doi 10.1515/ijcre-2013-0061
International Journal of Chemical Reactor Engineering 2013; 11(1): 469–477
Raquel De María, Ismael Díaz*, Manuel Rodríguez, and Adrián Sáiz
Industrial Methanol from Syngas: Kinetic Study
and Process Simulation
Abstract: In this study, a detailed rigorous kinetic model
is proposed for the industrial production of methanol
taking into account changes in total mole flowrate. The
kinetic model proposed is compared with the one proposed in literature (Rezaie et al., Chem Eng Process
Process Intensification 2005;44:911–21), showing significant differences in terms of compositions and total mole
flow. A complete simulation of the methanol production
process is developed with a commercial software. The
rigorous reactor model is integrated in the simulation
using the CAPE OPEN standard. Flowsheet simulation is
carried out, and results show small differences with those
found in previous studies (Luyben, Ind Eng Chem Res
2010;49:6150–63).
Keywords: methanol, reactor model, process simulation
got some good results using copper dispersed on zincbased catalysts (1960s). This development allowed the
use of milder conditions, strongly decreasing both costs
and process risks. This is still the base of the catalysts
employed today.
Methanol from syngas synthesis involves hydrogenation of CO (1) and CO2 (2) and reversed water–gas shift
reactions (3):
CO þ 2H2 $ CH3 OH
ΔH298 ¼ 90:55kJ=mol
ð1Þ
CO2 þ 3H2 $ CH3 OH þ H2 O
ΔH298 ¼ 49:43kJ=mol
ð2Þ
CO2 þ H2 $ CO þ H2 O
ΔH298 ¼ 41:12kJ=mol
ð3Þ
*Corresponding author: Ismael Díaz, Chemical Technology
Laboratory, School of Industrial Engineering, Technical University of
Madrid, C/José Gutiérrez Abascal 2, 28006, Madrid, Spain, E-mail:
[email protected]
Raquel De María: E-mail: [email protected], Manuel
Rodríguez: E-mail: [email protected], Adrián Sáiz: E-mail:
[email protected], Chemical Technology Laboratory,
School of Industrial Engineering, Technical University of Madrid,
C/José Gutiérrez Abascal 2, 28006, Madrid, Spain
1 Introduction
Nowadays, methanol is one of the most consumed commodities around the world with an expected global
demand of 61.4 million metric tons [1]. Its main applications are as fuel, additive or reactant in the fine chemical
industry, but others are emerging such as hydrogen carrier for fuel cell technology applications or denitrification
agent for wastewater treatment. So its importance in the
chemical industry is clearly demonstrated.
Initially, methanol was produced by wood distillation
which was proved a very inefficient method [2]. The first
industrial methanol production process needed a highpressure (around 300 atm) syngas reaction, and it was
patented by BASF in 1923. Catalysts used in these early
processes were based on ZnO/Cr2O3. The ICIs company
As shown in the heats of reaction, the global process
is exothermic, reaching highest conversions at low
temperatures. This fact, coupled with the high capacity
of the process, makes the reactor design to be the sticking
point in the process. Therefore, companies have invested
great efforts in the development of their own reactors.
Most of the designed industrial reactors are packed bed
reactors (i.e. ICI, Kellogg and Linde processes) where the
catalyst is fixed inside the tubes and cooling is provided
through a reactor jacket. Another design is the threephase reactor carried out by Chem Systems, where the
catalyst is fluidized in an inert liquid and the gas phase
is composed of reactants and products except methanol
which is absorbed by the liquid phase. This
design improves heat transfer and catalyst deactivation
aspects [3].
The aim of this study is to investigate the influence of
different kinetic approaches on the results of a validated
process simulation model. The remainder of this article is
organized as follows: Section 2 presents two kinetic models (one from literature and one provided by the authors),
Section 3 describes the process simulations where the
previous developed reactor model is integrated along
with the whole model performance, and finally, Section
4 draws some conclusions.
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2 Kinetic modelling
(c) Gas-phase mole balance
2.1 Literature models
εB Ct
dyi
Ft dyi
¼0¼
þ av Ct kgi ðyi ys Þ
dt
Ac dz
i ¼ 1; 2; . . . ; N
ð6Þ
The key aspect in the simulation of the methanol
process is the reactor behaviour. Many efforts have
been done for the correct modelling of the kinetic processes involved. Mainly, two kinds of models are proposed depending if the solid is taken or not into account
for the model. If only mole and energy balances are
applied to the fluid phase, then the model is called
homogeneous. If both solid- and gas-phase molar and
energy balances are carried out, then we have a heterogeneous model. The expressions here adopted for the
two models are adapted from the work of Rezaie et al.
