PREPRINT Renewable Ene gy, Volume 105, May 2017, Pages 84–95
DOI: 10.1016/j. enene.2016.12.030
1
Ene gy eco e y om wo-s age SWRO plan using PRO 1
wi hou ex e nal eshwa e eed s eam: heo e ical analysis1 2
3
Khaled Toua ia,b* 4
aDepa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Valladolid, 5
47011, Valladolid, Spain. Tel: +34 983423162; Fax: +34 98342316. 6
bLabo a o y o Na u al Wa e T ea men - Wa e Resea ches and Technologies Cen e , 7
Techno-pa k Bo j Ced ia, BP 273, 8020, Soliman, Tunisia. Tel: + 216 79325122 / 8
79325199; Fax: + 216 79325802.*Co esponding au ho : [email p o ec ed] 9
10
Jacobo Salamancaa 11
aDepa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Valladolid, 12
47011, Valladolid, Spain. Tel: +34 983423162; Fax: +34 983423161. 13
e na[email p o ec ed] 14
15
Hamza El ilb 16
bLabo a o y o Na u al Wa e T ea men - Wa e Resea ches and Technologies Cen e , 17
Technopa k Bo j Ced ia, BP 273, 8020, Soliman, Tunisia. Tel: + 216 79325122 / 79325199; 18
Fax: + 216 79325802. el [email protected] 19
Fe nando Tadeoa 20
aDepa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Valladolid, 21
47011, Valladolid, Spain. Tel: +34 983423162; Fax: +34 983423161. 22
e na[email p o ec ed] 23
24
25
26
27
28
29
30
31
1 Funded by Mineco P ojec DPI2014-54530-R and FEDER unds
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1
Abs ac : 2
Resea ch in o p essu e e a ded osmosis (PRO) as a me hod o ex ac ene gy om salini y 3
g adien s is on he ise. Seawa e Re e se Osmosis (SWRO) is now a leading echnology in 4
he desalina ion indus y wo ldwide, in bo h small and la ge scale applica ions, due o he 5
ema kable imp o emen s in memb ane pe o mance and associa ed ene gy e iciency. 6
None heless, SWRO desalina ion is inhe en ly mo e ene gy in ensi e when compa ed o 7
con en ional esh wa e ea men . The in eg a ion o PRO wi h SWRO sys ems is s udied 8
in e ms o ene gy consump ion and e luen changes. Fo his, wo no el in eg a ion 9
designs a e e alua ed, wi h SWRO-PRO speci ic ene gy consump ion being modeled using 10
SWRO condi ions a he he modynamic es ic ion, and a de eloped PRO model. The 11
esul s show lowe SWRO ene gy consump ion o bo h con igu a ions, wi h a educ ion in 12
consump ion o 12% o 18%, depending on he RO eco e y a ios. Las ly, he e ec o he 13
ini ial low a io on he dilu ion ac o has been s udied. To do so, he dilu ion was modeled 14
and s udied o di e en ope a ing condi ions. I was ound ha de imen al e ec s se e ely 15
educe he dilu ion, especially he in e nal concen a ion pola iza ion, which induces a 16
dec ease o ene gy eco e y when using he PRO p ocess. 17
Keywo ds: P essu e Re a ded Osmosis; Seawa e Re e se Osmosis; Ene gy eco e y; 18
Modeling; Dilu ion Fac o . 19
20
21
22
23
24
25
26
27
28
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Ene gy eco e y om wo-s age SWRO plan using PRO 1
wi hou ex e nal eshwa e eed s eam: heo e ical analysis. 2
3
1. In oduc ion 4
Desalina ion echnologies a e quickly g owing, combining enginee ing and science o de elop 5
inno a i e means o d inkable wa e p oduc ion [1]. In ac , se e al coun ies, especially in 6
he Middle Eas , al eady depend on seawa e desalina ion as he main sou ce o d inking 7
wa e [2,3], so desalina ion plan s ha e seen conside able expansion o e he pas decade: he 8
desalina ion capaci y is expec ed o each abou 100 million cubic me e s pe day a he end o 9
2016 [2]. The main challenge in desalina ion is he use o ene gy: As a d inking wa e 10
ea men echnology, seawa e desalina ion equi es mo e ene gy han con en ional esh 11
wa e ea men me hods [3]. Howe e , he powe consump ion is equen ly inaccu a ely 12
ep esen ed when compa ed o o he ea men echnologies ha p o ide sa e and eliable 13
public wa e supply [4, 5]. Typically, he ene gy consump ion ep esen s 44% o he o al 14
wa e cos o a SWRO plan [6]. Ano he challenge in he desalina ion indus y is he handling 15
o ejec b ine, which is he highly concen a ed by-p oduc o he desalina ion p ocess [7,8]. 16
Osmo ic Ene gy sys ems we e p oposed as a solu ion due o he ac ha i has been ound o 17
be e y p omising, wi h he po en ial o educing he cos o seawa e desalina ion as well as 18
he en i onmen al impac om b ine discha ge [9,10,11]. In o he wo ds, as a SWRO sys em 19
p oduces high wa e concen a ion (b ine) and PRO uses solu ions wi h high concen a ions, i 20
would be bene icial o hyb idize he wo p ocesses due o he eliance o he wo memb ane 21
p ocesses on he concen a ion o solu ions. In addi ion, The SWRO-PRO sys em has se e al 22
ad an ages. Compa ed o an op imized s and-alone SWRO sys em (SWRO wi h a eco e y 23
ene gy de ice), SWRO ene gy consump ion is educed by ene gy p oduc ion using PRO 24
[12]. Ano he ad an age o his sys em is ha he b ine gene a ed du ing he SWRO p ocess 25
is dilu ed back o seawa e concen a ion, hus minimizing he ad e se en i onmen al 26
impac ha seawa e RO b ine disposal can ha e on ma ine ecology/habi a s. Fu he mo e, 27
