Chemical Engineering Journal 347 (2018) 741–753
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Chemical Engineering Journal
journal homepage: www.elsevier.com/locate/cej
Methanol to dimethyl ether conversion over a ZSM-5 catalyst: Intrinsic
kinetic study on an external recycle reactor
Carlos Ortegaa, M. Rezaeia,b, V. Hessela, G. Kolba,c,
T
⁎
a
Micro Flow Chemistry & Process Technology, Chemical Engineering and Chemistry Department, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven,
The Netherlands
b
EPFL Valais Wallis EPFL SB ISIC LAS Rue de l'Industrie 17, Case postale 440, CH-1951 Sion, Switzerland
c
Fraunhofer ICT-IMM, Carl-Zeiss-Str. 18-20, D-55129 Mainz, Germany
H I GH L IG H T S
standard entropies of adsorption are used in the kinetic model description.
• Experimental
effect of water is first time described for methanol dehydration over ZSM-5.
• Inhibiting
adsorption of MeOH and a surface reaction as RDS.
• Dissociative
• Model is capable of modeling dehydration of pure methanol and crude methanol.
A R T I C LE I N FO
A B S T R A C T
Keywords:
Methanol
Dimethyl ether
DME
Intrinsic kinetic
Dissociative adsorption
In this work, several kinetic models have been studied for the methanol dehydration to dimethyl ether (DME),
applying a commercial ZSM-5 catalyst rather than state-of-the-art alumina.
The kinetic tests were carried out in a fixed-bed external-recycle reactor, in the absence of temperature and
concentration gradients.
Kinetic parameters of the different models were calculated and evaluated against physicochemical constraints
and guidelines on entropy values. After discrimination, it was concluded that a modification of a model previously developed by Klusáček & Schneider for methanol dehydration over different catalyst formulations than
alumina or zeolites describes best the methanol dehydration reaction, with excellent agreement between experimental data and calculated values. The selection of this model supports a mechanism in which methanol
experiences dissociative adsorption and a surface reaction is the rate determining step (RDS) of the catalytic
cycle.
The kinetic measurements were performed at a total pressure of 1 bar, partial pressure of methanol (pm) from
0.3 bar to 1 bar, temperatures from 140 °C to 190 °C, weight hourly space velocities (WHSV) from 15 h−1 to
100 h−1, and two different amounts of water content (0 and 30 wt%). Experiments at different methanol concentrations in the feed revealed a weak dependence of the rate on pm. It could be determined to our knowledge
for the first time that the reaction order with respect to water is negative, in the range of −0.80 to 0, thus
providing quantitative proof of the inhibition effect of water on the methanol dehydration reaction rate over
ZSM-5 catalysts, while DME showed no effect.
1. Introduction
Dimethyl ether (DME) is an environmentally-friendly, multimarket
chemical that can be easily liquefied and used as an intermediate or end
product. Its applications range from aerosol propellant to intermediate
in olefins or liquid fuel synthesis [1,2]. Additionally, it has a notable
potential as clean fuel in power generation or in automotive applications [1], with commercial examples already available [2]. In 2011,
DME demand was c.a. 3 million metric tons (T) [2] and by 2014 was
almost 4 million T [3], which demonstrate the importance of this
emerging fuel.
The dehydration of methanol (MeOH) is largely used for the
⁎
Corresponding author at: Micro Flow Chemistry & Process Technology, Chemical Engineering and Chemistry Department, Eindhoven University of Technology, P. O. Box 513, 5600
MB Eindhoven, The Netherlands.
E-mail address: g.a.kolb@tue.nl (G. Kolb).
https://doi.org/10.1016/j.cej.2018.04.160
Received 25 August 2017; Received in revised form 16 March 2018; Accepted 23 April 2018
Available online 24 April 2018
1385-8947/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Chemical Engineering Journal 347 (2018) 741–753
C. Ortega et al.
Notation
AIC
Ci,b
Cs
De
DaII
Eapp
ED,i
Etrue
FMeOH,0
FMeOH
hp
0
ΔHad
,i
ΔHr
k
kc
kT0
K eq
Ki
ni
N
NWP
OF
pi
r+
robs,V
Akaike’s information criterion (dimensionless)
concentration of species i in the bulk phase (mol·m−3)
concentration of species i on the surface of the catalyst
(mol·m−3)
gas diffusivity (m2·s−1)
second Damköhler number (dimensionless)
apparent activation energy (J·mol−1)
activation energy for diffusion of species i (J·mol−1)
true activation energy (J·mol−1)
inlet molar flow rate of methanol (mol·s−1)
outlet molar flow rate of methanol (mol·s−1)
gas phase to particle heat transfer coefficient (W·m-2·K-1)
standard enthalpy of adsorption of species i (J·mol−1)
reaction enthalpy (J·mol−1)
kinetic factor (mol·kgcat−1·s−1)
mass transfer coefficient (m·s−1)
kinetic factor at the reference temperature T0
(mol·kgcat−1·s−1)
equilibrium constant of the reaction (dimensionless)
adsorption constant of species i (bar−1)
order of reaction with respect to species i (dimensionless)
number of experimental measurements (dimensionless)
Weisz-Prater number (dimensionless)
objective function
robs
rp
R
R
Sg0,i
0
ΔSad
,i
T
T0
WHSV
xMeOH
yi,0
Greek symbols
κ
λ eff
ρb
χ
ω
number of parameters (dimensionless)
effective thermal conductivity of the particle (W·m−1·K−1)
bed density (kg·m−3)
Mears’ parameter to determine external heat transfer
limitations (dimensionless)
Mears’ parameter to determine external mass transfer
limitations (dimensionless)
determining a rate equation for the methanol dehydration to DME over
a commercial ZSM-5 catalyst, that is valid in a wide range of operating
conditions, including feeds with high water content (up to 30 wt%). The
importance of this assessment lays in the consequence it brings to reactor design [16]. First, ZSM-5 is a more acidic catalyst than γ-Al2O3,
and in consequence has higher activity; thus, it could be possible to
perform the dehydration reaction at lower temperature than in a conventional industrial unit and using a smaller reactor or at least one of
similar size. Second, we evaluate the use water at a level of 30 wt%
which is in the range of crude methanol (methanol obtained from a
production facility without purification). It means that it would be
possible to design a reactor to operate with not only pure methanol as
feed but with crude methanol as well. We show the zeolite can perform
well under these conditions and our kinetic model represents well the
data. The use of crude methanol as feed avoids the need of methanol
purification in the production process, thus simplifying process equipment and process layout. These topics are discussed in more details
below.
production of DME. The process is known as the indirect route of DME
synthesis [4], and several companies such as Uhde, Lurgi and Toyo
provide technologies to carry it out [1]. Since the reaction is limited by
equilibrium, the unreacted methanol must be recirculated to the inlet of
the conversion reactor, thus a high conversion per pass is desired. The
overall reaction and the standard enthalpy of reaction, at 298.15 K, are
shown in equation (1).
