Accepted Manuscript
Title: The effect of heat transfer on products of a thermally
coupled shell and tube reactor consisting of two processes:
Steam reforming of methane and oxidative coupling of
methane
Authors: Abbas Ghareghashi, Amir Sarrafi, Sattar Ghader
PII:
DOI:
Reference:
S0255-2701(18)30439-2
https://doi.org/10.1016/j.cep.2018.09.008
CEP 7377
To appear in:
Chemical Engineering and Processing
Received date:
Revised date:
Accepted date:
10-4-2018
15-8-2018
9-9-2018
Please cite this article as: Ghareghashi A, Sarrafi A, Ghader S, The effect
of heat transfer on products of a thermally coupled shell and tube reactor
consisting of two processes: Steam reforming of methane and oxidative coupling
of methane, Chemical Engineering and Processing - Process Intensification (2018),
https://doi.org/10.1016/j.cep.2018.09.008
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The effect of heat transfer on products of a thermally coupled shell and tube
reactor consisting of two processes: Steam Reforming of Methane and
Oxidative Coupling of Methane
Department of Chemical Engineering, College of Engineering, ShahidBahonar University of Kerman, Kerman, Iran
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Abbas Ghareghashia,b, Amir Sarrafia,b*, Sattar Ghadera,b
b
Iran National Science Foundation, 33, 5th St., North Kargar St., Tehran, Iran
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Graphical abstract
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Highlights (for review)
 An attractive idea of thermally coupled reactor model including the Steam Reforming of
Methane (shell side) and Oxidative Coupling of Methane (tube side) for the production of
hydrogen and ethylene is proposed.
 The performance of reactor was checked by varying several parameters such as steam to
methane ratio, temperature and nitrogen to methane ratio in SRM reactor, as well as
methane to oxygen ratio, nitrogen feed, contact time and temperature in OCM reactor with
changing of overall heat transfer coefficient.
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 A decrease in conversions of methane and oxygen, is shown by increasing overall heat
transfer coefficient in various CH4/O2 ratio in OCM process. An increase in overall heat
transfer coefficient in OCM process, causes a decrease in selectivity of C2 and the yield of
CO2.
 Increasing the contact time in OCM process has a great influence on the conversion of
methane in OCM that this effect is more at higher temperatures. In the heat transfer
coefficient of 0.014 (J.m-2.K-1), due to the increase in temperature of OCM reaction area,
as a result increasing the reactions rate, the conversion of oxygen reaches to 100% at the
reactor inlet. by increasing the overall heat transfer coefficient, the ethylene selectivity
decreases.
 In SRM process, an enhancement in the methane and oxygen conversions is shown by
increasing overall heat trasfer coefficient in various CH4/O2 ratio in OCM, where other
parameters are constant. Increasing of overall heat transfer causes to increase in hydrogen
and carbon monoxide yields.
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Abstract
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By increasing industrial development and social welfare growth, demand for industrial chemicals is increasing. Over the past few
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decades, there has been significant advances in meeting the chemical needs of the growing population, while the adverse effects on
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our environment have been minimized. In the present research on reactor structure modeling, a shell and tube reactor, including two
Steam Reforming of Methane (SRM) and Oxidative Coupling of Methane (OCM) processes, was investigated. In this reactor,
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catalysts of the OCM process were placed on the tube side and the catalysts of the SRM are in the shell side. Regarding that the
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reactions of the SRM process are endothermic and the reactions of the OCM process are exothermic, the heat transfer was carried
out through the wall of the pipe and the required heat for the SRM process was provided from the heat generated by the OCM
process. Investigating the effects of the total heat transfer coefficient on performance of each of the two reactors showed that with
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an increase in the total heat transfer coefficient, the C2 yield in the OCM reactor would decrease in high ratios of methane to oxygen
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and this ratio increased to 6 times. In addition, by increasing the overall heat transfer coefficient, the output hydrogen yield of the
SRM process increases up to 50 percent. In fact, increasing the overall heat transfer coefficient significantly affects the yield of the
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desired products including that of the ethylene at the output of the OCM reactor for up to 5%.
Keywords: Steam reforming of methane; Oxidative Coupling of Methane; Heat transfer; C2 yield; Hydrogen yield.
Introduction
The production of hydrogen and ethylene in the world has been increased dramatically over the past
few decades, which is mainly regarded as a result of the recent advances in their production processes. The
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process of ethylene production from natural gas has attracted many researchers in recent decades and research
in this area is still in progress. Despite the numerous studies in the ethylene production process, most
researchers have applied these processes in a laboratory scale and/or investigated the process theoretically.
However, due to low ethylene efficiency, energy requirements and high costs of separating the gas, they still
undergo economic development stages. In the past few decades, there has been high motivation among
industry professionals and researchers to enhance the yield of ethylene, fix operational problems and
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accordingly improve operation of the industrial units. The OCM process, which was one of the hottest topics
in scientific societies in the 1980s and 90s, has been re-considered by many researchers in recent years, as the
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only process in which natural gas is directly converted into more valuable hydrocarbons [1-8]. Since then,
research on this reaction could not attract the attention of researchers and research and development
departments of companies, due to low ethylene yields and, as a result, a low economic feasibility of this
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process [1-10]. However, due to the increasing dependence on natural gas and the increased use of methane
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as well as the ability to produce rock clay gas at competitive prices, the OCM process has been re-considered.
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This process not only allowed the consumption of the methane gas, but also the ability to convert methane to
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olefins in a reactor which is economically very attractive compared to other methods. This process was
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extensively investigated after the first paper on the OCM Process by keller and Bhasin was published [11].
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They discovered that when the reactor operates in a cyclic path, methane becomes a mixture of ethane,
ethylene, carbon dioxide and water vapor. In the mentioned study, a number of metal oxides were also
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examined for catalytic activity and their selectivity for ethylene [11]. The OCM process faces a number of
drawbacks. The most important of which in practical application is the release of high heat during the reaction
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due to rapid reactions and very high thermal effects [8,12,13]. That is why the formation of a hot spot has been
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observed in packed bed reactors, even in small diameters [12]. This problem can only be solved by improving
the design of the reactor, mainly because of the fact that the reaction heat, in addition to the kinetics of the
reaction, is also affected by the thermodynamics and fluid dynamics. One way is a shell and tube reactor that
can be used for coupling exothermic and endothermic reactions. In this structure, the released heat from the
exothermic reaction provides the required heat for the endothermic reaction. Various works on the coupling
of the exothermic and endothermic reactor systems have been reported [14-21]. Choudhary et al. [22]
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combined exothermic reactions with SRM process to provide the required energy for this endothermic process.
In this recommended reactor, H2/CO ratio of close to 2 and high methane conversions were obtained at high
