Design of the Triple and Quadruple Fixed-Bed Catalytic Reactor for Phthalic Anhydride Production

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1 HWAHAK KONGHAK Vol. 37, No. 4, August, 1999, pp (Journal of the Korean Institute of Chemical Engineers) * * ( , ) Design of the Triple and Quadruple Fixed-Bed Catalytic Reactor for Phthalic Anhydride Production Young-Sam Yoon and Pan-Wook Park* Kum River Water Quality Res. Lab., National Institute of Environmental Research *Dept. of Chem. Eng., Pusan National University (Received 29 January 1999; accepted 16 March 1999) 2 o-xylene! "#$! %& '#() *+!,-. / ("#7 8$9(, :!;(, "#7< :!= >)&.?@! "#$ AB45 CD. EF01.! "#$ $G H/ I <J K L -! "#$[1]M1 "#7 8$9(, :!;(, "#7< :! NO P3 QR 45C D. STU VR &O 3 N WS 7X AB MYZ [\1. *P ] ^ [ "#$. _`$ Da b!,-. &Fc! "#$ de 401. "#$ fg, B!,- z=2.58 moh b!,- L1=1.1, L2=1.0 L L3=0.48 m ij fg z=2.58 m koh L1=1.0, L2=0.5, L3=0.48 L L4=0.6 moh * de M01. Abstract The parametric sensitivity and optimal catalyst bed length of triple and quadruple fixed-bed catalytic reactors (FBCRs) are calculated using a two-dimensional pseudohomogeneous model for the partial oxidation of o-xylene to phthalic anhydride. The safety operation ranges of triple and quadruple FBCRs from various operating condition changes like initial concentration of the reactant, temperature of the cooling medium, and reactant and coolant flow rate are presented. Triple and quadruple FBCRs showed the behavior of wide operating range than single and double FBCRs on the initial concentration, coolant temperature, and reactant and coolant flow rate. Triple and quadruple FBCRs with nonuniform activities could assure safety operating condition and production increase by minute variation of operating condition. In order to design the FBCRs which could obtained maximum yield, we investigated the performance of FBCRs from catalyst bed length changes. Triple and quadruple FBCRs showed the best performance at L1=1.1, L2=1.0 and L3=0.48 m, and L1=1.0, L2=0.5, L3=0.48 and L4=0.6 m in case of total catalyst bed length z=2.58 m. Key words : Parametric Sensitivity, Maximum Yield, Phthalic Anhydride, Safety Operation Ranges, Fixed-Bed Catalytic Reactor 1. V 2 O 5 -TiO 2 o-xylene! "#$ % &'(, )! *! +) ' ",+ )-. ",+. /0 +! "#$ : ;! +B /@. C DEF G1 HIJ K LIM N OPQ R%1 ysyoon_3_sf@hanmail.net ST UV WX X4@ YZ-. [\ ",+ "#$ ]1I ^_ ^` Y! au ST bc 9d ef hi34 jk l, mno g <=?pfq (temperature runaway) r?@m g-. s )t ua L =(parametric sensitivity)v <=?pfq[2] 78 ua Y! au #w ST x 9d eyz ' ^Y [{ ^` U }-[3, 4]. )v ~) *! +) ' "#$ ƒp Uƒ ua {gz C= < = > 6, <=?pfq Œ ua L = Ž g= 522

