Zeferino, Cunha and Antunes - input2012

0

Cagliari, 10-12 May 2012

FACULTY OF SCIENCES

AND TECHNOLOGY

UNIVERSITY OF COIMBRA

Cagliari, 10-12 May 2012

João Zeferino, Maria C. Cunha e António Antunes

A robust model for regional wastewater system planning

Outline

I – ProblemPresentation

II – Optimization Approach

III – OptWastewater IV – Case Study V – Model results

• I – Problem presentation

• II – Optimization approach

A robust model for regional wastewater system planningFACULTY OF SCIENCES

AND TECHNOLOGY


10-12

May1

• III – OptWastewater

• IV – Case study

• V – Model results

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


AND TECHNOLOGY


10-12

May2

• Regional wastewater system planning

– A planning approach at regional level takes advantage of scale economies, while

achieving a better environmental performance.

• Halve, by 2015, the proportion of the population

without sustainable access to safe drinking water

and basic sanitation

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


AND TECHNOLOGY


10-12

May3

– Pump stations to lift wastewater if it is unfeasible or uneconomic to drain it by gravity

Regional Wastewater Systems Planning




• Guarantee the water quality in the

river that receives the treated

wastewater discharges

ECONOMIC / ENVIRONMENTAL

• Find the minimum cost configuration

for the system required to drain and

treat the wastewater

– Installation costs

– Operation and maintenance costs


AND TECHNOLOGY


10-12

May4

– Operation and maintenance costs

Optimization Model



III – OptWastewater IV – Case Study IV – Model results

Objective to optimize (costs) C minimize

Si

Nj

ij

NNj

ji NiQRQQ

IS

∈−=− ∑∑∈∪∈

,i

QRi

QijQji

Continuity


AND TECHNOLOGY


10-12

May

I

Nj

lj

NNj

jl NlQQ

IS

∈=− ∑∑∈∪∈

,0

Tk

NNj

jk NkQTQ

IS

∈=∑∪∈

,

∑∑∈∈

=TS Nk

k

Ni

i QTQR

l QljQjl

k

QTk

Qjk

5

Optimization Model




Objective to optimize (costs)

Si

Nj

ij

NNj

ji NiQRQQ

IS

∈−=− ∑∑∈∪∈

,

I

Nj

lj

NNj

jl NlQQ

IS

∈=− ∑∑∈∪∈

,0

Tk

NNj

jk NkQTQ

IS

∈=∑∪∈

,

C minimize

Continuity


AND TECHNOLOGY


10-12

May6

∑∑∈∈

=TS Nk

k

Ni

i QTQR

NjNNixQQxQ ISijijijijij ∈∪∈≤≤ ;,.. maxmin

Tk.kmaxk Nk,yQTQT ∈≤

Capacity

Hydraulic

model

• Bernoulli theorem

• Head losses (Manning-Strickler

equation)

• Flow velocity

• Sewer slope

• Diameters commercially availabe

Optimization Model





Si

Nj

ij

NNj

ji NiQRQQ

IS

∈−=− ∑∑∈∪∈

,

I

Nj

lj

NNj

jl NlQQ

IS

∈=− ∑∑∈∪∈

,0

Tk

NNj

jk NkQTQ

IS

∈=∑∪∈

,

C minimize

Continuity


AND TECHNOLOGY


10-12

May7

∑∑∈∈

=TS Nk

k

Ni

i QTQR


Capacity

Tmink Nk,DODO ∈≥

Tmaxk Nk,PP ∈≤

Tmaxk Nk,NN ∈≤

Environmental

Water quality model

• Based on QUAL2E from EPA

• Advection-Difusion equation

Tk.kmaxk Nk,yQTQT ∈≤

Optimization Model





Si

Nj

ij

NNj

ji NiQRQQ

IS

∈−=− ∑∑∈∪∈

,

I

Nj

lj

NNj

jl NlQQ

IS

∈=− ∑∑∈∪∈

,0

Tk

NNj

jk NkQTQ

IS

∈=∑∪∈

,

C minimize

Continuity


AND TECHNOLOGY


10-12

May8

∑∑∈∈

=TS Nk

k

Ni

i QTQR

{ } NjNNix ISij ∈∪∈∈ ;,1,0

{ } Tk Nk,,y ∈∈ 10

Tk NkQT ∈≥ ,0

NjNNiQ ISij ∈∪∈≥ ;,0

Environmental

Integrality and Nonnegativity

Tmink Nk,DODO ∈≥

Tmaxk Nk,PP ∈≤

Tmaxk Nk,NN ∈≤


CapacityTk.kmaxk Nk,yQTQT ∈≤

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 TECHNOLOGY


10-12

May9

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.

