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Fluidized bed reactors without and with selective membranes for the catalytic dehydrogenation of ethylbenzene to styrene
journalof MEMBRANE SCIENCE ELSEVIER
Journal of Membrane Science 101 (1995) 31-42
Fluidized bed reactors without and with selective membranes for the catalytic dehydrogenation of ethylbenzene to styrene Babiker K. Abdalla a, Said S.E.H. Elnashaie b'*'l aSchool of Chemical Engineering, University Science Malaysia, Perak Branch Campus, Seri lskander 31750 Tronoh, Perak, Malaysia bChemical Reaction Engineering Group (CREG), Chemical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia Received 20 April 1994; accepted in revised form 20 October 1994
Abstract A two-phase model, which takes into account the change of the number of moles associated with the reaction, is used to investigate the possibility of using ftuidized bed configurations without and with selective metallic (or composite) membranes to conduct the catalytic reversible endothermic reaction for the dehydrogenation of ethylbenzene to styrene. This reaction is usually carried out industrially in adiabatic fixed beds. The effect of different design and operating parameters for the two fluidized bed configurations is investigated and the results are compared with those of an equivalent industrial fixed bed unit. It is shown that through the proper choice of design and operating parameters a considerable increase in the styrene production, over that of the industrial fixed bed unit, can be achieved. Keywords: Palladium-ceramic membranes; Fluidized bed; Backmixing; Ethylbenzene; Styrene
1. Introduction Styrene is produced industrially by the reversible endothermic catalytic dehydrogenation of ethylbenzene in fixed bed reactors [ 1-4], which suffer from diffusional as well as thermodynamic limitations [ 5 9]. In this investigation the possibility of overcoming these disadvantages by using fluidized bed configuration is explored. Earlier Elnashaie and Adris [8] as well as Adris et al. [9] carried out a detailed investigation of the possibility of using the fluidized bed con* Corresponding author. Fax ( + 966-1 )4633563, e-mail: F45 K006 @SAKSU00.B ITNET 1 On leave from the Chemical Engineering Department, Cairo University, Egypt. 0376-7388/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI0376-7388(94)00271-1
figuration for the steam reforming of methane, where the effectiveness factor in the fixed bed configuration is of the order of 0.01-0.001 [8,9], while in the fluidized bed configuration it approaches unity. In the present case the improvement due to the use of fine powder in the fluidized bed, although appreciable, is not as great as in the case of the steam reforming, because the effectiveness factor in the industrial fixed bed reactors for styrene production is in the range 0.4-0.6 [ 10]. The bubbles in the fluidized bed act as natural membranes removing the hydrogen formed in the dense phase, and therefore enhance the forward dehydrogenation reaction [5-8] and suppress the side reaction producing toluene. On the other hand the rapidly rising bubbles cause the disadvantage of reactants by-pass which can be minimized by suitable distributor design and the use of internal components which inhibit bubble growth.
32
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
Another disadvantage of fluidized bed is the high degree of mixing which suppresses the rate of reaction, especially for first order reactions. For the particular case studied here the high degree of hydrogen mixing in the dense phase enhances the hydrodealkylation reaction to produce toluene. This disadvantage can be minimized by using a number of fluidized beds in series in order to decrease the degree of mixing [ 5 ]. Many investigators studied the use of the fixed bed configuration with selective membranes for dehydrogenation reactions [ 11-22]. The use of selective membranes enhances the efficiency of the systems by efficiently removing the hydrogen from the reaction mixture. The use of fluidized bed augmented with selective membranes has not been previously investigated for the ethylbenzene to styrene reaction. In the present study the effect of selective membranes, for the removal of hydrogen from the reaction mixture, on the performance of the fluidized bed configuration is investigated in some detail.
2. Theory 2.1. Formulation of the model equations The two phase postulate for fluidization is one of the principal assumptions underlying the different models of fluidized bed reactors [23]. The two phase model considers that the fluidized bed consists of a bubble phase and a surrounding dense (or emulsion) phase which contains most of the catalysts and the theory also postulates that all gases in excess of that necessary for minimum fluidization pass through the bed as bubbles [23]. 2.2. Assumptions The following assumptions are used in the formulation of the model equations: 1. The bubble phase is solid free and in plug flow [24]. 2. The extent of reaction in the bubble phase is negligible and reaction is taking place in the dense phase only [23]. 3. The dense phase is uniform in temperature and perfectly mixed [ 23 ].
4. The effective bubble size is taken as that which exists at 40% of the expanded bed height, and is used for the entire reactor [24]. 5. The mass and heat transfer resistances between the particles and the gas in the dense phase are negligible [23]. 6. The volumetric flow rate through the bubble phase is assumed to be constant [ 23 ]. 7. The ideal gas law applies to the gases in the bubble and dense phases. 2.3. Kinetics of the dehydrogenation reactions The reaction network for the dehydrogenation of the ethylbenzene to styrene is given by Sheel and Crowe [3] as follows: C6H5CH2 CH3 ~ C 6 H5 CHCH2 + H2
( 1)
C6H5 CH2 CH3 --'>C 6 H 6 + C 2H4
(2)
C6 Hs CHz CH3 4- Ha --* C6 H5 CH3 4- CH4
(3)
2H20 + C2H4 --* 2CO + 4H2
(4)
H 2 0 + C H 4 --*CO + 3H2
(5)
H 2 0 4- CO ----)CO2 4-H2
(6)
The corresponding rate expressions are given by: rl = kl (PEB -- PST PH2/KEB)
(7)
re = k2PEB
(8)
r3 = k3 PEBPH2
(9)
r4 __ k4 PH20 P 0.5 ETH
10)
r5 = k5PH20PMET
11)
PT
r6 = k6 ~
PH2oPco
12)
It is important and interesting to notice from the structure of this reaction network that the reaction does not stop at the thermodynamic equilibrium conversion of the main reaction (i.e. reaction 1), but can proceed beyond this hypothetical thermodynamic equilibrium; because of the continuous consumption of the product hydrogen in reaction 3 producing toluene. Thus the actual equilibrium position for this reaction network is 100% conversion. However from a practical point of view this approach to 100% conversion is extremely
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31--42
33
Table 1 Kineticrate coefficientsand equilibrium constantof the ethylbenzene
2.4. Mass and energy balances for the bubble phase
Reaction rate constants
The material and energy balance equations are developed for the bubble and dense phases. Taking an element of height Ah in the bubble phase; steady state mass balance for thejth component in the bubble phase is given by:
Reaction No.
Frequency factor [ 10]
Activation energy, kJ/kmol/K [3]
1
0.854
2
14.0047
207989.23
3
0.5585
91515.26
0.1183
103996.71
4 5
- 3.21
6
dNjB=AB(KED)JB(~ NjB]
90891.40
dh Let
65723.34
21.2423
AB(KEo)jB aj Or)
then equation (23) is rearranged and integrated to give the molar flow rate profile of componentj in the bubble phase:
AFo/RT), b a r [ 25 ]
AFo = a + bT+ c T 2 122725.157
b, k J / k m o l . K c, k J / k m o l ' K
(23)
73628.40
E q u i l i b r i u m c o n s t a n t KEB = e x p ( -a, k J / k m o l
QB ]
- 126.2674 2
-2.194×
NjB=Qs
10 - 3
slow if selective membranes for hydrogen removal are not used. The apparent rate coefficients were given by Sheel and Crowe [3 ]. These rate coefficients were corrected by Crowe [25]. The intrinsic rate coefficients were extracted by Elnashaie et al. [10] and are shown in Table 1. These intrinsic rate constants are the ones suitable for the fluidized bed, because of the fine powder catalyst used. The net rates of ethylbenzene and steam formation are given by: ethylbenzene
R E B ---- - - ( r I -4- r 2 q- r 3 )
(13)
steam
Rn2o = - (r4 + r5 + r6)
(14)
The net rate of formation of the styrene and the other by-products are given by: styrene
Rsx = r 1
( 15 )
benzene
Raz = r 2
(16)
toluene
RTOL = r3
(17)
ethylene
RETtt = r2 -- 0.5 r4
(18)
methane
RMET = r3 -- r5
(19)
hydrogen
Rn, = r~ - r3 + 2r4 + 3rs + r6
(20)
carbon monoxide
Rco = r4 + r5 - r6
(21 )
carbon dioxide
Rco_-= r6
(22)
[ NjD ( NjD Q----D-- Qo
NJB )e_,~jh] QB
(24)
The energy balance of the bubble phase is given by: dTB
dh Let
AB(HBD)B(TD_ TB) pGCpcQB AB(HBD)B Pc CpGQB
(25)
/3
then equation (25) can be rearranged and integrated; and the temperature profile in the bubble phase can be calculated using equation (26):
TB = TD -- (TD -- TBF)e- ~h
(26)
2.5. Mass and energy balances for the dense phase The mass balance for component i in the dense phase at steady state is given by: H
0
+ V( 1 - 6) ( 1 - e)ppRj
(27)
Equation (27) can be rearranged and the integral evaluated to give the molar flow rate of componentj in the dense phase. Substituting equation (24) into equation (27), and evaluating the integral of equation (27) then the molar flow rate of component j in the dense phase can expressed by:
34
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
Table 2 Hydrodynamic parameters used in the fluidized bed reactor calculations Parameter
Equation
Ref.