he impai ed wa e and SWRO p oduc wa e a e in sepa a e ci cui s, so he e is no con ac 28
be ween impai ed wa e and d inking wa e . Compa ed o a s and-alone PRO sys em (i.e., 29
i e - o-sea PRO), PRO ene gy p oduc ion in he SWRO-PRO sys em is augmen ed by he 30
highe concen a ion o he d aw solu ion (SWRO b ine). Ano he key ad an age o he 31
SWRO-PRO sys em is ha he in luen d aw solu ion is p e- ea ed by he RO p e- ea men 32
sys em. Thus, he b ine en e ing he PRO sub-sys em is ela i ely ee o oulan s. This 33
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d aw solu ion p e- ea men in he SWRO-PRO sys em a oids addi ional ene gy 1
expendi u e ha would be necessa y in a s and-alone PRO sys em. As he ene gy and 2
chemical cos s o p e- ea ing seawa e is a subs an ial ope a ing expendi u e in SWRO 3
desalina ion [13], he ac ha SWRO-PRO capi alizes on he p e- ea ed b ine educes 4
some p e- ea men conce ns, which can be signi ican in he PRO p ocess. As a 5
consequence o hese encou aging ad an ages, he in eg a ion o PRO in o SWRO has 6
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 7
in es iga ing he easibili y o SWRO-PRO sys ems [14,15,16,17,18]. In 2010, Japan 8
launched he Mega on wa e sys em. As pa o he p ojec , a p o o ype SWRO-PRO hyb id 9
plan was buil and ope a ed. Recycled wa e was supplied om a egional sewage ea men 10
acili y and concen a ed b ine om a SWRO plan , using PRO hollow ibe modules. The 11
p o o ype PRO plan go he maximum ou pu powe densi y o 13.8 W/m2 a 30 ba s o 12
hyd aulic p essu e di e ence, co esponding o 38% pe mea ion o pu e wa e in o he b ine 13
[14]. Ano he s udy was ca ied ou using an expe imen al pilo sys em, designed and 14
cons uc ed o in es iga e he educed SWRO ene gy consump ion by i s in eg a ion wi h 15
PRO [15,16]. The expe imen s showed ha he enhanced powe densi ies o he RO-PRO 16
sys em anged om 1.1 o 2.3 W/m2 and indica ed ha u u e RO-PRO sys ems may educe 17
he speci ic ene gy consump ion equi emen s o desalina ion by 1 kWh/m3 [16]. Ano he 18
wo k in es iga ed he easibili y o a RO desalina ion sys em powe ed by a s and-alone PRO 19
uni [17]. Un o una ely, he s udy did no ake in o conside a ion he e ec o he 20
concen a ion pola iza ion and he sal e e se lux on he pe o mance o he SWRO-PRO 21
sys em, which would a ec he esul s. Seawa e b ine om he TuaSp ing desalina ion plan 22
and was ewa e e en a e om he NEWa e plan we e used in [18] o ene gy eco e y. 23
Expe imen s ga e a powe densi y o 4.6 W/m2 a 20 ba ob ained wi h seawa e b ine as he 24
d aw solu ion and was e wa e as he eed solu ion. A ecen pape in es iga ed wo SWRO-25
PRO designs based on he posi ions o he p essu e exchange s and he pump, hen s udied as 26
a unc ion o SWRO eco e y [19]. 27
Howe e , mos o he p e iously s udied SWRO-PRO cases deal wi h con en ional 28
in eg a ion design, whe e one-s age SWRO b ine is he PRO d aw solu ion and a i e 29
wa e /was ewa e e luen is he PRO eed solu ion. This in eg a ion me hodology e eals 30
ha he amoun o ene gy p oduced is ela i ely low and equi es a eed solu ion om a low 31
salini y wa e sou ce, which inc eases he ene gy cos (p e- ea men , ins alla ions, e c…). 32
Mo eo e , p e ious s udies ha e been based on supplying he PRO wi h ex e nal eshwa e 33
sou ces. Howe e , i is well known ha he wo ld is acing a se ious esh wa e sca ci y 34
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p oblem [20]. Then, he use o esh wa e o ene gy eco e y should be a oided. 1
Fu he mo e, he use o was ewa e e luen s shows low ene gy eco e y pe o mance, due 2
o he se e e memb ane ouling and he necessi y o p e- ea men , which inc eases he 3
ene gy consump ion [18]. In his s udy, o he i s ime, an ope a ional wo-s age SWRO 4
uni is in eg a ed wi h PRO o educe i s ene gy consump ion. He ein, he use o an ex e nal 5
eed wa e sou ce is a oided, and an al e na i e loca ion o he PRO inside he p ocess is 6
p oposed. To do so, wo no el SWRO-PRO designs ha e been p oposed in e ms o he 7
PRO loca ion and he na u e o he eed solu ion. To accomplish his objec i e, a model o 8
he PRO sys em has been de eloped, aking in o conside a ion he memb ane 9
cha ac e is ics, e e se sal lux, concen a ion pola iza ion, and p essu e d op in he 10
memb ane module. The SWRO speci ic ene gy consump ion is calcula ed by conside ing 11
he SWRO a i s he modynamic limi , using models om he li e a u e [21]. Then, he 12
SWRO-PRO model was de eloped by combining he SWRO and PRO models. In addi ion, 13
he esul s o he model we e p esen ed o bo h con igu a ions conside ed and compa ed o 14
he ideal case. Las ly, he dilu ion ac o o he d aw solu ion was modeled and in es iga ed 15
as a unc ion o PRO de imen al e ec s. 16
17
2. Ma e ial and me hod 18
2.1. Desc ip ion o he SWRO desalina ion plan 19
To in es iga e he easibili y o PRO in eg a ion wi h he SWRO uni , a case s udy is 20
conside ed he e. A Re e se-Osmosis based desalina ion uni is used, in ended o p oducing 21
