82

0.89

Secondary clarifier sludge transfer pumps & pump-house

Total bare construction cost (CAPEX)

Crore ₹

0.92

1.06

1.16

1.25

1.33

1.41

1.50

1.65

1.80

1.96

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of secondary clarifier sludge transfer pumps & pump-house (OPEX)

Crore ₹

0.69

1.14

1.58

2.02

2.43

2.87

3.31

3.75

4.17

4.61

Overall cost inclusive of CAPEX & OPEX

Crore ₹

1.61

2.20

2.75

3.28

3.76

4.27

4.80

5.40

5.97

6.57

Estimated consolidated costs

Total bare construction cost (CAPEX)

Crore ₹

7.94

10.87

13.74

16.05

18.28

20.26

24.42

27.58

29.66

31.70

Levelized cost based on energy requirement, operation and maintenance for 25 years of life of WWTP

Crore ₹

4.76

7.80

10.89

13.82

16.74

19.61

22.70

25.65

28.49

31.30

Overall cost inclusive of CAPEX & OPEX

Crore ₹

12.70

18.67

24.63

29.87

35.02

39.87

47.12

53.23

58.15

63.00

Cost of land

Cost of land

Crore ₹

3.70

5.65

7.90

9.82

11.72

13.57

16.23

18.57

20.45

22.36

Overall cost

Overall cost

Crore ₹

16.39

24.32

32.52

39.69

46.74

53.44

63.35

71.80

78.60

85.36

Overall cost

Million $

2.05

3.04

4.07

4.96

5.84

6.68

7.92

8.97

9.83

10.67

Regression analysis and determination of MAPE

BOD removal

  

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

Capacity in mld

  

5

10

15

20

25

30

35

40

45

50

Design parameter

Unit

Value

Value

Value

Value

Value

Value

Value

Value

Value

Value

Predicted value (as per exponential cost function)

 

20.94

24.90

29.60

35.19

41.84

49.74

59.13

70.30

83.58

99.37

Value of R2

 

0.9488

Absolute percentage error

 

27.77

2.38

8.98

11.32

10.49

6.93

6.66

2.08

6.33

16.40

Mean absolute percentage error (MAPE)

 

9.94

Predicted value (as per linear cost function)

 

16.45

24.18

31.91

39.63

47.36

55.08

62.81

70.54

78.26

85.99

Value of R2

 

0.9988

Absolute percentage error

 

0.39

0.57

1.89

0.13

1.32

3.07

0.86

1.75

0.43

0.73

Mean absolute percentage error (MAPE)

 

1.12

Predicted value (as per logarithmic cost function)

 

5.39

26.42

38.73

47.46

54.23

59.76

64.44

68.49

72.06

75.26

Value of R2

 

0.9032

Absolute percentage error

 

67.14

8.64

19.08

19.58

16.01

11.82

1.71

4.61

8.32

11.83

Mean absolute percentage error (MAPE)

 

16.87

Predicted value (as per polynomial cost function)

 

16.55

24.21

31.88

39.57

47.27

54.99

62.72

70.47

78.23

86.01

Value of R2

 

0.9988

Absolute percentage error

 

0.99

0.45

1.97

0.29

1.13

2.89

1.00

1.85

0.48

0.75

Mean absolute percentage error (MAPE)

 

1.18

Predicted value (as per power cost function)

 

15.13

25.11

33.77

41.68

49.06

56.05

62.74

69.17

75.39

81.42

Value of R2

 

0.9918

Absolute percentage error

 

7.69

3.25

3.85

5.01

4.95

4.88

0.97

3.66

4.09

4.62

Mean absolute percentage error (MAPE)

 

4.30

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Sengupta, B., Mukherjee, S. (2023). Importance of Cost Functions for Biological Treatment of Wastewater. In: Mazumder, D. (eds) Sustainable Advanced Technologies for Industrial Pollution Control. ATIPC 2022. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. https://doi.org/10.1007/978-3-031-37596-5_6

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