2 523 %1 ^_ VŽ g 3^_) U -. ). % s3 r š U i\ œzz Zo g-. šžÿc ) "#$ simulator G X c ua 8 G0 simulator I C Z@ 3 U Ž g / ^` Œ %1^_ ª v «3@ m ' ua L =v 3 $ ;) Œ j m 8U 3)-. "#$ R%1 ST «34 D44 +B ^ˆ ± ²³.,/0 + ±v + µ. ;! <= #= ^ˆŽ g-[5, 6]. Wb ± +1¹ I 56v ±ºƒ +) 1¹' C# "» p. ¼5 ",+ jk j) hi 3@ L' Wb,/0 +) D z ± 1 ¹'ƒ ½-¾ ± <= ^ˆ! UH-. )v ~) ST UV WX n -W@ À1 78 9: C= 19: "Á IJ.n -W "#$ =7Ž g Â )1 / rv i? "# $ Ã@, ÄÅ "#$ % )W "#$»'Æ-. )W$ =7. i?$ ib4 78 9: C= ;! <= >4 +B! #= hçãƒè, )W$ :I ÉZ U 78 Ê= Œ ±<= Ë g Ì-Í 6 Uƒ" g /Î ÏU Œ %1^_ UF Ð Ñ-. ) Ò m8 Ó m8[1, 7]4 i? Œ )W "#$.Ô mõ m8 )W$ ÖWC W$,1IJ 78 9: +B.n, /Î ÏU, Ö W$ ØE 6 Ë Ù3@ ]1I,/z ' Í( 78 <= Œ Ê=, ± 78<=, œõ) ua L = ÚÛ ", c $ Ü) Œ j Ë aij U( 3 Ö W$ «34 # 6"Ø -. j a jk Ó Ý Œ G1» Þß j634 à¾ Ë á& m8u &' -. â Ò m8 Ó Vy œƒ¾ Ù3 / /Î ÏU t %1 ^_^` uá «3@ m 0 À1 p (i?, )W ÖW$ Ë@ À1) Œ -W$ c $ Ü) a 3 ^` 6I"Ø s3 šž! %? s3 r(f, + Œ ]TÎ 1¹, ã¾ ä å Œ s )C s3 8^ Œ ^Y2w(operation mode) s3@ ãr e-[8]. s s s3 šž!.ô34. 8Ž g i æ y.ô " computer )Z. È Çç Ë -è 2w é H-. ã 34 2w á2 á2@ )Á H ê?, œ ê? Œ Rê?šž Ë@ ë g-. Rê?šž(heterogeneous model) 4 "»7Øv 4 œ» "³ (, œ ê?šž(pseudohomogeneous model)! "»C U#-. Ò m8 ",+ o-xylene Ù3 á# šžÿã-. 8^ «j 2.54 cm, ì Ü ) 3.2 m, À1;) 2.58 m(öw$: L1=1.0, L2=1.1, L3=0.48 m, W$: L1=1.0, L2=0.5, L3=0.48, L4=0.6 m) D )(, «j) 6mm4 - íqîï pellet ð ã¾ UH V 2 O 5 U ñò mm óz ôõ' g-. <= molten salt(kno 3 :NaNO 2 =59 : 41, m.p=142 o C) ö dø ²ù@Š C + µ. ^ˆ0-. v ~! "#$ šž ík. Oúv ~! U# Ã-. (1) UH U pellet ð ã¾ ñò mm ó z ôõ'! ã¾è? â œ» <=v Ê =U "» <=, Ê=v cc ~-" q œ ê? šž U#-. (2) pellet y?# )", œ»v +1 ¹!?#-. (3) j Œ û pd œü + Œ F ý!? #-. (4) C / œ7 œþ Ê=v <=, ± 7 þ8<= j ^`@ -. (5) œ» ÿ= <= )» Z. 8", œõ! FÎ -. (6) $! 78 þ8ºƒ á2@ L -. (7) c i! Ê=U 1C#. C)â U#-. (8) ± Œ "» ÿ=?#-. (9) Õ= š i¾ ê?-. v ~! U# Z 2D, #w œ ê? šž œ» + Œ F ƒ " ± + ƒ C j Œ ^`! - C ~-[1, 9]. % ƒv F ƒ ( ρc p ) m T 2 T 1 ελ t ez ελ z 2 er = r 2 r r ( u (1) z f ( ρc p ) f T) + ε( H A )r A ε C j εd (2) t ez 2 2 C C j εd er j 1 -- C j = r ( u r r z f C j ) εr j (ρc p ) m =[(ρc p ) f ε+(ρc p ) s (1 ε)] (3) ± ƒƒ : c ( ρc p ) c c = u t c ( ρc p ) c h z w AT ( T c ) (4) j Œ ^`: T=T o, T c =T co, C j =C jo at t=0 (5) D ez C j z z = 0 = u o ( C j ) z = 0- C j z = 0+ at z=0 0rR (6) HWAHAK KONGHAK Vol. 37, No. 4, August, 1999