wa e o he elec olyza ion p ocess, and which is composed o he elemen s p esen ed in 22
Fig.1. This plan was de eloped by SETA S-L as a pa o he H2OCEAN p ojec [22]. The 23
desalina ion uni is based on wo independen lines, di ided in o wo s ages, which can be 24
connec ed o disconnec ed, as equi ed o main enance o ope a ional equi emen s. In o de 25
o educe he numbe o spa e pa s equi ed, bo h lines ha e he same componen s. The 26
p ocedu e is s a ed by a p e- ea men composed o h ee s eps: chlo ina ion o a oid o ganic 27
ma e , ul a- il a ion o block me als and pa icles in suspension, and inally, a backwash o 28
elimina e oulan s accumula ed on he memb ane su aces du ing he p ocess. 29
The i s pass o he SWRO uni consis s o a chemical ea men applied o emo e he 30
esidual chlo ine om he p e‐ ea men , hen bisulphi e is used ( o emo e he oxidan s 31
dissol ed in he wa e and p o ide a bac e ios a ic e ec ) and, inally, an i ouling is used o 32
mi iga e sal p ecipi a ion on he memb ane su aces o a oid he inc ease in ene gy 33

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consump ion. As a sa e y sys em o a oid damaging he memb ane, a mic o il e is ins alled 1
jus be o e he High P essu e Pump (HP) wi h a deg ee o 5 mic ons o il a ion. To eed he 2
i s -pass memb anes, an HP is equi ed; he wa e p oduced is s o ed in a wa e ank, whe eas 3
he b ine goes o an Ene gy Reco e y sys em (P essu e exchange PX). In ou ine ope a ional 4
condi ions, he eco e y ac o is a bi a ily selec ed o be 45%. 5
The Second RO Pass consis s o wo phases, i is i s dosed wi h an an i oule designed o 6
a oid sal p ecipi a ion and a mic o il e is ins alled wi h a deg ee o 5 mic ons o il a ion, 7
as a sa e y sys em o a oid memb ane ouling. Second, o eed he second-pass, he RO 8
equi es an HP o p essu ize he wa e be o e i en e s he memb ane. 9
The e e se osmosis eco e y is a ound 70%. The wa e p oduced is s o ed in a DEMI wa e 10
ank, whe eas he b ine goes o an ene gy eco e y sys em be o e being eused in he 11
p oposed osmo ic ene gy eco e y sys em o being e u ned o he Ul a-Fil a ion Tank. 12
13
14
15
16
17
18
19
20
21
22
Fig.1: Two-s age Re e se Osmosis desalina ion uni 23
24
2.2. SWRO-PRO con igu a ions and in eg a ion me hodologies 25
2.2.1. Fi s SWRO-PRO con igu a ion 26
A simpli ied p esen a ion o he i s SWRO-PRO con igu a ion is illus a ed in Fig.2: he 27
seawa e eed solu ion (Qsw) is i s p e-p essu ized in he p essu e exchange PX p io o 28
en e ing he desalina ion p ocess. Exi ing he i s s age SWRO sub-sys em (RO1) a e wo 29
s eams: a eshwa e pe mea e s eam (Qp) and a concen a ed b ine s eam (QR1). QSR1 is 30
hen dep essu ized o app oxima ely hal i s p essu e o each an adequa e condi ion o he 31
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
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PRO p ocess [7]. The pe mea e o he RO1 eeds he second s age RO sub-sys em (RO2). To 1
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 2
u bine could be employed o con e i in o elec ical ene gy. Following his 3
dep essu iza ion, he b ine s eam en e s he PRO sub-sys em as a high salini y (d aw) 4
solu ion (QR1 = QD). The eed solu ion o he PRO sub-sys em (QF = QR2) is he e en a e o 5
he second s age. Th ough osmosis, he p essu ized d aw solu ion ex ac s wa e om he 6
impai ed wa e sou ce unde isoba ic condi ions, esul ing in a dilu ed d aw solu ion (QDR). 7
The ene gy s o ed in he dilu ed d aw solu ion is hen exchanged wi h he seawa e RO eed 8
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 9
he SWRO-PRO sys em. The PRO eed solu ion bleed QFR is ejec ed o he sea. 10
11
12
13
14
15
16
17
18
19
20
Fig. 2: Fi s con igu a ion SWRO-PRO in eg a ion: S anda d wi h b ine mix u e. Da ke 21
colo s co espond o mo e concen a ed solu ions and he hickness o each a ow deno es he 22
app oxima e low a e. 23
24
2.2.2. Second SWRO-PRO con igu a ion 25
In he second con igu a ion, he eed solu ion en e ing he PRO sub-sys em was changed. The 26
e en a e o he second s age (QR2) was mixed wi h an addi i e p e- ea ed seawa e low 27
(Qad); he sum embodies he PRO eed solu ion. The amoun o seawa e low is chosen o 28
RO1
RO2
PRO
P
X
Qs
Qp
QR1
Q’
p
QR2
QDR
QFR
ERD
Q
D
T
h
e
QF = QR2
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gua an ee he condi ion ha he eed and d aw solu ion lows a e equal (QF = Qad+QR2 = QD). 1
Fo his, a con ollable al e (V) is placed o p o ide he desi ed amoun o Qad. The d aw 2
solu ion o he PRO is he b ine o he i s RO s age; his b ine passes h ough he ene gy 3
eco e y de ice (ERD) o adjus i s p essu e, when necessa y, o a sui able applied p essu e 4
alue (which is heo e ically he op imum p essu e alue o be applied o he d aw solu ion in 5
he PRO p ocess). I should be no ed ha he unc ioning o he ERD in his con igu a ion is 6
s udied la e , in sec ion 2.4.3. The exi ing PRO d aw solu ion low is hen conduc ed o he 7
