Shen, Z. J.; Min, J. C.
A icle
Ou doo ai s a e ha may cause mois u e condensa ion
in memb ane- ype o al hea exchange s using di e en
memb ane ma e ials
Ene gy Repo s
P o ided in Coope a ion wi h:
Else ie
Sugges ed Ci a ion: Shen, Z. J.; Min, J. C. (2020) : Ou doo ai s a e ha may cause mois u e
condensa ion in memb ane- ype o al hea exchange s using di e en memb ane ma e ials, Ene gy
Repo s, ISSN 2352-4847, Else ie , Ams e dam, Vol. 6, Iss. 1, pp. 227-233,
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Ene gy Repo s 6 (2020) 227–233
www.else ie .com/loca e/egy
6 h In e na ional Con e ence on Ene gy and En i onmen Resea ch, ICEER 2019, 22–25 July,
Uni e si y o A ei o, Po ugal
Ou doo ai s a e ha may cause mois u e condensa ion in
memb ane- ype o al hea exchange s using di e en memb ane
ma e ials
Z.J. Shen, J.C. Min∗
Depa men o Enginee ing Mechanics, Tsinghua Uni e si y, Beijing 100084, China
Recei ed 5 Augus 2019; accep ed 25 Augus 2019
Abs ac
To al hea exchange (THX) is an ai - o-ai hea exchange wi h a hea /mois u e exchanging co e made o wa e apo
pe meable memb ane, i is used o educe he building ene gy consump ion by eco e ing bo h hea and mois u e om
en ila ion ai . In ho and humid clima e, he memb ane su ace may ge a empe a u e below he dew poin o supply ou doo
ai , causing mois u e condensa ion a he memb ane su ace, which may deg ade he exchange pe o mance and inc ease he
heal h isk. In his esea ch, a ma hema ical model is buil o desc ibe he hea and mois u e ans e in he co e o a THX, he
e ec s o memb ane p ope ies on mois u e condensa ion a e analyzed, and he c i ical ou doo ai s a es o occu ence o he
mois u e condensa ion a e calcula ed. The esul s show ha la ge memb ane adso p ion cons an and la ge maximum mois u e
up ake may es ain he mois u e condensa ion, which occu s mo e easily a he in e sec ion o he supply and exhaus ai s eams.
The op imal memb ane p ope ies a e ecommended based on a comp ehensi e conside a ion o he sa e y and economy.
c
2019 Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
Pee - e iew unde esponsibili y o he scien i ic commi ee o he 6 h In e na ional Con e ence on Ene gy and En i onmen Resea ch, ICEER, 2019.
Keywo ds: To al hea exchange ; Memb ane p ope y; Mois u e condensa ion; Ou doo ai s a e
1. In oduc ion
The building ene gy consump ion accoun s o app oxima ely 40% o he global ene gy consump ion, as epo ed
by Ome [1]. Wi h he inc easing conce n o indoo ai quali y and ene gy sa ing, he memb ane- ype o al hea
exchange (THX), which has a hea /mois u e exchanging co e made o wa e apo pe meable memb ane ha
ans e s bo h hea and mois u e, is o en employed o educe he building ene gy consump ion associa ed wi h
he o ced en ila ion. The co e con ains nume ous al e na ely s acked la channels con ined by memb ane shee s,
supply ou doo ai and exhaus indoo ai low h ough he channels and exchange hea and mois u e ac oss he
memb anes. Min and Duan [2,3] compa ed ou di e en me hods o e alua e he pe o mance o a THX, and
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (J.C. Min).
h ps://doi.o g/10.1016/j.egy .2019.08.049
2352-4847/ c
2019 Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/
licenses/by-nc-nd/4.0/).
Pee - e iew unde esponsibili y o he scien i ic commi ee o he 6 h In e na ional Con e ence on Ene gy and En i onmen Resea ch, ICEER,
2019.
