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Studies of a pervaporation membrane batch reactor.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2011; 6: 575–580
Published online 29 March 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI:10.1002/apj.431
Research article
Studies of a pervaporation membrane batch reactor
K. Siva Kumar and S.V. Satyanarayana*
Department of Chemical Engineering, JNTUCE Anantapur-51 5002, India
Received 23 September 2009; Revised 19 December 2009; Accepted 18 January 2010
ABSTRACT: Pervaporation processes are being increasingly adopted for environmental applications, and also for
developments in many industrial reactions and their reactor systems. This study is related to pervaporation-facilitated
esterification. A parametric study was carried out in order to provide a fundamental understanding of the reactor
behaviour. A batch reactor integrated with a pervaporation unit was selected as the model system. The model validity
was confirmed by comparison with literature data. Simulations demonstrated that conversions exceeding equilibrium
limits can be achieved by using pervaporation to remove water from the reaction mixtures, and that complete conversion
of one reactant is possible when the other reactant is present in excess. Simulations also showed that conversion was
less effected by the presence of water, which can be either in the reaction medium or as an impurity of the reacting
reagent. The influence of several process parameters on reaction performance is discussed; for example membrane
permeability, membrane area, volume of the reaction mixtures, temperature, excess reactant versus conversion, and
water concentration in the reactor.  2010 Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: simulation; pervaporation; membrane reactor; esterification reactions
INTRODUCTION
The stringent environmental regulations and need of
cost effective processes make the chemical engineers to
strive for development of novel separation techniques.
In recent years membrane technology has emerged as
one of the viable unit operations in separation processes.
The potential applications of membrane technology in
reaction engineering are being recognized. There has
been an engineering effort to combine reaction and
separation into a single process unit so as to improve
process performance. Since permselective membranes
permit selective permeation of a component from a mixture, membrane reactors can help to enhance the conversion of thermodynamically or kinetically limited reactions through controlled removal of one or more reactant
or product species from the reaction mixture. In the past,
the main objective of incorporating a membrane into a
chemical reactor was to achieve reaction and separation
in one stage. Today membrane is used not only as a
separator but also as a catalyst. The membrane reactors
have the prospective to develop the process industry by
enhancing selectivity and yield, reducing energy consumption, improving operation safety, and miniaturizing the reactor system. Membrane reactors are used for
*Correspondence to: S.V. Satyanarayana, Department of Chemical
Engineering, JNTUACE Anantapur-51 5002, India.
E-mail: svsatya7@gmail.com
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Curtin University is a trademark of Curtin University of Technology
esterification, dehydrogenation, hydrogenation, water
gas shift reaction, methane steam reforming, oxidative
coupling of methane and enzymatic reactions[1 – 8] .
Pervaporation, an emerging membrane process specially used for organic–water and organic–organic
separations[9] , seems to be an appropriate choice. The
concept of using pervaporation to remove by-products
in an equilibrium-limited reactions was proposed in the
early stage of pervaporation research[10] , but the interest in pervaporation membrane reactors was reawakened
when pervaporation has proved to be a feasible separation technique in the chemical industry. But relatively
little work has been done on liquid-phase esterification
reactions due to lack of suitable membranes with good
perm selectivity and solvent resistance. Esterification
of carboxylic acids and alcohols is a typical example
of an equilibrium-limited reaction that produces water
as by-product. Pervaporation was commonly used for
the preparation of non- or less-volatile ester-chemicals
such as perfumes and ester-waxes. Pervaporation membrane reactors were studied for esterification of oleic
acid and ethanol, acetic acid and ethanol, acetic acid
and n-butanol, and acetic acid and benzyl alcohol[11 – 16] .
In this work a parametric study was carried out
for an esterification facilitated by pervaporation in an
attempt to provide a fundamental understanding of the
behaviour of the membrane reactor. A batch reactor,
the simplest of all reactor configurations, integrated
with pervaporation, was selected as the model reactor
576
K. SIVA KUMAR AND S. V. SATYANARAYANA
Asia-Pacific Journal of Chemical Engineering
system. The influence of several process parameters
such as membrane permeability, membrane area and
volume of the reaction mixtures, temperature, an excess
of reactant on the conversion and water concentration in
the reactor has been discussed. The model was validated
by comparing with literature values.
