REACTION ENGINEERINGEP 319CHAPTER 4 ISOTHERMAL REACTOR DESIGNNOOR ROSYIDAH SAJUNIrosyidah!"si!#i$%rsi&y'%d!'(yNo&%) P*%as% (a+% a,,oi#&(%#& -irs& .%-or% "o#s!*&a&io#s a#d "o(% -!**y ,r%,ar%d''14'1 D%si/# s&r!"&!r% -or iso&h%r(a* r%a"&or0.a&"h1 CSTR a#d P2R34'4 I#&rod!"&io# -or s,a"% &i(% 053 a#d Da(+oh*%r #!(.%r4'3 D%si/# -or (!*&i,*% r%a"&orsys&%(s4'4 Pr%ss!r% dro, i# r%a"&or4'6 R%$%rsi.*% r%a"&io#s2D%s"ri.% &h% "h%(i"a* r%a"&io# %#/i#%%ri#/ a*/ori&h( -or iso&h%r(a* r%a"&or d%si/# i# ord%r &o so*$% "h%(i"a* r%a"&io# %#/i#%%ri#/ ,ro.*%(sUs% &h% /i$%# ra&% *a7 a#d -%%d "o#di&io#s &o d%si/# .a&"h r%a"&ors1 CSTRs1 P2Rs -or iso&h%r(a* o,%ra&io#31' A,,*y Mo*% 8a*a#"% a#d D%si/# E9!a&io#4' 2i#d Ra&% La7:rA;+0T3 -or s,%"i-i" r%a"&io# or so(%&i(%s &o -i#d &h% r%a"&io# ra&% "o#s&a#&1 +Th% r%a"&or $o*!(% "o!*d a*so .% o.&ai#%d -ro( &his %9!a&io#4'1 DESIGN STRUCTURE 2OR ISOTHERMAL REACTOR0SCALE UP O2 LIAUID PHASE 8ATCH REACTOR DATA312A AkC r V) X 1 ( NVNC0 A AA VNrdtdX0 AA) X 1 ( kdtdXVNV) X 1 ( NkVNkCdtdX0 A0 A0 AA B A Given elementary first order reaction, 1. Mole Balance2. Rate a!". #toic$iometry %V&V0'(. Com)ine13X 11lnk1t Thereforekt dt k andX 11ln) X 1 (1Wheredt k) X 1 (1kdt) X 1 (dXt0X0X0t0 B A Gi$%# %*%(%#&ary -irs& Ord%r r%a"&io#1 *. +nte,rate2ro( &h% %9!a&io# a.o$%1 7% "a# o.&ai# &h% &i(% o- r%a"&io# i# a .a&"h r%a"&or 7i&h i#-or(a&io# o- &h% ra&% "o#s&a#& a#d "o#$%rsio#1 > o#*y -or a -irs& ord%r r%a"&io#14Th% -irs& ord%r ra&% *a7 -or &h% /%#%ra* r%a"&io#1 is 7ri&&%# as I#&%/ra&i#/ a.o$% %9!a&io# &o yi%*d +d&CdCAA AA+Cd&dC ktCClnAA01'1 DE2INITION O2 REACTION RATE2IRST ORDER REACTION2ro( &h% %9!a&io# a.o$%1 7% "a# o.&ai# &h% &i(% o- r%a"&io# i# a .a&"h r%a"&or 7i&h i#-or(a&io# o- &h% ra&% "o#s&a#& a#d i#i&ia* a#d -i#a* "o#"%#&ra&io# o- r%a"&a#& A -or a -irs& ord%r r%a"&io#B A 15VX NVNCA AA) 1 (0 VNrdtdX0 AAB A 21' MOLE 8ALANCE4' RATE LAB3' STOICHIOMETRY 0@;@C34' COM8INEGi$%# %*%(%#&arys%"o#d Ord%r r%a"&io#1 2A AkC r 20 A0 A2220 A0 A2A) X 1 ( kCdtdXVNV) X 1 ( NkVNkCdtdX 16)X 1X(kC1t Thereforekt dt k andX 1X) X 1 (1Wheredt k) X 1 (1C1kdt) X 1 ( CdX0 At0X02X0t020 A20 A B A 6' INTEGRATEGi$%# #o#: %*%(%#&arys%"o#d Ord%r r%a"&io#1 2ro( &h% %9!a&io# a.o$%1 7% "a# o.