Osmotic energy recovery from Reverse Osmosis using two-stage Pressure Retarded Osmosis.

P ep in o Toua i, K., Tadeo, F., & El il, H. (2017). Osmo ic ene gy eco e y om Re e se Osmosis using wo-s age P essu e Re a ded Osmosis. Ene gy, 132, 213-224. Final co ec ed e sion in Jou nal si e: h p://www.sciencedi ec .com/science/a icle/pii/S0360544217308071 Osmo ic ene gy eco e y om Re e se Osmosis using wo-s age P essu e Re a ded Osmosis Khaled Toua ia,b aLabo a o y o Na u al Wa e T ea men - Wa e Resea ches and Technologies Cen e , Techno-pa k Bo j Ced ia, BP 273, 8020, Soliman, Tunisia. Tel: + 216 79325122 / 79325199; Fax: + 216 79325802. bDepa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Valladolid, 47011, Valladolid, Spain. Tel: +34 983423162; Fax: +34 98342316.kha. oua [email protected]. Jacobo Salamancab bDepa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Valladolid, 47011, Valladolid, Spain. Tel: +34 983423162; Fax: +34 98342316. Fe nando Tadeob,* bDepa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Valladolid, 47011, Valladolid, Spain. Tel: +34 983423162; Fax: +34 98342316. *Co esponding au ho : e na[email p o ec ed]. Hamza El ila aLabo a o y o Na u al Wa e T ea men - Wa e Resea ches and Technologies Cen e , Techno-pa k Bo jCed ia, BP 273, 8020, Soliman, Tunisia. Tel: + 216 79325122 / 79325199; Fax: + 216 79325802. el [email protected]. [Esc iba aquí] 2 Abs ac : The in eg a ion o P essu e Re a ded Osmosis (PRO) wi h Seawa e Re e se Osmosis (SWRO) is s udied he e, concen a ing on he e ec on he o e all ene gy consump ion and on he e luen s. Fo his, wo al e na i e designs a e e alua ed: a p e iously s udied one-s age PRO (SWRO-1PRO) and a newly p oposed wo-s age PRO (SWRO-2PRO). The analysis esul s ob ained om ex apola ion o labo a o y da a using models show be e pe o mance o SWRO-2PRO (wi hou using ex e nal impai ed low-salini y wa e lows). The imp o emen o pe o mance hanks o PRO inc eases wi h he inc ease o he eed concen a ion and low. Keywo ds: P essu e Re a ded Osmosis; Seawa e Re e se Osmosis; Ene gy eco e y; Memb ane; Dilu ion Fac o . 1. In oduc ion The Ea h is a wa e y place [1]. Mo e han 71 pe cen o he Ea h's su ace is wa e - co e ed; howe e 97 pe cen o his wa e is saline wi h only 3% eshwa e [2]. Meanwhile, he popula ion is in a cons an need o po able wa e o se e al i al uses such as ag icul u al, indus ial and o he . Consequen ly, wa e sca ci y is becoming an inc easingly signi ican p oblem [3]. A s a is ical s udy showed ha a ound 20% o he wo ld's popula ion li es wi h a lack o po able wa e , while 80% may ace wa e sca ci y du ing he nex decade [4]. One o he p oposed solu ions o ace his wo ldwide p oblem and o o e come he esh wa e sca ci y is saline wa e desalina ion. Se e al desalina ion echniques we e hen comme cialized, such as Mul i-E ec Dis illa ion (MED), Mul i- s age Flash dis illa ion (MSF), Elec odialysis (ED), and Re e se Osmosis (RO) [5]. The RO p ocess is one o he mos popula and an e icien me hod ha leads he desalina ion indus y wi h abou 60% o p oduced wa e [6,7]. Compa ed o a ailable desalina ion p ocesses, RO is conside ed he mos ene gy-e icien echnology. Howe e , i is s ill conside ed ha RO ene gy consump ion should be educed [8]. Speci ic Ene gy Consump ion (SEC) educ ion has monopolized he ocus o echnological inno a ion and esea ch in his sec o . The ene gy cos s in seawa e e e se osmosis (SWRO) plan s may each 50% o he inal cos s o he p oduced wa e . Consequen ly, educing he [Esc iba aquí] 3 ene gy consump ion has been in ensi ely in es iga ed o dec ease he ene gy cos o RO sys ems. The in es iga ions we e ocusing on manu ac u ing high pe o mance memb anes [9], inco po a ing highe e iciency