1. Chemical Engineering Science 56 (2001) 395}402
Ethylene epoxidation in a catalytic packed-bed membrane
reactor: experiments and model
M. A. Al-Juaied, D. Lafarga, A. Varma*
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Abstract
A mathematical model was developed for the ethylene epoxidation reaction over a cesium-doped silver catalyst in a packed-bed
membrane reactor (PBMR) and compared with the experimental results. The dusty gas model, based on the Maxwell}Stefan
equations, was used to describe transport through the porous stainless-steel membrane. Two reactor con"gurations were investigated
where either oxygen (PBMR-O) or ethylene (PBMR-E) permeated through the membrane, with the co-reactant fed to the catalyst bed.
The model results were in good agreement with the experimental data. Simulations showed that the imposed pressure gradient
resulted in predominantly convective #ow through the membrane, which inhibited backdi!usion of components from the catalyst bed.
The variables studied included reaction temperature and inlet reactant concentrations. The model results, as also demonstrated
experimentally, con"rmed that the PBMR-E is the best con"guration, followed by the conventional "xed-bed reactor (FBR) and the
PBMR-O, respectively. 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Ethylene epoxidation; Ethylene oxide; Membrane reactor; Dusty gas model; Reactor model; Inorganic membranes
1. Introduction reactions where by the use of membrane reactors,
increase in yield of desired products has been demon-
Recent developments in the synthesis of inorganic strated (Lafarga, SantamarmH a & Menendez, 1994;
H
membranes make them attractive for many applications Coronas, Menendez & SantamarmH a 1994; Tonkovich,
H
including catalytic reactions in aggressive environments Jimenez, Zilka & Roberts, 1996a and Tonkovich, Zilka,
H
(cf. Bhave, 1991; Hsieh, 1996). Comprehensive reviews of
Jimenez, Roberts Cox, 1996b; Pena, Carr, Yeung
H
inorganic membrane reactors are available in the litera- Varma, 1998; Lafarga Varma, 2000).
ture (cf. Zaman Chakma, 1994; Saracco Spechia, The epoxidation of ethylene to obtain ethylene oxide is
1998; Saracco, Neomagus, Versteeg van Swaaij, 1999). an industrially important reaction, as the product is
Two di!erent concepts are used in the inert membrane a valuable intermediate in the chemical industry (cf. Be-
reactor applications. In one, the membrane is used to rty, 1983; Van Santen Kuipers, 1987). The reaction
preferentially separate reaction product(s) from an equi- scheme is generally considered to be parallel, with two
librium-limited reaction, resulting in conversions exceed- competing reactions involved: epoxidation and complete
ing thermodynamic values. The membrane can also be combustion. Depending on the conditions, a third reac-
used to preferentially remove the reaction component(s) tion involving the oxidation of ethylene oxide can also
that could react further to form undesired product(s), as occur, but its rate is typically much smaller than those of
in the case of consecutive reaction networks. In the other reactions (1) and (2):
concept, the membrane is used for segregation and con-
trolled addition of one or more reactants through the
membrane. An example of this application is the con-
trolled addition of reactants for partial oxidation
* Corresponding author. Tel.: #1-219-631-6491; fax:#1-219-631-
8366. The approach described in this work involves a cata-
E-mail address: avarma@nd.edu (A. Varma). lytic packed-bed membrane reactor with an inert porous
0009-2509/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 2 3 5 - 9

2. 396 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402
stainless-steel membrane. In order to describe transport The di!usion process in gas phase includes two di!er-
through the membrane, several earlier models (cf. ent asymptotic regimes, molecular and Knudsen di!u-
Itoh, Shindo, Haraya, Botata, Hakuta Yoshitome, sion, depending on whether collisions between molecules
1985; Mohan Govind, 1988; Tsotsis, Champagnie, or molecule}wall, respectively, control the process. Each
Vasileiadis, Ziaka Minet, 1993) used simplifying de- regime corresponds to a distinct di!usion coe$cient and
scriptions such as non-interacting Knudsen #ow. Recent to evaluate the overall value in the transition region, the
works have shown the necessity of using more rigorous Bosanquet formula can be used (Aris, 1975):
models, particularly, in the presence of pressure gradient
1 1 1
through the membrane (Saracco, Veldsink, Versteeg # , (1)
Van Swaaij, 1995; Neomagus, van Swaaij Versteeg, DC DC DC
G GK GI
1998). where
Mechanisms that may contribute to the total transport
through a porous membrane include Knudsen, mole- 1 L
DC DC x , DC DM ,
cular, and surface di!usion, as well as viscous #ow. GK 1!x GH H GH GH
G HJH$G (2)
A proper description of this transport is important for
2r 8R ¹
the design of membrane reactors and for the interpreta- DC N E ,
tion of experimental data. The transport process through GI 3 M
G
porous media has been investigated extensively and stud- and the other quantities are dened in the Notation.
