Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation

7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation

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Big Data Analysis of Hollow Fiber Direct Contact

Membrane Distillation (HFDCMD) for Simulation-based

Emirical Analysis

Albert S. Kim a, *, Seo Jin Kia, and Hyeon-Ju Kimb

a Civil and Environmental Engineering, University of Hawaii at anoa,

!"#$ %ole Street Holmes &'&, Honolulu, Hawaii ()'!!, USA

b%ee +ean ater Aliation esear/ Center, Korea esear/ 0nstitute

of S/is and +ean Engineering, 1oseong-gun, 1angwon-do !2(-'!!,

eubli of Korea

A manusrit for

Desalination

Abstract

!eywords3 Self-Organizing Map, Multiple linear regression

"# $ntroduction

embrane distillation 4%5 is a non-isot/ermal roess in w/i/ t/e

artial ressure gradient of evaorated water vaor is t/e driving fore for


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mass transfer wit/ an aomanied transformation between li6uid and gas

/ases 728. % reeived lose attention due to its aability to rodue lean

4distillated5 water using various energy resoures inluding industrial waste,

low-grade /eat, and alternative ones. e9etion of solutes in % roesses is

based on seletive evaoration of water moleules, w/ile solute moleules

stay in t/e li6uid feed /ase. 0n rinile, t/e re9etion ratio of % is as /ig/

as t/at of reverse osmosis 4+5, and even suerior for t/e removal of arseni

and boron 7!, &8. :/e urrent bottlene; of % te/nology inludes lower

distillate 4ermeate5


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system, and it does not re6uire e=ternal ondensers 728. @% rovides /ig/er

distillate


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transfer in solid and void membrane regions. C/arateristi arameters of

HD%C% roesses an be ategori?ed into t/ree grous3 425 oeration

ondition 4temeratures and


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furt/er to roose otimal oeration onditions. Usually, t/is aroa/ an

notieably redue t/e number of 4ostly5 e=eriments in variety of siene

and engineering disilines. /en a large amount of data are rodued

using a series of simulations, analysis of t/e big data is anot/er imortant

tas;. :/e ational Iig %ata esear/ and %eveloment 0nitiative was

announed by t/e US /ite House to /el solve some of t/e ations most

ressing /allenges for sienti disovery, environmental and biomedial

resear/, eduation and national seurity 7'8. 0t aims to ma;e t/e most of t/e

fast-growing volume of digital data and to imrove ;nowledge and insig/ts

from t/e large and omle= olletions of digital data. Sei engineering

roesses su/ as % /ave a variety of oeration variables and otions.

Controlling arameters of %C% easily e=eeds 2$ 4see Setion !.&.!5. 0f

ea/ arameter /as " andidate values, t/e total number of oeration ases

is "2$L (,G)",)!", w/i/ is almost 2$ millions. 0t is ratially imossible to

ondut t/is number of e=eriments wit/in a limited amount of time to nd

otimal onditions. 0f a /ysial model t/at an redit fundamental trend of

engineering /enomena is /owever available, ;ey governing arameters of

t/e % erformane and t/eir inter-relations/is an be readily identied by

analy?ing t/e big data of % simulations. Along t/is soe, we use our

revious modeling tool, seially develoed for HD%C% 7G8, generate

simulation oututs of an order of 2$ million ases, and analy?e t/e big data

using advaned statistial aroa/, i.e., self-organi?ing ma as omared to

onventional multile linear regression. 0n t/is aer, we aim to understand


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t/e relative signiane of ore arameters and t/eir imortane on

mass/eat transfer /enomena, lin; onventional dimensionless numbers to

t/e diret simulation results, and nally rovide a /enomenologial

orrelation for fast estimation of mass and /eat transfer.

%# &'eory and simulations

2.1. System confguration

e onsider a ylindrial vessel ontaining a large number of /ollow

bers of an order of at least a few t/ousands. :/e large number of bers and

geometrial omle=ity ma;e formidable to do diret simulations of ouled

/eat and mass transfer ourring t/roug/ individual bers. e reviously

develoed a model to analy?e t/e erformane of HD%C% by onsidering a

ylindrial ell, w/i/ was assumed to ontain imortant /ysial and

engineering /arateristis 7G8.

e onsider t/e /ot-outold-in 4H+C05 oeration mode of HD%C%,

w/ere t/e /ot and old streams


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:/e t/ermal ondutivity of membrane materials for % is of an order of

+4$.25 mNK. :/e /eat transfer from t/e /ot feed to t/e old ermeate

onsists of ondution t/oug/ t/e solid art of t/e membrane and

onvetion by t/e vaor use t/roug/ 4tortuous5 membrane ores, t/ey arry t/ermal

energy from t/e feed-membrane to t/e ermeate-membrane interfaes. :/is

inreases t/e ermeate temerature along t/e ber. @isous mass transfer is

negligible in %C% beause water and air moleules are onned in ore

saes.

