UNIVERSITI TEKNOLOGI MARA
FAKULTI KEJURUTERAAN KIMIA
REACTION ENGINEERING LABORATORY
(CHE506)
NAME:
STUDENT NO :
KHAIRUL AMIRIN BIN KHAIRUL ANUAR
2017632082
PUTERA NAJMEEN FARITH BIN ABDUL RAZAK
2017632096
NURUL AMIRAH BINTI MUSDAFA KAMAL
2017632124
NURUL AIDA BINTI MOHAMMAD
2017632132
NURUL KAMILAH BINTI KHAIROL ANUAR
2017632192
NURLINA SYAHIIRAH BINTI MD TAHIR
2017632214
GROUP
: EH2205I
EXPERIMENT
: TUBULAR FLOW REACTOR (BP101 – B)
DATE PERFORMED
: 24th SEPTEMBER 2018
SEMESTER
:5
PROGRAMME / CODE : CHEMICAL ENGINEERING / EH220
SUBMIT TO
: DR. FARID MULANA
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
Title
Abstract/Summary
Introduction
Aims
Theory
Apparatus
Methodology/Procedure
Results
Calculations
Discussion
Conclusion
Recommendations
Reference
Appendix
TOTAL MARKS
Allocated Marks (%)
Marks
5
5
5
5
5
10
10
10
20
10
5
5
5
100
Remarks:
Checked by:
Rechecked by:
---------------------------
---------------------------
Date:
Date:
TABLE OF CONTENT
1.0
ABSTRACT ................................................................................................................... 2
2.0
INTRODUCTION......................................................................................................... 3
3.0
OBJECTIVES ............................................................................................................... 4
4.0
THEORY ....................................................................................................................... 5
5.0
MATERIALS & APPARATUS ................................................................................... 9
6.0
METHODOLOGY ..................................................................................................... 10
7.0
RESULTS .................................................................................................................... 13
8.0
CALCULATIONS ...................................................................................................... 18
9.0
DISCUSSION .............................................................................................................. 18
10.0 CONCLUSION ........................................................................................................... 26
11.0 RECOMMENDATIONS............................................................................................ 27
12.0 REFERENCES ............................................................................................................ 28
13.0 APPENDICES ............................................................................................................. 29
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
1
1.0
ABSTRACT
The goals of the two experiment is to examine the effect of pulse input and step change input
in tubular flow reactor and to construct a residence time distribution (RTD) in both experiment.
In addition, a conductivity measurement of different conversion values between sodium
hydroxide and ethyl acetate is also determined for the third experiment. The first and second
experiment is conducted using the Tubular Flow Reactor (Model BP 101) where NaOH and
Et(Ac) solution are fed into the reactor with de-ionized water flow at constant 700 mL/min for
experiment 1 and salt solution at constant 700 mL/min for experiment 2. In experiment 3, the
conductivity of NaOH concentration by mixing 100 ml of deionised water with different
conversion is recorded for the calibration curve for the y – intercept value and the slope. The
conductivity value for inlet and outlet in the TFR is observed for every 30 seconds and the data
is recorded. The mean residence time, the variance, σ2 and skewness, s3 were three moment
of the residence time distribution (RTD) function calculated for Pulse Input and Step Input
experiment. Both experiment shows positive skewness, however, for Step Input Experiment
the skewness cannot be verified since the curve shows a rather directly proportional relation
over time and not a bell shape curve.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
2
2.0
INTRODUCTION
A tubular flow reactor is a vessel which the flow is continuous, steady state and organized so
that the conversion of the chemicals and other dependant variables are functions of position
within the reactor than the time. Tubular reactor similar to batch reactors in providing high
driving force which decrease as the reactions continue down the tubes. In ideal tubular reactor,
the reaction time is the same for all flowing material at any given tube cross section. Flow in
tubular reactor can be laminar as with the viscous fluid and it enormously deviate from ideal
plug flow behaviour or turbulent as with gases.
Usually, turbulent flow generally preferred to laminar flow because establishing turbulent
flow can cause in inconveniently long reactors or required undesirable high feed rates.
Moreover, the advantages of tubular flow reactor are high conversion rate per reactor volume,
efficient use of reactor volume and good for large capacity processes. The disadvantages of
tubular flow reactor are reactor temperature difficult to control and the composition variations.
The function of using residence time distribution is to study the chemical reactor
performance. In ideal tubular reactor, all the atoms leaving the reactor have been inside it for
exactly the same amount of time. The time for the atoms have spent in the reactor is called the
residence time of atoms in the reactor. The residence time distribution of a reactor is a
characteristic of the mixing that occurs in the chemical reactor. There is no axial mixing in a
tubular reactor, and this gap is reflected in the RTD. Nevertheless, the RTD exhibited by a
given reactor yield different clues to the type of mixing occurring within it and is one of the
most informative characterizations of the reactors.
