Upload
uline-ayu-pangesti
View
229
Download
0
Embed Size (px)
Citation preview
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 1/109
Distribu
Residencfor Chem
Reactors
Ulina Ayu Pan
1306447722
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 2/109
General Characteristics
13.1
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 3/109
Distributions ofResidence i!es
for "#e!icalReactors
Part 1Using t#e RD ti!efunction $%t& and!ean residence
ti!e t!
rid
Part 2RD data andfunction forcon)ersion
'redictions and
e*it concentration
General Characteristics
Residence Time Distribution:
o #el' c#aracteri+e non ideal reactdo not follo, t#e !odel de)elo'ed fPRs and PRs.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 4/109
General Characteristics
All euations and !odels in t#is boo are for c#e!
t#at are ideal 'erfectly !i*ed batc# and !i*ed co
o,e)er t#ese !odels are not al,ays a''licable
reactors %i.e. non(ideal&
#e 'erfor!ance and e5ciency of reactors in reala''lications !ay s#o, de)iation fro! t#e ideal.
ence non(ideal reactors ,ill be t#e 'rinci'le ana
for furt#er calculations.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 5/109
General Characteristics
PAR 1
#e t,o !aor ste's t#at ,ill i!'act t#e RD for non idare
1. o diagnose 'roble!s of reactors in o'eration
2. o 'redict con)ersion or e8uent concentration in e*reactors ,#en a ne, reaction is used in t#e reactor.
#e ai! is to analy+e and c#aracteri+e non(ideal reacto
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 6/109
General characteristics of Sy
-9-$: 1
( ;as(liuid continuous(stirred tan gaseous reactant bubble into t#e rreactant is fed t#roug# an inlet tubside.
( #e continuous liuid '#ase can be'erfectly !i*ed and t#e reaction rato t#e total bubble surface area.
( -o!e gas bubbles can esca'e t#e di=erent si+es.
( #e ti!e t#e bubble s'ends in t#e TIME RESIDENCE.
( #e analysis s#ould be based on t#of eac# bubbles >? a)erage resi
( otal reaction rate is obtain fro! sububbles in t#e reactor.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 7/109
-9-$: 2
( Paced bed reactors ,it# a catalyst s#o,s t#a@uid does not @o, t#roug# t#e reactor unifor!
( -o!e sections in t#e reactor s#o,s little resis,#ic# leads to !aor 'ortion of t#e @uid !ay
its 'at#,ay
( :olecules follo,ing t#is 'at#,ay do not s'en
t#e reactor as t#ose follo,ing t#roug# t#e regresistance to @o,.
( #ere is also a distribution of ti!es t#at !ole
reactor in contact ,it# t#e catalyst.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 8/109
-9-$: 3
( or "-Rs t#e inlet and outlet 'i'es are close to
( ans are !odeled ,it# a by'ass strea! ,#ere
occurred
( -tagnant regions %dead +ones& are often encount#ere is little or no e*c#ange of !aterial ,it# t#e
regions ,#ic# leads to no reaction occurring.
( $*'eri!ents ,ere done to deter!ine
t#e a!ount of t#e !aterial e=ecti)ely
by'assed and t#e )olu!e of t#e dead
+one.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 9/109
Concepts for Non-Ideal Re
"once'ts to describe non(ideal reactors are
1. #e distribution of residence ti!es in t#e
2. #e uality of !i*ing
3. #e !odel used to describe t#e syste!
n real and non(ideal reactors non(ideal @o,e*ist resulting in ine=ecti)e contacting andcon)ersions
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 10/109
13.1.1
Residence-Time Distribution
Function
#e use of R- is to analy+e t#e c#e!ical reactor<s 'erf
RD of a reactor is a c#aracteristic of t#e !i*ing t#at oc
c#e!ical reactor.
ro! RD calculations ,e can analy+e ,#en so!e !ole
uicly and ,#en so!e Bo)erstay t#eir ,elco!eC in t#e
Di=erent !i*ing 'atterns %PR no a*ial "-R t#orou
can re@ect t#e RD.