pumps, in eg a ing ene gy eco e y echnologies [10] and enewable ene gies [11]. Salini y g adien ene gy, which is eleased when wo solu ions wi h di e en concen a ions a e mixed, is conside ed o be a p omising sou ce o sus ainable ene gy [12]. P essu e Re a ded Osmosis (PRO) has been one o he mos widely in es iga ed p ocesses [13]. In a PRO p ocess, a semi-pe meable memb ane is used o sepa a e a low concen a ion s eam ( eed solu ion) and a high concen a ion s eam (d aw solu ion) o. I a hyd aulic p essu e lowe han he osmo ic p essu e di e ence be ween he eed and d aw solu ions is applied on he d aw solu ion side, he wa e pe mea es ac oss he memb ane om he eed solu ion o he d aw solu ion. Then, he olume o he d aw solu ion is expanded. The dilu ed d aw solu ion is pa ially dep essu ized h ough a hyd o- u bine o gene a e elec ici y [14]. SWRO b ine could be used as a PRO d aw solu ion o educe he ene gy consump ion o he desalina ion p ocess [15,16]. In ac , his b ine is cha ac e ized by i) ela i ely high concen a ion, ii) p e- ea ed by he RO p e- ea men sys em, iii) con olled by he eco e y demand. These cha ac e is ics may educe he ene gy consump ion by a oiding he p e ea men o PRO d aw solu ion compa ed o a s and-alone PRO uni [17,24]. Mo eo e , The SWRO b ine is s ill an en i onmen al p oblem ha should be sol ed [18]. I is p ojec ed ha 36 million m3/day o desalina ed wa e will be p oduced by SWRO by 2016 [19]. The e o e, simila amoun o b ine will be discha ged in he sea in he same yea . In eg a ing PRO wi h SWRO can be a solu ion o b ine dilu ion be o e being eleased in he sea. As a consequence o hese a ac i e ad an ages, he in eg a ion o PRO in o SWRO has a ac ed he a en ion o many esea che s and se e al s udies a e cu en ly in ol ed in in es iga ing he easibili y o SWRO-PRO sys ems [20-25]. Howe e , o he bes o ou knowledge, no wo ks we e published o s udy he easibili y o in eg a ing wo PRO s ages wi h wo-s age SWRO o wa e and ene gy p oduc ion. In p e ious wo ks, i was shown ha inc easing he numbe o SWRO s ages educes he ene gy consump ion o he p ocess [26]. In he cu en wo k, o he i s ime, a heo e ical s udy discussing he ene gy e iciency o wo-s age SWRO connec ed o wo- s age PRO is de eloped in he cu en wo k. Fo his, a model o he p ocess was de eloped, and he esul s we e compa ed o a simila SWRO-PRO design con aining only a one-s age PRO sub-sys em. In addi ion, a compa ison be ween he pe o mance o p essu e exchange s and PRO in bo h ideal and eal cases ( aking in o accoun he [Esc iba aquí] 4 la es de elopmen s o PRO memb anes and hei de imen al e ec s) was aised o iden i y hei e iciency in ligh o he la es echnological de elopmen . 2. Ma e ial and me hod 2.1. SWRO plan As a case s udy, a SWRO plan o p oducing wa e o an elec olyza ion p ocess is used (see Fig.1), which was de eloped by he company SETA, S-L as a pa o he H2OCEAN p ojec [27]. The desalina ion uni is based on wo independen lines, di ided in o wo s ages. P e- ea men composed o h ee p ocesses: chlo ina ion, ul a- il a ion, and backwash. The i s pass o he SWRO uni begins wi h a chemical ea men o emo e he esidual chlo ine; hen, bisulpha e and an i ouling a e added.A5 mic ons mic o il e is ins alled jus be o e he High P essu e Pump (HP).A P essu e exchange eco e s hyd aulic ene gy om he b ine. The eco e y ac o is selec ed o be 45% o he Fi s Pass and 70% o he Second Pass. The b ine o he second pass goes o an ene gy eco e y sys em be o e being eused in he p oposed osmo ic ene gy eco e y sys em. Fig.1: Two-s age e e se osmosis desalina ion uni . Da ke colo s co espond o mo e concen a ed solu ions and a ow hickness ep esen s he app oxima e low a e. 2.2. SWRO-PRO designs a. “2RO-1PRO”in eg a