PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
E ec o he ope a ing empe a u e on hyd odynamic and memb ane
pa ame e s in p essu e e a ded osmosis p ocess.
Khaled Toua ia, Fe nando Tadeoa*, Thomas Schies elb, Ch is ophe Hänelb
aDepa 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 983423161. * e nando@au om.u a.es
bF aunho e Ins i u e o In e acial Enginee ing and Bio echnology IGB, Nobels asse 12, 70569
S u ga , Ge many. Tel: +49 711970-4401; Fax: +49 711970-4200.
ABSTRACT
The osmo ic ene gy eco e ed by P essu e Re a ded Osmosis (PRO) om lows o
di e en salini ies is a ec ed by he empe a u e, so he e ec o he empe a u e in
di e en hyd odynamic and memb ane pa ame e s is s udied he e. I is shown ha
aising he ope a ing empe a u e o he sys em leads o a modi ica ion o he
hyd odynamic cha ac e is ics o he eed and d aw solu ions, and an imp o emen o he
in insic memb ane pa ame e s. Consequen ly, he ene gy eco e ed is highe a high
ope a ing empe a u es. These esul s a e alida ed wi h labo a o y esul s using
solu ions a di e en concen a ions and empe a u es.
Keywo ds: P essu e Re a ded Osmosis, Osmo ic Ene gy, Tempe a u e e ec s.
1. In oduc ion1
Ha es ing clean ene gy o sa is y he e e -
g owing ene gy demand o human socie y is o
g ea impo ance o he sus ainable
de elopmen o human ci iliza ion [1]. Wa e
and ene gy a e inex icably linked and mu ually
dependen , wi h each one a ec ing he o he ’s
a ailabili y. P essu e e a ded osmosis (PRO) is
one o he p ocesses ha shows he s ong link
be ween wa e and ene gy [2]. The PRO p ocess
uses he osmo ic p essu e as a d i ing o ce o
p oduce powe . The i s exploi a ions o
osmo ic powe ia PRO p ocesses we e ca ied
abou 40 yea s ago [3]. This is achie ed by an
asymme ic memb ane sepa a ing wo s eams
wi h di e en salini y. Wa e molecules a e
spon aneously anspo ed h ough a semi-
pe meable memb ane, om a low salini y
s eam (such as i e wa e , b ackish o was e
wa e ), a ambien p essu e, in o a p essu ized
high salini y s eam (seawa e o b ine), wi h he
aid o he osmo ic p essu e g adien ac oss he
memb ane [4]. The dilu ed d aw solu ion, wi h a
g ea e olume and/o p essu e, mo es a u bine
o p oduce elec ici y. In 2009, S a k a buil
he wo ld’s i s PRO osmo ic powe plan [5]
showing ha powe densi ies highe han 5W/m2
a e equi ed o a comme cially iable PRO
p ocess [6].
1 Funded by Mineco P ojec DPI2014-54530-R
and FEDER unds
The po en ial o ene gy ex ac ion om his
“salini y po en ial” esou ce ( o all i e
e luen s combined) amoun s o a ound 2.4/2.6
TW, close o p esen day global elec ici y
consump ions [7]. In he nea u u e, PRO
sys ems could be conside ed an e ec i e o m
o powe p oduc ion om enewable ene gy
sou ces, alongside o he es ablished enewable
echnologies (e.g., sola and wind) [7].
Howe e , se e al challenges ha e al eady been
iden i ied, especially conce ning memb ane
de elopmen [8].
Du ing he las ew decades, some labo a o y
expe imen s ha e shown ha PRO pe o mance
is a ec ed by he ope a ing p essu e, he
cha ac e is ics o he d aw and eed, and he
memb ane, e c. [6,8,10]. Many pape s ha e
s udied hese pa ame e s in g ea de ail.
Howe e , ew exis ing publica ions ha e
ocused on he impac o empe a u e [9,24].
Like any o he memb ane p ocesses,
empe a u e should play a signi ican ole in he
pe o mance o he PRO p ocess, as i has a
di ec in luence on he he modynamic
p ope ies o bo h he d aw and he eed
solu ions. In his pape , he e ec o he
empe a u e on he solu ions and he memb ane
pa ame e s is s udied. Resul s p o ided by his
s udy gi e in e es ing pe cep ions in o he PRO
ope a ing condi ions and memb ane p epa a ion.
PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
2 PRO backg ound
In PRO, eed and d aw solu ions a e sepa a ed
by a semi-pe meable memb ane; so wa e
spon aneously pe mea es h ough he Memb ane
om he eed o he d aw solu ion, d i en by he
osmo ic p essu e di e ence ac oss he
memb ane [4]. The ideal osmo ic p ocess can be
desc ibed by he he modynamic equa ions o
he wa e and sal luxes. The gene al equa ions
o anspo a e [13]:
𝐽𝐽𝑤𝑤 = 𝐴𝐴 (∆𝜋𝜋𝑚𝑚 − ∆𝑃𝑃) (1)
𝐽𝐽𝑠𝑠=𝐵𝐵(𝐶𝐶𝐷𝐷,𝑚𝑚−𝐶𝐶𝐹𝐹,𝑚𝑚) (2)
whe e Jw is he wa e lux, Js is he sal lux, A is
he wa e pe meabili y coe icien o he
memb ane, B is he sal pe meabili y coe icien
o he memb ane, CD,m and CF,m a e he solu e
concen a ions a he in e ace o he ac i e and
suppo laye s, espec i ely, ∆𝜋𝜋𝑚𝑚 is he
di e ence be ween osmo ic p essu es a he
su ace o he ac i e laye , and ∆P is he
hyd aulic p essu e applied on he d aw wa e
side. A schema ic o he sal concen a ion
p o ile ac oss a memb ane ope a ing in PRO
mode (ac i e laye acing he d aw solu ion) is
shown in Figu e 1.
Wi h he use o an asymme ic memb ane,
in e nal concen a ion pola iza ion (ICP) occu s
in he po ous laye o he memb ane, which
educes he osmo ic d i ing o ce ac oss he
ac i e laye , and hus he wa e lux. In PRO,
he o ien a ion o he Ac i e dense Laye acing
he D aw Solu ion (AL–DS) is conside ed o be
mechanically mo e s able, as he ex e nal
hyd aulic p essu e is applied on he d aw side
[11,12]. In his case, concen a i e ICP occu s
in he po ous laye o he memb ane.
Due o he ICP wi hin he po ous suppo ,
e e se sal pe mea ion ac oss he memb ane,
and he Ex e nal Concen a ion Pola iza ion
(ECP) in he d aw solu ion, he e ec i e
osmo ic d i ing o ce is lowe han he osmo ic
p essu e di e ence be ween he bulk d aw and
eed solu ions. Thus, a mo e ealis ic wa e lux
exp ession is:
𝐽𝐽𝑤𝑤 = 𝐴𝐴 (𝜋𝜋𝐷𝐷,𝑚𝑚 – 𝜋𝜋𝐹𝐹,𝑚𝑚− ∆𝑃𝑃) (3) (3)
whe e πD,m and πF,m a e he osmo ic p essu es a
he su ace o he ac i e, and suppo laye s,
espec i ely. Taking in o conside a ion he
e ec o ICP and ECP on he d i ing o ce, and
assuming ha he osmo ic p essu e is
p opo ional o he concen a ion and he
empe a u e (𝜋𝜋=𝛽𝛽𝐶𝐶𝛽𝛽𝛽𝛽), he wa e lux
exp ession is gi en by [4]:
𝐽𝐽𝑤𝑤=𝐴𝐴�𝜋𝜋𝐷𝐷,𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒�−𝐽𝐽𝑤𝑤
𝑘𝑘�−𝜋𝜋𝐹𝐹,𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒(𝐽𝐽𝑤𝑤𝐾𝐾)
1+𝐵𝐵
𝐽𝐽𝑤𝑤[𝑒𝑒𝑒𝑒𝑒𝑒(𝐽𝐽𝑤𝑤𝐾𝐾)−1]−∆𝑃𝑃� (4)
whe e πD,b is he bulk osmo ic p essu e o he
d aw solu ion nea he su ace o he ac i e
laye , πF,b is he bulk osmo ic p essu e o he
eed solu ion nea he su ace o he suppo
laye , β is he an’ Ho coe icien , R is he
uni e sal gas cons an , and T is he absolu e
empe a u e. The mass ans e coe icien k is
de ined as [7]:
𝑘𝑘=𝑆𝑆ℎ𝐷𝐷
𝑑𝑑ℎ (5)
whe e D is he di usion coe icien o he solu e
in he d aw solu ion, Sh is he She wood numbe
and dh is he hyd aulic diame e o he low
channel de ined as:
𝑑𝑑ℎ=4𝑆𝑆
𝑃𝑃𝑤𝑤 (6)
whe e S is he a ea o he low sec ion and Pw is
he hyd a ed pe ime e .
The solu e esis i i y K is de ined as [14]:
𝐾𝐾=𝜏𝜏𝑡𝑡𝑠𝑠
𝜀𝜀𝐷𝐷 =𝑠𝑠
𝐷𝐷 (7)
whe e ε, τ , s and s a e, espec i ely, he
po osi y, o uosi y, hickness and s uc u e
pa ame e .
