Separation and Purification Technology 47 (2005) 80–87
Analysis of the membrane thickness effect on the pervaporation
separation of methanol/methyl tertiary butyl ether mixtures
J.P.G. Villaluenga ∗ , M. Khayet, P. Godino, B. Seoane, J.I. Mengual
Department of Applied Physics I, Faculty of Physics, University Complutense of Madrid, 28040 Madrid, Spain
Received 11 March 2005; received in revised form 1 June 2005; accepted 2 June 2005
Abstract
The effect of the membrane thickness on the pervaporation separation of methanol and methyl tertiary butyl ether mixtures through
membranes was studied. Membranes of a wide range of thicknesses were prepared from two different polymers: cellulose acetate and
poly(2,6-dimethyl-1,4-phenylene oxide). For each membrane, the experiments were performed at the same feed pressure, feed temperature
and permeate pressure. The results showed that the permeate flux through both membrane types decreased markedly with increasing the
membrane thickness, while the separation factor remained nearly constant. This behavior was discussed in terms of a resistance-in-series
model.
© 2005 Published by Elsevier B.V.
Keywords: Mass transfer; Membranes; Modeling; Pervaporation; Separations
1. Introduction
Liquid mixtures can be separated by partial vaporization
through a dense permselective membrane. This separation
technique has been termed pervaporation in order to
emphasize the fact that the permeate undergoes a phase
change, from liquid to vapor, during its transport through
the membrane matrix. In this process, the feed mixture is
maintained in direct contact with one side of the membrane,
and the permeate is evolved, in the vapor state, from
the opposite side of the membrane, which is kept at low
pressure. The permeate is collected, in the liquid state after
condensation, on a cooled wall [1–5].
The characterization of a pervaporation process is usually
considered with regard to the variations of different operation
variables, such as the feed composition, the temperature, the
permeate pressure, the membrane thickness and the feed flow
velocity. The influence of membrane thickness on selectivity
and flux has been studied by a few workers. Binning et al. [6]
observed that the flux of a mixture of n-heptane and isooctane
∗
Corresponding author. Tel.: +34 91 394 4454; fax: +34 91 394 5191.
E-mail address: juanpgv@fis.ucm.es (J.P.G. Villaluenga).
1383-5866/$ – see front matter © 2005 Published by Elsevier B.V.
doi:10.1016/j.seppur.2005.06.006
(50/50 vol.%) through a plastic membrane was proportional
to the reciprocal membrane thickness and the selectivity was
independent of the thickness for membrane thicknesses in the
range of 20–50 ␮m.
Brun et al. [7], who studied the influence of the membrane
thickness on the selectivity using nitrile rubber membranes
and a mixture of butadiene and isobutene (60/40 vol.%), concluded that the selectivity was constant above a membrane
thickness of 100 ␮m, and a lower selectivity was found when
using membranes of 17 ␮m. The selectivity lowering for
thin membranes was explained by assuming the existence
of micropores in the membrane matrix, which allowed the
diffusion of molecules through them.
Spitzen et al. [8] studied the influence of the membrane
thickness on the separation of water/ethanol mixtures using
polyacrylonitrile membranes, and they found that the selectivity decreased drastically when using membranes with a
thickness below 20 ␮m. This behavior was also attributed to
the existence of the same artifacts in the membrane.
Aptel et al. [9] observed a selectivity lowering with a
decrease of the membrane thickness, for grafted polytetrafluoroethylene membranes, using water/dioxane mixtures.
Koops et al. [10] also investigated the effect of the membrane
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
thickness on the separation of water/acetic acid mixtures
using polysulfone, poly(vinyl chloride) and polyacrylonitrile
membranes. It was observed that the selectivity was independent of the membrane thickness above 15 ␮m, but below this
limiting thickness, the selectivity decreased with decreasing
membrane thickness. This dependence, which could not
be explained by differences in the polymer morphology,
or by flow coupling, was attributed to the formation of
induced defects in the membrane during the pervaporation
process.
Qunhui et al. [11] studied the influence of the membrane
thickness on the permselectivity of chitosan membranes, used
for the separation of water/ethanol mixtures. For membranes
with thicknesses lower than 30 ␮m, it was found that the
selectivity increased with the membrane thickness, whereas
for membranes with thickness higher than 50 ␮m, the membranes exhibited constant selectivities. It was also found that
the flux was proportional to the reciprocal of the membrane
thickness.