space velocities with specific process conditions such as reaction temperature and CH4/O2 ratio in the
feedstock. Patel and Sunol [23] modeled a membrane reactor for SRM that in one channel of this reactor, the
methane reaction with oxygen provides the needed heat for the SRM process. In this structure, the produced
hydrogen of reaction is released through the membrane. Results showed that increasing of fuel concentration
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in the reactor inlet, increased the hydrogen yield for up to 2 times and feedstock conversion reached to 100%.
Moreovere, the hydrogen yield increased for up to 95% with increasing steam to methane ratio. Vakili et. al.
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[24] simulated an autothermal reactor for saving money and energy in production of hydrogen and benzene.
In this model, the released heat of DME process transmitted into dehydrogenated of cyclohexane process. This
case, not only prevented the formation of hot spot in the DME process, but also the required heat for an
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endothermic process was also provided. The results of the autothermal reactor compared to the conventional
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DME synthesis reactor showed an increasing trend in DME yield and decreasing in the hydrogen conversion.
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For a long period of time, the SRM process has been considered by many researchers around the world
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because of interest for applications such as fuel cells, conversion of natural gas to liquid fuels, etc. The main
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product of this process is hydrogen, which in the years ahead is expected to be used as fuel in hydrogen and
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fuel cell engines. Currently, only a small proportion of the produced hydrogen is used as a carrier of energy
and considered primarily as a chemical product in the industry. SRM is a reversible endothermic process that
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is carried out at 400 to 700 ° C and operating pressure of 0.5 to 3 MPa on a nickel catalyst based on alumina
[25]. Numerous studies are carried out on the modeling of SRM reactor and improving its performance.
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Modeling of industrial SRM reactor by Soliman et al. [26] is one of the best researches on reforming reactors.
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To ensure the high accuracy, they considered diffusion resistance in the modeling of catalyst particles. The
effects of various parameters were also examined on reactor performance. Results indicated a very good
agreement with various industrial reforming data. Xu and Froment [27] reported a one-dimensional, stable
and heterogeneous model for simulation of an industrial steam reformer. Elnashaie [28] and Rajesh et. al. [29]
has been widely discussed and examined the previous researches done in this area. Pantoleontos et. al. [30]
also developed a dynamic model that improves the one-dimensional, steady state and heterogeneos model
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proposed by Xu and Froment [27]. The SRM process is inefficient due to a number of limitations in this
process. One of these limitations is that the reactions of the SRM process are endothermic, which requires a
great deal of cost with high energy consumption to provide the needed heat of reactions. By providing the
required heat of the SRM process from an exothermic process, the main disadvantages of the steam process,
i.e., environmental pollution of methane burning and high energy costs, are overcome and money and energy
are conseqquently saved.
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In this paper, OCM and SRM processes are investigated in a shell and tube reactor. The purpose of
this project is use of heat resulting from the exothermic process to provide the required heat for endothermic
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process and thus saving energy and money. A one dimentional model is considered for this shell and tube
reactor and the effects of various parameters such as CH4/O2 ratio, N2 feed and inlet temperature in OCM
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Process description and mathematical formulation
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trasfer coefficient on valuable products yield are investigated.
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process and H2O/CH4 ratio, N2/CH4 ratio and inlet feed temperature in SRM process as well as total heat
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Fig. 1 shows the schematic of a shell and tube reactor consisting of SRM and OCM processes. In this
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configuration, the OCM process is in the tube side and the SRM is in the shell side. The reactants (methane,
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steam and nitrogen as diluents) are compressed up to 29 bar and heated to 793.15 K and then enter the SRM
reactor where reforming reaction occurs. As soon as the SRM process is fed by reactant gases, the mass
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transfer occurs on the surface of the catalyst particles. In addition, heat transfer is also occurred between the
walls and gases as well as between the gas and solid phases. SRM reactor is a fixed bed reactor which is
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packed with Ni/MgAl2O4 catalyst. The operational conditions of the SRM reactor are listed in Table 1. The
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second process (OCM) accures in the tube side. In this process, feed gas containing methane and oxygen enters
the reactor. Nitrogen is also used in OCM feed as diluting component. Table 2 presents the specifications of
OCM reactor. These specifications were used for reactor simulation. Given that the OCM is an exothermic
process and the SRM is an endotheric process, heat transfer through the wall of the tube to the shell side
removes the generated heat of OCM process from this section and prevents the creation of hot spot and also
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increases the life of catalysts and yield of the desired products. Also, the released heat of the OCM process
moves to the SRM process and provides the required heat of process.
Table 1. SRM reactor characteristics [27]
Value
Internal tube diameter
0.1016 m
External tube diameter
0.1322 m
Tube length
12
m
Heated tube length
11.12
m
dpe
0.0173
m
dpi
0.0084
m
H
0.010
m
𝜌𝑠
2355.2
kg/m3
Thickness of active layer
0.002
m
Feed temperature
793.15
K
29
bar
5.168
kmol/hr
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Parameter
CH4 mole flow
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3.358
0.056
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CO2/CH4 molar ratio
0.122
N2/CH4 molar ratio
0.164
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H2/CH4 molar ratio
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Feed inlet pressure
H2O/CH4 molar ratio
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Catalyst ring dimensions
Table 2. OCM Reactor parameters and constants [31]
Parameter
Dimension
Inner diameter (mm)
38.1
Pressure (kPa)
110
Length of catalyst bed (mm)
12000
Catalyst weight, mcat (g)
0.007 - 1.000
Flow rate (STP), υSTP (m3 s−1)
4  10-6 - 13  10-4
Catalyst size (mm)
0.25 - 0.35
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Catalyst density (kgm−3)
3600
Reactions kinetics
SRM model
The methane steam reforming components include CH4, H2O, CO, H2 and CO2. In the endothermic
CO+H2O
CO2 +H2
CO2 +4H2
0
H 298
206kJ mol
0
H 298
41kJ mol
0
H 298
165kJ mol
(1)
(2)
(3)
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CH4 +2H2O
CO+3H2
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CH4 +H2O
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side of this thermally coupled reactor the following reactions occur [27].
R3=
DEN
2
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(5)
p4H 2 pCO2
k3
2
[p
p
]
CH 4 H 2O
p3.5
K3
H2
DEN
(4)
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p p
k2
[pCO p H 2O - H 2 CO2 ]
pH2
K2
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DEN
2
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R2 =
p3H 2 pCO
k1
[p
p
]
CH 4 H 2O
p2.5
K1
H2
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R1 =
N
The reaction rates for the equations are as follows and the kinetic parameters are tabulated in Table 3 [27]:
(6)
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DEN=1+K CH4 pCH4 +K CO pCO +K H2 p H2 +
K H2O p H 2O
(7)
p H2
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where R1, R2 and R3 represent the rate equations of reactions (1), (2) and (3), respectively. rate coefficients of
reactions are shown as k1, k2 and k3, the equilibrium constants of reactions are K1, K2 and K3, the adsorption
coefficient constants of each components are K CH4 , K CO , K H2 and K H2 O and Pi is the partial pressure of the