:/e ounter-urrent old stream obtains 4i5 t/e onduted /eat at t/e

solid membrane surfae and 4ii5 t/e onveted mass and arried /eat at t/e

ore outlets. :/e transfer rate of t/e water vaor determines t/e %

erformane wit/ redetermined oeration onditions. :/e /ot feed stream

looses /eat as mu/ as t/e old stream reeives, and t/erefore t/e

feedermeate stream temeratures dereasesinreases along t/e ber.

Ieause t/e lumen volume is usually smaller t/an t/e s/ell volume 4er

ber5, t/e lumen temerature varies more raidly in t/e longitudinal


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diretion t/an t/e s/ell temerature. 0n t/is ase, t/e dominant transfer

me/anisms in ea/ region are as follows3 4i5 momentum and /eat transfer

in t/e lumen and s/ell regions and 4ii5 /eat and mass transfer in t/e void and

solid membrane arts. :/ese me/anisms an be /arateri?ed

6uantitatively using reresentative dimensionless numbers.

0f Nf/ollow bers of inner and outer radii of a and b, resetively, are

a;ed in a ylindrial vessel of radius Rv, t/en t/e a;ing fration is

alulated as


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, and average volume er ea/ ber is c!L w/ere c 4


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5 is t/e ell radius 4see Dig. 24a55. :/roug/out t/is aer, t/e inner, s/ell, and

ell surfaes indiates rL a, b, and c, resetively. Dluid veloities are

assumed to be ?ero on t/e inner and s/ell surfaes of t/e HD membrane, and

tangential stress and radial temerature gradient are resumed to be ?ero

on t/e ell surfae. at/ematial details an be found in our revious wor;

7G8.


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2.2.Dimensionless number analysis or HFDCMD

2.2.1. Overview

0n % roesses, /eat transfer rate an be e=ressed as

425


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w/ere iL f, m, and p, indiating feed, membrane, and ermeate,

resetively. +n t/e same line, OTf, O Tm, and O Tp, are temerature

di>erenes between t/e bul; feed and feed-membrane interfae, aross t/e

membrane of t/i;ness m4L bP a5, and between t/e ermeate-membrane

interfae and bul; ermeate stream, resetively. As temerature is a oint

funtion in t/e ylindrial ell, !iand OTiare often imlied as lengt/-averaged

6uantities. it/in t/e HD membrane, we /ave !mL !m"Q#$%$R OTm, w/ere !m"is

t/e ure /eat transfer oeFient of t/e orous membrane and %$ is t/e

evaoration ent/aly of water. /enomenologially, t/e vaor erene between t/e /ot feed and old

ermeate temeratures3

4!5


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w/ere &m is t/e membrane mass transfer oeFient and ' is t/e artial

ressure of t/e vaor gas. :/e omle=ity omes from t/e ouling of (iand

#$t/roug/ !m. 0n steady state, (i in ea/ region s/ould be e6ual to ea/ ot/er

beause t/ere is neit/er soure nor sin; of /eat in t/e vessel. :/en, one

writes

4&5

Estimation of !fand !pis a ruial ste for t/e erformane analysis beause

t/ey vary wit/ geometrial and


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simulations5 is well aeted in % literature. :/ese orrelations reresent

t/e usselt number 4u5 as a funtion of eynolds 4e5, randtl 4r5, 1ras/o>

41r5 numbers as well as t/e ratio of /ydrauli diameter 4)!5 to /annel lengt/

4L5.

1ryta et al. 7(8 summari?ed 2& orrelations ommonly used for t/e

estimation of t/e usselt number in ylindrial onduts under laminar


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4"5

and

4)5


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and reorted t/at E6. 4)5 rovides better mat/ t/an E6. 4"5 wit/

e=erimental observation. Some resear/ers used two di>erent orrelations

to estimate /eat transfer oeFients in feed and ermeate sides searately.

Kim et al. 7228 used E6. 4)5 for t/e tube 4lumen5 side stream and used

1roe/ns orrelation for t/e s/ell side of a /ollow ber module 72!83

4G5

w/ere *is t/e yaw angle. Similarly, Edwie and C/ung 72&8 used two di>erent

emirial orrelations for /eat transfer of t/e /ot feed and old distillate

streams for HD%C%. /attaranawi; et al. 72#8 and Ho et al. 72"8 used E6. 4)5

for t/e


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:/e inner and outer radii of /ollow ber membrane 4i.e., a and b,

resetively5 are of an order of +4$.25 mm and t/e t/i;ness m /as a

omarable si?e to a. :/is imlies t/at urvature e>et of t/e /ollow ber

needs to be arefully onsidered in solving governing e6uations. 0n a steady

state 4 R tL $5, /eat and mass


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4'5

resetively. Ieause t/ere is neit/er soure nor sin; of /eat and mass in t/e

vessel, divergenes of + and #$ must vanis/. +ne an assume t/at /eat

transfer aross t/e HD membrane is redominant in t/e radial diretion

4indiated using subsrit r53


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4(5


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w/ere T is t/e absolute temerature wit/in membrane, is t/e t/ermal

ondutivity of t/e orous membrane and


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4


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5 is t/e e>etive molar ent/aly using