3 524 λ ez z z = 0+ = ( ρc p ) m u o ( T z = 0- T z = 0+ ) at z=0 (7) T=T o at z=0 for 0rR (8) C j = 0 r = 0 r h w = ( T T r c ) λ er T c = T co, C = 0, z = 0 z at r=0 and r=r (9) at r=0, 0<zL (10) at r=r (11) at z=l (12) (1)-(4) s34 šž C Œ j ^` (5)-(12) Petrov-Galerkin method 3Z á2 ai } - p# Newton-Raphson p C Predictor-Multicorrector algorithm@ 1 FEM(Finite Element Method).4 <= v ) Ê= 8-. y.ô Œ y.ô X,, ± Œ ) "5[1, 9, 10] íz ' g Fig. 1! Ö W "#$ ûpd <= ù@š Ö W$ ûpd à <= Ñ ƒè, à )W$ þ8 1KC K?y = I&. 3 3 yš nc =I ù )-. Ö W$ 1» $ Ü) 6 / _34 4 )W$ v T? 2.58 m Z Ã-. )v ~! Ö W$ simulator G s34 šž % 0 š ua! )W$ nc #Ñ) Z "[1], Ö W$ c $ =v c $ Ü)(1 $Ü) 2.58 m "#) aij )W$ v T? (1K=98.29%, K=78.92%) UF g Ö W Table 1. Optimal estimated values of triple and quadruple FBCRs from model simulation Triple-bed Catalyst bed First-bed Second-bed Third-bed Reactor length(m) Relative activity Hot spot( o C) Conversion Yield Quadruple-bed Catalyst bed First-bed Second-bed Third-bed Fourth-bed Reactor length(m) Relative activity Hot spot( o C) Conversion Yield $ ^` simulator GÃ-[1, 9]. Ö W$ 3 3. ^# a c $ = Œ 1$ Ü) 2.58 m "#I} w c $ Ü) ^#Ã-. ) ^` )W$ à þ8 1KC K 3 3I} nc Ö W$ U )W$C œ (Table 1 1KC K ) Uƒ ^` 78 +B jk <=U cc 22 o C(ÖW$)v 37 o C( W$) z š 'Æ-. )W$ à þ8 1KC K '= š 0 Ö W$ nc4 c $ Ü), c $ =, þ8 1K, K, c $ <= Ë # Table 1 í\ Ã-. Table 1 = )W$ $ = 1 U # ¼ -. )v ~) Ö W$ U 78 +B9: i? Œ )W$.! <= Uƒ æ! -W@ À1 ÞQ 1» ) c $ "Á ¼5 9: C= 4 ;! <= > 6Ž g VB Uƒ" g-. Table 1 g!v ~) Ö W$ )W $[1,7,9]C T?," ^`, +B 9: <= > jk i? Œ )W$. #$ O "#$ +56.nŽ g À U ƒp" g-. Fig. 1. Best fitting of triple (a) and quadruple (b)-bed catalytic reactor. (air :o-xylene=20 : 1, salt bath temp.=354.2 o C, reactor radius= m) 3-2. ]1 W U ^_ ^`( œ7 <=, Ê= Œ œ ÎC ± œ7 <= Œ œî)c ~! ua a ST ÚÛ%@Š &à šž) ØEv ^_ W? ' g ) ST(K, 1K Œ <= Ë R%#) D4 ( U Ž g # 6 ua L = Œ <=?pfq )*Ã ± <= Œ 78 Ê= 9d Fig. 2(a) /o-xylene (20 :1)?#z " = (F 1 =0.76, F 2 =2.0, F 3 =2.24) Uƒ ÖW$, Fig. 2(b) =(F 1 =0.51, F 2 =1.01, F 3 =1.91, F 4 =2.64) Uƒ W$ ± <= a 9d š nc)-. ±<= ÏU ÞQ c $ +B 9: + ;! <= >?@,", ûpd 1 9: -. ;! <= Uƒ jd qæ-. [\, ± <=U T c =370 o C(ÖW$)C T c =384 o C( W$) 1 o C ÏU' œ7'¾ 78 <=?pfq(temperature

