Design Project Presentation

Sarnia Polymer Corporation
Reactor Optimization
CHE 368
Cole Hamilton & Robert Cote

Design Rational for PBR
Packed Bed Reactor:
• Versatile in predicting temperature progression that closely
follows real operations.
• Gases passing through packed beds approximate plug flow.
• Effective for contacting the catalyst.
• Effective when utilizing large quantities of catalyst.
• Large packed beds make effective temperature control
difficult.
• For endothermic reactions, rate always decreases with
conversion so plug flow reactors should always be used.
*Information gathered from (3)

Base Case
• Independent Variables:
- Inlet Pressure = 5 atm
- Inlet Temperature = 950 K
- Feed Mass Flow Rate = 10,000 lb/hr
- Inlet Steam Mass Flow Rate = 0 lb/hr

Base Case: Summary of each
compound’s relevant properties

Base Case: Flow rates are put in terms of extent of reaction to
simplify and equilibrium constants given as a function of
temperature.

Base Case: Rates of reaction in terms of extent of
reaction.

Base Case: Extents of reaction as they appear in the
solve block.

Base Case: Converting outlet extents of reaction from the reactor
back into molar flow rates.

Base Case: Pressure and temperature as they appear in the solve
block along with outlet pressure and temperature from the
reactor at given catalyst weight.

Base Case: Outlet molar flow rates versus catalyst weight.

Base Case: Outlet temperature and pressure from the reactor
versus weight of catalyst.

Performance Sensitivities- Temp
• Increasing the temperature into the reactor
increases the temperature in the reactor and the
rate constants.
• Rates of reaction and extent of reaction increase
within a certain temperature range. This is what
effects the flow rates.
• Looking to optimize the profit by altering the
temperature to maximize styrene with respect to
limiting benzene and toluene.
– Unwanted reactions indicate wasted feed.

Influence of Temperature: T0 = 800K
Analyze Flows of Styrene (2), Hydrogen (3), Benzene (4), Ethylene (5), Toluene (6)
and methane (7) in terms of the how they balance in the profit function.

(Optimum for base conditions)
Analyze Flows of Styrene (2), Hydrogen (3), Benzene (4), Ethylene (5), Toluene (6) and
methane (7) in terms of the how they balance in the profit function.

Analyze Flows of Styrene (2), Hydrogen (3), Benzene (4), Ethylene (5), Toluene (6) and
methane (7) in terms of the how they balance in the profit function.

Performance Sensitivities- Pressure and Feed Rate
• Lowering the pressure significantly decreases the
rates of reaction of reactions 2 and 3, decreasing
the yield of benzene (4) and toluene (6).
• With the base case conditions, 1.7 atm is the
optimum inlet pressure to minimize the deficit
(maximize styrene (2) in comparison to benzene
(4) and toluene (6)).
• Because the process is losing money in this base
case design, minimizing the feed rate will
decrease this deficit at the base inlet pressure
and temperature.

Influence of Pressure- P0 = 1 atm
Notice the large increase in the difference between the production of the styrene (2) and
the production of the benzene (4) and toluene (6). See how this corresponds to the
increasing profit.

Influence of Pressure- P0 = 1 atm (Optimum for
base conditions)
There is an even greater increase in the difference between the production of
the styrene (2) and the production of the benzene (4) and toluene (6). See how
this corresponds to the increasing profit.

Influence of Pressure- P0 = 3 atm
Notice the difference between the production of styrene (2) and the production
of the benzene (4) and toluene (6) has decreased from the optimized case;
however the profit is not as negative as when the pressure was set to 5 atm.

Base Case Stream Table
Stream ID Units Initial Conditions Feed into Reactor Outlet Conditions
Temperature Kelvin 713.15 950 874.05
Pressure atm 5 5 5
Hydrocarbon Mass Flow Total lb/hr 10000 10000
Hydrocarbon Molar Flow Total lbmol/hr 94.53 121.828
Steam Mass Flow lb/hr 0 0
Molar Flow of Components
Ethylbenzene lbmol/hr 90.47 45.159
Styrene lbmol/hr 1.631 25.681
Hydrogen lbmol/hr 0 6.039
Benzene lbmol/hr 0.256 3.507
Ethylene lbmol/hr 0 3.251
Toluene lbmol/hr 2.169 20.18
Methane lbmol/hr 0 18.011
Catalyst Weight lb 500
Profit $/hr -207.707

Steam Contacting Method 1:
Heat Exchanger
*The steam mass flow rate is held constant at its maximum value (18,000 lb/hr) for each trial
**Optimum pressure was found to be less than one atmosphere for each trial but the lowest
achievable pressure for this process is 1 atm. It was found that 1 atm is the optimum pressure
at each trial for this method.