ies have shown that the dusty gas model (DGM) is The simplest model to describe di!usional transport of
a good model to use (Veldsink, Versteeg Van Swaaij, components is the Fick Model (FM):
1994 and Veldsink, van Damme, Versteerg Van
Swaaij, 1995). The Fick model is simpler than the DGM, DC d(x P)
N ! G G , i1,2, n. (3)
hence it is frequently used, but DGM is the preferred G R ¹ dr
E
model for description of transport through membranes.
We have recently investigated ethylene epoxidation in When a pressure gradient contributes to the total
a catalytic packed-bed membrane reactor (PBMR) ex- transport, the Darcy equation can be utilized and results
perimentally, and demonstrated that signicant improve- in the so-called extended Fick model (EFM):
ment in ethylene oxide selectivity and yield can be 1 d(x P) rx P dP
achieved over the conventional xed-bed reactor (FBR) N ! DC G # N G , i1,2, n. (4)
G R ¹ G dr 8 dr
(Pena et al., 1998; Lafarga Varma, 2000). In the present E
study, we rst report structural characterization of the The above Fick's-law-based models calculate indi-
membrane and its permeation characteristics. Then, by vidual component #ows independently of the others. The
using these independently determined parameters, a reac- di!usion process can be expressed more rigorously ac-
tor model based on the DGM #ux relations is used to cording to the Stefan}Maxwell equations, which results
simulate experimental results for the PBMR. An approx- in the DGM:
imate model that decreases computational e!ort signi-
L (x N !x N ) N
cantly is also suggested and is compared with the DGM G H H G ! G
PDC PDC
model. The reactor model includes kinetic rate expres- HJH$G GH GI
sions determined in a previous study (Lafarga, Al-Juaied, 1 dx x rP dP
Bondy Varma, 2000). A comparison between the FBR G# G N #1 , i1,2, n.
R ¹ dr PR ¹ 8 DC dr
and PBMR performances is also made for di!erent tem- E E GI
(5)
peratures and inlet reactant concentrations.
The DGM is fundamentally more correct than the
EFM because the convective motion is directly incorpor-
2. Model development ated into the model and drag e!ects caused by the
motion of other components are taken into account,
2.1. Gas transport through a porous membrane which are neglected in the EFM (Veldsink et al., 1995).
However, the DGM equations are more di$cult to solve
As stated above, various mechanisms can govern the numerically. A comprehensive review on the historical
transport of a gas mixture through porous membranes. background and derivation of the model equations can
For a given mixture, the relative importance of these be found elsewhere (cf. Mason Malinauskas, 1983).
mechanisms depends on the permeation conditions (i.e.
pressure, temperature, mole fractions) and characteristics 2.2. Membrane reactor model
of the membrane (e.g. pore size and volume, structure,
adsorption capacity). In many cases, the transport must A schematic diagram of the membrane reactor set-up
be described by a combination of mechanisms. is shown in Fig. 1. The catalyst is located in the shell (i.e.

3. M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402 397
expressions (Lafarga et al., 2000):
1.33;10 exp(!60.7/R ¹)P P
r E # - , (9)
(1#6.50P )
#
1.80;10 exp(!73.2/R ¹)P P
r E # - . (10)
(1#4.33P )
#
The in#uence of internal and external mass transfer
resistances for the catalyst was found to be negligible
using the Weisz}Prater criterion (Froment Bischo!,
1990), where for the experimental conditions the observ-
able was typically of the order of 10.