4 525 Fig. 2. Axial temperature profiles of triple (a) and quadruple (b)-bed catalytic reactors for coolant temperature changes. (air: o-xylene=20 :1, reactor radius= m) g-. /, Fig. 2 ^_ ^` W ± œ7 ÉZ <= ª 370 o C(ÖW$)C 384 o C( W$)))(, ) <= 1 o C ÏU <=?pfq?@a 0L " g-. Ö W$ jk i?$ ÉZ78 ± < = 355 o Cv )W$ 362 o C[3, 4, 7]. 370 o C(ÖW$)v 384 o C ( W$) i\ 1! ÉZ 78 ± <= ª Uƒâ ]1I,/Ž g 34 "V) ^YØ Y! ST %1 Ž g VB ƒpz 0-. Fig. 3! Œ ± œ7 <=?#(T c =T o = o C)z " œ7 Ê=4 /o-xylene ai, ¼ Ö W$ <= &à nc)-. o-xylene œ7 Ê= ÏU 78 9:(0<η Fig. 3. Axial temperature profiles of triple (a) and quadruple (b)-bed catalytic reactors for inlet concentration changes. (salt bath temp.=354 o C, reactor radius= m) <0.2) +B <= x ÏU?@A" g@, $ S ~! <= q" g-. ÖW$ jk Fig. 3(a)v ~) o-xylene U :1 <=?pfq?@,@(, W$ jk Fig. 3(b)v ~) 12.95: 1 <=?pfq?@,-. 78 Ê= a ÖW$ nc4 Fig. 3(a) jk $ <=U S ƒ ½ æ! 78 Ê= ÏU ÞQ 78 9: Î) ÏUz '", 78 9:,. / 0 +! 78 9: <= ;)z ' )v ~! ;! <= 4 S š ) 78 9: H&' ¼5 6 e o-xylene) $ C è 67'ƒ ½O S ~! <= š 'Æ-. Fig. 3(b) W$ ÖW$. 78 Ê= ÏU ÞQ 19: -. <=U >'" g-. ) W$ $ =U F 1 =0.51 ÖW$ F 1 =0.76. ¼5 78 Ê=U ÏU ÞQ )! $ C e Î) ÖW$. *O8 ) e ) ) ;! $ C z ' Ê= ÏU ÞQ 19: -. ;! <= 4-. Rê? Ö W "#$ ±<=v 78 Ê= a ST v ~) ÚÛÒ nc 6 rv ^_ W g ƒ ½! x l Í. Ö W$ šñ 0Lz 9ƒ ½:-. â "#$ À1$ ÏU 78 Ê= ÏU i I ; /Î ÏU t %1 ^_ VŽ g-. [\ ",+ ) ' "#$ jk Table 2. The performance of triple and quadruple FBCRs for coolant temperature and inlet concentration changes Figure number Fig. 2 Fig. 3 Reactor Triple-bed (T c =T o ) Quadruple-bed (T c =T o ) Triple-bed (air :o-x) Quadruple-bed (air :o-x) Coolant temp. ( o C) and initial conc. Conversion Yield First hot spot( o C) runaway runaway 20.0 : : : : : : : runaway 20.0 : : : : : : : runaway HWAHAK KONGHAK Vol. 37, No. 4, August, 1999

