Dynamic

Indian Chemical Engr. Section A, Vol. 48, No.3, July-Sept. 2006
164
A dynamic model of an industrial packed bed multi tubular
reactor used to manufacture ethylene oxide (EO) is
developed in this work. EO is manufactured by catalytic
oxidation of ethylene with oxygen over a silver-based catalyst.
A side reaction of ethylene with oxygen gives carbon dioxide
and water as by-products. These gas phase reactions are
highly exothermic. This model can be described by a system
of non-linear partial differential equations. gPROMS® is used
to integrate by common numerical techniques. This model is
benchmarked against an industrial EO reactor. The model
predicted data reasonably fits the plant data. The
heterogeneous two phase model developed initially is
reduced to a single phase homogeneous model. A
comparison of the two models is done and the accuracy is
tested against plant data. The simulation of the models can
well predict the reactor behaviour. The packed bed multi-
tubular reactor is modelled to gain an insight into the
production process. A pseudohomogeneous analysis is
considered sufficient for accurate data prediction of the
reactor. The simulation will allow operators to gain deeper
process understanding and to analyse optimal reactor
operating conditions.
Dynamic Modelling of An Industrial
Ethylene Oxide Reactor
Avi. A. Cornelio*
Process Control Laboratory, Department of Biochemical and Chemical Engineering,
Universität Dortmund, D-44221 Dortmund, Germany
* Currently at Department of Chemical Engineering,
Dalhousie University, Halifax, Canada B3J 2x4
E-mail: avi.cornelio@dal.ca
M
athematical models of fixed bed reactors
are needed to describe the steady-state
and dynamic behaviour for process design,
optimisation and control. The type of model and its
level of complexity in representing the physical
system depends on the use for which the model is
being developed. This report presents a methodical
model development procedure for a multi-tubular EO
packed bed reactor. The demand for EO and, hence,
its production continued to increase over the years.
The production [1] of EO is a critical process because
the reactor can generate eleven times as much heat
in a runaway condition as under normal operation
conditions. As given in reference 1, EO in any fraction
from 0.03 to 1 in the atmosphere is explosive at room
temperature. As a result, it is normally stored at 5O
C
under 4 kg /cm2
. Therefore, the safety issues for an
EO reactor are dominant as industry tries to operate
them in an economically advantageous manner.
Ethylene and oxygen are combined in a catalysed
reactor at 200-250O
C at 10-15 bar in a pressure shell
cooled boiling coolant to produce EO, CO2
, H2
O as
well as traces of acetaldehyde and formaldehyde.
Acetaldehyde is also formed (traces) during the
oxidation step by the isomerisation of EO.
As given in reference 1, silver has maintained
its position as the only known metal that can catalyse
the oxidation of ethylene to EO to a commercially
viable selectivity. The catalyst is supported on a low
surface area alumina. Modern silver based catalysts
have an initial selectivity of 79-81% and a maximum
selectivity of 83% is achievable. The life-time of a
modern catalyst is 8 months to 1 years. Inhibitors
are added to control the re-action rate and improve
the selectivity of the catalyst. The industrial gas
phase inhibitor is usually 1,2-dichloroethane and its
concentration is usually 1-30 ppm. Dichloroethane
(DCE) inhibits the combustion reaction to a greater
extent than the epoxidation reaction. In this way it
promotes the selectivity for EO. DCE is both an
inhibitor of the complete oxidation of ethylene and a
promoter of the selectivity for EO.
Applied Reaction Kinetics
The reaction rate expressions reported in literature
range from pure emperical co-relations to
complicated rate expressions. A steady state kinetic
rate equation was obtained by Park et al. [2]
confirming Langmuir Hinshelwood mechanism for
the reaction scheme in Eq. 1 and 2. Petrov et al.[3]
developed a kinetic model of ethylene epoxidation
over a supported silver catalyst and claimed that the
Rideal-Eley type of mechanism was dominant.
Westerterp et al. [4] suggested that at a large excess
of ethylene, as applied in the oxygen based units,
the rate equations simplify to first order kinetics in
the oxygen concentration. Borman et al. [5] have
established a rate expression for the selective
oxidation of ethylene in a wall cooled tubular packed
Paper received : 18.4.06 Revised paper accepted : 31.8.06

