CEMEPE, Skiathos island, Greece, June 24 to 28, 2007

A novel systemic approach to water resources optimization in

areas with limited water resources

E. Kondili1*, M. Mentzos2, C. Papapostolou1

1Optimisation of Production Systems Lab, Mechanical Eng. Dept., TEI Piraeus 2 Lab of Soft Energy Applications & Environmental Protection, TEI Piraeus

Objective of the work

To propose an optimization method for the distribution of water resources under constrained conditions as they appear in the Aegean Islands

Technical and environmental parameters are taken into account on the optimization problem, as well as cost variations of the different supply sources and water uses accordingly

The proposed approach may form the basis for a water planning decision support system in areas with limited water resources

Water shortage, an urgentWater shortage, an urgent problem…problem…

This year, the problem of limited water recourses

has been widely discussed, due to the intense

character of the water shortage.

Many infrastructure projects have been planned for

the islands (especially desalination plants)

If the current weather dominates during the next

year, then the availability of water in the proper

quantity and quality, will become a vital and in some

cases an unfeasible problem

Description of the problem 1/2

In Greece, and more specifically in the Aegean

Islands, water demand and supply is a difficult

problem that needs to be assessed and has

either a temporal character (appears only in

summer months) or a permanent one in extreme

cases (through out the year)

Description of the problem 2/2Description of the problem 2/2

Optimization models, as well as decision support systems have been implemented either for the optimal allocation of water resources or for the optimization of water systems. Nevertheless limited research work has been conducted in the field of the water supply chain management

The water shortage problem occurs when the demand exceeds the local availability and different users have conflicting demands

Water resources management in the Aegean Islands 1/3

Extended water shortage problems are faced in Cyclades and Dodecanese Islands mainly due to:

the geomorphology of the area

the low precipitation rate

the temporal increase of the population (tourists arrival especially in the summer months)

How can this problem be assessed?

with infrastructure projects (dams, reservoirs, or desalination plants)

or by or by ship transfer

Water resources management in the Water resources management in the Aegean Islands 2/3Aegean Islands 2/3

Cyclades complex, is mainly constituted from many small and in their majority arid islands

The medium- large sized ones i.e. Syros, Naxos, etc cover their water needs by desalination plants, dams and the existing groundwater resources

The small ones, acquire the demanded water by ship transfer and storage in inland water tanks

0

50000

100000

150000

200000

250000

300000

350000

WA

TE

R Q

UA

NT

ITY

(m

3 )

1997 1998 1999 2000 2001 2002 2003 2004 2005*

YEAR

IMPORTED WATER QUANTITY IN CYCLADES ISLANDS

During the last decade a water volume of 1,620,000m3 has been transferred to Cyclades with an overall cost 12,524,000 €

Water resources management in the Aegean Islands 3/3

In Dodecanese islands, only the large ones, like Rhodes and Kos, have their own water resources

The rest acquire the demanded quantity through transfer from the large ones

The last years some desalination plants have been constructed The imported quantity in Dodecanese Islands during the last decade has been 1,620,000m3 with an overall cost 12,524,000 €

0

100.000

200.000

300.000

400.000

500.000

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700.000

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WA

TE

R Q

UA

NT

ITIE

S (

m3 )

1997 1998 1999 2000 2001 2002 2003 2004

YEAR

IMPORTED WATER QUANTITIES IN DODECANESE ISLANDS

A Decision Support System implemented in water management…

The proposed optimization model taking into account:

The needs of the various users associated with the type of the water use (agriculture, urban uses, industry)

Their priorities

The type and the availability of water supply resources

Will allocate the water

Maximizing its total value and

Seeking to the optimal exploitation of the available water resources

Basic characteristics of the proposed model 1/2

Typical approach:

Construction of new infrastructure projects or

Water transfer through ships (expensive and unsustainable solution)

In this work an optimization mathematical model has been developed

For the management of the water demand (prioritizing of the needs) and the optimal use of the existing water resources

