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Groundwater Management Optimization
by ALL_WATER_gw
New problem formulation & additional functionalities.
Dr. Issam NOUIRI National Institute of Agronomy of Tunisia
Tenth Gulf Water Conference, 22-24 April 2012, Doha, Qatar
mailto:[email protected]
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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.
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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.
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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