2CH3 OH ↔ CH3 OCH3 + H2 O;ΔHr0 = −24.03 kJ ·mol−1
partial pressure of species i in the reaction mixture (bar)
−1
forward rate of reaction (molMeOH·m−3
)
cat ·s
observed reaction rate per volume of catalyst
−1
(molMeOH·m−3
)
cat ·s
observed reaction rate per mass of catalyst
−1
(molMeOH·kg−1
)
cat ·s
catalyst particle radius (m)
ideal gas constant (8.314 J·mol−1·K−1)
recycle ratio
standard ideal gas entropy of species i (J·mol−1·K−1)
standard entropy of adsorption of species i (J·mol−1·K−1)
temperature (K)
reference temperature (K)
weight hourly space velocity (kgMeOH·h−1·kgcat−1 or h−1)
methanol conversion
molar fraction of species i in the feed
(1)
Known processes use aluminum oxide catalysts, at relative high
temperatures, to promote the reaction [5]. However, high temperatures
are unfavorable since the reaction is exothermic and the conversion is
limited by the thermodynamic equilibrium. It is also known that the
reaction can be performed at a lower temperature by using ZSM-5 as
catalyst, as Tavan et al. [6] have shown by direct comparison of reaction performance on commercial γ-Al2O3 and HZSM-5 catalysts. The
ability of ZSM-5 to perform the reaction at lower temperatures originates from the increased acid strength of ZSM-5 over Al2O3. For an acid
catalyzed reaction, increased acidity of the catalyst would render
higher activity [7]. This has been particularly described by Alharbi
et al. [8] for the methanol dehydration to DME.
Compared to aluminum oxide catalysts, the use of lower temperature with ZSM-5 favors the thermodynamic equilibrium of the system
and higher conversions per pass could be achieved. The conversion of
methanol to DME on aluminum oxide catalysts has been well investigated and several kinetic studies are reported in literature
[6,9–12]. Less work has been done with ZSM-5 catalysts, although it
has recently gained more attention and few publications are available
[6,8,13].
The reaction mechanism of the methanol dehydration reaction on
ZSM-5 is still under debate [8]. Some authors support a mechanism in
which associative adsorption of methanol takes places (associative
pathway) [6,13,14], while others support a mechanism with dissociative adsorption of methanol (dissociative pathway) [15]. This
debate also leads to disputes on the suitability of kinetic expressions.
Therefore, in this work, the validity of kinetic models proposed in literature and of novel models is assessed, with the purpose of
2. Experimental details
2.1. Materials
A commercial ZSM-5 zeolite was used during the kinetic test measurements. The zeolite was obtained as powder, in the ammonium form,
and with a SiO2/Al2O3 ratio of 58 (see certificate of analysis [17]).
Physicochemical properties were measured via argon (Ar) physisorption, mercury intrusion porosimetry, X-ray diffraction (XRD), NH3-TPD
and scanning electron microscopy (equipment details are provided in
the Supplementary information). Before its use, it was: (i) pelletized in
a manual hydraulic press, for 2 min and 10 T of pressure; (ii) crushed in
an agate mortar; and (iii) sieved to the desired particle diameter size,
ranging from 160 µm to 250 µm.
Silicon carbide (SiC) was used as inert material to physically dilute
the catalyst bed. This dilution facilitates isothermal operation mainly
by reducing the heat release per unit volume in the bed and enhancing
heat conduction in the bed [18,19]. In a typical experiment, the
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Chemical Engineering Journal 347 (2018) 741–753
C. Ortega et al.
concentric to the reactor into the packed bed. Three thermocouples
inside the thermowell monitored the temperature of the gas stream in
the inlet, center, and outlet of the catalytic bed. At all times during
measurements, the temperature difference between any two thermocouples was less than 1 °C. A major part of the reactor outlet stream was
externally recycled to the inlet of the reactor by a diaphragm gas pump,
from KNF Verder, model N 012 ST.26E. The pump had a variable speed
motor that indirectly controlled the recycle flow rate. The recycle flow
could be varied from 1 L·min−1 to 10 L·min−1. Kinetic measurements
were done with a recycle flow of 5 L·min−1. Also, this pump could work
at 180 °C, which was necessary to avoid condensation in the recycle
stream. All lines and valves conducting the flow of gas were also heated
to 180 °C by means of heating cords, thus avoiding undesired condensation. This is denoted in Fig. 1 with red dotted lines (-·-·-·).
The product stream of the Reaction section is sent to the Analysis
section via a heated line to keep all compounds in the gas phase (see
Fig. 1). In the analysis section (iii), a heated valve system captured part
of the product stream and injected this sample into the gas chromatograph (GC) by means of an on-line injection valve. The GC (model
7890B – Agilent Technologies) and the heated valve system were supplied by Technical Knowledge Solutions GmbH (Teckso). This GC is
equipped with a flame ionization detector (FID) and a thermal conductivity detector (TCD), a capillary 50-m PONA column and a 30-m
Plot-Q column. Methanol and DME were analyzed in the FID, while N2
was measured in the TCD. The latter was of interest when the partial
pressure of MeOH in the feed was varied by mixing streams of methanol
and N2. In a typical experiment, process parameters (temperature,
space velocity, and partial pressures of methanol in the feed) were set at
the desired values; then, the product stream was analyzed in at least
seven (7) consecutive GC injections. Each GC analysis took approximately 5 min plus 1 min for stabilization of the GC before the following
analysis; therefore, the total analysis time for a particular experimental
setting was of approximately 40 min, and the reported value is an
average of all the measurements carried out at the desired condition.
catalytic bed was prepared by mixing 25–50 mg of catalyst with
250–500 mg of SiC. The amount of SiC varied to maintaining a weight
ratio catalyst/SiC of 1/10. The SiC was obtained from Alfa Aesar (Lot
no. 10187470) with an average particle size of 355 µm. This material
was sieved, and different particle size fractions were obtained. The
fraction with particle size of 160–250 µm was used for the dilution
purpose. The particle size fraction larger than 250 µm was used to pack
inert SiC beds on top and bottom of the catalytic bed. The top packing
has the function of a preheating zone (gas flow downwards), increases
the surface area available for heat transfer and ensures that the gas flow
reaches the desired temperature before entering the catalytic bed. The
bottom packing allows the gas flow to exit the catalytic bed with a
uniform flow pattern, without a sharp change from a packed section to
an empty-tube section. This material is chemically inert [20,21] and has
been used as foam support in methanol dehydration [20]. A chemical
analysis of the commercial SiC is reported elsewhere [22].
Reagents and auxiliary gases used during experimental tests were:
(i) methanol HPLC grade from Merck (LiChrosolv®), with a purity
greater than 99.8% and less than 0.03% water content; (ii) dimethyl
ether (DME 3.0) supply by LINDE with a purity greater than 99.9%; (iii)
dried compressed air; and (iv) pressurized nitrogen (from a liquid N2/
evaporator system).
2.2. Equipment
A semi-automated reaction system was used to perform the kinetic
measurements. A simplified scheme of the test rig is shown in Fig. 1.
The set-up consisted a feeding section, a reaction section and analysis
section.
In the feeding section (i), Bronkhorst mass flow controllers regulated the flow of liquid methanol, gaseous dimethyl ether, nitrogen and
auxiliary gases during catalyst pre-treatment and kinetic tests. For the
liquid feed, a mass flow controller using a Coriolis measurement principle was used (Model Series: CORI-FLOW, part number: M12V14IPAD-21-K-S). Liquid methanol is fed to an evaporator and the vapor
phase product is sent pure to the reactor or mixed with other gases such
as nitrogen and/or DME. To control the gas feed, mass flow controllers
using a thermal conductivity principle were used (Model Series: ELFLOW Select, part number: F-201CV-100-TAD-21-K).