228 Z.J. Shen and J.C. Min / Ene gy Repo s 6 (2020) 227–233
Nomencla u e
Cabso p ion cons an o memb ane
cpspeci ic hea o ai (J kg−1K−1)
Dwm mois u e di usi i y in memb ane (kg m−1s−1)
Hen halpy (kJ kg−1)
hcon ec i e hea ans e coe icien (W m−2K−1)
dchannel heigh (m)
Jmass lux (kg m−2s−1)
kcon ec i e mass ans e coe icien (kg m−2s−1)
Lwadso p ion hea (J kg−1)
Le Lewis numbe
m ai mass low a e (kg s−1)
mmin minimum o supply and exhaus ai mass low a e (kg s−1)
Nu Nussel numbe
Nnumbe o channels
q o al hea lux h ough memb ane (W m−2)
Tabsolu e empe a u e (K)
Whumidi y a io (kg kg−1)
wmax maximum mois u e up ake (kg/kg)
xFchannel leng h in xdi ec ion (m)
yFchannel leng h in ydi ec ion (m)
G eek symbols
δ hickness o memb ane (m)
εe ec i eness
θmois u e con en o memb ane su ace (kg kg−1)
λhea conduc i i y (W m−1K−1)
φ ela i e humidi y
Subsc ip s
e exhaus ai
H o al e ec i eness
L la en e ec i eness
m memb ane
S sensible e ec i eness
s supply ai
sa sa u a ion
poin ed ou ha he nume ical me hod wi h conside a ion o he adso p ion hea was he bes me hod o calcula e
such pe o mance, especially when he hea and mois u e ans e in di e en di ec ions. Al-Waked e al. [4]
in es iga ed he he mal pe o mance enhancemen o memb ane-based ene gy eco e y en ila o s o di e en
numbe s o low channels, low con igu a ions, ai low a es, and wea he condi ions. Lee e al. [5] unde ook
expe imen al in es iga ions on he cha ac e is ics o mois u e ans e wi h a THX co e made o di e en pape
memb anes. Enga ne is e al. [6] de eloped a heo e ical model o cu en gene a ion asymme ic composi e
memb anes used in he THX.
On a ho and humid day in he summe , he supply ou doo ai has a high ela i e humidi y, so he memb ane
su ace in con ac wi h i is ap o ge a empe a u e below i s dew poin , causing mois u e condensa ion a he
Z.J. Shen and J.C. Min / Ene gy Repo s 6 (2020) 227–233 229
memb ane su ace. The condensa e wa e may we he memb ane and change i s p ope y, leading o a deg aded
THX pe o mance. Ra a i Nas e al. [7] s a e ha he p oblems caused by he mois u e condensa ion in a THX
may include: (1) inc eases in he p essu e loss and o e all hea /mois u e ans e esis ances, and (2) inc ease in he
heal h isk. So, i is necessa y o ake measu es o es ain o e en elimina e he possible occu ence o mois u e
condensa ion.
In his esea ch, a ma hema ical model is buil o desc ibe he hea and mois u e ans e in he co e o a THX,
and he e ec s o he memb ane p ope ies including he memb ane adso p ion cons an and maximum mois u e
up ake on he mois u e condensa ion a e in es iga ed and analyzed. The c i ical ou doo ai s a es o he occu ence
o mois u e condensa ion a e calcula ed and summa ized o di e en memb ane p ope ies. The ela i e humidi y
con ou s a he memb ane su ace a e p esen ed, and he op imal memb ane p ope ies a e ecommended based on
a comp ehensi e conside a ion o he sa e y and economy.
2. Theo e ical model
Fig. 1 shows he basic model o he co e o a ypical THX. Because o he pe iodici y and symme y in geome y,
hal he olume o he exhaus ai s eam, hal he olume o he supply ai s eam and in e media e memb ane a e
aken o cons i u e he compu a ional domain.
Fig. 1. Basic model.
The model assumes ha he physical p ope ies o he ai luid and memb ane a e cons an , and he hea and
mois u e ans e s a e bo h a s eady s a e.
Supply ai :
mscp
N yF
∂Ts
∂x+2hs(Ts−Tms)=0,ms
N yF
∂Ws
∂x+2ks(Ws−Wms)=0 (1)
Exhaus ai :
mecp
N xF
∂Te
∂y+2he(Te−Tme)=0,me
N xF
∂We
∂y+2ke(We−Wme)=0 (2)
Memb ane:
q= −λm
∂Tm
∂z=λm
Tms −Tme
δ,J= −Dwm
∂θm
∂z=Dwm
θms −θme
δ(3)
u he ,
q=hs(Ts−Tms)+J Lw=he(Te−Tme)+J Lw,J=ks(Ws−Wms)=ke(We−Wme)(4)
whe e mis he ai mass low a e, Wis he humidi y a io, hand ka e he con ec i e hea and mass ans e
coe icien s, qand Ja e he hea and mois u e luxes ac oss memb ane, Nis he numbe o channels, xFand yF
a e he channel leng hs in he xand ydi ec ions, λmis he memb ane he mal conduc i i y, Dwm is he mois u e
230 Z.J. Shen and J.C. Min / Ene gy Repo s 6 (2020) 227–233
di usi i y in memb ane, θis he memb ane mois u e con en , δis he memb ane hickness, and Lwis he hea o
adso p ion o wa e apo on memb ane, which is assumed o be equal o he hea o apo iza ion o wa e . The
subsc ip s s, e, m and w e e o he supply ai , exhaus ai , memb ane and wa e apo , espec i ely.