[4] and Yusup et al. [5].
2.1.1 Heterogeneous model
The model considers mass and energy transfers
between solid and fluid phases as well as energy
exchange between reactor fluid phase and the coolant
in reactor jacket. Pressure drop was computed by Ergun’s
equation [6].
Some other assumptions were taken:
– Time independence (stationary condition).
– Neither axial nor radial dispersion.
– Coolant temperature keeps constant.
– Effectiveness factor (η) value equal to 1. This is a
conservative assumption because it has been
reported values higher than 1 for this factor, as in
Ref. 7.
– Intraparticular diffusion and catalyst deactivation
has not been taken into account.
– Ideal gas phase.
– Constant molar flux along the reactor.
Last assumption will be discussed later on Section 2.1.3
where the author’s model is proposed. Basic equations of
this model are:
(a) Solid-phase mole balance
ε B Ct
dyis
¼ 0 ¼ kgi ðyi ys Þ þ ηri ρB a i ¼ 1; 2; . . . ; N
dt
ð4Þ
(b) Solid-phase energy balance
ρB Cps
N
X
dyis
ηri ΔHfi
¼ 0 ¼ av hf ðT Ts Þ þ ρB a
dt
i¼1
ð5Þ
d) Gas-phase energy balance
εB Ct Cpg
dT
Ft
dT
¼0 ¼ Cpg
þ av hf ðT Ts Þ
dt
dz
Ac
πDi
þ
Ushell ðTshell T Þ
Ac
ð7Þ
e) Ergun’s equation
dP
1 εB 1 εB u2g ρg
6
1:75 þ 150
¼ L 10
dz
Re
ε3B Dp
ð8Þ
The resolution can be carried out, because it is a so-called
initial value problem with known boundary conditions at
the entrance of the reactor:
z ¼ 0 ! yi ¼ yi0
z ¼ 0 ! T ¼ T0
ð9Þ
2.1.2 Homogeneous model
This model is essentially the same than before with the
particularity that there is neither a temperature nor a
concentration gradient between the solid and fluid
phase. This means that yi ¼ yis and T ¼ Ts .
2.2 Mass homogeneous model
(author’s model)
Previous models were adopted from literature [4, 5],
and it was observed an imperfection in their basis.
Both of them supposed that total molar flux (Ft) remains
constant along the reactor. As it can be observed from
reactions involved, all the compounds are gases at
reaction temperature and pressure. Besides, it can be
seen that there are net changes in the mole number of
chemical substances. So, under these conditions, the
assumption of constant Ft is not valid. To overcome it, a
new model based on mass fractions and fluxes is proposed. In the new model, total mass flow (Wt) remains
constant.
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R. De María et al.: Industrial Methanol from Syngas
The model is derived from the homogeneous model
of Section 2.1.2, where
Fi ½i mole flow ¼
h
i
3=2
k3 KCO pCO pH2 pCH3 OH pH2 O = pH2 Kp2
h
i
r3 ¼
1=2
1=2
ð1 þ KCO pCO þ KCO2 pCO2 Þ pH2 þ KH2 O =KH2 pH2 O
ð16Þ
wi ½mass fractioni Wt ½total mass flow
Mi ½molecular weighti ð10Þ
2.4 Mass-transfer correlations
Model balances are expressed at follows:
(a) Gas-phase mass balance
0¼
Values of mass-transfer coefficient (kgi) were computed in
the reactor using the Cussler correlation [11].
Wt dwi
þ Mi ηρB a i ¼ 1; 2; . . . ; N
Ac dz
ð11Þ
kgi ¼ 1:17Re0:42 Sci0:67 ug
ð17Þ
(b) Gas-phase energy balance
0¼
Mixture diffusivity was estimated attending to Wilke’s
equation [12], and binary diffusivities were calculated
using the Fuller–Schetter–Giddins method [13].