n so!e cases ,#en !i*ing 'atterns are unno,n t#e R
by a gi)en reactor yields distincti)e clues to t#e ty'e of
occurring ,it#in a rector and can also #el' c#aracteri+e
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 11/109
RTD Function
era'a la!a ato!(ato! o!'@uida suda# berada dala! re
:e!beri infor!asi tentang 'enca!'uran %mixing& dal
reator
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 12/109
Measurement of RTD
13.2
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 13/109
Pengukuran RTD
:enguuronsentrasi tracer
'ada e8uentsebagai fungsi
,atu
racer diinesi 'adat0
:enggunaan tracer
PR?-$- "R("R RA"$
Earut se!'urgan
dala! ca!'uran
ida teradsorb'ada 'er!uaan
reator
-ifat Fsis sa!adengan reatan
nert
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 14/109
Metode Injeksi: Pulse Input
Experiment-eu!la# tracer, >o diinesi satu ali e dala! aliran f
eFsen dan ce'at. Gonsentrasi oultet diuur 'er ,atu.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 15/109
Analisis Single-Input & Si
Output
u!la# tracer yang !eninggalan rea,atu t H tIJt= inre!en ,atu onsentrasi eluaran tracer
Di!ana
Di!anaN0 otal !aterial teri
rasi !aterial dengan RD di antara t dan t I J
$%t& un
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 16/109
Kia >0 tida dieta#ui langsung
Persa!aan diintegralan !enadi
:aa deFnisi $%t& !enadi
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 17/109
entu integral RD function
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 18/109
Contoh Soal 13-1
A sa!'le of t#e tracer #ytane at 320 G ,as inected reactor and t#e e8uent concentration ,as !easure
of ti!e resulting in t#e data s#o,n in abel $13(1.1
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 19/109
Contoh Soal 13-1
a. :engga!bar ur)a "%t& dan $%t& sebagai fungsi ,
b. :enentuan frasi !aterial !eninggalan reatoberada sela!a 3(6 !enit dan 7.7L(M.2L !enit da
c. :enentuan frasi !aterial !eninggalan reatoberada sela!a 3 !enit atau urang dala! reat
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 20/109
Jawabana. Data 'ada abel $13(1.1 digunaan untu !e!'
se'erti di ba,a#
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 21/109
Untu !e!'erole# $%t& dari ur)a "%t& dilauan 'eur)a "%t& dengan !etode -i!'son 1/3 dan >I1 geselanutnya&.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 22/109
Menghitung Integral-i!'son 1/3 -i!'son 3/M
Untu >I1 > gena'
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 23/109
:aa $%t& da'at di#itung dengan !e!bagi "%t& dengan L0.0 g !in/!
-e#ingga di'erole# #asil sebagai beriut
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 24/109
b. Data yang di'erole# di'lot 'ada graF di ba,a#. agian ur)a ya
!enunuan frasi !aterial !eninggalan reator yang tela# be!enit dala! reator. Euas ur)a ini di#itung dengan !etode -i!'
%li#at 2 slide sebelu!&.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 25/109
L1N !aterial !eninggalan reator setela# 3(6 dala! reator
3.0N !aterial !eninggalan reator setela# 7.7!enit di dala! reator
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 26/109
c. rasi !aterial yang !eninggalan reator setela# berada di dala!
3 !enit atau urang adala# luas bagian ur)a dari * 0(3.
Dari 'er#itungan 20N !aterial !eninggalan reasetela# 7.7L(M.2L !enit di dala! reactor.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 27/109
Kendala Pulse Input
-ulit dala! !e!'erole# pulse yang cuu' 'ada in
nesi #arus dilauan dala! 'eriode sangat 'end
Dis'ersi antara titi inesi dan !asuan 'ada rea
sangat ecil #ingga da'at diabaian
Gurang aurat a'abila ur)a "%t& )s ,atu !e!ili'anang
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 28/109
13.2.2 Step Tracer Experiment #e second !ost used !et#od of inection input . n t#is !et#od ,e ,ill for!ulate a !general relations#i' bet,een ti!e()arying
and t#e corres'onding concentration in t#eOe s#all state t#e out'ut concentration frois related to t#e in'ut concentration by cointegral
nlet concentration
Pulse in'ut %Dirac delt
!'erfect 'ulse inection
-te' in'ut
Oe can deter!ine t#e cu!ulati e distribu
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 29/109
Oe can deter!ine t#e cu!ulati)e distribudirectly fro! ste' in'ut. A ste' in'ut in t#concentration for a syste! ,it# constant a constant rate of tracer addition to a feeinitiated at ti!e t0.