The speci ic sal lux in PRO, de ined as he
a io o sal lux o wa e lux, Js/Jw, is a ec ed
by he in insic anspo p ope ies o he
memb anes, as ollows [15]:
𝐽𝐽𝑠𝑠
𝐽𝐽𝑤𝑤= 𝐵𝐵
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 �1 + 𝐴𝐴𝐴𝐴𝑃𝑃
𝐽𝐽𝑤𝑤� (8)
whe e β is he an’ Ho coe icien , R is he
uni e sal gas cons an , and T is he absolu e
empe a u e.
CD,b
J
s
C
D,m
C
F,m
Feed solu ion
D aw solu ion
∆πm
x
x
δ
s
C
F,b
J
w
Suppo laye
Ac i e laye
PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
Fig.1: A schema ic ep esen a ion o he sal
concen a ion p o ile and wa e luxes ac oss a
memb ane in PRO a s eady s a e.
3 E ec o he ope a ing empe a u e on he
eed and d aw solu ion chemis y
3.1 The Osmo ic P essu e
The di e ence in osmo ic p essu e be ween
bulks is an impo an ac o in PRO: In ac , i is
he d i ing o ce o he p ocess. The eed
solu ion concen a ion is in gene al assumed o
ha e a e y low concen a ion, whe eas he
d aw wa e solu ion has a high concen a ion, so
as o achie e an app op ia e di e ence o alues
be ween he osmo ic p essu es. The
empe a u e has a signi ican impac on he
he modynamic p ope ies o he wa e . In ac ,
e e ing o he an’ Ho equa ion (𝜋𝜋=
𝛽𝛽𝐶𝐶𝛽𝛽𝛽𝛽), he osmo ic p essu e is is di ec ly
p opo ional o he empe a u e. I mus be
poin ed ou ha , o solu ions wi h a e y high
concen a ion, he osmo ic p essu e is no
p opo ional o he concen a ion; howe e , he
assump ion o p opo ionali y be ween he
osmo ic p essu e and he empe a u e is s ill
applicable: o example, ollowing he esul s in
[16], he exp ession o he osmo ic p essu e a a
gi en empe a u e T, as a unc ion o he
concen a ion C o a NaCl solu ion can be
app oxima ed by:
𝜋𝜋= 𝛽𝛽𝐴𝐴(3.805𝐶𝐶2+42.527𝐶𝐶+ 0.434) (9)
whe e TR is he no malized empe a u e:
𝛽𝛽𝐴𝐴= 𝐴𝐴
273.15 (10)
Fo simplici y’s sake, NaCl solu ions a e now
conside ed: Figu e 2 shows he expec ed e ec
o he empe a u e on he osmo ic p essu e o
he d aw wa e o di e en concen a ions.
Fig.2: Osmo ic p essu e o NaCl solu ion a
di e en empe a u es and concen a ions
ollowing Eq.(9).
I can be seen ha he osmo ic p essu e
inc eases when he empe a u e o he solu ion
inc eases. Howe e , he e ec o he
empe a u e on he osmo ic p essu e is mo e
signi ican when he concen a ion o he wa e
is mo e impo an : When he concen a ion is
0.2 M, he p essu e gain is a ound 1.5 ba when
he empe a u e is aised om 15 o 60°C;
whe eas he gain is a ound 7 ba s o 1M.
Re e ing o Eq. (1), as he wa e lux h ough
he memb ane is p opo ional o he di e ence
o osmo ic p essu es, hen, using a high
empe a u e clea ly leads o a be e d i ing
o ce o he p ocess. In PRO p ocesses, he
d i ing o ce is di ec ly ela ed o he d aw
solu ion concen a ion, which explains he
enhanced wa e lux a highe d aw solu ion
concen a ions. I is clea ha much highe
powe densi y can be ob ained using b ines o
high osmo ic p essu es (such as seawa e RO
b ine, MED b ine, he Dead Sea wa e )[25].
3.2 The Di usion coe icien D
The Di usion coe icien D is an impo an
pa ame e in PRO as he mass ans e o eed
solu ion k and solu e esis i i y K a e
p opo ional o D. This coe icien has a s ong
dependence on he empe a u e and he
concen a ion o he solu ion. This di usion
coe icien can be calcula ed empi ically using
he S okes-Eins ein ela ionship [17]:
𝐷𝐷=𝑘𝑘𝑏𝑏𝐴𝐴
6𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋 (11)
whe e kb is he Bol zmann Cons an , µ is he
kinema ic iscosi y o he NaCl solu ion, T is
he empe a u e o he solu ion, is he ion
adius and ρ is he densi y o he solu ion.