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L !#."!G ;Jmol and


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L ".!# V 2$P! ;JmolNK. Di;s law may reresent t/e vaor is t/e e>etive di>usion oeFient as a ombination of Irownian and

Knudsen di>usivity using Iosan6uets relations/i 7G, 2G, 2'8. 1eneral


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solutions for t/e ouled E6s. 4(5 and 42$5 were analytially obtained using

erturbation t/eory, and an iterative met/od was used to alulate loal and

lengt/-averaged roles of /eat and mass


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4225

w/ere 14L 4c!P b!5L5 is t/e li6uid volume and S$4L !4bQ c5L5 is t/e wetted

surfae area by t/e li6uid. :/en, we alulate

42!5

w/ere 2L b!R c! is t/e volume 4or a;ing5 fration of t/e rode inside t/e

ie. Digs. 24a5 and 4b5 /ave similar /arateristis at rL c. +ur revious

wor; assumed


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and


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4in Dig. 24a55, of w/i/ t/e former indiated t/ermally insulated surfae of t/e

rode-ontaining ie 4in Dig. 24b55. :/erefore, t/e e>etive diameter for /eat

transfer must be alulated using onduting surfae only 4instead of wetted

surfae5, ScL !bL. :/en we /ave


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42&5

beause S$W Scor 2T 2.$. +n summary, t/e /arateristi diameters of t/e

s/ell and lumen regions are


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42#5

and


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42"5

resetively.

eynolds number

:/e momentum transfer is /arateri?ed using eynolds number, dened as

a ratio of inertial and visous fores3


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42)5

w/ere t/e ;inemati visosity of water /varies wit/


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t/e 4ross-setion averaged5 usion rate is dened as randtl number3


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42G5

w/ere 4L 0$R cp 7m!s8 is t/e t/ermal di>usivity, cp 7J;gNK8 is t/e sei

/eat at onstant ressure, and 0$ 7mNK8 is t/e t/ermal ondutivity of


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water 72(8 4see Aendi= for t/eir deendene on temerature5. randtl

number inludes only t/ermal and visous roerties of water, w/i/ are

indeendent of module geometry and usion3 e L er. 0n lumen and s/ell regions, elet

numbers are denoted as


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42'5

and


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42(5

resetively, w/ere t/e ;inemati visosity /is reresented as a funtion of

temerature.

2.2.#. Soli! an! voi! membrane regions

*usselt number


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:/e ratio of onvetive to ondutive /eat transfer is reresented as usselt

number3


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4!$5


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w/ere 4by denition5 !7m !NK8 is t/e onvetive /eat transfer oeFient, Lc

7m8 is t/e /arateristi lengt/, and 0m 7mNK8 is t/e membrane /eat

ondutivity. Here, !an be interreted by /eat


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4!25

w/i/ indiates t/at +rL onstant. Conversely, +dereases wit/ reset to r

from t/e inner 4rL a5 to outer 4rL b5 surfaes. :/erefore, we let


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4!!5

w/ere YS+Z is t/e longitudinal average of S+ 4L r+5, w/i/ reresents t/e

amount of /eat lost in t/e feed stream er unit ber lengt/ er unit time.

CoeFient ! in E6. 4!!5 doubles t/e radial distane, i.e., diameter as

orresonding to LcL !b. 0n t/e steady state, YS+Z is e6ual to /eat obtained by

t/e old stream er unit ber lengt/ er unit time. Here we dene t/e

usselt number for HD%C% as


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4!&5


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eclet number

:/e vaor moleules di>use t/roug/ tortuous membrane ores from t/e

feed-membrane to ermeate-membrane interfaes. As t/ey arry t/ermal

energy, elet number is dened as


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4!#5


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w/ere D is t/e di>usion oeFient of vaor moleules in t/e membrane

ore. Similar to !Lc of E6. 4!!5, #$r is onstant wit/ reset to t/e radial

oordinate beause of

4!"5


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:/en, elet number is rewritten as


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4!)5

w/ere Y5$Z L Y#$rZ indiates t/e amount of vaor mass transferred aross t/e

membrane er unit ber lengt/ er unit time.

Structural factor

A /ollow ber membrane used for %C% an be /ysially /arateri?ed

using ore diameter 4)p5, t/i;ness 4m5, orosity 465, tortuosity 475, and

lengt/ 4L5. A t/in HD membrane of /ig/ orosity, less tortuosity, and larger

diameter rovides /ig/er


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4!G5


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w/ere t/e tortuosity is usually a dereasing funtion of orosity 7!$8. e

used Iee;mans tortuosity e=ression as a funtion of t/e orosity3

4!'5


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w/i/ is seially develoed for /ig/ly interonneted ores. %etails of

tortuosity disussion an be found elsew/ere 7G, !$8.