ecause inlet concentration is a constantcan for! integral function
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 30/109
Di=erentiate t#is e*'ression to obtain t#e RD funct
#e disadvantages of t#is tec#niue
( Di5cult to !aintain a constant tracer concentratio
( Di=erentiation can on occasion lead to large erro
( Earge a!ount of tracer used for t#is test e*'en
?t#er tracer tec#niues suc# as negati)e ste' %i.e efreuency(res'onse !et#ods and !et#ods t#at use
t#an ste's or 'ulses. #ese !et#ods are !ore di5c
aren<t e*'lained on t#is c#a'ter.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 31/109
Characteristics of theRTD
13.3
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 32/109
Characteristics of the R
E(t) sometimes called exit-age distribution function. $age of distribution of t#e e8uent strea! ,#ic# is !ost usefunctions connected ,it# reactor analysis because it clengt#s of ti!e )arious ato!s s'end at reaction conditions.
Integral relationships of E(t) e*'ressed continuously
#is euation deFned as cumulative istri!uti"n #uncti"n aOe can calculate %t& at )arious ti!es t fro! t#e area under )s t.
or e*a!'le in igure $13(1 3 %t& at 3 !in ,as 0 20 !eans t#at 2
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 33/109
or e*a!'le in igure $13 1.3 %t& at 3 !in ,as 020 !eans t#at 2!olecules s'ent 3 !in or less in t#e reactor.
#e s#a'e of %t& cur)e is s#o,n. Using $13(1.3 ,e can calculate %t!inutes. Oe can continue in t#is !anner to construct %t& in ig 13
#e cur)e is anot#er function t#at #as been deFned as nor!ali+ed'articular in'ut. $. 13(12 #as been used as deFnition of %t& and #at#at as a result it can be obtained as t#e res'onse to a 'ositi)e(ste'
MeanResidenceTime
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 34/109
Mean Residence Time
In the absence of dispersion, and for constant volumetric flow (v=v
what RTD exists for a particulate reactor, ideal or non ideal, this n
space time, τ, is equal to the first moment of RTD function E(t). Th
mean residence time is:
(13-14)
How to determine the total reactor volume using the cumulative d
function.
Prove tnt =Q for constant )olu!etric flo, ))o.
Volume of maize molecule, dV, leaving the reactor in a time dt:
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 35/109
y co!'leting t#e euation t#erefore
#e rig#t #and side is ust t#e !ean residence ti!e t#at t#e !ean residence ti!e is ust t#e s'ace ti!e Q
This result is the true onl" for closed system. Tvolume is determined from the e$:
%h & t f RTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 36/109
%her &oments of RTD
t is )ery co!!on to co!'are RDs by using t#eir !o!enttrying to co!'are t#eir entire distribution. or t#is 'ur'ose!o!ents nor!ally used. #e second !o!ent co!!only u
about t#e !ean and is called t#e )ariance. DeFned by
#e t#ird !o!ent is also taen about t#e !ean and is rela
s(e)ness' #e se,ness deFned by
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 37/109
Diagnostics andTroubleshooting
13.L.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 38/109
General Comments
RD can be used to diagnose 'roble!s in e*isting
#e RD func( tions $%r& and %t& can be used to !
