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CEMEPE, Skiathos island, Greece, June 24 to 28, 2007 A novel systemic approach to water resources optimization in areas with limited water resources 1Optimisation 2 E. Kondili1*, M. Mentzos2, C. Papapostolou1 of Production Systems Lab, Mechanical Eng. Dept., TEI Piraeus 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 urgent 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 2/2 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 ship transfer Water resources management in the Aegean Islands 2/3 Cyclades complex, is mainly constituted from many small and in their majority arid islands IMPORTED WATER QUANTITY IN CYCLADES ISLANDS 350000 The small ones, acquire the demanded water by ship transfer and storage in inland water tanks 300000 WATER QUANTITY (m 3) The medium- large sized ones i.e. Syros, Naxos, etc cover their water needs by desalination plants, dams and the existing groundwater resources 250000 200000 150000 100000 50000 0 1997 1998 1999 2000 2001 2002 2003 2004 2005* YEAR 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 last years desalination plants been constructed some have 800.000 700.000 WATER QUANTITIES (m 3) The rest acquire the demanded quantity through transfer from the large ones IMPORTED WATER QUANTITIES IN DODECANESE ISLANDS 600.000 500.000 400.000 300.000 200.000 100.000 0 1997 1998 1999 2000 2001 2002 2003 YEAR The imported quantity in Dodecanese Islands during the last decade has been 1,620,000m3 with an overall cost 12,524,000 € 2004 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 criterion Maximize Total Value of Water = Total Benefit = ∑ ∑B jt * Q jt t j Total Cost = Supply Cost + Penalties for the discrepancy between demand and real supply to the users including environmental costs The proposed mathematical model 4/5 Optimization criterion The benefits represent the water value, and they may be varying with time They are determined by the specific area, the time interval and the efficiency of the water uses. The proposed mathematical model 5/5 Model constraints The continuity equation in the water storage tank: Vt = Vt 1 + ∑Fit i - ∑Q jt j Upper and lower bounds of the water in the reservoir: Vmin <= Vt <= Vmax Capacity limitations of each supply scheme: Fit <= Sit 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. Q jt min <= Q jt <= D jt 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 Monthly water demand Benefits from the water use (€/m3) 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 Case study – Results 3 700 Model results – water storage Water Volume (in 1000 m ) 3 Water Volume (in 1000m ) Results, water allocation in the users 600 Urban Use 500 Irrigation 400 300 200 100 600 500 400 300 200 100 0 0 1 2 3 4 5 6 7 months 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 months months 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 12 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.