João Zeferino, Maria C. Cunha e António Antunes on "A robust model for regional wastewater system planning"

1. 0
FACULTY OF SCIENCES
AND TECHNOLOGY
UNIVERSITY OF COIMBRA
Cagliari, 10-12 May 2012
A robust model for regional
wastewater system planning
João Zeferino, Maria C. Cunha e António Antunes

2. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Outline
• I – Problem presentation
• II – Optimization approach
• III – OptWastewater
• IV – Case study
• V – Model results
10-12 FACULTY OF SCIENCES
May
A robust model for regional wastewater system planning AND TECHNOLOGY
UNIVERSITY OF COIMBRA
1

3. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Introduction
• Estimated 2.5 billion people without basic sanitation
– 90% of the wastewater daily discharged in developing countries is untreated
• Millennium Development Goals (1990-2015) :
– target 7C – ENSURE ENVIRONMENTAL SUSTAINABILITY
• Halve, by 2015, the proportion of the population
without sustainable access to safe drinking water
and basic sanitation
• Regional wastewater system planning
– A planning approach at regional level takes advantage of scale economies, while
achieving a better environmental performance.
10-12 FACULTY OF SCIENCES
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A robust model for regional wastewater system planning AND TECHNOLOGY
UNIVERSITY OF COIMBRA
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4. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Regional Wastewater Systems Planning
• The infrastructure for draining and treating wastewater includes the
following facilities:
– Wastewater treatment plants (WWTP) to process the wastewater
before it is discharged into rivers
– Sewer networks connecting the population centers with the WWTP
– Pump stations to lift wastewater if it is unfeasible or uneconomic to drain
it by gravity
10-12 FACULTY OF SCIENCES
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A robust model for regional wastewater system planning AND TECHNOLOGY
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5. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Regional Wastewater Systems Planning
ECONOMIC / ENVIRONMENTAL
• Find the minimum cost configuration • Guarantee the water quality in the
for the system required to drain and river that receives the treated
treat the wastewater wastewater discharges
– Installation costs
– Operation and maintenance costs
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A robust model for regional wastewater system planning AND TECHNOLOGY
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6. I – Problem II – Optimization
III – OptWastewater IV – Case Study IV – Model results
Presentation Approach
Optimization Model
minimize C Objective to optimize (costs)
Continuity QRi
∑Q ji − ∑ Qij = −QRi , i ∈ NS Qji i Qij
j∈N S ∪N I j∈N
∑
Q jl − ∑ Qlj = 0, l ∈ NI
Qjl l Qlj
j∈NS ∪ N I j∈N
∑Q jk = QTk , k ∈ N T
Qjk k
j∈N S ∪ N I
QTk
∑QRi = ∑ QTk
i∈N S k∈NT
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A robust model for regional wastewater system planning AND TECHNOLOGY
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7. I – Problem II – Optimization
III – OptWastewater IV – Case Study IV – Model results
Presentation Approach
Optimization Model
minimize C Objective to optimize (costs)
∑ Q ji − ∑ Qij = −QRi , i ∈ NS
j∈N S ∪ N I j∈N
∑ Q jl − ∑ Qlj = 0, l ∈ NI
j∈NS ∪ N I j∈N
∑ Q jk = QTk , k ∈ NT Continuity
j∈N S ∪ N I
∑QRi = ∑ QTk
i∈N S k∈NT
Capacity
• Bernoulli theorem
QTk ≤ QT maxk . yk , k ∈ NT • Head losses (Manning-Strickler
equation)
Hydraulic • Flow velocity
Q min ij .xij ≤ Qij ≤ Q max ij .xij , i ∈ N S ∪ N I ; j ∈ N
model • Sewer slope
• Diameters commercially availabe
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A robust model for regional wastewater system planning AND TECHNOLOGY
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8. I – Problem II – Optimization
III – OptWastewater IV – Case Study IV – Model results
Presentation Approach
Optimization Model
minimize C Objective to optimize (costs)
∑ Q ji − ∑ Qij = −QRi , i ∈ NS
j∈N S ∪ N I j∈N
∑ Q jl − ∑ Qlj = 0, l ∈ NI
j∈NS ∪ N I j∈N
∑ Q jk = QTk , k ∈ NT Continuity
j∈N S ∪ N I
∑QRi = ∑ QTk
i∈N S k∈NT
QTk ≤ QT maxk . yk , k ∈ NT
Q min ij .xij ≤ Qij ≤ Q max ij .xij , i ∈ N S ∪ N I ; j ∈ N
Capacity
Environmental
DO k ≥ DO min , k ∈ N T
• Based on QUAL2E from EPA
Pk ≤ Pmax , k ∈ N T
Water quality model • Advection-Difusion equation
N k ≤ N max , k ∈ N T
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A robust model for regional wastewater system planning AND TECHNOLOGY
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9. I – Problem II – Optimization
III – OptWastewater IV – Case Study IV – Model results
Presentation Approach
Optimization Model
minimize C Objective to optimize (costs)
∑ Q ji − ∑ Qij = −QRi , i ∈ NS
j∈N S ∪ N I j∈N
∑ Q jl − ∑ Qlj = 0, l ∈ NI
j∈NS ∪ N I j∈N
∑ Q jk = QTk , k ∈ NT Continuity
j∈N S ∪ N I
∑QRi = ∑ QTk
i∈N S k∈NT
QTk ≤ QT maxk . yk , k ∈ NT
Q min ij .xij ≤ Qij ≤ Q max ij .xij , i ∈ N S ∪ N I ; j ∈ N
Capacity
DO k ≥ DO min , k ∈ N T
Pk ≤ Pmax , k ∈ N T Environmental
N k ≤ N max , k ∈ N T
xij ∈ {0,1}, i ∈ N S ∪ N I ; j ∈ N
y k ∈ {0 ,1}, k ∈ N T
QTk ≥ 0, k ∈ N T
Integrality and Nonnegativity
Qij ≥ 0, i ∈ N S ∪ N I ; j ∈ N
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A robust model for regional wastewater system planning AND TECHNOLOGY
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10. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Uncertainty
• Uncertainty in the River Flow → Water quality
– Scenario Planning
• Robust Optimization - Mulvey et al. (1995)
– Involves the use of probabilities for the future scenarios and incorporates mean
and variability measures.
– Allows for possible infeasibilities in the solution for some scenarios.
• The approach embraces two robustness concepts:
– Solution robustness - relates to optimality, that is, whether the solution is
“close” to optimal for any scenario.
– Model robustness - relates to feasibility, that is, whether the solution is
“almost” feasible for any scenario.
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A robust model for regional wastewater system planning AND TECHNOLOGY
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11. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Robust Optimization Model
 