reactor as co!binations of ideal reactors
TypicalRTDsResultingFromDifferentNon
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 39/109
Typical RTDs Resulting From Different Non-
Reactor
%a& RD for near 'lug(Ro, reactor %b& RD for near 'erfectly !i*Paced(bed reactor ,it# dead +ones and c#anneling %d& RD for 'acein %c&S %e& tan reactur ,it# s#ort(circuiting by'assS %f& RD for tanc#anneling %by 'assing or s#ort circuiting& and a dead +one in ,#icslo,ly di=uses in and out
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 40/109
Diagnostics and Troubleshootin
the RTD for ldeal Reactors: CST :ole !ass balance
Res'on to a 'ulse tracer
O#ere Q is t#es'ace ti!e
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 41/109
(a) Perfect Operation
f Q is large t#ere ,il be a slo, decay of t#e out'ut transand $"t for a 'ulse in'ut. f t is s!all t#ere ,ill be ra'id transient "%t&. and $%t& for a 'ulse in'ut.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 42/109
(b) By-passing
A )olu!etric @o, rate U by'asses t#e reactor ,
)olu!etric @o, rate us enters t#e syste! )olu!e
U- I U&
#e subscri't - denotes t#at 'art of t#e @o, #a
by'assed and only U- enters t#e syste!. ecaus
of t#e @uid by'asses t#e @o, 'assing t#oug# t#e
,ill be less an t#e total )olu!etric rate U- T Uo
conseuently Q- Q
Q- ,il be greater t#an t#at if t#ere ,ere no by'as
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 43/109
Oe see fro! t#e %f& cur)e t#at ,e #a)e an initial u!' eual to t#e f'assed.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 44/109
(c) Dead Volume
ecause t#ere is a dead )olu!e ,#ic# t#e @uid does
t#ere is less syste! )olu!e V-D t#an in t#e case o'eration V-D T V. "onseuently t#e @uid ,ill 'ass t#
reactor ,it# t#e dead )olu!e !ore uicly t#an t#at o'eration.
t#e transients "%t& and $%t& ,ill decay !ore ra'idly ( t#a'erfect o'eration because t#ere is a s!aller syste! )ol( u
D dT blh U
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 45/109
Diagnostics and Troubleshooting Us
RTD for ldeal Reactors: Tubular Rea
'. erfect %peration of R
-'ace ti!e for 'erfect PR are
* R +ith ,hanneling (b"passing)
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 46/109
*. R +ith ,hanneling (b"passing)
-'ace ti!e for t#e reactor syste! ,it# by 'assing
ecause U- T U0 t#e s'ace ti!e
case of by'assing is greater ,#co!'ared to 'erfect o'eration
, R +ith Dead -olume
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 47/109
,.R +ith Dead -olume
#e dead )olu!e VD could be !anifested by internal ci
a t#e entrance to t#e reactor as s#o,n in igure 13(17.
"o!'ared to 'erfect o'eration t#e s'ace ti!e Q-D is s!aller a
t#e tracer s'ie ,ill occur before Q for 'erfect o'eration.
PFR/CSTRS RTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 48/109
PFR/CSTR Series RTD
-tirred tan reactors can be !odeled as a series o!i*ed "-R %)icinity near i!'eller& and PR %'at# 'efectly(!i*ed +one&
PFR/CSTRS i RTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 49/109
PFR/CSTR Series RTD
"onsider the ,TR follo+ed b" the R
"-R residence ti!e Q-
PR residence ti!e QP
Pulse tracer inected into "-R
"-R out'ut concentration as function of ti!e beco!
RD of reactor syste!
PFR/CSTRS i RTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 50/109
PFR/CSTR Series RTD
RD cur)es $%t& and %t& for "-R(PR series
"onsider the R follo+ed b" the ,TR t#e sa
a''ear at t#e entrance of t#e 'erfectly !i*ed sect
PFR/CSTRS i RTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 51/109
PFR/CSTR Series RTD
RD of t#e reactor syste! ,ill be e*actly t#e sa!e
"-R ,as follo,ed by PR.
#e seuence of "-R and PR in t#e syste! crea
RD results.
E 133C i S
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 52/109
Ex 13-3: Comparing Secon
Order Reaction Systems
irst syste! "-R follo,ed by PR
-econd syste! PR follo,ed by "-R
Qs QP 1 !in
1.0 !3/!ol.!in
" A0 1 !ol/!3
ind t#e con)ersion in eac# syste!.