Minimum fiuidization velocity
Umf=( ~
[231
)( ~/27.22 + 0.0408Ar- 27.2) \ RGap /
where
d_..~_~
A~ = p6(PD -- PG)g~ tZ~ Average bubble diameter
dB= dBM-- (dam -- dBo)e -°'3h/a~ where dBM= 0.652 [At( Uo- Umf)] 2/5 dBo= 0.00376( Uo- Umf)2
[301
Bubble rising velocity
UB = U o - Umf4- (g~dB)°5
[301
Bed voidage at minimum fluidization
Emf = 0.586( 1 "0 t0"029( PG t0"021
[311
ZJ
Uo - Um,
Volume fraction of bubble phase to overall bed
[231
UB
Reactor feed volumetric flow rate
QF= UoAa
[231
Bubble phase volumetric flow rate
QB= (Uo- Umf)AB
[23]
The dense phase feed volumetric flow rate
QDF= QF -- QB
[23]
(1-xj)
Diffusion coefficient of component j
[32]
xj i=1
i•j
Molecular binary diffusivity of components i andj Overall mass transfer coefficient
Mi+Mj i/2 Mi+Mj
D0;= (0 00214- 0 000492( M - - - ~ )
""
1
1
1
(KBD)jB
( KBc)jB
( KcD)jB
Vm, +
~ ~/1/2(
T3/2
]
] k PTO'ij~D]
[321
[311
D)m:g'~:"
(KcB)jB=6.78( ~mfDjmUB) 1/2 d~
Overall heat transfer coefficient
_ _1
(HBD)B
-- _ _1
+ - - 1-
(Hac)B
(HcD)B
) (KopoCpG) 1/2 gl/4 (HBc)B=4.5 UmfflGCpG -1-5.85 d~.5 dB
(HcD)B=21"44(KGpGCpG)~/2(emfUB) 1/2T
[311
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995)31-42
35
Table 3 Industrial fixed bed reactor feed, Operation conditions and specifications [ 31
products of the two phases are then mixed at the bed exit to form the exit stream of the fluidized bed dehydrogenation reactor. The exit molar flow rates of the
Item
product components and temperature are given by:
Value and dimension
NjE = NjD + NjB
Molar feed rates Ethylbenzene (EB) Styrene (ST) Benzene (BZ) Toluene (TOL) Steam (H20) Total molar feed Mass flow rate Inlet pressure Inlet temperature Catalyst bed diameter Catalyst bed length Catalyst bulk density Catalyst particle diameter
36.87 kg mol / h 0.67 kg mol/h 0.11 kg mol/h 0.88 kg mol/h 453.10 kg mol/h 491.63 kg mol/h 12238.79 kg/h 2.40 bar 922.59 ~ K 1.95 b m 1.70b m 2146.27 b kgCat/m 3 4.66 x 10- 3b m
( 31 )
TDQD + TB QB
TE
(32)
an + a~
The conversions and yields of reactants and products are calculated using the following equations for conversions:
(33)
Xj= NjF--NjE
Nj~
50.0
(1)
£
(2)
"Corrected by Crowe [33]. ~Corrected by Crowe [ 25 ].
40.0
( Nj~ Njo ) NjD = NjDF + QB QF QD ( 1 - e- ~J")
50.0
c" 2 0 . 0 o
(28)
+ V ( 1 - 6) ( 1 - e ) p p R j
The energy balance of the dense phase is given by: 10
E
c
o 10.0
<.D
(5)
10
NjDCpJD(TD -- Trf) =
j=l
E
NjDFCpJF(TDF -- T~y)
0.@ 895.0
j=l
, , , , , , , ,
, , , , , , , l l , l l , , , , , ,
08 .o
H
890.0
+ f
v
( H B D ) B ( T B -- T D ) A B d h
~z
0
06
v885.0 6
+V(1-a)(1-e)pe
}--' (-ZlH,)r~
(29)
Equation (29) is rearranged and the integral evaluated (using equation 26) to give, 10
/
*6
E .o c)
880.0
04
o_
iJ
E
i=1
/
875.0 x Ld
02 870.0
10
NjD CpjD( TD -- Trf) = E NjDFCpjDF(TDF -- Trf) j=l
j=l
+ PGCpa QG (TF
/~ Fixed
865.0
......... O0 Reactor
Bec
Exit
Temperoture
=
850.0
K
i ......... i ......... 0,0 1.0 2.0 3.0 Height to Diometer Ratio ( H / D )
- T D ) ( 1 -- e - / 3 H ) 6
+ V ( 1 - 6) ( 1 -- e ) p e ~_~ ( - A H i ) r~
(30)
i=l
The above equations provide the necessary mass and energy balances of the bubble and dense phases. The
Fig. 1. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different reactor height to diameter ratios. (1) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. O Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, O exit temperature, * average bubble diameter.
B.K. AbdaUa, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
36
60.0
i --~-dl=aH2tW ae.2 f ~o-V --~o]
£ 50.0
(35)
0
(2)
where ct.2 is the permeation rate constant of hydrogen given by
40.0 x~
~ 5o.o
27r a l l 2 - ln(Fo/F/)
d o 20.0
DCo
(36)
E >
with
J
g ~
10.0
D = 8.28 × 10 -4 exp( -
(s) 0.0 900.0
21700/RT)
Co = 302.97 X T - 1.o358
i i i i l l l l l l l l l l ~ l l ~ l
0.20
E] :E
80.0 o
v
895.0
S
015 v
E o ~3
8900 o
-010
~ 885.0
w
•
z~ z3 D oB
0.05
880.0
~o 5-
60.0
d
O) (2)
40.0 c" _<2 ~o
>o20.0
c o (D
K 875.0
. . . . . . . . .
0.0 Reactor
I . . . . . . . . .
1.0 H e i g h t to
I
0.00
. . . . . . . . .
2.0 Diameter Ratio
( H/D
3.0 )
(3> 0.0 898.0
Fig. 2. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different reactor height to diameter ratios for the reactor with bubble diameter correlation multiplied by 0.3. (1) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. O Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, O exit temperature, * average bubble diameter.
I I I I I I
I I I l l l ~ l l l l l
i
I
008
896.0 OO6 ~894.0
E o
D ~3
~ 892.0
0.04
E
m
~ 890.0 × LA
for yields:
I I I I I I I I
0.02
888.0
-- NjF Yj= N j E
(34)
N[ EBorH20 ] F
2.6. Rate of hydrogenpermeation throughthe palladium membrane The permeation rate of hydrogen gas through the palladium membrane is assumed to obey the half power pressure law [26]:
886.0
¢ Fixed Bed Exit T e m p e r a t u r e = 8 5 0 0 K ......... i ......... i ......... 0.00 0.0 1 0 2.0 3.0 R e a c t o r H e i g h t to D i a m e t e r R a t i o ( H / D )
Fig. 3. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different reactor height to diameter ratios for the reactor with bubble diameter correlation multiplied by 0.1. ( 1 ) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. O Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, 4> exit temperature, * average bubble diameter.
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
80.0
>
~ 600 5=
400
._~ c 200
0.0
.... 0.0
5.0 10.0 15.0 20.0 25.0 .300 Steam to Ethylbenzene Ratio (S/E)
Fig. 4. Ethylbenzene conversion, styrene and toluene yields for the
fluidizedbed reactorwithreducedbubblediameter(correlationmultiplied by 0.3) at different steam to ethylbenzene ratios (S/E) (dp= 3.6 x 10-4 m and TF= 922.59 K). O Ethylbenzeneconversion fluidizedbed, [] styreneyieldfluidizedbed, A tolueneyieldfluidized bed. and D is Fick's diffusion coefficient of hydrogen dissolved in palladium. Composite palladium-ceramic membranes with palladium films, made by depositing palladium over the surface of asymmetric tubular ceramic membranes are used [27].
2. 7. Hydrodynamic parameters
components molar flow rates in the dense phase and the temperature of the dense phase are introduced to subroutine zsPow. The feed conditions to the dehydrogenation reactor as well as the hydrodynamic parameters are calculated and fed into the solution algorithm. Different subroutines are used for this purpose. The rate of the hydrogen permeation through the palladium membrane is evaluated by integrating equation (35) numerically using an integration routine. The subroutine DCADRE (IMSL Math/PC-Library) [29] is used for this purpose. The amount of hydrogen permeated through the membrane tubes is subtracted from the moles of hydrogen produced in the dense phase. The molar flow rates of the components and the temperatures of the two phases and the exit conditions are calculated and tabulated.
3. Results and discussions
3.1. Sizing and operating parameters of the fluidized bed reactors The industrial reactor at Polymer Corporation (Sarnia, Ont., Canada) and its feed conditions are taken as basis for comparison with the fluidized bed reactors [ 3 ]. Table 3 shows the dimensions and operating conditions of the industrial fixed bed reactor.
The application of the two phase theory of fluidization requires the estimation of the hydrodynamic parameters. The correlations for the computation of the hydrodynamic parameters used are given in Table 2.
80.0
600
2.8. Solution of the model equations The model equations describing the dehydrogenation of ethylbenzene to styrene using the fluidized bed configuration are solved as follows: Equations (28) describe the flow rate of component i in the dense phase, they constitute a system of ten non-linear algebraic equations. Equation (30) describes the energy balance equation which is also a non-linear algebraic equation. These equations are amenable to numerical solution; and the NewtonRaphson numerical technique can be used. The subroutine zsPow (IMSL Math/PC-Library) [28] is used for this purpose. Initial guesses of the
37
~D
j
~4oo
c~>200 8
0,0
/
/
f (11
(2)
J
i l r l l ~ l l l l
800.0
i lill
i i l l l l l l l l l l l
iiii
ii
850.0 900.0 950.0 Reactor Feed Temperature (K)
ir
~11
1000.0
Fig. 5. Ethylbenzene conversion, styrene and toluene yields for the fluidized bed reactor with reduced bubble diameter (correlation multiplied by 0.3) at different feed temperatures ( S / E = 12.3, dp=
3.6 × 10-4 m). O Ethylbenzeneconversionfluidizedbed, [] styrene yield fluidizedbed, A toluene yield fluidized bed.