Min C + θ .∑ p s ∑ ∑ ( max { 0; DO max ks − DO pks }) 2  Robust formulation
 s∈S k∈N T p∈N E 
∑ Q ji − ∑ Qij = −QRi , i ∈ NS
j∈N S ∪ N I j∈N
∑ Q jl − ∑ Qlj = 0, l ∈ NI
j∈NS ∪ N I j∈N
∑ Q jk = QTk , k ∈ NT Continuity
j∈N S ∪ N I
∑QRi = ∑ QTk
i∈N S k∈NT
QTk ≤ QT maxk . yk , k ∈ NT
Q min ij .xij ≤ Qij ≤ Q max ij .xij , i ∈ N S ∪ N I ; j ∈ N
Capacity
xij ∈ {0,1}, i ∈ N S ∪ N I ; j ∈ N
y k ∈ {0 ,1}, k ∈ N T
QTk ≥ 0, k ∈ NT
Integrality and Nonnegativity
Qij ≥ 0, i ∈ N S ∪ N I ; j ∈ N
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A robust model for regional wastewater system planning AND TECHNOLOGY
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12. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Solution Method
Legend
• Hybrid algorithm implementation Population center
Possible sewer
Pump station
WWTP
simulated annealing - local improvement : Sewer
– Definition of the initial
incumbent solution
– Definition of the neighborhood
of an incumbent solution
– Definition of the cooling
schedule of the SA algorithm
Parameters: α1 , λ , γ , σ
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A robust model for regional wastewater system planning AND TECHNOLOGY
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13. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
http://sites.google.com/site/optwastewater
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A robust model for regional wastewater system planning AND TECHNOLOGY
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14. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
River Una Basin, Pernambuco
Brazil
Characteristics:
• Area: 6 736 km2
• Total inhabitants: 800 000
• River: 255 km
• 10 river reaches
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A robust model for regional wastewater system planning AND TECHNOLOGY
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15. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Scenarios
 