At each reactor axial position, z, the radial permeation
#uxes of species i, N , must be determined by solving the
G
DGM relations. In the present case, for six species (ethy-
lene, oxygen, nitrogen, ethylene oxide, carbon dioxide
and water) we have six unknown mole fractions (x ), six
G
unknown #uxes (N ), and the total tube pressure (P ).
G R
Since there is no reaction in the membrane and the
system operates in steady state, the membrane mass
Fig. 1. Schematic diagram of the reactor setup.
balance equations for all species can be written as
!
N 0, i1,2,6, r (r(r , z'0. (11)
G R Q
annulus) side. The reactor feed consists of two parts;
catalyst bed feed and the membrane tube feed. Reac- The DGM expressions, (see Eq. (5)) provide six addi-
tant(s) fed to the tube permeate through the membrane, tional equations. Finally, the sum of mole fractions,
react with co-reactants over the catalyst, and exit to- which must be unity, provides the last relation
gether.
L
x 1, r (r(r , z'0. (12)
2.2.1. Basic model equations G R Q
G
The steady-state mass balance equations for species i,
considering isothermal plug-#ow conditions on both the In order to solve this set of equations, 13 boundary
tube and shell sides, with negligible internal and external conditions are required. These correspond to species
mole fractions at the tube and shell sides (i.e. rr and
mass transfer resistances, are given by R
r , respectively), and the total pressure at the shell side of
Q
dF the membrane, P . These equations can be solved numer-
RG !2 r N , 0(r(r , z'0, i1,2, n, Q
dz R G PR R ically using the relaxation technique (cf. Press, Flannery,
(6) Teukolsky Vetterling, 1986), where the radial deriva-
tives in Eqs. (5) and (11) are replaced with nite di!erence
dF approximations for a total of M mesh points on the
QG 2 r N # (r !r) (1! )R , interval r (r(r .
dz Q G PQ U Q A @ G R Q
Relaxation rewards a good initial guess with rapid
r (r(r , z'0, i1,2, n, (7) convergence. For this, initial guesses of all variables are
Q U calculated using the linearized form of the DGM
where F and F are the axial molar #ow rates of species (Krishna, 1987), where average values for the mole frac-
RG QG tions and the total pressure are used, and the gradients
i on the tube and shell sides, respectively, z is the axial
direction, and R is the net reaction rate of species i given are estimated by assuming linear pressure and composi-
G tion proles along the length of the di!usion path. The
by
equations are solved iteratively until all residuals are
smaller than a specied value, typically 10.
R r, (8)
G GH H The reactor balance ODEs (6) and (7) are integrated by
H the Runge}Kutta method for the rst step in the z direc-
where ((0 for reactants and '0 for products) is the tion, with the initial conditions at the reactor inlet, the
GH
stoichiometric coe$cient for species i in reaction j with determined #uxes from solution of the DGM equations
rate r , following the previously determined kinetic rate and a guessed value of P , the tube side pressure. Next,
H R

4. 398 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402
a new step in the axial direction is taken with new values 3.2. Experimental setup
for the initial conditions calculated from the previous
step. To satisfy the mass balance at the reactor exit, the The membrane reactor setup (see Fig. 1) has been
guessed P value is changed (within the experimental
described in detail elsewhere (Pena et al., 1998; Lafarga
R
range). The calculation procedure also includes changes Varma, 2000). The PBMR uses a membrane for the
in the number of steps in the z direction, and repeats the distribution of ethylene or oxygen from the tube side to
calculations until the overall reactor mass balance is the shell side. The membrane was a 45 mm long 316 ¸
satised to a prescribed accuracy (error (0.1%). porous stainless-steel tube (Mott Metallurgical Corp;
0.20 m grade; 10 mm OD) welded to a non-porous
2.2.2. Approximate model for membrane transport 316 ¸-SS tube. The membrane was inserted in a 19 mm
An approximate model for membrane transport was OD quartz tube (17 mm ID). The catalyst was packed
also formulated. In this model, #ow in the membrane uniformly in the annular space formed between the mem-
tube is assumed to be equally divided along the tube brane and the quartz tube. There were two modes of
length. Thus, di!usive transport in the membrane is ne- operation; either ethylene #owed over the catalyst bed
glected and #ow is assumed to be purely convective. The and oxygen was distributed across the membrane
pressure on the shell side, P as shown in the experiments, (PBMR-O) or oxygen #owed over the catalyst bed and
Q
is 1.08}1.10 bar and on the tube side, P is constant with ethylene was distributed from the tube side (PBMR-E).