As desribed above, eynolds and randtl numbers /arateri?e /yisal an

etive di>usion oeFients, /ysial roerties 4inluding

referene onstants and temerature-deendent funtions5 of li6uid water

and water vaor. 1U D+:A 4gfortran version #.'.!5 was used to omile

t/e develoed ode set using 1U ma;e utility. /fdmd uses an inut le to

read 22 arameters as listed in :able 2. :/e En/ySoft a;age is 1U

liensed and oen to ubli. 1U +tave 4version &.'.25 was used for ost-

roessing, !% visuali?ation, and image onversion. Among several releases

of [inu= distribution, Ubuntu 4t/e latest version 2#.$# named trusty5 was

seleted for long-term, stable develoment. +t/er distributions inlude

edHat, Dedora, Cent+S, oenSUSe, and sienti [inu=. Ea/ distribution


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/as its own advantages and disadvantages. Ubuntu develoers are allowed

to uload ersonally develoed a;ages to t/eir own A. ubli users an

freely download, install, and use neessary software rograms under t/e

1U free liense agreement. 0n t/e same lig/t of oen software /iloso/y,

/fdmd 4as an indeendent aliation of En/ySoft5 is available by

aessing t/e orresonding aut/ors A 4see Aendi= for details5. 0n

addition, all t/e neessary software a;ages 4alled deendenies5 are also

freely available 4downloadable5 using a;age management software of t/e

Ubuntu distribution. Dor easy aess and use of /fdmd, gra/ial user

interfae 41U05 is develoed and inluded in t/e En/ySoft a;age, as

s/own in Dig. !4a5. :l:; srit is used to develo t/e /fdmd 1U0, w/i/ an

oen, save, and save as an inut le, and run, s/ow, ar/ive and lear

numerial and gra/ial results in a window. A /el le e=lains /ysial

meanings of inut and outut variables. :o e=and t/e aessibility of t/is

En/ySoft a;age, +rale @irtualIo= was used to run Ubuntu +S in

indows, a, and 4ot/er5 [inu= +Ss. 0n [inu=, t/e En/ySoft an be diretly

installed, but t/e use of @irtualIo= is also ossible. Dig. !4b5 s/ows t/e

En/ySoft @irtualIo= installed in a. :/e general erformane of Ubuntu +S

strongly deends on 4gra/ial5 des;to environment due to t/e limited

artial resoures available from t/e main +S. 1+E and K%E are e=ellent

but t/eir full imlementation on a @irtualIo= may signiantly /amer t/e

erformane of oerating systems. 0nstead, we used [ubuntu, w/i/ uses a

fast and lig/tweig/t oerating system wit/ a minimal des;to, alled [\%E.


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2.#.2. Cases an! result selection criteria

A single run of /fdmd generates !$ les 4' image and 2! data les5,

w/i/ are used by t/e +tave srit to summari?e and visuali?e simulation

results. :/e total si?e of all t/e !$ les is 2.! I. :wo dimensional

temerature roles in t/e lumen, membrane, and s/ell regions are stored in

& di>erent les 4ea/ /aving &$$-#$$ KI5 as big as image les. :o run a

HD%C% simulation, 22 arameters are re6uired, as listed in :able 2. :/ese

are temeratures and


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billion les, [inu= S/ell erformane is notieably degraded by /andling a

number of les, eseially to se6uentially read all les for statistial analysis.

Among t/e total 22,$"(,!$$ simulations, only /ysially meaningful

G,#"&,G2G ases are seleted for statistial analysis. 0f t/e HD membrane is

long and stream


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message assing interfae 405 and oen multile roessing 4oen55 are

used, but t/e large number of 9obs are instead divided into t/ree grous

based on t/e a;ing fration values. Ea/ grou of simulations were run in

di>erent omuting nodes, of w/i/ node /as two 6uad-ores 4' ores5 of

0ntel 45 \eon 45 CU E"" !.&& 1H? and 2) 1I of random aess memory.

:/e total & idential nodes 4in terms of /ardware onguration5 were

available and so !# 4L& V '5 /fdmd simulations were simultaneously

onduted at a time. Ea/ node too; 2G." /ours wit/ ' simultaneous 9obs

4i.e., one simulation 9ob er ore5. :/is is e6uivalent to an elased time as

long as 2G." V & V ' L #!$ /ours 4L2G." days5 of se6uential run using a

single ore. :/e G,#"&,G2G /ysially meaningful ases were searately

stored in t/ree les 4on t/ree nodes5, and t/en ombined into a single te=t

le of 2." 1I. Statistial analysis was done using t/is single data le,

ontaining ore information of ea/ run in ea/ le-line.

2.$. %ig Data &nalysis

2.$.1. 'n(ut !ata (re(aration

:wo data sets are reared from t/e raw data for statistial analysis3

one using real /ysial variables and anot/er using redues, dimensionless

variables. 0n t/e /ysial set, t/e tortuosity 475 is alulated using E6. 4!G5 as

a funtion of t/e membrane orosity 465. :/e tortuosity solely deends on

t/e orosity so t/at t/eir orrelation must be transarent and strong.