&ai# &h% &i(% o- r%a"&io# i# a .a&"h r%a"&or 7i&h i#-or(a&io# o- &h% i#i&ia* "o#"%#&ra&io# o- A1 ra&% "o#s&a#& a#d "o#$%rsio#1 > o#*y -or a s%"o#d ord%r r%a"&io#17Th% s%"o#d ord%r ra&% *a7 -or &h% /%#%ra* r%a"&io# is /i$%# .y S%,ara&i#/ &h% $aria.*%s a#d i#&%/ra&i#/ /i$%s+d&CdC4AA 4AA+Cd&dC +&C1C1CA A 1'1 DE2INITION O2 REACTION RATESECOND ORDER REACTION2ro( &h% %9!a&io# a.o$%1 7% "a# o.&ai# &h% &i(% o- r%a"&io# i# a .a&"h r%a"&or 7i&h i#-or(a&io# o- &h% i#i&ia* a#d -i#a* "o#"%#&ra&io# o- A1 ra&% "o#s&a#& o#*y -or a s%"o#d ord%r r%a"&io#18VNrdtdX0 AAD C B A + +Given non elementary reaction, 1. M-. BAANC.2. RA/. A0". #/-+C1+-M./R2(. C-MB+N.1ab: Rule 20)) X 1 (Xln11(kC1t Thereforekt dt k and) X 1 (Xln11) X )( X 1 (1Wheredt k) X )( X 1 (1C1kdt) X )( X 1 ( CdXBBB 0 At0BBBX0BX0t0B 0 AB 0 A Gi$%# #o# %*%(%#&ary r%a"&io# 6' INTEGRATED C B A + +21Gi$%# a /as ,has% r%a"&io# 7i&h -irs& ord%r 7i&h r%s,%"& &o A a#d 8&a+%s,*a"%i#a.a&"hr%a"&or'4C(o*Do-&h%i#*%&is-ro( r%a"&a#& A' Gi$%# &h% r%a"&io# ra&% "o#s&a#&1 +; 16 d(3E(o*'s1 CAC ; 6 (o*Ed(3 a#d "o#$%rsio#1 > ; C' 3' 2i#d &h% r%a"&io# &i(% i- &h% r%a"&io# is "o#d!"&%d i# a .a&"h r%a"&or 22B A AC kC r ) 51 ( 5 C51!0"0#here ) () (C) 1 ( 5 ) 1 () 1 (BB 00B00X ThereforeX CVX NVNX X CVX NVNCB AB A BAA AA VNrdtdX0 AAC B A +GI@EN NON ELEMENTARY REACTION1 1' MOLE 8ALANCE4' RATE LAB3' STOICHIOMETRY23$ )) %0 1 ( 51%0 51ln1 511(&51)) X 1 ( 51X 51ln1 511(&51t Thereforet dt and) X 1 (Xln11) X )( X 1 (1Wheredt) X 51 )( X 1 (1&51dt) X 51 )( X 1 ( &5dX) X 51 )( X 1 ( &5dtdX5) X 51 )( X 1 ( ) 5 )( 15 (VN) X 51 )( X 1 ( ) 5 )( 15 (VNC kCdtdXt0 BBBX0 BX0t020 A20 AB A Gi$%# #o# %*%(%#&ary r%a"&io# *. +N/.GRA/.C B A +0 A 0 A00 AC1NVNV 24B% 7i** *%ar# &h% d%si/# s&r!"&!r% -or 4 di--%r%#& sys&%()DESIGN STRUCTURETU8ULAR REACTOR 0P2R3CSTR25B% 7i** *%ar# &h% CSTR d%si/# s&r!"&!r% -or 4 di--%r%#& sys&%()CSTRLi9!id Phas% R%a"&io#Co#s&a#& @o*!(%1 0$;$C3S%"o#d Ord%r R%a"&io# 2irs& Ord%r R%a"&io#26D%si/# o- CSTR2irs& Ord%r R%a"&io# -or Li9!id Phas%271' D%si/# %9!a&io# o- CSTR4' Bh%# &h% $o*!(%&ri" -*o7 ra&% do%s #o& "ha#/% 7i&h r%a"&io# 0$ ; $o3 -or *i9!id ,has% r%a"&io#1 &h%r%-or%3' I# &%r(s o- &h% s,a"% &i(%1 AA 0 Ar' 'V1