Recently, Kanti et al. [12] studied the effect of the membrane thickness on the permselectivity for the dehydration
of a mixture of 95.4 wt.% ethanol and 4.6 wt.% water, using
blended chitosan/sodium alginate membranes. It was found
that the flux decreased significantly with the increase in
the membrane thickness from 25 to 190 ␮m, whereas the
selectivity increased to a lesser extent. The variation of the
selectivity with the membrane thickness was related to the
existence of a dry layer in the membrane on the permeate side,
which was responsible of the permselective properties of the
membrane. It was explained that the thickness of this dry
layer increased with the total membrane thickness, causing
a rise in the membrane mass transfer resistance. Therefore,
the selectivity increased when the membrane thickness was
increased. Sridhar et al. [13] observed the same behavior
for chitosan membranes using mixtures of water and
acetamide.
From the above-cited studies, it can be concluded that
an optimal membrane thickness is required in order to
obtain a constant selectivity, and below which the selectivity
decreases with membrane thickness decreasing. Moreover,
the flux through the membrane decreases with its thickness
to a variable extent.
On the other hand, different classes of models for pervaporation can be found in the literature. Reviews on pervaporation models were published by Feng and Huang [4] and
Lipnizki and Trägårdh [14]. One of the models developed to
study the mass transport in membranes is the resistance-inseries approach, which has been used by several researchers
in pervaporation [15–18]. Basically, this approach considers
that the mass transfer from the liquid feed to the permeate
vapor involves four successive steps: (i) a mass transfer from
the feed bulk to the feed–membrane interface boundary layer,
(ii) a sorption into the membrane, (iii) a mass transport in the
membrane matrix and (iv) a desorption to the permeate. Each
step is modeled with different approaches, and various fundamental assumptions have been considered.
81
The main objective of the current study is to investigate the membrane thickness influence on the pervaporation
separation of methanol/methyl tertiary butyl ether mixtures.
Dense membranes with a wide range of thicknesses were prepared by using two different polymers: cellulose acetate and
poly(2,6-dimethyl-1,4-phenylene oxide). The pervaporation
behavior for the separation of methanol and methyl tertiary
butyl ether from their mixtures was studied in terms of the
permeation rate and the separation factor. The analysis of the
influence of the membrane thickness on the pervaporation
performance was carried out by means of a resistance-inseries model.
2. Experimental
2.1. Materials
Cellulose acetate (CA) polymer of a molecular weight of
37,000, with a 39.8% degree of acetylation, was purchased
from Aldrich Chemicals. Poly(2,6-dimethyl-1,4-phenylene
oxide) (PPO) powder of an intrinsic viscosity of 1.57 dL/g
and a density of 1.04 g/cm3 was supplied by General Electric.
Two solvents were used in this study to prepare the casting
solutions: acetone for CA and chloroform for PPO. To carry
out the pervaporation experiments, methanol and methyl tertiary butyl ether (MTBE) of analytical purity grade (97–99%)
were used without further purification.
2.2. Membrane preparation
Casting solutions were first prepared by dissolving
3.3 wt.% of CA polymer in DMF. The membrane samples
were prepared by pouring a predetermined amount of polymer solution over a mirror-polished glass plate with a circular
edge. The solution was then dried in three steps. First, the bulk
of the solvent was removed by slow evaporation inside a fume
hood at an average humidity of 30% and at a temperature
of 23 ◦ C until the membrane was formed. Subsequently, the
membrane was kept in an oven at 70 ◦ C during 8 h. Finally,
the formed membrane was left overnight in a vacuum oven
at 70 ◦ C to remove the traces of the solvent.
The PPO polymer solution was prepared by using 4 wt.%
in chloroform. Different volumes of PPO solution were
spread smoothly over a leveled glass plate inside a stainless steel-made O-ring of about 10 cm inner diameter. The
casting ring was then covered with a filter paper to keep out
of dust. After 24 h at a temperature of 25 ◦ C, the membranes
were removed very cautiously by immersing the glass plate
in a water bath. The membrane was then dried at 25 ◦ C for
24 h in a fume hood, and for 72 h in vacuum to remove the
last traces of solvent.
The thickness of each membrane was measured by a
Millitron micrometer (Mahr Feinpruf 1202 IC) over at least
20 different spots, and the mean value was used in this
study.