PX o eco e he p essu e o he eed SWRO low (Qsw). The PRO eed solu ion bleed QFR is 8
ejec ed o he sea. Fig.3 illus a es he second SWRO-PRO con igu a ion. I should be 9
poin ed ou ha he choice o seawa e as an added low o he en e ing PRO eed solu ion is 10
based on he ac ha he SWRO plan is placed nea he sea, and no i e wa e is close o he 11
SWRO acili y. 12
13
14
15
16
17
18
19
20
21
Fig. 3: Second con igu a ion SWRO-PRO in eg a ion: s anda d wi h second b ine-seawa e 22
mix u e. Da ke colo s co espond o mo e concen a ed solu ions and he hickness o each 23
a ow deno es he app oxima e low a e. 24
25
2.3. Modeling he ideal ene gy consump ion o he SWRO-PRO sys em 26
2.3.1. Two-s age Re e se Osmosis (SWRO) 27
The heo e ical ene gy consump ion is he minimum amoun o ene gy equi ed o p oduce a 28
desi ed olume o pe mea e. Mo e p ecisely, he heo e ical Speci ic Ene gy Consump ion 29
RO1
RO2
PRO
PX
Qad
Q
p
QR1
Q’p
Q
R
QD
Q
D
T
h
e
se
ERD
Qsw
QF =QR2+Qad
T
h
e
QFR
(V)
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(SEC) gi es, o a gi en eco e y a e, he absolu e minimum amoun o ene gy by assuming 1
ha he e iciency o e e y componen (pumps, mo o s, Ene gy Reco e y De ices, e c.) is 2
100%. A he heo e ical limi o cons an -p essu e ope a ion, he one-s age e e se osmosis 3
(RO) sys em will ope a e wi h an applied hyd aulic p essu e equal o he inal osmo ic 4
p essu e o he b ine exi ing he RO module. Thus, he minimum speci ic ene gy o 5
desalina ion o a one-s age RO p ocess, SERO,desal, is equal o he inal b ine osmo ic 6
p essu e [21,30]: In ou case, conside ing wo RO s ages, he o al heo e ical ene gy 7
consump ion o he wo-s age RO sys em (𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑅𝑅1−𝑅𝑅𝑅𝑅2,𝑡𝑡ℎ𝑒𝑒𝑒𝑒) is he sum o he ene gy 8
consump ion o each s age: 9
10 𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑅𝑅1−𝑅𝑅𝑅𝑅2,𝑡𝑡ℎ𝑒𝑒𝑒𝑒= 𝜋𝜋𝑠𝑠𝑠𝑠�1
1−𝑌𝑌1+𝑌𝑌1
1−𝑌𝑌2� (1) 11
12
whe e 𝑌𝑌1 and 𝑌𝑌2 a e he eco e ies o RO1 and RO2, espec i ely. The sal ejec ion coe icien 13
Rs o bo h RO s ages is de ined as: 14
15 𝑅𝑅𝑠𝑠1= 1 −𝐶𝐶𝑝𝑝
𝐶𝐶𝑠𝑠𝑠𝑠 (2) 16
17 𝑅𝑅𝑠𝑠2= 1 −𝐶𝐶𝑝𝑝′
𝐶𝐶𝑝𝑝 (3) 18
19
whe e 𝑆𝑆𝑝𝑝 and 𝑆𝑆𝑝𝑝′ a e he sal concen a ion in he pe mea e solu ions o he i s and second 20
s ages, espec i ely. Fo simplici y, he sal ejec ion coe icien s a e conside ed equal 21
(Rs1=Rs2=Rs). Th oughou he s udy, a linea ela ion be ween sal concen a ion and osmo ic 22
p essu e, based on he an' Ho equa ion, is assumed (π=βRTC). This assump ion makes he 23
de elopmen o simple analy ical exp essions easy, wi hou a signi ican comp omise in 24
accu acy, because a concen a ion ele an o seawa e (Csw=35g/L) is low enough o he 25
an' Ho equa ion o be easonably accu a e. Fig. S1 (Supplemen a y ma e ial) desc ibes he 26
minimum sepa a ion ene gy o a wo-s age SWRO as a unc ion o Y1 acco ding o Eq. (1), 27
which is achie able only in an ideal, e e sible, he modynamic p ocess. In his case, since 28
he majo i y o he ene gy is consumed by he i s s age, he eco e y o he second s age is 29
main ained equal o 70% h oughou he s udy. I should be poin ed ou ha he minimum 30
speci ic ene gy does no include he ene gy equi ed o gene a e excess p essu e in he 31
module, o he ene gy spen on p e- ea men o pos - ea men . As can be seen in Fig. S1, he 32
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ull-scale memb anes su e om se e al d awbacks, such as concen a ion pola iza ion, 1
ouling, e e se sal di usion, and p essu e d ops, which make, o ins ance, high dilu ion 2
un eachable. Thus, in SWRO-PRO hyb id sys ems, h ee pa ame e s should be p ope ly 3
con olled, namely: he eco e y a io, he dilu ion ac o , and he PRO en e ing low a io. 4
5
Fig.7: Ideal speci ic ene gy consump ion o SWRO-PRO sys em as a unc ion o PRO 6
dilu ion o se e al RO1 eco e ies. Fig.7.A ep esen s he model esul s o he SWRO-PRO 7
sys em ope a ing unde he i s con igu a ion. Fig.7.B ep esen s he model esul s o he 8
SWRO-PRO sys em ope a ing unde he second con igu a ion. 9
10
2.4. Modeling he ene gy consump ion o he SWRO-PRO sys em unde ealis ic condi ions 11
2.4.1. PRO model 12
Real li e SWRO-PRO plan s would be less ene gy e icien han heo e ically calcula ed, due 13
o elec ical con e sion losses and dissipa ion. The amoun o addi ional ene gy equi ed 14
depends on he speci ic eco e y s a egy. In addi ion, he p oduced ene gy is p opo ional o 15
he mixing olume. Consequen ly, dilu ion o he d aw solu ion is ine i able. The e o e, he 16
osmo ic p essu e di e ence dec eases and educes he pe o mance o PRO. Besides ha , 17
p e ious wo ks had shown ha PRO memb ane pe o mance is limi ed by se e al limi ing 18
ac o s [26,27]. In ac , wi h a ealis ic memb ane and impe ec hyd odynamics, h ee 19
phenomena occu o educe he ans-memb ane wa e lux, as shown in Fig.S4. Fi s , he 20
po ous suppo laye induces in e nal concen a ion pola iza ion (ICP), which de imen ally 21
enhances πF,m by inc easing he solu e concen a ion a he eed-memb ane in e ace, hus 22