Ieause Y5$Z is strongly in


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seially, t/eir ratio 675, we intentionally inluded t/e tortuosity as t/e

2!t/ inut arameter. :wo outut arameters of t/is /ysial set are mass

and /eat transfer rate er ber lengt/, Y5$Z and YS+Z, resetively. 0n t/e

dimensionless set, 2! new redued variables are roosed3 redued s/ell

temerature 4Ts/lTlmn5, temerature olari?ation 4Ts/lTlmn P 25, e>etive

orosity 46e>L 675, strutural fator 4SD5, and dimensionless numbers 4e

and r of lumen and s/ell regions, e of all regions, and u of t/e membrane

region only5. Among t/em, e and u of t/e membrane region 4denoted

e^mbr and u^mbr, resetively5 are set as two outut variables, as

orresonding to Y5$Z and YS+Z of t/e /ysial set, resetively.

+n summary, t/e total number of inut variables are 2! and 2$ in t/e

/ysial and dimensionless data sets, resetively, w/i/ are used to redit

orrelation levels to transmembrane mass and /eat transfer rates. Self-

organi?ing ma 4S+5 and multile linear regression 4[5 were used to

analy?e t/ese two big data sets generated from a series of /fdmd numerial

simulations. A:[AI version G.) and 0I SSS Statistis version !2 were

used for S+ and [ analyses, resetively, as follows.

2.$.2. Sel)organi*ing ma( +SOM,

S+ e>etively identies atterns of and relations/is between inut

data using an unsuervised learning algorit/m and e=trat information from

omle= data sets by reating mas of t/e multi-dimensional and

so/istiated data 7!2]!&8. :/e S+ aro=imates t/e robability density


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funtion of t/e inut data and s/ows t/e data in a more omre/ensive

fas/ion of fewer dimensions 4!% or &%5. As t/e system stability is maintained

t/roug/ onvergene to an e6uilibrium ma, t/e S+ rovide great


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4!(5

is fully minimi?ed and so t/e onvergene is rea/ed. 0nitial weig/t values

are randomly assigned wit/ small magnitudes. :/e neuron /aving t/e

s/ortest distane to t/e inut vetor is /osen as a winner. :/e winner and

neig/boring neurons are allowed to /ange t/eir weig/ts to ;ee minimi?ing

t/e distanes. At ea/ iteration, t/e weig/ted vetor is udated as follows3


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4&$5

w/ere :9L 2 for t/e winning and neig/boring vetors, :9 L $ for ot/er

remaining vetors, and .4t5 is a fration for orreted learning. 0n S+

analysis, all inut data 4or variables5 were normali?ed into t/e range 7-2, 28

to ma;e ea/ variable /ave t/e same imat on t/e neuron struture in a

two-dimensional /e=agonal grid. :/e S+ ma nodes and data were

roessed by linear initiali?ation and bat/ training algorit/m, resetively

7&$8. :/e role of reresentative samles of a variable 4i.e., its distribution

attern5 was nally visuali?ed in individual omonent lanes. :/e ma si?e

of S+ was determined by 2$ V 2$ neurons rat/er t/an t/e default si?e 4


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, see ne=t setion for details5 to 6ui;ly investigate data atterns wit/ small

numbers of samles or outut neurons.


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2.$.#. Multi(le linear regression +M-,

:/e multile linear regression 4[5 is a statistial met/od to reveal

t/e linear relations/is between a deendent variable 4;5 and multile

indeendent variables 482, 8!, et5. [ an generate an e6uation t/at best

desribe linear ombinations between inuts and an outut 7!(8. 0n t/is

study, a logarit/mi transformation was used to normali?e t/e deendent

variable to satisfy t/e /omosedastiity re6uirement, i.e., t/e varianes of

t/e outut variable are normally distributed aross t/e range of reditor

variables. Stewise regression met/od was used to selet imortant

reditor variables in t/e regression roess using robability of $.$" and $.2

for entry and removal, resetively. :/e average inet t/e validity of t/e regression e6uation and

oeFients 7!'8.

+# esults and Discussion

Dig. & s/ows satial atterns of t/e 2# arameters of t/e /ysial data

set, analy?ed using t/e S+ met/od. :/e 2! inut data inlude t/e

alulated tortuosity, and two oututs are t/e /eat and mass transfer rates

er nger lengt/, 5$ and S+, resetively. Ea/ arameter ma 4i.e.,

omonent lane5 reresents t/e distribution of 2$$ samles, visually s/own


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in t/e 2$ by 2$ /e=agonal grid. :/is grid is redued from t/e total G,#"&,G2G

original samles. Color bars indiate ranges of arameter values and similar

ma atterns in general imly strong orrelations. Here we rst disuss t/e

data artitioning. As s/own in t/e fteent/ anel 4at t/e bottom row, seond

to t/e rig/t5, t/e samles were artitioned into ) di>erent grous based on

t/e /arateristi similarity of t/e inut arameters. :/e si=teent/ anel

s/owed %avies-Iouldin inde= versus t/e number of lusters tested. A lower

%avies-Iouldin inde= is a symmetri and non-native tion of t/e ratio of

/ow lusters are sattered. A lower inde= indiates a better lustering. 0n

ot/er words, t/e best lustering minimi?es t/e %avies-Iouldin inde=. 0n our

study, si= lusters will best e=lain t/e variation atterns of t/e HD%C%

arameters. Some S+ omonent anels /ave interesting atterns of

arameter variables. ost arameter mas s/ow gradient strutures of

vertial ?ig-?ag stries, inluding 2! inut and ! outut arameters.