A parameter frequently used to calculate RTD whether it was ideal or non-ideal gas was
space time, τ and equal to mean residence time, tm. Besides that, it is very common to compare
RTD by using their moments instead of trying to compare their entire distribution. For this
purpose, three moments are being used which are mean residence time tm, second moment
(variance) and third moment (skewness).
The variance, σ2 is define as an indication of the spread of the distribution and the greater
the value of this moment is, the greater the distribution’s spread will be. Lastly, the skewness,
s3 is define as measure the extent that a distribution is skewed in one direction or another in
reference to mean. Rigorously, for complete description of distribution, all moments must be
determined. So that these three are usually sufficient for a reasonable characterization of an
RTD.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
3
3.0
OBJECTIVES
The objectives for Experiment 1 are to examine the effect of pulse input in a tubular flow
reactor and to construct a residence time distribution (RTD) function for the tubular flow
reactor. Meanwhile, the objectives for Experiment 2 are to examine the effect of a step change
input in tubular flow reactor and to construct a residence time distribution (RTD) function for
the tubular flow reactor. In addition, for the third experiment the objective is to determine the
conductivity measurement of different conversion values between sodium hydroxide and ethyl
acetate.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
4
4.0
THEORY
The Residence – Time Distribution (RTD) for the saponification reaction between ethyl
acetate, Et(Ac) and sodium hydroxide, NaOH solution inside the Tubular Flow Reactor (BP101
– B) shows the characteristic of the mixing of both reactants that occurs inside the reactor.
Inside the reactor, the reactants are continually consumed as the reactant flow along the length
of the reactor.
𝐍𝐚𝐎𝐇 + 𝐄𝐭(𝐀𝐜) → 𝐍𝐚(𝐀𝐜) + 𝐄𝐭𝐎𝐇
𝐍𝐚𝐎𝐇 + 𝐄𝐭(𝐀𝐜)
→
𝐍𝐚(𝐀𝐜) + 𝐄𝐭𝐎𝐇
Figure 1- Tubular Flow Reactor. No radial variations in velocity, concentration,
temperature or reaction rate
The residence -time distribution function is represent in a plotted graph of E(t) as a
function of time. This function shows in a quantitative manner of how much time the mixed
fluid stays inside the reactor before leaving the reactor.
Figure 2 - The E Curve
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
RTD is determined experimentally by injecting chemically inert substance known as
tracer into the reactor at t = 0 and measuring the concentration of the tracer at the effluent
stream as a function of time (Fogler, 2006). The two most common methods of injecting tracer
into the reactor are pulse input and step input.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
5
Pulse Input In A Tubular Flow Reactor
Figure 4 – Typical Concentration – Time Curve at the Inlet and Outlet Stream
for Pulse Input Experiment
An amount of tracer is suddenly injected in one shot into the feedstream entering the reactor as
short a time as possible. The injection is for single input and single output system which only
flows carries the tracer material across the system boundary. RTD function, E(t) can be
determined directly from this experiment.
Since the volumetric flow rate is assumed constant,
𝐑𝐞𝐬𝐢𝐝𝐞𝐧𝐜𝐞 𝐓𝐢𝐦𝐞 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧, 𝐄(𝐭) =
Where,
𝐂(𝐭)
∞
∫𝟎 𝐂(𝐭)
𝐝𝐭
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟏
C(t) = Concentration of the tracer (mS/cm)
Step Change Input In A Tubular Flow Reactor
Figure 5 - Typical Concentration – Time Curve at the Inlet and Outlet Stream
for Step Change Input
A constant rate of tracer is added to the feed that is initiated at time t = 0. Thus, the inlet
concentration of the tracer, Co is constant with time. From this experiment, the cumulative
distribution can be determined directly, F(t).
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
6
Co(t) =
0
t<0
(Co) constant
t≤0
The cumulative distribution, F(t) represents the fraction of effluent that has been in reactor for
time t = 0 until t = t.
𝐂𝐮𝐦𝐮𝐥𝐚𝐭𝐢𝐯𝐞 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧, 𝐅(𝐭)
𝐂𝐨𝐮𝐭
]
=[
𝐂𝟎 𝐬𝐭𝐞𝐩
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟐
Differentiation of the cumulative distribution function yield to RTD function,
𝐑𝐞𝐬𝐢𝐝𝐞𝐧𝐜𝐞 𝐓𝐢𝐦𝐞 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧, 𝐄(𝐭) =
𝐝 𝐂(𝐭)
[
]
𝐝𝐭 𝐂𝟎 𝐬𝐭𝐞𝐩
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟑
The mean residence time, tm shows the average time the fluids stay inside the reactor (Rochelle
Fourie, 2016).
∞
𝐅𝐢𝐫𝐬𝐭 𝐌𝐨𝐦𝐞𝐧𝐭, 𝐌𝐞𝐚𝐧 𝐑𝐞𝐬𝐢𝐝𝐞𝐧𝐜𝐞 𝐓𝐢𝐦𝐞, 𝐭 𝐦 = ∫ 𝐭 𝐄(𝐭) 𝐝𝐭
𝟎
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟒
The spread of the distribution which is the magnitude of the variance, σ2 . The greater the
magnitude, the greater the distribution’s spread will be (Fogler, 2006).
