Groundwater Management Optimization

by ALL_WATER_gw

New problem formulation & additional functionalities.

Dr. Issam NOUIRI National Institute of Agronomy of Tunisia

inouiri@yahoo.fr

Tenth Gulf Water Conference, 22-24 April 2012, Doha, Qatar

mailto:inouiri@yahoo.fr

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Outline

Problematic,

General conceptual model and objective,

Problem formulation and resolution methodology,

ALL_WATER_gw presentation,

Case study application.

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How much water has to be taken from each well ?

Problematic

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FmaxD(se,d) & Cost(se,d)

S(se) S(1)

D(d)

General Conceptual Model

D(1) Demand

site nodes

Transmission

links

Groundwater

nodes

D(d, t) & Qty(d)

Wells

WEAP

MODFLOW

Qty (se) & Vol(se)

Max Abstraction(well) & Max Drawdown(well)

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Objective

The main objective of this work was to

develop a multi-objective optimization

tool for groundwater management.

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))(*))()((

)()((

wIwBOTMwHi

wVMaxDDwDWDWMaxfMin DD

Problem formulation (1/4)

OBJECTIVE FUNCTIONS

),(/)),(),,(( max

1

tdDtdDtdseFDMaxfMinNse

se

DS

d=1,…, NDmax and t=Δt,…, Tmax

Objective 1 :

Satisfy the water demands of the sites “d” at every time step “t”.

OBJECTIVES

Objective 2 :

Minimize the maximal drawdown.

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max max max

max max max

1

max

1

1 1

)()),,((

)),(),()),,(),,()),(),,((),,(((

T

tt

NSE

se

ND

d

D

T

tt

NSE

se

ND

d

D

C

CMaxLCMaxSTtdseF

tseFOStseCCStdseCCLtdseFOLtseVOStdseVOLtdseF

fMin

Problem formulation (2/4)

Objective 3 :

Minimize the unit cost of water.

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t and d se, dseDFtdseFD

),(),,(max

Problem formulation (3/4)

1. Water supply from each groundwater node to any demand site

must be lower than the maximal transmission link capacity.

)max(),( wellQtwellQ 2. Water abstraction from each well must be lower than the maximal

acceptable value.

))(max()),(( wellCellDDtwellCellDD 3. Water drawdown in each well cell must be lower than the maximal acceptable value.

CONSTRAINTS

4. Water quality supplied to each of the demand sites must be lower

than the maximal acceptable value.

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Resolution methodology

1. Multi-objective

Genetic Algorithm

2. PARETO

optimality Concept

21

2DS1 1)1(1 pp

MaxEQag)(fpMaxEQtyfpFitness DD

cfFitness 2

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WEAP - MODFLOW DSS

Start year End year

Historic MODFLOW model

Future MODFLOW model

Present

MODFLOW simulation to

compute the cell heads

Abstractions

optimization

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ALL_WATER_gw

Optimal

Abstractions

WEAP Model

WEAP-MODFLOW

DSS

ALL_WATER_gw in the Framework

WEAP – MODFLOW DSS

MODFLOW

Model

MODFLOW

Historic and

Future Models

User:

Priorities - Constraints

Options - Parameters

Outputs for

analyses

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ALL_WATER_gw User interface

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Read in the

WEAP Area

Read in the

Linkage and

the

MODFLOW

model

Summary of

the inputs

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Objectives and

constraints GA parameters

Objectives weights

Stopping parameters Progression

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Statistics of the

optimal solutions

Proposed optimal solutions

Evaluate and save

optimal solutions

Choose a well

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Case study application

9 groundwater nodes,

16 demand sites,

24 Transmission links,

Period: 1983 – 2015,

Monthly time step,

Optimization 2013-2015,

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WEAP-MODFLOW model for Zeuss Koutine

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Benguerdene Jerba Medenine Other Tataouine Zarzis

Water Demand (not including loss, reuse and DSM)

Scenario: Reference, All months (12)

Jan

1982

Feb

1983

Apr

1984

Jun

1985

Jul

1986

Sep

1987

Nov

1988

Jan

1990

Mar

1991

May

1992

Jul

1993

Sep

1994

Nov

1995

Jan

1997

Mar

1998

May

1999

Jul

2000

Sep

2001

Nov

2002

Jan

2004

Mar

2005

May

2006

Jul

2007

Sep

2008

Nov

2009

Jan

2011

Mar

2012

May

2013

Jul

2014

Sep

2015

Thousand C

ubic

Mete

r

1 500

1 400

1 300

1 200

1 100

1 000

900

800

700

600

500

400

300

200

100

0

Figure . Monthly water demand for domestic and touristic demand sites nodes.

