7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
1/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
2/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
3/88
system, and it does not re6uire e=ternal ondensers 728. @% rovides /ig/er
distillate
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
4/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
5/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
6/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
7/88
:/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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
8/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
9/88
, and average volume er ea/ ber is c!L w/ere c 4
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
10/88
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.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
11/88
2.2.Dimensionless number analysis or HFDCMD
2.2.1. Overview
0n % roesses, /eat transfer rate an be e=ressed as
425
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
12/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
13/88
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
#$t/roug/ !m. 0n steady state, (i in ea/ region s/ould be e6ual to ea/ ot/er
beause t/ere is neit/er soure nor sin; of /eat in t/e vessel. :/en, one
writes
4&5
Estimation of !fand !pis a ruial ste for t/e erformane analysis beause
t/ey vary wit/ geometrial and
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
14/88
simulations5 is well aeted in % literature. :/ese orrelations reresent
t/e usselt number 4u5 as a funtion of eynolds 4e5, randtl 4r5, 1ras/o>
41r5 numbers as well as t/e ratio of /ydrauli diameter 4)!5 to /annel lengt/
4L5.
1ryta et al. 7(8 summari?ed 2& orrelations ommonly used for t/e
estimation of t/e usselt number in ylindrial onduts under laminar
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
15/88
4"5
and
4)5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
16/88
and reorted t/at E6. 4)5 rovides better mat/ t/an E6. 4"5 wit/
e=erimental observation. Some resear/ers used two di>erent orrelations
to estimate /eat transfer oeFients in feed and ermeate sides searately.
Kim et al. 7228 used E6. 4)5 for t/e tube 4lumen5 side stream and used
1roe/ns orrelation for t/e s/ell side of a /ollow ber module 72!83
4G5
w/ere *is t/e yaw angle. Similarly, Edwie and C/ung 72&8 used two di>erent
emirial orrelations for /eat transfer of t/e /ot feed and old distillate
streams for HD%C%. /attaranawi; et al. 72#8 and Ho et al. 72"8 used E6. 4)5
for t/e
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
17/88
:/e inner and outer radii of /ollow ber membrane 4i.e., a and b,
resetively5 are of an order of +4$.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 $5, /eat and mass
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
18/88
4'5
resetively. Ieause t/ere is neit/er soure nor sin; of /eat and mass in t/e
vessel, divergenes of + and #$ 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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
19/88
4(5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
20/88
w/ere T is t/e absolute temerature wit/in membrane, is t/e t/ermal
ondutivity of t/e orous membrane and
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
21/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
22/88
4
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
23/88
5 is t/e e>etive molar ent/aly using
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
24/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
25/88
L !#."!G ;Jmol and
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
26/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
27/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
28/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
29/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
30/88
4225
w/ere 14L 4c!P b!5L5 is t/e li6uid volume and S$4L !4bQ c5L5 is t/e wetted
surfae area by t/e li6uid. :/en, we alulate
42!5
w/ere 2L b!R c! is t/e volume 4or a;ing5 fration of t/e rode inside t/e
ie. Digs. 24a5 and 4b5 /ave similar /arateristis at rL c. +ur revious
wor; assumed
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
31/88
and
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
32/88
4in Dig. 24a55, of w/i/ t/e former indiated t/ermally insulated surfae of t/e
rode-ontaining ie 4in Dig. 24b55. :/erefore, t/e e>etive diameter for /eat
transfer must be alulated using onduting surfae only 4instead of wetted
surfae5, ScL !bL. :/en we /ave
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
33/88
42&5
beause S$W Scor 2T 2.$. +n summary, t/e /arateristi diameters of t/e
s/ell and lumen regions are
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
34/88
42#5
and
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
35/88
42"5
resetively.
eynolds number
:/e momentum transfer is /arateri?ed using eynolds number, dened as
a ratio of inertial and visous fores3
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
36/88
42)5
w/ere t/e ;inemati visosity of water /varies wit/
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
37/88
t/e 4ross-setion averaged5 usion rate is dened as randtl number3
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
38/88
42G5
w/ere 4L 0$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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
39/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
40/88
42'5
and
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
41/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
42/88
:/e ratio of onvetive to ondutive /eat transfer is reresented as usselt
number3
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
43/88
4!$5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
44/88
w/ere 4by denition5 !7m !NK8 is t/e onvetive /eat transfer oeFient, Lc
7m8 is t/e /arateristi lengt/, and 0m 7mNK8 is t/e membrane /eat
ondutivity. Here, !an be interreted by /eat
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
45/88
4!25
w/i/ indiates t/at +rL onstant. Conversely, +dereases wit/ reset to r
from t/e inner 4rL a5 to outer 4rL b5 surfaes. :/erefore, we let
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
46/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
47/88
4!!5
w/ere YS+Z is t/e longitudinal average of S+ 4L r+5, w/i/ reresents t/e
amount of /eat lost in t/e feed stream er unit ber lengt/ er unit time.