0n t/e rst grou, :s/l, inr, otr, d^ore, lengt/, and KaaSolid /ave

t/is strutural tye from blue left to red rig/t, w/i/ /as lose similarity to

S6bar. 0n t/e seond grou, :lmn and afra /ave t/e vertial strie

strutures, but olor variations loo; disorderly osillating and are not as

onsistent as ot/ers. :/is indiates t/at :lmn and afra are less orrelated

to ot/ers. :/e t/ird grou onsists of u^bar and v^bar, of w/i/ anel mas

are very similar to ea/ ot/er, /aving t/e red-left to blue-rig/t gradient of

vertial ?ig-?ag stries. :/e trend of t/is t/ird grou is oosite to t/at of t/e


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rst grou. :/e fourt/ grou /as t/e inut arameter, orosity, and t/e

alulated arameter, tortuosity. :/e orosity ma attern is uni6ue to /ave

t/e /ori?ontal gradient of blue-to to red-bottom stries. As t/e tortuosity is

inversely roortional to t/e orosity, t/e tortuosity attern follows red-to

to blue-bottom /ori?ontal stries. :/ese two arameters are least orrelated

to ot/ers beause t/ey are very basi /ysial /arateristis of membrane

material. As e=eted, t/e inverse relations/i between t/e orosity and

tortuosity is learly s/own in t/e ma atterns. :/e ft/ grous is t/e outut

grou /aving Dw^bar and S6^bar. Dw^bar /as a uni6ue ma attern, w/i/

loo;s similar to t/e vertially


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Dig. # s/ows results of S+ analysis using t/e dimensionless data set of

total 2! variables 42$ inuts and ! oututs5. Similar to Dig. &, t/is large data

set is redued to 2$$ reresentative samles resented in omonent lanes

wit/ olor bars. e inlude :s/l^red, :em^ol, and. randtl^s/l in t/e rst

analysis grou of Dig. #. :s/l^red and :em^ol /ave t/e same gradient of of

t/e /ori?ontal stries3 blue-to to red-bottom. randtl^s/l also /as t/e

/ori?ontal /arateristis of reverse olor s/eme. :/e mas of t/ese t/ree

arameters better resemble t/at of elet^mbr, reresenting mass transfer

rate aross t/e HD membrane er unit lengt/. @ertial gradients are learly

s/own in mas of eynolds^lmn, elet^lmn, and elet^s/l /aving t/e red-

rig/t to blue-left gradient. elet^s/l loo;s similar to t/e above t/ree

aramets wit/ a slig/t diagonal attern. :/is trend is oosite to

usselt^mbr reresenting t/e /eat transfer rate aross t/e membrane. :/e

ma of e>etive orosity, i.e., orosity divided by t/e tortuosity, /as an

almost idential ma attern to t/at of usselt^mbr, indiating t/eir strong

orrelation. rnadtl^lmn also /as a vertial strie attern but t/e gradient

/as a ea; a away from left or rig/t end. Unli;e ot/er /ysial dimensionless

numbers, randtl^s/l /as t/e gradient struture of /ori?ontal stries. e

believe t/is inetive orosity, SD is less

orrelated to ot/ers, eseially elet^mbr and usselt^mbr. +t/er two less

orrelated arameters are randtl lmn and eynolds^s/l. ote t/a


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elet^mbr is best orrelated to :s/l^red and :emol, and usse;t^mbr s/ows

a sei similarity only to e>etive orosity. e t/in; t/at t/is S+ analysis

of t/e dimensionless data set does not rovide new sei information in

addition to t/ose from t/e /ysial data set. e disuss t/is issue in t/e ne=t

setion using t/e [ met/od.

:/e /ysial and dimensionless data sets are analy?ed using t/e multile

linear regression 4[5 met/od, w/i/ /ave 2$ and 2! inut arameters,

resetively, to redit two outomes, resetively. 0n t/e /ysial data set

Dw^bar and S6^bar are regressed using varying number of arameters from 2

to 2!, and elet^mbr and usselt^mbr are regressed using 2 to 2$

dimensionless variables. Dig. " s/ows auraies of t/e [ met/od in terms

of R!values of ea/ redited variables. :/e R!values of t/e four redited

deendent variables 4Dw^bar, S6^bar, elet^mbr and usselt^mbr 5 inrease

as t/e number of deendent variables inreases from 2 to #. Using more

t/an " deendent variables does not signiantly en/ane t/e reditability

of t/e [ met/od. At least, four variables are re6uired to e=lain variations

of Dwbar, S6bar, and eletbr, w/ereas t/ree arameters are enoug/ to

redit usselt^mbr.