Wt
dT πDi
þ
Cpg
Ushell ðTshell T Þ
dz
Ac
Ac
þ ρB a
N
X
ð12Þ
ηri ΔHfi
2.5 Heat-transfer correlations
i¼1
The overall heat-transfer coefficient was estimated
neglecting the wall effect as follows:
(c) Ergun’s equation
dP
1 εB 1 εB u2g ρg
6
¼ L 10
1:75 þ 150
dz
Re
ε3B Dp
ð13Þ
1
1
1
¼ þ
Ushell hi ho
ð18Þ
Where shell side heat-transfer coefficient can be estimated by Holman [14]:
2.3 Kinetics
In this model, kinetic expressions were taken from the
work of Graaf et al. [8]. Heat of formation correlations for
the species were calculated from bibliographic correlations [9, 10] in order to predict the change of the heat of
reaction with temperature. Values of both kinetics and
equilibrium temperature-dependent parameters were
taken from Graaf et al. [8]. Eqs [14–16] show the kinetic
expressions for the three existing reactions.
ho ¼ 7:96ðTshell Tsat Þ3
Pshell 0:4
Patm
Values of Pshell and Tshell are 41.2 bar and 525 K, respectively, as reported in literature for these reactors [15].
Tube side heat-transfer coefficient can be calculated
by conventional correlations Nu ¼ f ðRe; PrÞ [16]. For
example,
hi
Cpg μ 2=3 0:458 ρuDp 0:407
¼
k
εB
Cpg ρμ
μ
h
i
3=2
1=2
k1 KCO pCO pH2 pCH3 OH = pH2 Kp1
h
i
r1 ¼
1=2
1=2
ð1 þ KCO pCO þ KCO2 pCO2 Þ pH2 þ KH2 O =KH2 pH2 O
ð14Þ
h
i
3=2
1=2
k2 KCO pCO pH2 pCH3 OH pH2 O = pH2 Kp2
h
i
r2 ¼
1=2
1=2
ð1 þ KCO pCO þ KCO2 pCO2 Þ pH2 þ KH2 O =KH2 pH2 O
ð15Þ
ð19Þ
ð20Þ
2.6 Models comparison
Based on data collected from industrial plants [17], Rezaie
et al. [4] studied the influence of using the more
sophisticated heterogeneous model instead of the simple
homogeneous one. Conditions of the study are presented
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Table 1
Catalyst and reactor specifications.
Parameter
Value
Pressure (bar)
Inlet temp. (K)
Total molar flowrate (mol/s)
Composition (mol%):
CH3OH/CO2/CO/H2O/H2/N2/CH4
ρs (kg/m3)
dp (m)
Cps (kJ/kg·K)
λc (W/m·K)
av (m2/m3)
εS/τ
Number of tubes
Tube length (m)
76.98
503
0.64
the molar-based homogeneous model. In essence, the
model is the same than the molar homogeneous one, but
assuming mass basis for all the terms in eqs [11] and [12],
so total mass flow can be treated successfully as invariant.
As shown in Figure 2, there are significant differences
in the resulting profiles, being higher for H2 and CH4 for
which more than 10% difference is computed. The results
show that a global decreasing in mole flowrate is
obtained (final value of 0.59 mol/s in comparison with
0.64 mol/s from literature) as expected from the reaction
pathway (1–3). It makes all compositions higher than for
the mole-based case. The influence of choosing a kinetic
model over both temperature and pressure profiles is
negligible.
So, henceforth, the mass homogeneous model is
employed for simulating the methanol synthesis process.
0.5/9.4/4.6/0.04/65.9/9.3/10.26
1,770
5.47 10−3
5
4 10−3
627
0.123
2,962
7.022
in Table 1. Obtained results were in agreement with
Rezaie’s findings. It means, a simple homogeneous
model, which neglects differences of gas and solid
phases, can be employed satisfactorily as it can be seen
from Figure 1.