MATHEMATICAL MODEL
RCOOH + R OH ⇔ RCOOR + H2 O
(B)
1
−rA = k1 CA CB − k2 CE CW = k1 CA CB − CE CW
Ke
(3)
The rate of water formation can be expressed as
rW = k1 CA CB − k2 CE CW
Consider an esterification reaction of the type
(A)
The rate of disappearance of carboxylic acid (A) can
be expressed as
(E)
(W)
(1)
has been carried out in a batch reactor equipped with a
pervaporation unit, as shown in Fig. 1.
Assume isothermal operation and negligible change
in catalyst concentration. Applying a material balance
on any reactant or product species at any instant yields
d(Ci V )
= ±ri V − Ji S
dt
(2)
where subscript i denotes species i, C the concentration,
and J the permeation flux; r is the rate of disappearance
of the species in the reactor due to chemical reaction; for
product species, r is the rate of formation and takes positive sign. V and S are the volume of reaction mixtures
and the membrane area for permeation, respectively.
Since the stoichiometric coefficients for reactants and
products are equal, the numerical values of reaction rate
expressed with respect to any species i are equal.
(4)
where k1 and k2 are the rate constants for forward and
reverse reactions, respectively, and Ke (= k1 /k2 ) is the
equilibrium constant. Subscripts A, B, E, and W refer to
carboxylic acid, alcohol, ester, and water, respectively.
The permeation flux through a pervaporation membrane is usually concentration dependent. In this study,
the water concentration in the reaction mixtures was
less than 10.0% by weight, therefore, for the simplicity
of analysis, the water flux is assumed to be proportional
to water concentration[11] .
JW = PW CW
(5)
where P is a coefficient characterizing membrane
permeability.
Consider an ideal case where the membrane permeates only water and the initial concentration of the
less-abundant reactant (A) as CA0 as basis. The concentrations of various components in the reactor can be
calculated through the following equation[16] :
CA0 (θi − XA )
Ci = S
1 + Pi ( dt)
V
(6)
where subscript i denote species A, B, E, and W; θ
is the stoichiometric relationship of the compounds,
C
θB = CB0 and θE = θW = 0.
A0
Assuming the volume change of the reaction mixtures
in the membrane reactor is given by
Ji Mi
dV
=−
S
i ρi
dt
(7)
where Mi and ρi are molecular weight and density of
species i, respectively.
Defining dimensionless volume and water concentration in the reactor as, respectively
V
V0
cW
y=
cA0
v=
Figure 1. An idealized batch wise membrane
reactor (a) and its equivalent that integrate a
membrane unit with a batch reactor (b).
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
(8)
(9)
Asia-Pac. J. Chem. Eng. 2011; 6: 575–580
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
STUDIES OF A PV MEMBRANE BATCH REACTOR
From Eqns (2), (3), (5), and (6), we obtain the
equation for conversion of A at any time t.
dXA
= k1 CA0 [(1 − XA )(θB − XA )
dt




(θE + XA )(θW + XA )

−


S t
Ke 1 + PW
v0 v
(10)
For a ‘perfect’ water permeable membrane, PA =
PB = PE = 0. From Eqns (5), (7)–(9), the volume
change of the reaction mixtures in the membrane reactor
is calculated by
S
CA0 MW
dv
= −PW
y
(11)
dt
V0
ρW
From Eqns (2), (4), and (5) we obtain the equation
for water concentration in the reactor at any time t
dXA
y dv
S
y
dy
=
− PW
−
(12)
dt
dt
V0
v
v dt
For a given initial conditions of concentration and
volume, the concentration of the reaction mixture at
any instant can be solved provided that the knowledge
of reaction rate constants, membrane permeability,
membrane area, and initial volume of the reaction
mixture, molar ratio of reactants, and concentration of
a reactant are known. The membrane parameter Pw and
operating parameters
S and V0 are combined as a single
variable, i.e. PW VS , to measure the capacity of the
0
membrane unit for removing water from the reactor.