ion design A simpli ied p esen a ion o he i s SWRO-PRO design is p esen ed in Fig.2: he seawa e low (Qsw) is i s p e-p essu ized using he p essu e exchange PX p io o 1s s age RO 2nd s age RO P essu e exchange s P e- ea ed seawa e B ine o he sea To UF ank To indus ial p ocess HP [Esc iba aquí] 5 en e ing he desalina ion p ocess. Exi ing he i s s age SWRO sub-sys em (RO1) a e wo s eams: esh wa e pe mea e s eam (Qp) and a concen a ed b ine s eam (QR 1). QR 1is hen dep essu ized o each an adequa e p essu e condi ion o he PRO p ocess [28]. The pe mea e o he RO1 eeds he second s age RO sub-sys em (RO2). To eco e he b ine ene gy, an isoba ic o u bocha ged de ice could be used; al e na i ely, a u bine could be used o con e i in o elec ical ene gy. Following his dep essu iza ion, he b ine s eam en e s he PRO sub-sys em as a high salini y (d aw) solu ion (QR 1= QD). The eed solu ion o he PRO sub-sys em is he e en a e o he second s age(QF= QR 2). Th ough osmosis, he p essu ized d aw solu ion ex ac s wa e om he impai ed wa e sou ce unde isoba ic condi ions, esul ing in a dilu ed d aw solu ion (QDR). Th ough osmosis, he p essu ized d aw solu ion ex ac s wa e om he impai ed wa e sou ce unde isoba ic condi ions, esul ing in a dilu ed d aw solu ion (QDR). The ene gy s o ed in he dilu ed d aw solu ion is hen exchanged wi h he seawa e RO1 eed p io o discha ge in o de o eco e i s po en ial ene gy and inc ease he ene gy sa ings o he SWRO-PRO sys em. The PRO eed solu ion bleed QFR is ejec ed o he sea. QP 2 is he pe mea e low o he second RO s age. Fig. 2: Fi s in eg a ion design “2RO-1PRO”. Da ke colo s co espond o mo e concen a ed solu ions and a ow hickness ep esen s he app oxima e low a e. b. “2RO-2PRO”in eg a ion design RO1 RO2 PRO P X Qs 𝐐𝐐𝐏𝐏 𝟏𝟏 𝐐𝐐𝐑𝐑 𝟏𝟏 𝐐𝐐𝐏𝐏 𝟐𝟐 𝐐𝐐𝐑𝐑 𝟐𝟐 Q DR Q FR ERD The sea QD 𝐐𝐐𝐅𝐅=𝐐𝐐𝐑𝐑 𝟐𝟐 [Esc iba aquí] 6 The osmo ic p essu e di e ence be ween he eed and d aw solu ions, Δπ, is one o he mos impo an pa ame e s in he PRO p ocess [29]. In ac , i is he d i ing o ce o he wa e om he d aw side o he eed side. In addi ion, as shown in p e ious wo ks [30,34,35], he ini ial eed low a e ac ion, 𝜙𝜙, de ined as he a io o he ini ial mass low a e o he eed solu ion o he sum o he ini ial mass low a es o bo h eed and d aw solu ions, is also a key pa ame e when ope a ing a cons an applied p essu e. The e o e, o op imize he ene gy p oduc ion, hese wo pa ame e s we e conside ed in he second design, whe e wo PRO sub-sys ems a e connec ed o he p ocess. The d aw solu ion o he i s PRO sub-sys em (PRO1) is he e en a e o he i s RO s age and he eed solu ion is p e- ea ed seawa e , called he e Qad. The amoun o Qad is chosen o be equal o QR 1.Fo his, a con ollable al e (V) is placed o p o ide he desi ed amoun o Qad. The e en a e o he second RO s age eeds he second PRO sub-sys em (PRO2). The swea e bleed om PRO1, QFR, ep esen s he d aw solu ion o he second PRO sub- sys em. QFR is i s ly p essu ized using a high p essu e pump (HP). This p essu e is conside ed o be hal he osmo ic p essu e di e ence be ween he d aw and eed solu ions o PRO2. The p essu ized low Q is hen conduc ed o a u bine o elec ici y gene a ion. I should be poin ed ou he e ha he ene gy eco e y de ice (ERD) is heo e ically unc ionless when Y1≤ 50%. Abo e 50%, pa o he hyd aulic p essu e o RO1 e en a e can be eco e ed o p essu ize he PRO1 seawa e bleed. The sea 𝐐𝐐𝐏𝐏 𝟏𝟏 𝐐𝐐𝐏𝐏 𝟐𝟐 RO1 RO2 𝐐𝐐𝐑𝐑 𝟏𝟏 𝐐𝐐𝐑𝐑 𝟐𝟐 Qs ERD QD PRO1 Q DR P X Q FR 𝐐𝐐𝐅𝐅=𝐐𝐐𝐑𝐑 𝟐𝟐 PRO2 Tu bine Q To he sea Q ad [Esc iba aquí] 7 Fig. 3: Second in eg a ion design “2RO-2PRO”.Da ke colo s co espond o mo e concen a ed solu ions and a ow hickness ep esen s he app oxima e low a e. 2.3. Modeling 2.3.1. The modynamics When we mix wo solu ions wi h di e en