,_

AA 0 A0A0 A 0 0 AAA 0 ArC Cr) C ( ) C (r' 'V2

,_

AA 0 A0rC C V"B A 284' 2or &h% 2IRST ORDER irr%$%rsi.*% r%a"&io#1 &h% ra&% *a7 is /i$%# as6' Co(.i#% %9!a&io# 3 a#d 4 &o o.&ai#F' S!.s&i&!&% i# "o#$%rsio#1 > %9!a&io# &o o.&ai# &h% -i#a* %9!a&io# asA AkC r () X 1 ( kCX CkCC C0 A0 AAA 0 A

,_

*

,_

+k 1kX 3

,_

X 1Xk12ro( &h% %9!a&io# a.o$%1 B% "a# o.&ai# &h% "o#$%rsio# i# &%r(s o- s,a"% &i(% a#d ra&% "o#s&a#& -or -irs& ord%r -or &h% d%si/# o- CSTR'29D%si/# o- CSTRS%"o#d Ord%r R%a"&io# -or Li9!id Phas%301' D%si/# %9!a&io# o- CSTR4' Bh%# &h% $o*!(%&ri" -*o7 ra&% do%s #o& "ha#/% 7i&h r%a"&io# 0$ ; $o3 -or *i9!id ,has% r%a"&io#1 &h%r%-or%3' I# &%r(s o- &h% s,a"% &i(%1 A0 ArX 'V 12"B A

,_

AA 0 A0A0 A 0 0 AAA 0 ArC Cr) C ( ) C (r' 'V

,_

AA 0 A0rC C V314' 2or &h% SECOND ord%r irr%$%rsi.*% r%a"&io#1 &h% ra&% *a7 is /i$%# as6' Co(.i#% %9!a&io# 3 a#d 4 &o o.&ai#F' R%arra#/% .a"+ &o o.&ai#2A AkC r (

,_

2AA 0 A0kCC C V*

,_

,_

,_

2A02A022A00 A2AA 0 AX) (1XkC orX) (1 kCXX) (1 kCX CkCC C3B A 2ro( &h% %9!a&io# a.o$%1 B% "a# o.&ai# &h% "o#$%rsio# i# &%r(s o- s,a"% &i(% a#d ra&% "o#s&a#& -or s%"o#d ord%r -or &h% d%si/# o- CSTR'32.val4ate .val4ate( ) ( ) ( )Ao2Ao2Ao AokC 2kC 2 kC 2 1 kC 2 1X + +( )2AoX 1 kCX ( ) ( )k 2k 4 1 k 2 1X2 + +( ) ( ) ( ) 0 kC X kC 2 1 X kCAo Ao2Ao + + 33C-N/+N5.67(2ro( &h% ,r%$io!s %9!a&io# -or -irs& ord%r(2ro( &h% ,r%$io!s %9!a&io# -or s%"o#d ord%r(2or -irs& ord%r r%a"&io#1 &h% ,rod!"& +a#d -or s%"o#d ord%r1 &h% ,rod!"& +CAO is r%-%rr%d &o as &h% r%a"&io# DAMGOHLER NUM8ER(A di(%#sio#*%ss #!(.%r &ha& /i$%s a 9!i"+ %s&i(a&% o- &h% d%/r%% o- "o#$%rsio# i# CSTR(Da ; C'1 or H /i$%s *%ss &ha# 1CD "o#$%rsio# a#d Da;1C'C or I /i$%s /r%a&%r &h%# 9CD "o#$%rsio#

,_

+k 1kXA02kCX' %1X 34Da(+oh*%r N!(.%r -or 2IRST Ord%r Irr%$%rsi.*% R%a"&io#sDa(+oh*%r N!(.%r -or SECOND Ord%r Irr%$%rsi.*% R%a"&io#s35Gi$%# a# %*%(%#&ary /as ,has% r%a"&io#&a+%s ,*a"% i# a CSTR a& "o#s&a#& &%(,%ra&!r% o- 6CC G a#d "o#s&a#&,r%ss!r%o-1F'4a&('R%a"&a#&Aa#d8is%9!a*i# (o*ar' Gi$%# &h% r%a"&io# ra&% "o#s&a#&1 + ; 1C d(FE(o*4's1 2AC ; 6 (o*Es a#d "o#$%rsio#1 > ; C'9'