E 133C i S
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 53/109
Ex 13-3: Comparing Secon
Order Reaction Systems
irst s"stem:
econd s"stem:
E 133C igS
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 54/109
Ex 13-3: Comparing Secon
Order Reaction Systems
irst s"stem:
"-R !ole balance
PR !ole balance
"on)ersion %W1 ( 0.3M2X/1& 0.61M /1.0
Ex133:ComparingSecon
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 55/109
Ex 13-3: Comparing Secon
Order Reaction Systems
econd s"stem:
PR !ole balance
"-R !ole balance
"on)ersion %W1 ( 0.366X/1& 0.634 /3.2
PFR/CSTRSeriesRTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 56/109
PFR/CSTR Series RTD
"on)ersion results are dierent des'ite only a s!
di=erence.
RD is not a co!'lete descri'tion of structure for
reactor or syste! of reactors.
RD is uniue for a 'articular reactor
Reactor is not uniue for a 'articular RD
RD alone is not su5cient to deter!ine its 'erfor!
!ore infor!ation is needed.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 57/109
Part 2:Predicting Conversion
and Exit Concentration
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 58/109
Reactor Modeling Usingthe RTD
13.6
13.6. Reactor Modeling Using the RTD
Part 2 Predicting "on)ersion and $*it"oncentration
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 59/109
g g
Oays ,e use t#e RD data to 'redict con)ersion in non ideal reacto
:odel to 'redict con)ersion in realreactor
136ReactorModeling
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 60/109
13.6. Reactor Modeling
the RTD
#e RD tells us #o, long t#e )arious @uid ele!en
in t#e reactor
#e !i*ing of reacting s'ecies is one of t#e !aor
controlling t#e be#a)ior of c#e!ical reactors
or Frst(order reactions t#e con)ersion is inde'en
concentration
136ReactorModeling
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 61/109
13.6. Reactor Modeling
the RTD
&acromi#ing:
'roduces a distribution of residence ti!es )it*"ut, #o,e)er s'
!olecules of di=erent ages encounter one anot#er in t#e reacto
&icromi#ing:
describes #o, !olecules of di=erent ages encounter one anot#2 e*tre!es of !icro!i*ing
1. all !olecules of t#e sa!e age grou' re!ain toget#er as t#et#e reactor and are not !i*ed ,it# any ot#er age until t#ey%e*a!'le complete segregation&
2. !olecules of di=erent age grou's are co!'etely !i*ed at le)el ar soon as t#ey enter t#e reactor %e*a!'le complet
13.6. Reactor Modeling Using the RTD
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 62/109
:acro@uid
A @uid in ,#ic# t#e globules of agi)en age do not !i* ,it# ot#erglobules and could be)isuali+ed as noncoalescentglobules ,#ere all t#e!olecules in a gi)en globule#a)e t#e sa!e age
Microfluid
A fluid in which molecule
constrained to remain in
globule and are free to m
everywhere
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 63/109
Zero- ParameterModels
13.7
Segregation Model
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 64/109
g g
#e elements remain segregated fro! eac
t#e 4uid is termed completely segregated
elements of dierent ages do not mi# tog
all
• #e e*tre!es of co!'lete !iand co!'lete segregation li!its of t#e !icro!i*ing of a!i*ture.
• n t#e segregation !odel
be#a)e as batc# reactors o'edi=erent ti!es
SegregationModel
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 65/109
Segregation Model
Anot#er ,ay of looing at
segregation !odel for a
continuous @o, syste! is
PR s#o,n in Fgure belo,
SegregationModel
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 66/109
Segregation Model
#e @uid @o,s do,n t#e reactor in 'lu
$ac# e*it strea! corres'onds t"residence ti!e in t#e reactor
atc#es of !olecules are re!o)ed fro!at di=erent locations along t#e react
!anner as to du'icate t#e RD functio #e !olecules re!o)ed near t#e ent
reactor corres'ond to t#ose !oleculesresidence ti!es in t#e reactor
SegregationModel
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 67/109
Segregation Model
• #e reaction ti!e in any one of t#ese tireactors is eual to t#e ti!e t#at t#e 'aglobule s'ends in t#e reaction en)iron!