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
82
2.3. Pervaporation experiments
Pervaporation experiments were performed by using
the system described elsewhere [19,20]. It consists of a
separation cell, a circulation pump, two permeate traps,
two vacuum pumps and a pressure transducer. The effective
membrane pervaporation surface area was 28 cm2 . The feed
was circulated over the membrane sample. The feed pressure
was kept near 105 Pa. The permeate stream was evacuated by
one of the vacuum pumps, and the permeate was collected in
one of the traps immersed in a filled liquid nitrogen flask. In
all the experiments, the downstream pressure was maintained
less than 133 Pa. After the completion of each experiment,
the permeate collected inside the cold trap was warmed up to
room temperature, and then weighed. The feed and permeate
compositions were determined by measuring their refractive
index with an Abbey-type refractometer Model 60/ED. The
pervaporation selectivity of the membranes was studied in
terms of the separation factor, α, which is defined as:
α=
wp,i /wp,j
wb,i /wb,j
(1)
where wb and wp are the weight fractions of the components
i and j in the bulk feed and permeate, respectively. Indexes
i and j refer to the more permeable component and the less
permeable one, respectively.
In each experimental run, it was observed that the concentration in the feed solution after the completion of the
experiment was almost the same as that of the initial feed solution. Therefore, the feed concentrations could be considered
constant throughout the experiment. In each experimental
run, at least three samples were collected to determine the
total flux and the composition of the permeate. The alternative
use of two cold traps allowed a continuous sampling in order
to avoid interrupting the experiment. It must be mentioned
that both membranes exhibited initially high fluxes, which
then gradually reached steady-state values. This behavior is
due to the conditioning process, which is a time-dependent
adaptation of the membrane transport properties because of
the rapidly changed process conditions. This conditioning
time, which can last from minutes to several hours, could be
explained in terms of the polymer relaxation. All data given in
the present paper correspond to the final steady-state values.
In this study, the pervaporation experiments were conducted at a feed temperature of 25 ◦ C using; as feed, binary
mixtures of methanol/MTBE with a 21 wt.% of methanol, in
the case of the CA membranes and 47 wt.% methanol, in the
case of the PPO membranes, were employed.
some simplifying assumptions have been made: absence
of flow coupling effects, constancy of the diffusivity of the
components in the membrane, equilibrium at the membrane
interfaces and steady-state conditions. Based on the results
published in previous papers [19,20], the two first assumptions may seem not to be reasonable in the case of the
pervaporation of methanol and MTBE mixtures when PPO
and CA membranes are used; however, the consistency of
the results and the model predictions will be used in order to
justify the above assumptions.
The model considers that the transport across the system
is produced by a gradient of the chemical potential of the feed
mixture components. Thus, the flux, Ji , of component i can
be written as
Ji = −Li
dµi
dz
(2)
where dµi /dz is the gradient of chemical potential of component i and Li is a phenomenological coefficient.
The mass transport of component i from the bulk feed to
the feed membrane interface can be written as:
Ji = Lbl,i (µb,i − µbl,i )
(3)
where Lbl,i is the mass transfer coefficient in the boundary
layer formed at the membrane feed side, µb,i is the chemical
potential of component i at the bulk and µbl,i is the chemical
potential of component i at the feed–membrane interface.
The transport through the membrane matrix can be
expressed as:
Ji = Lm,i
(µmb,i − µmp,i )
l
(4)
where Lm,i is the mass transfer coefficient of component i in
the membrane, µmb,i and µmp,i are the chemical potentials of
i, in the membrane, at the feed–membrane interface and at
the permeate–membrane interface, respectively and l is the
membrane thickness.