In the reaction section (ii), a quartz tubular reactor and a recycle
pump were the main constituents. The reactor had an internal diameter
(ID) and an outside diameter (OD) of 7.8 and 13.1 mm, respectively. It
was heated by means of a split-tubular furnace with a maximum operating temperature of 900 °C and power output of 1100 W (series
3210, from Applied Test Systems). A thermowell, 1 mm OD, was placed
2.3. Determination of reactor performance and catalyst stability
Initial tests were carried out to evaluate: (i) the fluid dynamic behavior of the recycle reactor; (ii) the stability of the catalyst’s activity
under reaction conditions; (iii) the stability of the catalyst’s activity
during reaction/regeneration cycles; and (iv) the effect of recycle flow
on catalyst performance.
The fluid dynamic behavior of the recycle system was evaluated via
pulse tracer experiments [23]. From these experiments, the residence
time distribution (RTD) was determined and its profile was compared to
Fig. 1. Simplified scheme of reaction apparatus. Red line indicates heated lines.
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C. Ortega et al.
Different combustion stages are associated with different types of coke
having various H/C ratios. These observations are also in accordance
with Bibby et. al [34]. In addition, it has been observed that a small
amount of coke might remain after an oxidizing treatment at 550 °C but
this coke has little to no effect on the catalyst performance [32,35],
therefore the value of 550 °C has been set as the limit temperature for
regeneration.
After calcination, the catalyst was cooled down to reaction temperature under N2 flow (30 ml·min−1). Then, pure MeOH or a mixture
of 70 wt% MeOH/30 wt% H2O was fed via a Bronkhorst Cori-Flow
meter. The liquid feed was fed to a micro heat exchanger where it was
evaporated. Then, the gas phase MeOH feed could be further mixed
with N2, to lower the partial pressure of the reactant and evaluate its
effect during the kinetic testing. Pure MeOH, MeOH/H2O or MeOH/N2
mixtures were then fed to the recycle reactor.
Tests were carried out between 140 °C and 190 °C, at a total pressure
of 1 bar. The weight hourly space velocity (WHSV) was varied in the
range of 15 h−1 to 100 h−1. To achieve these conditions, both the feed
flow of MeOH and the weight of catalyst were modified. In all cases, the
catalyst had a particle diameter of 160 µm to 250 µm, and the superficial gas velocity at reactor inlet was 2.7 m·s−1. The outlet of the recycle reactor was sent to an on-line GC for analysis.
a perfect continuous stirred tank reactor (CSTR) fed with a pulse of
tracer, which did not create a perfect pulse, as the Dirac delta function
[24]. The continuous phase used was N2, and helium (He) was used as
tracer. The volume of tracer injected was 62.7 µL. The concentration of
the tracer in the outlet stream of the recycle reactor was followed by
means of quadrupole mass spectrometer (QMS).
In the stability test under reaction conditions, the activity of the
catalyst was measured for a period of 20 h, to detect signs of catalyst
deactivation. Conversion of methanol ( xMeOH ) was calculated according
to equation (2), where FMeOH,0 and FMeOH represent the inlet and outlet
molar flow rates of methanol. The test was done at 190 °C, feeding pure
methanol at a weight hourly space velocity (WHSV) of 20 h−1, and the
reactor configuration was single pass. This condition was selected to
operate the system at a conversion level of around 30%, far from
equilibrium, to avoid biased results that might be obtained at high
conversions.
xMeOH =
FMeOH ,0−FMeOH
.
FMeOH ,0
(2)
Prior to the kinetic measurements, a catalyst sample was pretreated
under oxidizing conditions, as described in Section 2.5. Also, in particular experiments the same catalyst loading was used. However, inbetween experiments the oxidizing pretreatment, named hereafter regeneration, was carried out. Oxidizing treatments at high temperature
can cause permanent deactivation on zeolite catalysts, thus a series of
tests working on reaction/regenerati cycles was carried out. After each
cycle, the activity of the catalyst was measured and compared to the
activity of the fresh catalyst.
Finally, a test to assess the effect of the recycle flow on catalyst
performance was carried out. In this test, the activity of the catalyst was
measured at feed flow rate of 2.5 g·h−1 of pure methanol, 140 °C and a
recycle flow rate from 1 L·min−1 to 5 L·min−1. In a similar way to the
stability test, the conversion achieved by the catalyst was determined.
Comparison of the activities measured in this range provides information on external mass transfer limitations. Mass transfer limitations
were also assessed by testing criteria shown in the next section.
2.6. Kinetic analysis
2.6.1. Model fitting and discrimination
Estimation of kinetic parameters was performed in MATLAB®, by
means of the command “nlinfit”. This function uses the LevenbergMarquardt algorithm [36] during the minimization process of the objective function (OF), which is given in (7).
Nexp
OF =
∑
(riexp−rical )2
(7)
i=1
riexp
rical
2.4. Testing criteria: exclusion of heat and transport limitations
and
are the experimental and calculated reaction rates of
where
methanol dehydration to DME, respectively. The experimental reaction
rate can be estimated from equation (8) [23], where Wcat represents the
weight of catalyst in kg, R is the recycle ratio, and the other variables
as defined above.
Mass and heat transfer limitations were evaluated according to the
criteria shown in Table 1 [25–28].
Wcat
= (R + 1)
FMeoH ,0
2.5. Activity test
If R is high enough the recycle reactor behaves as a well-mixed
continuous stirred tank reactor (CSTR) [23]. In our case, this approach
is also supported by the results of the fluid dynamics analysis, which are
explained in Section 3.2. We have used equation (9), solved for rMeOH , to
determine the experimental values of the reaction rate used in the
model fitting and discrimination steps.
Before and after any activity test, an oxidizing pretreatment (regeneration) was carried out. The catalyst was calcined under a flow of
synthetic air (30 ml·min−1). The calcination took place with a temperature program at three levels: 300 °C, 400 °C and 550 °C. From one
level to the other, the temperature was increased at a rate of
5 °C·min−1. Once each level was reached, it was kept constant for 2 h.
The oxidizing pretreatment had two purposes: (i) if a fresh catalyst
was used, then the ammonium form of the catalyst (NH4-ZSM-5) was
transformed into its proton from (H-ZSM-5); and (ii) for a catalyst
loading used in several experiments, the oxidizing temperature treatment removed adsorbed water and any coke deposits that could have
formed under reaction conditions. The step-wise temperature increase
was selected to control the amount of water (steam) formed during the
regeneration process and avoid permanent deactivation of the zeolite
during the treatment [31,32]. These particular temperatures (300 °C,
400° and 550 °C) were selected in accordance to observations made by
Sorensen [33]. This author performed a series of temperature programmed oxidation (TPO) analysis on coked ZSM-5 samples used in the
methanol-to-gasoline reaction. He observed that combustion of the
carbonaceous deposits starts at approximately 300 °C, showing a first
peak around just below 400 °C and a maximum in the vicinity of 550 °C.
xMeOH
∫
R ·x
R + 1 MeOH
dxMeOH
−rMeOH
(8)
Wcat
x
= MeOH
FMeoH ,0
−rMeOH
(9)
Kinetic expressions were written as function of a kinetic factor (ki )
Table 1
Testing criteria to neglect heat and mass transfer limitations.