In a new approach, we try to solve the weakest point
of both homogeneous and heterogeneous models: they are
developed assuming that total molar flowrate
keeps constant. Therefore, a mass homogeneous model
(Section 2.1.3) is proposed, evaluated and compared with
CH3OH
1
2
3
Mole fraction
5
6
7
0.075
H 2O
0.01
0.005
0
1
2
3
4
5
6
Temperature (K)
0.15
0.1
0.05
0
1
0
1
2
3
2
3
4
5
Reactor length (m)
6
7
4
5
6
7
H2
0.02
0.2
0.62
0.15
0.6
0.1
0.58
0.05
0
1
2
3
4
5
6
0
7
530
80
520
79.95
510
500
490
0
1
0
1
2
3
2
3
4
5
Reactor length (m)
6
7
4
5
6
7
4
N2
0.25
0.64
7
CH4
0.2
0
0.03
0.66
0.015
0.25
Mole fraction
4
Homogeneous
Heterogeneous
0.04
0.08
0.02
0
Homogeneous
Heterogeneous
0.09
0.085
0
CO
0.05
0.095
0.02
0
CO2
0.1
Homogeneous
Heterogeneous
0.04
Methanol synthesis process simulation has been previously studied in literature [18–20]. Validated results
were presented in detail by Luyben [18] and are the
basis of this work.
The main difference is in how the reactor is modelled.
Luyben modelled this reactor by changing the original
Pressure (bar)
Mole fraction
0.06
3 Process simulation
0
1
2
3
5
6
7
0
1
2
3
4
5
Reactor length (m)
6
7
79.9
79.85
79.8
79.75
Figure 1 Comparison between heterogeneous and homogeneous kinetic models for methanol synthesis.
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CH3OH
0.04
0.02
0
Molar homogeneous
Massic homogeneous
0
2
Mole fraction
0.02
0.08
0.03
2
0.66
4
H2
0.02
6
0
2
4
N2
6
0
2
4
6
0
2
4
Reactor length (m)
0.105
0.64
0.1
0.62
0.01
0.6
0.005
0.095
0.58
0
2
4
6
0
CH4
0.112
Temperature (K)
0.108
0.106
0.104
0
2
4
Reactor length (m)
2
4
0.09
6
530
0.11
0.102
0.04
0
CO
0.05
0.09
6
0.015
0
Mole fraction
4
H2O
CO2
0.1
6
80
520
Pressure (bar)
Mole fraction
0.06
510
500
490
0
2
4
6
79.9
79.8
79.7
Reactor length (m)
6
Figure 2 Comparison between mass and molar homogeneous kinetic models for methanol synthesis.
kinetic expressions to meet the process simulator format
and including the reactor as a standard unit simulation
block. In our work, we have also developed the process
model using Aspen Plus, but we have integrated an external model of the reactor into the simulation flowsheet
instead of using a reactor block. So, we have modelled
the reactor rigorously by solving the ODE system of equations keeping the original kinetic formulations coupled
with the mass homogeneous balance equations.
The reactor model developed in Matlab has been
integrated into the Aspen Plus flowsheet using the
CAPE OPEN standard [21].
The process flowsheet (Aspen Plus PFD) is depicted in
Figure 3, where syngas feed is firstly compressed from 1 to
110 bar in two-stage compressions with intermediate cooling (38°C). The resulting stream is adiabatically mixed
with vapour distillate from the methanol purification column (loop 1). Stream 8 is again mixed with unreacted
gases, separated and compressed after flash separations
(loop 2). Main stream (10) goes to the reactor being preheated in a feed-effluent heat exchanger (FEHE) with the
product stream of the reactor (loop 3). A stream containing
raw methanol from the bottom of the flash separators is
then fed to the distillation column. RK-Aspen properties
package was chosen for the whole simulation except for
the distillation column (atmospheric pressure), where
NRTL-RK package was employed.
Today generated Matlab code cannot yet be directly
embedded in the Aspen simulation flowsheet being
necessary to use a simulator interface. In this work, we
have used the COCO simulator interface application [22].
Matlab code, using CAPE OPEN was integrated in the
COCO simulator, and the flowsheet generated in this
simulator was embedded in the Aspen flowsheet.
Figure 4 shows the integration process.
The obtained reactor profiles (Figure 5) show a
decrease on hydrogen composition and an increase in
methanol concentration as expected. Temperature rapidly
increases due to the high heat-transfer coefficient computed (U ~ 3,000 W/m2 K), and pressure decreases as
predicted by Ergun’s equation.
Conversion per pass (reactor outlet related with reactor inlet) of hydrogen is 22%, 39% for carbon monoxide
and 15% for carbon dioxide, these values are slightly
different from literature ones, showing the influence of
reactor modelling assumptions. However, total carbon
conversion is marginally higher (for the same feed syngas
stream) resulting in 3,142 kmol/h of methanol at the end
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R. De María et al.: Industrial Methanol from Syngas
Figure 3 Methanol synthesis process flowsheet.