The transport of component i can also be written as follows:
Ji = Lov,i
(µb,i − µp,i )
l
(5)
where Lov,i is the overall mass transfer coefficient of component i, and µb,i and µp,i are the chemical potentials at the bulk
and at the permeate, respectively. If equilibrium conditions
are assumed at both membrane interfaces, the following relationship between the transport coefficients can be obtained
from Eqs. (3) to (5):
3. Theory
1
1
1
=
+
Lov,i
lLbl,i
Lm,i
As previously mentioned, the resistance-in-series
approach considers that the mass transfer of a mixture,
from the feed bulk to the permeate, takes place in four
successive steps. In order to make the model more useful,
Following Raghunath and Hwang [15], it is of practical
interest to write Eq. (6) in terms of typical transport coefficients often employed in pervaporation. In Eq. (2), the
chemical potential difference may be related to the differences in pressure, temperature, concentration and electrical
(6)
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
potential. In the case of pervaporation, where the driving force
is generated by concentration and pressure gradients, the following equation is applied:
dµi = RT d ln(γi xi ) + vi dp
(7)
where xi is the mole fraction of i, γ i the activity coefficient,
vi the molar volume of component i and p is the pressure. In
the case of a liquid, the integration of Eq. (7) gives
µi = µoi + RT ln(γi xi ) + vi (p − psat
i )
(8)
where µoi is the chemical potential of pure i at a reference
pressure, which is defined as the saturation vapor pressure,
psat
i . The following equation may be obtained from Eqs. (2)
and (8),
Li RT dxi
dp
− Li v i
Ji = −
xi dz
dz
Lm,i
(11)
(12)
where
cm,i =
ρm (xmb,i − xmp,i )
ln(xmb,i /xmp,i )
fb,i − fp,i
(psat γi xb,i − p2 xp,i )
= Qi i
l
l
(16)
where Qi is the overall or apparent permeability of component
i, and fb,i and fp,i are the fugacities of component i at the bulk
and at the permeate, respectively.
From Eqs. (15) and (16), under the assumptions discussed
above, it can be obtained that
pi Qi
RT
(17)
where
where Di is the diffusion coefficient of component i in the
membrane and ρm is the membrane density. The comparison
of Eqs. (10) and (11) gives
cm,i Di
=
RT
Ji = Qi
(9)
where xmb,i and xmp,i are the mole fractions of i in the
membrane, at the feed–membrane interface and at the
membrane–permeate interface, respectively.
If the diffusion of compounds in the membrane is Fickian
with a diffusion coefficient independent of the concentration,
it can be written
(xmb,i − xmp,i )
l
In various pervaporation studies [15,21], it was shown that
second term of the right-hand side is negligible.
In pervaporation, the overall flux is expressed in terms of
the fugacity difference between the bulk feed and the permeate as follows [22]:
Lov,i =
If the solution–diffusion model [21] is considered, this
equation can be applied within the membrane limits, and the
following expression is obtained:
Lm,i RT
xmb,i
Ji =
(10)
ln
l
xmp,i
Ji = ρm Di
83
(13)
On the other hand, by using Eq. (8) the difference in the
chemical potential between the bulk feed and permeate may
be expressed as follows:
γi xb,i
+ vi (p1 − p2 )
µb,i − µp,i = RT ln
(14)
xp,i
where xb,i and xp,i are the mole fractions of i at the bulk and
at the permeate, respectively, and p1 and p2 are, respectively,
the pressure at the feed and permeate. Using Eq. (14), Eq. (5)
can be rewritten as follows:
vi
γi xb,i
Lov,i RT
Ji =
+
ln
(15)
(p1 − p2 )
l
xp,i
RT
pi =
(psat
b,i − pp xp,i )
i γi x
γx
ln xi p,ib,i
(18)
Finally, Eq. (6) can be rewritten as follows:
pi
pi
1
=
+
Qi
RTLbl,i l Di cm,i
(19)
This equation can be expressed in a more practical form
1
1
1
=
+
Qi
ki l D i S i
(20)
where
ki =
RTLbl,i
pi
(21)
Si =
cm,i
pi
(22)
where ki is the mass transfer coefficient in the boundary layer
with respect to the fugacity difference and Si is the solubility coefficient of component i in the membrane. Eq. (20)
shows that the apparent permeability varies with the membrane thickness when the boundary layer contributes to the
mass transport of compounds. In addition, by plotting the
inverse permeability as a function of the inverse membrane
thickness, a straight line should be obtained. From the slope
of the line ki can be calculated, and from the intercept Di Si
can be estimated. It is worth quoting that Di Si is the intrinsic permeability of component i in the membrane (Pm,i ). An
interesting additional finding can be obtained from Eq. (20)
by considering that the overall mass transfer resistance of
component i (Rov,i = l/Qi ) consists of the sum of the resistance
in the liquid boundary layer (Rbl,i = 1/ki ) and a membrane
resistance (Rm,i = l/Pm,i ). Thus, it can be noticed that the sodefined overall mass resistance coefficient depends on the
membrane thickness.