• #e distribution of residence ti!es a!oglobules is gi)en by t#e RD of t#e 'art
SegregationModel
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 68/109
Segregation Model
SegregationModel
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 69/109
Segregation Model
For a batch reactor:
For constant volume and with
Segregation Model
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 70/109
Segegato ode
#us if ,e #a)e t#e RD t#e reaction
rate e*'ressiont#en for a segregared
@o, situarion %i. e. !odel& ,e #a)e
suFcient infor!ation to calculate t#e
con)ersion
"onsider t#e follo,ing Frst(orderreaction
For cons
Segregation Model
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 71/109
g g
-ol)ing for Y %t&
• :ain con)ersion for a Frst(order rea
Example 13-5:
MeanConversionCalculationsina
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 72/109
Mean Conversion Calculations in a
Reactor
"alculate t#e !ean con)ersion in t#e reactor ,e #
c#aracteri+ed by RD !easure!ents n $*a!'les
for a Frst(order liuid('#ase rre)ersible reaction
co!'letely segregated @uid
#e s'eciFc reaction rate is 0'+ !inG.
Solution 13-5
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 73/109
Solution 13-5
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 74/109
Slti 135
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 75/109
Solution 13-5
Slti 135
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 76/109
Solution 13-5
Maximum Mixedness Mod
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 77/109
#e reactor e*it is of course t#e latest 'ossible '
!i*ing can occur and any e=ect of !i*ing is 'ost
after all reaction #as taen 'lace as s#o,n in igur
can also t#in of co!'letely segregated @o, as be
of !ini!u! !i*edness.
Oe no, ,ant to consider t#e ot#er e*tre!e t#at
!i*edness consistent ,it# a gi)en residence(ti!e
Oe return again to t#e 'lug(@o, reactor ,it# sid
entrances only t#is ti!e t#e @uid enters t#e rea
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 78/109
y
its lengt# %igure 13(24&. As soon as t#e @uid en
reactor it is co!'letely !i*ed radially %but not
longitudinally& ,it# t#e ot#er @uid already in t#e
#e entering @uid is fed into t#e reactor t#roug#
entrances in suc# a !anner t#at t#e RD of t#e '
reactor ,it# side entrances is identical to t#e R
real reactor
n a reactor ,it# side entrances let Z be t#e ti!e i
t#e @uid to !o)e fro! a 'articular 'oint to t#e end
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 79/109
reactor. ln ot#er ,ords Z is t#e life e*'ectancy of t
t#e reactor at t#at 'oint %igure 13(2L&.
"onsider t#e @uid t#at enters t#e reactor t#
sides of )olu!e [V in igure 13(2L. #e @ui
enters #ere ,ill #a)e a life e*'ectancy bet,
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 80/109
enters #ere ,ill #a)e a life e*'ectancy bet,
ZI[ Z. #e fraction of fluid t#at ,ill #a)e t#
e*'ectancy bet,een t#e 'roduct of t#e tota
)olu!etric @o, rate )o and t#e fraction of
t#at #as life e*'ectancy bet,een Z and ZI
[Z. #at is t#e )olu!etric rate of fluid ente
t#roug# t#e sides of )olu!e [Z is )o $%Z& [
#e )olu!etric flo, rate at Z. VZ is t#e flo, rate t
at ZI[Z VZI[Z 'lus ,#at entered t#roug# t#e sid
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 81/109
at ZI[Z VZI[Z 'lus ,#at entered t#roug# t#e sid
[Z i.e.
#e )olu!etric Ro, rate Vo at t#e entrance to t#e
%Y 0& is +ero because t#e @uid only enters t#roug
along t#e lengt#.
ntegrating euation %13(L7& ,it# li!its VZ 0 at
)Z )Z at Z Z ,e obtain
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 82/109
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 83/109
#e boundary condition is as # I 03 t#en "A "$uation %13(62& Wor Y 0 for $uation %1 3(64&X.
o obtain a solution t#e euation is integrated ba
nu!erically starting at a )ery large )alue of Z an
,it# t#e final con)ersion at Z 0. or a gi)en R
reaction orders greater t#an one t#e !a*i!u! !
