Modeling and simulation of methanation catalytic reactor in ammonia unit

Abstract

In ammonia synthesis units the amount of CO and CO2 shall be minimized as they are considered as poisons for the related catalysts. To achieve this, methanation catalytic reactor is incorporated after the high and low temperature shift reactor to decrease the concentration of carbon monoxide and carbon dioxide to an allowable limit. The nature of the reactions taken place in methanation catalytic reactor is similar to that of steam reforming one. So the reaction kinetic is somehow known but the important point is the approach incorporated to measure the effectiveness factor of catalytic reactions. In this paper the influence coefficient has been measured using Orthogonal Collocation approach. The system equation set has been solved using the general available approaches.The results taken from simulation show a good compatibility with the available industrial data in Khorasan petrochemical complex.

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IISSN 1337-7027
Available online at www.vurup.sk/pc
Petroleum & Coal 49 (1), 46-53, 2007
MODELING AND SIMULATION OF METHANATION
CATALYTIC REACTOR IN AMMONIA UNIT
Kayvan Khorsand*, Mehdi A. Marvast, Narges Pooladian, Madjid
Kakavand, *corresponding author
Research Institute of Petroleum Industry(RIPI)
Tehran, Iran, P.O. Box: 18745-4163
Received December 4, 2006; accepted June 25 , 2007
Abstract
In ammonia synthesis units the amount of CO and CO2 shall be minimized as they are considered as
poisons for the related catalysts. To achieve this, methanation catalytic reactor is incorporated after the
high and low temperature shift reactor to decrease the concentration of carbon monoxide and carbon
dioxide to an allowable limit.
The nature of the reactions taken place in methanation catalytic reactor is similar to that of steam
reforming one. So the reaction kinetic is somehow known but the important point is the approach
incorporated to measure the effectiveness factor of catalytic reactions. In this paper the influence
coefficient has been measured using Orthogonal Collocation approach. The system equation set has
been solved using the general available approaches.
The results taken from simulation show a good compatibility with the available industrial data in
Khorasan petrochemical complex.
Keywords: Methanation, Modeling, Simulation, Catalytic Reactor, Effectiveness factor
1. Introduction
Carbon monoxide and carbon dioxide are considered as catalyst poisons in lots of
hydrogenation processes such as ammonia production. So in ammonia production units as
well as other hydrogen production units, after adsorption of carbon dioxide, the amount of the
residual carbon oxides shall be decreased as much as possible. In an ammonia unit,
methanation is the last step of purgation. In this section the concentration of carbon monoxide
and carbon dioxide is 0.1 to 0.5 percent, which will be purged using catalytic reaction with
hydrogen. The concentration of residual carbon oxides in outgoing gas of the methanation
reactor will be less that 5 ppm .
Methanation is a catalytic reaction from kinetic point of view and adiabatic considering its
thermal characteristics. So in simulation of this reactor, the mathematical model includes the
kinetics of the reactions carried out on the catalyst. Also considering penetration of reactor
gases to internal surface of the catalyst, the mass transfer issues will be very important. In
this paper, kinetic and mass transfer relations have been incorporated in simulation to yield
proper results.
2. Modeling of Methanation Reactor
2. 1 Reaction Kinetics [1,2,3,4]
The following assumptions have been considered in modeling of the reactor:
1. Gas mixture is considered ideal
2. System is in steady state condition