∞
𝐒𝐞𝐜𝐨𝐧𝐝 𝐌𝐨𝐦𝐞𝐧𝐭, 𝐕𝐚𝐫𝐢𝐚𝐧𝐜𝐞, 𝛔𝟐 = ∫ (𝐭 − 𝐭 𝐦 )𝟐 𝐄(𝐭) 𝐝𝐭
𝟎
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟓
The extent that a distribution is skewed in one direction is measured by the skewness’s
magnitude which also means how differs the distribution is compared to the normal distribution
(Rouse, 2012).
𝐓𝐡𝐢𝐫𝐝 𝐌𝐨𝐦𝐞𝐧𝐭, 𝐒𝐤𝐞𝐰𝐧𝐞𝐬𝐬, 𝐬𝟑 =
𝟏
∞
𝟑
𝟑 ∫ (𝐭 − 𝐭 𝐦 ) 𝐄(𝐭) 𝐝𝐭
𝛔𝟐 𝟎
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟔
7
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
𝐟(𝐗)𝐝𝐗 =
Where,
𝐡
(𝐟 + 𝟒𝐟𝟏 + 𝟐𝐟𝟐 + 𝟒𝐟𝟑 + 𝟐𝐟𝟒 + ⋯ + 𝟒𝐟𝐍−𝟏 + 𝐟𝐍 )
𝟑 𝟎
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟕
N = Number of segment
𝐡=
𝐗𝐍 − 𝐗𝟎
𝐍
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟖
8
5.0
MATERIALS & APPARATUS
1. Tubular Flow Reactor (Model: BP 101)
2. De-ionized water
3. Sodium Hydroxide (NaOH)
4. Ethyl Acetate (Et(Ac))
5. Stopwatch
Figure 6 - Tubular Flow Reactor (Model: BP 101) (Front View)
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
9
6.0
METHODOLOGY
6.1
Preparation of Calibration Curve for Conversion Vs Conductivity
1) 1 litre of sodium hydroxide, NaOH (0.1 M), 1 litre of sodium acetate, Na(Ac) (0.1
M), and 1 litre of de-ionised water, H2 were prepared.
2) The conductivity values of the mixture was determined for each conversion by
mixing the ratio of the solution mixtures on appendix A with the 100 ml de-ionised
water.
6.2
General Start Up
1) All the valves are ensured to be closed except for valve V7.
2) The following solutions are prepared for Experiment 1, Experiment 2 and
Experiment 3.
Tank
Experiment 1 & 2
Experiment 3
B1
Deionized water
0.1M NaOH solution
B2
0.05 NaCl solution
0.1M Et(Ac) solution
The water de-ionizer is connected to the laboratory water supply.
3) The power for the control panel is switched on.
4) The water jacket B4 and pre-heater B5 is filled with clean water. The valves V13
and V8 are opened. Then, pump P3 is switched on to circulate the water through
pre-heater B5.
5) The stirrer motor M1 is switched on and the speed is set up to be 200 rpm.
6) Valves V2 and V10 are opened. Then, pump P1 is switched on. The pump is
adjusted to flow rate of 700mL/min at flow meter FI-01. Then, valve V10 is
closed and pump P1 is switched off.
7) Valves V6 and V12 are opened. Then, pump P2 is switched on. The pump is the
adjusted to flow rate of 700 mL/min at flow meter FI-02. Then, valve V12 is
closed and pump P2 is switched off.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
10
6.3
Experiment 1 – Pulse Input in Tubular Flow Reactor
1) The general start-up procedures was done.
2) Valve V9 was opened and pump P1 was switched on.
3) Flow controller for Pump P1 was adjusted to give an approximated constant flow
rate of 700 ml/min of de-ionized water into the reactor R1 at FI-01.
4) The de-ionized water was allow to flow through the reactor R1 until the conductivity
values at both inlet (QI-01) and outlet (QI-02) were stable at low levels. Both
conductivity values were recorded.
5) Valve V9 was closed and pump P1 was switched off.
6) Valve V11 was opened and pump P2 was switched on while the timer was started
simultaneously.
7) Pump P2 flow controller was adjusted to give an approximated constant flow rate of
700 ml/min for salt solution into the reactor R1 at FI-02.
8) The salt solution was allowed to flow for 1 minute. The timer was reset and restart.
9) Valve V11 was closed and Pump P2 was switched off. Then, valve V9 was quickly
opened and Pump P1 was quickly switched on.
10) Flow controller for P1 was adjusted to give a constant de-ionized water flow rate of
700 ml/min.
11) Conductivity values at both inlet (QI-01) and outlet (QI-02) were recorded at regular
intervals of 30 seconds until all readings become almost constant and they
approached stable low level values.