2i#d &h% $o*!(% o- r%a"&or1 @

C B A + 2361' Mo*% 8a*a#"% -or CSTR4' Ra&% La7 -or %*%(%#&ary r%a"&io#3' S&oi"hio(%&ry) 2or /as ,has% sys&%(1 &h% "o#"%#&ra&io# o- r%a"&a#& A is12"C21B21A +C B A 2 +374' S&oi"hio(%&ry) Iso&h%r(a* 0T;TC31 7i&h #o ,r%ss!r% dro, 0P;PC36' D%&%r(i#% &h% $a*!% o- -ro( &h% %9!a&io#s1 yAC ; C'6 0%9!a* (o*ar3) X 1 () X 1 (C C0 A A +(

,_

+ 1aba)ad* *0 A 0 AC21B21A +50 1212150

,_

*C B A 2 +38F' S!.s&i&!&% ; :C'6 i#&o %9!a&io# 4 &o o.&ai# J' 2or /as ,has% sys&%(1 &h% "o#"%#&ra&io# o- r%a"&a#& 8 isK' S&oi"hio(%&ry) Iso&h%r(a* 0T;TC31 7i&h #o ,r%ss!r% dro, 0P;PC3389) X 50 1 () X 1 (C C0 A AC21B21A +) X 1 (+ X ) a , b ( -C CB0 A B + 399'B% +#o7 &h%r%-or%1C'S!.s%9!%#&*y d%&%r(i#% CAC:C21B21A +1**0 A0 BB ) 50 1 (+ 50 1 -0XXC CA B( )%%.. AAd/ , /ol 20) 0 5000/olat/d/ 0120) at/ !1" ( 50RT2 *C..

,_

104011' Co(.i#% i# %9!a&io# 4 ,r%$io!s*y &o o.&ai# &h% r%a"&io# ra&% as14' Th% CSTR $o*!(% is d%&%r(i#%d as -o**o7i#/1112C21B21A +22%% 2"%%0% 2)+ 30 ( 50 1 -+ 30 1 -20

10) 50 1 () 1 (

,_

,_

dmmols moldmXXkC C kC r ABAA$)+ 30 ( 50 1 -+ 30 1 -20

10) 30 ( , 522%% 2"0

,_

,_

dmmols moldms molrX FVAA41D%si/# o- T!.!*ar R%a"&ors0P2R342B% 7i** *%ar# &h% d%si/# s&r!"&!r% -or 4 di--%r%#& sys&%()T!.!*ar R%a"&orLi9!id Phas% R%a"&io#Co#s&a#& @o*!(% 0$;$C32irs& Ord%r R%a"&io# :rA ; +CaGas Phas% R%a"&io#@aria.*% @o*!(%1 000TT224X) (1