Criteria
Limitation
Weisz-Pratter
[29]
Mears [26]
Internal (intraparticle)
mass transfer
External (interphase)
mass transfer
Internal (intraparticle)
heat transfer
ω=
External (interphase)
Heat transfer
χ=
Anderson [30]
Mears [26]
744
Equation
DaII = NWP =
(
robs·ρb·rp·n
k c·CA,b
Eq. N°
r p2·robs,V
De·Cs
⩽ 0.3
(4)
⩽ 0.15
Eapp ΔHr ·robs·r p2
)
λ eff ·T
R·T
(3)
(5)
< 0.75
ΔHr ·robs·ρb·rp·Ea
hp·T2·R
< 0.15
(6)
Chemical Engineering Journal 347 (2018) 741–753
C. Ortega et al.
3. Results
and adsorption constants of species i (Ki ). The kinetic factors were expressed as a reparametrized Arrhenius function according to [37–39],
with apparent activation energy (Eapp ), as depicted in equation (10).
Adsorption constants were expressed as function of the standard en0
tropy of adsorption (ΔSad
,i ) and standard enthalpy of adsorption
0
(ΔHad,i ), according to equation (11) [40].
Eapp ⎛ 1 1 ⎞ ⎤
−
k = kT0 Δexp ⎡−
⎢ R ⎝ T T0 ⎠ ⎥
⎦
⎣
⎜
0
3.1. Catalyst characterization
The mordenite framework inverted (MFI) structure of the catalyst
used in this investigation was confirmed by XRD analysis. Textural
properties were characterized by argon (Ar) physisorption, see Fig. 2.
The results show a total surface area is 452 m2·g−1, and the total pore
volume of 0.251 cm3·g−1. Temperature program desorption of ammonia (NH3-TPD) was used to characterize the acidity of the zeolite
[49]. Two different acid sites were identified and associated to Brønsted
acid sites of medium and high strength, similarly to what other authors
have shown [50–53]. Measured and theoretical acidity correlated well,
with a ratio measured acidity/theoretical acidity of 0.9, in good
agreement with ratios reported by other authors [50]. The theoretical
acidity was calculated following the procedure explained by [50] and
using the chemical formula of the zeolite, (SiO2)58 (Al2 O3) H+. The calculation resulted in a value of 27.9·10−5 molNH3/ g HZSM 5, while the
measured acidity value was 25.1·10−5 molNH3/ g HZSM 5. Finally, scanning electron microscopy (SEM) images were used to observe the
morphology of the catalyst and determine crystal size. An average
crystal size of c.a. 300 nm was determined via this method. Details on
equipment used, characterization procedures, and further discussion of
results are given in the Supplementary information.
⎟
(10)
0
ΔSad,i ⎤
⎡ ΔHad,i ⎤
Ki = exp ⎡
⎢ R ⎥·exp ⎢− RT ⎥
⎣
⎦
⎦
⎣
(11)
A reparameterization is required to minimize the correlation between the pre-exponential factor and the argument of the exponential
function, thus simplifying the convergence during the minimization
process [38,39]. Also, physicochemical constraints, shown in Table 2,
were considered during the evaluation of the kinetic models tested
[40–44].
In addition, the kinetic models were evaluated considering: (a)
parity plots of experimental rate versus calculated rate of reaction; (b)
predicted value plots, to analyze residual [37]; and (c) Akaike’s information criterion [45] to make a relative rank of the models that
performed well.
The predicted value plots, to analyze residuals, was supplemented
with the one-sample t-Test [46]. This test is used to test a hypothesis on
a sample’s mean, when the sample comes from a normally-distributed
population with unknown variance. In the case of residuals, the mean of
the population is assumed to be zero (0), and the variance is unknown,
thus the test can be applied. The evaluation was done by using the
MATLAB® command “ttest”, which will return a value of zero (0) if the
mean of the residuals is zero (0) and the sample is normally distributed.
The calculation is done at a significance level of 5%.
In reference to the Akaike’s information criterion [45], it allows to
rank models according to their performance, relative to each other. The
AIC, equation (12), depends on the number of experimental measurements (N ), the residual sum of squares of the regression analysis (OF ),
as defined above, and the number of parameters (κ ).
OF ⎞
AIC = N ·ln ⎛
+ 2κ
⎝ N ⎠
3.2. Determination of reactor performance and catalyst stability
The fluid dynamic behavior of the recycle reactor (RR) was characterized by measuring the residence time distribution (RTD), via the
tracer-pulse technique [23,24]. The behavior could be similar to plug
flow (with some degree of dispersion) or well-mixed continuous stirred
tank reactor (CSTR), depending on the recycle ratio used [23]. The
result is shown in Fig. 3. Experimental data is represented by black
circles with 95% confidence interval (CI) bars. The blue line denotes the
model of a CSTR, as explained in Section 2.3. The excellent agreement
between the experimental data and the model confirms that the recycle
reactor behaves as a well-mixed CSTR reactor. Thus, the design equation of a CSTR (see Eq. (9)) can be used in the interpretation of conversion and rate data obtained from this system. Further details on the
RTD experiment and results are included in the Supplementary information.
The stability of the catalyst under reaction conditions, during a 20 h
test run, showed that activity of the catalyst remains constant, in accordance to results reported by Alharbi et al. [8]. Some variability in
the conversion was observed, but this was caused by fluctuations in the
MeOH feed system. This result assures the steadiness of catalyst activity
during the kinetic test measurements, which lasted at most 8 h. A plot of
methanol conversion vs time on stream (TOS) is included in the
Supplementary information.
In some experiments, an identical load of catalyst was used in a
series of reaction/regeneration cycles. The regeneration consisted of a
temperature treatment as described in Section 2.5. To determine if a
significant degree of irreversible deactivation was taking place due to
reaction/regeneration cycles, the activity of a load of ZSM-5 was
monitor over 4 cycles. The results indicate that there is not a significant
difference between activity of the catalyst in the 1st and 4th cycle.
(12)
2.6.2. True activation energy and reaction order
Once a kinetic model was selected, the true activation energy (Etrue )
and the order of the reaction with respect to methanol (nm ) and water
(nn ) were estimated. The relation between Eapp and Etrue is given by the
partial derivative of the forward reaction rate (r +) with respect to the
temperature. The general definition is given by equation (13) [47,48].
Eapp = RT 2
∂
ln(r +)
∂T
(13)
Finally, the order of the reaction with respect to methanol (nm ) and
water (n w ) is considered. In a power law kinetic, the reaction order is
given by the power of the concentrations or partial pressures present in
the kinetic expression. However, for a LHHW kinetics the order of the
reaction is somewhat more complex and the order of the reaction is
given by the partial derivative of the forward reaction rate with respect
to the partial pressure of the species in consideration [47], as shown in
equation (14).
ni = pi
∂
ln(r +)
∂pi
Table 2
Physicochemical constraints.