Criterion:

the maximization of the water value

Basic characteristics of the proposed model 2/2

The objective of this model is to determine:

The appropriate water quantities allocated to each user

The optimal output flows, from each on of the available supply sources

The proposed mathematical model 1/5

Parameters

Bjt Benefit for the use of the water from user j at time interval t (in €/m3)

Djt Demand of water from user j at time interval t (m3)

QjtMIN Minimum water flow to user j at time interval t (m3)

Sit Capacity of the supply source i (m3) at time interval t

Pjt Penalty for not satisfying the demand of user j at time interval t (€/m3)

Vmax Maximum volume of water that can be stored in the storage tank (m3)

Vmin Minimum volume of water that should be stored in the storage tank (m3)

Cit Cost of water from supply source i at time interval t (€/m3)

The proposed mathematical model 2/5

Variables

Fit Flow of water from supply source i at the time interval t (m3)

Qjt Water flow allocated to user j at time interval t (m3)

Vt Water volume stored in the reservoir at time interval t (m3)

The proposed mathematical model 3/5

Optimization criterionMaximize Total Value of Water =

Total Benefit =

Total Cost = Supply Cost + Penalties for the discrepancy between demand and real supply to the users including environmental costs

∑∑ *j

jtjtt

QB

The proposed mathematical model 4/5

Optimization criterion

The benefits represent the water value, and they may be varying with timeThey are determined by the specific area, the time interval and the efficiency of the water uses.

The proposed mathematical model 5/5

Model constraintsThe continuity equation in the water storage tank:

∑+= 1i

ittt FVV - ∑j

jtQ

Upper and lower bounds of the water in the reservoir:

maxmin <=<= VVV t

Capacity limitations of each supply scheme:

itit SF <=

Flows allocated to each user should not exceed the corresponding Demands. Furthermore, it may be desirable to assign a minimum water quantity to some users.

jtjtjt DQQ <=<=min

Case study – Data 1/2

Case study data:

Time horizon 12 months, time step 1 month

Water supply sources

1:Desalination 2: Ground reservoir, 3: Transfer by ships

Water Users A: Urban Use, B: Irrigation

Water Demand (Figure 1)

Benefits (Table 1)

VMAX, VMIN 1.000.000 m3 and 10.000 m3 respectively

Capacity of water supply

S1=300000, S2=200000m3/month, S3=1000000 m3/year

Water supply cost C1t= 3 €/m3, C2t= 4,4 €/m3, C3t= 7 €/m3

Case study – Data 2/2

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1 2 3 4 5 6 7 8 9 10 11 12

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Wate

r Vol

ume

(in

1000m

3)

Urban

I rrigation

Monthly water demand

Months

1 2 3 4 5 6 7 8 9 10 11 12

BAt 5 5 5 15 20 25 25 25 10 5 5 5

BBt 5 5 5 5 5 5 5 5 5 5 5 5

Benefits from the water use (€/m3)

Case study – Results

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1 2 3 4 5 6 7 8 9 10 11 12

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Wat

er V

olum

e (in

100

0m3)

Urban Use

I rrigation

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600

1 2 3 4 5 6 7 8 9 10 11 12

months

Wat

er V

olum

e (in

100

0 m

3)

months

Results, water allocation in the users Model results – water storage

The water is mainly distributed to the water users with the highest water value. Consistently the water quantities stored in the tanks are greater during the winter whilst practically annihilating during the summer

Conclusions

The current model sets the fundamentals for a Decision

Support System which will be able to support the allocation

of the water flows from each supply source, compromising

the demands and priorities that are assigned to each user.

This approach of water systems planning provides the

capability of an integrated study and investigation of the

role of all the system parameters and gives a better insight

to the problem of the optimal allocation of water resources,

considering the value and priorities of the water usage.

Support

This research has been conducted within the framework of the ARCHIMEDES II Environment Funding of Research Groups, cofunded by the EU and the Greek Ministry of Education.