The ode equations (10)–(12) are solved numerically
to get X , v , and y at any time t.
Effect of PW vs on conversion of oleic acid
0
Figure 2 is a plot of variation of conversion
of oleic
acid with time as a function of PW VS at θB = 2.10.
0
As expected with increase of time, the conversion is
increasing. Further, one can observe that conversion of
the membrane reactor can go beyond the equilibrium
conversion, which is the maximum conversion that
would be obtained.
At a given reaction time the higher
the value of PW VS , the higher the conversion. As
0
value increased from 0.0 to 2.5 h−1 , the
PW VS
0
conversion increased from 0.82 to 0.97. This is obvious
because the concentration of water in the reactor
will be reduced more rapidly when the membrane
is more permeable and/or when the membrane area
per unit reaction volume is lager. For the given case
of illustration, the reactor
performance approaches the
upper limit when PW VS = 2.5 h−1 . The model and
0
experimental values[11] coincide for the case ofwithout
pervaporation and with pervaporation at PW VS =
0
1.2365 h−1 .
Effect of PW vs0 on water concentration
in the reactor
Figure 3 illustrates how water concentration in the
reactor
changes with reaction time as a function of
PW VS . During the early period of reaction, the rate
0
of chemical reaction is high, whereas water concentration gradually increases until it reaches maximum when
its formation and removal rates are equal. Thereafter
the water removal is faster than formation, resulting in
depletion of water in the reactor. Naturally, for a given
RESULTS AND DISCUSSION
Consider an esterification of oleic acid with ethanol at
348 K using p-toulenesulfonic acid as catalyst in a polyetherimide membrane reactor as a model system[11] . The
following parameters are used in the simulation work:
k1 =
k0
(1 + aCW )
where
k0 = 0.311939 m3 /kmol h
a = 0.65697
Ke = 3.175309
CA0 = 2.1989 kmol/m3
CC = 0.0190 kmol/m3
T = 348 K
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Effect of PW vs
on conversion of oleic
0
acid. This figure is available in colour online at
www.apjChemEng.com.
Figure 2.
Asia-Pac. J. Chem. Eng. 2011; 6: 575–580
DOI: 10.1002/apj
577
578
K. SIVA KUMAR AND S. V. SATYANARAYANA
reaction system, the larger the value of PW VS , the
0
shorter the time required for water to reach maximum
concentration and smaller the magnitude of the maximum water concentration. This is confirmed by the
results of an experiment that the final reaction mixtures
did not contain water after 6 h of reaction mixtures of
oleic acid and ethanol (in excess) at 75 ◦ C[11] .
Effect of excess of ethanol on conversion
of oleic acid
When one of the reactant species is used in excess,
a complete conversion of the other reactant may be
achievable. Figure 4 shows the effect of concentration
of excess reactant (ethanol in this case) on the conversion at PW VS = 1.2365 h−1 . The molar ratio of excess
0
reactant to limiting reactant (i.e. ethanol to oleic acid),
θB , is varied from 1.0 to 5.0. Figure 4 shows that there is
Effect of PW vs on water concentration in
0
reactor (simulation values). This figure is available in colour
online at www.apjChemEng.com.
Figure 3.
Figure 4. Effect of initial molar ratio of ethanol to oleic acid
(CB0 /CA0 ) on conversion of oleic acid. This figure is available
in colour online at www.apjChemEng.com.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering
good matching of simulated values with experimental
values[11] at θB of 2.10. As θB value increased from
1.0 to 5.0, the conversion increased from 0.81 to 0.98.
Further, Fig. 4 shows that larger the excess, faster
the reaction to reach completion. This is superior to
simple batch reactor where no matter what the excess
of one reactant; the limiting reactant is never completely
reacted.
