Reactor II

Report
Ref: Seider et al, Product and process design principles, 3rd ed., Wiley, 2010.
1
Temperature Control
 Temperature control is an important consideration in reactor
design.
 Adiabatic operation is always considered first because it
provides the simplest and least-expensive reactor.
 However, when reactions are highly exothermic or endothermic,
some methods must be used for controlling the temperature of
reactor such as:
2
• Heat-exchanger reactor (a)
• Use of diluent (b)
• A series of beds with inter- heater or cooler (c)
• Cold-shot cooling or hot-shot heating (d)
3
Industrial Examples
 A useful measure of the degree of exothermicity or
endothermicity is the Adiabatic Temperature Rise (ATR) for
complete reaction with reactants in the stoichiometric ratio.
 An industrial example of heat-exchanger reactor : Phthalic
anhydide produced by the oxidation of ortho-xylene with air in
the presence of vanadium pentoxide catalyst particles. The
reaction, which is carried out at about 375 oC and 1.2 atm, is
highly exothermic with an ATR of about 1170 oC, even with
nitrogen in the air providing some dilution. Hundreds of long
tubes of small diameter, inside the shell, are packed with catalyst
particles and through which the reacting gas passes downward.
4
Industrial Examples
 A heat-transfer medium consisting of a sodium nitrite-potassi-
um nitrate-fused salts circulates outside the tubes through the
shell. The heat transfer rate distribution is not adequate to
maintain isothermal condition, but its temperature changes is
less than 40 oC.
 An industrial example of diluent usage : Styrene is produced
by the catalytic dehydrogenation of ethylbenzene at 1.2 atm and
575 oC. The reaction is sufficiently endothermic, with an ATR of
about -460 oC. To maintain a reasonable temperature, a large
amount of steam (inert) that preheated to 625 oC, is added to the
feed (molar ratio of steam to ethylbenzene is about 20:1).
5
Industrial Examples
 An industrial example of inter-cooler usage : Sulfur trioxide,
which is used to make sulfuric acid, is produced by catalytic
oxidation of sulfur dioxide in air with vanadium pentoxide
catalyst particles at 1.2 atm and 450 oC. Adiabatic operation is
not feasible because of an ATR of about 710 oC, even with
nitrogen in the air providing some dilution. Hence, the reactor
system consists of four adiabatic reactor beds, of the same
diameter but different height, in series, with a heat exchanger
between each pair of beds.
 When the ATR is higher, such as in the manufacture of ammonia
from synthesis gas, the cold-shot design is recommended.
6
Desired Temperature Trajectory
 For 1-D fixed-bed catalytic reactors, it is desirable to reduce the
vessel volume to a minimum. This objective can be achieved by
matching the trajectory of the mass- and energy-balance
equations along the length of reactor (X(z), T(z)), to the
trajectory corresponding to the maximum reaction rate, (X*, T*),
as closely as possible.
 Thus, tube-cooled (or heated) reactors, cold-shot (or hot-shot)
converters, and multiple adiabatic beds with inter-coolers (or
inter-heaters) need to be carefully designed in such a way that
(X(z), T(z)) ≈ (X*, T*).
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Desired Temperature Trajectory
 As an example , consider an
exothermic reversible reaction in a
PFR. For this case, the rate of the
reverse reaction increases more
rapidly with increasing temperature
than the rate of forward reaction.
Also, the reverse reaction is slow and
the forward reaction is fast at low
temperature. Thus, for a maximum
rate of reaction, the temperature
should be high at low conversions
and low at high conversions.
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Desired Temperature Trajectory
 The feed enters at point A (TA , X1).
If the entering temperature cannot be
increased, it is best to operate isothermally at TA until the conversion at
point C is reached, and than follow
the optimal profile CB to the desired
conversion (X4).
 Alternatively, a larger reactor volume
will be needed, if isothermal
operation is used (trajectory ACD).
 If instead of a PFR, a CSTR were used, the optimal operating
temperature for achieving X4 would be TB, which corresponds to
the maximum reaction rate for that conversion.
9
Multiple Steady States in an Autothermal Reactor
 The reactor feed temperature has
an important effect on the
stability of an auto-thermal
reactor, that is, a reactor whose
feed is preheated by its effluent.
 For a reversible exothermic reaction, as in ammonia synthesis,
the heat generation rate varies nonlinearly with reaction
temperature, with a maximum at some intermediate temperature.
In contrast, the rate of heat removal is almost linear with the
reaction temperature, with a slope dependent on the degree of
heat exchange between the outlet and the inlet.
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Multiple Steady States in an Autothermal Reactor
 The intersection of line (b) and
curve (a) sometimes leads to
three possible operating
conditions: (O) the non-reacting
state (stable), (I) the ignition
point (unstable), and (S) the
desired operating point (stable).
 The temperature difference between operating points I and S is
called stability margin. Clearly, operation at S with larger
stability margin would be more robust to disturbances. Thus a
design with increased rate of heat transfer (line b’) and a design
without considering the decreasing of catalyst activity (line a’),
can lead to loss of stability.
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Example 7.3: Optimal Bypass Distribution in a ThreeBed, Cold-Shot Ammonia Synthesis Converter
 A reactor for synthesis of ammonia consists of three cylindrical,
2-m-diameter adiabatic beds, packed with catalyst for bed
lengths of 1.5 m, 2 m, and 2.5 m, respectively. The reactor feed
is split into three branches, with the 1st branch becoming the
main feed entering the 1st bed after being preheated by the hot
reactor effluent from the 3rd bed. The 2nd and 3rd branches, with
flow fractions of φ1 and φ2, provide cold-shot cooling at the 1st
and 2nd bed effluents.
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Example 7.3: Optimal Bypass Distribution in a ThreeBed, Cold-Shot Ammonia Synthesis Converter
 As summarized in the following Table, the reactor feed consists
of two sources, the first of which is a make-up feed stream
mainly hydrogen and nitrogen (synthesis gas) in stoichiometric
molar ratio of 3:1. The second feed is a recycle stream consisting
of unreacted synthesis gas, recovered after removing the
ammonia product. It is desired to optimize the allocation of
the bypass fractions to maximize the ammonia production.
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Example 7.3: Solution
 Ammonia is synthesized by the following reversible reaction:
0 . 5 N 2  1 . 5 H 2  NH
3
  91000  0 .5 1 . 5
  140000 
10
R a  10 exp 
 PN 2 PH 2  1 . 3  10 exp 
 PNH 3
RT
 RT