Robust Optimization Model




Robust formulation{ }( )

−+ ∑ ∑∑

∈ ∈∈ T EN NS k p

pksks

s

s DOmaxDO;p.C 2 0 max Min θ

Si

Nj

ij

NNj

ji NiQRQQ

IS

∈−=− ∑∑∈∪∈

,

I

Nj

lj

NNj

jl NlQQ

IS

∈=− ∑∑∈∪∈

,0

Continuity


AND TECHNOLOGY


10-12

May10

NjNNj IS ∈∪∈

Tk

NNj

jk NkQTQ

IS

∈=∑∪∈

,

∑∑∈∈

=TS Nk

k

Ni

i QTQR

{ } NjNNix ISij ∈∪∈∈ ;,1,0

{ } Tk Nk,,y ∈∈ 10

Tk NkQT ∈≥ ,0

NjNNiQ ISij ∈∪∈≥ ;,0

Continuity

Integrality and Nonnegativity


CapacityTk.kmaxk Nk,yQTQT ∈≤

Solution Method




• Hybrid algorithm implementation

simulated annealing - local improvement :

– Definition of the initial

incumbent solution

Population center

Possible sewer

Sewer

Pump station

WWTP

Legend


AND TECHNOLOGY


10-12

May11

– Definition of the neighborhood

of an incumbent solution

– Definition of the cooling

schedule of the SA algorithm

Parameters: α1 , λ , γ , σ




http://sites.google.com/site/optwastewater


AND TECHNOLOGY


10-12

May12

River Una Basin, Pernambuco




Brazil


AND TECHNOLOGY


10-12

May13

Characteristics:• Area: 6 736 km2

• Total inhabitants: 800 000

• River: 255 km

• 10 river reaches

Scenarios




{ }( )

−+ ∑ ∑∑


pksks

s



AND TECHNOLOGY


10-12

May14

1, 2, 3 and 4 5 and 6 7 and 8 9 and 10

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

6 [ 2.0 , 2.2 [ [ 4.0 , 4.4 [ [ 8.0 , 8.8 [ [ 16.0 , 17.6 [ 22.57

7 [ 2.2 , 2.4 [ [ 4.4 , 4.8 [ [ 8.8 , 9.6 [ [ 17.6 , 19.2 [ 15.92

8 [ 2.4 , 2.6 [ [ 4.8 , 5.2 [ [ 9.6 , 10.4 [ [ 19.2 , 20.8 [ 7.91

9 [ 2.6 , 1.8 [ [ 5.2 , 5.6 [ [ 10.4 , 11.2 [ [ 20.8 , 22.4 [ 2.77

10 [ 2.8 , 3.0 [ [ 5.6 , 6.0 [ [ 11.2 , 12.0 [ [ 22.4 , 24.0 [ 0.68

ps

(%) [ Qmin

, Qmax

[ (m 3 /s)

River Reach

Scenario

1 2 3 4 5 6 7 8 9 10

1 7.48 7.04 7.08 7.05 7.06 7.03 7.30 7.01 7.58 7.00

5 8.04 7.67 7.70 7.72 7.67 7.66 7.89 7.66 8.20 7.66

10 8.33 8.00 8.00 8.01 8.01 8.00 8.19 8.00 8.36 8.00

Scenario

River Reach

DOmaxks (mg/L)

DOmaxks

Model Solving





AND TECHNOLOGY


10-12

May15

Model Results




DOmaxks

DOpks

C = 141.95 M€

θ = 0

{ }( )

−+ ∑ ∑∑


pksks

s



AND TECHNOLOGY


10-12

May

DOpks

DOpks

θ = 0.1 θ = 10

C = 194.37 M€C = 170.21 M€

16

Conclusion




• Optimization for regional wastewater systems planning

• Decision support tool – OptWastewater – user friendly software


AND TECHNOLOGY


10-12

May

• Application to real world situations

• Simulated annealing algorithm calibration

• Robust optimization model

17

Zeferino, Cunha and Antunes - input2012

Technology

Transcript of Zeferino, Cunha and Antunes - input2012