Tubular Plug Flow Reactor
MUHAMMAD ADLI BIN ABDULLAH (2020489808)
MUHAMMAD ALIF BIN AHMAD (2020898448)
NAILY QAISAH BINTI NAZLI (2020878116)
NOR MAISURAH BINTI HASBULAH (2020834696)
Abstract – The objectives of these experiments are to
investigate the effects of pulse change and step change in
a tubular flow reactor as well as to calculate the residence
time distribution (RTD) for both experiments. In addition,
we conduct an experiment to determine the calibration
curve. In the first experiment, sodium hydroxide solution
(NaOH) and ethyl acetate solution (Et (Ac)) are fed into
the reactor at a constant flow rate of 700 mL/min of
deionized water, whereas in the second experiment, the salt
solution is fed at a constant flow rate. Every 30 seconds,
the data is collected. The conductivity is measured to
determine the calibration curve by mixing the calculated
concentration on NaOH solution with deionized water. The
mean residence time, variance and skewness of all the data
collected during the experiment 1 are 0.912 min, 0.194
min2, 0.14 min3 while for experiment 2 are 2.038 min,
0.323 min2 and -0.493min3. The objectives for these
experiments were achieved.
I. INTRODUCTION
Tubular reactors are steady-state, continuous flow
vessels that can be used to mix various chemical
substances. It is dependent on the position of the
reactants rather than time to complete the chemical
reactions.
The plugs travel in the reactor’s axial
direction, each with a different composition than the
ones before and after it. Each plug is treated as a
separate entity, effectively acting as an infinitesimally
small batch reactor with mixing that approaches zero
volume. The residence time of the plug element is
derived from its position in the reactor as it flows down
the PFR. When scaling flow reactors, one of the
factors to consider is residence time distribution
(RTD).
Tubular reactors are favored by many people
due to their numerous benefits. The most practical
reactors for use in a variety of applications are tubular
reactors. This reactor's main benefits include its
simplicity of mechanical design and ease of
maintenance and cleaning due to lack of any moving
parts. In addition, it has features such as low pressure
drops compared to other reactors and displays
extremely high conversion rates per volume. Next, it
is an ideal apparatus for observing any quick reactions
and can be applied to large-scale operations.
Residence time distribution (RTD) is a
probability distribution function of a chemical reactor
where it estimates the amount of time a fluid element
might spend inside the reactor. When comparing the
behavior of actual reactors to their ideal models,
chemical engineers use the RTD to characterize the
mixing and flow within the reactors. This is helpful not
only for troubleshooting current reactors but also for
forecasting reaction yields and designing new reactors.
Figure 1: Model of Plug Flow Reactor
1
II. OBJECTIVES
The objectives of Experiment 1 are to
examine the effect of a pulse input and to construct a
residence time distribution (RTD) function for the
tubular flow reactor.
For Experiment 2, it is conducted to examine
the effect of a step change and to construct the
residence time distribution (RTD) function for the
tubular flow reactor. Lastly, to determine the
conductivity measurement of different values between
NaOH and Et (Ac).
The RTD can be experimentally estimated by
inserting a chemically inert substance known as a
tracer into the reactor now t = 0 and then measuring
the concentration of the tracer in the effluent stream as
a function of time (Fogler, 2006). The pulse input and
the step input are the two techniques of delivering
tracer into the reactor that are used the most frequently.
Since the volumetric flow rate is assumed
constant,
𝐑𝐞𝐬𝐢𝐝𝐞𝐧𝐜𝐞 𝐓𝐢𝐦𝐞 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧,
𝐸(𝑡) =
𝐶(𝑡)
∞
∫0
𝐶(𝑡) 𝑑𝑡
III. THEORY
Where, C(t) = Concentration of the tracer (mS/cm)
The Time Distribution (RTD) for the
saponification reaction inside the Tubular Flow
Reactor (BP101-B) shows the mixing of the ethyl
acetate, Et (Ac), and the sodium hydroxide, NaOH
solution. Reactor internals are constantly consuming
the reactants since the flow of reactants is continuous.
Step change input in a tubular flow reactor
Figure 4- Typical concentration- time curve at the inlet and outlet
stream for step change input
Figure 2: Tubular Flow Reactor with no radial variations in
velocity, concentration, temperature or reaction rate.