4
Ra 
kmol of N 2 consumed
3
,
T  K,
kJ
R  8 . 314
m s
,
kmol K
Pi  atm
 After multiplying the rate equation by 2 and changing the unit of
partial pressure to Pascal, we have:
rk  1 . 95  10
where :
6
rk 
  91000  0 .5 1 .5
  140000 
5
exp 
P
P

2
.
57

10
exp
 N2 H2

 PNH 3
RT
 RT



kmol
3
m s
,
T  K,
R  8 . 314
kJ
kmol K
,
Pi  Pa
14
Example 7.3: Solution
 At first, a value of 0.1 is assumed for each bypass fraction and
the process was simulated in ASPEN PLUS (the PR EOS was
used for property prediction). The simulated process was saved
with filename: <example7_3_current.bkp>.
 For founding the optimum temperature trajectory based on the
NH3 mole percent and the rate of reaction, the partial pressure of
H2 and N2 must be expressed in terms of NH3 mole fraction.
This can be done by component mass balance as follows:
n N 2 , out  n N 2 , in  0 . 5 , n H 2 , out  n H 2 , in  1 . 5 , n NH 3 , out  n NH 3 , in  
n CH 4 , out  n CH 4 , in , n Ar , out  n Ar , in  n total, out  F0  
Where the F0 is the total molar flow rate of the combined feed
and ξ is the molar extent of reaction.
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Example 7.3: Solution
 PN 2
PNH 3
 F 0 x f , N 2  0 . 5
 
F0  

 F 0 x f , NH 3  
 
F0  


 F0 x f , H 2  1 . 5
 Pt , PH  
2


F0  




 Pt


F0 x NH 3  x f , NH 3

 Pt  x NH Pt   
3

1  x NH 3




Where xf,i is the feed mole fraction of species i.
 Consequently, the rate of reaction can be computed as a function
of the temperature and mole percent of NH3, as shown in the
following figure for operating pressure of 150 atm.
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 The above figure can be reproduced in MATLAB by running the
m-file: <example7_3_current.m>. As can be seen from the
results by using a value of 0.1 for each bypass fraction, the conc.
of ammonia in the effluent stream is 12.9%.
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Example 7.3: Solution
 To maximize the ammonia production in the reactor, the
following optimization problem must be solved:
max 
w.r.t
 1 , 2
f ( x )  0

o
T

300
C
 1
s. t. 
o
T

300
C
 2
    0 . 6
2
 1
 The first constraint refers to the reactor model. The second and
third constraints are selected for achieving a suitable stability
margin. The last constraint is arbitrary.
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Example 7.3: Solution
 The above optimization problem was solved by Successive
Quadratic Programming (SQP) method in ASPEN PLUS (the
filename is: <example7_3_optim.bkp>). The final ammonia
composition in the reactor effluent is 16.1 mol%, obtained
with optimal bypass fractions φ1=0.23 and φ2=0.24.
 The composition-temperature trajectories for the optimal
bypass distribution, is shown in the following figure. This
figure can be reproduced in MATLAB by running the mfile:<example7_3_optim.m>.
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Example 7.3: Solution
Investigate the performance of the optimized process, if the
catalyst activity decreases by a factor of 0.2 (80% decrease
in catalyst activity).
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