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
38
70.0
..600
s r,
¥500
/"~-
u
o
O) (2)
s 40 0
.300 o
~>20.0
o o
100
(3) 8880
-300
-25 0 8840
2O 0
~J 880 0
150
E E 8760
o
100 uJ 8720
50 Fixed Bed Exit T e m p e r a t u r e =
8680
850.0
K
. . . . . . . . . IIH ..... I I I ' r ' ' I ' ' ' N ' r H N r l I H I ' I ' ' H I I I I I ' I ' ' I N ' ' ' ' ' ' ' 00 2.0 4.0 60 80 10.0 120 N u m b e r of Fluidized Beds in Series
0.0 140
Fig. 6. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different number of fluidized bed reactors in series without selective membranes. (1) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. © Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, 0 exit temperature; * average bubble diameter (averaged over all the beds for each case).
The total catalyst weight of the industrial reactor is used as the total catalyst weight for the fluidized bed reactor, in order to achieve consistent comparison between the two configurations. Fig. 1 shows that for the same H/D ratio as the industrial fixed bed reactor, the fluidized bed reactor gives lower XEB, lower YST and higher YTOL.This is due to the two main disadvantages of fluidized bed configuration discussed earlier, namely reactant by-pass by bubbles (low XEB) and a high degree of mixing (high }'TOE) both effects result in low YST.Increasing H/D causes the situation to deteriorate further giving lower XEB and YST and higher YTOL"However decreasing H / D improves the situation where XEB and YST increase sharply while YTOL decreases slowly. The value of XEB does not exceed that of the fixed bed configuration except for H/ D < 0.05, while YST always remains lower and YTOL higher than those of the industrial fixed bed reactor. It is thus clear that the situation is not as clear and straightforward as with steam reforming [ 8,9 ]. Careful design of the fluidized bed is obviously necessary in order to exploit the advantages of this configuration and minimize the effect of its main disadvantages. It is also essential to recognize the fact that the feed conditions (S/E and feed temperature) suitable for the fixed bed configuration are not necessarily the ones suitable for the fluidized bed configuration. Therefore our parametric investigation should include the following factors: 1. Effect of bubble diameter 2. Effect of S/E ratio 3. Effect of feed temperature 4. Effect of backmixing (i.e, effect of the number of fluidized beds in series used) The first three factors will be investigated for a single fluidized bed, then the dividing up of the fluidized bed
Table 4 Results of the fluidized bed reactor (correlation of dB multiplied by 0.1 ) assuming no H2 mass transfer between the dense and the bubble phases as compared with those of the normal one Item
Reactor with H 2 mass transfer between the bubble and dense phases ( 1 )
Reactor without H2 mass transfer between the bubble and dense phases (2)
Reduction % = [ ( l ) - ( 2 ) 1 / ( 1 ) x 100
XEB
62.20% 39.39% 7.94% 14.87%
55.55% 19.47% 5.87% 30.22%
10.69 50.57 26.07 - 103.23
~z YTOL
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31--42 80.0
the hydrodealkylation reaction for the formation of toluene.
60.0
3.3. Steam to ethylbenzene ratio (S/E) (1) 2L~
8 4O 0
/ /
g o Q)
39
Z
20.0
8 O0
~ ........
I ..... ~ 5 N u m b e r of
, ' ~ ....... 10 15 M e m b r o n e Tubes
20
Fig. 7. Ethylbenzene conversion and styrene and toluene yields for the fluidized bed reactor with reduced bubble diameter ( H / D = 0.87, S / E = 12.3, d p = 3 . 6 × 10 -4 m) at different number of membrane tubes (sweep gas molar flow rate 225 kmol/h at membrane tube pressure 1.013 bar). ( 1 ) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. 0 Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed with membranes, A toluene yield fluidized bed with membranes.
into a number of beds in series will be investigated in order to study the effect of backmixing.
3.2. Effect of bubble diameter The problem of reactants by-pass associated with the large bubbles can be tackled by creating bubbles of smaller diameters; through the use of different distributors and/or internals. In order to simulate this situation the average bubble diameter (Table 2) is multiplied once by 0.3 (Fig. 2) and once by 0.1 (Fig. 3) and the model is solved using the different H / D values as before. In Fig. 2 XEB is higher than that of the industrial fixed bed reactor for the industrial value of H / D and increases further as H / D decreases. However YsT is still lower and }'TOEis still higher than the industrial values even for very small values of H/D. In Fig. 3, where the bubble diameter multiplication factor is 0.1, XEB is always much higher than that of the fixed bed industrial reactor, while YsT is very close to that of the industrial reactor (at H / D 0.05 it is slightly higher than the industrial reactor), however YVOLis still appreciably higher than the industrial reactor indicating that the backmixing in the fluidized bed enhances considerably
We investigate here the effect of S/E for a fluidized bed having the same H / D as the industrial fixed bed and use the bubble size correlation multiplied by 0.3 in order to moderately reduce the effect of reactants bypass. Fig. 4 shows the effect of the S/E on values of the XEB , YsT and YTOL for the fluidized bed reactor with reduced bubble diameter, catalyst particle diameter of 3.6 × 10 -4 m and reactor feed temperature of 922.59 K. The S/E ratio is changed while the total amount of the steam and ethylbenzene in the feed are kept constant. The values Of XEB and YsT increase and the YTOL decreases as the S/E increases.
3.4. Reactor feed temperature (TF) Fig. 5 shows the effect of feed temperature on the values OfXEB, YsT and YTOL for the fluidized bed reactor with reduced bubble diameter (multiplication factor = 0.3) using the industrial S/E and catalyst particle diameter of 3.6 × 10 - 4 m . It is clear that the feed temperature increase causes the increase of the XEB and YTOL, while the YST remains lower than that for the industrial reactor.
3.5. Effect of backmixing This factor is most easily investigated by dividing the fluidized bed reactor into a number of beds in series (i.e. one on top of the other). This will decrease the degree of axial mixing and it will also clearly affect the average bubble size because of the gas redistribution as small bubbles at the entrance of each bed. Fig. 6 shows the combined plot of XEB , YsT, YTOL, TE and da versus the number of fluidized beds in series (nB). The results of Fig. 6 show that XEa and YsT increase as the number of beds increases. The values of the XEa obtained are higher than the industrial fixed bed reactor for nB> 2. The values of YsT obtained are also higher than the industrial one when na > 3. The values of YTOLobtained are higher than the industrial one. Fig. 6 also shows that YTOLmildly decreases as the number of the fluidized beds in series increase but is still higher than the industrially obtained value. Fig.
40
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
6 also shows that the overall average dB and the exit temperature TE decrease as the number of beds increases.
3.6. Role of the bubbles as natural membranes To show clearly the role of the bubbles in the fluidized bed as natural membranes removing the hydrogen formed in the dense phase, and therefore enhancing the forward dehydrogenation reaction [ 5-7] and suppressing the formation of toluene, a hypothetical case with the rate of hydrogen transfer from the dense phase to the bubble phase put equal to zero is computed, when the bubble diameter correlation is multiplied by 0.1. Table 4 shows the result of assuming no hydrogen mass transfer between the dense and the bubble phases. Table 4 shows a small reduction in the XES, large reductions in YSTand Yaz, and a large increase in YTOL"The reasons for the reduction in the XEB, YST and YBz and the increase in the YTOL are quite obvious, because the increased amount of the H2 in the dense phase increases the backward step of the reversible reaction and also increases the hydrodealkylation reaction (i.e. reaction 3) which is responsible for the production of the toluene.
3. 7. Reactor with hydrogen permeable membrane tubes In this case hydrogen is removed from the reaction site by the use of thin films of palladium membranes deposited over porous support materials. For a single membrane tube case (nT = 1) a membrane tube of inner diameter 0.345 m made of porous material (e.g. ceramic) with a thin palladium film (thickness = 5 . 1 0 - 4 mm) deposited on its surface, is passing vertically through the centre of the reactor. For the base case an inert gas of molar flow rate equal to 225.0 kmol/ h at a pressure of 1.013 bar flows concurrently with the reactants flowing in catalyst side. The fluidized bed reactor with the industrial H/ D = 0 . 8 7 with reduced bubble diameter (correlation multiplied by 0.3) the industrial S / E = 12.3 and the industrial feed temperature of 922.59 K is used for this part of the investigation. The fluidized bed catalyst particles diameter (dp) is equal to 3.6 X 10-4 m as used earlier, and the effect of the number of membrane tubes is investigated.
The effect of increasing the number of palladium tubes is studied where the total cross-sectional area of membrane tubes was assumed to be equivalent to that of the single tube passing through the centre. The flowing sweep gas was assumed to be equally divided through the membrane tubes. Fig. 7 shows the effect of varying the number of membrane tubes on the XEB , YSTand YTOLas compared with the corresponding values for the industrial fixed bed reactor and the fluidized bed reactor without membrane (nx = 0). It is clear that the removal of the hydrogen by the use of these membrane tubes causes a continuous increase in XEBand liST and a continuous decrease in YTOL.For nT = 16, YTOLis almost zero and the selectivity to styrene is almost 100%. Combining the different factors that improve the reactor performance it was found that a configuration with 7 fluidized beds in series, 16 membrane tubes, tube side sweep gas molar flow rate of 1600 kmol/h. membrane tube pressure of 0.03 bar, feed temperature of 975 K, H / D = 0 . 5 and S / E = 2 5 can give XEB and Ysv as high as 96.5% and 92.4% respectively.