component i. The kinetic parameters of the above reaction rates are given in Table 3.
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Table 2. Kinetic parameters of methane steam reforming rates [27]
ki
A (ki )exp[ Ei / (RT )]
for i 1,2,3
Ki
A (Ki )exp[
H i / (RT )]
for i
1,2,3
Kj
A (k j )exp[
H j / (RT )]
for j
CH 4 , H 2 O,CO , H 2
Activation energies (E)
Enthalpies change of reaction (
E1= 240.1
H
)
H 1 = 206.1
H CO = -70.65
H 2 = -41.15
H H 2 = -82.90
H 3 = 164.9
H CH 4 = -38.28
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E3= 243.9
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E2= 67.13
H H 2O = 88.68
Pre-exponential terms
A
A (k 2 ) 1.955 106 (kmol.bar 1 .kg 1 )
1
A (K 1 )
4.707 1012 (bar 2 )
2
TE
A (K 2 ) 1.142 10
M
1.02 1015 (kmol.bar 2 .kg 1 .h 1 )
D
A (k 3 )
U
1
4.225 1015 (kmol.bar 2 .kg 1 .h 1 )
N
A (k 1 )
A (K 3 ) 5.375 1010 (bar 2 )
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A (K CO ) 8.23 10 5 (bar 1 )
6.12 10
A (K CH 4 )
6.65 10 4 (bar 1 )
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A (K H 2 )
A (K H 2O ) 1.77 105 (bar 1 )
Kinetic model of OCM
In the tube side of this reactor an exothermic OCM process occurs with reactions that are reported by
Stansch et al. [31]. The following reactions are considered for OCM process:
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Step 1 : CH4 + 2O2  CO2 + 2H2O
(8)
Step 2 : 2CH4 + 0.5O2  C2 H6 + H2 O
(9)
(10)
Step 4 : CO + 0.5O2  CO2
(11)
Step 5 : C2 H6 + 0.5O2  C2 H4 + H2O
(12)
Step 6 : C2 H4 + 2O2  2CO + 2H2O
(13)
Step 7 : C2 H6  C2 H4 + H2
(14)
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Step 3 : CH4 + O2  CO + H2O + H2
Step 8 : C2 H4 + 2H2O  2CO + 4H2
(15)
Step 9 : CO + H2O  CO2 + H2
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(16)
Step 10 : CO2 + H2  CO + H2O
(17)
The reaction rates for each step are given below and the kinetic parameters of these reactions are tabulated in
 E a ,7 / RT
r8  k 0,8e
 E a ,8 / RT
2, j
/ RT
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PO2 )n2 PCH 4
PO2 ) n  K j ,co2 e
PC 2H 6
PCm2H8 6 PHn28O
 E a ,9 / RT
H ad ,o2, j / RT
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H ad ,o
(K 0,o2 e
(18)
H ad ,co
2,j
/ RT
(19)
PCO2 ]2
(20)
(21)
(22)
PCOm102 PHn102
(23)
PC O m9 PHn29O
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r9  k 0,9e
 E a,2 / RT
j  1,3  6
PCO2 ) 2
D
k 0,2e
r7  k 0,7e
n
H ad ,co 2, j / RT
(1  K j ,co2 e
[1  (K 0,o2 e
m
PC j PO2j )
TE
r2 
 E a , j / RT
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rj 
(k 0, j e
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Table 4:
 E a ,10 / RT
A
r10  k 0,10e
Step
Table 4. kinetic parameters of OCM reactions [19].
k 0, j
-1
-1
(mol g s pa
1
0.2  10-5
-(m+n)
)
E a, j
-1
(kJ mol )
48
1
K j ,co (pa )  ad,co
mj
nj
0.24
0.76
2
9
0.25  10-12
2
-1
(kJ mol )
-175
1
K j ,o (pa )  ad,o
2
2
-1
(kJ mol )
182
1.0
0.40
0.83  10-13
-186
3
0.52  10-6
68
0.57
0.85
0.36  10-13
-187
4
0.11  10-3
104
1.0
0.55
0.40  10-12
-168
5
0.17
157
0.95
0.37
0.45  10-12
-166
6
0.06
166
1.0
0.96
0.16  10-12
-211
7
1.2  107a
226
8
9.3  103
300
0.97
0
9
0.19  10-3
173
1.0
1.0
10
0.26  10-1
220
1.0
1.0
0.23  10-11
-124
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23.2
Units are mol s-1 m-3 pa-1
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a
2
Reactors modeling
SRM reactor model
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Gas phase
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The continuity equations of the SRM process are expressed as follows:
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(24)
(25)
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𝑑𝑋𝐶𝑂2 Ω𝜌𝐵 𝜂𝐶𝑂2 𝑟𝐶𝑂2
=
0
𝑑𝑧
𝐹𝐶𝑂
2
M
𝑑𝑋𝐶𝐻4 Ω𝜌𝐵 𝜂𝐶𝐻4 𝑟𝐶𝐻4
=
0
𝑑𝑧
𝐹𝐶𝐻
4
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where rCH 4 and rCO 2 are the CH4 disappearance rate and the rate of CH4 conversion into CO2 in steam
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reforming process, respectively, and the density of catalytic bed is shown by 𝜌𝐵 . The molar flow rate of CH4,
CO2 and N2 in feedstock is shown by Fi 0 . Xi, z and
are respectively conversion of components, reactor
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length and the reactor cross section. 𝜂𝐶𝐻4 and 𝜂𝐶𝑂2 are the effectiveness factor for CH4 disappearance and for
CO2 formation, respectively. The energy equation is defined by the following relation:
𝑑𝑇
1
𝑈
=
[𝜌𝐵 ∑(−Δ𝐻𝑖 )𝑟𝑖 𝜂𝑖 − 4
(𝑇 − 𝑇𝑟 )]
𝑑𝑧 𝑐𝑝 𝜌g 𝑢𝑠
𝑑𝑡𝑖
10
(26)
In this equation, T is the temperature of the gas. us, cp and ρg refer to superficial velocity, specific heat and
density of the gas phase, respectively. Δ𝐻𝑖 and 𝜂𝑖 are the enthalpy change and the effectiveness factor of each
reaction, respectively, and i represents the chemical components. ρB and ri are the catalyst density of catalytic
bed and and the reaction rate, respectively,. Three other variables are; the overall heat transfer coefficient (U),
the inner diameter of the reactor tube (dti) and the tube wall temperature (Tr). The following equation is used
f
g
u s2
(27)
gd p
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dpt
dz
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T
to momentum balance:
where the pressure drop is in pascal, dp is the equivalent diameter that is calculated by Brauer [32], 𝜀 is the
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bed porosity that is estimated by Reichelt and Blasz [33] and f is the friction factor that is defined as follows
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1 − 𝜀 1.74 + 150(1 − 𝜀)
𝜀
Re𝑑𝑝
(28)
M
𝑓=
N
(Ergun equation) [34]:
T 0 ; pt
pt 0
TE
x CO2 ;T
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x CH 4
D
The boundary conditions for the gas phase at z=0 are as follows:
The heat transfer coefficient can be formulated as follows:
1
𝑑𝑡𝑖
𝑑𝑡𝑒
1
=
ln ( ) +
𝑈 2𝜆𝑠𝑡
𝑑𝑡𝑖
𝛼𝑖
A
CC
(29)
Three other variables are; inner diameters (dti) and external diameters (dte) of the reactor tube, as well as
convective heat transfer coefficient (𝛼𝑖 ) that can be obtained as follows:
𝛼𝑖 =
8𝜆𝑒𝑟 𝛼𝑤
8𝜆𝑒𝑟 + 𝛼𝑤 𝑑𝑡𝑖
(30)
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where
0
𝛼𝑤 = 𝛼𝑤
+ 0.444RePr
𝜆g
𝑑𝑝
(31)
𝜆𝑒𝑟 = 𝜆0𝑒𝑟 + 0.14𝜆g RePr
(32)
0
In this equation, 𝜆𝑔 is the gas thermal conductivity. 𝛼𝑤
is obtained by:
8.694
(𝑑𝑡𝑖 )
0
4⁄ 𝜆𝑒𝑟
3
(33)
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T
0
𝛼𝑤
=
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R
where 𝜆0𝑒𝑟 is defined by Kunii and Smith [35].
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Solid phase
The concentration gradients of each components inside the catalyst particle is obtained as:
N
1 𝑑
𝑑𝑝𝑠,𝑖
/
(𝐷𝑒,𝑖 𝜉 2
) = 10−2 𝑅𝑇. 𝑅𝑝2 . 𝑟𝑖 . 𝑝𝑠 . 𝜌𝑠
2
𝜉 𝑑𝜉
𝑑𝜉
𝑖 = 𝐶𝐻4 , 𝐶𝑂2
M
A
(34)
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and the catalyst density, respectively.
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In this equation, 𝜉, Rp, R and 𝜌𝑠 are the particle radial position, the equivalent radius, the universal gas constant
ps ,CO2 ; ps ,CH 4 ; ps ,H 2 ; ps ,CO ; ps ,H 2O
T
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ps
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The boundary conditions for the solid phase are as follows:
𝑑𝑝𝑠,𝐶𝑂2 𝑑𝑝𝑠,𝐶𝐻4
=
=0
𝑑𝜉
𝑑𝜉
𝑝𝑠,𝐶𝐻4 = 𝑝𝑠,𝐶𝐻4
A
𝑝𝑠,𝐶𝑂2 = 𝑝𝐶𝑂2 ,
𝑎𝑡
𝜉=0
𝑎𝑡
(35)
𝜉=1
(36)
The partial pressure of the other components are obtained by:
ps ,CO
pCO
(
De ,CO2
De ,CO
)( pCO2
ps ,CO2 ) (
De ,CH 4
De ,CO
12
)( ps ,CH 4
pCH 4 )
(37)
ps ,H 2O
p H 2O
p s ,H 2
pH 2
(
(
De ,CO2
De ,CO2
De ,H 2O
De ,H 2
)( pCO2
)( pCO2
ps ,CO2 ) (
ps ,CO2 ) (
De ,CH 4
3De ,CH 4
De ,H 2O
De ,H 2
)( ps ,CH 4
)( ps ,CH 4
pCH 4 )
pCH 4 )
(38)
(39)
In this equation, the diffusivity of the component A ( Dei ) is obtained as:
𝜀𝑠
̅
𝐷
𝜏 𝐴
1
D mA
D A ri
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1
(40)
1
(41)
D kA ri
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𝐷𝑒𝑖 =
̅𝐴 = ∑ 𝐷𝐴 (𝑟𝑖 )𝑆(𝑟𝑖 )
𝐷
(42)
𝑖
U
𝑉g,𝑖
𝑉g,𝑖
=
∑𝑖 𝑉g,𝑖
𝑉g
(43)
N
𝑆(𝑟𝑖 ) =
A
In this equation, 𝜀𝑠 , DmA and DkA are the catalyst particle porosity, the molecular diffusivity and the Knudsen
M
diffusivity of component A, respectively. 𝜏, S(ri) and Vg are the tortuosity factor, the pores volume fraction
𝑉
(𝑟𝑗 )𝑜𝑏𝑠 = ∫ 𝑟𝑗 (𝜌𝑠 )
(44)
EP
0
𝑑𝑉
𝑉
TE
The actual rates are calculated as:
D
with radius ri and the voids volume in catalyst (1 gram), respectively.
CC
The effectiveness factor can be calculated as:
𝑉
𝑑𝑉
∫0 𝑟𝑖 (𝑃𝑠 )𝜌𝑠 𝑉
𝜂𝑖 =
𝑟𝑖 (𝑃𝑠 𝑠 )𝜌𝑠
A
(45)
OCM process (tube side)
The assumptions such as steady state, One dimensional plug flow reactor and ideal gas are considered for
OCM process.
13
For the gas phase, the mass and energy balance equations can be formulated as follows:
 Ft dyi
 av ct k gi  yis  yi   0
Ac dz
(46)
 Ft
 Di
dT
C pg
 av h f Ts  T  
U shell Tshell  T   0
Ac
dz
Ac
(47)
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In this equation, yi is the mole fraction of gas-phase. y i  y i ,in ,T  T in are the boundary conditions of bulk
phase at z=0.
av ct kgi  yi  yis   B ri  0
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The following equations show the mass and energy balance equations for the catalyst pellets:
i  1, 2, , N
(49)
A
N
U
av h f T  Ts    B ri  H i   0
(48)
M
In this equation, ys and Ts are the mole fractions on the catalyst surface and solid phase temperature,