educing he ans-memb ane d i ing o ce. Second, wi hou pe ec hyd odynamics in he 23
d aw solu ion low channel, dilu i e ex e nal concen a ion pola iza ion (ECP) de elops, 24
which lowe s πD,m and educes he d i ing o ce. Las ly, because he memb ane is no longe 25
1
2
3
4
010 20 30 40 50
Speci ic ene gy ( kWh/m3)
DF (%)
Y1 = 30%
Y1 = 40%
Y1 = 50%
Y1 = 60%
A
‐6
‐4
‐2
0
2
4
020 40 60 80 100
Speci ic ene gy ( kWh/m3)
DF (%)
Y1 = 30%
Y1 = 40%
Y1 = 50%
Y1 = 60%
B
DFmax

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17
pe ec ly selec i e, e e se sal di usion (RSD) akes place, esul ing in uncon olled mixing 1
and, he e o e, educed ene gy ex ac ion in he p ocess. The wa e lux ac oss he memb ane, 2
Jw, can be de ined in e ms o he memb ane wa e pe meabili y coe icien , A; he osmo ic 3
p essu e a he d aw side o he memb ane ac i e laye , πD,m; he osmo ic p essu e a he eed 4
side o he memb ane ac i e laye , πicp; and he hyd aulic p essu e di e ence ac oss he 5
memb ane: 6
𝐽𝐽𝑠𝑠=𝐴𝐴�𝜋𝜋𝐷𝐷,𝑚𝑚−𝜋𝜋𝑖𝑖𝑖𝑖𝑝𝑝−∆𝑃𝑃�=𝐴𝐴(∆𝜋𝜋𝑚𝑚−∆𝑃𝑃) (13) 7
whe e Δπm is he osmo ic p essu e di e ence ac oss he memb ane ac i e laye . Based on ilm 8
heo y, equa ions ha e been de eloped o de e mine he concen a ion on ei he side o he 9
memb ane wi h e e se sal lux and concen a ion pola iza ion accoun ed o [25, 26]: 10
𝑆𝑆𝐷𝐷,𝑚𝑚=�𝑆𝑆𝐷𝐷,𝑏𝑏+𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠�𝑒𝑒𝑒𝑒𝑒𝑒�−𝐽𝐽𝑠𝑠
𝑘𝑘𝐷𝐷�−𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠 (14) 11
𝑆𝑆𝐷𝐷,𝑚𝑚=�𝑆𝑆𝐷𝐷,𝑏𝑏+𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠�𝑒𝑒𝑒𝑒𝑒𝑒�𝐽𝐽𝑠𝑠
𝑘𝑘𝐹𝐹�−𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠 (15) 12
𝑆𝑆𝑖𝑖𝑖𝑖𝑝𝑝=�𝑆𝑆𝐷𝐷,𝑏𝑏+𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠�𝑒𝑒𝑒𝑒𝑒𝑒�𝐽𝐽𝑠𝑠
𝑘𝑘𝐹𝐹�𝑒𝑒𝑒𝑒𝑒𝑒(𝐽𝐽𝑠𝑠𝐾𝐾)−𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠 (16) 13
whe e CD,b is he bulk d aw concen a ion, CF,b is he bulk eed concen a ion, and kD and kF 14
a e he mass ans e coe icien in he d aw and eed sides, espec i ely. K is he solu e 15
di usion coe icien . The wa e lux and he sal lux a e ela ed by he ollowing ela ion 16
[27]: 17
𝐽𝐽𝑠𝑠
𝐽𝐽𝑠𝑠=𝐵𝐵
𝐴𝐴𝐴𝐴𝑅𝑅𝑇𝑇�1 + 𝐴𝐴∆𝑃𝑃
𝐽𝐽𝑠𝑠� (17) 18
19
whe e B is he sal pe meabili y coe icien , and ΔP is he hyd aulic p essu e applied on he 20
d aw solu ion side. Assuming he an’ Ho ela ionship be ween osmo ic p essu e and 21
concen a ion [25]: 22
23 𝐽𝐽𝑠𝑠=𝐴𝐴��𝜋𝜋𝐷𝐷,𝑏𝑏+𝐵𝐵
𝐴𝐴�1 + 𝐴𝐴∆𝑃𝑃
𝐽𝐽𝑠𝑠��𝑒𝑒𝑒𝑒𝑒𝑒�−𝐽𝐽𝑠𝑠
𝑘𝑘𝐷𝐷�−�𝜋𝜋𝐷𝐷,𝑏𝑏+𝐵𝐵
𝐴𝐴�1 + 𝐴𝐴∆𝑃𝑃
𝐽𝐽𝑠𝑠��𝑒𝑒𝑒𝑒𝑒𝑒(𝐽𝐽𝑠𝑠𝐾𝐾)𝑒𝑒𝑒𝑒𝑒𝑒�𝐽𝐽𝑠𝑠
𝑘𝑘𝐹𝐹�−∆𝑃𝑃� (18) 24
25
The a ia ions along he memb ane's leng h a e o en neglec ed in models designed o 26
simula e bench scale sys ems because he e ec is di icul o obse e o e e y small 27
memb ane samples [26]. Howe e , he passage o wa e h ough he memb ane was ollowed 28
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18
by ic ion, which should cause some hea ing o solu ions. I he wa e low had been c ea ed 1
due o he p essu e d op on ei he side o he memb ane, his would ha e led o he loss o pa 2
o he ene gy eleased. These include low a es, concen a ions and hyd aulic p essu es, as 3
well as all o he a iables ha a e dependen on hem. Thei local alues should be conside ed 4
o accu a e modeling. These spa ial a ia ions can be accoun ed o ei he by aking an 5
a e age o inle and ou le a iables, o by conside ing he memb ane as a ini e di e ence 6
model [26,27]. To de elop a model o ull-scale PRO applica ions, he la shee memb ane 7
a ea is di ided in o segmen s pe pendicula o he wa e low, e alua ing low condi ions a 8
speci ic poin s along he memb ane module. In his case, eed and d aw solu ion lows a e 9
assumed o be in a co-cu en low mode. Fig.S3 illus a es a single segmen o a la shee 10
PRO memb ane. The pe mea e low h ough he PRO memb ane Qw can signi ican ly dilu e 11
he d aw solu ion concen a ion CD, which esul s in educed lux pe o mance compa ed o 12
he small size es memb ane. Such a dilu ion e ec needs o be explici ly accoun ed o in a 13
la shee module. Due o his a ia ion, h ee main pa ame e s a e e alua ed a each poin 14
along he memb ane: he wa e lux, he p essu e and he concen a ions. The model 15
de elopmen s eps a e p esen ed in he Supplemen a y ma e ial. 16
17
2.4.2. SWRO model 18
The ene gy consump ion o each RO s age in a wo-s age RO plan , a he limi o he 19
he modynamic es ic ion and in he absence o ene gy eco e y, is de eloped in [21]: 20
21
SECRO1=Rsπsw
ηP1Y1(1−Y1) (19) 22
23
SECRO2=Rsπp
ηP2Y2(1−Y2) (20) 24
25
whe e Rs is he sal ejec ion, and 𝜂𝜂𝑃𝑃 is he pump con e sion. The speci ic ene gy cos o RO, 26
in he p esence o an ene gy eco e y de ice (ERD), ope a ing a he limi o he 27
he modynamic es ic ion, is: 28
29 𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑅𝑅1
𝐸𝐸𝑅𝑅𝐷𝐷 = 𝑅𝑅𝑠𝑠𝜋𝜋𝑠𝑠𝑠𝑠�1−𝜂𝜂𝐸𝐸𝐸𝐸𝐷𝐷[1−𝑌𝑌1]
𝜂𝜂𝑃𝑃𝑌𝑌1[1−𝑌𝑌1]� (21) 30
31
whe e 𝜂𝜂𝐸𝐸𝑅𝑅𝐷𝐷 is he e iciency o he ene gy eco e y de ice. 32
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2.4.3. ERD ene gy eco e y 1
The eco e y o ene gy om SWRO sys ems has been a majo ac o in he educ ion o he 2