Block Flow Diagram- PBR with Heat
Exchanger
Actual mass of the catalyst was calculated using data specific to our catalyst given in
the problem statement rather than the 500 lb given in the base case.

Optimization of PBR with Heat Exchanger
• Notice minimizing the pressure to 1 atm and
maximizing the temperature of the steam to 1050
K are two of the optimized conditions.
– Optimized pressure is below 1 atm.
– Lowering steam pressure increases the amount of
steam needed to be used (decreases profit).
• Lowering steam flow, at a given steam
temperature, decreases product flow rates and the
profit (for conditions below maximum steam
pressure and temperature).
• To optimize, find an inlet temperature and feed
flow rate that maximize the amount of styrene (2)
produced in comparison to benzene (4) and
toluene (6).

Energy Balance
• Because the steam is not being injected, it does not alter the
reaction as shown in the base case.
• Must include the energy balance as mass flow rate and
temperature of the steam affect the profit.
Note the steam leaving the heat exchanger will not reach the inlet temperature to
the reactor (T0). A factor of 10 K is added to T0 on the steam side of the energy
balance to account for this.

Trial 1a
*Approximate maximum profit at these conditions before exceeding maximum steam flow rate (18000 lb/hr)
0
5
10
15
20
25
30
35
870 875 880 885 890 895 900 905 910
Profit($/hr)
Inlet Temperature (K))
Profit vs Temperature @1 atm
11000 lb/hr
12000 lb/hr
13000 lb/hr

Trial 1b
*Approximate maximum profit at these conditions before exceeding maximum steam flow rate (18000 lb/hr)
0
5
10
15
20
25
30
35
0 2000 4000 6000 8000 10000 12000 14000 16000
Profit($/hr)
Mass Feed Rate (lb/hr)
Profit vs Feed Rate @1 atm
890 K
900 K
910 K

Heat Exchanger Packed Bed Stream Table
Pressure atm 1 1 0.969
Steam Temperature Kelvin 1050 1050
Profit $/hr 34.167

Steam Contacting Method 2:
Direct Injection
*The steam mass flow rate is held constant at its maximum value (18,000
lb/hr) for each trial

Block Flow Diagram- PBR with Direct
Injection of Steam

Optimization of PBR with Direct Injection
• Maximizing the steam flow rate and the steam
temperature again maximizes the difference in
wanted vs unwanted products.
– Optimized pressure is not below 1 atm.
• Inlet pressure and temperature into the reactor,
as well as the feed flow rate are to be optimized
to obtain the maximum pressure.
• Optimized profit of $370.94 $/hr is greater than
the profit of $34.17 $/hr using a heat exchanger.

Adjustments from Base Case
Alters the total output flow within the rate
of reaction equations
Alters the total value of the flow* heat
capacities, used in the temperature
equation of the ODE solve block- same
equation as the base.

Energy Balance
Note the temperature of the steam reaches that of the feed upon heating because
of the direct injection. Steam flow rate and steam temperature are within the
profit function:

Trial 1a
*950 K Data omitted for exceeding maximum steam temperature (1050 K)
310
315
320
325
330
335
340
345
350
355
3 4 5 6
Profit($/hr)
Inlet Pressure (atm)
Profit vs Pressure @7000 lb/hr
930 K
940 K

Trial 2a
**All data for Trial 3a was omitted for exceeding maximum steam temperature (1050 K)
340
341
342
343
344
345
346
347
348
3 4 5 6
Profit($/hr)
930 K

Trial 1b
*Approximate maximum profit at these conditions before exceeding maximum steam temperature (1050 K)
315
320
325
330
335
340
345
350
355
360
365
370
928 930 932 934 936 938 940 942 944 946
Profit($/hr)
Profit vs Temperature @7000 lb/hr
4.2 atm
4.4 atm
4.6 atm