composi ions and concen a ions, an ene gy known as he Gibbs ee ene gy o mixing is eleased. This ene gy elease is achie able only unde e e sible p ocess. In a e e sible PRO p ocess, he ene gy p oduced is equal o he Gibbs ee ene gy o mixing [30]. The mola Gibbs ee ene gy o mixing, ΔGm, is he ene gy pe mole o mixed solu ion p oduced in a iso he mal and isoba ic mixing [30] de ined as: ∆Gm=∑xi,Mi ln�γi,Mxi,M�−nF nM∑xi,Fln�γi,Fxi,F� i−nD nM∑xi,Dln�γi,Dxi,D� i (1) Whe e nM, nF, and nD a e he o al amoun s (in moles) o mobile species in he mixed, eed, and d aw solu ions, espec i ely; xi,M, xi,F, and xi,D a e he mole ac ions o species “i” in he mixed, eed, and d aw solu ions, espec i ely; and γi,M, γi,F, and γi,D a e he ac i i y coe icien s o species “i” in he co esponding solu ions. Fo dilu e solu ions, he ac i i y coe icien s a e app oxima ed as uni y. Eq (1) can be simpli ied o be he speci ic Gibbs ee ene gy o mixing pe olume o o al mixed solu ion, by assuming a negligible con ibu ion o he solu e o he olume o he solu ion. The e o e, ∆𝐺𝐺𝑉𝑉 is exp essed as: as a unc ion o he mola concen a ions o he eed, d aw, and mixed solu ions, as well as he eed olume ac ion, 𝜙𝜙: ∆GVM βRT = CMln(CM)−𝜙𝜙CFln(CF)−(1−𝜙𝜙)CDlnCD (2) whe e CF, CD, and CM a e he mola concen a ions o he eed, d aw, and mixed solu ions, espec i ely. 𝜙𝜙 is he low a io de ined as nF/nM=𝜙𝜙, nD/nM = 1- 𝜙𝜙 and β is he an' Ho ac o o s ong elec oly es (e.g., β= 2 o NaCl). Eq. (2) canno be di ec ly used due o he ac ha CM is unknown. A p e ious wo k [30] de eloped an exp ession o he speci ic ideal wo k, 𝑊𝑊QF 0 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖, de ined as ene gy pe uni olume o he ini ial eed solu ion when ΔP = Δπ h oughou e e sible he modynamic: [Esc iba aquí] 8 WQF 0 ideal=∆Gmix,ideal βRT = CFINln(CFIN)−𝜙𝜙CF0ln(CF0)−(1−𝜙𝜙)CD 0ln CD 0 (3) whe e, 𝐶𝐶𝐹𝐹0 and 𝐶𝐶𝐷𝐷 0 a e he ini ial eed and d aw solu ion concen a ions, espec i ely. CFIN is he concen a ion o he mixed solu ion when no longe wa e pe mea ion, in o he wo ds, when he concen a ions o he d aw and eed solu ions a e equals and he ne osmo ic d i ing o ce anishes (i.e., Δπ = 0). The concen a ion CFIN is de ined as [30]: 𝐶𝐶𝐹𝐹𝐹𝐹𝐹𝐹=(1−𝜙𝜙)𝐶𝐶𝐷𝐷 0+𝜙𝜙𝐶𝐶𝐹𝐹0 (4) The amoun o pe mea e, ∆𝑄𝑄𝐹𝐹𝐹𝐹𝐹𝐹, ha ul ima ely passes in o he d aw solu ion can be calcula ed by is exp essed as: ∆𝑄𝑄𝐹𝐹𝐹𝐹𝐹𝐹=𝑄𝑄𝐹𝐹0�1−𝐶𝐶𝐹𝐹 0 𝐶𝐶𝐹𝐹𝐹𝐹𝐹𝐹� (5) The ee ene gy o mixing, ΔGmix,ideal, calcula ed o he second design, is high compa ed o he i s design. A 50% eco e y, he heo e ical maximum ex ac able ene gy is 0.32kWh/m3 compa ed o 0.2kWh/m3 o he i s s age. Theo e ical analysis shows a be e pe o mance o he second design. This s udy is now compa ed wi h ealis ic es0.0ul s de eloped in he up-coming sec ion. [Esc iba aquí] 9 Fig. 4: Gibbs ee ene gy o mixing, ΔGmix,ideal, as a unc ion o RO1 eco e ies o bo h designs desc ibed in sec ion 2.2. The change in ee ene gy o mixing is exp essed as he ene gy eleased pe uni olume o he eed solu ion. The lows QR 1 and QR 2we e calcula ed using eco e ies, Y1 and Y2. 2.3.2 Minimum speci ic ene gy o SWRO plan . Speci ic ene gy consump ion is an impo an pa ame e in RO. I is de ined as pump ene gy consump ion pe uni amoun o p oduced pe mea e wa e . The minimum speci ic ene gy (SE) ep esen s he ene gy needed o p oduce a uni olume o pe mea e, when he applied hyd aulic p essu e is equal o he b ine osmo ic p essu e a exi o he memb ane module. Consequen ly, SE can be exp essed using he ini ial osmo ic p essu e, π eed, and he eco e y a io, Y. A he heo e ical limi o cons an -p essu e ope a ion, he RO sys em ope a es wi h an applied hyd aulic p essu e ha is equal o he inal osmo ic p essu e o he b ine exi ing he RO module. The e o e, he minimum speci ic ene gy