12) The general shut-down procedures was done.
13) Graph conductivity values vs time from the recorded data was plotted.
14) Value of E(t) was determined and graph of E(t) as a function of time was plotted.
15) Value of RTD function plotted was compared with the Experiment 2.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
11
6.4
Experiment 2 – Step Change Input in Tubular Flow Reactor
1) The general start-up procedures was done.
2) Valve V9 was opened and Pump P1 was switched on.
3) Flow controller for Pump P1 was adjusted to give an approximated constant flow
rate of 700 ml/min of de-ionized water into the reactor R1 at FI-01.
4) The de-ionized water was allow to flow through the reactor R1 until the
conductivity values at both inlet (QI-01) and outlet (QI-02) were stable at low
levels. Both conductivity values were recorded.
5) Valve V9 was closed and pump P1 was switched off.
6) Valve V11 was opened and pump P2 was switched on while the timer was started
simultaneously.
7) Conductivity values at both inlet (QI-01) and outlet (QI-02) was recorded
repeatedly at regular intervals of 30 seconds until all readings were almost constant.
8) The general shut-down procedures was done.
9) Graph conductivity values vs time from the recorded data was plotted.
10) Value of E(t) was determined and graph of E(t) as a function of time was plotted.
11) Value of RTD function plotted was compared with the Experiment 1.
6.5
General Shut Down
1) Pumps P1, P2 and P3 are all switched off. Then, valves V2 and V6 are closed.
2) The heater is then switched off.
3) The cooling water circulating through the reactor is keep while the stirrer motor is
running to allow the water jacket to cool down to room temperature.
4) The power for the control panel is then switched off.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
12
7.0
RESULTS
Table 1 - Table for Preparation of Calibration Curve
Solution Mixture
Concentration
Conductivity
of NaOH (M)
(mS/cm)
100 mL
0.0500
23.6
25 mL
100 mL
0.0375
14.90
50 mL
50 mL
100 mL
0.0250
9.21
75%
25 mL
75 mL
100 mL
0.0125
4.23
100%
-
100 mL
100 mL
0.0000
0.0654
Conversion
0.1 M
0.1 M
NaOH
Na (Ac)
0%
100 mL
-
25%
75 mL
50%
H2 O
Table 2 – Experiment 1: Pulse Input in a Tubular Flow reactor
Time
Conductivity
(min)
(mS/cm)
E(t),
min-1
tE(t)
(t-tm)2E(t)
(t-tm)3E(t)
min2
min3
Inlet
Outlet
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.5
3.7
0.2
0.2143
0.1072
0.4158
-0.5791
1.0
0.1
0.3
0.3214
0.3214
0.2562
-0.2288
1.5
0.0
0.3
0.3214
0.4821
0.0496
-0.0195
2.0
0.0
0.4
0.4286
0.8572
0.0049
0.0005
2.5
0.0
0.3
0.3214
0.8035
0.1185
0.0719
3.0
0.0
0.3
0.3214
0.9642
0.3939
0.4361
3.5
0.0
0.1
0.1072
0.3752
0.2769
0.4450
4.0
0.0
0.0
0.0
0.0
0.0
0.0
4.5
0.0
0.0
0.0
0.0
0.0
0.0
5.0
0.0
0.0
0.0
0.0
0.0
0.0
5.5
-
-
0.0
0.0
0.0
0.0
6.0
-
-
0.0
0.0
0.0
0.0
Flow Rate
= 700 mL/min
Input Type
= Pulse Input
Reactor Volume
= 4L
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
13
Table 3 - Moments of Residence Time Distribution Function (Pulse Input)
Mean Residence Time, tm
1.8929 min
Variance, 𝛔𝟐
0.7922 min2
0.0176 min3
Skewness, s3
Table 4 - Experiment 2: Step Input In Tubular Flow Reactor
Time
Conductivity
(min)
(mS/cm)
Inlet
E(t),
Outlet
min-1
tE(t)
(t-tm)2E(t)
(t-tm)3E(t)
min2
min3
C(t)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.5
2.9
0.0
0.0
0.0
0.0
0.0
1.0
3.3
0.0
0.0
0.0
0.0
0.0
1.5
3.5
0.0
0.0
0.0
0.0
0.0
2.0
3.5
0.0
0.0
0.0
0.0
0.0
2.5
3.6
0.1
0.027
0.0675
0.0966
0.1827
3.0
3.6
0.2
0.0541
0.1623
0.3094
0.7401
3.5
3.7
0.2
0.0541
0.1894
0.4523
1.3080
4.0
3.6
0.2
0.0541
0.2164
0.6223
2.1106
4.5
3.7
0.3
0.0811
0.3650
1.2282
4.7798
5.0
3.7
0.3
0.0811
0.4055
1.5641
6.8689
5.5
3.7
0.3
0.0
0.0
0.0
0.0
6.0
3.7
0.3
0.0
0.0
0.0
0.0
Flow Rate
= 700 mL/min
Input Type
= Step Input
Reactor Volume
= 4L
Table 5 - Moments of Residence Time Distribution Function (Step Input)
Mean Residence Time, tm
0.6084 min
Variance, 𝛔𝟐
1.7560 min2
Skewness, s3
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
4.1138 min3
14
Conductivity vs Conversion
Conductivity (mS/cm)
25
20
y = -23.096x + 21.949
R² = 0.9783
15
10
5
0
-5
0%
20%
40%
60%
80%
100%
120%
Conversion (%)
conductivity
Linear (conductivity )
Figure 7 - Graph of Conversion against Conductivity of Calibration Curve
The graph shows the conductivity decreases linearly with conversion. Thus, the higher
the conversion, the smaller the conductivity. The slope of the linear line is slope = -23.096, and
the y – intercept = 21.949. Thus, at the conductivity 21.949 mS/cm, the conversion to product
is approximately zero.
