An Optimisation-based Approach for Integrated Water Resources Management

Transcription

1 20 h Euroean Symosum on Comuer Aded Process Engneerng ESCAPE20 S Perucc and G Buzz Ferrars (Edors) 2010 Elsever BV All rghs reserved An Omsaon-based Aroach for Inegraed Waer Resources Managemen Songsong Lu, a Peros Gas, b,c Lazaros G Paageorgou a a Cenre for Process Sysems Engneerng, Dearmen of Chemcal Engneerng, Unversy College London, Torrngon Place, London WC1E 7JE, UK, E-mal: laageorgou@uclacu b Dearmen of Envronmenal Engneerng, Techncal Unversy of Cree, Chana, 73100, Greece c Hellenc Mnsry of Envronmenal Plannng and Publc Wors, (a) General Secreara of Publc Wors,Secal Servce of Publc Wors for Greaer Ahens Sewerage and Sewage Treamen, Varva 12, Ahens, 11474, and (b) Cenral Waer Agency, Passon 147, Ahens, 11251, Greece Absrac Ths aer consders an negraed waer managemen roblem for a regon lacng fresh and ground waer resources, whch comrses (a) he omal lacemen of desalnaon, waer reclamaon and wasewaer reamen lans, (b) he calculaon of he omal caaces of he above facles, and (c) he calculaon of he omal conveyance sysem for desalnaed, reclamed waer and wasewaer Ths roblem s formulaed as a mxed-neger lnear rogrammng (MILP) model, wh an obecve o mnmse he annualsed oal cos ncludng caal and oerang coss Fnally, he roosed model s aled o a real case for he Gree sland of Syros n he Aegean Sea Keywords: negraed waer resources managemen, MILP, desalnaon, wasewaer reamen, waer reclamaon 1 Inroducon In he las decade, omsaon echnques have wdely been used n he feld of negraed waer resources managemen Medellín-Azuara e al [1] aled an economc-engneerng omsaon model o exlore and negrae waer managemen alernaves such as waer mares, reuse and seawaer desalnaon n Ensenada, Mexco Han e al [2] resened a mul-obecve lnear rogrammng model o allocae varous waer resources among mulusers and aled o oban reasonable allocaon of waer suly and demand n Dalan, Chna Cunha e al [3] resened an omsaon model for regonal wasewaer sysems lannng, ogeher wh a smulaed annealng (SA) algorhm o omse layou of sewer newors, locaon of reamen lans, ec Wh he ncreasng waer consumon worlde, sudy of usng varous waer sources avalable o fulfll he waer demand has become an moran ssue recenly In hs wor, we am o develo an omsaon-based aroach usng mxed-neger lnear rogrammng (MILP) echnques for he negraed waer resources managemen n a waer defcen nsular area, where fresh waer moraon s a arcularly exensve and non-susanable oon [4] The alernave waer recourses, whch can mee he demands for waer, are seawaer desalnaon and waer reclamaon from wasewaer