165
bed reactor without any chlorine inhibitor. Petrov et
al. later modified their kinetic model in reference 3
to a rate expression with a DCE term embedded in
reference 6. The authors tested a variety of published
equations. We have used the rate expressions given
by Petrov et al. [6] containing a DCE term in our
work. The reaction scheme is given below.
The kinetic rate equations containing the DCE
partial pressure term have been obtained from Petrov
et al. [6] and are given below.
Where E, O, DCE stands for ethylene, oxygen
and dichloroethane, respectively. The quantities in
Eq.s 3 and 4 are measured in the following units:
The reaction orders, k7
and k8
, with respect to
DCE, are dimensionless. This means that k7
and k8
have constant values at all reaction temperatures as
given by Petrov et al. [6] The reaction orders, k7
and
k8
are the powers of the DCE term in Eqs. 3 and 4
respectively. The kinetic rate constants k1
-k6
have
an Arrhenius dependency on temperature and can
be expressed as :
The value of the rate constants and the
frequency factors with activation energies can be
obtained from reference 6.
The Heterogeneous Model
In a one-dimensional model, radial variations of
concentration and temperature are not considered.
Industrial reactors have a high axial aspect ratio. The
radial dispersion of concentration and temperature
within the reactor bed is negligible due to
comparatively small radius of the tubes. Thermo-
physical properties like the density and velocity of
the gas phase vary due to temperature, pressure and
mole changes. The reaction rate constants vary with
temperature exponentially. Axial variations of the
fluid velocity arising from the axial temperature
changes and the change in number of moles due to
the reaction are accounted by using the continuity
and the momentum balance equation.
The major assumptions underlying the model are the
following :
l Gas properties are functions of temperature,
pressure and total moles as dictated by the ideal
gas law since reactions occur at pressures around
10 bar.
l For simplicity, the heat of reaction and the gas
heat capacities are considered constant. These
values are averaged over the catalyst bed. The
physical properties of the solid catalyst and the
wall are taken as constant as well. Their effects
are negligible as the conditions within the reactor
introduce only minor variations in these
parameters.
l The packed bed is assumed to be uniformly packed
with negligible wall effects and small tube
diameter. As suggested by Froment et al. [7], a
void fraction profile induces a radial variation in
fluid velocity. Hoiberg et al. [8] confirmed that
packed beds with radial aspect ratio lesser than
50 showed negligible radial variations of velocity.
The EO reactor in the plant has a radial aspect
ratio of 10. Hence, the radial variations of the
velocity due to variations in the void fraction can
be neglected.
l The radiation effects between the solid catalyst
and the gas is considered negligible. It has been
reported in Khanna et al. [9] that radiation
between the solid catalyst and gas can
significantly affect the temperature dynamics in
packed bed systems operating in excess of 673 K.
Since the operating conditions of the EO reactor
are well below 673 K, radiation terms are not
included in the model.
l We are interested to study the effect of the
operating parameters on the EO reactor
operation. This is a macroscale problem as defined
by Froment et al. [7]. The catalyst particles have
been considered to be non-porous. The resistance
to heat and mass transfer in the catalyst pellet is
considered negligible due to the above
assumption. The rate of reaction is uniform
throughout the particle and reaction occurs on
the solid surface. The effectiveness factor for each
of the reactions is unity.
A complete description of the reactor bed