(14)
745
Descriptor
Constraint
Kinetic rate pre-exponential factor [kT0 ] (mol·kgcat−1·s−1)
Apparent activation energy [Eapp ] (J·mol−1)
kT0 > 0
Eapp > 0
0 ] (J·mol−1)
Enthalpy of adsorption for species i [ΔHad
,i
0 > 0
−ΔHad
,i
0 ] (J·mol−1·K−1)
Entropy of adsorption for species i [ΔSad
,i
0 < S0
0 < −ΔSad
g ,i
,i
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C. Ortega et al.
Table 3
Results on testing criteria to neglect heat and mass transfer limitations.
Criteria
Weisz-Pratter [29]
Equation
DaII = NWP =
robs·ρb·rp·n
k c·CA,b
Mears [26]
ω=
Anderson [30]
( )
Mears [26]
Result from this investigation
Eapp
R·T
χ=
r p2·robs,V
De·Cs
⩽ 0.3
5.6·10−5
⩽ 0.15
ΔHr ·robs·r p2
λ eff ·T
ΔHr ·robs·ρb·rp·Ea
hp·T2·R
1.6·10−2
< 0.75
< 0.15
6.7·10−3
1.0·10−3
3.3. Testing criteria: exclusion of heat and transport limitations
Results of testing criteria on mass and heat transfer limitations are
shown in Table 3. It can be observed that all testing criteria have been
met. Thus, it is concluded that the reaction is neither mass nor heat
transfer limited, and that all measurements were performed in the kinetic regime. The procedure followed in the calculations of these criteria and the estimation of different properties are discussed in detailed
in the Supplementary information.
Fig. 2. Ar adsorption/desorption isotherm of catalyst sample.
3.4. Activity tests
3.4.1. Effect of reactants and products
It has been shown that methanol dehydration to DME is insensitive
to the total pressure of the system [12]. However, the methanol molar
fraction in the feed might have an influence on the kinetics. To this end,
a series of tests were carried out at WHSV of 100 h−1, temperature
between 140 °C and 190 °C, and partial pressure values of methanol of
0.33, 0.67 and 1.0 bar. Results are shown in Fig. 4. The conversion was
kept low, to minimize the effect caused by the products.
The results show that at temperature of 165 °C and lower, where the
conversion was less than 2%, the reaction rate of methanol consumption is insensitive to the partial pressure of methanol, indicating zero
order reaction on methanol partial pressure, similar to the behavior
observed by Alharbi et al. [8] over an heteropoly acid catalyst. Since
the conversion is low, effects of the reverse reaction can be neglected
[57]. Under these conditions, the desorption of a product is the ratecontrolling step, and the surface of the catalyst might be considered
completely saturated with methanol. On the other hand, at
Fig. 3. RTD function [E] of the recycle reactor. Comparison between experimental data (circles with error bars) and model (continuous blue line). (For
interpretation of the references to colour in this figure legend, the reader is
referred to the web version of this article.)
Details on average conversion and 95% confidence interval (CI) for the
1st and 4th cycles are included in the Supplementary information material.
Finally, the effect of recycle flow rate on catalyst performance was
evaluated. After statistical analysis of the results, no significant difference in methanol conversion was observed with change in recycle gas
flow rate. In these experiments, the WHSV is constant but the superficial gas fluid velocity changes, which does have an effect on the mass
transfer coefficient (kc ) [54,55]. Since the conversion remained constant, it can be concluded that external mass transfer limitations are
absent, in accordance to [55,56]. Details on experimental conditions
and results are described in the Supporting information.
Fig. 4. Effect of methanol partial pressure on reaction rate; WHSV = 100 h−1.
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temperatures of 177 °C and 190 °C, the reaction rate slightly increases
as the methanol partial pressure rises. In this case, the rate determining
step (RDS) could be: (i) adsorption of the reactant; (ii) surface reaction
with, or without dissociation of methanol; and (iii) desorption of a
product [57].
The effect of water has been widely reported. Water adsorbs on
active sites and inhibits the reaction [9,58], thus lower reaction rates
are observed. The addition of water to the feed (as explained in Section
2.5) has an effect on the equilibrium of the reaction and reduces the
maximum conversion that can be attained. This effect has been analyzed by determining how the equilibrium conversion changes with
temperature and water content in the feed. Equilibrium data were obtained from a sensitivity analysis performed in Aspen Plus V7.2 at 1 bar
and temperature in the range of 100 °C to 400 °C. An RGibbs reactor
was used in the modeling process and the Peng-Robinson equation of
state was used as thermodynamic method, in accordance to studies
made by other authors [59,60]. The results are shown in Fig. 5.
Plot (A) shows how the equilibrium conversion of methanol changes
with water molar fraction in the feed. The increase in feed water content reduces the methanol equilibrium conversion that can be attained,
since it favors the reversible reaction (DME + H2O → MeOH). This is
shown for different reaction temperatures. As the temperature increases, the equilibrium conversion suffers a further decrease and this is
caused by the reduction of the equilibrium constant with an increase in
temperature. This behavior was expected since it is characteristic of
exothermic reactions. An isotherm at 350 °C has been included to illustrate the typical outlet temperature of an industrial DME reactor
working with Al2O3 as catalyst [61]. As can be observed, a significant
improvement on the equilibrium conversion can be achieved by using
ZSM-5 as catalyst, which operates at lower temperature and would
allow an increase conversion per pass of approximately 5–10%. In an
industrial plant, the higher attainable conversion would easily translate
into lower power consumption since less unconverted methanol would
need to be recycled to the inlet of the DME reactor. The effect of temperature is further illustrated in Fig. 5(B). In this plot, three curves
representing fixed water quantities in the feed are shown. When pure
methanol is fed, then the higher equilibrium conversion can be
achieved. If 30 wt% of water is added to the feed, then the equilibrium
conversion that can be reached decreases. However, if the operating
temperature is low, it would still be possible to achieve methanol
conversions close to 90%, and this exalts the benefit of the use of ZSM-5
as catalyst, which can work at lower temperature than the Al2O3 catalyst commonly used in industrial practice. The higher the amount of
water, then stronger the effect on equilibrium conversion, as shown by
the yellow line which represent 70 wt% of water in the feed.
Fig. 6. Logarithmic rate of methanol conversion vs 1/T. Pure methanol feed
and WHSV = 100 h−1.
In the case of DME, it has been reported that this species does not
adsorb on the catalyst; thus, it doesn’t compete for adsorption on active
sites and doesn’t inhibit the reaction. This observation was experimentally confirmed for sulfonic resins [58,62], but to our knowledge,
there is no experimental evidence on ZSM-5. To determine the effect of
DME on the methanol conversion, two sets of experiments were performed at T = 190 °C, WHSV = 100 h−1, and partial pressure of methanol in the feed of 0.33 bar. In the first set of experiments, nitrogen
was used as gas balance; in the second set, nitrogen was substituted
with DME. The results showed that in both cases the conversion was
6%, thus, the effect of DME is similar to that of an inert gas, for example
nitrogen, at least as long as the conversion is sufficiently small and the
reverse reaction is negligible. Tests were limited to low conversion also
to avoid effects of water adsorption that might bias the interpretation of
the results.