The empi ical equa ions ha e been p oposed o
es ima e he kinema ic iscosi y as [18]:
𝜋𝜋
𝜋𝜋𝑤𝑤= 1 + 𝑒𝑒𝐶𝐶𝑆𝑆 𝑒𝑒𝑒𝑒𝑒𝑒�𝐶𝐶𝑠𝑠𝑓𝑓
𝑔𝑔𝐴𝐴𝑅𝑅+𝑖𝑖� (12)
whe e 𝜇𝜇𝑤𝑤 is he wa e ’s kinema ic iscosi y a
empe a u e T, whe e e = 0.12, = 0.44, g =
3.713, and i = 2.792 a e he i ing pa ame e s
( alues gi en o NaCl solu ions), and CS he
mola concen a ion
The empe a u e also a ec s he dynamic
iscosi y 𝜈𝜈. Fo example, his dependence was
desc ibed in [19] o NaCl solu ions as ollows:
𝜈𝜈(𝛽𝛽)= 2.414 ×10�247.8
𝑇𝑇−140−5� (13)
Using Eq. (11)-(13), Fig. 2 shows he e ec o
empe a u e on he di usi i y o he wa e
0
10
20
30
40
50
60
70
10 20 30 40 50 60
Osmo ic p essu e ( ba )
Tempe a u e (°C)
C = 0.4 M
C = 0.2 M
C = 0.6 M
C = 1 M
PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
h ough he memb ane. I can be seen ha in he
ange o empe a u e s udied, he alue o he
di usion coe icien is almos ipled. A low
empe a u es ( om 15⁰C o 20⁰C), he e ec o
he solu ion concen a ion on he di usi i y is
no signi ican , as compa ed o high
empe a u es, whe e i becomes mo e
conside able. This is due o he ac ha he
NaCl solu ion is conside ed a blending o an
a ac i e in e ac ion be ween pa icles when
in e ac ions be ween pa icles wi hin he sol en
ook place. When he empe a u e goes up, he
iscosi y o he solu ion dec eases and he
in e ac ion be ween he pa icles is educed due
o he mal agi a ion. Thus, he di usion
coe icien ends o dec ease as concen a ion
inc eases.
Fig.2: Di usion coe icien o NaCl solu ions a
di e en empe a u es and concen a ions.
3.3 Reynolds, Schmid and She wood
numbe s
The mass ans e coe icien (k) depends on he
ele an physical p ope ies o he luid, he
geome y used along wi h ele an dimensions,
and he a e age eloci y o he luid i we a e
conside ing low in an enclosed condui , o he
app oach eloci y i he low is o e an objec .
Dimensional analysis can be used o exp ess his
dependence in dimensionless o m. The
dimensionless e sion o he mass ans e
coe icien is he She wood numbe (Sh). The
She wood Numbe depends on he Reynolds
numbe (Re), and he Schmid numbe (Sc). The
She wood numbe is hen de ined as [20]:
𝑆𝑆ℎ = 0.04 𝛽𝛽𝑒𝑒0.75𝑆𝑆𝑆𝑆0.33 (Tu bulen low) (14)
𝑆𝑆ℎ= 1.85 �𝛽𝛽𝑒𝑒.𝑆𝑆𝑆𝑆𝑑𝑑ℎ
𝐿𝐿� (Lamina low) (15)
whe e L is he leng h o he wa e channel and
dh is he hyd aulic diame e o he low channel.
The Reynolds and Schmid numbe s a e
calcula ed as ollows:
𝛽𝛽𝑒𝑒=𝑉𝑉.𝑑𝑑.𝜋𝜋
𝜋𝜋=𝑉𝑉.𝑑𝑑
𝑣𝑣 (16)
𝑆𝑆𝑆𝑆=𝑉𝑉
𝜋𝜋𝐷𝐷 (17)
whe e V is he eloci y o he wa e , d is he
diame e o he pipe, 𝜌𝜌 is he densi y o he
wa e , 𝑣𝑣 he dynamic iscosi y o he luid, and
𝜇𝜇 is he cinema ic iscosi y.
As shown in Eqs. (16) and (17), he
dimensionless numbe s Re and Sc depend on
pa ame e s which also depend on he
empe a u e, such as he iscosi y and he
di usion coe icien . Fig.4 shows ha , a high
empe a u es, he e ec o he concen a ion on
Sc is negligible. Con a y o he Sc numbe , he
concen a ion e ec seems o be non-signi ican
a low empe a u es. Raising he empe a u e o
he p ocess leads o he modi ica ion o he low
egime om lamina o u bulen , because o he
s ong e ec o he empe a u e on he Re alue.