84
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
Fig. 1 shows the data on the overall flux, and the methanol
and MTBE fluxes through PPO membranes, as a function of
the membrane thickness. The composition of the feed solution was the same in all cases, i.e. a 47 wt.% methanol in a
methanol/MTBE mixture. Both the overall flux and the partial
fluxes of methanol and MTBE decreased with the membrane
thickness. For example, the overall flux obtained when using
the thinnest membrane (28 ␮m) is approximately twice that
of the thickest membrane (126 ␮m). It was also observed that
plots of fluxes versus the reciprocal of the membranes thickness gave straight lines with correlation coefficients higher
than 0.99. Fig. 2 presents the results of the overall, methanol
and MTBE fluxes, obtained using CA membranes of different thicknesses. The feed was a mixture of methanol and
MTBE with 21 wt.% of methanol. Both the overall flux and
the component fluxes decreased with membrane thickness.
The overall flux, as an example, is about twice that of the
thinnest membrane (20 ␮m) than for the thickest one (96 ␮m).
In addition, as observed for PPO membranes, it was also
checked that the fluxes were proportional to the inverse of
the membrane thickness with correlation coefficients higher
than 0.98.
It can be observed in Figs. 1 and 2 that the overall permeation flux through the PPO membranes is greater than that of
the CA membranes. Based on the solution–diffusion model,
the permeability of the membranes is determined by the solubility and diffusivity of permeants in the membranes. It was
shown in previous papers [19,20] that the liquid sorption of
PPO was larger than that of CA due to the higher affinity
of the PPO membranes towards the liquid mixture than that
of CA. This makes PPO membrane to swell more than CA
membrane. Because of the higher swelling, the diffusivity of
permeants in the PPO membrane was larger than in the CA
membrane. Consequently, the higher flux observed for the
PPO membrane is due to the greater solubility and diffusivity of the permeants. On the other hand, in the present study, it
is also observed that the MTBE flux of CA membranes is two
orders of magnitude lower than that of methanol. This indicates that the selectivity of CA membranes is higher than that
of PPO membranes, although both PPO and CA membranes
are methanol selective. In Fig. 3, the separation factors of both
membrane types are presented as a function of the membrane
thickness. There is no clear tendency between the separation
factor and the membrane thickness within experimental error.
It seems that the separation factor is about 2.1 for PPO membranes and around 192 for CA membranes. It was found [20]
that the higher separation factor of CA membranes was due
to the combination of both high sorption and diffusion selectivities. In contrast, the lower separation factor exhibited by
the PPO membranes was due to a low sorption selectivity as
it was reported elsewhere [19].
As stated earlier, the data given in Figs. 1–3 were analyzed by using the resistance-in-series approach developed
in the preceding section. First, the values of Qi were calculated from Eq. (16). Data on the mole fractions of methanol
Fig. 2. Overall and partial fluxes of methanol and MTBE as a function of
the membrane thickness for CA membranes.
Fig. 3. Separation factor in pervaporation of methanol/MTBE mixtures
through PPO and CA membranes.
Fig. 1. Overall and partial fluxes of methanol and MTBE as a function of
the membrane thickness for PPO membranes.
4. Results and discussion
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
85
Table 1
Constant values in Eq. (23) for methanol and MTBE
Methanol
MTBE
a1
a2
a3
a4
−8.54796
−7.82516
0.76982
2.95493
−3.1085
−6.94079
1.54481
12.17416
and MTBE, at the bulk and at the permeate, were obtained
experimentally, as well as the pressure at the permeate side.
The considered thicknesses of the membranes were those of
the dry membranes. The saturation vapor pressure values for
methanol and MTBE were calculated by using the following
equation [23]:
sat pi
a1 x + a2 x1.5 + a3 x3 + a4 x6
ln
=
(23)
pc
1−x
where pc is the critical pressure of component i, x is equal
to 1 − T/Tc , where Tc is the critical temperature. Values for
dimensionless constants a1 , a2 , a3 and a4 are given in Table 1.
Experimental data of the activity coefficients of methanol
and MTBE, as a function of temperature and concentration
in their mixtures, were reported by Coto et al. [24]. Based
on these data, the following expression can be written for
the dependence of the activity coefficients of methanol and
MTBE on their mole fractions at 25 ◦ C:
4
3
2
+ b2 xb,i
ln γi = b1 xb,i
+ b3 xb,i
+ b4 xb,i + b5
(24)
Values for dimensionless constants b1 , b2 , b3 , b4 and b5 are
given in Table 2.