 150 1   
 1.75

   Re

TE
2
dP  g u s  1  


dz  d p   3
(50)
EP

D
respectively. Momentum balance for the reactor (Ergun’s equation) is:
CC
The formation net rates of each component was given by ri 

ij
R j where Rj represent rate of reaction j
A
and  ij is the stoichiometric coefficient.
Numerical solution
The governing equations of model form a system of coupled equations comprising algebraic and
ordinary differential equations. After rewriting the model equations at steady-state conditions, a set of
algebraic equations is obtained. The reactor is then divided into 500 separate sections and the Runge-Kutta
14
method is used to solve the non-linear algebraic equations in each section. For more precise calculations, the
number of meshes used in the code is very important. According to eq. 46-48, the number of meshes was
evaluated from 50 to 600. For example, methane conversion rate and carbon dioxide output are shown in the
Figs. 2 and 3 in different mesh sizes. In these figures, h is the number of meshes in reactor length. These Figs.
are drawn to show that after a specific number of meshes, the increase in the number of meshes no variation
was seen in results, and the graphs are overlapping. Finally in the number of meshes of more than 500
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variations were made in differential. Therefore, the most suitable number of meshes for calculations is 500.
This imposes a problem about how best to define "h" in the order of convergence. We shall not pursue this
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but only remark that if a mesh is refined to improve the accuracy of the numerical solution, we must refine it
everywhere, not just in selected parts of the region. For a linear shape function, errors decrease as O(h).
Simulations were carried out in order to investigate the variations of the yield, conversion, temperature and
U
selectivity of each component in the reactor length. In this study, by keeping the input feed characteristics of
N
each process unchanged, changes in the output products and process conditions in the other processes are
M
A
examined.
D
Results and discussion
TE
Simulations were carried out for a thermally coupled reactor consisting of two processes; SRM process
that catalysts of this process are located on the shell side, and OCM process that reactions of this process take
EP
place on the tube side. Numerical simulation was utilized to compare results of shell and tube reactor
consisting of OCM and SRM at process conditions such as temperature, CH4/O2 ratio, H2O/CH4 ratio, N2/CH4
CC
ratio and overal heat transfer coefficient. These parameters are changed in OCM and SRM processes feedstock
A
and their effect on products of each of the reactors is studied.
Validation of OCM reactor model
Based on the experimental data reported by Stansch [31], the validation of the model was tested in the fixed
bed OCM reactor [31]. In this validation, each of the reactors was individually compared with experimental
data. Indeed, in validation, single reactors were compared, but in the proposed model, enhancements in two
15
reactors were evaluated. As can be seen from Figs. 4 and 5, the comparison between experimental data and
the results of modeling was conducted at different temperatures and input feed ratios of CH4/O2=12 and
CH4/O2=7. The results show that the highest methane conversion is achieved at a temperature of 1023 and
CH4/O2=7, which are 7.1 and 6.18, respectively. The relative error of 1.13% is calculated from the modeling
values. In these conditions, the selectivity and yield of ethylene from the experimental results are 53.7 and
3.8, and the results of modeling are 50.98 and 3.15. The maximum error from modeling in different
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temperature conditions and feedstock shows 23.17% for methane conversion. For ethylene yield and
selectivity, the relative errors are 14.05% and 19.3%, respectively. However, in higher feedstock ratios and
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lower temperatures, more agreement is obtained between the results of modeling and those of the laboratory
data. Errors could be due to ignoring reactions in gas phase that occurred before and after the catalyst bed in
the model calculations. In fact, gas phase reactions like thermal decomposition and oxidation are occurred in
U
these regions. Moreover, OCM reaction is a gas/solid heterogeneous reaction and therefore factors such as
N
Mass and heat transfer resistances as well as the axial and radial dispersion could affect the reactor
M
Validation of Steam Reforming of Methane reactor
A
performance and led to the error differences.
D
For the SRM reactor, the derived model from this study is compared with the industrial reactor data
TE
provided by Xu et al. [27] in terms of methane and steam conversion, temperature, pressure, and partial
EP
pressure of the components. As can be seen in Table 5, a conversion of 60.3 is obtained from the results of the
calculations in this process for methane, which in comparison to pilot plant data (=58), showed a relative error
CC
of 3.96%. Moreover, for partial pressure of hydrogen and carbon monoxide, the values of 6.05 and 0.2849 are
obtained in the calculations, which showed a relative error of 0.33% and 5.5% in comparison to the pilot plant
A
data, respectively. Generally, the results of modeling are in a good agreement with pilot plant data. The small
deviation between the results is due to the considered assumptions in model as well as mass and heat
resistances.
Table 5. Comparison between CR model results with pilot plant data for SRM reactor.
16
Parameter
Pilot plant data
Calculated
Error (%)
XCH4 (%)
58
60.3
3.96%
XCO2 (%)
33
31.5
4.5%
Pt
25.7
24.77
3.6%
T
1023
1070
4.6%
Partial pressure at Z=4 from the inlet
0.27
0.2849
5.5%
H2
6.07
6.05
0.33%
CH4
4
4.09
2.25%
CO2
1.62
1.44
11.11%
H2O
15.75
15.94
1.2%
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U
Simulation results
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CO
N
In this section, the effects of different parameters such as CH4/O2 ratio, inlet feed of nitrogen, contact time
A
and temperature in the feedstock of OCM process as well as H2O/CH4 ratio, N2/CH4 ratio and temperature in
M
the SRM process has been investigated on the feed conversion, yield and selectivity of the desired products of
D
thermally coupled reactor. The desired products of the OCM and SRM processes are C2 and hydrogen,
TE
respectively. One of the most important parameters to be considered in this shell and tube reactor system is
the effect of the overall heat transfer coefficient between the shell and tube, since the required heat for the
EP
SRM process is provided by OCM process. Finally, the best input conditions and the best process conditions
are obtained to increase the production of the desired products. Fig. 6(a) shows the change in methane
CC
conversion with total heat transfer coefficients in different ratios of CH4/O2 and the constant value of N2 in
A
the OCM reactor. Results show that the methane conversion decreased with increasing the total heat transfer
coefficient (U), which is more sensitive to U in lower coefficients. In this figure, it is also observed that with
increasing CH4/O2 ratio, methane conversion is reduced. However, changes in methane conversion with the
overall heat transfer coefficient, in different ratios of CH4/O2, shows the same trend. As shown in Fig. 6(a),
the more conversion of methane (16%) is obtained at higher oxygen concentrations (CH4/O2= 6). The
conversion of oxygen decreases with increasing U according to Fig. 6(b). In low quantities of U, the
17
conversion of oxygen reaches to 100%. An increase in the CH4/O2 ratio also results in a decrease in oxygen
conversion, which is due to a reduction in methane reaction rate. Indeed, given that the OCM reaction is
extremely exothermic, and in addition, this process is carried out in the tube side, if the removal of the heat
from the reaction area is not efficiently done, the reaction temperature of the reactor will increase sharply and
causing the desired products to be converted to carbon dioxide. As a result, the overall heat transfer coefficient
will have a significant effect on desired products of the OCM process. If the generated heat of OCM process
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is well discharged from the reaction area, the best performance and the highest yield can be expected from
this process. In the OCM process, the reaction rate increases with increasing temperature. In lower heat
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R
transfer coefficients, due to the heat exhaustion to a small amount from the reaction area, the temperature of
the reaction area increases, and subsequently the rate of OCM reactions increases. As reported by Tye et. al.
[36], the conversion of reactants, yield and selectivity of products increases with increasing temperature to
U
1093 K.
N
In Fig. 7, the yield and selectivity of C2 are shown as the desired product of OCM as a function of the overall
A
heat transfer coefficient in different ratios of CH4/O2. In the low CH4/O2 ratios (CH4/O2=6), due to the fact
M
that the temperature increases significantly, if the heat at low heat transfer coefficients does not release, the
D
desired product of C2 converted to carbon dioxide by thermal decomposition or water-gas shift reactions that
TE
are endothermic. This process continues as long as these endothermic reactions reduce the reaction
temperature and get away from critical point. As shown in Fig. 7(a), by increasing U, a decreasing trend is
EP
observed for the yield, but in a ratio of CH4/O2=6, due to the excessive increase in temperature, a different
mechanism is observed. In low amounts of U, due to the increase in catalytic temperature, the reaction of the
CC
thermal decomposition of C2 to carbon dioxide is carried out and its yield decreases. With increasing U, the
A
area temperature reaches to below the critical point and, given that the increase in temperature increases the
reaction rate, the ethylene yield increases. At high U values, due to the logical increase in temperature, a clear
trend is observed that increases the C2 yield by increasing the CH4/O2 ratio. Fig. 7(b) shows the C2 selectivity
by changing of U in various CH4/O2 ratios. As can be seen, a different trend is observed in the CH4/O2=6 ratio
due to the increase in temperature and reaching the hot spot. As can be seen in Figure 6, regarding the carbon
dioxide yield trend, the difference in the trend of C2 yield in low CH4/O2 ratios is justifiable. In the CH4/O2=6
18
ratio, significant increase in CO2 yield is observed which is due to the conversion of the produced C2 to the
carbon dioxide due to overheating of the reaction. This process continues as long as these endothermic
reactions result in a reduction in the reaction temperature and exit from the critical point. As shown in Fig. 8,
with increasing U, a decreasing trend is observed for the yield, but in a ratio of CH4/O2=6, due to the excessive
increase in temperature, a different trend is observed. In low amounts of U, due to the increase in area
temperature, the reaction of thermal decomposition of C2 to carbon dioxide is carried out and its yield
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decreases. With increasing U, the temperature of the reaction medium is reached to below the critical point
and regarding the fact that the increase in temperature, increases the reaction rate, the ethylene rate increases
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conseuently.
Figure 9 shows the temperature variations in the OCM (tube side) and SRM (shell side) processes by changing
the overall heat transfer coefficient (U) in different ratios of CH4/O2. As can be seen in Fig. 9(a), the U
U
coefficient has a significant effect on the OCM process temperature. Moreovere the increase of this factor
N
prevents the excessive increase of the reaction area temperature. However, with high heat transfer coefficients,
A
the heat is transmitted between the two processes in a way that each of them are in the best operating
M
conditions. As shown in Fig. 9(b), the temperature variation of the SRM process increases with increasing the
D
overal heat transfer coefficient. In these ranges of coefficients, the released heat of the OCM process is
TE
transferred to the SRM process, which increases the temperature of the process conseuently. In low CH4/O2
ratios, due to the significant increase in the temperature of the OCM, the SRM process temperature is also
EP
increased.
Figure 10. shows the variations of methane and steam conversions in SRM process with the total heat transfer