Trial 2b
340
345
350
355
360
365
370
375
929 930 931 932 933 934 935 936 937 938
Profit($/hr)
Inlet Temperature (K)
4.2 atm
4.4 atm
4.6 atm

Trial 3b
325
330
335
340
345
350
355
360
919 920 921 922 923 924 925 926 927 928
Profit($/hr)
4.2 atm
4.4 atm
4.6 atm

Trial 1c
342
344
346
348
350
352
354
356
358
360
362
7900 8000 8100 8200 8300 8400 8500 8600 8700 8800
Profit($/hr)
Profit vs Feed Rate @930 K
4.2 atm
4.4 atm
4.6 atm

Trial 2c
345
350
355
360
365
370
375
6900 7000 7100 7200 7300 7400 7500 7600 7700 7800
Profit($/hr)
4.2 atm
4.4 atm
4.6 atm

Trial 3c
340
345
350
355
360
365
370
375
5900 6000 6100 6200 6300 6400 6500 6600 6700 6800
Profit($/hr)
Mass Feed Rate (lb/hr
4.2 atm
4.4 atm
4.6 atm

Direct Injection Packed Bed Stream Table
Temperature Kelvin 713.15 940 879
Pressure atm 4.5 4.5 4.455
Profit $/hr 370.937

Alternative Design Rational- Adiabatic
FBR Modeled as a CSTR
Fluidized Bed Reactor:
• Does not resemble a plug flow reactor and is
modeled as CSTR.
• Requires more catalyst than a packed bed for
the same conversion.
• Effective in controlling temperature when
operating in a narrow temperature range.
• Effective when utilizing small quantities of
catalyst.

Adjustments of FBR from PBR
Adjustments are due to the differences
between energy balances of a PFR and a
mixed flow. In this case we are modeling
an adiabatic FRB as a CSTR.
Mixed Flow Energy Balance:

FBR Modeled as CSTR ODE Solver
Note the lack of pressure drop as it is adiabatic

Steam Contacting Method 3: Heat
Exchanger Adiabatic Fluidized Bed
Modeled as a CSTR
*The steam mass flow rate is held constant at its maximum value
(18,000 lb/hr) for each trial
**Optimum pressure was found to be less than one atmosphere for each
trial but the lowest achievable pressure for this process is 1 atm. It was
found that 1 atm is the optimum pressure at each trial for this method.

Optimization of FBR- Heat Exchanger
• Notice minimizing the pressure to 1 atm and maximizing
the temperature of the steam to 1050 K are two of the
optimized conditions.
– Optimized pressure is below 1 atm.
– Lowering steam pressure increases the amount of steam
needed to be used (decreases profit).
• Although there is a negative profit, data indicates that
there are conditions of inlet pressure and temperature
and a mass flow rate that minimize the deficit, aside
extremely low values of mass flow rate.
• As the mass flow rate approaches zero, the reaction does
not take place, and the deficit decreases.
– Not a profitable model.

Trial 1a
*Values at 6000 lb/hr & 960 K and 7000 lb/hr 950 & 960 K the maximum steam temperature (1050 K) was exceeded so
the data were omitted
**Further optimization of this reactor was deemed unnecessary as all independent variable combinations were
resulting in negative profits
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
935 940 945 950 955 960 965
Profit($/hr)
Profit vs Temperature @1 atm
5000 lb/hr
6000 lb/hr
7000 lb/hr

Alt Design Heat Exchanger Fluidized Bed Stream Table
Pressure atm 1 1 1
Profit $/hr -21.411

Steam Contacting Method 4: Direct
Injection Adiabatic Fluidized Bed
Modeled as a CSTR
*The steam mass flow rate is held constant at its maximum value (18,000
lb/hr) for each trial

Optimization of FBR- Direct Injection
• Just as is the case for the direct injection of
steam with the PBR, maximizing steam flow
rate and temperature maximizes the difference
in wanted vs unwanted products.
– Optimized pressure is not below 1 atm.
• Inlet pressure and temperature into the
reactor, as well as the feed flow rate are to be
optimized to obtain the maximum pressure.
• Optimized profit of $156.04 is less than the
optimized profit of $370.94 for the direct
injection into the PBR.