166
involves PDEs, DEs and AEs describing the gas phase
and solid surface temperatures, gas phase and solid
surface concentrations, pressure drop across the
packed bed.
Total Mass and Momentum Conservation
Consider the case of a single tube as given in
Fig. 1. Let ni
be the molar flow rate of component i
at the inlet and exit of the differential section. The
dynamic equation of the total mass (m) in the
catalytic bed at the entrance and exit of the
differential section filled with catalyst particles
Fig. 1 : Elemental Section of a Single Tube with
Catalyst Particles with Convective and Diffusive
Flow of Fluid
gives the continuity equation. The following
expression can be derived for the continuity equation.
with the initial condition
... 6
... 7
and the boundary condition
... 8
In order to characterise the fluid velocity ug
(t,x ), we need to consider the conservation of
momentum over the differential element. The
momentum (v) mass of the material multiplied by
its velocity. The rate of change of momentum in the
fluid is v. The rate of generation of momentum in
the element is given by the sum of all exerted on the
material in the element. These can include pressure
forces, viscous shear forces and gravitational forces.
Therefore,
... 9
and the boundary condition
... 10
... 11
... 12
... 13
... 14
This is the momentum balance equation
necessary to describe the flow and pressure fields in
the packed bed. The third term of Eq. (9) comes from
the forces exerted due to the fluid pressure (PT
). The
fourth termof equation 9 consists of the coefficient β
which is a friction factor (Ergun’s equation [10]. It
was adopted to account for the viscous friction and
shear forces in the fluid itself and through the packed
bed. [11] The gravitational force exerted in a vertical
tube due to the static head is given by the last term
of Eq. 9.
Component Mole Balance
The generalised expression for the dynamic mole
balance for the individual components for either
phase within the elemental volume of length dx is
given by
Gas Phase
In the gas phase, transfer of moles occur due to bulk
flow, diffusion and external mass transfer resistances.
The number of moles of each component at any
instant in the elemental volume is the product of
the individual molar concentration (C4
) and the
elemental volume (Vsection) at that instant. The
inclusion of the bulk flow term results from the
change of the molar flux due to the bulk motion of
the fluid. The fluid velocity (ug) varies with position
and time. The diffusive mass transfer rate is given
by the Fick’s first law. [12] The reaction occurs on
the catalyst surface. Therefore, a mass transfer
resistance exists between the catalytic surface and
the bulk of the fluid. This is given by the source/sink
term of Eq. [15]. Therefore, the following expression
can be derived by incorporating the above thermo-
physical phenomeneon.
... 15
... 16

167
To complete the second order PDE (expression 16),
we need to add two boundary conditions. The most
frequently used ones are the Danckwert’s[13]
boundary conditions.
The boundary conditions are
with the initial condition,
... 17
... 18
Solid Phase
In the solid phase, transfer of moles occur due to
external mass transfer resistances and reaction
occurring on the surface of the catalyst. Since the
catalyst particles are immobile, the diffusive and
convective terms are negligible. The following
equation has been derived for the solid phase. The
following equations are valid for the solid phase.
Inserting these equations into the main balance
equation with Ap /Vp = 4 /Dp for a cylindrical catalyst
pellet and assuming a non-porous catalyst, we have
Energy Balance
The generalised expression for the unsteady
energy balance similar to the mole balance can be
given by
... 19
Where
... 20
... 21
... 22
... 23
... 24
... 25
Dividing the equation by VSection
ε, we obtain
... 26
... 27
... 28
Gas Phase
In the gas phase, transfer of heat occurs due to bulk
flow, external heat transfer resistances and the heat
exchange between the coolant1
and the bed across
the wall. The heat content in the elemental volume
is the sensible heat exchange arising due to a
temperature difference. The bulk flow term arises
from the temperature change due to the bulk motion
of the fluid. The diffusive heat transfer rate is given
by the Fourier’s law. [7] The exothermic reaction
occurs on the catalyst surface. Therefore, a heat
transfer resistance exists between the catalytic
surface and the bulk of the fluid. This is given by the
source/sink term of Eq. (28). Therefore, the following
expression can be derived by incorporating the above
thermo-physical phenomeneon.
The overall heat transfer coefficient (Usg) is the
resistance to heat transfer between the solid and the
gas phase. The overall heat transfer coefficient ( gc)
is the resistance to heat transfer between the gas in
the tube side and the coolant in the shell side. We
have assumed a negligible heat transfer resistance
between the bed and the coolant. This means that
all the heat generated due to reaction is transferred
to the bulk gas.
Solid Phase
In the solid phase, transfer of heat occurs due to
external heat transfer resistances and reaction
occurring on the surface of the catalyst. The following
equations are valid for the solid phase.
... 29
... 30
with the initial
condition,
and the boundary condition,
... 31
... 32
... 33
... 34
1
We have assumed that the temperature of the coolant changes
along the reactor length but remains steady at a point.