Conductivity (mS/cm)
Conductivity Outlet vs Time
0.5
0.4
0.3
0.2
0.1
0
-0.1 0
1
2
3
Time (min)
4
5
6
conductivity outlet
Figure 8 - Graph of Conductivity against Time (Pulse Input)
The graph shows the C(t) curve with a bell shape pattern. From t = 0 until t = 2, the
conductivity increase over time but from t = 2 until t = 5, the conductivity decreases over time.
However, there is three peaks instead of one peak in case of ideal reactor.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
15
Conductivity (mS/cm)
Conductivity Outlet vs Time
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05 0
1
2
3
4
Time (min)
5
6
7
Conductivity Outlet
Figure 9 - Graph of Outlet Conductivity against Time (Step Input)
The graph shows the conductivity increase linearly over time. However, there are few
fluctuation at around t = 1.8 min until t = 2 min and t = 3.5 min until t = 4 min.
E(t), min-1
Graph of E(t) vs Time,t
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05 0
0
0
0.4286
0.3214 0.3214
0.3214 0.3214
0.2143
0.1072
0
1
2
3
4
5
t, min
Figure 10 - Residence Time Distribution Function for the Reactor (Pulse Input)
The graph shows the residence time distribution (RTD) function against time. The E(t)
curve shows a bell-shape pattern with three peaks at t = 1 min, t = 2 min and t = 3 min.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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E(t), min-1
Graph of E(t) vs Time,t
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0.08110.0811
0.05410.05410.0541
0.027
0
0
0
0
0
0
0.5
1
1.5
2
2.5
t, min
3
3.5
4
4.5
5
E(t)
Figure 11 - Residence Time Distribution Function for the Reactor (Step Input)
The graph shows the residence time distribution (RTD) function over time. The E(t)
curve increase linearly over time.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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8.0
CALCULATIONS
Sample Calculation for Space Time, 𝝉
𝐒𝐩𝐚𝐜𝐞 𝐓𝐢𝐦𝐞, 𝛕 =
Space Time, τ =
𝐕𝐨𝐥𝐮𝐦𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐑𝐞𝐚𝐜𝐭𝐨𝐫
𝐕𝐨𝐥𝐮𝐦𝐞𝐭𝐫𝐢𝐜 𝐅𝐥𝐨𝐰𝐫𝐚𝐭𝐞
4L
(700 mL/min)
Space Time, τ = 5.7143 min
1L
1000mL
Experiment 1: Pulse Input in Tubular Flow Reactor
∞
1. Calculate the value of integral ∫0 𝐶(𝑡)𝑑𝑡.
For N+1 points, where N is even:
Where,
∫
XN
X0
h
f(x)dx = (f0 + 4f1 + 2f2 + 4f3 + 2f4 + ⋯ + 4fN−1 + fN )
3
XN − X0
N
4min − 0min
= 0.5
h=
8
h=
The 4.5th minutes and 5th are not included because the value will still show zero value.
4
∫ 𝐶(𝑡)𝑑𝑡 =
0
4
∫ 𝐶(𝑡)𝑑𝑡 =
0
𝟒
0.5
(0 + 4(0.2) + 2(0.3) + 4(0.3) + 2(0.4) + 4(0.3) + 2(0.3) + 4(0.1)
3
+ 0)
0.5
(5.6)
3
∫ 𝐂(𝐭)𝐝𝐭 = 𝟎. 𝟗𝟑𝟑𝟑 𝐦𝐒. 𝐦𝐢𝐧/𝐜𝐦
𝟎
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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2. Divide each value of C(t) with the integral to obtain a value of E(t).
Sample calculation at 0.5th minute:
E(t) =
C(t)
4
∫0 C(t)dt
mS
cm
E(t) =
0.9333 mS. min/cm
0.2
𝐄(𝐭) = 𝟎. 𝟐𝟏𝟒𝟑 𝐦𝐢𝐧−𝟏
3. Calculation on Moments in RTD function:
∞
a) Mean Residence Time, t m = ∫0 tE(t)dt.