In he case o NaCl solu ions, he e ec o he
concen a ion is no signi ican . In ac , he
a ia ion o he iscosi y and densi y o he
wa e , wi hin he ange o concen a ions
s udied, was no so impo an as o a ec he
dimensionless pa ame e s Re. Fo eal luids
(seawa e , b ine was ewa e ...), he esul should
be simila , due o he ac ha he Reynolds
numbe is no s ongly a ec ed by he
concen a ion, as shown in Fig.5-a. Howe e ,
he ma ix complexi y o eal luids can a ec
he iscosi y. Fo seawa e and b ine, hese
e ec s a e negligible, because mo e han 75%
o he ma ix is NaCl; bu o was ewa e , he
composi ion o he ma ix is gene ally
uncon ollable as i con ains o ganic ma e ,
dissol ed polyme ic was e, e c…, which
s ongly a ec he iscosi y o he lows and
hei eloci ies.
2
4
6
8
10
10 20 30 40 50 60
D (10-9 m2/s)
Tempe a u e (°C)
C = 0.1 M
C = 0.3 M
C = 0.6 M
C = 1 M
60000
80000
100000
120000
140000
160000
180000
10 20 30 40 50 60
Reynolds numbe (Re)
Tempe a u e (°C)
C = 0.1 M
C = 0.3 M
C = 0.6 M
C = 1M
(a)
PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
Fig. 5: (a) Reynolds, (b) Schmid and (c)
She wood numbe s o NaCl solu ions a
di e en empe a u es, ollowing (14)-(17).
4 E ec o he ope a ing empe a u e on he
memb ane pa ame e s
4.1 The bounda y laye hickness δ
I is well known ha when a iscous luid lows
along a ixed impe meable wall o pas he igid
su ace o an imme sed body, he eloci y a any
poin on he wall o o he ixed su ace is ze o.
The ex en o which his condi ion modi ies he
gene al cha ac e o he low depends upon he
alue o he iscosi y. I he body is o a
s eamlined shape, and i he iscosi y is small,
he e ec appea s o be con ined wi hin (na ow
egions adjacen o he solid su aces) bounda y
laye s. A bounda y laye may be lamina o
u bulen . A lamina bounda y laye is one
whe e he low akes place in laye s, each laye
sliding pas he adjacen laye s. Lamina
bounda y laye s a e ound only when he
Reynolds numbe s a e small. A u bulen
bounda y laye , on he o he hand, is ma ked by
mixing ac oss se e al laye s. Thus, he e is an
exchange o mass, momen um and ene gy on a
much bigge scale as compa ed o a lamina
bounda y laye . A u bulen bounda y laye
o ms only a la ge Reynolds numbe s. Eq.(18)
and (19) desc ibe he hickness o he bounda y
laye o di e en low egimes [22]:
𝛿𝛿= 5.0×𝑒𝑒
�𝐴𝐴𝑒𝑒𝑥𝑥 (Tu bulen low) (18)
𝛿𝛿=𝑒𝑒0.382
(𝐴𝐴𝑒𝑒𝑥𝑥)1
5 (Lamina low) (19)
whe e he dis ance x is along he memb ane (see
ig.1) and Rex is he local Reynolds numbe . I
has been shown ha , when he hickness o he
bounda y laye is smalle , he mass ans e is
mo e impo an [21]. The e ec o he
empe a u e on he hickness o he bounda y
laye was s udied. Fig. 6 shows ha he e ec o
he concen a ion is no eally compa able o he
e ec o he empe a u e on he bounda y laye
hickness. The bounda y laye has an impo an
dependence on he egime o he low: as he
Reynolds numbe becomes la ge , he iscous
e ec s a e no as impo an a he on o he
bounda y laye , bu become much mo e
impo an nea he end o he bounda y laye .
Also, he la ge he Reynolds numbe , he
hinne he bounda y laye becomes. Thus,
when he empe a u e o he wa e becomes
impo an , he iscosi y o he solu ion is
educed, which leads o an inc ease in he alue
o he Reynolds numbe . In summa y, he
inc ease o he ope a ing empe a u e leads o a
hinne bounda y laye and a highe mass
ans e ac oss i .
Fig.6: The hickness o he bounda y o NaCl
solu ions a di e en empe a u es, ollowing
(18).