4. Conclusions
The direct use of fluidized bed configurations for the catalytic dehydrogenation of ethylbenzene can increase the ethylbenzene conversion but does not increase the styrene yield. Suitable arrangements to create small bubble size to decrease reactants by-pass and the use of a number of fluidized beds in series to decrease backmixing can increase the ethylbenzene conversion and the styrene yield. The parametric study showed that the styrene yield can be increased by using a steam to ethylbenzene ratio higher than the industrial ratio. The application of selective membranes to the fluidized bed reactor increases considerably the ethylbenzene conversion and the styrene yield, over that of fluidized bed without membranes and the industrial fixed bed reactors. Suitable choice of design parameters and operating conditions gives high ethylbenzene conversion and styrene yield. In addition to increasing the ethylbenzene conversion and styrene yield, the removal of the hydrogen by the selective membranes increases the selectivity to styrene; by reducing the yields of some by-products, especially toluene. A fluidized bed configuration with a number of beds in series and selective
B.K. Abdalla, S.S.E.H. Elnashaie/Journal of Membrane Science 101 (1995) 31-42
membrane for hydrogen removal can give XEB and YST as high as 96.5% and 92.4%, respectively,
Q re, Ri
6. List of symbols
T Uo, UB, Umf
6.1. Notation AB, AD, At
Co
@, Cps dB, dp D, Dej, Dj,,
gc
h,H Hi
(H.D)B
(KBD) JB
K~
KEB M, nB
N~ nT Pi
PT P
cross-sectional area of bubble phase, dense phase and reactor tube; m 2 molar concentration of H2 in the membrane, kmol / m 3 heat capacity of component i and of the gas mixture, kJ/kmol bubble and particle diameter, m diffusivity of Hz through the membrane, binary diffusivity of components ~and j and diffusivity of component j, m2/h gravitational acceleration, m/h 2 reactor tube and expanded bed height, m heat of reaction ;, kJ/kmol interphase heat transfer coefficient between bubble and dense phase based on bubble volume, kJ/m3/ h/K interphase mass transfer coefficient between bubble and dense phase based on bubble volume, 1/ h thermal conductivity of the gas, kJ/K/m/h rate constant of reaction ~, kmol/ kgCat/h/barN ethylbenzene equilibrium constant, bar molecular weight of component i number of fluidized beds in series molar flow rate of component j, kmol/h number of palladium membrane tubes partial pressure of component ~,bar total pressure of the reactor, bar partial pressure of Hz in the membrane, bar
xi
41
volumetric flow rate, m3/h rate of reaction e and rate of formation of component j, kmol/ kgCat/h temperature, K superficial gas velocities of fresh feed, of bubble phase and fresh feed at minimum fluidization, m / h mole fraction of component i, dimensionless
6.2. Greek letters 6 e emf PD, PC ~r~j /~
bubble phase volume fraction to the total volume of the bed, dimensionless catalyst pellet porosity factor, dimensionless dense phase voidage at minimum fluidization, dimensionless density of the catalyst, density of gas mixture, k g / m 3 Lennord-Jones force constant, viscosity of the gas mixture, kg. h/ m2
~D /'o,
collision integral for viscosity, dimensionless outer and inner radii of the permeable tube, m
6.3. Subscripts B D E F G
i,j
rf
bubble phase dense phase exit from the reactor feed to the reactor gas mixture components i and j taken binary reference conditions
References [ 1 ] R.R. Wenner and E.C. Dybdal, Catalytic dehydrogenation of ethylbenzene, Chem. Eng. Progr., 44 (1948) 275. [2] B. Davidson and M.J. Shah, Simulation of the catalytic cracking process for styrene production, IBM J. Res. Dev., 9 (1965) 388.
42
B.K. AbdaUa, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
[3] J.G.P. Sheel and C.M. Crowe, Simulation and optimization of an existing ethylbenzene dehydrogenation reactor, Can. J. Chem. Eng., 47 (1969) 183. [4] D.E. Clough, W.F. Ramirez, Mathematical modeling and optimization of the dehydrogenation of ethylbenzene to form styrene, AIChE J., 22 (1976) 1097. [5 ] K.M. Wagialla and S.S.E.H. Elnashaie, Fluidized bed reactor for methanol synthesis. A theoretical investigation, Ind. Eng. Chem. Res., 30 (1991) 2298. [6] S.S.E.H. Elnashaie, K.M. Wagialla and A.M. Helal, The use of mathematical and computer models to explore the applicability of fluidized bed technology for highly exothermic catalytic reactions: II Oxidative dehydrogenation of ethylbenzene to styrene, Math. Comput. Modelling, 15 ( 1991 ) 43. [7] S.S.E.H. Elnashaie, K.M. Wagialla and M.E.E. Abashar, The use of mathematical and computer models to explore the advantages of fluidized bed technology for catalytic reactions with equilibrium/diffusional limitations, Ammonia synthesis, Math. Comput. Modelling, 16 (1992) 35. [8] S.S.E.H. Elnashaie and A.M. Adris, A fluidized bed steam reformer of methane, in ed. J.R. Grace. L.W. Schemit, and M.A. Bergougnou (Eds.), Fluidization VI, Engineering Foundation, New York, 1989, p. 319. [9] A.M. Adds, S.S.E.H. Elnashaie and R. Hughes, A fluidized bed membrane reactor for the steam reforming of methane. Can. J. Chem. Eng., 69 (1991) 1061. [ 10] S.S.E.H. Elnashale, B.K. Abdalla and R. Hughes, Simulation of the industrial fixed bed catalytic reactor for the dehydrogenation of ethylbenzene to styrene: heterogeneous dusty gas model, Ind. Eng. Chem. Res., 32 (1993) 2537. [ 11 ] N.A. Itoh, Membrane reactor using palladium. AIChE J., 33 (1987) 1576. [ 12] N. Itoh, Y. Shindo, K. Haraya and T. Hakuta, A membrane reactor using microporous glass for shifting equilibrium of cyclohexane dehydrogenation, J. Chem. Eng. Jpn., 21 (1988) 399. [ 13] B.K. Abdalla and S.S.E.H. Elnashaie, A membrane reactor for the production of styrene from ethylbenzene, J. Membrane Sci., 85 (1993) 229. [ 14] H. Nagamoto and H. Inoue, A reactor with catalytic membrane permeated by hydrogen, Chem. Eng. Commun, 34 (1985) 315. [ 15] J.C.S. Wu and P.K.T. Liu, Mathematical analysis on catalytic dehydrogenation of ethylbenzene using ceramic membranes, Ind. Eng. Chem. Res., 31 (1992) 322. [ 16] N. Itoh, Maximum conversion of dehydrogenation in palladium membrane reactors, J. Chem. Eng. Jpn., 24 (1991) 664.
[ 17] S. Uemiya, N. Sato, H. Ando, T. Matsuda and E. Kikuchi, Steam reforming of methane in a hydrogen-permeable membrane reactor, Appl. Catal., 67 ( 1991 ) 223. [18] T. Matsuda, I. Koike, N. Kubo and E. Kikuchi, Dehydrogenation of isobutane to isobutene in palladium membrane reactor, Appl. Catal. A, 96 (1993) 3. [ 19] Y.V. Gokhale, R.D. Noble and J.L. Falconer, Analysis of a membrane enclosed catalytic reactor for butane dehydrogenation, J. Membrane Sci., 77 (1993) 197. [20] J. Shu, B.P.A. Grandjean, A. Van Neste and S. Kaliaguine, Catalytic palladium-based membrane reactors: a review, Can. J. Chem. Eng., 69 (1991) 1036. [ 21 ] Y.L. Becker, A.G. Dixon, W.R. Moser and Y.H. Ma, Modelling of ethylbenzene dehydrogenation in a catalytic membrane reactor, J. Membrane Sci., 77 (1993) 233. [22] J.C.S. Wu, T.E. Gerdes, J.L. Pszczolkowski, R.R. Bhave, P.K.T. Liu and E.S. Martin, Dehydrogenation of ethylbenzene to styrene using commercial ceramic membranes as reactors, Sep. Sci. Technol., 25 (1990) 1489. [23] J.R. Grace, Modelling and simulation of two-phase fluidized bed reactors, NATO, ASI Ser., ser. E., Vol. 110, Chem. Reactor Design Technology, 1986, p. 245. [24] C. Fryer and O.E. Potter, Bubble size variation in two-phase models of fluidized bed reactors, Powder Technol., 6 (1972) 317. [25] C.M. Crowe, Dept. Chem. Eng., McMaster Univ., personal communication, Nov. 10, 1989. [26] G. Bohmholdt and E. Wicke, Diffusion of H2 and D2 in Pd and Pd alloy, Z. Phys. Chem., Neue Folge, 56 (1967) 133. [27] J.P. Collins and J.D. Way, Preparation and characterization of a composite palladium-ceramic membrane, Ind. Eng. Chem. Res., 32 (1993) 3006. [28] J. More, B. Garbow and K. Hillstrom, User Guide for Minpack1, Argonne National Laboratory Report ANL-80-74, Argonne, IL, August, 1980. [29] C. De Boor, CADRE: an algorithm for numerical quadrature, in J.R. Rice (Ed.), Mathematical Software, Academic Press, New York, 1971, Chap. 7. [30] S. Mori and C.Y. Wen, Estimation of bubble diameter in gaseous fluidized beds, AIChE J., 21 (1975) 109. [31] D. Kunii and O. Levenspiel, Fluidization Engineering, John Wiley and Sons, New York, 1969. [32] R.C. Reid and T.K. Sherwood, The Properties of Gases and Liquids. McGraw Hill, New York, 1966. [33] C.M. Crowe, Dept. Chem. Eng., McMaster Univ., personal communication, Aug. 20, 1992.