cos o desalina ed seawa e , o a poin whe e i is beginning o o e a challenge o 3
con en ional sou ces. In ou case, an ERD is placed a e he i s RO s age o eco e ene gy 4
om he ejec ed b ine. As men ioned p e iously, he ERD educes he p essu e o he b ine 5
o a sui able alue o PRO ope a ional applied p essu e ( 𝛥𝛥𝑃𝑃≈∆𝜋𝜋𝑚𝑚
2). This condi ion is a key 6
pa ame e o he op imum pe o mance o he PRO p ocess. In he second con igu a ion, he 7
osmo ic p essu e o he PRO eed solu ion is ela i ely high a low RO1 eco e ies, which is 8
no he case o he i s con igu a ion. The e o e, he ene gy eco e ed using ERD depends 9
on he osmo ic p essu e ha en e s he PRO module. As πF changes wi h he eco e y, he 10
con ibu ion o ERD in he second con igu a ion also a ies ega ding he osmo ic p essu e o 11
he PRO eed solu ion. Then, he ene gy eco e ed by ERD in he second con igu a ion will 12
be much lowe han in he i s one. Sub ac ing Eq. (21) om Eq.(19), he ene gy eco e ed 13
by he ERD a he he modynamic es ic ion is exp essed as ollows: 14
15 𝑆𝑆𝑆𝑆𝐸𝐸𝑅𝑅𝐷𝐷
1 = −𝑅𝑅𝑠𝑠𝜋𝜋𝑠𝑠𝑠𝑠�𝜂𝜂𝐸𝐸𝐸𝐸𝐷𝐷[1−𝑌𝑌1]
𝜂𝜂𝑃𝑃𝑌𝑌1[1−𝑌𝑌1]� (22) 16
17 𝑆𝑆𝑆𝑆𝐸𝐸𝑅𝑅𝐷𝐷
2 = −𝑅𝑅𝑠𝑠[𝜋𝜋𝑠𝑠𝑠𝑠−𝜋𝜋𝐷𝐷]�𝜂𝜂𝐸𝐸𝐸𝐸𝐷𝐷[1−𝑌𝑌1]
𝜂𝜂𝑃𝑃𝑌𝑌1[1−𝑌𝑌1]� (23) 18
19
The subsc ip s 1 and 2 e e o he i s and second con igu a ion, espec i ely. The osmo ic 20
p essu e πF in Eq.(23) highligh s he e ec o he PRO eed osmo ic p essu e. As can be seen 21
in Fig.S5, he con ibu ion o ERD o he ene gy eco e y is much highe in he i s 22
con igu a ion. In ac , in usual RO eco e y (40% ≤ Y1≤ 60%), he ERD ene gy eco e y is 23
be ween 1.32 and 2 kWh/m3. Thus, he ERD e ec i ely educes he SEC by almos 50%. This 24
esul is well-known in he li e a u e [21]. Using he second con igu a ion, he ERD 25
con ibu ion is no signi ican due o he high p essu e equi ed o he PRO p ocess. A high 26
eco e y, he ERD ene gy becomes sligh ly signi ican due o he dilu ion o he added 27
seawa e by he ejec ed wa e o he second RO s age. 28
29
30
31
32
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3. Resul s and discussion 1
3.1. Modeling pa ame e s 2
The simula ions in his s udy a e based on he cha ac e is ics o a cellulose ace a e la -shee 3
memb ane used in ou p e ious wo k, whe e a powe densi y o 6.2 W/m2 a 13 ba has been 4
ob ained in lab-scale es s using 1.026 M NaCl solu ion as he d aw solu ion and 8.55mM 5
NaCl solu ion as he eed solu ion [25]. The cha ac e is ics o he memb ane and he 6
hypo he ical module pa ame e s a e summa ized in Table S1. The ini ial seawa e low was 7
chosen a bi a ily o be 256m3/h, which is he eal amoun o ea ed wa e in he SETA-8
SWRO plan s udied he e. The swea e concen a ion is chosen o be 0.6M (35g/L). The 9
added low a e Qad is conside ed o be p e- ea ed be o e being in ol ed in he p ocess. I 10
should be no ed ha he e ec o o ganic ouling is no conside ed in his s udy, so he ene gy 11
p oduced may be lowe in he p esence o eed wa e cha ged wi h na u al o ganic ma e 12
(NOM). 13
3.2.PRO model esul s 14
The SEPRO model was in es iga ed by s udying he esponse o he PRO sub-sys em a e he 15
a ia ion in he e ec o he ope a ing condi ions (d aw and eed solu ion concen a ions). As 16
can be seen in Fig.8, he inc ease in he d aw solu ion concen a ion leads o an inc ease in he 17
ene gy eco e y by he sub-sys em. On he o he hand, he inc ease in he eed solu ion 18
concen a ion is ollowed by a dec ease in he ene gy. Las ly, he inc ease in he d aw solu ion 19
empe a u e imp o es he pe o mance o he PRO due o he imp o emen in he e ec i e 20
osmo ic p essu e and also he in insic memb ane pa ame e s, such as he wa e pe meabili y 21
coe icien . These esul s a e in ag eemen wi h he model beha io using a lab-scale PRO 22
memb ane. Fig.9 illus a es he SEPRO in Eq. (S1), co esponding o he PRO model esul s o 23
he p oposed con igu a ions when dilu ing RO1 b ine back o he sea, as a unc ion o he 24
SWRO eco e y using he cellulose ace a e la -shee memb ane wi h he cha ac e is ics 25
p esen ed in Table S1. When eco e y inc eases, he d aw solu ion concen a ion inc eases, 26
and he SEPRO also inc eases. The minimum SEPRO eco e ies a e 0 kWh/m3 o bo h 27
con igu a ions. This magni ude inc eases wi h RO1 eco e y o each an SEPRO p oduc ion o 28
0.702 kWh/m3 a 77% o eco e y. Compa ed o he heo e ical SEPRO p oduc ion (Fig. 5), he 29
model p oduces a speci ic ene gy ema kably a om he ideal case. 30
31
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1
Fig.8 PRO speci ic ene gy p oduc ion (SEPRO) modeled as a unc ion o eed and d aw 2
solu ion concen a ions unde op imum PRO hyd aulic p essu e. Feed and d aw solu ion 3
lows a e conside ed equal. Fo (A): he eed solu ion concen a ion is 8.55mM. Fo (B): he 4
d aw solu ion is 1.026M. T=25°C. 5
6
7
Fig.9: PRO speci ic ene gy p oduc ion (SEPRO) modeled as a unc ion o RO1 eco e y o a 8
cellulose ace a e la -shee memb ane unde op imal ΔP o bo h p oposed con igu a ions. 9
10
3.3.SWRO-PRO model esul s 11
The o al ene gy consump ion o he SWRO-PRO sys em o bo h con igu a ions is s udied 12