According to Satterfield [63] the reaction regime can be determined
from a plot of log(rate) vs inverse of absolute temperature. Exemplary
results are shown in Fig. 6 for a feed of pure methanol at
WHSV = 100 h−1, and in Fig. 7 for a mixed feed of 70 wt% methanol/
Fig. 5. (A) Methanol equilibrium conversion versus molar faction of water in the feed; and (B) Methanol equilibrium conversion versus temperature (°C).
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divinylbenzene copolymer used as catalyst. The authors assumed that
only one type of active center was involved in the dissociative adsorption of methanol, and the RDS is a surface reaction. They observed
that K d → 0 , after fitting their experimental data; thus, K d was considered negligible in the model. As in the previous case, the original
model was modified, to include a driving force term, as explained by
Yang and Hougen [57].
The last model was recently developed by Ha et al. [13]. They
proposed new reaction pathways for the dehydration of methanol over
metal-modified ZSM-5 catalysts. The mechanisms included the adsorption of two methanol molecules and their activation, and the presence of adsorbed methyl carboxonium ion (CH3OH2+). Each individual step in the mechanism was assumed as RDS in order to derive
kinetic expression. The equation that performed best is included in
Table 4, and it considers the dehydration of the methyl carboxonium
ion (CH3OH2+) into a methoxy species and adsorbed water as RDS.
3.5.2. Model fitting and discrimination
Before the fitting procedure, kinetic constants were reparametrized
using equation (10) and a reference temperature (T0 ) of 438.15 K. After
evaluation of the kinetic models, three of them fulfilled the physicochemical constraints shown in Table 2. Also, the kinetic parameters
were significantly different from zero (0). The models and their OF
values are shown in Table 4.
As described in the previous subsection and shown in Table 4, the
modified models of Gates & Johanson and Klusáček & Schneider contain the driving force term. This term is included within the square
brackets in the corresponding equations, and it was neglected by the
authors. It is determined from partial pressures of reactants and products in the gas phase and the equilibrium constant (K eq ). The equilibrium constant was calculated from the standard Gibbs energy of formation (ΔGo ). Correlations and constants used in the determination of
ΔGo can be found in [41,66,67].
Also, it must be noted that the adsorption constant for DME (K d )
was omitted from all models. This is known to be valid for reaction
systems including sulfonic acid ion exchange resins as catalyst [58,62].
In the present study, the catalytic system was different, thus the assumption had to be confirmed, as described in Section 3.4.1. After
confirmation, K d was set to zero (0) in all kinetic models. This is also
supported by the work of Ding et al. [68], who found an enthalpy of
adsorption of DME (ΔHad,d ) on H-ZSM-5 of −18 kJ·mol−1. This value is
below the commonly cited limiting energy between physisorption and
chemisorption [69], −40 kJ·mol−1, thus indicating that DME might be
physisorbed on the surface, but not chemisorbed. Although it is not
possible to distinguish physisorption from chemisorption only by the
heat of adsorption [69,70], low values of ΔHad,d favor the decision of
neglecting the adsorption constant of DME when compared to the adsorption constants of water (ΔHad,w ) or methanol (ΔHad,m ). It is worth
mentioning that theoretical studies in literature show values of DME
enthalpy of adsorption on ZSM-5 as high as −98 kJ·mol−1 [71], and the
authors claim that experimental evidence shown by [72] supports their
calculation. However, this is only true when the number of molecules
per unit cell is less than two (2). At higher concentration values the
enthalpy of adsorption quickly decays reaching a plateau value c.a.
Fig. 7. Logarithmic rate of methanol conversion vs 1/T. Mixed feed of 70 wt%
methanol and 30 wt% water, and WHSV = 14 h−1, based on methanol fraction
in the feed.
30 wt% water and methanol WHSV = 14 h−1. It can be observed that
the experimental data falls in straight lines, and the slopes are different
from zero (0). This strong dependence of rate on temperature is another
indication for the assumption that the reaction regime is not limited by
external mass transfer.
3.5. Kinetic analysis
Kinetic tests were performed in the temperature range of
140–190 °C. At these temperatures, only the desired products were
observed. Small amounts of side products, hydrocarbons smaller than
(C5−), could be detected at temperatures higher than 200 °C.
3.5.1. Kinetic models
Nineteen kinetic models were evaluated. The models were both
power law and Langmuir-Hinshelwood-Hougen-Watson (LHHW) type.
The LHHW models were obtained from literature [6,9,10,58,64,65].
They were used as proposed by the authors or modified by the inclusion
of a driving force term, as described by [57]. Also, these models were
developed for the methanol to DME reaction on acid catalysts such as γAl2O3, sulfonic acid ion exchange resins and HZSM-5, considering
various RDS, e.g. methanol adsorption with dissociation, without dissociation, surface reaction, among others. The models that performed
best during the kinetic analysis are described below and their equations
are shown in Table 4. The remaining models are shown in the
Supplementary information.
The first model in Table 4 corresponds to a modified version of the
model of Gates & Johanson [58]. The model was modified to include a
driving force term, as explained by Yang and Hougen [57]. The original
model was developed for methanol dehydration over a sulfonic acid ion
exchange resin. The authors considered non-dissociative adsorption of
methanol, and the RDS was the combination of two molecules of methanol adsorbed in adjacent sites. Also, the authors assumed that DME
was weakly adsorbed on the catalyst. This means that DME adsorption
constant (K d ) was negligible compared to the adsorption constants of
methanol (Km ) and water (Kw ). Thus, it was removed from the adsorption term of the equation.
The second model was developed from Klusáček & Schneider [64],
to explain the dehydration of methanol on sulphonated styrene-
Table 4
Kinetic models and OF values.
Model
Modified Gates & Johanson
Modified Klusáček &
Schneider
Ha et al. [13]
748
Kinetic expression
r=
r=
r=
2 K )]
k (Km pm )2 [1 − pd pw / (pm
eq
(1 + Km pm + Kw pw )2
2 K )]
kKm pm [1 − pd pw / (pm
eq
(1 + 2 Km pm + Kw pw )2
2 K )]
kKm pm [1 − pd pw / (pm
eq
(1 + Km pm + Kw pw )
OF Value
1.84·10
−5
Eq. N°
(15)
1.12·10−5
(16)
1.52·10−5
(17)
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C. Ortega et al.
−40 kJ·mol−1 when the concentration per unit cell of molecules is
equal to or greater than three (3) [72].
From the OF results (Table 4), it seems that the modified model of
Klusáček & Schneider is the best. However, difference between the
objective function values is too small to be used as a clear indicator for
discrimination. Therefore, the rival kinetic models were further evaluated via parity plots of experimental versus calculated reaction rates
as well as residual analysis plots. These are shown in Fig. 8.
The parity plots of the three models (graphs A1, A2, and A3) show
good agreement between experimental and predicted rates.
Experimental measurements are shown with 95% confidence interval
bars. They are all on top or close to the line y = x (continuous-red line),
and within the simultaneous 95% confidence bounds, confirming the
good agreement between experimental data and calculated results. The
good agreement was already expected from the low OF results, shown
in Table 4.