Journal of Membrane Science 101 (1995) 31-42
Fluidized bed reactors without and with selective membranes for the catalytic dehydrogenation of ethylbenzene to styrene Babiker K. Abdalla a, Said S.E.H. Elnashaie b'*'l aSchool of Chemical Engineering, University Science Malaysia, Perak Branch Campus, Seri lskander 31750 Tronoh, Perak, Malaysia bChemical Reaction Engineering Group (CREG), Chemical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia Received 20 April 1994; accepted in revised form 20 October 1994
Abstract A two-phase model, which takes into account the change of the number of moles associated with the reaction, is used to investigate the possibility of using ftuidized bed configurations without and with selective metallic (or composite) membranes to conduct the catalytic reversible endothermic reaction for the dehydrogenation of ethylbenzene to styrene. This reaction is usually carried out industrially in adiabatic fixed beds. The effect of different design and operating parameters for the two fluidized bed configurations is investigated and the results are compared with those of an equivalent industrial fixed bed unit. It is shown that through the proper choice of design and operating parameters a considerable increase in the styrene production, over that of the industrial fixed bed unit, can be achieved. Keywords: Palladium-ceramic membranes; Fluidized bed; Backmixing; Ethylbenzene; Styrene
1. Introduction Styrene is produced industrially by the reversible endothermic catalytic dehydrogenation of ethylbenzene in fixed bed reactors [ 1-4], which suffer from diffusional as well as thermodynamic limitations [ 5 9]. In this investigation the possibility of overcoming these disadvantages by using fluidized bed configuration is explored. Earlier Elnashaie and Adris [8] as well as Adris et al. [9] carried out a detailed investigation of the possibility of using the fluidized bed con* Corresponding author. Fax ( + 966-1 )4633563, e-mail: F45 K006 @SAKSU00.B ITNET 1 On leave from the Chemical Engineering Department, Cairo University, Egypt. 0376-7388/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI0376-7388(94)00271-1
figuration for the steam reforming of methane, where the effectiveness factor in the fixed bed configuration is of the order of 0.01-0.001 [8,9], while in the fluidized bed configuration it approaches unity. In the present case the improvement due to the use of fine powder in the fluidized bed, although appreciable, is not as great as in the case of the steam reforming, because the effectiveness factor in the industrial fixed bed reactors for styrene production is in the range 0.4-0.6 [ 10]. The bubbles in the fluidized bed act as natural membranes removing the hydrogen formed in the dense phase, and therefore enhance the forward dehydrogenation reaction [5-8] and suppress the side reaction producing toluene. On the other hand the rapidly rising bubbles cause the disadvantage of reactants by-pass which can be minimized by suitable distributor design and the use of internal components which inhibit bubble growth.
32
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
Another disadvantage of fluidized bed is the high degree of mixing which suppresses the rate of reaction, especially for first order reactions. For the particular case studied here the high degree of hydrogen mixing in the dense phase enhances the hydrodealkylation reaction to produce toluene. This disadvantage can be minimized by using a number of fluidized beds in series in order to decrease the degree of mixing [ 5 ]. Many investigators studied the use of the fixed bed configuration with selective membranes for dehydrogenation reactions [ 11-22]. The use of selective membranes enhances the efficiency of the systems by efficiently removing the hydrogen from the reaction mixture. The use of fluidized bed augmented with selective membranes has not been previously investigated for the ethylbenzene to styrene reaction. In the present study the effect of selective membranes, for the removal of hydrogen from the reaction mixture, on the performance of the fluidized bed configuration is investigated in some detail.
2. Theory 2.1. Formulation of the model equations The two phase postulate for fluidization is one of the principal assumptions underlying the different models of fluidized bed reactors [23]. The two phase model considers that the fluidized bed consists of a bubble phase and a surrounding dense (or emulsion) phase which contains most of the catalysts and the theory also postulates that all gases in excess of that necessary for minimum fluidization pass through the bed as bubbles [23]. 2.2. Assumptions The following assumptions are used in the formulation of the model equations: 1. The bubble phase is solid free and in plug flow [24]. 2. The extent of reaction in the bubble phase is negligible and reaction is taking place in the dense phase only [23]. 3. The dense phase is uniform in temperature and perfectly mixed [ 23 ].
4. The effective bubble size is taken as that which exists at 40% of the expanded bed height, and is used for the entire reactor [24]. 5. The mass and heat transfer resistances between the particles and the gas in the dense phase are negligible [23]. 6. The volumetric flow rate through the bubble phase is assumed to be constant [ 23 ]. 7. The ideal gas law applies to the gases in the bubble and dense phases. 2.3. Kinetics of the dehydrogenation reactions The reaction network for the dehydrogenation of the ethylbenzene to styrene is given by Sheel and Crowe [3] as follows: C6H5CH2 CH3 ~ C 6 H5 CHCH2 + H2
( 1)
C6H5 CH2 CH3 --'>C 6 H 6 + C 2H4
(2)
C6 Hs CHz CH3 4- Ha --* C6 H5 CH3 4- CH4
(3)
2H20 + C2H4 --* 2CO + 4H2
(4)
H 2 0 + C H 4 --*CO + 3H2
(5)
H 2 0 4- CO ----)CO2 4-H2
(6)
The corresponding rate expressions are given by: rl = kl (PEB -- PST PH2/KEB)
(7)
re = k2PEB
(8)
r3 = k3 PEBPH2
(9)
r4 __ k4 PH20 P 0.5 ETH
10)
r5 = k5PH20PMET
11)
PT
r6 = k6 ~
PH2oPco
12)
It is important and interesting to notice from the structure of this reaction network that the reaction does not stop at the thermodynamic equilibrium conversion of the main reaction (i.e. reaction 1), but can proceed beyond this hypothetical thermodynamic equilibrium; because of the continuous consumption of the product hydrogen in reaction 3 producing toluene. Thus the actual equilibrium position for this reaction network is 100% conversion. However from a practical point of view this approach to 100% conversion is extremely
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31--42
33
Table 1 Kineticrate coefficientsand equilibrium constantof the ethylbenzene
2.4. Mass and energy balances for the bubble phase
Reaction rate constants
The material and energy balance equations are developed for the bubble and dense phases. Taking an element of height Ah in the bubble phase; steady state mass balance for thejth component in the bubble phase is given by:
Reaction No.
Frequency factor [ 10]
Activation energy, kJ/kmol/K [3]
1
0.854
2
14.0047
207989.23
3
0.5585
91515.26
0.1183
103996.71
4 5
- 3.21
6
dNjB=AB(KED)JB(~ NjB]
90891.40
dh Let
65723.34
21.2423
AB(KEo)jB aj Or)
then equation (23) is rearranged and integrated to give the molar flow rate profile of componentj in the bubble phase:
AFo/RT), b a r [ 25 ]
AFo = a + bT+ c T 2 122725.157
b, k J / k m o l . K c, k J / k m o l ' K
(23)
73628.40
E q u i l i b r i u m c o n s t a n t KEB = e x p ( -a, k J / k m o l
QB ]
- 126.2674 2
-2.194×
NjB=Qs
10 - 3
slow if selective membranes for hydrogen removal are not used. The apparent rate coefficients were given by Sheel and Crowe [3 ]. These rate coefficients were corrected by Crowe [25]. The intrinsic rate coefficients were extracted by Elnashaie et al. [10] and are shown in Table 1. These intrinsic rate constants are the ones suitable for the fluidized bed, because of the fine powder catalyst used. The net rates of ethylbenzene and steam formation are given by: ethylbenzene
R E B ---- - - ( r I -4- r 2 q- r 3 )
(13)
steam
Rn2o = - (r4 + r5 + r6)
(14)
The net rate of formation of the styrene and the other by-products are given by: styrene
Rsx = r 1
( 15 )
benzene
Raz = r 2
(16)
toluene
RTOL = r3
(17)
ethylene
RETtt = r2 -- 0.5 r4
(18)
methane
RMET = r3 -- r5
(19)
hydrogen
Rn, = r~ - r3 + 2r4 + 3rs + r6
(20)
carbon monoxide
Rco = r4 + r5 - r6
(21 )
carbon dioxide
Rco_-= r6
(22)
[ NjD ( NjD Q----D-- Qo
NJB )e_,~jh] QB
(24)
The energy balance of the bubble phase is given by: dTB
dh Let
AB(HBD)B(TD_ TB) pGCpcQB AB(HBD)B Pc CpGQB
(25)
/3
then equation (25) can be rearranged and integrated; and the temperature profile in the bubble phase can be calculated using equation (26):
TB = TD -- (TD -- TBF)e- ~h
(26)
2.5. Mass and energy balances for the dense phase The mass balance for component i in the dense phase at steady state is given by: H
0
+ V( 1 - 6) ( 1 - e)ppRj
(27)
Equation (27) can be rearranged and the integral evaluated to give the molar flow rate of componentj in the dense phase. Substituting equation (24) into equation (27), and evaluating the integral of equation (27) then the molar flow rate of component j in the dense phase can expressed by:
34
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
Table 2 Hydrodynamic parameters used in the fluidized bed reactor calculations Parameter
Equation
Ref.