The residence-time distribution function is
shown as a plotted graph of E(t) as a function of time.
This graph represents the function. This function
provides a quantitative representation of the amount
of time that the fluid mixture occupies inside the
reactor before it is allowed to exit the reactor.
IV. PROCEDURES
The feed is started at time t = 0, and a steady rate of
tracer is fed to it. As a result, the tracer, Co, has a
constant inlet concentration over time. This
experiment allows for direct determination of the
cumulative distribution, F (t).
The cumulative distribution, F(t) represents the
fraction of effluent that has been in the reactor for time
t = 0 until t = t.
Cumulative Distribution, F(t)
=[
Figure 3– Illustration of tracer injection at t = 0 and detection for
the tracer concentration at the effluent stream to determine the
Residence Time Distribution for the system
𝐶𝑜𝑢𝑡
]
𝐶0 𝑠𝑡𝑒𝑝
2
Differentiation of the cumulative distribution function
yield to RTD function,
𝐑𝐞𝐬𝐢𝐝𝐞𝐧𝐜𝐞 𝐓𝐢𝐦𝐞 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧, 𝐄(𝐭)
𝐸(𝑡) =
𝑑 𝐶(𝑡)
[
]
𝑑𝑡 𝐶0 𝑠𝑡𝑒𝑝
IV.MATERIAL AND APPARATUS
1. Tubular Flow Reactor (Model: BP 101)
2. Deionized water
3. Sodium Hydroxide (NaOH)
4. Ethyl Acetate (Et (Ac))
5. Stopwatch
The mean residence time, tm shows the average time
the fluids stay inside the reactor (Rochelle Fourie,
2016). 𝐅𝐢𝐫𝐬𝐭 𝐌𝐨𝐦𝐞𝐧𝐭, 𝐌𝐞𝐚𝐧 𝐑𝐞𝐬𝐢𝐝𝐞𝐧𝐜𝐞 𝐓𝐢𝐦𝐞,
∞
𝑡𝑚 = ∫0
𝑡𝐸(𝑡) 𝑑𝑡
The spread of the distribution is the magnitude of the
variance, 𝜎2 . When the magnitude increases, so does
the dispersion of the distribution (Fogler, 2006).
𝐒𝐞𝐜𝐨𝐧𝐝 𝐌𝐨𝐦𝐞𝐧𝐭, 𝐕𝐚𝐫𝐢𝐚𝐧𝐜𝐞,
∞
𝜎2 = ∫
(𝑡 − 𝑡𝑚 )2 𝐸(𝑡) 𝑑𝑡
0
The magnitude of the skewness indicates the degree to
which a distribution deviates from the normal
distribution, providing a measure of the degree to
which the distribution is skewed in one direction
(Rouse, 2012).
𝐓𝐡𝐢𝐫𝐝 𝐌𝐨𝐦𝐞𝐧𝐭, 𝐒𝐤𝐞𝐰𝐧𝐞𝐬𝐬,
3
𝑠 =
∞
1
(𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡
3∫
𝜎2
0
Numerical Evaluation of Integrals In order to
∞
determine the integral of ∫0 𝐶(𝑡) 𝑑𝑡 . For N + 1
points, where N is even, (Fogler, 2006)
𝑋𝑁
∫
𝑋0
ℎ
𝑓(𝑋)𝑑𝑋 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3
3
+ 2𝑓4 +. . . +
4𝑓𝑁−1 + 𝑓𝑁
Where, N = Number of segments
ℎ=
𝑋𝑁 − 𝑋0
𝑁
Figure 4-Tubular Flow Reactor (Model BP 101) (Front View)
V. PROCEDURE
General startup procedure:
Make sure that all valves, except for valves
V7, were in the closed position. Both the 0.1M NaOH
solution and the 0.1M Et (Ac) solution were produced
in tank B1 and tank B2 correspondingly.
The power supply for the control panel has
been activated. Both the pre-heater B5 and the water
jacket B4 were loaded with purified water. The pump
designated as P1 was activated. The flow rate of the
pump was modified to be 700 mL/min as measured by
the flow meter F1-01. While the valves V2 and V1
were opened, the stirrer motor, M1, was activated and
its speed was increased to 200 revolutions per minute
(rpm).