o desalina ion o a RO p ocess, SERO,desal, is exp essed as ollows [35]: 0 1 2 3 020 40 60 80 100 ΔG mix,ideal (kWh/m3) Y1(%) Mixing Q1Rwi h Q2R(Design 1) 0 0,5 1 1,5 020 40 60 80 100 ΔG mix,ideal (kWh/m3) Y1(%) Mixing Q1Rwi h Qad (Design 2) 0 0,5 1 1,5 020 40 60 80 100 Δ G mix,ideal (kWh/m3) Y1(%) Mixing Q2Rwi h QFR(Design 2) 0 1 2 3 020 40 60 80 100 ΔG mix,ideal (kWh/m3) Y 1 (%) To al ene gy (Design 2) [Esc iba aquí] 16 he added p e- ea ed seawa e low Qad= QR 1. Respec ing he condi ion QD = QF, he exp ession o he i s s age PRO ene gy p oduc ion, 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 2.1, becomes: 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 2.1=𝛽𝛽𝑅𝑅𝛽𝛽 4(𝐶𝐶𝑅𝑅1−𝐶𝐶𝑑𝑑𝑠𝑠)𝑃𝑃𝐷𝐷𝑃𝑃𝑅𝑅𝑅𝑅1 (23) whe e DFPRO1 is he dilu ion ac o o he second PRO s age. Fig.8 shows he a ia ion o he ene gy eco e ed espec ing he pe o mance o he PRO memb ane o di e en RO1 eco e ies. As expec ed, high eco e ies induce high ene gy p oduc ion due o he inc ease in he osmo ic p essu e o he PRO d aw solu ion. In addi ion, a high pe o mance o he memb ane leads o an inc ease o ene gy by inc easing he dilu ion. Also, he op imized eed low a io 𝜙𝜙 gua an ees he enhancemen o ene gy eco e y, as seen p e iously in sec ion 2.3.3. In his design case, he wo PRO sub-sys ems a e linked, whe e he eed bleed solu ion o PRO1 is he d aw solu ion o PRO2. Consequen ly, he pe o mance o he PRO1 memb ane go e ns ha o PRO2. The d aw solu ion low o PRO2 was calcula ed acco ding o he pe o mance o PRO1, as p esen ed in Fig.9. The a ia ion o QFR is go e ned by he ollowing ela ionship: QFR= Qad�1−DFPRO1� (24) When he dilu ion ac o o he i s PRO s age inc eases, he PRO2 d aw solu ion s eam dec eases and ice- e sa. Howe e , high dilu ions lead o high osmo ic p essu es o PRO2 he d aw solu ion due o he mig a ion o he wa e om Qad o QR 1. This inc ease o osmo ic p essu e is bene icial o ene gy gene a ion, due o he ac ha a high osmo ic p essu e di e ence enhances he PRO p ocess. [Esc iba aquí] 17 Fig.8: Speci ic ene gy p oduc ion 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 1 o he i s PRO sub-sys em (“2RO-2PRO” design) as a unc ion o dilu ions �DFPRO1� o di e en RO1 eco e ies. Fig.9: Amoun o he eed bleed s eam exi ing he i s PRO sub-sys em and i s co esponding osmo ic p essu e as a unc ion o dilu ions �DFPRO1�. Simila o he 2RO-1PRO model de eloped in sec ion 2.3.2, he second PRO sub-sys em o he “2RO-2PRO” design is go e ned by Eq.(22). In ac , he eed and d aw solu ion s eams o PRO2 depend, espec i ely, on Y1 and DFPRO1. Fo his, he en e ing s eams a e no equal, so he dilu ion ac o o he second PRO s age, DFPRO1, should be de e mined based on eco e ies as well as he pe o mance o he i s PRO s age o calcula e he ene gy p oduced. Following he same s eps as sec ion 2.3.3, he speci ic ene gy p oduc ion o PRO2, 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 2, is: 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 2.2=DFPRO2(1−𝜙𝜙)(𝐶𝐶𝐹𝐹𝑅𝑅−𝐶𝐶𝑅𝑅2)𝛽𝛽𝑅𝑅𝛽𝛽 2 (25) 0 0,1 0,2 0,3 020 40 60 80 100 SE1PRO (kWh/m3) DF PRO1 (%) Y1= 30% Y1= 40% Y1= 50% Y1= 60% 0 40 80 120 160 200 020 40 60 80 100 Q FR (m3) DF PRO1 (%) Y1= 30% Y1= 40% Y1= 50% Y1= 60% 0 50 100 150 200 250 300 350 020 40 60 80 100 π FR (ba ) DF PRO1 (%) [Esc iba aquí] 18 whe eDFPRO2is he dilu ion ac o o he second PRO s age. 