BKF3741 Chemical Reaction Engineering Laboratory

SEMESTER 2 SESSION 2020/2021

RESIDENCE TIME DISTRIBUTION ANALYSIS OF A CONTINUOUS STIRRED

TANK REACTOR
How Jian Sin, Mohamad Nasrudin bin Zulkifli, Nurul Izzah binti Hamdan, Saunthariya a/p
Murili, Shubahshini a/p Mayelvaganam
Section 04, Group 03
Dr. Ruzinah binti Isha
Department of Chemical Engineering, College of Engineering
Universiti Malaysia Pahang, 26300 Gambang, Pahang, MALAYSIA.

ABSTRACT
The objectives of the experiment of residence time distribution (RTD) analysis of continuous
stirred tank reactor were to obtain RTD data from tracer injection and to estimate RTD
parameters. The experiment was started with the preparation of 9 sample of 0.5g of salt (NaCl)
to obtain the calibration curve for the concentration of table salt (NaCl) versus conductivity by
manipulating the mass of NaCl from 0.5g, 1.0g, 1.5g, 2.0g, 2.5g, 3.0g, 3.5g, 4.0g, 4.5g and 5.0g
in 1500 mL deionized water respectively to obtain the conductivity for different concentration
of NaCl. For the experimental part, the vessel was filled up with 1500 mL deionized water. A
solution of 5g salt (NaCl) in 1.5L water was prepared and the salt solution transferred into the
reactor and then the pump and stirrer was turned on. The valve was opened and the water
flowrate were adjusted to 150ml/min. The sample from the reactor were collected at every 2
minutes and the conductivity reading was determined from the sample and all observations are
recorded to obtained the conductivity value of the solution. The process repeated until the
conductivity value obtained is constant. Based on the calibration curve, the concentration of
NaCl was directly proportional to its conductivity due to the ionization of NaCl producing free
moving ions in the compound. The performance of CSTR in the experimental part depended on
the flow and mixing patterns in the reactor to a great extent. The concentration of NaCl is
decreasing when the time increase. This phenomenon occurred due to the decreasing
concentration of NaCl ions in CSTR as dilution happened. Besides, the residence time
distribution function, E(t) decreased as time increased. Hence it could be concluded that the
reactor behaved as an ideal CSTR.

Keywords: sodium chloride; deionized water; CSTR; residence time distribution; conductivity.

1. Introduction
The performance of a continuous chemical reactor depends to a great extent on the flow and
mixing patterns in the reactor. Most often, the theoretical features of ideal reactors have been
introduced in plug flow reactor or perfectly-mixed reactor Fogler (2006). In fact, most of the
calculations or design equations of reactors are based on ideal reactors. Nevertheless, the
behavior of an actual continuous chemical reactor cannot always be described in terms of either
ideal plug flow or perfect mixing. Imperfect mixing in stirred tanks, non-uniform flow
velocities in tubular reactors, and diffusion in any direction in which concentrations vary make
the exact relationship between fed and product variables difficult to represent mathematically.

1
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

Therefore, the flow pattern of a reactor needs to be known in order to estimate conversion,
hence a need to carry out residence time distribution analysis or RTD.

The RTD can be obtained by performing tracer or stimulus–response experiments, in which a

tracer is injected instantaneously (a pulse input) or at a constant rate (a step input) at the inlet
of a flow system and its concentration C(t) is measured at the exit as a function of time Fogler
(2006). RTD analysis is generally applicable to a flow system with one-inlet stream where a
tracer is injected.

2. Methodology
2.1. Materials
Deionized water, salt (NaCl).
2.2. Apparatus
Beaker, measuring cylinder, magnetic stirrer, conductivity meter, continuous stirred
tank reactor.
2.3. Preparation of calibration curve
Calibration curve was started with 0.5g of salt was weighed. Then, another 9 samples
of 0.5g of salt each was prepared. Next, 1.5L of deionized water was poured in the container.
After that, water container was put on the magnetic stirrer and the water was stirred.
Conductivity of the water was recorded. 0.5g of salt was added into the water. When the salt
has been dissolved, the conductivity was recorded. Last but not least, the procedure was
repeated for 9 other samples. Lastly, Conductivity for all 9 sample solutions was recorded.

2.4 Experimental procedure

Experimental procedure was started when deionized water was poured into the vessel.
Then, solution of 5g salt in 1.5L water was poured into the reactor. Next, the pump and stirrer
were turned on. The valve was opened and the water flow rate was adjusted to 150ml/min. After
that, the sample was collected for every two minutes. Last but not least, conductivity of the
solution was determined and the value was recorded. Lastly, the procedure was repeated until
constant conductivity value of the sample was obtained.