CoeFient ! in E6. 4!!5 doubles t/e radial distane, i.e., diameter as
orresonding to LcL !b. 0n t/e steady state, YS+Z is e6ual to /eat obtained by
t/e old stream er unit ber lengt/ er unit time. Here we dene t/e
usselt number for HD%C% as
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
48/88
4!&5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
49/88
eclet number
:/e vaor moleules di>use t/roug/ tortuous membrane ores from t/e
feed-membrane to ermeate-membrane interfaes. As t/ey arry t/ermal
energy, elet number is dened as
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
50/88
4!#5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
51/88
w/ere D is t/e di>usion oeFient of vaor moleules in t/e membrane
ore. Similar to !Lc of E6. 4!!5, #$r is onstant wit/ reset to t/e radial
oordinate beause of
4!"5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
52/88
:/en, elet number is rewritten as
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
53/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
54/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
55/88
4!G5
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
56/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
57/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
58/88
/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.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
59/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
60/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
61/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
62/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
63/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
64/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
65/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
66/88
, see ne=t setion for details5 to 6ui;ly investigate data atterns wit/ small
numbers of samles or outut neurons.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
67/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
68/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
69/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
70/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
71/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
72/88
4&25
w/ere
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
73/88
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,
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
74/88
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 -
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
75/88
inr. 1iven t/at, ore saes of an order of
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
76/88
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
77/88
V 4otr P inr5 geometrially determine t/e vaor transfer rate. d^ore 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. d^ore in Dwbar disaears
in S6bar, and relaed by :lmn. Comaring t/e fourt/ arameters 4d^ore 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, orosity^e>, elet^lmn, and elet^s/l for
rediting elert^mbr and orosity^e>, 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.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
78/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
79/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
80/88
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
81/88
membrane elet and usselt numbers. ore imortantly dimensionless
analysis uses t/e same set of four indeendent arameters. +ne an
systematially omare in
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
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(,
ay !$2$. 0SS $&$#-&'(#. U[ /tt3www.
sienediret.omsieneartileiiS$&$#&'(#$($!$)"!.
7#8 Kai u ang, :ai-S/ung C/ung, and are; 1ryta. Hydro/obi @%D
/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#$$!#$&.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
83/88
7G8 Albert S Kim. Cylindrial ell model for diret ontat membrane
distillation 4%C%5 of densely a;ed /ollow bers. Journal of embrane
Siene, #""32)']2'), Aril !$2#.
0SS $&G)G&''. doi3 2$.2$2)9.memsi.!$2&.2!.$)G. U[
/tt3www.sienediret. omsieneartileiiS$&G)G&''2&$2$&$!.
7'8 +IAA A%00S:A:0+ U@E0[S I01 %A:A 00:0A:0@E3 A+UCES
h!$$ 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 $&G)-G&''. doi3 /tt3d=.doi.org
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
84/88
2$.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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
85/88
!53")]'', !$22. 0SS $$$2-')'). doi3 %+032$.2$2)9.is.!$2$.$(.$$". U[
/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.!$2!.2$.$"#. U[
/tt3lin;ing/ub.elsevier.omretrieveiiS$&G)G&''2!$$'$2$.
72'8 C. H. Iosan6uet. :/e otimum ressure for a di>usion searation lant.
Iritis/ :A eort, age I"$G, 2(##.
72(8 aria [ @ amires, Carlos A ieto de Castro, u/i agasa;a, A;ira
agas/ima, ar J Assael, and illiam A a;e/am. Standard eferene
%ata for t/e :/ermal Condutivity of ater. Journal of /ysial and
C/emial eferene %ata, !#4&532&GG]2&'2, 2((". doi3
2$.2$)&2."""()&. U[ /tt3lin;.ai.orglin;J!#2&GG2.
7!$8 Ie/?ad 1/anbarian, Allen 1. Hunt, obert . Ewing, and u/ammad
Sa/imi. :ortuosity in orous edia3 A Critial eview. Soil Siene Soiety
of Ameria Journal, GG4"532#)2] 2#GG, !$2&. 0SS $&)2-"((". doi3
2$.!2&)sssa9!$2!.$#&". U[ /tts3www.soils.org
ubliationssssa9abstratsGG"2#)2.
7!28 :euvo Ko/onen. Self-+rgani?ed Dormation of :oologially Corret
Deature as. Iiologial Cybernetis, #&3"(])(, 2('!.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
86/88
7!!8 :euvo Ko/onen. Analysis of a simle self-organi?ing roess. Iiologial
Cybernetis, ##4!53 2&"]2#$, 2('!. 0SS $$-2!$$. doi3
2$.2$$GID$$&2G(G&. U[ /tt3d=.doi.org2$. 2$$GID$$&2G(G&.
7!&8 :euvo Ko/onen. Self-+rgani?ing as. Sringer, Ierlin, &rd edition,
!$$2.
7!#8 H itter and K S/ulten. Convergene roerties of Ko/onens toology
onserving mas3 . ater resear/, #"42#53#2'&](G, August !$22. 0SS 2'G(-!##'.
doi3 2$.2$2)9.watres.!$22.$".$!2. U[
/tt3www.sienediret.omsieneartile iiS$$#&2&"#22$$!'#&.
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
87/88
7!'8 Andy Dield. %isovering statistis using SS. Sage ubliations [td,
:/ousand +a;s, CA, !nd edition, !$$".
7!(8 A Kalte/, H9ort/, and Ierndtsson. eview of t/e Self-organi?ing
a 4S+5 Aroa/ in ater esoures3 Analysis, odelling and
Aliation. Environ. odel. Softw., !&4G53'&"]'#", !$$'. 0SS 2&)#-'2"!.
doi3 2$.2$2)9.envsoft.!$$G.2$.$$2. U[
/tt3d=.doi.org2$.2$2)9.envsoft.!$$G.2$.$$2.
7&$8 J @esanto, J Himberg, E Al/oniemi, and J ar/an;angas. S+ toolbo= for
atlab ". :e/nial reort, Esoo, Dinland, !$$$. U[
/tt3www.is./ut.somtoolbo=a;age aerste/re.df.
7&28 S.C. Cut/eon, J. [. artin, and :. +. Jr. Iarnwell. Handbood of
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
7/25/2019 Big Data Analysis of Hollow Fiber Direct Contact Membrane Distillation
88/88
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.
Top Related