Effect of initial concentration of water
on conversion of oleic acid
Figure 5 illustrates how conversion changes with reaction time for varying
initial concentrations of water
(CW0 ) at PW VS = 1.2365 h−1 . Initial water concen0
tration is varied from 0 to 2.0 kmol/m3 . As our main
objective is to compare the experimental values with
simulation values and the experimental values[11] are
available only for 6 h, so simulations are carried out
only for 6 h. Conversion is increasing with increasing
time and attaining almost constant value in 6 h time.
The model values are matching with the experimental
values given in the literature[11] at 0% water concentration. Further, Fig. 5 shows that with increase of initial
water concentration, there is large difference between
conversions at shorter time interval (0–3 h) and the
difference is small at longer time (6 h). Therefore, in
6 h time the difference between conversion is 0.03 (i.e.
0.95 at 0% and 0.92 at 2.0 kmol/m3 water concentration) when the water concentration is changed from 0.0
to 2.0 kmol/m3 . It may be expected that if simulations
are carried out for more time there may not be any difference in the conversion with increase of initial water
concentration. This may be attributed to the fact that
membrane permeates only water. Generally, in conventional reactor, thermodynamic equilibrium conversion
will be effected (decreases) by the presence of product
Figure 5. Effect of initial concentration of water (CW0 ) on
conversion of oleic acid. This figure is available in colour
online at www.apjChemEng.com.
Asia-Pac. J. Chem. Eng. 2011; 6: 575–580
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
STUDIES OF A PV MEMBRANE BATCH REACTOR
and a complete conversion of one reactant is obtainable
when the other reactant is in excess. In a membrane
reactor, the presence of water, which can be either reaction medium or impurity of the reacting reagent, has a
little effect on conversion. For PEI membrane, water
disappeared completely from the reaction mixture at
6 h and the conversion became 98.3%. The PV-aided
esterification of oleic acid can be performed at higher
concentrations of water and temperature.
NOMENCLATURE
Effect of Temperature on Conversion of
Oleic acid. This figure is available in colour online at
www.apjChemEng.com.
Figure 6.
component (water in this case) in the reactants. This
is one of the important features of membrane reactor
compared to conventional reactor.
Effect of temperature on conversion of oleic
acid
Figure 6 illustrates the effect of temperature, which in
turn affects the reaction
rate constant k1 , equilibrium
constant Ke , and PW VS on the reactor performance.
0
The conversion increases with increase of temperature.
As expected, with increase of temperature from 333 to
353 K the conversion increases from 0.80 to 0.96. The
fast reactions with severe equilibrium limitations benefit the most from continuous removal of by-product
by a membrane. In practice, a large k1 value is always
preferred and can be obtained by elevating reaction temperature and using a suitable catalyst, while little control
over Ke value can be achieved. Only slight variation in
Ke with temperature is expected for esterification reactions in which the difference in enthalpy of products
and reactants is small, as is the case ethanol acetic
acid esterification[17] . However, increasing temperature
often enhances membrane permeability significantly. It
is obvious that the reaction temperature, another important operating parameter, influences the performance of
a membrane reactor primarily through its effects on permeation rate and reaction rate.
CONCLUSIONS
A parametric study of pervaporation-facilitated esterification was carried out. It was illustrated that conversion can be enhanced by using pervaporation to
remove water from the reactor simultaneously. Conversions exceeding equilibrium limits can be achieved,
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Greek letters
ρ density, kg/m3
θ stoichiometric relationship of the compounds
ν relative volume
Letters
C concentration, kmol/m3
J flux, kmol/(m2 h)
r reaction rate, kmol/(m3 .h)
S membrane area, m2
V volume of reaction mixture, m3
k reaction rate constant, m6 /(kmol2 h)
Ke equilibrium constant
t time, h
y relative water concentration
a rate reduction parameter
k0 absolute forward rate constant
PW permeability coefficient, m/h
T temperature, K
X conversion
M molecular weight
Subscripts
1
2
i
A
B
E
W
c
0
forward reaction
backward reaction
species of reaction medium
oleic acid
ethanol
ethyl oleate
water
catalyst
condition at t = 0
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 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering
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Asia-Pac. J. Chem. Eng. 2011; 6: 575–580
DOI: 10.1002/apj
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