Figure 4 Scheme of reactor modelling implementation.
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R. De María et al.: Industrial Methanol from Syngas
CH3OH
Mole fraction
0.1
0.08
0.08
0
2
4
6
8
10
12
0.075
0
2
4
6
8
10
0.06
12
0.6
0.032
0.01
0.55
0.03
0.005
0.5
0.028
0
2
4
6
8
10
CH4
0.22
0.21
0
2
0
2
4
6
8
10
12
0.026
550
Temperature (K)
0.23
0.2
0.45
12
2
4
4
6
8
Lenght of reactor (m)
10
12
500
450
400
6
8
10
12
8
10
12
10
12
N2
0
2
0
2
4
6
110
Pressure (bar)
0
0
H2
H2O
0.015
Mole fraction
CO
0.12
0.1
0.05
0
Mole fraction
CO2
0.085
0
2
4
6
8
Lenght of reactor (m)
10
12
109
108
107
4
6
8
Lenght of reactor (m)
Figure 5 Reactor composition, temperature and pressure profiles.
of the process instead of 3,274 kmol/h obtained in Ref. 18,
representing a 3.8% of change. Differences in total mole
flowrates of the main outlet stream are reported in
Table 2. Detailed results of all process streams are
included in Table 3.
Some temperature differences (5°C in the inlet and
around 15°C in the outlet) have been observed in the
reactor-FEHE system regarding Luyben’s work. In our
simulations, we have calculated a heat duty of 40.9 MW
instead of 44.3 MW from literature (8% change). It is due
to the higher overall heat exchanger coefficient calculated taking into account equipment hydrodynamic by
eqs [18–20]. Global heat duties do not differ very much
Table 2
Differences in molar flowrates (kmol/h).
Stream ID
Ref. 13
This work
Vent
Methanol
Water
F1
872
3,311
707
4,019
1,034
3,203
738
4,098
between both works, being for total heat consumed
below 10% (209 MW vs 229 MW).
4 Conclusions
A conventional methanol synthesis reactor was modelled
by using three different approaches: molar homogeneous,
molar heterogeneous and mass homogeneous models. It
was shown that both heterogeneous and homogeneous
models resulted in similar compositions for the tested
reactor. Significant differences were obtained when applying the proposed mass approach for the reactor, allowing
changes for the total mole flowrate along the reactor. The
model is rigorously implemented in commercial process
simulation software showing small differences in terms of
the final amount of methanol obtained.
Acknowledgements: The authors gratefully acknowledge
Jasper van Baten comments and support when dealing
with the implementation of Matlab model into process
simulation software.
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74.0
Pressure
248.5
CH4
0.069
0.23
0.002
0.675
0.003
0.022
CO2
CO
H2O
H2
N2
CH4
CH3OH
0
34.4
Mole frac
7,724.9
26.3
H2O
N2
2,630.3
CO
H2
785.5
CO2
CH3OH
(kmol/h)
Mole Flow
0.0
371.4
Temp. (K)
(atm)
4
0.022
0.003
0.675
0.002
0.23
0.069
0
248.5
34.4
7,724.9
26.3
2,630.3
785.5
0.0
74.0
311.1
5
Stream results.