CC
coefficient in different ratios of H2O/CH4 in the feedstock of the SRM process, while the other parameters are
A
held constant. As seen in the figure, increase of the total heat transfer coefficient, increases the methane and
steam conversions. The heat transfer coefficient (U) has a significant effect on the SRM process. Given that
the SRM process is strongly endothermic, a heat source is required to provide the required heat of this process.
With increasing the U coefficient, the amount of heat transferred between the two processes increases and the
required heat of the SRM process is provided accordingly. As a result, the reforming reactions receive the
needed heat and these reactions are done with more intense. Therefore, the rate of conversion of methane and
19
steam increases at high heat transfer coefficients. This trend increases with increasing slope for up to heat
transfer coefficient of around 0.14, and then the conversion remains almost constant which is mainly due to
the fact that the amount of the required heat of the SRM process is provided at this heat transfer coefficient.
Hence further increase of this factor does not affect the SRM reactions. Since the increase of steam percentage
in the feedstock reduces the amount of steam conversion, by increasing the H2O/CH4 ratio, the methane
conversion increases while the steam conversion would decrease.
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In Fig. 11, the hydrogen and carbon monoxide yields in the SRM process is shown by varying the overall heat
transfer coefficient in different ratios of H2O/CH4 in the feedstock of this process. As depicted in the figure,
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yield of each of the components increases with increasing heat transfer coefficient, but the yield of hydrogen
increases with greater slope, mainly because increasing the amount of heat entering the reaction area increases
the rate of each of the reactions. However, in the water-gas shift reaction, as with increasing temperature some
U
of the produced carbon monoxide convert to hydrogen, much more amount of hydrogen is produced than
N
carbon monoxide. Figure 12 shows temperature variations in OCM and SRM processes (shell and tube side)
A
with total heat transfer coefficients in different ratios of H2O/CH4. As shown inthe Figure, by increasing the
M
H2O/CH4 ratio, the temperature of the SRM process decreases. Increasing the amount of steam in the
D
feedstock, increases the rate of the SRM reactions which in turn leads to more heat requirment for the
TE
endothermic SRM process and consequently a reduction in the process temperature is expected. Due to the
thermal relationship between the two processes, reducing the process temperature of the SRM processreduces
EP
the temperature of the OCM side.
In Fig. 13, variation of methane and oxygen conversion, as well as C2 selectivity in the OCM reactor with
CC
change of the reactor input temperature in various nitrogen feeds to OCM reactor are shown. The presence of
A
nitrogen in the feedstock as a diluent has a significant effect on the performance of the reactor. In fact, nitrogen
controls the temperature of the reactor by jamming the reactor temperature, and has a significant effect on
conversion of the reactants and the products selectivity. further distribution of nitrogen in the feedstock causes
a uniform distribution of temperature over the OCM process. By increasing the nitrogen in the feed, the
conversion of methane and oxygen decreases. In fact, with decreasing of the temperature due to the increase
in nitrogen content in the feedstock, the rate of OCM reactions decreased, resulting in a decrease in methane
20
and oxygen conversions. However, at temperatures higher than 1098 K, increase in conversion can be seen in
high percentages of nitrogen. As shown in Fig. 13(c), the selectivity of C2 decreases with increase of nitrogen
in the feedstock, and changes occur in this trend if the process temperature exceeds up to 1098 K. These
changes are due to the negative effect of the excessive increase of temperature on the C2 selectivity.
The effect of the inlet temperature to the SRM reactor on H2 selectivity and CO2 yield, as well as the outlet
temperature of SRM and OCM processes, by changing the input N2/CH4 ratio to the SRM reactor is shown in
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Fig. 14. As shown in Fig. 14(a), the hydrogen selectivity is reduced by increasing the inlet temperature of the
SRM reactor. This is because of rising the temperature result in increasing the rate of the SRM reactions and
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production of the products, but given that these reactions also produce significant amounts of CO2, the watergas shift reaction is accelerated, and in this reaction, the hydrogen becomes to CO and steam. Increasing the
ratio of N2/CH4 does not have much effect on hydrogen selectivity. By increasing the inlet temperature of the
U
SRM process, the yield of carbon dioxide increases. Although some of the produced CO at high temperatures
N
participates in the water-gas shift reaction and converts to CO and steam, but due to the high production of
A
this material, with increasing temperature, the yield increases. As shown in Fig. 14 (b), increasing the N2/CH4
M
ratio at the feedstock of the SRM process increases the CO2 yield which is due to the balanced distribution of
D
temperature as a result of an increase in nitrogen in the feedstock. This increase in the yield can be attributed
TE
to the reduction of the hydrogen production by reducing the amount of methane and steam in the feedstock
that in this case the water-gas shift reaction proceeds in the forward direction and leads to increase in CO2
EP
production. In Figs. 14 (c) and (d), the variation of the output temperature from each of the OCM and SRM
processes with the inlet temperature at different ratios of N2/CH4 of SRM is shown. As seen in these Figures,
CC
the increase in the input temperature of the SRM process leads to increase in the output temperature of the
A
process and consequently, in a constant heat transfer coefficient, the output temperature of the OCM process
is also increased. Increasing the ratio of N2/CH4 in feedstock will increase the output temperature of each of
the processes. Because by decreasing the amount of methane in the feedstock of the SRM reactor, the watergas shift reaction, which is an exothermic reaction, proceeds in the forward direction and leads to the increase
of the temperature of the SRM process and thereby increasing the temperature of the OCM process.
21
Fig. 15. shows the variation of methane and oxygen conversions, as well as C2 selectivity in OCM process,
by changing the contact time of OCM process, in different overal heat transfer coefficients. Increasing the
contact time shows a great influence on the conversion of methane which is more obvious at higher
temperatures. In fact, by decreasing the heat transfer coefficient, the produced heat of the OCM process goes
out slightly from the reaction area. As a result, the reaction temperature increases. furthermore,increasing the
temperature increases the rate of OCM reactions, and as a result increases the methane and oxygen
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conversions. In Fig. 15(b), it is observed that for the heat transfer coefficient of 0.014 (J.m-2.K-1), according
to the increase in temperature of OCM reaction area and consequently increasing the reaction rate, the
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conversion of the oxygen reaches to 100% at the reactor inlet. As a result, in the rest of the reactor, the OCM
reactions are not carried out. As shown in fig. 15(c), by increasing the overall heat transfer coefficient, the
ethylene selectivity decreases. In this figure, it is shown that by increasing the contact time, the selectivity
U
decreases in the high heat transfer coefficient. This is because of decreasing in the reaction rates and increasing
N
in the oxygen amounts of reaction area, the C2 oxidation, consequently, reduction in selectivity of C2.
A
Fig. 16 shows the variation of mole fraction and selectivity of each components in OCM reactor length. As
M
can be seen in Fig. 16(a), mole fraction of each product during the OCM process has an increasing trend. This
D
graph is drawn in a condition assuming that the feedstock ratios of the reactor and process conditions to be
TE
constant. Fig. 16(b) shows the mole fraction variations of methane and oxygen as reactants of OCM process.
As can be seen, the mole fraction variation of each of the reactants are justified by the rate equation of each
EP
of reactions. The selectivity of each components along the OCM reactor is shown in Fig. 16(c). As can be
seen, due to the fact that the methane and oxygen amount as reactants are high at the beginning of the reaction,
CC
OCM reactions have made significant development, but due to the decrease in the amounts of reactants, the
A
severity of the reactions is significantly reduced. As a result, at the beginning of the reaction, the products
selectivity is greatly increased and thereafter, slight changes are observed.
Fig. 17 shows the variation of consentration and yield of each components in SRM reactor length. As shown
in fig. 17(a) changes in methane and steam concentrations through the reactor length have a downward trend,
and hydrogen, carbon dioxide and carbon monoxide have an acsending trend. . Hydrogen concentration
increases with greater slope compared to other products, which is due to the hydrogen production in all SRM
22
reactions, while carbon dioxide is produced in two reactions and carbon monoxide in only one reaction. The
observed steep slope at the beginning of the reactor is due to the high concentrations of the reactants and more
reactions rate at the beginning of the process. The variation of the products’ yield in the SRM process is
depicted in Fig. 17(b). At the beginning of the reaction, given that the reactants have the highest
concentrations, the reaction rates are high at the beginning of the reactor. As a result, the yield of the products
at the beginning of the reactor increases with greater slope, but then, with decreasing reactants, a relatively
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moderate slope is observed.
In Figure 18, variation of temperature is shown in each of the OCM and SRM reactors length, in which other
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specifications such as feedstock of the reactors and process conditions assumed to be constant. In this Fig.,
the temperature of the SRM process is reduced at the beginning of the reactor due to the increase in the rate
of endothermic reactions. However, due to the heat absorption from the OCM process, the temperature
U
increases during this process, which is located in the reactor shell. The reduction of the observed temperature
N
of the OCM process, which is an exothermic process, is due to the heat absorption from this process by the
M
A
SRM process.
CONCLUSIONS
D
In this paper, a thermally coupled reactor consisting of two processes was simulated for Heat transfer between
TE
two processes and energy saving. The reactor consists of two separated sides for exothermic and endothermic
EP
reactions. The OCM reactions occur in the tube side of the reactor to provide the necessary heat, while the
endothermic steam reforming process occur in the shell side of the reactor. The effect of the overall heat
CC
transfer, feed ratio, contact time and inlet temperature of endothermic and exothermic streams on hydrogen
and ethylene yields as well as methane conversion was investigated. The new proposed configuration
A
represents some important improvements in comparison to conventional reactors as follows: (1) Reduces the
capital cost of the reactors; (2) Supplies the required heat for the endothermic process; (3) Increases the H2
production yield; and (4) Produces C2 as a valuable by-product. The results showed that by increasing the
overall heat transfer, C2 yield and carbon dioxide conversion decreased in the exothermic side. Moreover, H2
yield and CH4 conversion increased in the endothermic side as a result of the increase in heat transfer between
23
shell and tube. The results also indicate that OCM and SRM reaction in a shell and tube reactor is feasible and
beneficial.
Appendix A: The detailed equations of FDM
In this paper, equations are solved by fourth-order Runge-Kutta methods that are most widely used and are
derived in similar fashion. The general form of this approach is as follows:
U
Mass balance equation for OCM:
N
1
1
av A s ct k gi (( y ns  k 1 )  ( y n  k 1 ))
2
2
2