3
During the time that valves V13 and V8 were
being opened, pump P3 was activated so that water
could be pumped through pre-heater B5. Both the
valve V10 and the pump P1 were turned off at the
same time.
After that, the valves V6 and V12 were
allowed to fully open. After that, the pump known as
P2 was activated. At flowmeter FI-02, the adjustment
for pump P2 was made to be 700 mL/min. In the end,
the valve V12 was shut off, and the pump P2 was
turned off.
Experiment 1:
To begin, go through the standard beginningof-operations steps. After that, the valve V9 should be
opened, and pump P1 should be turned on. The flow
controller for pump P1 should then be adjusted so that
a constant flow rate of deionized water enters reactor
R1 at a rate of approximately 700 ml/min at the FI-01
location. The next step is to allow the flow of
deionized water through the reactor to continue until
both the inlet (QI-01) and outlet (QI-02) conductivity
values are stable at low levels. Make a note of both
conductivity readings. Turn off the pump, and then
close the valve V9. Turn the pump P2 on while also
opening the valve V11. Turn on both clocks at the
same time. Adjust the flow controller on the pump P2
so that there is a consistent flow rate of salt solution
into the reactor R1 at 700 milliliters per minute at FI02.
Experiment 2:
Carry out the general processes for starting
things up. Turn the pump P1 on while also opening the
valve V9. Adjust the flow controller on the pump P1
so that there is a steady flow of deionized water into
the reactor R1 at approximately 700 ml/min at the FI01 location. Water that has been deionized should be
allowed to continue flowing through the reactor until
the conductivity values at the inlet (QI-01) and output
(QI-02) remain stable at low levels.
Take a record of both conductivity readings.
Pull the plug on the valve V9 and turn the pump P1
off. Turn the pump P2 on while also opening the valve
V11. Turn on both clocks at the same time.
Conductivity readings should be taken at regular
intervals of 30 seconds, first at the intake (QI-01) and
then at the outflow (QI-02). Keep recording the
conductivity values until all of the readings become
almost identical.
General shut down:
All three pumps, P1, P2, and P3, have been
turned off. After that, the valves V2 and V6 are shut
off. After that, the switch for the heater is turned off.
While the stirrer motor is operating, the cooling water
that is moving through the reactor is maintained to
permit the water jacket to gradually come down to
ambient temperature. After that, the power supply to
the control panel is disconnected completely.
After allowing the salt solution to run freely
for one minute, you should then reset the timer and
begin counting again. The time will begin counting
down from this point, which is the average pulse input.
Turn off the pump, and then close the valve V11. After
that, immediately turn on pump P1 and open valve V9
as rapidly as possible. Adjusting the P1 flow controller
should be done to keep the flow rate of deionized water
at a constant level of 700 milliliters per minute.
Conductivity readings at the inlet (QI-01) and outlet
(QI-02) should be recorded starting immediately. The
readings should be taken at regular intervals of 30
seconds. Keep recording the conductivity values until
all of the readings have become almost identical and
are getting closer to the stable low-level values.