!odel gi)es t#e lo,er bound on con)ersion.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 84/109
Comparing X seg and X mm
Comparing X seg and X mm
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 85/109
X seg is con)ersion 'redicted by segregation !odel
X mm is con)ersion 'redicted ,it# !a*i!u! !i*edn
Di=erence of X seg and X mm is signiFcant no !atter #o,
0.\\ is desire suc# as in to*ic ,aste destruct
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 86/109
Using Software
Packages
13.M
Solving a Problem using O
Sft P k
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 87/109
Software Packages
itting t#e$%t& "ur)e
to
Polyno!ial
-egregation:odel
:
Solving a Problem using ODE Sol
FittingtheE(t)CurvetoPoly
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 88/109
Fitting the E(t) Curve to Poly
inding !ean con)ersion %& by integrating bet,een t 0 and t .
?btaining !ole balance on Y%t& fro! batc# reactor
Orite t#e rate la, in ter!s of con)ersion
Solving a Problem using ODE Sol
FittingtheE(t)CurvetoPoly
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 89/109
Fitting the E(t) Curve to Poly
-'ecify $%t& and %t&.
"o!bine di=erential euation of Y $%t& and %t& euations and in'
-ol)er.
Solving a Problem using ODE Sol
FittingtheE(t)CurvetoPoly
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 90/109
Fitting the E(t) Curve to Poly
Do $1%t& and $2%t& 'olyno!ial trial and see if it !atc#es t#e cur)e a
-ee if $2%t& negati)e use I state!ents in t#e Ftting 'rogra!.
"#ec t#e area under $%t& cur)e. t !ust be )irtually one and t#e c
distribution %t& at long ti!es is ne)er greater t#an 1.
Solving a Problem using O
Sl S ti M d
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 91/109
Solver:Segregation Mod
-ol)e t#e euation using ?D$ -ol)er to get t#e !ean of e*it con)et#e con)ersion at any ti!e.
Solving a Problem using ODE Solver:Maximum Mixedness
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 92/109
f t#e soft,are 'acages ,on]t integrate bac,ardc#ange t#e )ariable suc# t#at t#e integration 'roc
as decreases fro! so!e large )alue to +ero.
or! a ne, )ariable -
^ is t#e di=erence bet,een t#e longest ti!e !easurecur)e and .
Solving a Problem using ODE
Solver:Maximum Mixedness
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 93/109
t is no, integrates bet,een t#e li!it - ? and - 200 tocon)ersion at - 200 ,#ic# corres'onds to 0.
-ee if t#e 'olyno!ial and !ae sure t#at it does not beco!
large ti!es.
:ae sure in t#e !a*i!u! !i*edness calculations is t#at
not go to +ero.
f so setting t#e !a*i!u! )alue of %t& at 0.\\\ rat#er t#an 1
ntegrate t#e 'olyno!ial for $%t& to get %t& and t#en setting t#of %& at 0.\\\.
f %t& is e)er greater t#an one ,#en Ftting a 'olyno!ial t#
blo, u' ,#en integrating t#e last euation nu!ericay.
13.8.1 Heat Effects
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 94/109
Pendeatan ini #anya aan berlau untu reasi falau aliran )olu!etri teta' onstan.
Untu o'erasi adiabati dan ["'0
Eau reasi s'esiFnya
Dengan asu!si ba#,a $ %r& tida di'engaru#i ole#
di reator
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 95/109
RTD and Multiple
Reactions
13.5
13.9.1Segregation Mode
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 96/109
Dala! !odel 'e!isa#an ita !e!'erti!basetia' BglobulesC di reator untu !e!ilii
yang berbeda dari reatan %"A& dan 'rodu
Untu reator batc# onstan )olu!enya di
sedang berlangsung 'ersa!aan esei!b
!olnya adala#
• Persa!aan('ersa!aan ini diselesaian secara sidengan 'ersa!aan di ba,a# ini u ntu !eng#a t i #i
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 97/109
13.9.2 Maximum Mixedness
Untu !eng#itung !a*i!u! !i*edness digunaan ru!us
onsentrasi a#ir
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 98/109
Perbandingan Reaktor
Batch dan Kontinyu
andsame
co
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 99/109
A"
a single- or multi-stage process in which a certainquantity of inputs (raw materials, auxiliary
materials, energy, etc.) are fed into the chemicalreaction unit (of the entire reaction) under
conditions suitable for obtaining the desiredreaction (temperature, pressure, required time,
etc.)