2 S Lu e al 2 Problem Saemen In hs wor, we consder an nsular area whch s waer defcen The waer demand s exclusvely sasfed by desalnaed seawaer and reclamed waer from wasewaer Desalnaon yelds oable qualy waer a a relavely hgh cos, whle reclamed waer can be used for non-oable urban, ndusral and agrculural alcaons a roducon cos sgnfcanly lower o ha of desalnaed waer The area s dvded no several sub-regons based on he oulaon dsrbuon and land erran The omal allocaon n each regon of desalnaon, wasewaer reamen and waer reclamaon lans are o be deermned Wasewaer s colleced from all sources and s conveyed o a wasewaer reamen lan, where s reaed o mee he secfc dscharge lms Then, ar of he reaed wasewaer may undergo furher reamen (a an exra cos) n order o mee he reclamed waer qualy crera, whle he remanng s dscharged no he sea For smlcy, s assumed ha here s no waer loss n he rocess of wasewaer reamen and waer reclamaon The desalnaed waer can be used as oable waer; bu may also be augmened wh reclamed waer for non-oable uses The schemac grah of he waer/wasewaer flows n a regon s gven n Fg 1 I s assumed ha boh quales of waer and wasewaer are allowed o be freely dsrbued among mos of he regons Thus, he nfrasrucure needs for waer dsrbuon and sorage, ncludng he man elne newor, umng saons, and sorage ans, are also omsed Wasewaer Treamen Plan Waer Reclamaon Plan S Q W Q Prmary & Secondary Treamen W sw Terary Treamen Q W rw Q rw W W rw D n Desalnaon Plan Desalnaon P Q Fg 1 Schemac grah of he flows of varous yes of waer and wasewaer Q n In hs roblem, gven are he arwse dsances, umng dsances and elevaons beween he relave oulaon cenres of he regons, daly oable/non-oable waer demand, wasewaer roducon, caal coss of he relave lans wh dfferen szes, roducon coss of desalnaed and reclamed waer, reaed wasewaer, dameers and un coss of elnes (nsalled), un coss, maxmum flow raes and umng elevaons of ums, un sorage cos and sorage reenon me, cos of elecrcy, and waer/wasewaer velocy o deermne he locaons and caaces of he lans, elne man newor characerscs, daly roducon volumes of he lans, daly mans flows of desalnaed waer, reclamed waer and wasewaer, and ums (number and caaces) a each esablshed ln, so as o mnmse he annualsed oal cos, ncludng caal coss for lans, elnes, umng saons, and sorage ans, and oerang/energy coss for waer roducon, wasewaer reamen and umng 3 Mahemacal Formulaon The negraed waer resources managemen roblem s formulaed as an MILP model, as descrbed nex: D Q rw

3 An Omsaon-based Aroach for Inegraed Waer Resources Managemen 31 Mass Flow Balance From Fg 1, we can see ha before he wasewaer reamen n regon, colleced wasewaer flows, Q, lus wasewaer suly, S, s equal o dsrbued wasewaer flows, Q, lus oal wasewaer for reamen, W Q + S = Q W +,, (1) The reaed wasewaer roducon, W, s equal o he summaon of dscharged sw rw wasewaer amoun, W, and reclamed waer roducon, W sw rw W = W + W,, (2) rw rw The reclamed waer roducon, W, lus ncomng reclamed waer flows, Q, and neracve desalnaed waer flow, Q n, s equal o ougong reclamed waer, Q rw, n and non-oable waer demand, D rw n rw rw n Q + Q + W = Q + D,, (3) In he desalnaon lan, he summaon of desalnaed waer roducon, P, and ncomng desalnaed waer, Q, s equal o he summaon of ougong desalnaed n waer, Q, oable waer demand, D, and desalnaed waer flow, Q n Q + P = Q + Q + D,, (4) 32 Plan Caal Cos The caal coss of he desalnaon lans (DPCC), wasewaer reamen lans (WTPCC) and waer reclamaon lans (WRPCC), whch are funcons of lan caaces, are ecewse lnearsed n he model DPCC = CC λ, (5) ~ A λ A =, and λ E =, (6) where CC and A ~ are he cos and caacy a he brea on n he desalnaon lan caal cos funcon n regon, and A are osve varables for he caacy and λ are SOS2 varables, whle bnary varable E ndcaes wheher a desalnaon lan s allocaed n regon Smlar consrans and varables are also defned for he caal cos of wasewaer reamen lans and waer reclamaon lans 33 Pelne Newor Caal Cos There are oenally hree dfferen elne newors, each used for desalnaed waer, wasewaer or reclamed waer The caal cos (PeCC) s calculaed by he un cos of e ye mulled by he lengh of es (L ) We also nroduce bnary varables Y o ndcae f e ye s seleced beween regons and for waer and wasewaer ransoraon The flow rae of waer/wasewaer, Q ~, s deermned by he e dameer (d ) and he flow velocy (v) The daly flow and flow rae of desalnaed waer are relaed by he oeraon me rooron varable, γ We nroduce YG γ Y o lnearse he nonlnear erm, as gven below:

4 S Lu e al ~ ~ Q = Q Y Q YG γ =,,, (7) P P Smlar consrans for he daly flows and flow raes of wasewaer and reclamed waer are also develoed 34 Pumng Saon Caal Cos The cos of a umng saon ncludes he cos of a ar of ums (oerang and sandby) and a shell cos By deermnng he number of each ye of ums seleced, we can ge he umng saon caal cos (PSaCC) For he seleced ums, he maxmum allowable flow rae should be no less han he real flow rae, and he summaon of he um s maxmum umng elevaons should be no less he elevaon beween regons lus he head loss, whch s gven by he Hazen-Wllam Equaon Incororang he e selecon, he head loss from regon o can be wren as: ~ Q Y 1852 ΔH = b α ( ),, (8) 4 87 C d where b s converson consan, α s umng dsance beween regons, and C s roughness coeffcen 35 Sorage Caal Cos The sorage caal cos (SorageCC) s gven by he un sorage cos, daly waer demand (oable and non-oable), and waer reenon days 36 Producon Oerang Cos Smlar o he lan caal coss n Secon 32, he roducon oerang coss are funcons of he waer/wasewaer amouns Pecewse lnear aroxmaons are used o calculae he above roducon oerang coss of desalnaed waer, reaed wasewaer and reclamed waer For desalnaon, P ~ and PEC are he roducon amoun and un energy usage a brea on, EP s he cos of elecrcy and N s he duraon of season P are he daly roducon varables durng season and ξ are SOS2 varables, whle X s a bnary varable, whch s equal o 1 f he desalnaon lan n regon has roducon durng season The annual desalnaon roducon cos (DC) s gven by: ~ DC = N EP PEC P ξ (9) ~ P = P ξ, and ξ = X,, (10) Smlar consrans for annual roducon coss of reaed wasewaer (WTC) and reclamed waer (WRC) are also used here 37 Pumng Cos The umng cos (PumngC) s equal o he umng energy mulled by he cos of elecrcy The daly requred umng energy s gven by he daly waer flow, elevaon, head loss and um effcency By usng Eqs (7) and (8), we have he followng equaons for he umng energy for desalnaed waer: ~ b L Q 1 ~ PumE = ρ g Q H + YG [ ( ) ], (11) 487 β d C where β s he desalnaed waer um effcency, ρ s he waer densy, and g s he gravy The requred umng energy for wasewaer and reclamed waer s derved smlarly