R
the value depending on the #ow condition (Pena et al.,
1998). Thus, viscous transport across the membrane is 3.3. Determination of the structural parameters
approximately constant. The DGM calculations showed
that #ow through the membrane is primarily convective In order to calculate species #uxes through the mem-
and the di!usive transport typically contributes less than brane, N , the structural parameters should be estimated
10% of the total #ow. G
independently. These parameters were determined from
Using this approximation, the tube side equation (6) is single gas permeation experiments for various gases. The
dropped, and in Eq. (7) N is calculated as F /¸ where same experimental setup described above in the absence
G RG
¸ is the reactor length. The use of DGM accounts for the of catalyst bed was used to perform the permeation
coupling of convective #ow with the individual partial experiments of di!erent pure gases through the mem-
pressure gradient, and permits to assess the magnitude of brane. In the case of pure gas permeation, the DGM
backdi!usion. However, in the present case, the approx- Eq. (5) reduces to
imate model also performs rather well, as discussed later
in Section 4.6. 2 r (P !P ) 8
N N R Q
G 3 t R ¹M
E G
3. Experimental r (P !P ) (P #P )
#N R Q R Q . (13)
8 tR ¹ 2
E
3.1. Catalyst preparation and characterization
A plot of the permeability, N /(P !P ), versus the
G R Q
average membrane pressure, (P #P )/2, gives a straight
The catalyst preparation was based on the procedure R Q
developed by Bhasin, Ellgen and Hendrix (1990). The line with slope and y-intercept equal to
!Al O pellets (Norton SA 5102, cylindrical, 3 mm
r
N
OD) were pretreated by acid leaching with hydrochloric
8 tR ¹
acid and calcined at 11003C for 24 h. The dried pellets E
were used as support for impregnation with a solution and
containing silver oxide, cesium hydroxide, lactic acid and
hydrogen peroxide. A calcination treatment with N 2r 8
N ,
(5003C for 5 h) was then performed to decompose the 3 t R ¹M
E G
lactic acid. Finally, to stabilize the activity, the catalyst
was treated alternatively under oxygen and hydrogen respectively. From these values, the apparent pore radius,
#ows (3 h each, 100 sccm) in two oxidation}reduction r , and the value of the porosity to tortuosity ratio, /
N
cycles at 3503C. (both based on the assumption that the pores are uni-
The nal catalyst contained 13.54 wt.% Ag and 0.005 form-sized and cylindrical), can be calculated directly.
wt.% Cs (based on dried weight of the support and
reduced catalyst). The support was densely covered with 3.4. Reaction experiments
0.3}0.5 m silver crystallites. The silver surface area was
925 cm Ag g-cat, while the BET surface area was All experiments were performed with the same batch of
0.97 m g-cat. catalyst. The experimental reaction procedure, activation

5. M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402 399
of the catalyst, and the experimental results are described
elsewhere (Pena et al., 1998; Lafarga Varma, 2000).
During the course of the experiments, the catalyst activ-
ity was checked regularly by performing an experiment at
standard conditions.
The data were obtained at di!erent inlet reactant con-
centrations and catalyst temperatures. The total #ow rate
in all the experiments was 200 sccm. The temperature
was varied in the range 210}2703C for each feed composi-
tion. In the xrst set of experiments, oxygen concentration
was varied over 3, 6, 9 and 12%, while maintaining
ethylene concentration xed at 6%. In the second set,
ethylene concentration was varied over 3, 6, 9 and 12%,
while maintaining oxygen concentration xed at 6%.
These concentrations are based on the overall composi- Fig. 2. Permeation measurements of helium, nitrogen and oxygen
tion and not of the separated feed. The diluent in all the through the membrane plotted according to Eq. (13).
experiments was nitrogen and the molar ratio between
the nitrogen introduced with ethylene (N ) and oxygen
#
(N ) was held xed at N /N 1.5.