Min C + θ . ∑ p s ∑ ∑ ( max { 0 ; DO max ks − DO pks }) 2

 s∈ S k∈ N T p∈ N E 
River Reach
DOmaxks
1, 2, 3 and 4 5 and 6 7 and 8 9 and 10 ps
Scenario [ Q min , Q max [ (m 3 /s) (%)
1 [ 1.0 , 1.2 [ [ 2.0 , 2.4 [ [ 4.0 , 4.8 [ [ 8.0 , 9.6 [ 0.68
2 [ 1.2 , 1.4 [ [ 2.4 , 2.8 [ [ 4.8 , 5.6 [ [ 9.6 , 11.2 [ 2.77
3 [ 1.4 , 1.6 [ [ 2.8 , 3.2 [ [ 5.6 , 6.4 [ [ 11.2 , 12.8 [ 7.91
4 [ 1.6 , 1.8 [ [ 3.2 , 3.6 [ [ 6.4 , 7.2 [ [ 12.8 , 14.4 [ 15.92
5 [ 1.8 , 2.0 [ [ 3.6 , 4.0 [ [ 7.2 , 8.0 [ [ 14.4 , 16.0 [ 22.57 River Reach
6 [ 2.0 , 2.2 [ [ 4.0 , 4.4 [ [ 8.0 , 8.8 [ [ 16.0 , 17.6 [ 22.57 1 2 3 4 5 6 7 8 9 10
7 [ 2.2 , 2.4 [ [ 4.4 , 4.8 [ [ 8.8 , 9.6 [ [ 17.6 , 19.2 [ 15.92 Scenario DOm ax ks (mg/L)
8 [ 2.4 , 2.6 [ [ 4.8 , 5.2 [ [ 9.6 , 10.4 [ [ 19.2 , 20.8 [ 7.91 1 7.48 7.04 7.08 7.05 7.06 7.03 7.30 7.01 7.58 7.00
9 [ 2.6 , 1.8 [ [ 5.2 , 5.6 [ [ 10.4 , 11.2 [ [ 20.8 , 22.4 [ 2.77 5 8.04 7.67 7.70 7.72 7.67 7.66 7.89 7.66 8.20 7.66
10 [ 2.8 , 3.0 [ [ 5.6 , 6.0 [ [ 11.2 , 12.0 [ [ 22.4 , 24.0 [ 0.68 10 8.33 8.00 8.00 8.01 8.01 8.00 8.19 8.00 8.36 8.00
10-12 FACULTY OF SCIENCES
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A robust model for regional wastewater system planning AND TECHNOLOGY
UNIVERSITY OF COIMBRA
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16. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Model Solving
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A robust model for regional wastewater system planning AND TECHNOLOGY
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17. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Model Results
 
θ=0
Min C + θ . ∑ p s ∑ ∑ ( max { 0 ; DO max ks − DO pks }) 2
 C = 141.95 M€
 s∈ S k∈ N T p∈ N E 
DOmaxks
DOpks
θ = 0.1 θ = 10
C = 170.21 M€ C = 194.37 M€
DOpks
DOpks
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A robust model for regional wastewater system planning AND TECHNOLOGY
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18. I – Problem II – Optimization
III – OptWastewater IV – Case Study V – Model results
Presentation Approach
Conclusion
• Optimization for regional wastewater systems planning
• Decision support tool – OptWastewater – user friendly
software
• Application to real world situations
• Simulated annealing algorithm calibration
• Robust optimization model
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A robust model for regional wastewater system planning AND TECHNOLOGY
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