3. Relations of mass transfer, temperature, and momentum are assumed to be one-
dimensional. Also distribution of concentration, heat and pressure is uniform in each cross
section of the reactor.
4. Axial mass and heat transfer are assumed to be negligible.
Researches show that among the 11 equations outlined in table 1, the following thee primary
equations play substantial role:
+↔+
242
3CO H CH H O (1)
+↔+
222
CO H O CO H (2)
+↔+
22 42
42CO H CH H O (3)
In fact the above equations are the reverse of steam reforming reactions.
Table-1: Probable reactions in methanation reactor [5]
298
ΔH,kg/mol
Reactions No -206.1
OHCHHCO 242
3
+
↔
+
1 41.15
222 HCOOHCO
+
↔
+
2 -165
OHCHHCO 2422 24
+
↔
+
3
-247.3
224 22 HCOCOCH
+
+
↔
+
4 -330
OHCOCOCH 224 243
+
+
↔
+
5 -74.82
24 2HCCH
+
↔
6
-173.3
2
2COCCO
+
↔
7 131.3
OHCHCO 22
+
↔
+
8 90.13
OHCHCO 222 2
+
↔
+
9
187.6
OHCCOCH 24 232
+
↔
+
10 15.3
OHCCOCH 224 22
+
↔
+
11
Considering the Xu & Froment kinetic [5], reaction rate equations 1 to 3 are as follow:
For reaction 1: ⎛⎞
=−
⎜⎟
⎜⎟
⎝⎠
2
24
2
32
1
12.5 1
/
()
HCO
HO CH
H
PP
k
rPP DEN
PK
For reaction 2: ⎛⎞
=−
⎜⎟
⎝⎠
22
2
2
2
2
22
/
()
HCO
CO H o
H
PP
k
rPP DEN
PK
For reaction 3:
()
⎡⎤
=−
⎢⎥
⎢⎥
⎣⎦
22
42
2
4
2
3
32
3.5 12
HCO
CH H O
H
PP
k
rPP
KK
PDEN
In which
2
/1 224422 PHPKPKPKPKDEN OHOHCHCHHHCOCO
+
+
+
+=
For steam reforming: ⎪
⎩
⎪
⎨
⎧
+=
+=
−=
31
32
21
4
2
rrr
rrr
rrr
CH
CO
CO
(4)
For methanation:
()
()
⎪
⎩
⎪
⎨
⎧
+−=
′
+−=
′
−=
′
31
32
12
4
2
rrr
rrr
rrr
CH
CO
CO
(5)
Rate constants of the above equations are defined as functions of temperature [5,6]:
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
47

hkg
kPakmol
T
k
hkgkPakmol
T
k
hkg
kPakmol
T
k
.
.0.29336
exp10290.2
.
.3.8074
exp10390.4
.
.0.28879
exp10490.9
5.0
16
3
1
4
2
5.0
16
1
⎟
⎠
⎞
⎜
⎝
⎛−×=
⎟
⎠
⎞
⎜
⎝
⎛−×=
⎟
⎠
⎞
⎜
⎝
⎛−×=
− (6)
CO
K, 4
CH
K, 2
H
KAnd OH
K2 are the constants which related to surface adsorption in
equilibrium that are functions of temperature. The functions types are given in the
references[6].
The equilibrium constants of reactions 1-3 are defined as below:
2
213
2
2
1
;
063.4
0.4400
exp
;11.30
0.26830
exp76.10266
kPaKKK
T
K
kPa
T
K
=
⎟
⎠
⎞
⎜
⎝
⎛−=
⎟
⎠
⎞
⎜
⎝
⎛+−×=
(7)
2. 2 Mass, Energy and Momentum Balance Equations [5,6,7]
Before modeling of the reactor, equilibrium constraints on considered system have to be
considered. For instance the process is exothermal and increase of temperature will reduce
the conversion rate.
Considering that two of the three main reactions are independent from each other, by
definition of two corresponding variables, by means of the conversion rate, it is possible to
determine all the concentration variables.
0,4
40,4
4CH
CHCH
CH F
FF
X−
= (8)
0,4
0,22
2CH
COCO
CO F
FF
X−
= (9)
With the above definitions, it will be possible to drive all the model’s flow rates in terms of
2
CO
X and 4
CH
X. For example the molar flow rate of methane 4
CH
Fwill be as follows:
)1( 40,44 CHCHCH XFF −= (10)
Hence, partial pressures are defined based on the components molar flow rates:
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
+−
=
4
0,
40,
240,40,2
22
(
CHCHtotal
COCHCHOH
tOH XFF
XXFF
PP (11)
(
)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
−
=
40,40,
40,4
42
1
CHCHtotal
CHCH
tCH XFF
XF
PP (12)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
++
=
40,40,
240,40,2
22
)3(
CHCHtotal
COCHCHH
tH XFF
XXFF
PP (13)
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
48

⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
+
=
40,40,
240,4 2
)3(
CHCHtotal
COCHCH
tCO XFF
XXF
PP (14)
Substituting of the above partial pressure equations of feed and product in reaction rate
equations will cause the rate equations to be in terms of conversion rate variables. Now it will
be possible to derive the balance equations.
Mass balance equations for 4
CH and 2
CO are as follow:
)( 331
4rr
d
dF
B
Z
CH
ηηπρ
++= (15)
)( 33
22
2rr
d
dF
B
Z
CO
ηηπρ
++−= (16)
In which
z
is the length of the reactor (m),
π
is the cross section of the reactor ( 2
m
), B
ρ
is
the catalyst mass density ( 3
m
kg ) and 321 ,,
η
η
η
are Effectiveness Factors of the reaction.
321 ,, rrr are reaction rates ( rcatalyst.h kg kgmol ) in absence of penetration constraints.
Substitution of molar flow with conversion variables yields:
0,4
4)( 3311
CH
B
Z
CH Frr
d
dX
ηηπρ
+−
= (17)
0,4
2)( 3322
CH
B
Z
CO Frr
d
dX
ηηπρ
+−
= (18)
Energy balance equation, with considering that the reactor is adiabatic, simultaneously solved
with equations 17 and 18:
()
[]
333222111 )()()(
1
ηηηρ
ρ
ρ
rHrHrH
uCdz
dT B
sg g
Δ−+Δ−+Δ−= (19)
In which g
ρ
is the density of gas mixture and s
u is its artificial speed inside reactor.
Momentum balance equation, which yields pressure drop along the reactor, is as follows:
dp
u
f
dz
dP sg
t
2
ρ
−= (20)
In which dp is the equivalent diameter of the catalyst particle. To determine friction coefficient
f, experimental and semi-experimental relations are used.
The artificial speed can be determined by means of continuity equation:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛+
⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
0,
40,40, 2
0,
total
CHCHtotal
t
t
sos F
XFF
To
T
P
P
uu (21)
Inlet flow speed so
ucan be calculated using molar flow rate and input temperature and
pressure conditions:
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
49

⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
0,
0, 0,
t
o
total
sP
RT
F
u
π
(22)
Boundary conditions for balance equations (17-20) are as below:
0,,0,0 0,0
24
=
=
=
=
=zatPPTTXX ttCOCH (23)
The set of equations with the mentioned boundary conditions are solved using Matlab
software.
3. Calculation of Reaction Effectiveness Factor [5,8]
Mass transfer or penetration resistances against the reaction materials, play important
roles in the results obtained from modeling of catalytic reactions. So to modify the kinetic
behavior of reaction rate equations, Effectiveness Factor is defined.
In achieved modeling, the effectiveness factors can be calculated by definition of
penetration equations in radial direction of the catalyst.
Continuity equations for 4
CH and 2
CO in an spherical element is as follows:
0)(.
131
2
2
,4
4=++
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
×rrRT
dr
dP
r
dr
d
r
Dg
CH
CHe
ρ
(24)
0)(.
132
2
2
,2
2=+−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
×rrRT
dr
dP
r
dr
d
r
Dg
CO
COe
ρ
(25)
In which 4
,CHe
Dis the effective penetration coefficient in component i. Catalyst particle
has been considered to be isothermal and it is assumed that there isn’t any heat transfer from
the catalyst particle to the outside. The obtained equations shall be solved in every radial
position of the reactor with the assigned boundary conditions. Having partial pressures of
4
CH and 2
CO , concentrations of other components could be obtained by means of
stoichiometry. Xu & Froment has used a similar model for determination of effective
penetration factor. The boundary conditions for dimensionless catalytic particle equations are
as below:
00
24 ===
ζ
ζζ
at
d
dP
d
dP COCH (26)
1
,, 244
=
===
ζ
atPPPP BCOCOCHCH B (27)
In which
ζ
is the dimensionless radius of the catalyst particle, 4
CH
P, 2
CO
P are local
partial pressures in catalyst and BCH
P,
4, BCO
P,
2 show the partial pressures in the fluid outside
the particle. As the catalyst is assumed to be isothermal, there will be no energy balance
equation satisfied for that and the reaction rate will be determined in fluid temperature. Also
partial differential equations 26 and 27 have been derived by differential approximation.
These equations are converted to a set of algebraic equations, which have been solved by
Newton method. Because of the complexity of reaction rate equations, jacopian numerical
method has been incorporated instead of analytical method. When effectiveness factor
equations are solved, then the balance equations of the reactor will be also solvable.
3. 1 Simulation Results
Reactor dimensions, catalyst specifications, operating conditions and concentration of
the reactor input components adopted from available documents of methanation reactor of
Khorasan Petrochemical Complex Ammonia Unit. It has been given in table (2) [9]. Simulation
results and input/output data of the industrial reactor has been compared in table (3).
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
50