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 2.2 is p esen ed in Fig.10.As can be clea ly seen, he inc ease o he RO1 eco e y induces a dec ease in he ene gy p oduced. Fo example, he ene gy dec eases by almos 50% when he eco e y is inc eased om 40% o 60%. This beha io is epea able, ega dless o he pe o mance o he memb ane, x. This esul is a ibu ed o he osmo ic p essu e inc ease o QR 1 and he dec ease o QFR low. The ene gy eco e ed by he sys em is he sum o ene gies p oduced by bo h PRO1 and PRO2. The o al Speci ic ene gy p oduc ion 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅1+𝑃𝑃𝑅𝑅𝑅𝑅2 is p esen ed in Fig.11. I can be clea ly seen ha he ene gy p oduced dec eases in line wi h he inc ease o he RO1 eco e y. Fo low dilu ions, he o al ene gy p oduced is no signi ican when ope a ing a low eco e ies. In his si ua ion, he ene gy p oduced becomes signi ican only o high dilu ions (DFPRO2≥60%). Fo example, he ene gy p oduced a 40% dilu ion (x = 0.8) is only 0.13kWh/m3 when Y1=30%, whe eas i is 0.7kWh/m3 a 80% dilu ion, which co esponds o mo e han a i e imes inc ease o only a doubled dilu ion. Fo ela i ely high eco e ies, o al SEPRO is s ill signi ican when he dilu ion is ela i ely low. In sum, a low eco e ies and ela i ely high dilu ion, he con ibu ion o he second PRO s age in ene gy eco e y is mo e impo an in compa ison o he second PRO s age. Howe e , a high eco e y a es, he i s PRO s age con ibu es mo e in ene gy eco e y. As a compa ison be ween he wo designs, Fig.7 and Fig.11 show ha he pe o mance o “2RO-2PRO” is much be e han “2RO-1PRO”. As mos desalina ion plan s ope a e unde 40%-50% eco e y a es, he ene gy ha can be p oduced using “2RO-1PRO” anges be ween 0.11 o 0.19kWh/m3. Fo “2RO-2PRO”, he ene gy anges be ween 0.7 o 0.93 kWh/m3. O cou se he addi ion o a second PRO s age will inc ease he capi al cos o he SWRO-PRO p ocess, bu an economic s udy should be ca ied ou o con i m o deny he easibili y o his design. Compa ed o he heo e ical alues o ex ac able ene gy (e.g. Gibbs ene gy o mixing), he ealis ic esul s a e a om he heo e ical calcula ed ene gy. In ac , his expec ed esul is caused by he low mixing a e due o memb ane pe o mance and ene gy losses ( ic ional losses and unused ene gy). [Esc iba aquí] 19 Fig.10: Speci ic ene gy p oduc ion 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅 2 o he second PRO sub-sys em (“2RO-2PRO” design) as a unc ion o dilu ions �DFPRO2� o di e en RO1 eco e ies. 0 0,2 0,4 0,6 0,8 1 1,2 1,4 020 40 60 80 100 SEPRO (kWh/m3) DFPRO2(%) x=0.3 x=0.5 x=0.8 Y1=30% 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 020 40 60 80 100 SEPRO (kWh/m3) DF PRO2 (%) x=0.3 x=0.5 x=0.8 Y1=40% 0 0,1 0,2 0,3 0,4 0,5 0,6 020 40 60 80 100 SEPRO (kWh/m3) DF PRO 2(%) x=0.3 x=0.5 x=0.8 Y1=50% 0 0,1 0,2 0,3 0,4 020 40 60 80 100 SEPRO (kWh/m3) DF PRO 2(%) x=0.3 x=0.5 x=0.8 Y1=60% [Esc iba aquí] 20 Fig.11: To al Speci ic ene gy p oduc ion 𝑆𝑆𝑆𝑆𝑃𝑃𝑅𝑅𝑅𝑅1+𝑃𝑃𝑅𝑅𝑅𝑅2 o he “2RO-2PRO” design as a unc ion o dilu ions �DFPRO1� o di e en RO1 eco e ies. 2.4. Maximum o dilu ion model alida ion Du ing he p e ious sec ion, he dilu ion ac o was modeled based on he memb ane pe o mance and he eed low a io o es ima e he ene gy p oduced by PRO, especially when he PRO en e ing lows a e no equal. To e i y he DF model, ΔQ is de e mined using p essu e and low balances o he “2RO-1PRO” design. The same me hodology can be used o he second con igu a ion “2RO-2PRO”. The powe eco e ed in PRO is maximized he osmo ic p essu e di e ence be ween he eed and d aw solu ions is equal o he hyd aulic p essu e di e ence ΔP. The d aw solu ion exi s he module unde an osmo ic p essu e equal o he sum o he osmo ic p essu e o he eed low,QR 2, and he applied hyd aulic p essu e ΔP. This equilib ium can be desc ibed as ollows: 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 020 40 60 80 100 SEPRO1+PRO2(kWh/m3) DF PRO1 (%) Y1=30% x=0.3 x=0.5 x=0.8 0 0,2 0,4 0,6 0,8 1 1,2 020 40 60 80 100 SEPRO1+PRO2(kWh/m3) DF PRO1 (%) Y1=40% x=0.3 x=0.5 x=0.8 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 020 40 60 80 100 SEPRO1+PRO2(kWh/m3) DF PRO1 (%) Y1=50% x=0.3 x=0.5 x=0.8 