CONTINUOUSco
extraout
(produ
pr
energ
in a dsta
contro
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 100/109
A"
In the batch process, in the reactor and at any
given period of time, various actions take place in
the wake of which a concentration of reactants and
products varies so long as the reaction progresses.
At the conclusion of the process the mixture is
removed from the reactor and it then undergoes the
appropriate separation and processing stages
(either physical or chemical) at the required level ofcleanliness.
CONTINUOUScontro
prd
main
concen
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 101/109
A"
In the batch process, the shift from one stage to the
next is carried out in series and so the overall time
of the process is, in fact, the sum of the times
required for the various stages, and it is relatively
extensive.
In contrast, the required volume of the tanks for a
specific batch process is greater than that requiredfor a parallel continuous process.
CONTINUOUS
In theprocess, al
are
sim
(although
different
system)
overall tim
for th
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 102/109
A"
In general terms, a batch installation requiresmore manpower while a continuous installation
requires greater computerized and automatedcontrol. Experience shows us that over time, an
initial investment in control is more feasible thatthe high day-to-day costs of manpower.
CONTINUOUS
*atch rocess ,o y'es of!aterials
"an be used ,it# all ty'esof !aterials %,it# non(@o,
$asier@o,in
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 103/109
!aterials !aterials it is easier touse t#e batc# 'rocess&.
%today!ater'roduccontinin)estdecisi)
nstallationsi+e
Relati)ely largeinstallations. Very bigin)est!ent in land andinstallations.
Relati)install-igniFland a
Reactor "#anges occur in t#econcentrations of!aterials o)er ti!e.
At all lconditconsta%durab
eeding ra,!aterials
Ra, !aterials are fedbefore t#e start of t#ereaction.
"onstara, !t#e en
*atch rocess ,on
" t l f t#
-i!'le control. t is easier tocontrol reaction conditions%' 'ressure te!'erature&
"o!'leAuto!abe used
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 104/109
"ontrol of t#eset of actions
in t#e syste!
%' 'ressure te!'erature&.:anual control can also bedone.
be usedreactor !ore d
!ust bet#e rate!ateria
Product%s&
$*traction of !aterials onlyafter all t#e actions areFnis#ed ,it# t#e conclusionof t#e reaction.
"ontinu'roductduring t
roubles#ooting
A fault or dealing ,it# a
batc# reuiring Bre'airC doesnot cause 'roble!s in t#eot#er stages. A''ro'riatetests are conducted aftereac# stage.
#e ins
interconfault in sto''agot#ers. been dabe re'asa!e ,conditio
*atch rocess ,o
uantities'roduced
Preferable ,#en'roduction of s!alluantities of a s'eciFc
Preferascale '
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 105/109
'roduced uantities of a s'eciFc!aterial are 'lanned.
Variety of'roducts int#e 'lant
Preferable ,#en t#e 'lant
'roduces a ,ide )ariety of!aterials and ,#en t#e'roduct is liely to bec#anged no, and again,#ile using t#e sa!ereactor.
Prefera
and 'e'roduc
Productde)elo'!e
nt stage
Preferable ,#en t#e
'rocess is relati)ely ne,and still unfa!iliar. n t#iscase t#e initial in)est!entis in a s!aller batc#reactor and t#us t#eecono!ic ris is s!aller.
Prefera
conclusstages and ecfeasibil
In both methods:
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 106/109
Recycling of ra, !aterials according to econo!ic be carried out.
Reuired 'roduct uality can be attained in accordcusto!er reuire!ents and econo!ic feasibility.
?'ti!al e5ciency can be attained according to re
conditions and econo!ic feasibility.
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 107/109
Perbedaan t dan
t a
8/17/2019 PR 1-Bioreaktor-Ulina Ayu Pangesti
http://slidepdf.com/reader/full/pr-1-bioreaktor-ulina-ayu-pangesti 108/109
t
t merupakan lama waktu yang ditentukan sebagaibasis dalam berbagai konteks perhitungan atau
persamaan.
a
meru
lama
tingga
m
r