Minimum fiuidization velocity
Umf=( ~
[231
)( ~/27.22 + 0.0408Ar- 27.2) \ RGap /
where
d_..~_~
A~ = p6(PD -- PG)g~ tZ~ Average bubble diameter
dB= dBM-- (dam -- dBo)e -°'3h/a~ where dBM= 0.652 [At( Uo- Umf)] 2/5 dBo= 0.00376( Uo- Umf)2
[301
Bubble rising velocity
UB = U o - Umf4- (g~dB)°5
[301
Bed voidage at minimum fluidization
Emf = 0.586( 1 "0 t0"029( PG t0"021
[311
ZJ
Uo - Um,
Volume fraction of bubble phase to overall bed
[231
UB
Reactor feed volumetric flow rate
QF= UoAa
[231
Bubble phase volumetric flow rate
QB= (Uo- Umf)AB
[23]
The dense phase feed volumetric flow rate
QDF= QF -- QB
[23]
(1-xj)
Diffusion coefficient of component j
[32]
xj i=1
i•j
Molecular binary diffusivity of components i andj Overall mass transfer coefficient
Mi+Mj i/2 Mi+Mj
D0;= (0 00214- 0 000492( M - - - ~ )
""
1
1
1
(KBD)jB
( KBc)jB
( KcD)jB
Vm, +
~ ~/1/2(
T3/2
]
] k PTO'ij~D]
[321
[311
D)m:g'~:"
(KcB)jB=6.78( ~mfDjmUB) 1/2 d~
Overall heat transfer coefficient
_ _1
(HBD)B
-- _ _1
+ - - 1-
(Hac)B
(HcD)B
) (KopoCpG) 1/2 gl/4 (HBc)B=4.5 UmfflGCpG -1-5.85 d~.5 dB
(HcD)B=21"44(KGpGCpG)~/2(emfUB) 1/2T
[311
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995)31-42
35
Table 3 Industrial fixed bed reactor feed, Operation conditions and specifications [ 31
products of the two phases are then mixed at the bed exit to form the exit stream of the fluidized bed dehydrogenation reactor. The exit molar flow rates of the
Item
product components and temperature are given by:
Value and dimension
NjE = NjD + NjB
Molar feed rates Ethylbenzene (EB) Styrene (ST) Benzene (BZ) Toluene (TOL) Steam (H20) Total molar feed Mass flow rate Inlet pressure Inlet temperature Catalyst bed diameter Catalyst bed length Catalyst bulk density Catalyst particle diameter
36.87 kg mol / h 0.67 kg mol/h 0.11 kg mol/h 0.88 kg mol/h 453.10 kg mol/h 491.63 kg mol/h 12238.79 kg/h 2.40 bar 922.59 ~ K 1.95 b m 1.70b m 2146.27 b kgCat/m 3 4.66 x 10- 3b m
( 31 )
TDQD + TB QB
TE
(32)
an + a~
The conversions and yields of reactants and products are calculated using the following equations for conversions:
(33)
Xj= NjF--NjE
Nj~
50.0
(1)
£
(2)
"Corrected by Crowe [33]. ~Corrected by Crowe [ 25 ].
40.0
( Nj~ Njo ) NjD = NjDF + QB QF QD ( 1 - e- ~J")
50.0
c" 2 0 . 0 o
(28)
+ V ( 1 - 6) ( 1 - e ) p p R j
The energy balance of the dense phase is given by: 10
E
c
o 10.0
<.D
(5)
10
NjDCpJD(TD -- Trf) =
j=l
E
NjDFCpJF(TDF -- T~y)
0.@ 895.0
j=l
, , , , , , , ,
, , , , , , , l l , l l , , , , , ,
08 .o
H
890.0
+ f
v
( H B D ) B ( T B -- T D ) A B d h
~z
0
06
v885.0 6
+V(1-a)(1-e)pe
}--' (-ZlH,)r~
(29)
Equation (29) is rearranged and the integral evaluated (using equation 26) to give, 10
/
*6
E .o c)
880.0
04
o_
iJ
E
i=1
/
875.0 x Ld
02 870.0
10
NjD CpjD( TD -- Trf) = E NjDFCpjDF(TDF -- Trf) j=l
j=l
+ PGCpa QG (TF
/~ Fixed
865.0
......... O0 Reactor
Bec
Exit
Temperoture
=
850.0
K
i ......... i ......... 0,0 1.0 2.0 3.0 Height to Diometer Ratio ( H / D )
- T D ) ( 1 -- e - / 3 H ) 6
+ V ( 1 - 6) ( 1 -- e ) p e ~_~ ( - A H i ) r~
(30)
i=l
The above equations provide the necessary mass and energy balances of the bubble and dense phases. The
Fig. 1. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different reactor height to diameter ratios. (1) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. O Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, O exit temperature, * average bubble diameter.
B.K. AbdaUa, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
36
60.0
i --~-dl=aH2tW ae.2 f ~o-V --~o]
£ 50.0
(35)
0
(2)
where ct.2 is the permeation rate constant of hydrogen given by
40.0 x~
~ 5o.o
27r a l l 2 - ln(Fo/F/)
d o 20.0
DCo
(36)
E >
with
J
g ~
10.0
D = 8.28 × 10 -4 exp( -
(s) 0.0 900.0
21700/RT)
Co = 302.97 X T - 1.o358
i i i i l l l l l l l l l l ~ l l ~ l
0.20
E] :E
80.0 o
v
895.0
S
015 v
E o ~3
8900 o
-010
~ 885.0
w
•
z~ z3 D oB
0.05
880.0
~o 5-
60.0
d
O) (2)
40.0 c" _<2 ~o
>o20.0
c o (D
K 875.0
. . . . . . . . .
0.0 Reactor
I . . . . . . . . .
1.0 H e i g h t to
I
0.00
. . . . . . . . .
2.0 Diameter Ratio
( H/D
3.0 )
(3> 0.0 898.0
Fig. 2. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different reactor height to diameter ratios for the reactor with bubble diameter correlation multiplied by 0.3. (1) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. O Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, O exit temperature, * average bubble diameter.
I I I I I I
I I I l l l ~ l l l l l
i
I
008
896.0 OO6 ~894.0
E o
D ~3
~ 892.0
0.04
E
m
~ 890.0 × LA
for yields:
I I I I I I I I
0.02
888.0
-- NjF Yj= N j E
(34)
N[ EBorH20 ] F
2.6. Rate of hydrogenpermeation throughthe palladium membrane The permeation rate of hydrogen gas through the palladium membrane is assumed to obey the half power pressure law [26]:
886.0
¢ Fixed Bed Exit T e m p e r a t u r e = 8 5 0 0 K ......... i ......... i ......... 0.00 0.0 1 0 2.0 3.0 R e a c t o r H e i g h t to D i a m e t e r R a t i o ( H / D )
Fig. 3. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different reactor height to diameter ratios for the reactor with bubble diameter correlation multiplied by 0.1. ( 1 ) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. O Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, 4> exit temperature, * average bubble diameter.
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
80.0
>
~ 600 5=
400
._~ c 200
0.0
.... 0.0
5.0 10.0 15.0 20.0 25.0 .300 Steam to Ethylbenzene Ratio (S/E)
Fig. 4. Ethylbenzene conversion, styrene and toluene yields for the
fluidizedbed reactorwithreducedbubblediameter(correlationmultiplied by 0.3) at different steam to ethylbenzene ratios (S/E) (dp= 3.6 x 10-4 m and TF= 922.59 K). O Ethylbenzeneconversion fluidizedbed, [] styreneyieldfluidizedbed, A tolueneyieldfluidized bed. and D is Fick's diffusion coefficient of hydrogen dissolved in palladium. Composite palladium-ceramic membranes with palladium films, made by depositing palladium over the surface of asymmetric tubular ceramic membranes are used [27].
2. 7. Hydrodynamic parameters
components molar flow rates in the dense phase and the temperature of the dense phase are introduced to subroutine zsPow. The feed conditions to the dehydrogenation reactor as well as the hydrodynamic parameters are calculated and fed into the solution algorithm. Different subroutines are used for this purpose. The rate of the hydrogen permeation through the palladium membrane is evaluated by integrating equation (35) numerically using an integration routine. The subroutine DCADRE (IMSL Math/PC-Library) [29] is used for this purpose. The amount of hydrogen permeated through the membrane tubes is subtracted from the moles of hydrogen produced in the dense phase. The molar flow rates of the components and the temperatures of the two phases and the exit conditions are calculated and tabulated.
3. Results and discussions
3.1. Sizing and operating parameters of the fluidized bed reactors The industrial reactor at Polymer Corporation (Sarnia, Ont., Canada) and its feed conditions are taken as basis for comparison with the fluidized bed reactors [ 3 ]. Table 3 shows the dimensions and operating conditions of the industrial fixed bed reactor.
The application of the two phase theory of fluidization requires the estimation of the hydrodynamic parameters. The correlations for the computation of the hydrodynamic parameters used are given in Table 2.
80.0
600
2.8. Solution of the model equations The model equations describing the dehydrogenation of ethylbenzene to styrene using the fluidized bed configuration are solved as follows: Equations (28) describe the flow rate of component i in the dense phase, they constitute a system of ten non-linear algebraic equations. Equation (30) describes the energy balance equation which is also a non-linear algebraic equation. These equations are amenable to numerical solution; and the NewtonRaphson numerical technique can be used. The subroutine zsPow (IMSL Math/PC-Library) [28] is used for this purpose. Initial guesses of the
37
~D
j
~4oo
c~>200 8
0,0
/
/
f (11
(2)
J
i l r l l ~ l l l l
800.0
i lill
i i l l l l l l l l l l l
iiii
ii
850.0 900.0 950.0 Reactor Feed Temperature (K)
ir
~11
1000.0
Fig. 5. Ethylbenzene conversion, styrene and toluene yields for the fluidized bed reactor with reduced bubble diameter (correlation multiplied by 0.3) at different feed temperatures ( S / E = 12.3, dp=
3.6 × 10-4 m). O Ethylbenzeneconversionfluidizedbed, [] styrene yield fluidizedbed, A toluene yield fluidized bed.