4.2 E ec o he empe a u e on he mass
ans e coe icien k
The p ocess o Mass T ans e ac oss an
in e ace in he bulk o a phase is he esul o a
chemical po en ial d i ing o ce, which is
usually exp essed in e ms o concen a ions o
he species. The a e o ans e o a gi en
species pe uni a ea no mal o he in e ace, i.e.,
he lux, depends on some o he physical
p ope ies o he sys em and on he deg ee o
Tu bulence o he phases in ol ed. As he
ela ionship be ween he lux and hese
120
125
130
10 20 30 40 50 60
She wood numbe (Sh)
Tempe a u e (°C)
C = 0.3 M
C = 0.6 M
C = 1 M
C = 0.1 M
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
10 20 30 40 50 60 70
Schmid numbe (Sc)
Tempe a u e (°C)
C = 0.1 M
C = 0.3 M
C = 0.6
C = 1 M
3
3,5
4
4,5
5
10 20 30 40 50 60
δ (10-4m)
Tempe a u e (°C)
C = 0.1 M
C = 1 M

PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
pa ame e s is no easily de eloped om
undamen als o mass ans e , coe icien s ha e
been de ined ha lump hem all oge he . These
de ini ions a e o he o m: Flux = coe icien
×(Concen a ion di e ence). [23]
In he PRO case, he mass ans e coe icien
(k) cha ac e izes he anspo o wa e om he
eed solu ion o he d aw solu ion h ough he
ac i e laye . The mass ans e coe icien
desc ibed in Eq. (5) depends on pa ame e s ha
also depend on he empe a u e. In his sec ion,
he e ec o he empe a u e on he mass
ans e coe icien is s udied expe imen ally.
Fou d aw solu ions wi h di e en
concen a ions we e es ed (0.1M, 0.3M, 0.6M
and 1M o NaCL), whe eas he concen a ion o
he eed wa e was kep equal o 0.00855M o
NaCl. The applied p essu e ∆P was hal o he
osmo ic p essu e di e ence be ween each o he
wo solu ions. Expe imen al esul s a e shown in
igu e 7. Simila o he o he pa ame e s s udied,
k is signi ican ly a ec ed by he wo king
empe a u e. The alue o k was quad upled in
he ange o empe a u e s udied. Howe e , he
e ec o he solu ion concen a ion is no
signi ican a low empe a u es. The
expe imen al esul seems o be in co ela ion
wi h he p e ious sec ions. In ac , he mass
ans e coe icien depends s ongly on he
di usi i y and he bounda y laye . As shown in
igu e 2 and 6, high empe a u es lead o high
di usi i y and low bounda y hickness.
Acco ding o ilm heo y, a high di usi i y wi h
a hin bounda y laye enhance he a e o mass
ans e [26].
Fig.7: The mass ans e coe icien (k) o NaCl
solu ions a di e en empe a u es
(expe imen al esul s).
4.3 E ec o he empe a u e on he solu e
esis i i y K
The solu e esis i i y (K), desc ibed as in Eq.
(7), is a pa ame e used o de e mine he
in luence o he in e nal concen a ion
pola iza ion on he wa e lux. Smalle K alue
means less ICP, esul ing in highe pu e wa e
lux. To de e mine K expe imen ally o
di e en ope a ing empe a u es, a
ea angemen o Eq. (4) was used, as shown
below:
𝐾𝐾=1
𝐽𝐽𝑤𝑤𝑙𝑙𝑙𝑙�𝜋𝜋𝐷𝐷,𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒�−𝐽𝐽𝑤𝑤𝑘𝑘
��+𝐽𝐽𝑤𝑤−𝐵𝐵
𝐴𝐴+∆𝑃𝑃�1−𝐵𝐵
𝐽𝐽𝑤𝑤�
𝜋𝜋𝐹𝐹,𝑏𝑏+𝐵𝐵
𝐴𝐴+∆𝑃𝑃.𝐵𝐵
𝐽𝐽𝑤𝑤� (20)
Expe imen al esul s we e ca ied ou o wo
d aw solu ions (0.6M and 1M o NaCl) and
NaCl eed solu ion (0.00855M). The pa ame e s
we e calcula ed using expe imen al esul s,
pe o med in he ange o empe a u es om
15⁰C o 60⁰C. The applied p essu e ∆P was
always ixed o be hal ha o he osmo ic
p essu e di e ence be ween each o he wo
solu ions.
Fig.8: The solu e esis i i y (K) o he NaCl
solu ion a di e en solu ion empe a u es and
concen a ions (expe imen al esul s).
Fig. 8 e eals ha , a low empe a u es, K is
impo an , and he e ec o he concen a ion o
he d aw solu ion on K is clea ly conside able.
In ac , Eq. (20) shows ha K is in e sely
p opo ional o he wa e lux o he memb ane,
so o each he bes pe o mance, he solu e
esis i i y should be as low as possible. Fig. 9
shows ha he solu e esis i i y ends o educe
he wa e lux o he p ocess: when K is high,
he wa e lux is signi ican ly smalle . In ac , K
depends on he s uc u e pa ame e s: when s
dec eases, K dec eases oo, due o he ac ha
he memb ane becomes hinne when he
ope a ing empe a u e inc eases. This is due o
he simul aneous e ec o he empe a u e and
p essu e: he inc ease o he ope a ing
empe a u e makes he memb ane polyme
so e , so angen ial o ces caused by he applied
p essu e educe s. Thus, o educe he e ec o
K on he wa e lux o he memb ane and hus
on he ene gy p oduced using PRO, i would be
be e o ope a e wi h a high empe a u e,
ollowing he esul s in Fig. 8 and Fig. 9.