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 020 40 60 80 100 SE PRO1+PRO2 (kWh/m 3 ) DF PRO1 (%) Y1=60% x=0.3 x=0.5 x=0.8 [Esc iba aquí] 21 πR 2+∆P = Qswπsw (1−Y1)Qsw+∆Q (26) whe e πR 2 is he osmo ic p essu e o he second s age ejec ed wa e . Simila ly, he eed low exi s he module unde an osmo ic p essu e equal o he osmo ic p essu e o QR 1, sub ac ed om he applied hyd aulic p essu e ΔP. The equilib ium condi ion a he d aw inle side o he PRO module is exp essed as: πsw=QR 2πR 2 QR 2−∆Q+∆P (27) As men ioned p e iously, he op imum applied p essu e is he hal o he osmo ic p essu e di e ence. Hence, , ΔP is exp essed in his case as: ∆P = πsw 2(1−Y1) (28) To calcula e ΔQ, Eqs. (26) and (27) a e sol ed simul aneously using he condi ion p esen ed in Eq. (28). Sol ing he equa ion sys em yields: ∆Q = QR 2�1−πR 2 πsw2−2Y1 1−2Y1� (29) Finally, he exp ession o he dilu ion ac o is: DF =∆Q QR 1= Y11−Y2 1−Y1�1−πR 2 πsw2−2Y1 1−2Y1� (30) Fo he c i ical eco e y Y1=50%, he dilu ion ac o is calcula ed using: lim 𝑌𝑌1→0.5𝑃𝑃𝐷𝐷= 0.3 (31) Fig.12 shows he esul s o maximum dilu ion ob ained using Eq.(30) o di e en eco e ies using he “2RO-1PRO” design. This esul is compa ed o Fig.6 ( igh , x=1). I can be seen clea ly ha he esul s a e simila o he ange o eco e y s udied. The [Esc iba aquí] 22 same me hodology is used o calcula e he maximum dilu ion o he second design by modi ying Eqs. (26), (27), (28) and (29) using he co esponding s eams and osmo ic p essu es. Fig.12: Maximum dilu ion o di e en RO1 eco e ies. 3. E ec o he SWRO ini ial eed concen a ion Csw and s eam Qsw The impac o eed salini y upon he pe o mance o he PRO p ocess was e alua ed using h ee eed salini ies; 35, 40 and 45 g/L (0.6, 0.68 and 0.77M) o bo h p oposed designs. This ange o concen a ion simula es he dis ibu ion o he seawa e salini y wo ldwide. The dilu ion ac o was chosen a bi a ily o be 60%. Fig.13 shows he a ia ion o he speci ic ene gy p oduc ion o he SWRO-PRO p ocess. I is ob ious ha he inc ease o he RO eed concen a ion leads o he inc ease o he ene gy p oduced ega dless o he design used. In ac , he RO eed concen a ion inc ease inc eases he concen a ion o he RO b ine, which is he d aw solu ion o he PRO sub-sys ems; hen he osmo ic p essu e di e ence inc eases and enhances he wa e passage ac oss he memb ane. Fo (A), which p esen s he esul s o he i s design, he inc ease o he concen a ion om 35 o 45g/L induces an inc ease o he eco e ed ene gy o only 0.02kWh/m3 a 50% eco e y. Fo (B), he second design case, he ene gy eco e ed is 0.1kWh/m3a 50% eco e y. Howe e , unde he same condi ions, he ene gy consump ion SECSWRO inc eases by 0.86kWh/m3. This ac shows ha he ene gy consump ion inc ease a e is much mo e apid han he ene gy eco e ed inc ease a e when he eed salini y inc eases. The e ec o he inle RO eed s eam is also discussed. The amoun o he ini ial Qsw was a ied om 256m3/h o 50000m3/h and he dilu ion ac o was chosen a bi a ily o be 60% o bo h PRO s ages. The inc ease o he RO capaci y enhances he ene gy eco e y 12,3 19,8 30,0 45,3 0 10 20 30 40 50 60 30 40 50 60 Maximum o dilu ion (%) Y 1 (%) [Esc iba aquí] 23 o bo h s udied designs. This ac is due o he inc ease o wa e lux ac oss he PRO memb ane which inc eases he ou pu ene gy. I can also be seen ha he ene gy inc ease ends o each a maximum whe e he inc ease o he Qsw has no e ec (Fig 13-C and D). The la e esul is a ibu ed o he ac ha he inc eases o Qsw leads o he dec ease o 𝜙𝜙 a low alues (𝜙𝜙 <<0.5), which limi s he pe o mance o he PRO. Inc easing he ini ial eed low will ce ainly inc ease he capi al cos o he SWRO-PRO p ocess because o he need o a g ea e PRO memb ane su ace, sui able p essu e exchange s and u bines. Fu he wo k mus be done in his di ec