5 526 % +56 -W@ #=.nž gæ-. Table 2 &à šž œ7 Ê=v <= a ÖW$ v W$ L = 3@ n C)-. Table 2 Ö W "#$ œ7 <=v Ê = ÏU ÞQ +B <=U ÏU'(, ÞQ 1K! ÏU'ƒ È K) L <-., WX r! ñ ~! 1KC K = ^_ ^`! ÖW$ - W$ U + 1! ª Uƒ" g-. ñ ÉZ Ê= Œ ± <= ª W$ U Ö W$. >$ 1! ª ^Y U g-. ñ šñ ^_^` a. Ó i? Œ )W $. k Ã-. ÞQ -W@ À 1I?@Š %1 ª ^_ ^` ai?@š /Î ÏUv V 4 K L Ž g U UH-. )v ~! r! Papageorgiou [11], Pirkle Ë[12] š ncv?y ± Œ 78 œî 9d Fig. 4 =(F 1 =0.76, F 2 =1.63, F 3 =2.24) ÖW "#$ v =(F 1 =0.51, F 2 =1.01, F 3 =1.91, F 4 =2.64) W "#$ ± œî a Þß " #$ % ST "A ù@š ñ šñ ± œî ÏU ÞQ %,/ + D 4. +B <= >l) LÃ-., ÖW$ U W$. $ +B 9:,/ + ÏU B 9: <= > l) ;z B-. ± œî L.,/ + 6S I ƒm@ 4. +B <= ÏUIJ hi34 jk ñ šñ 0.07 m/s(öw$)v m/s( W$) <=?pfq r Ã -., U -W@ À1C ÞQ ± œî ^Y ª r@\ ÏUÃ-. Fig. 5 Ö W $ 78 œî a Þß % ST ^ nc)-. 78 œî ÏU 78 Ê= ÏUv œ jk 78 +B 9: Fig. 4. Axial temperature profiles of triple (a) and quadruple (b)-bed catalytic reactors for coolant flow rate changes. (air:o-xylene=20 :1, salt bath temp.=354.2 o C, reactor radius= m) Fig. 5. Axial temperature profiles of triple (a) and quadruple (b)-bed catalytic reactors for reactant flow rate changes. (air: o-xylene=20 :1, salt bath temp.=354.2 o C, reactor radius= m) 4. ñ šñ +B <= ÏUI, -., 78 œî ÉZ ª :I $ U *! W$) 1! ÉZ ª UD-. ñ 78 œî ÏU ÞQ )! 78 9: e Î ÏU 4. *! è e Table 3. The performance of triple and quadruple FBCRs for coolant and reactant velocity changes Figure number Fig. 4 (Coolant velocity changes) Fig. 5 (Reactant velocity changes) Reactor Coolant and Conversion reactant velocity(m/s) Yield First hot spot( o C) Triple-bed runaway Quadruple-bed runaway Triple-bed runaway Quadruple-bed runaway

6 527 o-xylene) ) ;! $ Cz ' 78 œî ÏU ÞQ 78 9: <= > l ) þ8 +B 9: <= >l - z B-. ) nc 1K, K " +B<= í ØE Table 3 Ã-. m w (L1=1.0, L2=0.5, L3=0.48, L4=0.6) š ' Æ-. ÖW$C W$ jk ÖW$ K) W$. 1»3@ ;z B-. ) W$ ÖW$ c $ Ü) E# <@ _34 ] 1 4 1K 98%, K ) ) K) ;! 3 á#ã-. Ö W "#$ jk 1 Ü) aia ƒ ½" iƒ c $ Ü)v jè aij nc Fig. 6-8C Table 4-7 Ã-. Ö W "#$ c $ cc L1, L2, L3 " L4 ñ" ^ c $ FG Hƒ 1 $ Ü) 2.58 m "# I} w Ï LIJ :-. Ö W$ šñ )! $ Ü) Iz J ) ;! $ Ü) ÏUIJU¾ ;! UH $ Ü) Ï U ÞQ 1K! ÏU" K! LÃ-. )v ~! Ç Y_. ÖW$ jk 1K 98%, K 78% ) Uƒ Table 4v ~) (L1=1.0, L2=1.1, L3=0.48), (L1=1.1, L2=1.0, L3=0.48), (L1=1.0, L2=1.2, L3=0.38) Œ (L1=1.0, L2=1.0, L3=0.58) K u gæ-. ) K u W K 79.51% UV ;! UH (L1=1.1, L2=1.0, L3=0.48) U ÖW$ 1 $ Ü) 2.58 m w 3 c $ Ü)Ã-. W$ jk 3 ^`4 1K 98%, K 78% ) UH c $ Ü) «ÓÝÃ-. â W "#$ c $ 3 Ü) 1 $ Ü) 2.58 Fig. 7. Axial and radial temperature profiles of triple-bed catalytic reactor for reactor radius changes. (air: o-xylene=20 :1, salt bath temp.