4
VI. RESULTS
Experiment 1:
3.0
0.0
0.0
0.0
0.0
0.0
0.0
3.5
0.0
0.0
0.0
0.0
0.0
0.0
Table 2: Data for Pulse Input in Tubular Reactor
Conver
sion
(%)
Solution Mixtures
(mL)
NaOH
(0.1M)
0
100
Na (Ac)
(0.1M)
0
Concent
ration of
NaOH
(M)
Conduc
tivity
(𝜇 s)
Mean Residence Time, tm
H2O
-
100
0.0500
7.83
25
100
0.0375
6.87
0.912 min
Variance, 𝜎 2
0.194 min2
Skewness, s3
0.14 min3
Table 3: Data for tm, 𝜎 2 and s3 for Pulse Input
Flow Rate: 700 mL/min
25
75
Input Type: Step Input
50
50
50
100
0.0250
3.96
75
25
75
100
0.0125
2.13
100
-
100
100
0.0000
1.06
Table 1: Table for Preparation of Calibration Curve
Time
(min)
0.0
Conductivi
ty
(𝜇 s/cm)
E(t)
min 1
tE
(t)
(ttm)2E(t)
min2
(ttm)3E(t)
min3
Inlet
Outl
et
0.0
0.0
0.0
0.0
0.0
0.0
0
0.5
5.0
0.1
0.018
0.009
0.043
-0.066
Flow Rate: 700 mL/min
1.0
5.1
1.3
0.236
0.236
0.254
-0.264
Input Type: Pulse Input
1.5
5.5
5.0
0.909
1.364
0.263
-0.142
2.0
5.5
5.3
0.964
1.928
0.001
-0.053 x
10-3
2.5
5.5
5.3
0.964
2.41
0.206
0.095
3.0
5.5
5.3
0.964
2.892
0.892
0.858
3.5
5.5
5.3
0.964
3.374
2.061
3.013
Time
(min)
Conductivity
(𝜇 s/cm)
E(t),
min 1
tE
(t)
(ttm)2E(
t)
min2
(ttm)3E
(t)
min3
Inlet
Outlet
0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.5
0.0
4.8
0.717
0.359
0.122
-0.05
1.0
0.0
4.8
0.717
0.717
0.006
0.001
Mean Residence Time, tm
2.038 min
1.5
0.1
2.7
0.403
0.605
0.139
0.082
Variance, 𝜎 2
0.323 min2
2.0
0.0
0.3
0.045
0.09
0.053
0.058
Skewness, s3
-0.493 min3
2.5
0.0
0.0
0.0
0.0
0.0
0.0
Table 4: Data for Step Input in Tubular Reactor
Table 5: Data for tm, 𝜎 2 and s3 for Step Input
5
2.5
0.5
Sample Calculations:
∫0
Experiment 1 Pulse Input:
tm = 0.912 min
∞
Calculation for ∫0
1.
C(t) dt
4.
Calculation for (t-tm)2E(t) min2
ℎ
𝑋
∫𝑋 𝑁
= 0.122
𝑓(𝑥) 𝑑𝑥 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 +
3
0
2𝑓4 +. . .4𝑓𝑁−1 + 𝑓𝑁 )
5.
𝑋𝑁 −𝑋0
ℎ=
2.5𝑚𝑖𝑛 − 0𝑚𝑖𝑛
= 0.5
5
2.5
0.5
(0 + 4(4.8) + 2(4.8) + 4(2.7) + 2(0.3))
3
𝐶(𝑡) 𝑑𝑡 =
∫
Calculation for (t-tm)3E(t) min3
(t-tm)3E(t) min3 = [(0.5-0.912)3] (0.717)
𝑁
0
2.5
3
(t-tm)2E(t) min2 = [(0.5-0.912)2] (0.717)
For N+1
ℎ=
𝑡𝐸(𝑡) 𝑑𝑡 = ( ) (5.47) = 0.912 min
= -0.05
6.
Space Time, τ
Space Time, τ =
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑜𝑟
𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒𝑠
0.5
𝐶(𝑡) 𝑑𝑡 = ( 3 ) (40.2) = 6.7 𝜇 s min / cm
∫0
2.
E(t) =
Calculation for E(t)
Space Time, τ =
Space Time, τ = 5.714 min
𝐶(𝑡)
2.5
7.
𝐶(𝑡) 𝑑𝑡
∫0
Calculation for Variance, 𝜎 2
When time at 0.5 min
E(t) =
𝜎2 = ∫
0
4.8 𝜇𝑠 / 𝑐𝑚
6.7 𝜇𝑠 𝑚𝑖𝑛 / 𝑐𝑚
3.
Calculation for Moments in RTD Function
∞
Means Residence Time, tm = ∫0
2.5
∫
0
ℎ=
(𝑡 − 𝑡𝑚 )2 𝐸(𝑡) 𝑑𝑡
𝜎2 =
0.5
(0 + 4(0.122) + 2(0.006) + 4(0.139)
3
+ 2(0.053))
𝜎2 = (
0.5
)(1.162) = 0.194 𝑚𝑖𝑛2
3
𝑋𝑁 − 𝑋0
𝑁
2.5𝑚𝑖𝑛 − 0𝑚𝑖𝑛
= 0.5
5
2.5
0
𝑡𝐸(𝑡) 𝑑𝑡
ℎ
𝑡𝐸(𝑡) 𝑑𝑡 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 +. . .4𝑓𝑁−1
3
+ 𝑓𝑁 )
ℎ=
∞
ℎ
= (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 +. . .4𝑓𝑁−1 + 𝑓𝑁 )
3
E(t) = 0.717 min 1
∫
4𝐿
(700 𝑚𝐿/𝑚𝑖𝑛)(1𝐿/1000𝑚𝐿)
𝑡𝐸(𝑡) 𝑑𝑡 =
0.5
(0 + 4(0.359) + 2(0.717) + 4(0.605)
3
+ 2(0.09))
6
Calculation for Skewness, s3
8.