The reaction rates observed in this investigation varied in the range
of 0.001–0.07 molMeOH·kgcat−1·s−1. These observations agree well with
those of Ha et al., who evaluated the methanol dehydration reaction
using pure methanol in their feed (without dilution with inert gas) and
an alkali-modified ZSM-5 with SiO2/Al2O3 = 80. On the contrary,
lower reaction rate values were reported for the same reaction and type
Fig. 8. Graphs on left column (1): Parity plots of experimental vs. calculated rate of conversion; Graphs on right column (2): Residual analysis. Each model is shown
in a dedicated row. From top to bottom: modified Gates & Johanson (A), modified Klusáček & Schneider (B), and Ha et al. (C). All rates are expressed in
molMeOH·kgcat−1·s−1.
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Different values of enthalpy of adsorption of methanol on ZSM-5 are
reported in literature, with values ranging from −26 kJ·mol−1 to
−115 kJ·mol−1 [68,71,77,78]. Results presented in Table 5 show that
−1
0
to −70 kJ·mol−1, in accordance with
ΔHad
,m varies from −45 kJ·mol
values reported in literature [72,77,79] for ZSM-5. In particular, the
0
ΔHad
,m determined from the model of Klusáček & Schneider [64] is in
close agreement with the value of −65 kJ·mol−1 reported by [80],
determined via density functional theory (DFT). In the case of enthalpy
−1
0
of adsorption of water (ΔHad
to
,w ), the results vary from −73 kJ·mol
−93 kJ·mol−1, also in good agreement with values reported by Lee
et al. [78] for heat of adsorption of water in zeolite. These authors
showed that heat of adsorption varied with coverage, starting at approx. −100 kJ·mol−1, and varying to approximately −80 kJ·mol−1 at
high coverage of water (400 µmol/g). These high values of enthalpy of
adsorption reveal the very exothermic nature of water interaction with
the zeolite structure, as Zhang et al. [81] suggested.
It is important to note that the above comparisons applying experimental results determined in this investigation correspond to those
reported by other authors using ZSM-5 with a wide range of Si/Al ratios, meaning that different acidic and hydrophilic properties are in
play. However, direct comparison of adsorption enthalpies of water and
methanol in ZSM-5 with different Si/Al is appropriate, considering that
isosteric heats of adsorption are fairly independent of the Si/Al ratio
once a certain number of molecules had been adsorbed in the zeolite
[81,82].
These models also obey the entropy constraints shown in Table 2.
Both standard entropies of adsorption, of methanol and water, are negative and fall below the corresponding gas phase values of methanol
(Sg0,m = 240 J·mol−1·K−1), and water (Sg0,w = 189 J·mol−1·K−1), reported by [66]. In the case of the Ha et al. model [13] the value is
actually at the limit of an entropy constraint. The predicted value of
−1 −1
0
·K , and it lays just at the boundary of the
ΔSad
,w is 189 ± 2 J·mol
0
maximum value that ΔSad
,w should reach. It is not possible to conclude
that the value is significantly greater than 189 J·mol−1·K−1, thus this
model is still considered satisfactory, and included in the further analysis.
Vannice et al. [44] offers a guideline to make use of the entropy of
adsorption on the discrimination process, see eq. (18). The upper limit
of this recommendation was empirically determined from entropies of
chemisorption and the linear correlation between entropy and enthalpies of adsorption detected by Everett [83]. In this equation, entropy is given in J·mol−1·K−1 and enthalpy is given in J·mol−1. Results
are summarized in Table 5.
of catalyst by Migliori et al. [65]. This discrepancy could be caused by a
combination of low partial pressure of methanol in the feed used by
these authors and the use of a catalyst with higher SiO2/Al2O3 ratio,
thus less acidic, as has been reported by Alharbi et al [8].
Zhang et al. [12] also reported similar methanol reaction rates but
on γ-Al2O3 catalysts working at higher temperatures, in the range of
240° to 340 °C. These results can be explained by the lower acidity of γAl2O3 with respect to ZSM-5 [6]. We conclude that by carrying out the
reaction over a ZSM-5 catalyst, it is possible to work at a lower temperature than with γ-Al2O3 catalysts (typically used in industry) but
maintaining similar reaction rates. Therefore, the use of ZSM-5 catalyst
could allow the reduction of the size of the equipment required to
achieve a certain productivity, and it would also allow a higher conversion per pass since the equilibrium conversion is favored at lower
temperature.
The residuals were evaluated via predicted value plots as described
by Kittrell [37]. The analysis helps to identify non-random variations in
the data, which can be used to further discriminate among the remaining models. These plots are presented on the right side of Fig. 8, in
graphs C1, C2, and C3. According to these results, all models seem to
perform equally well, with residuals randomly distributed above and
below zero (0). As described in Section 2.6, the residuals were also
tested using the MATLAB® command “ttest”. Results showed that all
models fulfilled the null hypothesis, i.e. all residual samples are normally distributed and their mean is zero (0). Also, it is concluded that
systematic errors are not present in the measurements, but only random
experimental error, which is intrinsic to the reaction tests and measurements, as explained by [37]. Based on these results, all models seem
equally adequate. Further discrimination was achieved by close analysis of the kinetic parameters shown in Table 5.
It is shown that activation energy [Ea ] for all models are around
106 kJ·mol−1, within 10% of the value reported by Alharbi et al. [8] of
95 kJ·mol−1 on HZSM-5 with Si/Al = 10. However, other authors
[6,13] have found values in the range of 52–69 kJ·mol−1. The source of
the discrepancy is unknown. It could be caused by a compensation
relation (see Constable-Cremer in [73]), which is a linear correlation
between observed frequency factors and apparent activation energies
for a series of catalysts and a particular reaction, or one catalyst and a
series of similar reactions [73,74]. In this comparison, the compensation effect could be related to changes in the acid strength of the catalysts, produced by the metal modifications implemented by these authors. Likewise, Alharbi et al. [8] have shown a linear correlation
between turn over frequency and acid strength for different catalysts,
including HZSM-5 with different Si/Al ratios. Another plausible explanation is related to kinetic measurements affected by internal mass
transfer limitations, which we consider possible, taking into account the
large particle sizes these authors used during experimentation
(420–841 µm). If pore diffusion limits the reaction, the measured activation energy is the mean of the activation energy measured in the
kinetic regime and the activation energy for pore diffusion (ED ) [63,75].
Considering that ED of methanol on HZSM-5 is 12.3 kJ·mol−1 [76], and
the activation energy measured in the kinetic regime is c.a.
106 kJ·mol−1 (reported in this study) the mean value results in an activation energy of c.a. 59 kJ·mol−1, which is in close proximity to the
values reported by [6,13].
0
0
−ΔSad
,i < 51.1−0.0014·ΔHad,i
(18)
0
All ΔSad
,m fulfil the guideline given by Vannice et al. [44]. That is
0
not the case for ΔSad
,w . The results obtained in the modified model of
Gates & Johanson and Ha et al. [13] are significantly greater than the
limit determined by the recommendation [44], also shown in Table 6.
These results give strong indication that the models should be discarded
or considered with great caution, since it may indicate that one of the
parameters lacks of physical meaning. The modified model Klusáček &
Schneider [64] has a different interpretation. It is not possible to con0
clude that the value obtained of ΔSad
,w is significantly higher than the
recommendation, thus it is considered satisfactory.