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
38
70.0
..600
s r,
¥500
/"~-
u
o
O) (2)
s 40 0
.300 o
~>20.0
o o
100
(3) 8880
-300
-25 0 8840
2O 0
~J 880 0
150
E E 8760
o
100 uJ 8720
50 Fixed Bed Exit T e m p e r a t u r e =
8680
850.0
K
. . . . . . . . . IIH ..... I I I ' r ' ' I ' ' ' N ' r H N r l I H I ' I ' ' H I I I I I ' I ' ' I N ' ' ' ' ' ' ' 00 2.0 4.0 60 80 10.0 120 N u m b e r of Fluidized Beds in Series
0.0 140
Fig. 6. Ethylbenzene conversion, styrene and toluene yields, reactor exit temperature and average bubble diameter at different number of fluidized bed reactors in series without selective membranes. (1) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. © Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed, A toluene yield fluidized bed, 0 exit temperature; * average bubble diameter (averaged over all the beds for each case).
The total catalyst weight of the industrial reactor is used as the total catalyst weight for the fluidized bed reactor, in order to achieve consistent comparison between the two configurations. Fig. 1 shows that for the same H/D ratio as the industrial fixed bed reactor, the fluidized bed reactor gives lower XEB, lower YST and higher YTOL.This is due to the two main disadvantages of fluidized bed configuration discussed earlier, namely reactant by-pass by bubbles (low XEB) and a high degree of mixing (high }'TOE) both effects result in low YST.Increasing H/D causes the situation to deteriorate further giving lower XEB and YST and higher YTOL"However decreasing H / D improves the situation where XEB and YST increase sharply while YTOL decreases slowly. The value of XEB does not exceed that of the fixed bed configuration except for H/ D < 0.05, while YST always remains lower and YTOL higher than those of the industrial fixed bed reactor. It is thus clear that the situation is not as clear and straightforward as with steam reforming [ 8,9 ]. Careful design of the fluidized bed is obviously necessary in order to exploit the advantages of this configuration and minimize the effect of its main disadvantages. It is also essential to recognize the fact that the feed conditions (S/E and feed temperature) suitable for the fixed bed configuration are not necessarily the ones suitable for the fluidized bed configuration. Therefore our parametric investigation should include the following factors: 1. Effect of bubble diameter 2. Effect of S/E ratio 3. Effect of feed temperature 4. Effect of backmixing (i.e, effect of the number of fluidized beds in series used) The first three factors will be investigated for a single fluidized bed, then the dividing up of the fluidized bed
Table 4 Results of the fluidized bed reactor (correlation of dB multiplied by 0.1 ) assuming no H2 mass transfer between the dense and the bubble phases as compared with those of the normal one Item
Reactor with H 2 mass transfer between the bubble and dense phases ( 1 )
Reactor without H2 mass transfer between the bubble and dense phases (2)
Reduction % = [ ( l ) - ( 2 ) 1 / ( 1 ) x 100
XEB
62.20% 39.39% 7.94% 14.87%
55.55% 19.47% 5.87% 30.22%
10.69 50.57 26.07 - 103.23
~z YTOL
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31--42 80.0
the hydrodealkylation reaction for the formation of toluene.
60.0
3.3. Steam to ethylbenzene ratio (S/E) (1) 2L~
8 4O 0
/ /
g o Q)
39
Z
20.0
8 O0
~ ........
I ..... ~ 5 N u m b e r of
, ' ~ ....... 10 15 M e m b r o n e Tubes
20
Fig. 7. Ethylbenzene conversion and styrene and toluene yields for the fluidized bed reactor with reduced bubble diameter ( H / D = 0.87, S / E = 12.3, d p = 3 . 6 × 10 -4 m) at different number of membrane tubes (sweep gas molar flow rate 225 kmol/h at membrane tube pressure 1.013 bar). ( 1 ) Ethylbenzene conversion industrial fixed bed, (2) styrene yield industrial fixed bed, (3) toluene yield industrial fixed bed. 0 Ethylbenzene conversion fluidized bed, [] styrene yield fluidized bed with membranes, A toluene yield fluidized bed with membranes.
into a number of beds in series will be investigated in order to study the effect of backmixing.
3.2. Effect of bubble diameter The problem of reactants by-pass associated with the large bubbles can be tackled by creating bubbles of smaller diameters; through the use of different distributors and/or internals. In order to simulate this situation the average bubble diameter (Table 2) is multiplied once by 0.3 (Fig. 2) and once by 0.1 (Fig. 3) and the model is solved using the different H / D values as before. In Fig. 2 XEB is higher than that of the industrial fixed bed reactor for the industrial value of H / D and increases further as H / D decreases. However YsT is still lower and }'TOEis still higher than the industrial values even for very small values of H/D. In Fig. 3, where the bubble diameter multiplication factor is 0.1, XEB is always much higher than that of the fixed bed industrial reactor, while YsT is very close to that of the industrial reactor (at H / D 0.05 it is slightly higher than the industrial reactor), however YVOLis still appreciably higher than the industrial reactor indicating that the backmixing in the fluidized bed enhances considerably
We investigate here the effect of S/E for a fluidized bed having the same H / D as the industrial fixed bed and use the bubble size correlation multiplied by 0.3 in order to moderately reduce the effect of reactants bypass. Fig. 4 shows the effect of the S/E on values of the XEB , YsT and YTOL for the fluidized bed reactor with reduced bubble diameter, catalyst particle diameter of 3.6 × 10 -4 m and reactor feed temperature of 922.59 K. The S/E ratio is changed while the total amount of the steam and ethylbenzene in the feed are kept constant. The values Of XEB and YsT increase and the YTOL decreases as the S/E increases.
3.4. Reactor feed temperature (TF) Fig. 5 shows the effect of feed temperature on the values OfXEB, YsT and YTOL for the fluidized bed reactor with reduced bubble diameter (multiplication factor = 0.3) using the industrial S/E and catalyst particle diameter of 3.6 × 10 - 4 m . It is clear that the feed temperature increase causes the increase of the XEB and YTOL, while the YST remains lower than that for the industrial reactor.
3.5. Effect of backmixing This factor is most easily investigated by dividing the fluidized bed reactor into a number of beds in series (i.e. one on top of the other). This will decrease the degree of axial mixing and it will also clearly affect the average bubble size because of the gas redistribution as small bubbles at the entrance of each bed. Fig. 6 shows the combined plot of XEB , YsT, YTOL, TE and da versus the number of fluidized beds in series (nB). The results of Fig. 6 show that XEa and YsT increase as the number of beds increases. The values of the XEa obtained are higher than the industrial fixed bed reactor for nB> 2. The values of YsT obtained are also higher than the industrial one when na > 3. The values of YTOLobtained are higher than the industrial one. Fig. 6 also shows that YTOLmildly decreases as the number of the fluidized beds in series increase but is still higher than the industrially obtained value. Fig.
40
B.K. Abdalla, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
6 also shows that the overall average dB and the exit temperature TE decrease as the number of beds increases.
3.6. Role of the bubbles as natural membranes To show clearly the role of the bubbles in the fluidized bed as natural membranes removing the hydrogen formed in the dense phase, and therefore enhancing the forward dehydrogenation reaction [ 5-7] and suppressing the formation of toluene, a hypothetical case with the rate of hydrogen transfer from the dense phase to the bubble phase put equal to zero is computed, when the bubble diameter correlation is multiplied by 0.1. Table 4 shows the result of assuming no hydrogen mass transfer between the dense and the bubble phases. Table 4 shows a small reduction in the XES, large reductions in YSTand Yaz, and a large increase in YTOL"The reasons for the reduction in the XEB, YST and YBz and the increase in the YTOL are quite obvious, because the increased amount of the H2 in the dense phase increases the backward step of the reversible reaction and also increases the hydrodealkylation reaction (i.e. reaction 3) which is responsible for the production of the toluene.
3. 7. Reactor with hydrogen permeable membrane tubes In this case hydrogen is removed from the reaction site by the use of thin films of palladium membranes deposited over porous support materials. For a single membrane tube case (nT = 1) a membrane tube of inner diameter 0.345 m made of porous material (e.g. ceramic) with a thin palladium film (thickness = 5 . 1 0 - 4 mm) deposited on its surface, is passing vertically through the centre of the reactor. For the base case an inert gas of molar flow rate equal to 225.0 kmol/ h at a pressure of 1.013 bar flows concurrently with the reactants flowing in catalyst side. The fluidized bed reactor with the industrial H/ D = 0 . 8 7 with reduced bubble diameter (correlation multiplied by 0.3) the industrial S / E = 12.3 and the industrial feed temperature of 922.59 K is used for this part of the investigation. The fluidized bed catalyst particles diameter (dp) is equal to 3.6 X 10-4 m as used earlier, and the effect of the number of membrane tubes is investigated.
The effect of increasing the number of palladium tubes is studied where the total cross-sectional area of membrane tubes was assumed to be equivalent to that of the single tube passing through the centre. The flowing sweep gas was assumed to be equally divided through the membrane tubes. Fig. 7 shows the effect of varying the number of membrane tubes on the XEB , YSTand YTOLas compared with the corresponding values for the industrial fixed bed reactor and the fluidized bed reactor without membrane (nx = 0). It is clear that the removal of the hydrogen by the use of these membrane tubes causes a continuous increase in XEBand liST and a continuous decrease in YTOL.For nT = 16, YTOLis almost zero and the selectivity to styrene is almost 100%. Combining the different factors that improve the reactor performance it was found that a configuration with 7 fluidized beds in series, 16 membrane tubes, tube side sweep gas molar flow rate of 1600 kmol/h. membrane tube pressure of 0.03 bar, feed temperature of 975 K, H / D = 0 . 5 and S / E = 2 5 can give XEB and Ysv as high as 96.5% and 92.4% respectively.