∞
∫
0
(𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡
ℎ
= (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 +. . .4𝑓𝑁−1 + 𝑓𝑁 ) =
1.
3
0.1
E(t) =
5.5
(0 + 4(−0.05) + 2(0.001) + 4(0.082) + 2(0.058))
0.5
= ( )(0.246) = 0.041 min3
3
= √𝜎
3
𝜎2
=
1
𝜎2
s3 =
1
∫
s3 = (
∞
2.5
∫
1
ℎ=
(𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡
𝑡𝐸(𝑡) 𝑑𝑡 =
0
Sample Calculations:
Experiment 2 Step Input:
Calculation for
∞
∫0
C(t) dt
For N+1
𝑓(𝑥) 𝑑𝑥 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 +
3
0
2.5
∫0
0.5
𝑡𝐸(𝑡) 𝑑𝑡 = ( ) (12.23) = 2.038 min
3
tm = 2.038 min
4.
𝑁
2.5
∫
0
+
2.5
∫0
= 0.043
𝑋𝑁 −𝑋0
ℎ=
Calculation for (t-tm)2E(t) min2
(t-tm)2E(t) min2 = [(0.5-2.038)2] (0.018)
2𝑓4 +. . .4𝑓𝑁−1 + 𝑓𝑁 )
ℎ=
0.5
(0 + 4(0.009) + 2(0.236) + 4(1.364)
3
+ 2(1.928) +
2.41
3.
ℎ
𝑋
∫𝑋 𝑁
𝑋𝑁 − 𝑋0
𝑁
2.5𝑚𝑖𝑛 − 0𝑚𝑖𝑛
= 0.5
5
2.5
)(0.041) = 0.14 𝑚𝑖𝑛3
𝑡𝐸(𝑡) 𝑑𝑡
ℎ
𝑡𝐸(𝑡) 𝑑𝑡 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 +. . .4𝑓𝑁−1
3
+ 𝑓𝑁 )
0.194
=
= 0.292
0.664
∫
0.292
Calculation for Moments in RTD Function
ℎ=
3 0
𝜎2
)
∞
= √ 0.441 = 0.664
𝜎2
𝐶0
Means Residence Time, tm = ∫0
0
1
𝜎2
(
= 0.018 𝑚𝑖𝑛−1
2.
= √ 𝜎 2 = √0.194 = 0.441
𝜎
𝐶(𝑡)
𝑑𝑡
𝐶0 = 5.5 min
3
0.5
𝑑
E(t) =
2.5𝑚𝑖𝑛 − 0𝑚𝑖𝑛
= 0.5
5
Calculation for (t-tm)3E(t) min3
(t-tm)3E(t) min3 = [(0.5-2.038)3] (0.018)
= -0.066
0.5
𝐶(𝑡) 𝑑𝑡 = (0 + 4(0.1) + 2(1.3) + 4(5) + 2(5.3)
3
5.3)
0.5
𝐶(𝑡) 𝑑𝑡 = ( 3 ) (38.9) = 6.48 𝜇 s min / cm
7
5.
Calculation for Variance, 𝜎 2
𝜎2 = ∫
∞
(𝑡 − 𝑡𝑚 )2 𝐸(𝑡) 𝑑𝑡
0
ℎ
= (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 +. . .4𝑓𝑁−1 + 𝑓𝑁 )
3
𝜎2 =
0.5
(0 + 4(0.043) + 2(0.254) + 4(0.263)
3
+ 2(0.001) + 0.206)
0.5
𝜎 2 = ( )(1.94) = 0.323 𝑚𝑖𝑛2
3
6.