=354.2 o C, catalyst length=2.58 m) Fig. 6. Axial temperature profiles of triple-bed catalytic reactor for catalyst bed length changes. (air:o-xylene=20 :1, salt bath temp.=354.2 o C, reactor radius= m) Fig. 8. Axial and radial temperature profiles of quadruple-bed catalytic reactor for reactor radius changes. (air: o-xylene=20 :1, salt bath temp.=354.2 o C, catalyst bed length= 2.58 m) HWAHAK KONGHAK Vol. 37, No. 4, August, 1999

7 528 Table 4. The performance of triple FBCR for catalyst bed length changes The effect of first & second catalyst bed length changes L1 L2 L3 T1 T2 T The effect of second & third catalyst bed length changes L1 L2 L3 T1 T2 T The effect of first & third catalyst bed length changes L1 L2 L3 T1 T2 T ) ;! $ Ü)U Ü ¼5 /0 ) ) ;! $ L I ) ÏU' 1K! ;ƒè K! L' jd Ã-. ) Ö W "#$ 3 c $ Ü) E# n C, U -W@ À1C ÞQ %1 ^_ 9:! ÏU ƒè i? Œ )W$C T? ^_ ^` Œ 1 $ Ü) w c $ Ü) aè K ÏU e Ã-. c $ Ü)v ^_ ^` TI aij ]1- ¾ K Œ /Î ÏUU U -. â -W$ =7. /Î ÏU t "#$ ûpd y ;! <= >?@A +B 6 U U -. Fig. 7-8 " Table 6-7! Ö W "#$ j a š nc)-. j ÏU i? Œ )W$ Table 5. The performance of quadruple FBCR for catalyst bed length changes The effect of first & second catalyst bed length changes The effect of first & third catalyst bed length changes

8 529 Table 5. Continued The effect of first & fourth catalyst bed length changes The effect of second & third catalyst bed length changes The effect of second & fourth catalyst bed length changes The effect of second & third catalyst bed length changes Table 6. The performance of triple catalytic FBCR for reactor radius changes Condition Radius(m) L1 L2 L3 T1 T2 T3 Radius +2% Radius +5% Radius +7% Radius +10% Radius +12% Radius +13% Radius +14% runaway v 7MUƒ +B 9: ;! <= >?@,ƒè, ÏUl! üc 4 #$ z š 'Æ-[9]. +B j pd <= :I j) ÏU ÞQ Wb,/0 + ± +1¹ I ƒm Œ 4 <= j U Åz B-. )v ~) -W$ c $ Ü) a Œ j a k 0L ST O! t 1KC K= rp ) Ã-. â Ž ¼ Ü), 1 $ Ü), c $ Ü) HWAHAK KONGHAK Vol. 37, No. 4, August, 1999

9 530 Table 7. The performance of quadruple FBCR for reactor radius changes Condition Radius(m) Conversion Radius +5% Radius +10% Radius +15% Radius +20% Radius +30% Radius +40% Yield Œ j Ë 1 # y š =! ) ØE * -¾ I& ;\ Q? g æ@ à )W$ þ8 1K Œ K Ö W$ 3 3IJ Ö W$ c $ Ü) Œ c $ = Ö W$ simulator u,ã-. U -W@ À10 Ö W$ +B 9: )W$. +! <= >?@,-. ÞQ, 0 = Uƒ "#$ )Z¾ "#$ : ;! <= > 4 +B 56.nŽ g-. &à šž! )W$ v œ KC 1K /IM g= š 0 ÖW, " W$. )W$ +B 9: 22 o C(ÖW$)v 37 o C( W$) ;! <= >?