,_

+ S%"o#d Ord%r R%a"&io# :rA ; +Ca42irs& Ord%r R%a"&io# :rA ; +CaS%"o#d Ord%r R%a"&io# :rA ; +Ca4431' Gas a#d *i9!id ,has% r%a"&io#s /%#%ra**y "arri%d o!& i# &!.!*ar r%a"&ors' Th% i#&%/ra* -or( o- &h% d%si/# %9!a&io# as -o**o7i#/ 07h%# a.s%#"% o- ,r%ss!r% dro, or h%a& %="ha#/%34' 2or -irs& ord%r r%a"&io#1 &h% ra&% *a7 %=,r%ssio# is s!.s&i&!&%d i# %9!a&io# 13' 2or s%"o#d ord%r r%a"&io#1 &h% ra&% *a7 %=,r%ssio# is s!.s&i&!&%d i# %9!a&io# 112"X0A0 AkCdX; VX02A0 AkCdX; V44D%si/# o- T!.!*ar R%a"&ors2irs& Ord%r R%a"&io#2or Li9!id Phas%453' 2or 2irs& Ord%r r%a"&io#1 7% +#o7 &ha& &h% ra&% *a7 %=,r%ssio# is as -o**o7i#/)4' S!.s&i&!&% i# &h% "o#"%#&ra&io# &%r(s i#&o &h% %9!a&io# &o o.&ai#8Y USING INTEGRAL EAUATION1 2IND THE 2INAL TERM 2OR THE REACTOR @OLUME*X0A0 AkCdX; VX 11lnkC'dX) X 1 (1kC'kCdX' V0 A0 AX00 A0 AX0A0 A ) X 1 ( C C0 A A 46D%si/# o- T!.!*ar R%a"&ors2irs& Ord%r R%a"&io#2or Gas Phas%471' 2or /as ,has% r%a"&io#s a& "o#s&a#& &%(,%ra&!r% a#d ,r%ss!r%1 &h% i#*%& a#d o!&*%& $o*!(%&ri" -*o7 ra&% is %=,r%ss%d as -o**o7i#/4' Th%r%-or%1 &h% "o#"%#&ra&io# "a# .% %=,r%ss%d as a -!#"&io# o- "o#$%rsio#(483' 2or 2irs& Ord%r r%a"&io#1 7% +#o7 &ha& &h% ra&% *a7 %=,r%ssio# is as -o**o7i#/)4' S!.s&i&!&% i# &h% "o#"%#&ra&io# &%r(s i#&o &h% %9!a&io# &o o.&ai#8Y USING INTEGRAL EAUATION1 2IND THE 2INAL TERM 2OR THE REACTOR @OLUME*X0A0 AkCdX; VdX' X 1 %' X 1 %kC;kCdX; VX00 A0 AX0A0 A + 498Y USING INTEGRAL EAUATION1 2IND THE 2INAL TERM 2OR THE REACTOR @OLUMETHERE2OREdX' X 1 %' X 1 %kC;kCdX; VX00 A0 AX0A0 A + ; "o#$%rsio#E= ) >; C'K>% ; %9!*i.ri!( "o#$%rsio#> ; >% 0 >37h%r% >% ; C'K6 >; C'KE= )> ; C'K60C'K3 ; C'FKRa&% La7 :rA ; + CA4C8To d%&%r(i#% &h% > or @R%a"&or -or r%$%rsi.*% r%a"&io#s1