he e. As men ioned p e iously, he s udy only akes in o accoun he e ec o he eco e y 13
a io o he i s RO s age, so ha o he second s age is conside ed cons an (Y2=70%). 14
Acco ding o Fig.10 and Fig.11, he SESWRO-PRO consump ion is much lowe o he ideal case 15
han o he model esul s o bo h con igu a ions. This beha io is due o he ac ha he 16
ideal SEPRO p oduc ion is no iceably highe han he model SEPRO p oduc ion. Because o he 17
highe s a ing alue o he model SESWRO-PRO and he lowe a e a which he model SERO-PRO
18
0
0,4
0,8
1,2
1,6
0,4 0,8 1,2 1,6 2
-SEPRO (kWh/m3)
D aw solu ion concen a ion (M)
A
0
0,2
0,4
0,6
0,8
0 0,1 0,2 0,3 0,4
-SEPRO (kWh/m3)
Feed solu ion concen a ion (M)
B
‐0,8
‐0,7
‐0,6
‐0,5
‐0,4
‐0,3
‐0,2
‐0,1
0
020 40 60 80 100
SEPRO (kWh/m3)
Y
1
(%)
con igu a ion 1
con igu a ion 2

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consump ion dec eases, he model o he SWRO-PRO sys em is no able o each ene gy 1
neu ali y (SESWRO-PRO = 0). Fig.10 shows he a ia ion o he modeled ene gy consump ion 2
SECSWRO-PRO wi h he applied p essu e ΔP unde wo RO1 eco e y a ios wi hou using an 3
ERD. I can be seen ha SECSWRO-PRO, when Y1= 40%, is highe han he case when Y1 = 50% 4
o bo h con igu a ions. Mo eo e , a a low eco e y a io, he pe o mance o he second 5
con igu a ion is be e han he i s one in e ms o ene gy gene a ion and low applied 6
p essu e. When he eco e y a io inc eases, he second con igu a ion shows a be e 7
pe o mance han he i s , due o he dec ease in he PRO eed solu ion concen a ion. As a 8
compa ison, o (A), he maximum ene gy eco e y is 2.45 % and 4 % when Y1= 40% and 9
50%, espec i ely. Fo (B), he ene gy eco e y is 6% and 8% when Y1= 40% and 50%, 10
espec i ely. Fig. 16 shows a compa ison be ween he o al ene gy consump ion o he SWRO 11
plan wi h he p esence o PRO and ERD. I can be seen ha he maximum SESWRO-PRO
12
consump ion poin o each RO eco e y is he poin a which he e is no PRO sub-sys em 13
con ibu ion (DF = 0). In o he wo ds, his is he maximum SERO consump ion o each RO 14
eco e y. Fo con igu a ion (A), he con ibu ion o he PRO sub-sys em is e y limi ed a a 15
low RO1 eco e y a io (Y1< 30%), whe e mo e han 96% o he ene gy eco e y is 16
accomplished by ERD. This is due o he low amoun o ejec ed wa e coming om he 17
second RO s age, which cons i u es he eed solu ion o he PRO sub-sys em. This esul 18
co esponds, heo e ically, o less han 20% o dilu ion. In addi ion, he high concen a ion o 19
he d aw solu ion may induce se e e concen a ion pola iza ion, which educes he 20
pe o mance o he memb ane. Con a y o con igu a ion (A), he con ibu ion o PRO is 21
conside able a a low eco e y a io because he amoun o PRO eed solu ion is p o ided 22
di ec ly om he p e- ea ed seawa e and emains nea ly cons an a his ange o RO1 23
eco e y a io (Y1< 20%). The con ibu ion o he PRO in he o al ene gy eco e ed is a ound 24
45%. This high alue is because o he limi ed con ibu ion o ERD in his case due o he 25
high PRO eed solu ion concen a ion. Also, when he PRO eed low a io was main ained 26
equal o uni y, he expe imen al dilu ion ac o inc eased. Fo example, when Y1= 40%, he 27
ene gy eco e ed co esponds o DF= 40%, which is double he dilu ion in he i s 28
con igu a ion case. This esul clea ly shows he s ong ela ionship be ween he eed low 29
a io and he dilu ion ac o in he PRO p ocess. To summa ize, he no able di e ence 30
be ween he ideal case and he model case is ela ed o he memb ane pe o mance. In ac , o 31
each high alues o dilu ion, an imp o emen in he wa e pe meabili y ac oss he memb ane 32
is undamen al. Mo eo e , a oiding he e e se sal di usion by educing he sal 33
pe meabili y o he ac i e laye ma e ial enhances he dilu ion ac o . Las ly, imp o ing he 34
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inne s uc u e o he PRO memb ane suppo laye , o educe he e ec o he in e nal 1
concen a ion pola iza ion and op imize he ope a ing condi ions in o de o minimize he 2
ex e nal concen a ion pola iza ion, is a challenge ha can gua an ee a be e PRO dilu ion 3
and he e o e mo e eco e ed ene gy. 4
5 Fig.10: SWRO-PRO speci ic ene gy wi hou using ERD, as a unc ion o he applied p essu e 6
ΔP o di e en RO eco e ies o he model case. (A) ep esen s he esul o he i s 7
con igu a ion and (B) o he second con igu a ion. 8 9
10
Fig. 11: SWRO-PRO speci ic ene gy consump ion as a unc ion o he RO1 eco e y o he 11
p oposed con igu a ions. Pump e iciency, memb ane sal ejec ion, and ERD e iciency we e 12
aken as 90%, 98%, and 95%, espec i ely. 13
14
15
4. Dilu ion ac o in ealis ic condi ions 16
The dilu ion ac o e lec s he amoun o eed wa e ha is mixed wi h he d aw wa e o 17
p oduce ene gy. This pa ame e is s ongly dependen on he memb ane pe o mance and he 18
2,2
2,4
2,6
2,8
3
3,2
010 20 30 40 50 60
SECSWRO-PRO (kWh/m3)
ΔP (ba )
Y1 = 40%
Y1 = 50%
A
2,2
2,4
2,6
2,8
3
3,2
010 20 30 40
SECSWRO-PRO (kWh/m3)
ΔP (ba )
Y1 = 40%
Y1 = 50%
B
0
1
2
3
4
5
6
7
8
9
020 40 60 80 100