4
t m = ∫ tE(t)dt =
0
Where,
h
(f + 4f1 + 2f2 + 4f3 + 2f4 + ⋯ + 4fN−1 + fN )
3 0
XN − X0
N
4min − 0min
= 0.5
h=
8
h=
tm =
tm =
0.5
(0 + 4(0.1072) + 2(0.3214) + 4(0.4821) + 2(0.8572) + 4(0.8035)
3
+ 2(0.9642) + 4(0.3752) + 0)
0.5
(11.3576)
3
𝐭 𝐦 = 𝟏. 𝟖𝟗𝟐𝟗 𝐦𝐢𝐧
∞
b) Second moment, Variance, σ2 = ∫0 (t − t m )2 E(t)dt.
∞
h
σ2 = ∫ (t − t m )2 E(t)dt = (f0 + 4f1 + 2f2 + 4f3 + 2f4 + ⋯ + 4fN−1 + fN )
3
0
σ2 =
σ2 =
0.5
(0 + 4(0.4158) + 2(0.2562) + 4(0.0496) + 2(0.0049) + 4(0.1185)
3
+ 2(0.3939) + 4(0.2769) + 0)
0.5
(4.7532)
3
𝛔𝟐 = 𝟎. 𝟕𝟗𝟐𝟐 𝐦𝐢𝐧𝟐
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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c) Third moment, Skewness, s3 =
1
3
σ2
∞
∫0 (t − t m )3 E(t)dt.
∞
h
∫ (t − t m )3 E(t)dt = (f0 + 4f1 + 2f2 + 4f3 + 2f4 + ⋯ + 4fN−1 + fN )
3
0
∞
∫ (t − t m )3 E(t)dt
0
=
0.5
(0 + 4(−0.5791) + 2(−0.2288) + 4(−0.0195)
3
+ 2(0.0005) + 4(0.0719) + 2(0.4361) + 4(0.4450) + 0)
∞
∫ (t − t m )3 E(t)dt = 0.0148 min3
0
σ = √ σ2 = √0.7922 = 0.8901
1
σ2 = √σ = √0.8901 = 0.9434
3
σ2 =
3
s =
σ2
1
σ2
=
0.7922
= 0.8397
0.9434
∞
1
3
)
(t
(0.0148)
E(t)dt
=
∫
−
t
m
3
0.8397
σ2 0
1
𝐬𝟑 = 𝟎. 𝟎𝟏𝟕𝟔 𝐦𝐢𝐧𝟑
Experiment 2: Step Input in Tubular Flow Reactor
1.
Divide each value of C(t) with final concentration value, C0 of the inlet and differentiate it
against time to obtain a value of E(t).
C0 = 3.7 min
Sample calculation at 2.5th minute:
0.1 t
E(t) =
3.7 min
𝐄(𝐭) = 𝟎. 𝟎𝟐𝟕 𝐦𝐢𝐧−𝟏
E(t) =
d C(t)
(
)
dt C0
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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2.
Calculation on Moments in RTD Function:
∞
a) Mean Residence Time, t m = ∫0 tE(t)dt.
5
h
t m = ∫ tE(t)dt = (f0 + 4f1 + 2f2 + 4f3 + 2f4 + ⋯ + 4fN−1 + fN )
3
0
Where,
XN − X0
h=
N
5min − 0min
= 0.5
10
h=
5
t m = ∫ tE(t)dt
0
tm =
0.5
(0 + 4(0) + 2(0) + 4(0) + 2(0) + 4(0.0675)
3
+ 2(0.1623) + 4(0.1894) + 2(0.2164) + 4(0.3650) + 0.4055)
=
0.5
(3.6505)
3
𝐭 𝐦 = 𝟎. 𝟔𝟎𝟖𝟒 𝐦𝐢𝐧
∞
b) Second moment, Variance, σ2 = ∫0 (𝑡 − 𝑡𝑚 )2 𝐸(𝑡)𝑑𝑡.
5
ℎ
∫ (𝑡 − 𝑡𝑚 )2 𝐸(𝑡)𝑑𝑡 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 + ⋯ + 4𝑓𝑁−1 + 𝑓𝑁 )
3
0
5
σ = ∫ (𝑡 − 𝑡𝑚 )2 𝐸(𝑡)𝑑𝑡
2
σ2 =
0
0.5
(0 + 4(0) + 2(0) + 4(0) + 2(0) + 4(0.0966)
3
+ 2(0.3094) + 4(0.4523) + 2(0.6223) + 4(1.2282) + 1.5641)
=
0.5
(10.53599)
3
𝛔𝟐 = 𝟏. 𝟕𝟓𝟔𝟎 𝒎𝒊𝒏𝟐
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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c) Third moment, Skewness, s3 =
∞
5
1
3
σ2
∞
∫0 (𝑡 − 𝑡𝑚 )3 𝐸(𝑡)𝑑𝑡.