@,-. u a L = m8 input u a av 0 +B <= < c "#$ <=?pfq 8Ã-. Ö W$ c $ Ü) a. K = g Ö W$ c $ Ü) ÖW$ jk, 1 $ Ü) z=2.58 m c $ Ü) L1= 1.1, L2=1.0 Œ L3=0.48 m " W$ jk L1=1.0, L2=0.5, L3=0.48 Œ L4=0.6 mã-. "#$ #w ^Y ^ `! ÈR %? s3 r Œ s Õ= #ý datau ³8 g-¾ s3 šž Z À\ &ào g@(, u,0 simulator Z À1 p ) I 634 # = g-. A : heat transfer area per unit volume [m 1 ] C j : concentration of component (j=1, 2, 3) [kmol/m 3 ] c p D er D ez E i : specific heat [kj/kg K] : radial diffusion coefficient [m 2 /s] : radial diffusion coefficient [m 2 /s] : activation energy of reaction (i=1, 2, 3) [kj/kmol] ( H i ) : heat of reaction (i=1, 2, 3) [kj/kmol] k i : Arrhenius type rate constant (i=1, 2, 3) [s 1 ] k 0i : pre-exponential factor (i=1, 2, 3) [s 1 ] L : reactor length [m] R : radius of reactor tube [m] r : radius coordinate [m] r i : rate of i-th reaction [kmol/m 3 s] T : temperature [K] T c : temperature of coolant [K] T o : inlet fluid temperature [K] t : time [s] h w : heat transfer coefficient [w/m 2 K] u c : coolant velocity [m/s] u f : fluid velocity [m/s] u o : inlet fluid velocity [m/s] z : axial coordinate [m] ε : void of bed ρ : density [kg/m 3 ] λ er : effective radial thermal conductivity [kj/m s K] : effective axial thermal conductivity [kj/m s K] λ ez c : coolant e : effective f :fluid j : component o : initial m : mixture s : solid 1. Yun, Y. S., Park, P. W., Rho, H. R. and Jeong, Y. O.: HWAHAK KONGHAK, 35, 380(1997). 2. Bilous, O. and Amundson, N. R.: AIChE J., 2, 117(1956). 3. Juncu, Gh. and Floarea, O.: AIChE J., 41, 2625(1995). 4. Hlavacek, V.: Ind. Engng. Chem., 62, 8(1970). 5. Karanth, N. G. and Hughes, R.: Cat. Rev. Sci. Eng., 9(2), 119(1974). 6. Parent, Y. O., Caram, H. S. and Coughlim, R. W.: AIChE J., 29, 443 (1983). 7. Yun, Y. S., Park, P. W., Jeong, Y. O. and Han, S. B.: HWAHAK KONG- HAK, 35, 717(1997). 8. Froment, G. F.: Chem. Ing. Tech., 4, 374(1974). 9. Yoon, Y. S.: Ph. D. Dissertation, Pusan National University(1998). 10. Jeong(Park), Y. O.: Ph. D. Dissertation, University of Houston, U.S.A (1989). 11. Papageorgiou, J. N. and Froment, G. F.: Chem. Eng. Sci., 51, 2091 (1996). 12. Pirkle, J. C. and Wachs, I. E.: Chem. Eng. Prog. Aug., 29(1987)

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