Ft
av A s ct k gi ( y ns  y n )
Ft
A
1
y n 1  y n  h (
6
TE
D
M
1
1
av A s ct k gi (( y ns  k 2 )  ( y n  k 2 )) a A c k (( y  k )  ( y  k ))
v s t gi
ns
3
n
3
2
2
2

)
Ft
Ft
Energy balance equation for OCM:
EP
 Ft
 Di
dT
C pg
 av h f Ts  T  
U shell Tshell  T   0
Ac
dz
Ac
dT av Ac hf T s T   D i


U shell T shell T 
dz
FC
FC
t pg
t pg
av Ac hf T ns T n 
CC
k 1  hf (z n , y n )  h (
FC
t pg
(A-1)
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IP
T
1
y n 1  y n  (k 1  2k 2  2k 3  k 4 )
6
k 1  hf (z n , y n )
1
1
k 2  hf (z n  h , y n  k 1 )
2
2
1
1
k 3  hf (z n  h , y n  k 2 )
2
2
k 4  hf (z n  h , y n  k 3 )

 Di
FC
t pg
U shell T n ,shell T n )
A
1
1


av Ac hf  (T ns  k 1 )  (T n  k 1 ) 
1
1
2
2


k 2  hf (z n  h , y n  k 1 )  h (
2
2
FC
t pg
 Di
1
1


U shell  (T n ,shell  k 1 )  (T n  k 1 ) )
Ft C pg
2
2


24
(A-2)
1
1


av Ac hf  (T ns  k 2 )  (T n  k 2 ) 
1
1
2
2


k 3  hf (z n  h , y n  k 2 )  h (
2
2
FC
t pg
 Di
1
1


U shell  (T n ,shell  k 2 )  (T n  k 2 ) )
Ft C pg
2
2


1


av Ac hf  (T ns  k 3 )  (T n  k 3 ) 
2


k 4  hf (z n  h , y n  k 3 )  h (
FC
t pg
 Di
IP
T
1
1


U shell  (T n ,shell  k 3 )  (T n  k 3 ) )
Ft C pg
2
2


As a result:
U
1
1


av Ac hf  (T ns  k 1 )  (T n  k 1 ) 
2
2


2(
FC
t pg
 Di
A
M

U shell  (T n ,shell
FC

t pg
1


av Ac hf  (T ns  k 3 )  (T n  k 3 ) 
1
1
2



 k 2 )  (T n  k 2 ) )  (
2
2
FC

t pg
 Di
D
 Di
N
1
1


U shell  (T n ,shell  k 1 )  (T n  k 1 ) ) 
FC
2
2


t pg
1
1


av Ac hf  (T ns  k 2 )  (T n  k 2 ) 
2
2


2(
FC
t pg
EP
TE
1
1


U shell  (T n ,shell  k 3 )  (T n  k 3 ) ))
FC
2
2


t pg
CC
The rest of the equations are written in the same way.
SYMBOLS
av
A
Ac
(A-3)
SC
R
a A h T T n   D i
1
y n 1  y n  h (( v c f ns

