Zeferino, Cunha and Antunes - input2012

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

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Zeferino, Cunha and Antunes - input2012

  1. 1. 0 FACULTY OF SCIENCES AND TECHNOLOGY UNIVERSITY OF COIMBRA Cagliari, 10-12 May 2012A robust model for regionalwastewater system planningJoão Zeferino, Maria C. Cunha e António Antunes
  2. 2. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation 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. 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 May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 2
  4. 4. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation 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 May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 3
  5. 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 4
  6. 6. I – Problem II – Optimization III – OptWastewater IV – Case Study IV – Model resultsPresentation 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 5
  7. 7. I – Problem II – Optimization III – OptWastewater IV – Case Study IV – Model resultsPresentation 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 6
  8. 8. I – Problem II – Optimization III – OptWastewater IV – Case Study IV – Model resultsPresentation 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 7
  9. 9. I – Problem II – Optimization III – OptWastewater IV – Case Study IV – Model resultsPresentation 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 8
  10. 10. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation 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. 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 9
  11. 11. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 10
  12. 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 11
  13. 13. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation Approach http://sites.google.com/site/optwastewater 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 12
  14. 14. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation Approach River Una Basin, Pernambuco Brazil Characteristics: • Area: 6 736 km2 • Total inhabitants: 800 000 • River: 255 km • 10 river reaches 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 13
  15. 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 psScenario [ 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 May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 14
  16. 16. I – Problem II – Optimization III – OptWastewater IV – Case Study V – Model resultsPresentation Approach Model Solving 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 15
  17. 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 = 10C = 170.21 M€ C = 194.37 M€ DOpks DOpks 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 16
  18. 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 10-12 FACULTY OF SCIENCES May A robust model for regional wastewater system planning AND TECHNOLOGY UNIVERSITY OF COIMBRA 17

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