Trial 1a
132
134
136
138
140
142
144
146
148
150
3 4 5 6
Profit($/hr)
960 K
970 K

Trial 2a
*970 & 980 K Data omitted for exceeding maximum steam temperature (1050 K)
142.8
143
143.2
143.4
143.6
143.8
144
144.2
144.4
144.6
3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
Profit($/hr)
960 K

Trial 3a
*970 & 980 K Data omitted for exceeding maximum steam temperature (1050 K)
149.2
149.4
149.6
149.8
150
150.2
150.4
150.6
150.8
151
3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
Profit($/hr)
960 K

Trial 1b
140
142
144
146
148
150
152
154
156
964 966 968 970 972 974 976
Profit($/hr)
4 atm
4.2 atm
4.4 atm

Trial 2b
134
136
138
140
142
144
146
148
150
152
954 956 958 960 962 964 966
Profit($/hr)
4 atm
4.2 atm
4.4 atm

Trial 3b
125
130
135
140
145
150
155
944 946 948 950 952 954 956 958 960 962
Profit($/hr)
4 atm
4.2 atm
4.4 atm

Trial 1c
132
134
136
138
140
142
144
146
148
150
152
4000 4200 4400 4600 4800 5000 5200 5400 5600
Profit($/hr)
4 atm
4.2 atm
4.4 atm

Trial 2c
100
110
120
130
140
150
160
3000 3200 3400 3600 3800 4000 4200 4400 4600
Profit($/hr)
4 atm
4.2 atm
4.4 atm

Trial 3c
100
105
110
115
120
125
130
135
140
145
150
2500 2700 2900 3100 3300 3500 3700 3900 4100
Profit($/hr)
Mass Feed Rate (lb/hr
4 atm
4.2 atm
4.4 atm

Alt Design Direct Injection Fluidized Bed Stream Table
Temperature Kelvin 713.15 967 879
Pressure atm 4.3 4.3 4.455
Profit $/hr 156.036

Analysis of Rates of Reactions and Production of All Reactors
PBR FBR PBR FBR
Rate of RXN 1 (lbmol/ lb*hr) 7.882*10^-4 0.001 3.459*10^-4 0.002
Rate of RXN 2 (lbmol/ lb*hr) 3.692*10^-5 7.45*10^-5 1.131*10^-5 5.635*10^-5
Rate of RXN 3 (lbmol/ lb*hr) 3.022*10^-4 2.058*10^-4 4.498*10^-4 7.469*10^-4
Flow of Styrene Out (lbmol/ hr) 33.97 19.81 30.25 22.651
Flow of Benzene Out (lbmol/hr) 1.983 1.152 0.96 0.954
Flow of Toluene Out (lbmol/hr) 6.567 3.982 11.399 11.742
Feed Rate (lb/hr) 7770 5200 12100 7000
Percent Diff Styrene vs sum of
unwanted compounds 74.83% 74.08% 59.14% 43.95%
Direct Injection of Steam Heat Exchanger
The PBR with direct injection of steam is the most profitable reactor. It has very low reaction rates
for 2 and 3, and the largest percent difference between producing desired styrene and unwanted
toluene and benzene. The FBR with the direct injection of steam produces the least amount of
benzene and toluene collectively; however, the PBR has a higher profit due to the larger amount of
styrene being made (mass feed rate is 33% greater). The PBR using a heat exchanger is able to
operate at a high flow rate, but it produces a large amount of toluene, decreasing the profit. As
seen on the chart, the FBR utilizing a heat exchanger has a very poor percent difference between
styrene and the two main unwanted products without an exceptionally large feed rate.

Evaluation of Adiabatic FBR to PBR
As can be seen from the conversions of Ethylbenzene for the four cases, a high conversion of
this reactant does not necessarily coordinate to a higher profit. The importance lies in how
much of the desired products are formed from the ethylbenzene.
• Conversion of Ethylbenzene

Appendix
• Thermodynamic Equilibrium
This graph compares the equilibrium constant given in the
problem statement to the general equilibrium constant equation
versus temperature. It is clear that both of these methods yield
similar results because their data overlaps one another.

References
(1) Levine, Ira N. "Atomic Weights." Physical
Chemistry. 6th ed. New York: McGraw-Hill,
1978. 990-91. Print.
(2) Yaws, Carl L. Chemical Properties Handbook.
N.p.: n.p., n.d. - Access Engineering from
McGraw-Hill. Web.
(3) Levenspiel, Octave. Chemical Reaction
Engineering. 3rd ed. New York: Wiley, 1972.
Print.

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