ion. Fig.13: Speci ic Ene gy p oduc ion o SWRO-PRO o di e en RO eed concen a ions and lows. (A) and (C) o one-s age PRO. (B) and (D) o wo-s age PRO. 4. E ec o he second s age eco e y 0 0,4 0,8 1,2 1,6 020 40 60 80 100 Speci ic ene gy (kWh/m3) Y1(%) Csw = 0.6M Csw = 0.68M Csw = 0.77M A 0 0,4 0,8 1,2 1,6 020 40 60 80 100 Speci ic ene gy (kWh/m3) Y1(%) Csw = 0.6M Csw = 0.68M Csw = 0.77M B 0 0,4 0,8 1,2 1,6 020 40 60 80 100 Speci ic ene gy (kWh/m3) Y 1 (%) Qsw = 256 m3/h Qsw = 1000 m3/h Qsw = 2000 m3/h Qsw = 5000 m3/h Qsw = 50000 m3/h 0 1 2 3 4 020 40 60 80 100 Speci ic ene gy (kWh/m3) Y 1 (%) Qsw = 256 m3/h Qsw =1000 m3/h Qsw = 2000m3/h Qsw = 5000 m3/h Qsw =50000 m3/h C D [Esc iba aquí] 24 Th oughou he p e ious sec ions, he eco e y a e o he second SWRO, Y2, was a bi a ily ixed acco ding o he sugges ions o he cons uc o and he p oduc ion needs. In his sec ion, he a ia ion o he second s age eco e y is s udied. Fo his, h ee possible alues o Y2 we e in es iga ed (e.g., 60%, 70% and 80%). The inc ease o Y2 leads o mo e ene gy consump ion acco ding o Eq.( 9). The a ia ion o he ene gy consump ion wi h Y2 is shown in Fig.14-b. Inc easing he eco e y om 70% o 80% causes a ise in SECSWRO by 0.7kWh/m3. On he o he hand, dec easing he eco e y o 60% educes he ene gy consump ion by 0.35kWh/m3. The ene gy eco e ed by he o al sys em (using he second design he e) is p esen ed in Fig.14-a. I can be seen ha he inc ease o Y2 educes he ene gy eco e y. This is due o he inc ease in he PRO eed s eam a low Y2, which inc eases he ini ial eed low a io o app oach 0.5, and inc eases he dilu ion ac o , so he ene gy inc eases. O e all, lowe second s age eco e y educes he ene gy consump ion and inc eases he ene gy eco e y. In his case, he choice o he second s age eco e y is p imo dial, due o he ac ha he indus ial p ocess o he p esen uni depends on i . Consequen ly, i is ad isable o he ope a o s o educe he eco e y o he second s age when he p oduc ion a e o he elec olyza ion p ocess is dec eased o educe he SEC and o inc ease he ene gy eco e y. Fig.13: Speci ic Ene gy p oduc ion o SWRO-PRO and speci ic ene gy consump ion o SWRO o di e en RO second s age eco e y. The calcula ion o he ene gy eco e ed (a) was ca ied ou using esul s de eloped p e iously o he second SWRO-PRO design. 4 Conclusions 0 0,1 0,2 0,3 0,4 30 40 50 SEPRO (kWh/m3) Y 1 (%) Y2 = 60% Y2 = 70% Y2 = 80% a 0 1 2 3 4 30 40 50 SEC SWRO(kWh/m3) Y 1 (%) Y2 = 60% Y2 = 70% Y2 = 80% b [Esc iba aquí] 25 In he cu en s udy, wo con igu a ions o he in eg a ion o P essu e Re a ded Osmosis we e s udied, ha p o ide addi ional ene gy eco e y o exis ing Seawa e Re e se Osmosis plan s wi hou he equi emen o addi ional eed sou ces. To analyze he e ec , a ma hema ical model desc ibing he ene gy p oduced was i s de eloped o bo h con igu a ions. The i s SWRO-PRO design (“1RO-2PRO” design) shows a low pe o mance a he ecommended eco e y a io o he RO p ocess (40-50%), as compa ed o he second design (“2RO-2PRO” design). We expec mo e eco e ed ene gy o he i s con igu a ion i he eed solu ion is p o ided om ou side he sys em, due o he ac ha he p esen eed solu ion is coming om he b ine o he second s age, which p o ides low wa e lows. The s udy showed ha he capaci y o he SWRO and he ini ial seawa e concen a ion s ongly a ec he pe o mance o PRO. The addi ional elemen s o he SWRO uni equi e an inc ease in he capi al cos o he p ocess, so as u he wo k an economic s udy should be done o e eal when he inco po a ion o wo PRO sub- sys ems, is economically easible. ACKNOWLEDGEMENTS This wo k was suppo ed by MiCInn 2014-54530-R. J. Salamanca hanks he inancial suppo gi en by MiCInn. We also acknowledge he pe sonnel o SETA S.L. o many help ul con ibu ions. Symbols