4. Conclusions
The direct use of fluidized bed configurations for the catalytic dehydrogenation of ethylbenzene can increase the ethylbenzene conversion but does not increase the styrene yield. Suitable arrangements to create small bubble size to decrease reactants by-pass and the use of a number of fluidized beds in series to decrease backmixing can increase the ethylbenzene conversion and the styrene yield. The parametric study showed that the styrene yield can be increased by using a steam to ethylbenzene ratio higher than the industrial ratio. The application of selective membranes to the fluidized bed reactor increases considerably the ethylbenzene conversion and the styrene yield, over that of fluidized bed without membranes and the industrial fixed bed reactors. Suitable choice of design parameters and operating conditions gives high ethylbenzene conversion and styrene yield. In addition to increasing the ethylbenzene conversion and styrene yield, the removal of the hydrogen by the selective membranes increases the selectivity to styrene; by reducing the yields of some by-products, especially toluene. A fluidized bed configuration with a number of beds in series and selective
B.K. Abdalla, S.S.E.H. Elnashaie/Journal of Membrane Science 101 (1995) 31-42
membrane for hydrogen removal can give XEB and YST as high as 96.5% and 92.4%, respectively,
Q re, Ri
6. List of symbols
T Uo, UB, Umf
6.1. Notation AB, AD, At
Co
@, Cps dB, dp D, Dej, Dj,,
gc
h,H Hi
(H.D)B
(KBD) JB
K~
KEB M, nB
N~ nT Pi
PT P
cross-sectional area of bubble phase, dense phase and reactor tube; m 2 molar concentration of H2 in the membrane, kmol / m 3 heat capacity of component i and of the gas mixture, kJ/kmol bubble and particle diameter, m diffusivity of Hz through the membrane, binary diffusivity of components ~and j and diffusivity of component j, m2/h gravitational acceleration, m/h 2 reactor tube and expanded bed height, m heat of reaction ;, kJ/kmol interphase heat transfer coefficient between bubble and dense phase based on bubble volume, kJ/m3/ h/K interphase mass transfer coefficient between bubble and dense phase based on bubble volume, 1/ h thermal conductivity of the gas, kJ/K/m/h rate constant of reaction ~, kmol/ kgCat/h/barN ethylbenzene equilibrium constant, bar molecular weight of component i number of fluidized beds in series molar flow rate of component j, kmol/h number of palladium membrane tubes partial pressure of component ~,bar total pressure of the reactor, bar partial pressure of Hz in the membrane, bar
xi
41
volumetric flow rate, m3/h rate of reaction e and rate of formation of component j, kmol/ kgCat/h temperature, K superficial gas velocities of fresh feed, of bubble phase and fresh feed at minimum fluidization, m / h mole fraction of component i, dimensionless
6.2. Greek letters 6 e emf PD, PC ~r~j /~
bubble phase volume fraction to the total volume of the bed, dimensionless catalyst pellet porosity factor, dimensionless dense phase voidage at minimum fluidization, dimensionless density of the catalyst, density of gas mixture, k g / m 3 Lennord-Jones force constant, viscosity of the gas mixture, kg. h/ m2
~D /'o,
collision integral for viscosity, dimensionless outer and inner radii of the permeable tube, m
6.3. Subscripts B D E F G
i,j
rf
bubble phase dense phase exit from the reactor feed to the reactor gas mixture components i and j taken binary reference conditions
References [ 1 ] R.R. Wenner and E.C. Dybdal, Catalytic dehydrogenation of ethylbenzene, Chem. Eng. Progr., 44 (1948) 275. [2] B. Davidson and M.J. Shah, Simulation of the catalytic cracking process for styrene production, IBM J. Res. Dev., 9 (1965) 388.
42
B.K. AbdaUa, S.S.E.H. Elnashaie / Journal of Membrane Science 101 (1995) 31-42
[3] J.G.P. Sheel and C.M. Crowe, Simulation and optimization of an existing ethylbenzene dehydrogenation reactor, Can. J. Chem. Eng., 47 (1969) 183. [4] D.E. Clough, W.F. Ramirez, Mathematical modeling and optimization of the dehydrogenation of ethylbenzene to form styrene, AIChE J., 22 (1976) 1097. [5 ] K.M. Wagialla and S.S.E.H. Elnashaie, Fluidized bed reactor for methanol synthesis. A theoretical investigation, Ind. Eng. Chem. Res., 30 (1991) 2298. [6] S.S.E.H. Elnashaie, K.M. Wagialla and A.M. Helal, The use of mathematical and computer models to explore the applicability of fluidized bed technology for highly exothermic catalytic reactions: II Oxidative dehydrogenation of ethylbenzene to styrene, Math. Comput. Modelling, 15 ( 1991 ) 43. [7] S.S.E.H. Elnashaie, K.M. Wagialla and M.E.E. Abashar, The use of mathematical and computer models to explore the advantages of fluidized bed technology for catalytic reactions with equilibrium/diffusional limitations, Ammonia synthesis, Math. Comput. Modelling, 16 (1992) 35. [8] S.S.E.H. Elnashaie and A.M. Adris, A fluidized bed steam reformer of methane, in ed. J.R. Grace. L.W. Schemit, and M.A. Bergougnou (Eds.), Fluidization VI, Engineering Foundation, New York, 1989, p. 319. [9] A.M. Adds, S.S.E.H. Elnashaie and R. Hughes, A fluidized bed membrane reactor for the steam reforming of methane. Can. J. Chem. Eng., 69 (1991) 1061. [ 10] S.S.E.H. Elnashale, B.K. Abdalla and R. Hughes, Simulation of the industrial fixed bed catalytic reactor for the dehydrogenation of ethylbenzene to styrene: heterogeneous dusty gas model, Ind. Eng. Chem. Res., 32 (1993) 2537. [ 11 ] N.A. Itoh, Membrane reactor using palladium. AIChE J., 33 (1987) 1576. [ 12] N. Itoh, Y. Shindo, K. Haraya and T. Hakuta, A membrane reactor using microporous glass for shifting equilibrium of cyclohexane dehydrogenation, J. Chem. Eng. Jpn., 21 (1988) 399. [ 13] B.K. Abdalla and S.S.E.H. Elnashaie, A membrane reactor for the production of styrene from ethylbenzene, J. Membrane Sci., 85 (1993) 229. [ 14] H. Nagamoto and H. Inoue, A reactor with catalytic membrane permeated by hydrogen, Chem. Eng. Commun, 34 (1985) 315. [ 15] J.C.S. Wu and P.K.T. Liu, Mathematical analysis on catalytic dehydrogenation of ethylbenzene using ceramic membranes, Ind. Eng. Chem. Res., 31 (1992) 322. [ 16] N. Itoh, Maximum conversion of dehydrogenation in palladium membrane reactors, J. Chem. Eng. Jpn., 24 (1991) 664.
[ 17] S. Uemiya, N. Sato, H. Ando, T. Matsuda and E. Kikuchi, Steam reforming of methane in a hydrogen-permeable membrane reactor, Appl. Catal., 67 ( 1991 ) 223. [18] T. Matsuda, I. Koike, N. Kubo and E. Kikuchi, Dehydrogenation of isobutane to isobutene in palladium membrane reactor, Appl. Catal. A, 96 (1993) 3. [ 19] Y.V. Gokhale, R.D. Noble and J.L. Falconer, Analysis of a membrane enclosed catalytic reactor for butane dehydrogenation, J. Membrane Sci., 77 (1993) 197. [20] J. Shu, B.P.A. Grandjean, A. Van Neste and S. Kaliaguine, Catalytic palladium-based membrane reactors: a review, Can. J. Chem. Eng., 69 (1991) 1036. [ 21 ] Y.L. Becker, A.G. Dixon, W.R. Moser and Y.H. Ma, Modelling of ethylbenzene dehydrogenation in a catalytic membrane reactor, J. Membrane Sci., 77 (1993) 233. [22] J.C.S. Wu, T.E. Gerdes, J.L. Pszczolkowski, R.R. Bhave, P.K.T. Liu and E.S. Martin, Dehydrogenation of ethylbenzene to styrene using commercial ceramic membranes as reactors, Sep. Sci. Technol., 25 (1990) 1489. [23] J.R. Grace, Modelling and simulation of two-phase fluidized bed reactors, NATO, ASI Ser., ser. E., Vol. 110, Chem. Reactor Design Technology, 1986, p. 245. [24] C. Fryer and O.E. Potter, Bubble size variation in two-phase models of fluidized bed reactors, Powder Technol., 6 (1972) 317. [25] C.M. Crowe, Dept. Chem. Eng., McMaster Univ., personal communication, Nov. 10, 1989. [26] G. Bohmholdt and E. Wicke, Diffusion of H2 and D2 in Pd and Pd alloy, Z. Phys. Chem., Neue Folge, 56 (1967) 133. [27] J.P. Collins and J.D. Way, Preparation and characterization of a composite palladium-ceramic membrane, Ind. Eng. Chem. Res., 32 (1993) 3006. [28] J. More, B. Garbow and K. Hillstrom, User Guide for Minpack1, Argonne National Laboratory Report ANL-80-74, Argonne, IL, August, 1980. [29] C. De Boor, CADRE: an algorithm for numerical quadrature, in J.R. Rice (Ed.), Mathematical Software, Academic Press, New York, 1971, Chap. 7. [30] S. Mori and C.Y. Wen, Estimation of bubble diameter in gaseous fluidized beds, AIChE J., 21 (1975) 109. [31] D. Kunii and O. Levenspiel, Fluidization Engineering, John Wiley and Sons, New York, 1969. [32] R.C. Reid and T.K. Sherwood, The Properties of Gases and Liquids. McGraw Hill, New York, 1966. [33] C.M. Crowe, Dept. Chem. Eng., McMaster Univ., personal communication, Aug. 20, 1992.