168
Model Simplification
The total mass balance and the equation of motion
have to be solved simultaneously. There is no direct
equation for the pressure gradient term in the
momentum balance equation. This can be solved by
adding a pressure correction Eq. (11) (Poisson
equation). We have tried to avoid this complication.
The importance of the continuity equation is to help
in evaluating the actual velocities within the reactor
bed as influenced by the mole, temperature and
pressure changes. The gas mass velocity is defined
as the product of the density and velocity. The EO
reactor that operates in the process plant shows that
the difference between the total mass of gas at the
entrance and exit is negligible. This is due to high
gas velocities and negligible losses. The total mass is
conserved.
Hence, the assumption of a constant mass velocity
for the given operating conditions is applicable and
the continuity Eq. (6) is reduced to
Where
... 35
... 36
... 37
... 38
... 39
... 40
... 41
Inserting these equations into the main balance, we
have
Dividing the equation by ρBVsectionCρB (1 -ε ), we
have
With the initial condition
... 42
A flow model (continuity and the momentum
balance) has been derived in the previous section.
Expanding the partial derivatives of Eq. (9) and
applying the continuity equation, we obtain,
Let us estimate the relative importance of the
first term of Eq. (43) as compared with the pressure
gradient (term3). Under operating conditions, the
maximum pressure gradient along the reactor would
be about 2 ×104
Pa/m and the acceleration term would
be about 1 -2 m
/sec2
. The acceleration term can be
considered negligible compared to the pressure
gradient term. Therefore,
This does not mean that the velocity remains
constant. The EO reactor is operated at gas velocities
of 1 -2m
/sec . At these velocities, the Reynold’s number
( Re) for a pipe diameter of 39.1 mm and 11.78 m3
of
gas density exceeds a value of 2500. Hence, it can be
considered that the flow is fully developed.
Gases in general have a very low viscosity and
this means that the forces resulting from shear
stresses do not contribute much to the momentum
balance equation. We now obtain an equation that
reflects the changes in pressure along the bed
assuming uniform packing and negligible wall effects.
Because of the use of constant mass velocity, the
importance of the actual velocities is actually
restricted to cases where the pressure relationships
like the Ergun’s Eq. (10) is considered. We finally
arrive at the simplified momentum balance equation
Eq. (49). The continuity equation is solved as a set of
algebraic equation and the pressure drop across the
bed with the velocity gradient is given by the
momentum balance equation.
The energy Eq. (29) derived for the gas phase
has to be simplified in order to reduce the complexity.
The assumption of negligible axial thermal dispersion
effects is quite common. The second order PDE can
be reduced to a first order PDE requiring only one
boundary condition. The high gas velocities
contribute to a negligible thermal dispersion effects.
It has been shown [9] (for a different reacting system)
... 43
... 44
... 45

169
that neglecting the axial thermal dispersion in the
gas does not affect the solution profiles much.
Therefore, Eq. (57) can,
hence, be derived by expanding the partial derivatives
and applying the simplified continuity equation. The
complete description of the reactor bed involves three
partial differential equations and two ordinary
differential equations. These describe the density and
velocity of the gas mixture, the partial pressure of
individual com-ponents in the gas phase and on the
catalyst surface, the temperature of the gas. Eq. (57)
can, hence, be derived by expanding the partial
derivatives and applying the simplified continuity
equation. The complete description of the reactor bed
involves three partial differential equations and two
ordinary differential equations. These describe the
density and velocity of the gas mixture, the partial
pressure of individual com-ponents in the gas phase
and on the catalyst surface, the temperature of the
gas and catalyst surface, and the pressure drop along
the reactor length. The model equations with the
their initial and boundary conditions have been listed
in Fig. 2. Each element of Vector Ri corresponds to
ethylene,oxygen, EO, carbon dioxide, water, methane,
DCE, ethane, orgon and nitrogen, respectively.
... 45
Model Realistaion
The reactor model was coded in gPROMS
®
and
various numerical techniques were tested to obtain
a solution. For simplicity, we have used the second
order Central Finite Difference Method (CFDM) for
solving the coupled equations. The number of
elements selected for discretisation of the spatial/time
domain was 50. This was adjusted to obatain the
desired accuracy and an efficient computation time.
The numerical values of the parameters used
for the analysis of the model are based on published
results [4, 15–17]. The mass transfer parameters
have been obtained from reference 16. Some of the
catalyst related parameters have been obtained from
reference 15. The data related to the reactor
dimensions and operating conditions are the values
used in the plant. The inlet gas mixture contains 10
components. They are ethylene, oxygen, EO, carbon
dioxide, water, methane, DCE, ethane, Argon and
Nitrogen. Methane is used as a diluent and its inlet
concentration is very high. Table 2 gives an overview
of a typical EO reactor parameters. The operating
conditions and the composition of the inlet gas feed
used in the calculations are given in Table 3. The
amount of water (vapour) moving into the reactor is
negligible.
As the catalyst used in the reactor is different
from the one used by Petrov et al.[6], frequency factor
of rate constants k1
and k3
have been used as the
tuning parameters in this study. Petrov et al.6
found
the frequency factor of rate constants k1
and k3
to be
6.867 and 10.62, respectively. In this work, the
frequency factor of rate constants k1
and k3
have been
tuned to 20.052 and 12.3192 respectively. The
selectivity of the catalyst operated in the plant is
about 85 -87%. The experimental selectivity
determined in reference 6 is about
45 -57%. In other words, the catalyst used in the plant
is of higher selectivity than the one used by Petrov
et al. [6]. Hence tuning the frequency factors to
achieve the desired selectivity is justifiable.
In Table 1, the actual and the dynamic
simulation values of the gas concentration are
compared. The steady state is achieved soon due to a
very fast dynamical behaviour.
The results in Table 1 have been obtained at
steady state. It is clear that the model predictions
are very close to actual values measured in the plant.
Data was reconciled and it was found that the
temperature on the shell side varied along the tube
length. We have tried to approximate the temperature
gradient along the length by means of a polynomial
function. Fig. 3 gives the polynomial approximation
of the coolant temperature as compared to the plant
data. A third order polynomial is generated using
the function polyfit in MATLAB®
. The temperature
of the coolant is now dependent on the axial
distribution but explicitly independent of time at that
position.
Property Conditions at outlet
Simulation Plant
Gas composition
yC
2
H
4
0 3705 0 3743
yO
2
0 0359 0 0358
yEO 0 0369 0 0386
yCO
2
0 0419 0 0420
Temperature 268O
C 268O
C
Pressure 13.8 bar 13.9 bar
Selectivity 86.5% 87.23%
Table 1 : Simulation Results and Validation