:able ! s/ows oeFients of four redited variables in t/e form of


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4&25

w/ere


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by one, 4log-transformed5 Dwbar inreased by 2.'$ V 2$P# units.5 @alidity of

t/is redition using unstandardi?ed oeFients are 6uantied using

standard error 4SE5 values, w/i/ are mu/ smaller t/an unstandardi?ed

oeFients,


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arameters of Dwbar and S6bar are d^ore and :lmn, resetively. ass

transfer rate er unit lengt/, Dwbar, is rimarily restrited by t/e vaor

evaoration rate at t/e interfae between /ot feed and 4outer5 membrane

surfaeX and it is inversely roortional to t/e membrane t/i;ness, otr -


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inr. 1iven t/at, ore saes of an order of


76/88


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V 4otr P inr5 geometrially determine t/e vaor transfer rate. dôre is r

n;ed t/e fourt/ in t/e [ of Dwbar. 0nterestingly, t/is indiates t/at t/

lumen temerature is not as imortant as t/e ore si?e of HD membrane. :/e

least inerene, i.e., :s/l P :lmn. Unli;e Dwbar, HD geometry is more

imortant in S6bar, followed by temeratures. dôre in Dwbar disaears

in S6bar, and relaed by :lmn. Comaring t/e fourt/ arameters 4dôre and

lmn in reditions of Dwbar and S6bar, resetively5 s/ows /ysial insig/t t

at mass transfer is rimarily initiated by t/e /ot feed temerature an

As indiated above, elet^mbr and usselt^mbr reresent dimensionless

forms of mass and /eat transfer rates, Dwbar and S6bar, resetively.

0nterestingly, t/e dimensionless data set /as four ommon, most signiant

arameters, indiretly imlying t/at t/e dimensionless analysis an rovide

meaningful /ysial results using t/e omat forms. :/is arameters are

ran;ed in order3 :s/l^red, orosityê>, elet^lmn, and elet^s/l for

rediting elert^mbr and orosityê>, elet^s/l, elet^lmn, and :s/l^red

for regressing S6bar. Among t/em, elet^s/l always /as t/e negative sign,

ran;ed t/e first and t/ird in terms of _ of usselt^mbr and elet^mbr,

resetively. ote t/at lumen and s/ell elet numbers are based on t/ermal

di>usion and membrane elet number is based on vaor di>usion t/roug/

membrane ores.


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0n rediting elet^mbr, t/e redued s/ell 4feed5 temerature :s/l^red is

found to be t/e most signiant arameter wit/ =L $.G#, w/i/ is /ig/ly

analogous to =L $.G$ of :s/l in Dwbar regression. :s/l^red /as t/e least

imat on usselt^mbr redition as e=eted from t/e fat t/at :s/l and

:lmn in S6bar regression are ran;ed t/e t/ird and fourt/, resetively.

otieably small = value of :s/l^red e=lains t/e lateau trend of

usselt^mbr lot 4in Dig. "5 after t/e number of indeendent variables more

t/an t/ree. 0t is interesting t/at :em^ol does not s/ow u in rediting any

of membrane transort dimensionless numbers. E>etive orosity aears

bot/ in regression e6uations, and ran;ed t/ird and fourt/ of membrane

usselt and elet numbers, w/i/ were absent in Dwbar and S6bar

reditions. :/is e>etive orosity is as imortant as elet^lmn 4=L $.)&5 in

usselt^mbr redition. Strutural fator does not s/ow u as imortant

inut arameters in analysis of t/e dimensionless set. 0n bot/ /ysial and

dimensionless sets, mirostruture of t/e membrane is found to be

seondarily imortant as omared to marosoi geometry and oeration

onditions.

[umen and s/ell 4t/ermal5 elet numbers aear to be ;ey ontrolling

arameters of bot/ membrane elet and usselt numbers. [umen elet

number /as stronger in


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veloity and /ydrauli diameter are linearly roortional to t/e lumen elet

number. As t/e 4only5 lumen temerature inreases t/e ;inemati visosity

dereases so t/at t/e lumen elet number inreases. 0n most emirial

orrelations develoed or used for /eat transfer /enomena of %C%

roesses, visosity and density are often assumed to be onstant or =ed at

sei temeratures. As t/ese temerature-deendent ets of s/ell elet number 4of E6.

2(\\5 to mass/eat transfer /enomena. 1iven t/e s/ell veloity, a /ig/er

HD a;ing redues volumetri


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a;ing ratio indiates /ig/er volumetri erene between t/e s/ell and lumen temeratures, i.e., driving fore of

t/e transfer /enomena. :/ere is no doubt t/at feed temerature and feed-

distillate temerature di>erene lay ;ey roles in mass and /eat transfer.

%imensionless numbers su/ as eynolds, randtl, and elet numbers

/arateristi


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membrane elet and usselt numbers. ore imortantly dimensionless

analysis uses t/e same set of four indeendent arameters. +ne an

systematially omare in


82/88

7&8 %eyin Hou, Jun ang, \iang/eng Sun, /ao;un [uan, C/angwei /ao,

and \iao9ing en. Ioron removal from a6ueous solution by diret ontat

membrane distillation. Journal of Ha?ardous aterials, 2GG42-&53)2&])2(,

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sienediret.omsieneartileiiS$&$#&'(#$($!$)"!.