U shell T n ,shell T n ) 
6
FC
FC
t pg
t pg
Cross section area of tube (m2)
Specific surface area of catalyst pellet (m2.m-3)
cp
Specific heat (kJ.mol−1.K)
Ct
Total concentration (mol.m−3)
Cj
concentration of species j (mol.m−3)
25
tube diameter (m)
dp
equivalent diameter (m)
DmA
molecular diffusivity of component A
DkA
Knudsen diffusivity of component A
f
friction factor
Ft
Total molar rate (mol.s−1)
hf
Gas-catalyst heat transfer coefficient (W.m−2 .K −1)
∆Hi
enthalpy change of reaction (kJ.mol−1)
kgi
Mass transfer coefficient between gas and solid phase for component i (m.s-1)
ri
rate of formation of reaction i (mol.g−1.s-1)
R
universal gas constant
Rp
equivalent radius
T
temperature (K)
Tr
tube wall temperature (K)
Tshell
Temperature of coolant stream, in fixed-bed reactor (K)
us
superficial velocity (m.s−1)
U
Overall heat transfer coefficient (W.m−2. K-1)
Overall heat transfer coefficient between coolant and process streams (W.m−2. K−1)
Greek letters
ρs
ρB
CC
εs
convective heat transfer coefficient
catalyst bed porosity
A
𝛼𝑖
EP
Ushell
TE
D
M
A
N
U
SC
R
IP
T
dt
catalyst density
density of catalyst in the bed (g.m−3)
ρg
density of gas phase (kg.m−3)
αH
Hydrogen permeation rate constant (mol.m−1.s−1.Pa−0.5)
𝜂𝑖
effectiveness factor of each reactions
26
effectiveness factor for CH4 disappearance
𝜂𝐶𝑂2
effectiveness factor for CO2 formation
𝜆g
gas thermal conductivity
Ω
reactor cross section
𝜉
particle radial position
A
CC
EP
TE
D
M
A
N
U
SC
R
IP
T
𝜂𝐶𝐻4
27
References
[1] W. Hinsen, M. Baerns, Oxidative coupling of methane to C2 hydrocarbons in the presence of different
catalysts. Chem. Info. 14 (1983) 47.
[2] C.A. Jones, J.J. Leonard, J.A. Sofranko, Fuels for the future: remote gas conversion, Energy & fuels. 1
(1987) 12-16.
IP
T
[3] D.J. Driscoll, W. Martir, J.X. Wang, J.H. Lunsford, Formation of gas-phase methyl radicals over
magnesium oxide, J. Am. Chem. Soc. 107 (1985) 58-63.
SC
R
[4] J.H. Lunsford, The catalytic oxidative coupling of methane, Ang. Chem. Int. Ed. Engl. 34 (1995) 970-980.
[5] Z. Zhang, X.E. Verykios, M. Baerns, Effect of electronic properties of catalysts for the oxidative coupling
of methane on their selectivity and activity, Catal. Rev. 36 (1994) 507-556.
U
[6] J.A. Sofranko, J.J. Leonard, C.A. Jones, The oxidative conversion of methane to higher hydrocarbons. J.
N
Catal. 103 (1987) 302-310.
M
oxygenates, Catal. today. 4 (1989) 463-470.
A
[7] J. Kuo, C. Kresge, R. Palermo, Evaluation of direct methane conversion to higher hydrocarbons and
D
[8] L. Mleczko, M. Baern, Catalytic oxidative coupling of methane—reaction engineering aspects and process
TE
schemes, Fuel. Proc. Tech. 42 (1995) 217-248.
[9] Y. San Su, J.Y. Ying, W.H. Green, Upper bound on the yield for oxidative coupling of methane, J. Catal.
EP
218 (2003) 321-333.
375.
CC
[10] J.A. Labinger, Oxidative coupling of methane: An inherent limit to selectivity. Catal. let. 1 (1988) 371-
A
[11] G. Keller, M. Bhasin, Synthesis of ethylene via oxidative coupling of methane: I. Determination of active
catalysts. J. Catal. 73 (1982) 9-19.
[12] D. Wang, M. Rosynek, J. Lunsford, Oxidative coupling of methane over Mn/Na2WO4/MgO and related
catalysts, Preprints-American Chemical Society. Div. Petrol. Chem., 41 (1996) 135-137.
[13] F. Dautzenberg, J. Schlatter, J. Fox, J. Rostrup-Nielsen, L. Christiansen, Catalyst and reactor requirements
for the oxidative coupling of methane, Catal. tod. 13 (1992) 503-509.
28
[14] E. Lopez, V. Gepert, A. Gritsch, U. Nieken, G. Eigenberger, Ethanol steam reforming thermally coupled
with fuel combustion in a parallel plate reactor. Ind. & Eng. Chem. Res. 51 (2012) 4143-4151.
[15] T.P. Tiemersma, T. Kolkman, J.A.M. Kuipers, M. van Sint Annaland, A novel autothermal reactor
concept for thermal coupling of the exothermic oxidative coupling and endothermic steam reforming of
methane. Chem. Eng. J. 203 (2012) 223-230.
[16] N. Itoh, T.H. Wu, An adiabatic type of palladium membrane reactor for coupling endothermic and
IP
T
exothermic reactions. J. Mem. Sci. 124 (1997) 213-222.
[17] G. Kolios, J. Frauhammer, G. Eigenberger, Efficient reactor concepts for coupling of endothermic and
SC
R
exothermic reactions. Chem. Eng. Sci. 57 (2002) 1505-1510.
[18] M. van Sint Annaland, R.C. Nijssen, A novel reverse flow reactor coupling endothermic and exothermic
reactions: an experimental study. Chem. Eng. Sci. 57 (2002) 4967-4985.
N
endothermic reactions. Chem. eng. sci. 61 (2006) 459-472.
U
[19] R.C. Ramaswamy, P.A. Ramachandran, M.P. Duduković, Recuperative coupling of exothermic and
A
[20] M.S. Kulkarni, M.P. Duduković, A bidirectional fixed‐bed reactor for coupling of exothermic and
M
endothermic reactions. AIChE. J. 42 (1996) 2897-2910.
D
[21] R.C. Ramaswamy, P.A. Ramachandran, M.P. Duduković, Coupling exothermic and endothermic
TE
reactions in adiabatic reactors. Chem. Eng. Sci. 63 (2008) 1654-1667.
[22] V.R. Choudhary, A.M. Rajput, B. Prabhakar, NiO/CaO‐Catalyzed Formation of Syngas by Coupled
EP
Exothermic Oxidative Conversion and Endothermic CO2 and Steam Reforming of Methane. Angew. Chem.
Int. Ed. 33 (1994) 2104-2106.
CC
[23] K.S. Patel, A.K. Sunol, Modeling and simulation of methane steam reforming in a thermally coupled
A
membrane reactor. Int. J. Hydrogen Energy. 32 (2007) 2344-2358.
[24] R. Vakili, E. Pourazadi, P. Setoodeh, R. Eslamloueyan, M. R. Rahimpour, Direct dimethyl ether (DME)
synthesis through a thermally coupled heat exchanger reactor. Appl. Energy. 88 (2011) 1211-1223.
[25] Z. Chen, J.R. Grace, C.J. Lim, A. Li, Experimental studies of pure hydrogen production in a
commercialized fluidized-bed membrane reactor with SMR and ATR catalysts, Int. J. Hydrog. Energy, 32
(2007) 2359-2366.
29
[26] M. Soliman, S. El-Nashaie, A. Al-Ubaid, A. Adris, Simulation of steam reformers for methane, Chem.
Eng. Sci. 43 (1988) 1801-1806.
[27] J. Xu, G.F. Froment, Methane steam reforming: II. Diffusional limitations and reactor simulation, AIChE
J. 35 (1989) 97-103.
[28] S.S. Elnashaie, Modelling, simulation and optimization of industrial fixed bed catalytic reactors, CRC
Press, 1994.
performance using genetic algorithm, Ind. Eng. Chem. Res. 39 (2000) 706-717.
IP
T
[29] J. Rajesh, S.K. Gupta, G.t. Rangaiah, A.K. Ray, Multiobjective optimization of steam reformer
SC
R
[30] G. Pantoleontos, E.S. Kikkinides, M.C. Georgiadis, A heterogeneous dynamic model for the simulation
and optimisation of the steam methane reforming reactor, Int. J. Hydrog. Energy, 37 (2012) 16346-16358.
[31] Z. Stansch, L. Mleczko, M. Baerns, Comprehensive kinetics of oxidative coupling of methane over the
U
La2O3/CaO catalyst, Ind. Eng. Chem. Res. 36 (1997) 2568-2579.
N
[32] H. Brauer, Druckverlust in Füllkörpersäulen bei Einphasenströmung. Chem. Ing. Tech. 29 (1957) 785-
A
790.
M
[33] R. Wolfgang, E. Blaß, Strömungstechnische Untersuchungen an mit Raschig‐Ringen gefüllten
D
Füllkörperrohren und‐säulen. Teil I: Einphasen‐Gasströmung. Chem. Ing. Tech. 43 (1971) 949-956.
TE
[34] S. Ergun, Fluid flow through packed columns. Chem. Eng. Prog. 48 (1952) 89-94.
[35] D. Kunii, J. Smith, Heat transfer characteristics of porous rocks, AIChE J. 6 (1960) 71-78.
EP
[36] C.T. Tye, A.R. Mohamed, S. Bhatia, Modeling of catalytic reactor for oxidative coupling of methane
A
CC
using La 2 O 3/CaO catalyst, Chem. Eng. J. 87 (2002) 49-59.
30
M
A
N
U
SC
R
IP
T
Figures:
D
Figure 1. A schematic of a shell and tube reactor included OCM and SRM processes.
TE
4
A
CC
EP
CO2 yield (%)
3
2
1
0
0
0.1
0.2
Overal heat coefficient (U)
h=50
h=100
h=200
h=300
h=500
h=600
31
0.3
Fig. 2. The CO2 yield in OCM process, by changing the total heat transfer coefficient in different h space-size ratios of in the
feedstock of this process ((T in)SRM=793.15 K, (H2O/CH4)SRM=3.358, (N2/CH4)SRM=0.164, (N2 feed)OCM=0.337, (CH4/O2)OCM=12
(Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
OCM reactor
12
10
8
6
IP
T
CH4 conversion (%)
14
4
2
0
0.1
0.2
Overal Heat coeficient (U)
SC
R
0
h=100
h=200
h=300
h=500
h=600
U
h=50
0.3
N
Fig. 3. The conversion of (a) methane and (b) oxygene in oxidative coupling of methane reactor, by changing the total heat
A
transfer coefficient in the feedstock of this process ((T in)SRM=793.15 K, (H2O/CH4)SRM=3.358, (N2/CH4)SRM=0.164, (N2
10
OCM reactor
EP
CH4 conversion (%)
12
TE
D
M
feed)OCM=0.337, (CH4/O2)OCM=12 (Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
8
A
CC
6
4
2
0
1020
1030
1040
1050
1060
1070
1080
Temperature (K)
Simulated
Experimental data
(a)
32
1090
1100
1110
OCM reactor
80
C2 selectivity (%)
70
60
50
40
30
20
10
0
1020
1030
1040
1050
1060
1070
1080
1090
1100
1110
Simulated
IP
T
Temperature (K)
Experimental data
SC
R
(b)
OCM reactor
8
U
6
5
N
4
3
2
A
C2 Yield (%)
7
0
1020
1030
M
1
1040
1050
1060
1070
1080
1090
1100
1110
Temperature (K)
Experimental data
TE
D
Simulated
(c)
Figure 4. Comparison between experimental and simulated data of OCM reactor (a) CH4 conversion (b) C2 selectivity (c) C2
A
CC
EP
yield (CH4 mole fraction=0.612, O2 mole fraction=0.051, N2 mole fraction=0.337).
33
OCM reactor
CH4 Conversion (%)
16
14
12
10
8
6
4
2
0
1020
1030
1040
1050
1060
1070
1080
1090
1100
1110
Simulated
IP
T