ℎ
∫ (𝑡 − 𝑡𝑚 )3 𝐸(𝑡)𝑑𝑡 = (𝑓0 + 4𝑓1 + 2𝑓2 + 4𝑓3 + 2𝑓4 + ⋯ + 4𝑓𝑁−1 + 𝑓𝑁 )
3
0
∫ (𝑡 − 𝑡𝑚 )3 𝐸(𝑡)𝑑𝑡
0
0.5
(0 + 4(0) + 2(0) + 4(0) + 2(0) + 4(0.1827) + 2(0.7401)
3
+ 4(1.3080) + 2(2.1106) + 4(4.7798) + 6.8689)
=
5
∫ (𝑡 − 𝑡𝑚 )3 𝐸(𝑡)𝑑𝑡 = 6.2754 𝑚𝑖𝑛3
0
𝜎 = √ σ2 = √1.7560 = 1.3251
1
𝜎 2 = √𝜎 = √1.3251 = 1.1511
3
𝜎2
3
=
s =
σ2
1
𝜎2
=
1.7560
= 1.5254
1.1511
4
1
3
)
(𝑡
(6.2754)
𝐸(𝑡)𝑑𝑡
=
∫
−
𝑡
𝑚
3
1.5254
σ2 0
1
𝐬𝟑 = 𝟒. 𝟏𝟏𝟑𝟖 𝒎𝒊𝒏𝟑
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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9.0
DISCUSSION
Experiment 1 and 2 is mainly to study the effect of pulse input and step input in a tubular flow
reactor. In order to study the effect, the residence time distribution (RTD) function, E(t) curve
of the tubular flow reactor is constructed. Besides, a calibration curve for conductivity versus
conversion is also prepared for saponification reaction of ethyl acetate Et(Ac) and sodium
hydroxide NaOH. For the calibration curve of conductivity versus conversion, the slope and yaxis intercept value is determined from the equation of the curve yield using excel. Based on
Figure 7, the slope = -23.096, while the y – axis intercept = 21.949.
For Pulse Input experiment, the C(t) curve shows a bell shape pattern with three peaks.
This three peaks shows that the flow inside the reactor is not ideal. For a flow to be ideal, the
C(t) curve needs to be increase and decrease with only one peak as shown in Figure 4. Thus,
this lead to assumption of the present of disturbance inside the reactor which most probably be
a dead volume. As for the C(t) curve for Step Input Experiment, the curve increase linearly
over time. However, approximately at t = 3 min until t = 4 min, the flow become constant
before back to the increase linearly pattern. This also shows the present of disturbance since an
ideal flow for step input is that the C(t) curve increase linearly with no fluctuation as shown in
Figure 5.
The tracer is a chemically inert substances allowed to be injected into the feed stream
and follows the reactants and products flow without disturbing the reaction in any ways. The
tracer flows in a single input at t = 0 and single output flows at t = t. The tracer concentration
which is represented in conductivity measurement is taken to determine three moments of the
Residence Time Distribution (RTD) function which are the mean residence time, t m, the
variance, σ2 , and also the skewness, s3.
The mean residence time measures the average time of the fluids staying inside the
reactor. Pulse Input Experiment measures the tm = 1.8929 min which represent the tracer
staying inside the reactor from t = 0 and t = t is approximately for about 1.8929 min. As for the
Step Input Experiment, the tm = 0.6084 min. This means that the reactants are allowed to react
and the product flows out to the effluent stream is approximately at the detected average time
interval.
The differences in the average time is due to the differences of the inlet concentration
of the salt solution between the two experiments. For the Pulse Input Experiment, the salt
solution is only allowed to flow into the reactor for 1 minutes, then the flow is stop before the
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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de-ionized water flow is set to be constant. This resulting in higher average time since the fluid
become less concentrated and the salt solution is spread throughout the reactor, making it
harder for the salt molecule to flow to the effluent stream. Differ with Step Input Experiment,
where the salt solution is allowed to flow constantly. So, although the salt solution also spread
throughout the reactor, the salt molecule is easier to flow out to the effluent stream due to the
constant flow of the salt solution into the reactor.
However, both value of the mean residence time is smaller than the space time for the
reactor which is 5.7143 min. This shows that fluid exit rather early. Based on (Fogler, 2006),
there could be dead volume manifested by internal circulation at the entrance of the tubular
reactor as shown in Figure 12, as the mean residence time smaller than the space time. The
dead volume takes up space that is not accessible and that is why the salt solution exit early
from the system volume.
Figure 12 - Dead Volume which resulting in early exit of fluids
The second moment is the variance of the RTD function. This variance shows the
spread of the distribution. Pulse Input Experiment measures the variance, σ2 = 0.7922 min2 and
Step Input Experiment measures the variance, σ2 = 1.7560 min2. The greater the magnitude,
the greater the distribution’s spread will be. Based on the magnitude, the dispersion of the salt
solution for Experiment 1 inside the reactor is lesser than in Experiment 2. This is also the same
case as in the mean residence time, tm. Since, smaller value of salt solution is allowed to flow
inside the reactor, the dispersion is also restricted. Thus, making the magnitude of the variance
for Step Input Experiment much greater since the distribution’s spread is also higher due to
constant flow of salt solution into the reactor.