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/ollow ber membranes wit/ narrow ore si?e distribution and ultra-t/in

s;in for t/e fres/ water rodution t/roug/ membrane distillation.

C/emial Engineering Siene, )&4(53!"'G]!"(#, ay !$$'. 0SS

$$$(!"$(. doi3 2$.2$2)9.es.!$$'.$!.$!$. U[

/tt3lin;ing/ub.elsevier.om retrieveiiS$$$(!"$($'$$$($$.

7"8 Jung-1il [ee and oo-Seung Kim. umerial modeling of t/e vauum

membrane distillation roess. %esalination, &&23#)]"", %eember

!$2&. 0SS $$22(2)#. doi3 2$. 2$2)9.desal.!$2&.2$.$!!. U[

/tt3www.sienediret.omsieneartileii S$$22(2)#2&$$#(&2.

7)8 1uo6iang 1uan, \ing ang, ong ang, obert Dield, and Ant/ony 1.

Dane. Evaluation of /ollow ber-based diret ontat and vauum

membrane distillation systems using asen roess simulation. Journal of

embrane Siene, #)#32!G]2&(, August !$2#. 0SS $&G)G&''. doi3

2$.2$2)9.memsi.!$2#.$&.$"#. U[ /tt3www.sienediret.om

sieneartileiiS$&G)G&''2#$$!#$&.


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7G8 Albert S Kim. Cylindrial ell model for diret ontat membrane

distillation 4%C%5 of densely a;ed /ollow bers. Journal of embrane

Siene, #""32)']2'), Aril !$2#.

0SS $&G)G&''. doi3 2$.2$2)9.memsi.!$2&.2!.$)G. U[

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7'8 +IAA A%00S:A:0+ U@E0[S I01 %A:A 00:0A:0@E3 A+UCES

h!$$ 0[[0+ 0 E % 0@ES:E:S, !$2!. U[

/tt3www.w/ite/ouse.gov

sitesdefaultlesmirositesostbig^data^ress^release^nal^!.df.

7(8 1ryta, :omas?ews;a, and A oraws;i. embrane distillation wit/

laminar our, and Kim C/oon g.

erformane investigation of a solar-assisted diret ontat membrane

distillation system. Journal of embrane Siene, #!G4$53"]&)#, January

!$2&. 0SS $&G)-G&''. doi3 /tt3d=.doi.org


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2$.2$2)9.memsi.!$2!.2$.$$'. U[

/tt3www.sienediret.omsieneartile iiS$&G)G&''2!$$G"!2.

72!8 H.1. 1roe/n. 0net of ore si?e

distribution and air


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/tt3www.sienediret.omsieneartile iiS$$$2')')2$$$2G!G.

72G8 Albert S Kim. A two-interfae transort model wit/ ore-si?e distribution

for rediting t/e erformane of diret ontat membrane distillation

4%C%5. Journal of embrane Siene, #!'3#2$]#!#, Debruary !$2&. 0SS

$&G)G&''. doi3 2$.2$2)9.memsi.!$2!.2$.$"#. U[

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agas/ima, ar J Assael, and illiam A a;e/am. Standard eferene

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Sa/imi. :ortuosity in orous edia3 A Critial eview. Soil Siene Soiety

of Ameria Journal, GG4"532#)2] 2#GG, !$2&. 0SS $&)2-"((". doi3

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7!'8 Andy Dield. %isovering statistis using SS. Sage ubliations [td,

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Hydrology. 1raw-Hill, ew or;, 2st edition, 2((&.

Cations for .gures

Dig. 2. S/emati of 4a5 a /ollow ber loated in a imaginary ylindrial ell,

w/i/ reresents a number of densely a;ed bers in a vessel and 4b5

onduts of /eat transfer onsisting of a solid rod inside a ylindrial

imermeable ie. Ea/ /as lengt/ L.

Dig. !. Snas/ots of 4a5 /fdmd 1U0 and 4b5 +rale @irtualIo=.

Dig. &. @ariation of variables 4i.e., 2# omonent lanes5 of reresentative

samles analy?ed by a Self-+rgani?ing a in a 2$-by-2$ /e=agonal grid. 0n

t/e gure, data artitioning 4s/own in t/e fteent/ anel5 indiates


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individual lusters t/at /ave similar /arateristis w/i/ are divided by t/e

minimum %avies-Iouldin inde= of ) lusters 4s/own in t/e si=teent/ anel5.

Dig. #. @ariation of variables 4i.e., 2! omonent lanes5 of reresentative

samles analy?ed by a Self-+rgani?ing a in a 2$-by-2$ /e=agonal grid.

Unli;e Dig. 2, various dimensionless numbers were used as inut variables in

t/e analysis.

Dig. ". :/e fration of variane 4i.e., oeFient of determination R!5 e=lained

by t/e regression e6uation wit/ di>erent numbers of reditor variables.

Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation

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