- # -
For all the di!erent feed compositions and temper-
atures, the performance of PBMR (with ethylene or oxy-
gen permeating through the membrane) was compared
with the conventional FBR. The latter was achieved by
co-feeding ethylene and oxygen (mixed feed) from the
shell side in the same reactor setup, with the membrane
inlet plugged, thus, behaving as a solid non-porous tube.
4. Results and discussion
In this section, we describe results of the PBMR model
as compared with the experiments (Pena et al., 1998), and
also present results for the FBR under the same reaction Fig. 3. Flux prole as a function of distance along the reactor for
PBMR-O at 3% oxygen and 12% ethylene in feed.
conditions. As noted above, the PBMR was operated in
two modes by distributing either the oxygen (PBMR-O)
or ethylene (PBMR-E) from the tube side with an applied
pressure gradient to the shell side containing the catalyst. membrane tube to the shell side, and negative in the
opposite direction. As shown, there is no product transfer
4.1. Pure gas permeation results from the shell to the tube side, due to high pressure drop
across the membrane and the relatively small driving
Fig. 2 shows results of the permeation experiments force as compared to the feed components. Near the
with pure oxygen, nitrogen, and helium presented graphi- reactor inlet, ethylene di!uses from the shell to the tube
cally according to Eq. (13). The average r and / values side in the uphill direction of #ow. Later, as the concen-
N
were calculated from the slope and y-intercept to be 93.7 tration of ethylene increases in the tube, it reverses its
and 0.167 nm, respectively. These, together with Eq. (13), direction because of the convective #ow, in spite of the
lead to the dashed lines shown in the gure, where a good opposing ethylene partial pressure gradient. It is clear
agreement with the experimental data may be observed. that since oxygen is consumed by reaction on the shell
These average values are used in the subsequent calcu- side, its #ux change is larger than for nitrogen. Similar
lations. results are also found for the PBMR-E, but in this case
the nitrogen permeation #ux is higher since N 'N .
# -
4.2. DGM predictions and evaluation of backdiwusion
4.3. Comparison of PBMR-O experiments with model
Fig. 3 shows the #ux proles in PBMR-O (12% ethy- predictions
lene and 3% oxygen in the feed) along the reactor length.
The arrows indicate the directions of mass transfer, Fig. 4 presents a quantitative comparison between the
where the #ux is positive when the transport is from the experiments and the PBMR-O model predictions for

6. 400 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402
Fig. 4. Comparison of PBMR-O experimental (lled symbols) and
calculated (open symbols) results. Selectivity to ethylene oxide vs. Fig. 5. Comparison of PBMR-E experimental (lled symbols) and
ethylene conversion for various feed oxygen levels at 6% ethylene. calculated (open symbols) results. Selectivity to ethylene oxide vs.
ethylene conversion for various feed oxygen levels at 6% ethylene.
selectivity to ethylene oxide as a function of ethylene
conversion, for di!erent levels of oxygen in the feed. The
structural parameters of the membrane determined in
Section 4.1 were used in the simulations. No other adjust-
able parameters were used. Both the experiments and the
calculations show that ethylene oxide selectivity increases
with oxygen concentration in the feed and decreases with
increase of temperature. As for the FBR (Lafarga et al.,
2000), the model predicts the experimental results satisfac-
torily, but the deviations increase for lower P /P ratios.
- #
The reason for this is that the kinetic expressions (9) and
(10) are not as accurate for low oxygen concentrations,
and this problem becomes more acute for the PBMR-O as
the O level is relatively low over the entire catalyst bed.
Similar conclusions can also be drawn for the case
where ethylene concentration is varied in the feed, while
maintaining the oxygen concentration xed. In this case,
the selectivity increases as ethylene concentration de-
creases. In general, as noted earlier, high oxygen to ethy-
lene ratio increases the selectivity to ethylene oxide.