Figs. 4 and 5 give the inverse of the calculated Qi values of methanol and MTBE as a function of the inverse
of membrane thickness, for the PPO and CA membranes,
respectively. It can be observed that such plots yield straight
Table 2
Constant values in Eq. (24) for methanol and MTBE
Methanol
MTBE
b1
b2
b3
b4
b5
0.8554
0.8326
−2.5627
−2.1289
3.8749
2.937
−3.4947
−2.8673
1.3236
1.2239
Fig. 4. Inverse of the overall permeability of methanol and MTBE as a
function of the reciprocal membrane thickness for PPO membranes.
Fig. 5. Inverse of the overall permeability of methanol and MTBE as a
function of the reciprocal membrane thickness for CA membranes.
lines with reasonably good correlation coefficients, about
0.99 for PPO membranes and about 0.98 for CA membranes.
Based on these results, both the intrinsic permeability in
the membranes, Pm,i , and the mass transfer coefficients in
the boundary layer, ki , were calculated for methanol and
MTBE. In the case of PPO, the permeability coefficients
of methanol and MTBE are, respectively, 3.5 × 10−13 and
1.4 × 10−13 (kg m/m2 s Pa). In the case of CA membrane,
the permeability of methanol and MTBE are, respectively,
2.1 × 10−13 and 1.2 × 10−15 (kg m/m2 s Pa). These results
agree well with those presented earlier by other authors for
pervaporation of methanol/MTBE mixture using PPO and
CA membranes [20,25]. For both membranes, methanol permeability is greater than MTBE one. This may be attributed
not only to the methanol preferential sorption but also to the
diffusion selectivity, because the diffusional cross section of
methanol is much lower than that of MTBE [19,20].
Moreover, an ideal separation factor can be calculated
as the ratio between the intrinsic membrane permeability of
methanol and MTBE in each membrane. The obtained values
are 2.5 and 175 for PPO and CA membranes, respectively.
By comparing these results with those reported in Fig. 3, it
can be seen that both sets of data are nearly the same. This
confirms the validity of the theoretical approach used in this
study.
Furthermore, the mass transfer coefficient, Ri , of
methanol and MTBE in the liquid boundary layer, of
the PPO membrane are, respectively, 7.8 × 10−9 and
3.6 × 10−9 (kg/m2 s Pa). The mass transfer coefficient in the
boundary layer of the CA membrane of methanol and MTBE
are, respectively, 6.2 × 10−9 and 5.2 × 10−11 (kg/m2 s Pa).
For methanol the difference between the mass transfer coefficients obtained in PPO and CA membranes is about 11%,
whereas for MTBE the difference goes up to 36%. This may
be attributed to the different membranes and feed solutions
used.
On the basis of the theoretical framework developed in
the preceding section, the mass resistance coefficients of
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
86
Table 3
Mass resistance coefficients of methanol and MTBE in PPO membranes as
a function of the membrane thickness
l (␮m)
28
38
73
81
118
126
Rm,methanol (108 m2 s Pa/kg)
Rm,MTBE (108 m2 s Pa/kg)
0.88
1.2
2.3
2.6
3.7
4.0
2.0
2.7
5.2
5.8
8.4
9.0
methanol and MTBE, in the boundary layer and in the membranes were estimated from Eq. (20). In the case of PPO,
the mass resistance coefficients of methanol and MTBE in
the liquid boundary layer are, respectively, 1.3 × 108 and
2.8 × 108 (m2 s Pa/kg). In the case of CA membrane, the values of methanol and MTBE are, respectively, 1.6 × 108 and
1.9 × 1010 (m2 s Pa/kg). The values obtained of the resistance
coefficients in the membranes are given in Tables 3 and 4.
It can be observed that the mass resistance coefficients of
methanol are the same order of magnitude in both membranes, whereas the values for MTBE are noticeably larger in
the CA membranes than in the PPO membranes. Moreover, it
is important to note that there is a limiting membrane thickness, below which the contribution of the boundary layer
resistance to the overall resistance is larger than the membrane resistance. As the membrane thickness is increased,
the contribution of the membrane resistance becomes greater
than the resistance in the boundary layer. So, in the case of
PPO membranes, the resistance in the boundary layer is larger
than in the membrane matrix, when membranes with a thickness of lower than 38 ␮m approximately are used. Above this
thickness, the resistance in the PPO membranes becomes
larger than in the liquid boundary layer. In the case of CA
membranes, this limiting thickness is about 23 ␮m for MTBE
and 33 ␮m for methanol.