Speci ic ene gy (kWh/m3)
Y
1
(%)
Fi s con igu a ion
Second con igu a ion
SWRO wi hou ERD
PREPRINT Renewable Ene gy, Volume 105, May 2017, Pages 84–95
DOI: 10.1016/j. enene.2016.12.030
24
d i ing o ce, Δπ. In o he wo ds, inc easing he wa e lux ac oss he memb ane leads o he 1
inc ease in he dilu ion. In he ideal case wi h a pe ec memb ane, he wa e lux depends 2
only on he osmo ic p essu e di e ence. Then, o achie e high dilu ions, he concen a ions o 3
eed and d aw solu ions should be op imized. In ealis ic condi ions, he maximum dilu ion is 4
no eachable because o se e al limi ing ac o s, such as he concen a ion pola iza ion (CP) 5
and e e se sal di usion (RSD), which educe he pe o mance o he memb ane. The 6
ealis ic dilu ion ac o is in es iga ed in he cu en sec ion. 7
The maximum amoun o eed low ha c osses he memb ane o be mixed wi h he d aw 8
solu ion, ∆𝑄𝑄𝑚𝑚𝐷𝐷𝑚𝑚 , can be calcula ed using he ollowing equa ion [32]: 9
10
∆𝑄𝑄𝑚𝑚𝐷𝐷𝑚𝑚=�𝐶𝐶𝐷𝐷,𝑏𝑏−�𝐶𝐶𝐹𝐹,𝑏𝑏
�𝐶𝐶𝐷𝐷,𝑏𝑏+∅
1−∅�𝐶𝐶𝐹𝐹,𝑏𝑏𝑄𝑄𝐷𝐷 (24) 11
12
Eq. (24) is applicable only o an ideal memb ane wi h pe ec hyd odynamics. The 13
ea angemen o Eq. (24) using Eqs.(5) and (6) gi es he maximum dilu ion ac o : 14
15
𝐷𝐷𝐷𝐷𝑚𝑚𝐷𝐷𝑚𝑚=𝑟𝑟�𝐶𝐶𝐷𝐷−�𝐶𝐶𝐹𝐹
�𝐶𝐶𝐷𝐷+1
𝐷𝐷�𝐶𝐶𝐹𝐹 (25) 16
17
whe e 𝑆𝑆𝐷𝐷 and 𝑆𝑆𝐷𝐷 a e he d aw and eed solu ion concen a ions. To in oduce he impac o 18
de imen al e ec s, Eq.(25) is modi ied by subs i u ing CD and CF by Eqs.(14),(15) and (16) 19
acco ding o he a ia ion o he e ec i e eed and d aw concen a ions desc ibed in Fig.S4 20
(Supplemen a y ma e ial). Table S2 summa izes he di e en equa ions o DF o each case 21
s udied. The ealis ic dilu ion ac o can be de e mined using he pa ame e s desc ibed in 22
Table S1 and he modeling esul s o sec ion 3.2. To in es iga e he e ec o each de imen al 23
e ec , DFmax is modeled unde se e al ope a ing condi ions. In ac , he d aw solu ion is 24
assimila ed o he seawa e RO b ine concen a ion (1.2 M o NaCl) and he eed solu ion is 25
modi ied o each s udied case om eshwa e o i e wa e concen a ion. The modeling 26
esul s a e p esen ed in Fig.18. The maximum dilu ion is ob ained using an ideal memb ane 27
wi h no e e se sal di usion JS (RSD), concen a ion pola iza ion, and an ad anced s a e-o -28
he-a memb ane wi h pe ec hyd odynamics. In his case, he wa e lux Jw is di ec ly 29
p opo ional o he osmo ic p essu e di e ence = 𝜋𝜋𝐷𝐷,𝑏𝑏− 𝜋𝜋𝐷𝐷,𝑏𝑏 . The maximum dilu ion 30
achie able in his case is 92%. When conside ing only he e ec o he ex e nal concen a ion 31
pola iza ion, which is caused by non ideal hyd odynamics in he d aw solu ion low channel, 32
PREPRINT Renewable Ene gy, Volume 105, May 2017, Pages 84–95
DOI: 10.1016/j. enene.2016.12.030
25
which induces he dilu i e Ex e nal Concen a ion Pola iza ion (dilu i e ECP) a he d aw side 1
and he concen a i e Ex e nal Concen a ion Pola iza ion (concen a i e ECP) a he eed 2
side, he alues o he dilu ion ac o dec ease by almos 8% om he ideal case. This 3
beha io is caused by he dec ease in he e ec i e osmo ic p essu e di e ence om 𝛥𝛥𝜋𝜋 o 4 𝛥𝛥𝜋𝜋𝐸𝐸𝐶𝐶𝑃𝑃=𝜋𝜋𝐷𝐷,𝑚𝑚− 𝜋𝜋𝐷𝐷,𝑚𝑚 (see Fig.S4). Wi h he exis ence o RSD, he dec ease in he DF is 5
a ound 24% om he ideal case. In ac , RSD causes he d op in he d i ing o ce due o he 6
pene a ion o sal om he d aw o he eed side, which induces a dec ease o Jw. To 7
emphasize he e ec o he concen a ion pola iza ion and in e nal concen a ion, he 8
concen a ion o i e wa e (0.015M) is conside ed. Unde hese condi ions, he dec ease in 9
he DF eaches 52 %. As can be clea ly seen, mos o he DF educ ion is due o he in e nal 10
concen a ion pola iza ion wi h a con ibu ion o 28%. ICP, caused by he accumula ion o 11
sal a he ac i e laye /suppo laye bounda y, dec eases he d i ing o ce om 𝛥𝛥𝜋𝜋 o 12 𝛥𝛥𝜋𝜋𝑚𝑚=𝜋𝜋𝐷𝐷,𝑚𝑚− 𝜋𝜋𝑖𝑖. Consequen ly, a se e e d op occu s in Jw; he e o e, DF dec eases 13
d as ically. As he ene gy is di ec ly p opo ional o he dilu ion, he DF loss om he ealis ic 14
PRO ope a ion may ha e a signi ican impac on he ne speci ic ene gy eco e ed om he 15
p ocess. The op imiza ion o he memb ane pe o mance is a c i ical ope a ion o gua an ee 16
high ene gy eco e y. I should be poin ed ou ha his s udy does no conside he e ec o 17
o ganic ouling. In ac , i was shown in a p e ious s udy ha ouling se e ely educes he 18
wa e lux and he e o e he dilu ion. This ene gy loss caused by memb ane limi a ions, in 19
conjunc ion wi h he p e- ea men ene gy equi emen s, pumping ene gy cos s, ine iciencies 20
in he hyd o- u bine and p essu e exchange , may limi he amoun o ene gy ha es ed om 21
he PRO p ocess. O cou se, he inc ease in he concen a ion di e ence be ween he eed and 22
d aw solu ion concen a ions may p o ide a sizable amoun o ene gy using he PRO p ocess. 23
Ne e heless, he inc ease in he PRO en e ing solu ion concen a ion should be well chosen 24
and ea ed o a oid he accen ua ion o he concen a ion pola iza ion and he e e se sal 25
di usion, which lead o he dec ease in he d i ing o ce; he osmo ic p essu e di e ence. 26
27