The equa ion desc ibing he mois u e adso p ion cha ac e is ics o wa e apo a he memb ane su ace can be
ep esen ed by Inc ope a [8]
θ=wmax
1−C+C/φ (5)
whe e φis he ai ela i e humidi y, wmax is he maximum mois u e con en o he memb ane ma e ial, and Cis
he memb ane adso p ion cons an , which de e mines he shape o he adso p ion cu e. Eq. (5) is widely used o
desc ibe he mois u e adso p ion cha ac e is ics o he memb ane ma e ials used in a THX, as in Niu & Zhang [9],
Min & Su [10–12], and Min & Duan [2,3].
The con ec i e hea and mass ans e coe icien s be ween he ai and memb ane a e gi en by
h=hs=he=Nuλ
2d(6a)
k=ks=ke=h
cpLe2/3(6b)
whe e dis he channel heigh , Nu is he Nussel numbe , which has a alue o 7.54 o ully de eloped lamina low
be ween pa allel pla es wi h a cons an empe a u e bounda y condi ion [13], and Le is he Lewis numbe , which is
app oxima ely 0.85 o a empe a u e ange o 0–40 oC [14].
The THX pe o mance is e alua ed using he sensible, la en and o al e ec i enesses, gi en by
εS=ms(Tsi −Tso)+me(Teo −Tei)
2mmin (Tsi −Tei)(7a)
εL=ms(Wsi −Wso)+me(Weo −Wei)
2mmin (Wsi −Wei)(7b)
εH=ms(Hsi −Hso)+me(Heo −Hei)
2mmin (Hsi −Hei)(7c)
The equa ion o judging he c i ical ai s a e o no occu ence o mois u e condensa ion is as below:
Wms <Wsa (8)
whe e Wms is he humidi y a io o supply ai , and Wsa is he sa u a ion humidi y a io a he memb ane su ace,
which co esponds o a ela i e humidi y o 100%.
3. Resul s and discussion
The model has al eady been alida ed in ou p e ious esea ches (e.g., Min e al. [15], Min & Duan [2]). The
alues aken o he THX co e dimensions and memb ane pa ame e s a e p esen ed in Table 1. The indoo ai
empe a u e and ela i e humidi y a e se as 26 oC and 50%, while he ai eloci y is se as 2 m/s, which co esponds
o an ai mass low a e o 0.2 kg/s.
Table 1. THX co e dimensions and memb ane pa ame e s.
THX co e dimensions Memb ane pa ame e s
xF,yF[m] 0.25 λm[W/m K] 0.1
d[mm] 2 Dwm [10−7kg/m s] 0.1
N180 C0.1–10
δ[mm] 0.1 wmax [kg/kg] 0.15–0.35
Fig. 2 illus a es he c i ical ou doo ai s a es o he occu ence o mois u e condensa ion o memb ane ma e ials
wi h di e en adso p ion cons an s (C). No mois u e condensa ion akes place i he ou doo ai s a e alls in he
lowe -le egion in Fig. 2a, which is con ined by he cu e o each adso p ion cons an . All cu es a e almos linea
and end o shi owa ds he uppe - igh co ne when he adso p ion cons an is inc eased, implying ha a la ge

Z.J. Shen and J.C. Min / Ene gy Repo s 6 (2020) 227–233 231
Fig. 2. C i ical ou doo ai s a es o di e en memb ane adso p ion cons an s.
adso p ion cons an allows a highe empe a u e and ela i e humidi y a which no mois u e condensa ion akes
place, so he memb ane ma e ial wi h a la ge adso p ion cons an has a be e an i-mois u e condensa ion ea u e.
Fig. 2b depic s he c i ical empe a u es co esponding o 100% ela i e humidi y o di e en adso p ion cons an s
in pa icula , i indica es ha he la ge he memb ane adso p ion cons an he highe he ou doo ai empe a u e
o no occu ence o he mois u e condensa ion.
Fig. 3 shows he a ia ions o a ious e ec i enesses wi h he memb ane adso p ion cons an . Wi h inc easing
adso p ion cons an , he sensible e ec i eness changes sligh ly while he la en and o al e ec i enesses i s
inc ease, a e expe iencing a slow change s age, u n o dec ease. The maximum appea s a an adso p ion cons an
ha is la ge han bu e y close o he alue o uni y.