The extent to which the boundary layer affects the overall transport resistance depends not only on the membrane
thickness, but also on the permeability of the membrane. For
example, Nijhuis et al. [26] studied the effect of the membrane
thickness on the performance of polydimethylsiloxane, ethylene propylene rubber and polyoctenamer membranes, used
for the removal of toluene and trichloroethylene from water.
It was found that boundary layer at the liquid/membrane
interface affected the transport of the water and the organic
compounds. In fact, for highly permeable membranes, such
Table 4
Mass resistance coefficients of methanol and MTBE in CA membranes as a
function of the membrane thickness
l (␮m)
Rm,methanol (108 m2 s Pa/kg)
Rm,MTBE (1010 m2 s Pa/kg)
20
23
33
46
72
96
0.95
1.1
1.6
2.2
3.4
4.6
1.7
1.9
2.8
3.8
6.0
8.0
as the polydimethylsiloxane ones, the mass transfer resistance at the liquid boundary layer contributes significantly
to the overall transport resistance, being the rate-determining
step depending on the existing hydrodynamic conditions. On
the contrary, for less permeable membranes, such as those
prepared with ethylene propylene rubber, the overall mass
transfer resistance is dominated by the membrane resistance,
which becomes significant with increasing the membrane
thickness. Raghunath and Hwang [15] conducted pervaporation experiments with polydimethylsiloxane and polyetherblock-polyamide membranes using dilute phenol and toluene
aqueous solutions. It was investigated the effect of the membrane thickness on the permeability of the organic compound,
which was the preferentially permeated component. It was
concluded that the organic transfer resistance in the boundary layer was significant, by limiting the overall mass transfer
through the membrane, when the membrane resistance to the
transport of organic was low. In the present study, it is found
that for highly selective membranes, such as those prepared
with CA, and for reasonably good permeable membranes,
such as PPO membranes, both the boundary layer resistance
and the membrane resistance contribute to the overall transport resistance.
As previously mentioned, the selectivity was found to be
almost independent of the membrane thickness when both
PPO and CA membranes were used (Fig. 3). Based on this
experimental observation and on others [15,26,27], it can
be stated that for pervaporation systems in which the overall mass transfer resistance is dominated by the membrane
resistance or the liquid boundary layer and the membrane
resistances are comparable, i.e. the present study, the selectivity remains nearly independent of the membrane thickness;
on the contrary, when the overall mass transfer resistance is
dominated by the boundary layer resistance, the selectivity
depends on the membrane thickness.
5. Conclusions
Cellulose acetate and poly(2,6-dimethyl-1,4-phenylene
oxide) membranes were used for the separation of methanol
from methyl tertiary butyl ether by pervaporation. Membranes of different thicknesses were prepared in order to
evaluate the influence of the variation of membrane thickness on the process performance.
It was found that the transmembrane flux decreased
markedly with the membrane thickness for all the membranes used. Moreover, the overall flux was proportional to
the reciprocal of the membrane thickness. On the other hand,
both membrane types are methanol selective, and it was not
observed, within the experimental accuracy, any effect of the
variation of membrane thickness on the pervaporation separation factor.
The pervaporation results, which were analyzed by applying a resistance-in-series model, indicate that, besides a resistance to the transport of methanol and methyl tertiary butyl
J.P.G. Villaluenga et al. / Separation and Purification Technology 47 (2005) 80–87
ether in the membranes, there is an additional resistance at the
liquid feed/membrane interface. It was found that when thinner membranes were used, the boundary layer resistance was
larger than the membrane resistance. As the membrane thickness is increased, the membrane resistance becomes greater
than the resistance in the liquid boundary layer. The turning point has been localized for cellulose acetate membrane
between 23 and 33 ␮m of membrane thickness, while for
poly(2,6-dimethyl-1,4-phenylene oxide) membrane is near
38 ␮m.
Acknowledgements
The authors acknowledge the financial support from
the Spanish Ministry of Science and Technology (MCYT)
through its project PPQ2003-03299. Thanks are due to Prof.
T. Matsuura from the Industrial Membrane Research Institute
(IMRI) for supplying PPO polymer.
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