(!s& "a*"!*a&% &h% (a=i(!( "o#$%rsio# &ha& "a# .% a"hi%$%d a& &h% iso&h%r(a* r%a"&io# &%(,%ra&!r%1 7hi"h is &h% %9!i*i.ri!( "o#$%rsio#0>%3 .y !si#/ G"3GC C: C 0C + rCDC8 A A2 22 E>AMPLE O2 BRITING THERMODYNAMIC EAUILI8RIUM RELATIONSHIP 2OR A RE@ERSI8LE CHEMICAL REACTIONTh%r%-or% &h% "o#"%#&ra&io# %9!i*i.ri!( "o#s&a#&1 G" -or &h% a.o$% r%a"&io# is)942or /%#%ra* r%a"&io#1A 82or &h% a.o$% r%$%rsi.*% r%a"&io#1 &h% #%& ra&% o- -or(a&io# o- A is &h% s!( o- ra&%s o- -or(a&io# -ro( &h% -or7ard r%a"&io# a#d &h% r%$%rs% r%a"&io#r A ; r A1 #%& ; r A1 -or7ard N r A1 r%$%rs%2or &h% -or7ard -or(a&io# r%a"&io#1 r A1 -or7ard ; : + A C A2or &h% r%$%rs% -or(a&io# r%a"&io#1 r A1 r%$%rs% ; + :A C 8Th%r%-or% -or ra&% o- -or(a&io# o- A1 r A) r A ; r A1 #%&; r A1 -or7ard N r A1 r%$%rs% ; :+ A C A N + :A C 8Th%r%-or% -or ra&% o- disa,,%ara#"% o- A1 :r A) :r A ; r A1 #%&; r A1 -or7ard N r A1 r%$%rs% ; + A C A : + :A C 8kAk-A95B% +#o7 &h% ra&% o- disa,,%ara#"% o- A1 :r A) :r A ; r A1 #%&; r A1 -or7ard N r A1 r%$%rs% ; + A C A : + :A C 8As d%&%r(i#%d ,r%$io!s*y &h% %9!i*i.ri!( "o#s&a#&1 G" is /i$%# as1 Th%r%-or% &h% ra&% *a7 -or &h% a.o$% r%$%rsi.*% %9!a&io# .%"o(%sA& %9!i*i.ri!(1 :rA ; C1 a#d a-&%r r%arra#/i#/ 7% o.&ai# &h% %9!i*i.ri!( "o#s&a#&1 G" as AACkk0)0CC ( k rCBA A A ABCCC0 962or /%#%ra* r%a"&io#14A 8 N CB% +#o7) r A ; r A1 #%& ; r A1 -or7ard N r A1 r%$%rs%2or &h% -or7ard -or(a&io# r%a"&io#1 r A1 -or7ard ; : + A CA42or &h% r%$%rs% -or(a&io# r%a"&io#1 r A1 r%$%rs% ; + :A C8 CCTh%r%-or% -or ra&% o- -or(a&io# o- A1 r A) r A ; r A1 #%&; r A1 -or7ard N r A1 r%$%rs% ; : + A CA4 N + :A C8 CCTh%r%-or% -or ra&% o- disa,,%ara#"% o- A1 :r A) :r A ; r A1 #%&; r A1 -or7ard N r A1 r%$%rs% ; + A CA4 : + :A C8 CCkAk-A97Th%r%-or% -or ra&% o- disa,,%ara#"% o- A1 :r A) As d%&%r(i#%d ,r%$io!s*y &h% %9!i*i.ri!( "o#s&a#&1 G" is /i$%# as1 Th%r%-or% &h% ra&% *a7 -or &h% a.o$% r%$%rsi.*% %9!a&io# .%"o(%sA& %9!i*i.ri!(1 :rA ; C1 a#d a-&%r r%arra#/i#/ 7% o.&ai# &h% %9!i*i.ri!( "o#s&a#&1 G" as ) C CkkC ( k C C k C k rC BAA2A A C B A2A A A AACkk0)0C CC ( k rCC B2A A A 2AC BCCC C0 98Th% /as ,has% iso(%riLa&io# r%a"&io# is /i$%# as -o**o7i#/) Th% r%$%rsi.*% r%a"&io# is &o .% "arri%d o!& i# a #o#:iso&h%r(a* -*o7 sys&%( 7i&h ,!r% A as &h% o#*y -%%d a& 4FC oC 7i&h &o&a* ,r%ss!r% o- &h% sys&%( is 31C +PA' Gi$%# &h% s,%"i-i" r%a"&io# ra&%1 + is 11C s:1 a#d &h% "o#s&a#& %9!i*i.ri!( "o#s&a#&1 G" ; C'JJ (o*EL' Us% R ; K'314 +Pa'd(3E(o*'G'1'D%&%r(i#% &h% %9!i*i.ri!( "o#$%rsio#1 >%4'Ca*"!*a&% &h% CSTR $o*!(% #%"%ssary &o a"hi%$% K6D o- &h% %9!i*i.ri!( "o#$%rsio# 0>;C'K6>%3 i- /i$%# &h% -%%d ra&% o- A ; 3C LEs'B 2 A 99SOLUTION15"0 X Eet We) X 1 () X 1 (C) X 1 () X 2 (C&&0"&0CC0/ e=u6l6br6u InX 1X 2C) X 1 (X ' 2 'C) X 1 () X 1 (C 7 1 ) 1 1 1 )( 1 ( * 7) X 1 () X 1 ( ' 'C : r* Ato)h6o/etJ , /ol 0&0) 152&% 2"0 ( %1!1) %10 )( 1 (RT2 *CeA.222A.A2BCA.oA. BBA. A.oA. AAoA.A.++ ++ + + + + D%&%r(i#% &h% %9!i*i.ri!( "o#$%rsio#1 >%100SOLUTIONCa*"!*a&% &h% CSTR $o*!(% #%"%ssary &o a"hi%$% K6D o- &h% %9!i*i.ri!( "o#$%rsio# 0>;C'K6>%3 i- /i$%# &h% -%%d ra&% o- A ; 3C LEsLrX FVs L mol r ThereforeL molXXC CL molXXC CKCC k rXAAOCSTRAAO BAO ACBA A132&000) &%0 )( %0 )( 0&0 ( , &000&&0) 05310 (01030 110, 05310&%0 1) &%0 ( 20&012, 01030) &%0 1 () &%0 1 (0&0) 1 () 1 (&%0 ) 15"0 )( 150 (22

,_

++++

,_

101