Table-2: Methanation reactor design and operation specifications [9].
Dimensions 4.8 m length of methanator 2.686 m inside diameter of the methanator
The Catalyst pellet
spherical particles Shape 0.00494-0.00476 m Diameter 0.625 Porosity 2.74 Tortuosity factor 1014 kg/m3
Bulk density 0.0010583 m Catalyst length 8000 A°
Mean pore radius actual design Inlet conditions
3298.251 3392.288 Feed flow rate, kmol/hr 13523 16.557 Methane flow rate, kmol/hr 577.78 586.30 Temperature, K 1823.82 2074.75 Pressure, kPa Composition, Mol% Actual Design 0.1600 0.4280 CO 0 0.0500 CO2 73.410 74.052 H2 0.41 0.488 CH4 0.120 0.483 H2O 25.9 24.499 Inerts
In figures 1 and 2, distribution of methane and carbon dioxide concentration along the
reactor has been illustrated. As expected, it shows decrease of the carbon dioxide while
increase of methane along the reactor. Molar flow rates of the outlet components show a
good compatibility with the output data of the available industrial reactor. This matter is also
satisfied for the temperature and pressure conditions. Figures 3 and 4 illustrate temperature
and pressure distribution along the reactor catalytic bed. Because of absence of industrial
data along the bed, there is only the output data, which could be comparable. These figures
show good compatibility with the industrial data.
Table-3: Simulation Results and Industrial Methanation Reactor Data [9].
Input Output
Industrial Simulation Industrial
CO, kmol/hr 20.5 0 0.0
CO2, kmol/hr 3.4 0 0.0
H2, kmol/hr 4186.7 4407.53 4111.5
CH4, kmol/hr 26.1 55.61 50.1
H2O kmol/hr 58.0 92.12 85.3
Inerts, kmol/hr 16.6 16.6 16.6
In table 4 the error percentage of the simulation have been given.
Table-4: Comparison of simulation data with those of the industrial data
Error% Simulation Actual
0 0 0 CO2 mol% 10% 0.0132 0.012 CH4 mol% 1.5% 598 589 Tout ,K 0.6% 29.381 29.2 Pout , bar
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
51

Fig-1: Methane concentration along the bed
Fig-2: Carbon Dioxide concentration along
the reactor
Fig-3: Temperature variation along the
reactor Fig-4: Pressure variation along the reactor
4. Conclusions
The achieved simulation shows that penetration constraints of the feed gases play an
important role in control of the reaction rate. Considering the effects of the mass transfer
resistances in reaction kinetics, called effectiveness factor, considerable results have been
obtained which show quite a good compatibility with the industrial data. This is turn satisfies
the simulation which has been done for the methanation reactor.
Acknowledgements
We acknowledge the fully collaborations by Khorasan petrochemical complex to disposal of
industrial data within this investigation.
Nomenclature
p
C: Heat capacity
e
D: Effective penetration
dp : Equivalent particle diameter
F: Molar flow
f: Fraction coefficient
K
: Equilibrium constant
k: Reaction constant
P
: Pressure
R
: Gas constant
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
52

T
: Temperature
s
u: Artificial aped
X
: Conversion
z: Reactor length
Greek letters
π
: Reactor cross-section area
ρ
: Density
η
: Effectiveness factor
ξ
: Dimensionless radius of particle
5. References
[1] D.W.Allen, E.R. Gerhard, and M.R. Likins, “ Kinetics of methan-Steam reaction”, Ind. Eng.
Chem. P.D.D., 14,3, 256, 1975.
[2] J. R. H. Ross, and M. C. F. Steel, “ Mechanism of the steam reforming of methane over a
coprecipitated nickel-alumina catalyst”, J. Chem. Soc., Farad. Trans., 1, 1, 10, 1973.
[3] A. H. zhang, J. Zhu and W.H. Duan, “ CO methanation on Ni(1 1 1) and modified Ni3Al(1 1 1)
surface: A first-principle study”, Surface Science, 3 Nov, 2006 .
[4] M. B. I. Choudhury, S.Ahmed, M.A. Shalabi and T. Inui, “ Preferential methanation of CO in a
syngas involving CO2 at lower temperature range”, App. Catal. A, Vol 314, Iss 1, 47, 2006.
[5] J. Xu, G.F. Froment, “Methane Steam Reforming, Methanation and Water-Gas shift Intrinsic
Kinetics”, AIChE , vol. 1, No. 1,1989.
[6] S. S. E.H. Elnashaie and S.S. Elshishini, “ Modeling, Simulation and Optimization of Industrial
Fixed Bed Catalytic Reactors”, Gordon and Breach Science Publishers, vol. 7, 1993.
[7] M. V. Twigg, Catalyst Handbook, Wolfe Publishing Ltd, Second Edition, 1989.
[8] M. S. Batista, E. I. Santiago, E. M. Assaf and E. A. Ticianelli, “Evaluation of the water-gas shift
and CO methanation processes for purification of reformate gases and the coupling to a PEM
fuel cell system”, J. Power Sources, 145, 1, 50, 2005.
[9] Khorasan Petrochemical Complex Documents, Ammonia Unit, Industrial Data.
Kayvan Khorsand et al./Petroleum & Coal 49(1) 46-53 (2007)
53