5 An Omsaon-based Aroach for Inegraed Waer Resources Managemen 38 Obecve Funcon The obecve s o mnmse he annualsed oal cos, ncludng he oerang coss and caal coss, whch are annualsed by he recovery caal facor (CRF): OBJ = DC + WTC + WRC + PumngC + n r (1 + r) (12) ( DPCC + WTPCC + WRPCC + PeCC + PSaCC + SorageCC) n (1 + r) 1 where r s he annual neres rae and n s he lengh of he roec n years 4 Case Sudy Now, we aly he roosed model o Syros, an sland n Aegean Sea, Greece The exsng nfrasrucure on he sland s no consdered n he roblem In he roblem, he roec s for 20 years, and an annual neres rae of 5% s used The sland s dvded no 6 regons (R1-R6), and he oulaon cenre for every regon s a sea level, aar from R1 whch s a elevaon of 250 m The waer demands and wasewaer suly vary beween summer me (hgh, 4 monhs) and he res of a year (low, 8 monhs): Table 1 Esmaed daly waer demands and wasewaer suly n Syros (summer/wner) (m 3 /day) R1 R2 R3 R4 R5 R6 oable waer demand 150/ / / / / /300 non-oable waer demand 250/0 900/ /50 880/30 580/30 380/30 wasewaer suly 150/ / / / / /250 The caal cos and oerang roducon cos of he lans are ecewse lnearsed by 4 brea ons, where he caacy/roducon s 100, 1000, 2500 and 5000 m 3 /day, resecvely There are 8 yes of avalable es (4 for desalnaed and reclamed waer and 4 for wasewaer), and 8 yes of ums (4 for desalnaed and reclamed waer and 4 for wasewaer) The waer sorage should sasfy wo days demand n summer me The roosed MILP model has been mlemened n GAMS 228 usng solver CPLEX 111 on a Inel Penum GHz, 100 GB RAM machne The omaly ga was se o 5% There are 1636 consrans, 1009 connuous varables, and 756 neger/bnary varables n he model Afer a comuaonal me of 164 s, an obecve of $2,954,339 s obaned The breadown of he omal annualsed oal cos s gven n Fg 2, whle he omal allocaons of lans n each regon and elne lns are resened n Fg 3 Sorage Cos, $793,599 Pumng Saon Cos, $20,542 Pelne Cos, $166,624 Waer Reclamaon Plan Cos, $94,204 Wasewaer Treamen Plan Cos, $461,876 Treaed Wasewaer Producon Cos, $43,754 Reclamed Waer Producon Cos, $6,774 Desalnaed Waer Producon Cos, $1,048,695 Pumng Cos, $44,128 Desalnaon Plan Cos, $274,144 Fg 2 Breadown of he omal obecve Desalnaon lan Wasewaer reamen lan Waer reclamaon lan Desalnaed waer elne Wasewaer elne Reclamed waer elne Fg 3 Omal lan allocaons/elne lns The omal deals of he omal soluon are shown n Table 2, ncludng nformaon for each esablshed ln (flow/drecon, ye of es, ye and number of ums) The omal daly roducon of each lan s gven n Fg 4

6 S Lu e al ln waer ye* Table 2 Soluon deals for each esablshed ln e dameer (n) flow rae (m 3 /day) drecon um ye (m 3 /day) oerang um no rw rw * : desalnaed waer, rw: reclamed waer, : wasewaer Desalnaon Treamen Reclamaon Daly Volume (m 3 /day) D T R D T R D T R D T R D T R D T R D T R D T R D T R D T R D T R D T R Summer Wner Summer Wner Summer Wner Summer Wner Summer Wner Summer Wner R1 R2 R3 R4 R5 R6 Regon/Season Fg 4 Omal daly roducon/reamen volumes of all lans n summer me and wner me 5 Concludng Remars The roblem of negraed waer and wasewaer resources managemen of a waer defcen sland has been addressed A mxed neger lnear rogrammng model has been roosed for he roblem, by mnmsng he annualsed oal cos The omsaon-based aroach has successfully been aled o he Gree sland of Syros 6 Acnowledgemens The auhors graefully acnowledge Mr George Vaongos for hs asssance on he esmaon of waer demand and wasewaer roducon, Mr Nearos Kasrs for hs asssance n waer and wasewaer umng rsng and calculaons and Mr Chrsos Loums for he esmaon of he reamen facles coss SL acnowledges he fnancal suor from ORSAS, KC Wong Educaon Foundaon, UK FCO, and CPSE References [1] J Medellín-Azuara, LG Mendoza-Esnosa, JR Lund, and RJ Ramírez-Acosa, Waer Sc Technol, 55 (2007) 339 [2] Y Han, S Xu, and X Xu, Waer Resour Manage, 22 (2008) 911 [3] MC Cunha, L Pnhero, J Zeferno, A Anunes, and P Afonso, J Waer Resour Plan Manage-ASCE, 135 (2009) 23 [4] P Gas and G Tchobanoglous, J Envron Manage, 90 (2009) 2601