170
Continuity
Boundary
Momentum
with
Boundary
Mole balance
Gas Phasee
Initial
Boundary
Solid Phase
Energy blalance
Gas Phasee
Initial
Initial
Boundary
Solid Phase
Initial
Reaction
Additional Equations
... 47
... 48
... 49
... 50
... 51
... 52
... 53
... 54
... 55
... 56
... 57
... 58
... 59
... 60
... 61
... 3
... 4
... 62
... 63
... 64
... 65
... 66
... 67
... 68
... 69
... 70
Fig. 2 : The Heterogeneous Model

171
Pseudohomogeneous Model
The aim in this Section is to develop a one
dimensional, dynamic pseudohomogeneous model
with axial distribution. Thus, the interfacial
gradients need not be modelled. Measurement
difficulties that arise in model verification or
parameter estimation using a heterogeneous analysis
are also often cited as reasons for a homogeneous
analysis. Researchers have developed various criteria
for the applicability of the pseudohomogeneous
In this expression, β is the dimensionless heat
transfer coefficient, ∆Λ is the total heat generation
in the reactor, and γ is the fraction of the heat effect
going into the solid phase (for more details on the
description of these parameters, please refer to
reference 7, 9). The temperature difference should
be small or negligible. The average temperature
difference for the EO packed bed reactor in many
cases is below 5K or sometimes negligible. This has
been shown in Fig. 4. Hence, we can assume that a
pseudohomogeneous analysis is valid.
CoolantTemperature(O
C)
Reactor length (m)
Fig. 3 : Polynomial Approximation of the Coolant
Temperature
... 71
... 72
Catalyst parameters Reactor parameters
ε 0.6 L 12.8 m
ρB 870 kg /m3
Dt 39.1 mm
cρB 1000 J /kgK Nt 4731
Dρ 3.9 mm
Heat transfer Mass transfer
parameters parameters
Usg 550W
/m2
K kfilm 0.025m
/s
Ugc 270W
/m2
K Davg 4.9 ×10-6
m2
/s
Table 2 : Typical Reactor Parameters
Reactor inlet conditions
ug 1.04m
/s ρg
11.79 kg/m3
Tg 136O
C TcGGlant 255O
C
cpg 1160J
/kgK PT 15.97 bar
µ 1.73 ×10-5kg/ms
Inlet mole fraction
yC2
H4
0.4054 yO2
0.0703
yεO 0.005 yCO2
0.0298
yCH4
0.3938 yDCE 5.45PPM
yC2
H6
0.00124 yARGON 0.085
yN2
0.0141
Table 3 : Typical Operating Conditons
model. For the pseudo-homogeneous analysis
criterion, a predictive expression for the temperature
difference between the gas and solid phase
temperatures for a fixed bed reactor is given by Wei
et al.[7] The criterion is
In our original system of partial differential
equations, to obtain a pseudohomogeneous model,
the two energy and mass balances have to be
combined. The gas and solid properties are assumed
to be equal i.e.:,
The packed bed reactor system would now
contain four partial differential equations. They
describe the density and velocity of the gas mixture,
the concentration of individual components, the
temperature and the pressure drop along the reactor
Temperature(O
C)
Reactor length (m)
Fig. 4 : Change of bulk and surface temperature
along the bed during startup