Simulation results

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Reference

changement climatique MODFLOW Cell Head

Layer: 1, Row : 24, Column: 25

Jan

1982

Dec

1982

Dec

1983

Dec

1984

Dec

1985

Dec

1986

Dec

1987

Dec

1988

Dec

1989

Dec

1990

Dec

1991

Dec

1992

Dec

1993

Dec

1994

Dec

1995

Dec

1996

Dec

1997

Dec

1998

Dec

1999

Dec

2000

Dec

2001

Dec

2002

Dec

2003

Dec

2004

Dec

2005

Dec

2006

Dec

2007

Dec

2008

Dec

2009

Dec

2010

Dec

2011

Dec

2012

Dec

2013

Dec

2014

Dec

2015

50

40

30

20

10

0

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Meter

37.5 to 40.0

35.0 to 37.5

32.5 to 35.0

30.0 to 32.5

27.5 to 30.0

25.0 to 27.5

22.5 to 25.0

20.0 to 22.5

17.5 to 20.0

15.0 to 17.5

12.5 to 15.0

10.0 to 12.5

7.5 to 10.0

5.0 to 7.5

2.5 to 5.0

0.0 to 2.5

MODFLOW Cell Head

Year: 2015, Scenario: Reference, Layer: 1, month: December

Column

5048 46

44 4240

38 3634 32

30 2826 24

22 2018 16

14 1210 8

Mete

r

35

30

25

20

15

10

5

0

Row

4240

3836

3432

3028

2624

2220

1816

1412

108

64

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Figure. Overview of the “DEMAND_FRACT.csv” file produced by

ALL_WATER_gw.

Optimization results

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OPTIMIZATION

Reference

Average Cost of Water (per m^3)

All months (12)

Jan

2010

Mar

2010

May

2010

Jul

2010

Sep

2010

Nov

2010

Jan

2011

Mar

2011

May

2011

Jul

2011

Sep

2011

Nov

2011

Jan

2012

Mar

2012

May

2012

Jul

2012

Sep

2012

Nov

2012

Jan

2013

Mar

2013

May

2013

Jul

2013

Sep

2013

Nov

2013

Jan

2014

Mar

2014

May

2014

Jul

2014

Sep

2014

Nov

2014

Jan

2015

Mar

2015

May

2015

Jul

2015

Sep

2015

Nov

2015

U.S

. D

olla

r

2.1

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Figure. Optimized and Reference “Average Cost of Water” (KWh per m3).

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OPTIMIZATION

Reference

MODFLOW Cell Head

Layer: 1, Row : 23, Column: 28

Jan

1982

Oct

1982

Aug

1983

Jun

1984

Apr

1985

Feb

1986

Dec

1986

Oct

1987

Aug

1988

Jun

1989

Apr

1990

Feb

1991

Dec

1991

Oct

1992

Aug

1993

Jun

1994

Apr

1995

Feb

1996

Dec

1996

Oct

1997

Aug

1998

Jun

1999

Apr

2000

Feb

2001

Dec

2001

Oct

2002

Aug

2003

Jun

2004

Apr

2005

Feb

2006

Dec

2006

Oct

2007

Aug

2008

Jun

2009

Apr

2010

Feb

2011

Dec

2011

Oct

2012

Aug

2013

Jun

2014

Apr

2015

54

52

50

48

46

44

42

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

8

6

4

2

0

OPTIMIZATION

Reference

MODFLOW Cell Head

Layer: 1, Row : 23, Column: 30

Jan

1982

Oct

1982

Aug

1983

Jun

1984

Apr

1985

Feb

1986

Dec

1986

Oct

1987

Aug

1988

Jun

1989

Apr

1990

Feb

1991

Dec

1991

Oct

1992

Aug

1993

Jun

1994

Apr

1995

Feb

1996

Dec

1996

Oct

1997

Aug

1998

Jun

1999

Apr

2000

Feb

2001

Dec

2001

Oct

2002

Aug

2003

Jun

2004

Apr

2005

Feb

2006

Dec

2006

Oct

2007

Aug

2008

Jun

2009

Apr

2010

Feb

2011

Dec

2011

Oct

2012

Aug

2013

Jun

2014

Apr

2015

52

50

48

46

44

42

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

8

6

4

2

0

Figure. Optimized and Reference cells heads of two piezometers.

Summary & Conclusions

ALL_WATER_gw can be used in the framework of

WEAP-MODFLOW or as stand alone tool.

It considers the main objectives and constraints for

groundwater management,

For real groundwater, it was able to identify optimal

management solutions,

ALL_WATER_gw is a free tool.

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شكراMerci

Thank You

Danke schön