The third moment to be considered in both experiment is the skewness, s3. This moment
shows how differs the distribution is compared to the normal distribution. In Pulse Input
Experiment, the skewness measured is s3 = 0.0176 min3 and in Step Input Experiment, the
skewness measured is s3 = 4.1138 min3. Both shows positive skewness which means the
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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Residence Time Distribution (RTD) function is skewed to the right. This means that, the fluids
inside the reactor going out earlier than the ideal situation. Based on the magnitude, the Pulse
Input skewness is closer to zero, thus nearer to the normal distribution compared to the Step
Input skewness which is 4.1138, rather too far from the normal distribution.
Based on the E(t) curve, the skewness can be verified as a positive skewness for the
Pulse Input Experiment. However, differs for Step Input Experiment where the skewness
cannot be verified since the curve shows a rather directly proportional relation over time and
not a bell shape curve. This problem could lies from the assumption for the calculation of the
E(t) value for the Step Input Experiment from the calculation part, since the direct value gain
from the experiment is cumulative distribution, F(t). In order to get the E(t) value, the F(t)
expression need to be differentiate. Since the differentiation of the F(t) value will yield to zero
since the value of the inlet and outlet conductivity is already determined from the experiment,
we assume that the F(t) value is to be multiply with time, t before being differentiated for the
E(t) value, so that there is present of variable t in the F(t) function. However, this somehow
resulting in the non-bell shape curve of the E(t) curve.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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10.0
CONCLUSION
From the experiment above, we able to examine the effect of pulse input and step change in a
tubular flow reactor and we can also distinguish both effects. The residence time distribution
(RTD) function also can be construct for the tubular flow reactor. Based the result obtained,
the sample calculations were done, and graphs were plotted
For experiment 1, the flow rate was kept constant at 700ml/min and de-ionized water
was used. The sum of C(t) came to a result of 1.9 mS.min/cm and the sum of E(t) came to result
of 2.0357 min-1. From the figure 1, we can see that from the start it was increasing for 2 minutes
and then it constantly drops until reach 4th minutes. This means that a unit pulse response was
recorded at the outlet stream, indicating a flow of conductivity. The mean residence time, t m
for pulse input was 1.8929 min whereas the variance, σ2 and skewness, s3 were 0.79922 min2
and 0.0176 min3.
For experiment 2, the effect of step change input was examined. The flow rate was also
kept constant at 700ml/min and same as de-ionized water used. The results and calculations
show that the sum of the conductivity was 1.3 mS.min/cm and the sum of E(t) was 0.5945 min1
. From figured 2, it shows that the data increases after 2 minutes and then constant for a minute
and then increases back. The mean residence time, tm for pulse input was 0.6084 min whereas
the variance, σ2 and skewness, s3 were 1.7560 min2 and 4.1138 min3.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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11.0
RECOMMENDATIONS
First, read and do the general start up and shut down procedure for each experiment to make
sure there is are no left over inside the chamber. Next, we need to make sure that all the valve
is completely open during the experiment and completely close when the experiment is done
according to the procedure given. Besides, other than Pulse Input and Step Input method, we
could also try to determine the residence time distribution (RTD) function using other traces
techniques such as negative step and frequency – response methods. Other than that, the
assumption being made need to be based on literature review and related book of chemical
reaction engineering. Lastly, wait for several minutes before record the outlet conductivity data
when the flow rate was already stabilized.
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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12.0
REFERENCES
Alqurri, S. (7 Jun, 2017). Tubular reactor. Retrieved from Slide Share:
https://www.slideshare.net/saidalqurri/tubular-reactor
Fogler, H. S. (2006). Element of Chemical Reaction Engineering. Michigan: Prentice Hall.
Plug flow reactor model. (n.d.). Retrieved from Wikipedia:
https://en.wikipedia.org/wiki/Plug_flow_reactor_model
Rochelle Fourie, M. N. (2016). Analysis and Comparison of the Residence Time
Distributions (RTDs) of a Continuous Stirred-Tank Reactor (CSTR), a Plug Flow
Reactor (PFR) and a Tubular Plug Flow Reactor (TPFR). In Advances in Chemistry
Research. USA: Nova Science Publisher.
Rouse, M. (December, 2012). Skewness. Retrieved from WhatIs.TechTarget:
https://whatis.techtarget.com/definition/skewness
Tubular reactor or plug flow reactor. (19 May, 2008). Retrieved from Bio Mine Wiki:
http://wiki.biomine.skelleftea.se/wiki/index.php/Tubular_reactor_or_plug_flow_react
or
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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13.0
APPENDICES
LAB REPORT ON TUBULAR FLOW REACTOR (L4)
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