172
Continuity
Boundary
Momentum
with
Boundary
Mole balance
Initial
Boundary
Energy balance
Reaction
Additional Equations
... 75
... 76
... 77
... 78
... 79
... 80
... 81
... 82
... 83
... 84
... 85
... 86
... 3
... 4
... 87
... 88
... 89
... 90
... 91
... 92
length. The model equations have been listed in Fig.
5 with their initial and boundary conditions. Each
element of vector Ri corresponds to ethylene, oxygen,
EO, carbon dioxide, water, methane, DCE, ethane,
argon and nitrogen, respectively.
Homogeneous versus Heterogeneous Model
In this Section, the homogeneous reactor model is
compared with the heterogeneous model. The
simulation results of the homogeneous model have
Fig. 5 : Pseudohmogeneous Model
been given in Fig. 6(a), 6(b), 6(c), 6(d) and 6(e).
Solution times using the homogeneous model are 5-
10 % less than that of the full two-phase analysis.
The density and velocity profiles along the length at
steady state is given by Fig. 6(a) and Fig. 6(b),
respectively. The pressure drop profile along the
reactor axis is perfectly replicated by the
homogeneous model in spite of removing the velocity
gradient and the gravity terms as given in Fig. 6(c).

173
Fig. 6 : Steady State Profiles of the EO Reactor along the Reactor Axis

174
Fig. 7 : Comparison of Various Models against Plant Date

175
The total pressure of the gas mixture at the exit is
the same for both the models. Fig. 6(d) shows the
temperature profile of the reactor along the reactor
axis. The temperature profile of both the
heterogeneous and homogeneous models for the gas
phase has very small difference initially. This may
be due to a lower number of discretisation points
used for the homogeneous analysis. Simulations here
verify that the numerical stability of the model by
retaining the dispersive effects is greatly enhanced
although minor additional effort may be necessary
in the model development. Fig. 6(e) shows the change
in the mole fraction of important species (C2
H4
, EO)
along the reactor length at steady state. There is a
negligible difference in the mole fraction profiles due
to model reduction.
Validation against Plant Data
Comparing the model performance against the actual
plant data, it was found that the model could predict
the behaviour of the reactor well. This detailed and
validated model can now be used to study the
influence of the operation parameters on the reactor
performance. Fig. 7(a) gives the comparison of the
EO production rate in tonne/hr as predicted by the
models against the plant data for the past 1000
seconds. The error is negligible and the production
rate of the plant is about 18 tonne/hr of EO. Finally,
temperature data along the reactor axis can be used
for validation purposes. The following data has been
reconciled for the reactor temperature at various
points of the reactor axis and it has been found to be
remaining steady. The reactor bed temperature has
a maximum of 10% difference between the model
predictions and the plant data, which are reasonable.
Conclusion
In this work, a dynamic heterogeneous model of an
industrial EO reactor was developed. This
heterogeneous model was simplified to a
pseudohomogeneous model. The models were
compared and validated against the industrial EO
reactor. A kinetic model developed by Petrov et al.[6]
was incorporated into the multi-tubular reactor
model, developed for the purpose of performance
optimisation of the reactor. The model was
benchmarked against the industrial reactor and it
predicted plant data well. We claim that for an
industrial EO reactor system, the temperature
between the catalyst surface and the gas phase is
negligible (<10K). A heterogeneous model involves
a larger number of equations than the
pseudohomogeneous model. Since the temperature
difference between the surface and the gas is
negligible, a pseudohomogeneous analysis is
considered sufficient for accurate data prediction of
the reactor. The dynamics related to the EO reaction
is fast and the steady state is soon achieved. Normally,
the hot spot moves down the bed as the reaction
progresses.
A pseudohomogeneous model avoids modelling
complexity and is an appropriate scheme for an
industrial EO reactor. The procedure for developing