Fig. 3. Va ious e ec i enesses o di e en memb ane adso p ion cons an s.
Comp ehensi e conside a ion o Figs. 2 and 3 esul s sugges s ha C=2.5 would be a good choice o
he memb ane adso p ion cons an , because he ele an memb ane yields no only a good an i-condensa ion
pe o mance bu also a high e ec i eness.
Figs. 4 and 5a e simila o Figs. 2 and 3, hey a e o he maximum mois u e up ake o he memb ane. The esul s
in Fig. 4 look e y simila o hose in Fig. 2, a la ge maximum mois u e up ake yields a highe ela i e humidi y
and empe a u e a which no mois u e condensa ion akes place, meaning ha he memb ane ma e ial wi h a la ge
maximum mois u e up ake has be e an i-condensa ion pe o mance. Fig. 5 shows ha , as he maximum mois u e
up ake inc eases he sensible e ec i eness dec eases e y sligh ly while he la en and o al e ec i enesses inc ease
signi ican ly, so he inc ease in he maximum mois u e up ake may con ibu e o he economic imp o emen in
gene al. Comp ehensi e conside a ion o Figs. 4 and 5sugges s ha a la ge alue should be aken o he maximum
mois u e up ake in o de o ge a be e e ec i eness pe o mance and less heal h isk.
232 Z.J. Shen and J.C. Min / Ene gy Repo s 6 (2020) 227–233
Fig. 4. C i ical ou doo ai s a es o di e en maximum mois u e up akes.
Fig. 5. Va ious e ec i enesses o di e en maximum mois u e up akes.
Fig. 6 illus a es he ela i e humidi y con ou s a he memb ane su ace o 35 oC ou doo ai empe a u e and
70% ou doo ai ela i e humidi y o wo di e en memb ane ma e ials. One memb ane has a p ope y o C=1
and wmax =0.25 kg/kg, called he no mal memb ane, and he o he has a p ope y o C=2.5 and wmax =0.35
kg/kg, called he ecommended memb ane. Fo bo h memb anes, he zone wi h a highe ela i e humidi y appea s
in he lowe -le egion, which is he in e sec ion o he supply ou doo and exhaus indoo ai s eams, a which
Fig. 6. Rela i e humidi y con ou s a he memb ane su ace.
Z.J. Shen and J.C. Min / Ene gy Repo s 6 (2020) 227–233 233
he mois u e condensa ion occu s mo e easily because o he highe ela i e humidi y. Compa ison o Figs. 6a and
6b sugges s ha he ecommended memb ane has educed humidi ies as compa ed wi h he no mal memb ane,
implying ha he mois u e condensa ion occu s mo e di icul ly a he ecommended memb ane su ace han a he
no mal memb ane su ace, which may in e p e he eason why he memb ane wi h a la ge adso p ion cons an and
a la ge maximum mois u e up ake ha e a be e an i-condensa ion pe o mance. Fu he , he e ec i enesses o he
THX using he wo di e en memb ane ma e ials a e also calcula ed and he esul s show ha he ecommended
memb ane yields almos he same sensible e ec i eness as he no mal memb ane bu gi es 3.7 pe cen age poin
highe la en e ec i eness and 2.9 pe cen age poin highe o al e ec i eness han he no mal memb ane.
4. Conclusions
•The ou doo ai ela i e humidi y and empe a u e anges o no occu ence o mois u e condensa ion o
di e en memb ane p ope ies a e p o ided, i is ound ha he la ge he memb ane adso p ion cons an and
maximum mois u e up ake he be e he an i-mois u e condensa ion pe o mance.
•The memb ane ha has a mode a e adso p ion cons an and a la ge maximum mois u e up ake may yield
no only a good an i-mois u e condensa ion pe o mance bu also a high e ec i eness pe o mance. The
ecommended memb ane ha has a p ope y o C=2.5 and wmax =0.35 kg/kg can no only es ain he
occu ence o mois u e condensa ion bu also gi e a good economy as compa ed o he no mal memb ane ha
has a p ope y o C=1 and wmax =0.25 kg/kg.
•The mois u e condensa ion akes place mo e easily a he in e sec ion o he supply and exhaus ai s eams
because o he highe ela i e humidi y in ha egion.
Acknowledgmen
This s udy is unded by Beijing Municipal Na u al Science Founda ion (NO. 3182015).
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