∞
Graph 1: Conductivity VS Conversion
Calculation for Skewness, s3
(𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡
∫
0
ℎ
= (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3
3
+ 2𝑓4 +. . .4𝑓𝑁−1 + 𝑓𝑁 )
0.5
=
(0 + 4(−0.066) + 2(−0.264)
3
+ 4(−0.142) +
2(−0.053 𝑥 10
−3
) + 0.095
Graph 2: Conductivity Outlet VS Time
0.5
= ( )(-1.265) = -0.211 min3
3
𝜎
= √ 𝜎 2 = √0.323 = 0.568
1
𝜎2 = √ 𝜎
3
𝜎2 =
s3 =
1
∫
∞
3 0
𝜎2
s3 = (
1
0.428
= √ 0.568 = 0.754
𝜎2
1
𝜎2
=
0.323
= 0.428
0.754
Graph 3: RTD, E(t) VS Time
(𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡
)(−0.211) = −0.493 𝑚𝑖𝑛3
Graph 4: Conductivity Outlet VS Time
8
Graph 5: RTD, E(t) VS Time
The residence time distribution is displayed
as departure time E(t) versus time-based on the data
that was collected for the second objective and
reported in the table. How long the atoms were within
the reactor is determined by their residence time
(Fogler, 2006). Therefore, mean residence time (tm)
measures how long fluids typically stay inside the
reactor. For the pulse input experiment, the computed
tm = 0.912 min refers to the material atoms that spent
the same amount of time in the reactor. Because of
this, the reactants are allowed to react, and the product
is released into the effluent stream at a rate that is
almost identical to the measured average time interval
(tm = 2.038 min) in the step input experiment.
VII. DISCUSSIONS
In a tubular flow reactor, two lab experiments
with pulse input and step input have been performed.
The goals are to investigate how a pulse input and step
change affect a tubular reactor, and then to construct a
residence time distribution (RTD) function for the
tubular flow reactor following the experiment.
Deionized water entered the reactor at a constant flow
rate of 700 ml/min. The conductivity of the solution at
its input and outflow was monitored throughout the
experiment until it reached a consistent value.
The C(t) curve for the Pulse Input experiment
displays a bell-shaped pattern with three peaks. These
three peaks demonstrate that the reactor's internal flow
is not optimal. Graph 2 illustrates how the C(t) curve
must increase and decrease with only one peak for a
flow to be optimum. As a result, it is assumed that
there is a disturbance inside the reactor, which is most
likely a dead volume. The Step Change Experiment's
C(t) curve shows a linear rise in slope with time.
However, the flow becomes steady from roughly t = 0
min to t = 0.5 min before returning to the increasing
linear trend. Since a perfect flow for step Input is one
in which the C(t) curve advances linearly with no
variation as seen in Graph 4, this also demonstrates
the existence of disturbance.
The variations in the mean residence periods
were due to differences in the input concentration of
the salt solution between the two trials. Before the
pulse input experiment permits the salt solution to
flow into the reactor for a maximum of one minute, the
deionized water flow is intended to be continuous at a
rate of 700 ml/min. The residence durations require a
smaller amount to react since the reactant has been
saturated before being reacted to its maximum point.
This is demonstrated by the bell-shaped curve when
the conductivity considerably rises from t=0 to t=1 but
falls when the volume of salt solution inside the
reactor diminishes. The salt solution is allowed to flow
continuously in the step-input experiment until all the
conductivity readings are nearly constant. As a result,
the reaction will intensify until it reaches its maximum
rate, which indicates that the conductivity becomes
constant at time t=5 and beyond.
Additionally, the RTD function calculates the
second moment as variance (2). The magnitude of this
moment, known as variance, serves as a measure of
the distribution's "spread." The bigger the value of this
moment, the wider the distribution will be (Fogler,
2006). The calculated variance for the pulse input
experiment is 0.194 min2, which is lower than the
calculated variance for the step input experiment,
which is 0.323 min2. According to the magnitude
computed, the pulse input experiment's salt solution
dispersion inside the reactor is more than it was for the
step input experiment.