2
4
6
8
10
12
14
10 20 30 40 50 60
k ( 10-4 m/s)
Tempe a u e (°C)
C = 0.1M
C = 0.3M
C = 0.6M
C = 1M
0,00
0,20
0,40
0,60
0,80
1,00
1,20
1,40
1,60
10 20 30 40 50 60
Solu e esis i i y K .10
6
(s/m)
Tempe a u e (°C)
C =0.6 M
C = 1M
PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
Fig.9: Va ia ion o he wa e lux in PRO wi h
he solu e esis i i y K (expe imen al esul s
wi h 1M d aw and 0.00855M eed NaCl
solu ions).
4.4 E ec o he empe a u e on he wa e
lux (Jw)
The wa e lux (Jw) a di e en ope a ing
condi ions is now s udied expe imen ally: h ee
d aw solu ions we e es ed (0.5M, 0.66M and
1M o NaCl) a a ange o empe a u es a ying
om 20⁰C o 60⁰C. The eed solu ion was esh
wa e (NaCl 0.00855M) and he applied
p essu e ensu ed ha ∆P was hal he osmo ic
p essu e di e ence be ween he wo solu ions.
Some expe imen al esul s a e p esen ed in
Fig.10.
As he wa e lux (Jw) depends on he
concen a ion o he d aw solu ion, when his
concen a ion is high, he wa e lux inc eases
due o he high alue o he osmo ic p essu e
di e ence, which is he mean d i ing o ce o
he sys em. This can be seen in he expe imen al
esul s: he wa e lux inc eases wi h he
ope a ing empe a u e o all he es ed
ope a ing condi ions. Fo example, when he
concen a ion o he d aw solu ion is 1M, he
wa e lux doubled om 20⁰C o 60⁰C, so he
ene gy ha can be p oduced could also be
doubled. This esul can be a ibu ed o he
a ia ion o he anspo pa ame e o he
memb ane due o he empe a u e. In ac , his
inc ease o he wa e lux is due o he
imp o emen o he wa e pe meabili y o he
memb ane (A), which depends s ongly on he
empe a u e, and he imp o emen o he mass
anspo coe icien (k), as shown in sec ion
4.3.
Fig. 10 shows he expe imen al a ia ion o he
sal lux (Js) as a unc ion o he empe a u e, a
di e en d aw solu ion concen a ions. As
expec ed, he sal lux inc eases when he d aw
solu ion concen a ion is high. I can also be
seen ha Js inc eases when he empe a u e
inc eases. This is a nega i e e ec , as he
e e se solu e di usion can cause a signi ican
educ ion in bo h he PRO wa e lux and he
powe densi y: D aw solu es di using h ough
he memb ane accumula e in he po ous
subs a e due o he wa e lux ha has he
opposi e low di ec ion. This leads o a buildup
o d aw solu e concen a ion wi hin he po ous
suppo laye , con ibu ing o he inc ease o he
ICP a he su ace o he suppo laye , in u n
leading o a dec ease in he e ec i e osmo ic
p essu e di e ence and he wa e lux.
The e e se solu e di usion occu s
simul aneously wi h he o wa d wa e
pe mea ion in he e e se di ec ion. A use ul
quan i y is he speci ic solu e lux (Js/Jw) ha
desc ibes he amoun o d aw solu es
pe mea ing h ough he memb ane no malized
by he olume ic wa e lux. The s udy o he
a io (Js/Jw) a di e en empe a u es (see Fig.
11) e eals ha , a low empe a u es (T< 35⁰C),
he inc ease o he wa e lux is dominan as
compa ed o he inc ease o he sal lux.
Howe e , when he empe a u e o he d aw is
signi ican ly high he plo o (Js/Jw) ends o a
ho izon al shape which means ha he
dominance o he wa e lux is clea ly educed.
Thus, he di usion o sal om he d aw
solu ion in o he suppo laye becomes mo e
impo an which induces a se e e in e nal
concen a ion pola iza ion. This esul e eals
ha wo king a high empe a u e s ill limi ed by
he undesi able e ec o he solu e di usion,
due o i s co ela ion wi h ICP and memb ane
ouling, which inc eases a high empe a u es
o a la shee memb ane.