Temperature (K)
Experimental data
SC
R
(a)
OCM reactor
80
60
U
50
N
40
30
20
A
C2 selectivity (%)
70
10
1030
1040
1050
1060
M
0
1020
1070
1080
1090
1100
1110
1090
1100
1110
Temperature (K)
Experimental data
(b)
OCM reactor
EP
12
TE
D
Simulated
A
CC
C2 Yield (%)
10
8
6
4
2
0
1020
1030
1040
1050
1060
1070
1080
Temperature (K)
Simulated
Experimental data
(c)
34
Figure 5. Comparison between experimental and simulated data of OCM reactor (a) CH4 conversion (b) C2 selectivity (c) C2
yield (CH4 mole fraction=0.699, O2 mole fraction=0.095, N2 mole fraction=0.206).
20
16
12
8
4
0
0.1
0.2
Overal Heat coeficient (U)
CH4/O2=6
CH4/O2=8
CH4/O2=12
(a)
OCM reactor
0.0
0.1
A
N
U
100
80
60
40
20
0
0.2
0.3
Overal heat coefficient (U)
CH4/O2=8
CH4/O2=12
(b)
TE
D
CH4/O2=6
M
Oxygen conversion (%)
0.3
IP
T
0.0
SC
R
CH4 conversion (%)
OCM reactor
Fig. 6. The conversion of (a) methane and (b) oxygene in oxidative coupling of methane reactor, by changing the total heat
EP
transfer coefficient in different ratios of CH4/O2 in the feedstock of this reactor ((Tin)SRM=793.15 K, (H2O/CH4)SRM=3.358,
A
CC
(N2/CH4)SRM=0.164, (N2 feed)OCM=0.337, (Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
35
C2 Yield (%)
OCM reactor
6.0
4.0
2.0
0.0
0.0
0.1
0.2
0.3
Overal Heat coeficient (U)
CH4/O2=8
CH4/O2=12
IP
T
CH4/O2=6
(a)
SC
R
80
60
40
20
0
0.0
U
C2 selectivity (%)
OCM reactor
0.1
0.2
0.3
N
Overal heat coefficient (U)
CH4/O2=8
A
CH4/O2=6
CH4/O2=12
M
(b)
D
Fig. 7. The C2 (a)yield and (b) selectivity in OCM process, by changing the total heat transfer coefficient in different ratios of
CH4/O2 in the feedstock of this process ((T in)SRM=793.15 K, (H2O/CH4)SRM=3.358, (N2/CH4)SRM=0.164, (N2 feed)OCM=0.337,
A
CC
EP
TE
(Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
36
OCM reactor
CO2 yield (%)
8
6
4
2
0
0.0
0.1
0.2
0.3
Overal heat coefficient (U)
CH4/O2=8
CH4/O2=12
IP
T
CH4/O2=6
Fig. 8. The CO2 yield in OCM process, by changing the total heat transfer coefficient in different ratios of CH4/O2 in the feedstock
A
CC
EP
TE
D
M
A
N
U
contact time=3.75 kg.s.m-3)
SC
R
of this process ((Tin)SRM=793.15 K, (H2O/CH4)SRM=3.358, (N2/CH4)SRM=0.164, (N2 feed)OCM=0.337, (Tin)OCM=1023 K, OCM
37
OCM reactor
Temperature (K)
1600
1400
1200
1000
800
0
0.1
0.2
0.3
Overal heat coefficient (U)
CH4/O2=8
CH4/O2=12
IP
T
CH4/O2=6
(a)
SC
R
900
850
800
750
0
U
Temperature (K)
SRM reactor
0.1
0.2
0.3
N
Overal heat coefficient (U)
CH4/O2=8
CH4/O2=12
M
A
CH4/O2=6
(b)
D
Fig. 9. Temperature variation in (a) OCM and (b) SRM processes (tube side), by changing the total heat transfer coefficient in
different ratios of CH4/O2 in the feedstock of this process ((Tin)SRM=793.15 K, (H2O/CH4)SRM=3.358, (N2/CH4)SRM=0.164, (N2
A
CC
EP
TE
feed)OCM=0.337, (Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
38
CH4 conversion (%)
SRM reactor
25
20
15
10
5
0
0.1
0.2
0.3
Overal heat transfer (%)
H2O/CH4=2
H2O/CH4=3
H2O/CH4=4
H2O/CH4=5
IP
T
(a)
0
0.1
0.2
H2O/CH4=2
H2O/CH4=3
H2O/CH4=5
A
H2O/CH4=4
0.3
U
Overal heat transfer (U)
SC
R
14
12
10
8
6
4
N
H2O conversion (%)
SRM reactor
M
(b)
Fig. 10. The conversion of (a) methane and (b) steam in SRM process, by changing the total heat transfer coefficient in different
D
ratios of H2O/CH4 in the feedstock of this process ((Tin)SRM=793.15 K, (N2/CH4)SRM=0.164, (CH4/O2)OCM=3.358, (N2
A
CC
EP
TE
feed)OCM=0.337, (Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
39
SRM reactor
50
H2 yield (%)
40
30
20
10
0
0.1
0.2
0.3
H2O/CH4=2
H2O/CH4=3
H2O/CH4=4
SRM reactor
U
4
N
3
2
A
CO yield (%)
H2O/CH4=5
SC
R
(a)
IP
T
Overal heat transfer (U)
M
1
0
0
0.1
0.2
0.3
EP
TE
H2O/CH4=2
D
Overal heat transfer (U)
H2O/CH4=3
H2O/CH4=4
H2O/CH4=5
(b)
Fig. 11. The yield of (a) hydrogen and (b) CO in SRM process, by changing the total heat transfer coefficient in different ratios of
(Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
A
CC
H2O/CH4 in the feedstock of this process ((Tin)SRM=793.15 K, (N2/CH4)SRM=0.164, (CH4/O2)OCM=3.358, (N2 feed)OCM=0.337,
40
OCM reactor
1200
1100
1000
900
0
0.1
0.2
0.3
Overal heat transfer (U)
H2O/CH4=3
H2O/CH4=4
SRM reactor
U
880
N
840
760
0
0.1
A
800
M
SRM temperature (K)
(a)
920
H2O/CH4=5
SC
R
H2O/CH4=2
IP
T
OCM temperature (K)
1300
0.2
0.3
Overal heat transfer (U)
H2O/CH4=3
H2O/CH4=4
H2O/CH4=5
(b)
TE
D
H2O/CH4=2
Fig. 12. Temperature variation (a) OCM (tube side) and (b) SRM (shell side) processes, by changing the total heat transfer
EP
coefficient in different ratios of H2O/CH4 in the feedstock of SRM process ((Tin)SRM=793.15 K, (N2/CH4)SRM=0.164,
A
CC
(CH4/O2)OCM=3.358, (N2 feed)OCM=0.337, (Tin)OCM=1023 K, OCM contact time=3.75 kg.s.m-3)
41
CH4 conversion (%)
OCM temperature
10
5
0
950
1000
1050
1100
1150
N2 feed =0.01
N2 feed =0.4
N2 feed =0.2
N2 feed =0.6
SC
R
OCM reactor
100
50
0
1000
1050
N
950
U
O2 conversion (%)
(a)
IP
T
OCM inlet temperature (K)
1100
1150
A
OCM inlet temperature (K)
N2 feed =0.2
N2 feed =0.6
M
N2 feed =0.01
N2 feed =0.4
(b)
D
OCM reactor
50
40
TE
60
EP
C2 selectivity (%)
70
30
20
A
CC
950
1000
1050
1100
1150
OCM inlet temperature (K)
N2 feed =0.01
N2 feed =0.4
N2 feed =0.2
N2 feed =0.6
(c)
Fig. 13. Variation of (a) methane and (b) oxygen conversions, as well as (c) ethylene selectivity in OCM processes,jn by
changing the inlet temperature of OCM process, in different percents of N2 in the feedstock of this process ((Tin)SRM=793.15 K,
(N2/CH4)SRM=0.164, (H2O/CH4)SRM=5.168, (CH4/O2)OCM=3.358, (Tin)OCM=1023 K, U=0.14 J.m-2.K-1, OCM contact time=3.75
kg.s.m-3)
42
H2 selectivity (%)
SRM reactor
260
240
220
200
700
800
900
1000
SRM inlet temperature (K)
N2/CH4=0.01
N2/CH4=0.5
N2/CH4=1
IP
T
(a)
700
SC
R
60
55
50
45
40
35
U
CO2 yield (%)
SRM reactor
800
900
N
SRM inlet temperature (%)
N2/CH4=0.5
M
A
N2/CH4=0.01
A
CC
EP
TE
D
(b)
43
N2/CH4=1
1000
950
900
850
800
700
800
900
1000
SRM inlet temperature (K)
N2/CH4=0.01
N2/CH4=0.5
N2/CH4=1
IP
T
SRM outlet temperatuere (K)
SRM reactor
(c)
SC
R
1100
1050
1000
900
850
700
750
800
850
U
950
900
N
OCM temperature (K)
OCM reactor (%)
950
1000
A
SRM inlet temperature (K)
N2/CH4=0.5
N2/CH4=1
M
N2/CH4=0.01
(d)
D
Fig. 14. Variation of (a) hydrogen conversion, (b) CO2 yield, as well as output temperature of (c) SRM and (d) OCM processes,
TE
by changing the inlet temperature of SRM process, in different ratios of N2/CH4 in the feedstock of this process ((Tin)SRM=793.15
kg.s.m-3)
A
CC
EP
K, (H2O/CH4)SRM=5.168, (CH4/O2)OCM=3.358, (N2 feed)OCM=0.337 ,(Tin)OCM=1023 K, U=0.14 J.m-2.K-1, OCM contact time=3.75
44
CH4 conversion (%)
10
OCM reactor
5
0
0
10
20
30
40
50
60
70
80
Contact time (mcat/vstp, kg.s.m-3)
IP
T
Overal heat coefficient (U)=0.014 J.m-2.K-1
Overal heat coefficient (U)=0.14 J.m-2.K-1
Overal heat coefficient (U)=1.4 J.m-2.K-1
100
OCM reactor
50
0
20
40
60
80
U
0
SC
R
O2 conversion (%)
(a)
N
Contact time (mcat/vstp, kg.s.m-3)
A
Overal heat coefficient (U)=0.014 J.m-2.K-1
Overal heat coefficient (U)=0.14 J.m-2.K-1
Overal heat coefficient (U)=1.4 J.m-2.K-1
M
60
40
30
20
10
EP
0
20
30
40
50
60
70
80
Contact time (mcat/vstp, kg.s.m-3)
Overal heat coefficient (U)=0.014 J.m-2.K-1
Overal heat coefficient (U)=0.14 J.m-2.K-1
Overal heat coefficient (U)=1.4 J.m-2.K-1
(c)
A
CC
OCM reactor
D
50
TE
C2 selectivity (%)
(b)
Fig. 15. Variation of (a) methane and (b) oxygen conversion, as well as (c) C2 selectivity in OCM, by changing the contact time
of OCM process, in different overal heat transfer coefficients ((Tin)SRM=793.15 K, (H2O/CH4)SRM=5.168, (N2/CH4)SRM=0.164,
(CH4/O2)OCM=3.358, (N2 feed)OCM=0.337 ,(Tin)OCM=1023 K)
45
Mole flow (mol/s)
0.004
OCM reactor
0.003
0.002
0.001
0
0
0.2
H2O
H2
0.4
0.6
0.8
1
Dimensionless reactor length
CO
CO2
C2H6
C2H4
0.009
OCM reactor
0.006
0.096
0.003
0.094
0
0
0.2
0.4
0.6
0.8
A
(b)
TE
D
M
OCM reactor
Selectivity (%)
O2
N
CH4
1
U
Dimensionless reactor length
70
60
50
40
30
20
10
0
SC
R
0.098
IP
T
0.1
CH4 mole flow (mol/s)
O2 mole flow (mol/s)
(a)
0
0.2
0.6
0.8
1
Dimensionless reactor length
CO
CO2
C2H6
C2H4
(c)
CC
EP
H2
0.4
Fig. 16. Variation of (a,b) mole fraction and (c) selectivity of each components in OCM reactor length ((Tin)SRM=793.15 K,
A
(H2O/CH4)SRM=5.168, (N2/CH4)SRM=0.164, (CH4/O2)OCM=3.358, (N2 feed)OCM=0.337 ,(Tin)OCM=1023 K, U=0.14 J.m-2.K-1, OCM
contact time=3.75 kg.s.m-3)
46
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
CH4
H2O
CO
H2
CO2
(a)
SRM reactor
SC
R
50
Yield (%)
1
Dimensionless reactor length
IP
T
Consentrasion (mol/lit)
SRM reactor
40
30
20
10
0
0.2
U
0
0.4
0.6
0.8
1
CO
CO2
A
H2
N
Dimensionless reactor Length
H2O
M
(b)
D
Fig. 17. Variation of (a) consentration and (b) yield of each components in SRM reactor length ((Tin)SRM=793.15 K,
(H2O/CH4)SRM=5.168, (N2/CH4)SRM=0.164, (CH4/O2)OCM=3.358, (N2 feed)OCM=0.337 ,(Tin)OCM=1023 K, U=0.14 J.m-2.K-1, OCM
A
CC
EP
TE
contact time=3.75 kg.s.m-3)
47
Temperature (K)
1050
1000
950
900
850
800
750
0
0.2
0.4
0.6
0.8
1
Dimensionless reactor Length
SRM
OCM
IP
T
Fig. 18. Variation of temperature in each of OCM and SRM reactors length ((Tin)SRM=793.15 K, (H2O/CH4)SRM=5.168,
(N2/CH4)SRM=0.164, (CH4/O2)OCM=3.358, (N2 feed)OCM=0.337 ,(Tin)OCM=1023 K, U=0.14 J.m-2.K-1, OCM contact time=3.75
A
CC
EP
TE
D
M
A
N
U
SC
R
kg.s.m-3)
48