Stream ID
Table 3
0.022
0.003
0.675
0.002
0.23
0.069
0
248.5
34.4
7,724.9
26.3
2,630.3
785.5
0.0
108.6
358.2
6
0.089
0.002
0
0.003
0.006
0.372
0.528
14.1
0.3
0.0
0.4
0.9
58.6
83.1
108.6
800
7
0.023
0.003
0.666
0.002
0.227
0.073
0.007
262.6
34.6
7,724.9
26.8
2,631.3
844.2
83.1
108.6
369.1
8
0.244
0.033
0.54
0.001
0.063
0.112
0.008
11,375.6
1,528.2
25,203.7
23.4
2,923.6
5,247.5
369.9
108.6
334.9
9
0.2
0.027
0.565
0.001
0.095
0.105
0.008
11,638.1
1,562.8
32,928.6
50.1
5,554.9
6,091.6
453.0
108.6
341
10
0.2
0.027
0.565
0.001
0.095
0.105
0.008
11,638.1
1,562.8
32,928.6
50.1
5,554.9
6,091.6
453.0
108.6
414.7
11
0.225
0.03
0.498
0.014
0.058
0.105
0.071
11,638.1
1,562.8
25,780.1
723.0
2,990.0
5,418.7
3,690.8
105.9
545.4
13
0.225
0.03
0.498
0.014
0.058
0.105
0.071
11,638.1
1,562.8
25,780.1
723.0
2,990.0
5,418.7
3,690.8
105.9
471.8
14
0.225
0.03
0.498
0.014
0.058
0.105
0.071
11,638.1
1,562.8
25,780.1
723.0
2,990.0
5,418.7
3,690.8
105.1
311.1
15
0.24
0.033
0.557
0
0.063
0.102
0.004
11,104.3
1,536.6
25,780.1
11.2
2,924.0
4,715.4
178.2
105.1
311.1
16
0.096
0.005
0
0.128
0.012
0.127
0.632
533.8
26.3
0.0
711.8
66.0
703.3
3,512.6
105.1
311.1
17
0.24
0.033
0.557
0
0.063
0.102
0.004
10,856.0
1,502.2
25,203.7
11.0
2,858.6
4,610.0
174.2
105.1
311.1
19
0.24
0.033
0.557
0
0.063
0.102
0.004
10,856.0
1,502.2
25,203.7
11.0
2,858.6
4,610.0
174.2
108.6
314.7
20
0.357
0.018
0
0.009
0.045
0.438
0.134
519.6
26.0
0.0
12.4
65.0
637.5
195.7
2.0
311.1
21
0.003
0
0
0.171
0
0.016
0.809
14.3
0.3
0.0
699.4
0.9
65.8
3,316.9
2.0
311.1
22
0.357
0.018
0
0.009
0.045
0.438
0.134
519.6
26.0
0.0
12.4
65.0
637.5
195.7
108.6
759.1
23
0.2
0.027
0.565
0.001
0.095
0.105
0.008
11,638.1
1,562.8
32,928.6
50.1
5,554.9
6,091.6
453.0
108.6
423.1
24
0.089
0.002
0
0.003
0.006
0.372
0.528
14.1
0.3
0.0
0.4
0.9
58.6
83.1
1.0
323.1
26
0
0
0
0.016
0
0.002
0.981
0.2
0.0
0.0
52.5
0.0
7.2
3,142.8
1.0
323.1
Methanol
0.022
0.003
0.675
0.002
0.23
0.069
0
248.5
34.4
7,724.9
26.3
2,630.3
785.5
0.0
50.5
323
Syngas
0.24
0.033
0.557
0
0.063
0.102
0.004
248.3
34.4
576.4
0.3
65.4
105.4
4.0
105.1
311.1
Vent
0
0
0
0.877
0
0
0.123
0.0
0.0
0.0
646.5
0.0
0.0
91.0
1.0
358.7
Water
476
R. De María et al.: Industrial Methanol from Syngas
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R. De María et al.: Industrial Methanol from Syngas
477
Nomenclature
εB
Ct
yis
kgi
yi
η
ri
ρB
a
Cps
av
hf
Ts
T
ΔHfi
Ft
Ac
Di
Bed porosity
Total mole concentration
Molar fraction of i component in the solid phase
Mass-transfer component of i component
Molar fraction of i component in the gas phase
Effectiveness factor
Reaction rate of i component
Bed density
Catalytic activity
Heat capacity of solid phase
Catalyst surface area
Heat-transfer coefficient
Temperature of the solid phase
Temperature of the gas phase
Enthalpy of formation of component i
Total mole flowrate
Cross-section area of each tube
Tube diameter
Ushell
Tshell
L
Re
Dp
ug
ρg
Wt
wi
Mi
ki
Ki
Kpi
N
P
Sci
hi
ho
Overall heat-transfer coefficient
Shell side temperature
Length of reactor
Reynolds number
Particle diameter
Gas velocity
Gas density
Total mass flow
Mass fraction of component i
Molecular weight of component i
Reaction rate constant for the ith rate equation
Adsorption equilibrium constant for component i
Equilibrium constant based on partial pressure for
component i
Number of components
Total pressure
Schmidt number for component i
Tube side individual heat-transfer coefficient
Shell side individual heat-transfer coefficient
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Download Date | 2/13/15 9:41 PM