Table 5
Summary of kinetic parameters.
Model
Modified Gates & Johanson
Modified Klusáček & Schneider
Ha et al. [13]
Kinetic parameters
kT0·102
Eapp (kJ·mol−1)
−1 −1
0
−ΔSad
,m (J·mol ·K )
−1
0
−ΔHad
,m (kJ·mol )
−1 −1
0
−ΔSad
,w (J·mol ·K )
−1
0
−ΔHad
,w (kJ·mol )
1.69 ± 8·10-2
8.16 ± 0.51
1.70 ± 7·10-2
103.4 ± 3.1
109.3 ± 3.7
104.4 ± 2.9
73 ± 2
137 ± 12
91 ± 2
44.5 ± 0.7
70.3 ± 5.4
49.5 ± 0.6
182 ± 2
153 ± 26
189 ± 2
89.6 ± 0.3
73.1 ± 12.0
93.3 ± 0.3
750
Chemical Engineering Journal 347 (2018) 741–753
C. Ortega et al.
4. Conclusions
Table 6
Entropies of adsorption and maximum entropy according to guideline.
Kinetic model
Modified Gates &
Johanson
Modified Klusáček
& Schneider
Ha et al. [13]
−1 −1
0
-ΔSad
,m (J·mol ·K )
−1 −1
0
-ΔSad
,w (J·mol ·K )
From
Regression
Limit by
guideline
From
Regression
Limit by
guideline
73 ± 2
113
182 ± 2
177
137 ± 12
150
153 ± 26
153
91 ± 2
120
189 ± 2
182
The present studied focused on the kinetic analysis of methanol to
dimethyl ether conversion on a commercial ZSM-5 zeolite. The MFI
structure of the commercial zeolite was confirmed via XRD, and its
textural properties were determined via gas physisorption and mercury
intrusion porosimetry. NH3-TPD analysis allowed the identification of
two types of acid sites with medium and high strength. Also, crystal size
(used in the preliminary calculations) was measured from SEM images,
and an average value of c.a. 300 nm was determined.
Previous to the kinetic analysis, a series of preliminary studies were
performed. It was demonstrated that the recycle reactor had a fluid
dynamic behavior similar to CSRT. Also, from long test runs and reaction/regeneration cycles, it was proven that ZSM-5 is an effective and
stable catalyst to convert MeOH to DME. Moreover, it is highly selective
when operated under appropriate conditions (T < 190 °C). By-products were not detected during the experimental work of this investigation. Moreover, the effect of heat and mass transfer, inside and
outside the catalyst particle, were evaluated using Weisz-Prater
number, and criteria from Mears and Anderson. All criteria were met,
thus it was concluded that experimental tests were done in the kinetic
regime.
In reference to the kinetic models, there wasn’t a significant difference between the performance of the modified models of Gates &
Johanson, Klusáček & Schneider, and the model of Ha et al. [13]. The
kinetic parameters estimated with these models had physical and statistical significance. However, on the basis of the analysis made in this
study, by means of a recommendation from Vannice et al. [44] on
adsorption entropies and Akaike’s information criterion [45], it is
concluded that the modification applied to the model of Klusáček &
Schneider results a kinetic equation that is robust and provides excellent performance in the description of methanol to DME conversion
over ZSM-5. This supports a mechanism with dissociative adsorption of
methanol and a surface reaction as rate determining step. It should be
emphasized that kinetic and adsorption parameters, from the modified
model of Klusáček & Schneider, fulfilled all physicochemical constraints
and recommendations, and the enthalpies of adsorption were in good
agreement with independent data of adsorption on ZSM-5 and DFT
studies.
Finally, the effect of operating conditions was considered to determine the true activation energy and order of the reaction with respect to methanol and water. It was shown that the true activation
energy, calculated in this work, comes close to the value estimated by
[84] via DFT calculations. Moreover, it was shown that the order of the
reaction with respect to methanol is positive, whereas the order with
respect to water is negative. The latter is in agreement with the reported
inhibiting effect of water on the conversion of MeOH to DME over
catalysts, which are different to ZSM-5.
To discriminate further, the Akaike’s Information Criterion (AIC)
was used, and the results are shown in Table 7. The modified model of
Klusáček & Schneider showed the lowest AIC, thus it is considered the
best among the rival models.
After careful evaluation of the kinetic models, assessment of the
physicochemical constraints, consideration of the entropy recommendation from Vannice et al. [44], and the results of AIC, it is
concluded that the modified Klusáček & Schneider kinetic model is the
best to describe the methanol to DME conversion over ZSM-5. Moreover, the selection of this model, supports a mechanism in which methanol experiences dissociative adsorption and the RDS is a surface
reaction, in accordance to the work of Klusáček & Schneider, and more
recently Moses et al. [15].
3.5.3. True activation energy and reaction order
The apparent activation energies, determined from regression, may
differ from the true activation energy of the process, and this is evidenced below. It has been indicated that the Eapp changes with experimental conditions, since the surface coverage of the reactants may
change within the experimental spectrum evaluated [47,73]. In fact,
Bond et al. [73] have explained that in the absence of mass transfer
effects the relation between Eapp , Etrue and ΔHad,i may lead to a decrease
in the slope of an Arrhenius plot. Application of the definition provided
in Section 2.6.2 for the kinetic expression developed by Klusáček &
Schneider [64] leads to equation (19).
⎛ ΔHm Km pm + ΔHw Kw pw ⎞
Eapp = Etrue + ΔHm−2·⎜
⎟
⎝ 1 + 2 Km pm + Kw pw ⎠
(19)
The evaluation of this equation, using the experimental conditions
of this research and the estimated kinetic parameters, indicates that the
true activation energy is in the range between 80 and 130 kJ·mol−1, the
upper limit being within 15% of the value reported by Blaszkowski and
van Santen [14,80]. This is considered as a good agreement, provided
that the accuracy of DFT calculations are in the range of ± 10 kJ·mol−1
[84].
Finally, the definition provided in Section 2.6.2 was used along with
the kinetic expression proposed by Klusáček & Schneider and modified
in this work. Then, the orders of reaction with respect to methanol (nm )
and water (n w ) result from equations (20) and (21).
nm = 1−2·
n w = −2·
Acknowledgment
This work was supported by the European Commission in the scope
of the 7th Framework program BIOGO project [grant number: 604296]
https://www.biogo.eu/.
Km pm
(1 + 2 Km pm + Kw pw )
(20)
Kw pw
(1 + 2 Km pm + Kw pw )
(21)
Table 7
Akaike’s information criterion.
Their evaluation yields nm in the range of 0.07–0.45, which indicates a slight influence of methanol partial pressure on the reaction
rate. This is in good agreement with the experimental results shown in
Fig. 4 and the reaction order of 0.23 reported by Alharbi et al. [8].
Additionally, nw is in the range of −0.80 and 0, in agreement with the
observation that water has an inhibiting effect on the reaction rate, as
reported by different authors [9,58].
751
Model
AICi
Modified Gates & Johanson
Modified Klusáček & Schneider
Ha et al. [13]
−341
−353
−346
Chemical Engineering Journal 347 (2018) 741–753
C. Ortega et al.
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