Fig.10: a ia ion o he wa e lux Jw and he
sal lux Js wi h he PRO empe a u e a
2
3
4
5
6
7
8
678910 11 12
Wa e lux Jw ( 10-6.m/s)
solu e esis i i y K (105s/m)
20⁰C
30⁰C
40⁰C
50⁰C
60⁰C
0
1
2
3
4
5
6
7
15 25 35 45 55 65
Wa e lux Jw (10-6 m/s)
Tempe a u e (
⁰
C)
C = 1M
C= 0.66 M
C = 0.5M
(a)
0
0,5
1
1,5
2
2,5
3
3,5
4
15 25 35 45 55 65
Sal lux Js [g/(s.m²)].10-2
Tempe a u e (
⁰
C)
C = 0.5M
C =0.66M
C = 1M
(b)
PREPRINT Desalina ion and Wa e T ea men 2016 57 ( 23 ) pp. 10477 – 10489,
DOI: 10.1080/19443994.2015.1039600
di e en d aw solu ion concen a ions.
(expe imen al esul s).
Fig.11: a ia ion o he a io (Js/Jw) wi h he
PRO empe a u e a di e en d aw solu ion
concen a ions. (expe imen al esul s).
5 CONCLUSION
The e ec o he empe a u e on he P essu e
Re a ded Osmosis p ocess has been
in es iga ed. I was shown expe imen ally ha
he empe a u e a ec s many pa ame e s o he
memb ane and he hyd odynamic cha ac e is ics
o he eed and d aw solu ions. I has been
shown ha , in gene al, wo king a high
empe a u es inc eases he wa e lux o he
p ocess, and consequen ly he powe eco e y.
The disad an ages o high empe a u es a e he
isk o accumula ion o sal a he su ace o he
memb ane suppo laye , due o he ac ha
aising he empe a u e also leads o he inc ease
o he sal e e se lux (Js), and he deg ada ion
o he memb ane. These can be o e come by he
de elopmen o speci ic high- empe a u e
memb anes wi h a high esis ance o e e se sal
lux.
ACKNOWLEDGEMENTS
This wo k was co- unded by he se en h
amewo k p og am, unde g an 288145
(H2OCean), wi hin he ocean o omo ow join
call 2011.
LIST OF SYMBOLS
A Wa e pe meabili y coe icien . (m.s-1.Pa-1)
B Sal pe meabili y coe icien . (m.s-1)
CD,m Sal concen a ion o he memb ane su ace a he
d aw solu ion side. (g.l-1)
CF,m Sal concen a ion on he memb ane su ace a he side
o he eed side .(g.l-1)
CD,b Sal concen a ion o he eed s eam.(g.l-1)
CF,b Sal concen a ion on he memb ane su ace a he side
o he eed.(g.l-1)
Cs Mola concen a ion o NaCl solu ion. (M)
ΔCm Concen a ion di e ence on he memb ane su ace.(g.l-
1)
dh Hyd aulic diame e o he low channel. (m)
D Di usion coe icien o he solu ion. (m2.s-1)
d Diame e o he pipe.(m)
Jw Wa e lux ha c osses he memb ane. (m/s)
Js Sal lux ha c osses he memb ane. (g/m2.s)
k Mass ans e coe icien . (m.s-1)
K Solu e esis i i y. (s.m-1)
kb Bol zman cons an . (-)
Pw The hyd a ed pe ime e . (m)
ΔP T ansmemb ane P essu e. (Pa)
Δπ Di e ence o osmo ic p essu e be ween he d aw wa e
and he eed wa e . (Pa)
Ion adius. (m)
R Gas cons an . (J.mol·1K-1)
Re Reynolds numbe . (-)
Rex local Reynolds numbe . (-)
s S uc u e pa ame e o he suppo laye . (m)
Sc Schmid numbe . (-)
Sh She wood numbe . (-)
TR The no malized empe a u e (-)
TD,b Tempe a u e o he d aw wa e bulk. (°C)
TF,b Tempe a u e o he eed wa e bulk. (°C)
V eloci y o he luid. (m/s)
η Dynamic iscosi y o he solu ion. (Pa.s)
πD,m Osmo ic p essu e a he su ace o he ac i e laye . (Pa)
πF,m Osmo ic p essu e a he su ace o he suppo laye .
(Pa)
πD,b Osmo ic p essu e a he d aw bulk. (Pa)
πF,b Osmo ic p essu e a he eed bulk. (Pa)
s Leng h o he suppo laye . (m)
τ To uosi y o he memb ane. (-)
ε Po osi y o he memb ane. (-)
β an' Ho coe icien . (-)
δ Thickness o he bounda y laye . (m)
ρ Densi y o he solu ion. (kg/ m3)
µw Wa e kinema ic iscosi y. (m2/s)
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