9
This happened because the salt solution from
experiment 1 was already within the tube, which
caused the reaction to happen quickly but not just with
the salt solution that was already there. Because the
spread of the distribution is also constrained by the
volume of salt solution present inside the reactor, the
step input's variance is smaller than the pulse input.
The skewness, represented as s3, is the third
moment to be considered in both experiments. In this
instance, the distribution's deviation from the normal
distribution is visible. The measured skewness in the
step input experiment is s3 = -0.493 min3, while the
measured skewness in the pulse input experiment is s3
= 0.14 min3. Both exhibit positive skewness, which
denotes a rightward skewing of the Residence Time
Distribution (RTD) function. In other words, the fluids
inside the reactor burn out earlier than they would
under perfect circumstances. In comparison to the Step
Input skewness, which is -0.493 min3 and perhaps too
distant from the normal distribution, the Pulse Input
skewness is closer to zero and, as a result, closer to the
normal distribution.
Finally, a calibration curve for conductivity
vs conversion is also produced for the saponification
reaction between ethyl acetate Et (Ac) and sodium
hydroxide NaOH. Excel is used to produce the slope
and y-axis intercept value for the conductivity vs.
conversion calibration curve using the curve yield
equation. The slope is -0.0731 according to the
presented graph, and the y-axis intercept is 8.026.
VIII. CONCLUSION
We were able to analyze the effect of pulse input and
step change in a tubular flow reactor because of the
experiment described above, and we were also able to
differentiate between the two effects. There is also the
possibility of constructing the residence time distribution
(RTD) function for the tubular flow reactor. Calculations
and graphs were made based on the results of the samples
that were taken, which were then plotted.
In the first trial, the flow rate was maintained at 700
ml/min throughout, and the participants used deionized
water. The total of C(t) was calculated to have a value of
6.7 𝜇 s min / cm, while the total of E(t) was calculated to
have a value of 0.717 min 1. When we look at graph 2, we
can see that at first, it was going up, but after one minute,
it started going down, and it kept going down until it
reached the 2.5-minute mark. This indicates that a flow of
conductivity is occurring because of the recording of a unit
pulse response at the outlet stream. The variance, 𝜎 2 , and
skewness, s3, for the pulse input were 0.194 𝑚𝑖𝑛2 and
0.14 𝑚𝑖𝑛3 , respectively. The mean residence time, tm, for
the pulse input was 0.912 minute.
In the second experiment, we looked at how a step
change in input affected the outcome. The flow rate was
likewise maintained at a constant level of 700 ml/min and
was the same as that of the deionized water that was used.
According to the findings and the calculations, the total
amount of conductivity was 6.48 𝜇 s min / cm and the total
amount of E(t) was 0.018 𝑚𝑖𝑛−1 . Figure 2 demonstrates
that there is a rise in the data after two minutes, followed
by a period of stability for one minute. The variance, 𝜎 2 ,
and skewness, s3, for the pulse input were0.323 𝑚𝑖𝑛2 and
−0.493 𝑚𝑖𝑛3 , respectively. The mean residence time, tm,
for the pulse input was 2.038 minutes.
IX. RECOMMENDATION
Before beginning the experiment, it is
imperative that you better understand yourself with the
standard operating procedure and follow it to the
extent. Next, we must ensure that every valve is fully
open before beginning the experiment and fully closed
after it has been completed. The residence time
distribution (RTD) function could also be determined
using trace techniques like the negative step and
frequency - response methods in addition to the Pulse
Input and Step Input methods. Assumptions made
outside of this context, however, should be supported
by a literature review and appropriate books on
chemical reaction engineering. Finally, once the flow
rate has stabilized after waiting a few minutes, record
the data for the outlet conductivity.
10
References
FilsonFilter. (n.d.). Tubular Reactor: The
Ultimate FAQ Guide - Filson
Filter. Filson Filters. Retrieved
November 13, 2022, from
https://www.filsonfilters.com/tubul
ar-reactor
Plug Flow Reactor. (n.d.). Vapourtec.
Retrieved November 13, 2022,
from
https://www.vapourtec.com/flowchemistry/plug-flow-reactor/
Residence_Time_Distribution. (n.d.).
chemeurope.com. Retrieved
November 13, 2022, from
https://www.chemeurope.com/en/e
ncyclopedia/Residence_Time_Distr
ibution.html
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