a pseudohomogeneous model is not complex. The
computation time for solving the model equations is
small due to the reduced number of equations. The
main disadvantage of a pseudohomogeneous model
is the possibility to obtain a numerical solution with
ease. A numerical solution for the heterogeneous
model is possible with higher discretisation points
than the pseudohomogeneous model with the same
number of discretisation points.
This is mainly due to the interacting equations
and the presence of higher order derivatives which
enhances the possibility to obtain a solution
numerically.
Finally, significant variables can now be
identified in order to be used as control variables for
optimization studies. The simulation will allow
operators to gain deeper process understanding and
to analyse optimal reactor operating conditions.
Acknowledgement
The suggestions of Dr. Stefan Krämer, Process Control
Laboratory, Department of Bio-chemical and Chemical
Engineering, Universität Dortmund, is very gratefully
acknowledged.
References
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Chemistry, pages 117–135, VCH Verlagsgesellschaft mbH,
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on a silver catalyst: Unsteady and Steady State Kinetics,
Journal of Catalysis, 105(1):81–94, (1987).
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Steady State Ethylene Epoxidation over A Supported Silver
Catalyst, Applied Catalysis, 18:87-103, (1985).
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Nomenclature
AE Algebaric Equation
DCE Dichloroethane
DE Differential Equation
EO Ethylene Oxide
PDE Partial Differential Equation
Roman Letters
ACSA Cross-sectional area of the tube m2
Ap Surface area of the catalyst particle m2
ASA Total surface area of a single tube m2
Ci Concentration of component i kmol /m3
Ci0 Concentration of component i at the inlet of the reactor kmol /m3
Cis Concentration of component i on the surface of the catalyst kmol /m3
Cis0 Initial concentration of component i on the surface of the catalyst kmol /m3
cpB Specific heat capacity of the catalyst bed J /kgK
cpg Specific heat capacity of the gas mixture J /kgK
Dp Diameter of the catalyst pellet m
Davg Average Diffusion coefficient of the gas mixture m2/
s
Dt Diameter of a single tube in the reactor m
Fi Force acting due to a phenomenon i N
gx Acceleration due to gravity m/s2
∆ Hj Standard heat of j th reaction J/kmol
k Reaction rate constant 1/s
kfilm External mass transfer coefficient m/s
L Length of the tubular reactor m
Lp Length of the catalyst pellet m

177
Greek Letters
ε Bed voidage –
β Friction factor given by Ergun’s equation –
λ Average thermal conductivity of the gas mixture W/mK
µ Average viscosity of the flowing gas kg /ms
Vij Stoichiometric coefficient of the i th component in the j th reaction
ρΒ Catalyst bed density kg /m3
ρgo Initial Density of the gas mixture kg /m3
ρg Density of the gas mixture kg /m3
V Momentum of the gas mixture kgm/s2
Indices
0 Inlet or initial condition
i Number of components in the system
j Number of reactions considered
L Exit condition
T Total property for example pressure
Superscripts
gas Gas phase
solid Solid phase
Mavg Average molecular weight of the gas mixture kg/kmol
Mi Molecular weight of component i kg/kmol
n Molar flow rate kmol/s
Nt Number of tubes in the reactor –
PT Total pressure at the gas at the entrance of the reactor N/m2
PT Total pressure at the gas at any instant and position in the tube N/m2
q Heat flow per unit area W/m2
q Heat content of the system J
Ri Overall rate of formation/disappearance of component i due to reaction kmol/kgcat-s
R Universal gas constant= 8314 J/kmolK
rj Rate of j th reaction kmol/kgcat-s
S Selectivity of the catalyst for ethylene oxide %
t Time domain s
Tg Temperature of the gas phase K
Tg0 Initial temperature of the gas phase K
Ts0 Initial surface temperature of the catalyst K
Ts Temperature of the surface of the catalyst particle K
ug0 Initial velocity of the gas mixture m/s
ug Velocity of the gas mixture m/s
X Overall conversion of ethylene %
Y Overall yield of the process %
yi Mole fraction of component i –
z Spatial domain m

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