4.4. Comparison of PBMR-E experiments with model
predictions
Fig. 5 shows a comparison between the model predic-
tions and the experimental results for various levels of
oxygen. Both, the experiments and the calculations, ex-
hibit the same features as the PBMR-O (Section 4.3) Fig. 6. Comparison of experimental (lled symbols) and calculated
regarding the variations of reactant concentrations and (open symbols) results for the di!erent reactor congurations. Selectiv-
temperature. However, the model match is better for the ity to ethylene oxide at 12% ethylene conversion vs. (a) oxygen concen-
PBMR-E as compared to the PBMR-O, because now the tration in feed at 6% ethylene, and (b) ethylene concentration in feed at
6% oxygen.
e!ect of low oxygen to ethylene ratio is less pronounced.
4.5. Comparison of diwerent reactor conxgurations
results for the two PBMR congurations as well as the
To summarize the results, in Fig. 6 a comparison is FBR. The selectivity to ethylene oxide is shown as a
presented between the model and the experimental function of oxygen (Fig. 6a) and ethylene (Fig. 6b)

7. M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402 401
concentrations in the feed at 12% ethylene conversion. In case (typically less than 10%). Both models require no
all cases, for both the experiments and model, selectivity adjustable parameters. However, the DGM is more gen-
to ethylene oxide increases when oxygen concentration erally applicable because it includes both the viscous and
increases or ethylene concentration decreases. The gure di!usion transport mechanisms. It was important in the
also shows the important conclusion that, for all reaction present study to assess the backdi!usion e!ect, which
conditions, the relative performance is in the order cannot be done using the approximate model.
PBMR-E'FBR'PBMR-O.
4.6. PBMR simulations using approximate model for 5. Concluding remarks
membrane transport
This study provides a mathematical model that
The approximate model for membrane transport de- describes the performance of a packed bed membrane
scribed in Section 2.2.2 was compared with the DGM. reactor (PBMR) for the ethylene epoxidation reaction
Figs. 7a and b show results of the DGM and approxim- network. The model uses intrinsic reaction kinetics, plug-
ate models for PBMR-O and PBMR-E at 12% oxygen #ow behavior over the packed bed catalyst and the dusty
and 6% ethylene feed, respectively. gas model (DGM) for membrane transport. A good
Clearly, the DGM compares well with the experi- agreement between the model and experimental results
mental results. Further, predictions using the approxim- was obtained. The model deviations were noticeable in
ate model are relatively close to those obtained from the a few cases for the PBMR-O, particularly at low oxy-
DGM model. Similar results were also found at other gen/ethylene ratios where the oxygen conversion is high,
feed reactant concentrations. The good agreement be- because the kinetic expressions utilized (Lafarga et al.,
tween the two models is due to the fact that the di!usive 2000) are not as accurate for low oxygen concentrations.
transport contribution is relatively small in the present The model results showed that the use of a membrane for
feed distribution leads to improvements in selectivity and
yield to ethylene oxide as compared to a FBR. In the
PBMR-E conguration, the local partial pressure of
ethylene is reduced relative to a FBR, due to segregation
of ethylene across the membrane, and, as a result, the
selectivity to ethylene oxide is larger. On the other hand,
the selectivity in a PBMR-O is lower because the local
oxygen concentration is lower than in a FBR.
The model faithfully reproduced all experimental ob-
servations. Specically, as observed in the experiments,
the model demonstrated increased selectivity to ethylene
oxide as oxygen concentration increased or the temper-
ature decreased. It showed that the reactor performance
is in the order PBMR-E'FBR'PBMR-O. An ap-
proximate reactor model was also developed, where #ow
through the membrane was assumed to be uniform over
its entire length. Predictions of this model were relatively
close to those obtained using the DGM, because convec-
tive #ow dominates over di!usion for the membrane
utilized. In general, the developed reactor model can be
used successfully for predicting and optimizing operating
conditions for ethylene epoxidation in packed-bed mem-
brane reactors. It can also be adapted for use with other
reaction systems.
Notation
D Knudsen di!usion coe$cient of component
GI
i, m s
Fig. 7. Comparison of DGM (open circles) and approximate (open
D binary di!usion coe$cient of species i in j, m s
triangles) model results for 6% ethylene and 12% oxygen feed. Selectiv- GH
ity to ethylene oxide vs. ethylene conversion for (a) PBMR-O, and (b) ¸ reactor length, m
PBMR-E. M molecular weight of component i, Kg mol
G

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G national Chemical Engineering, 25, 138}142.
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