2.5 Shutdown procedure

Shutdown and cleaning were started when the pump and stirrer was switched off. All
the solution in both tanks was cleared and then the valve was closed.

3. Result and discussion

3.1 Plot the calibration curve of conductivity vs concentration of NaCl and discuss the
relationship between these parameters.

2
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

Conductivity(mS/cm) vs Concentration of
NaCl(mol/L)
8
Conductivity (mS/cm) y = 121.69x + 0.1282
6 R² = 0.9996
4

0
0 0.01 0.02 0.03 0.04 0.05 0.06
Concentration (mol/L)

Figure 1: Graph Conductivity (mS/cm) vs Concentration (mol/L)

From the above graph, the equation that derived is y=121.69x + 0.1282 where y represents the
conductivity in mS/cm while x represents the concentration of solutions in mol/L. Moreover,
the concentration of solution is directly proportional to the conductivity.
3.2 Discussion
1. Plot the transient concentration profile.
Based on the collected data, the RTD parameters are time, conductivity, concentration, and
E(t). We have the equation of from figure 1,

𝑦 = 121.69𝑥 + 0.1282

𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = 121.69 (𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛) + 0.1282

So, y is the conductivity and x is the concentration, we can rearrange into equation below to
find concentration at different time:
𝑦 − 0.1282
𝑥=
121.69

Time, t (min) Conductivity reading (mS/cm) Concentration of NaCl(mol/L)

0 7.22 0.05828
2 5.42 0.04349
4 3.70 0.02935
6 3.02 0.02376
8 2.45 0.01908
10 1.91 0.01464
12 1.54 0.0116
14 1.19 0.00873
16 0.99 0.00708
18 0.78 0.00536
20 0.57 0.00363
22 0.45 0.00264
24 0.39 0.00215

3
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

26 0.29 0.00133
28 0.25 0.001
30 0.22 0.00075
32 0.20 0.00059
34 0.19 0.00051
36 0.18 0.00043
38 0.18 0.00043
40 0.17 0.00034
42 0.17 0.00034
44 0.16 0.00026
46 0.16 0.00026
48 0.16 0.00026
Table 1: Concentration values with different times

Concentration of NaCl (mol/L) vs Time (min)

0.07
0.06
0.05
Concentration (mol/L)

0.04
0.03
0.02
0.01
0
0 10 20 30 40 50 60
-0.01
-0.02
Time (min)

Figure 2: Graph of concentration versus time, C(t)

2. Determine the RTD parameters based on the collected data.

With the concentration obtained, we can determine the parameter of residence time
distribution function, E(t). To obtain E(t) curve from the C(t) curve, we just using integral
method, which is the area under the C curve, then we calculate the area under curve by using
Simpson’s rule. So,

𝐶(𝑡)
𝐸 (𝑡 ) = 48
∫0 𝐶 (𝑡)𝑑𝑡

4
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

48
So, we must calculate for ∫0 𝐶 (𝑡)𝑑𝑡 part by using Simpson’s three-eight rule (four-
point). We must break the data into several parts as the formula will not suffice over the entire
range of data in table 3.2.

Simpson’s three-eighths rule:

Where,

The calculations for Simpson’s rules are shown below:

12 3
∫0 𝐶(𝑡) 𝑑𝑡 = 8(4) [0.05828 + 3(0.02935) + 3(0.01908) + 0.0116] = 0.3228

24 3
∫12 𝐶(𝑡) 𝑑𝑡 = 8(4) [0.0116 + 3(0.00708) + 3(0.00363) + 0.00215] = 0.06882

36 3
∫24 𝐶(𝑡) 𝑑𝑡 = 8(4) [0.00215 + 3(0.001) + 3(0.00059) + 0.00043] = 0.01103

48 3
∫36 𝐶(𝑡) 𝑑𝑡 = 8(4) [0.00043 + 3(0.00034) + 3(0.00026) + 0.00026] = 0.003735

48
∫0 𝐶(𝑡) 𝑑𝑡 =0.3228 + 0.06882 + 0.01103 + 0.003735 = 0.4064

Thus, to calculate E(t), we can use the equation below:

𝐶(𝑡)
E(t) = 0.4064

Time (min) Concentration E(t)

(mol/L)
(min-1)

0 0.05828 0.1434

2 0.04349 0.107

4 0.02935 0.0722

6 0.02376 0.0585

5
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

8 0.01908 0.0469

10 0.01464 0.036

12 0.0116 0.0285

14 0.00873 0.0215

16 0.00708 0.0174

18 0.00536 0.0132

20 0.00363 0.0089

22 0.00264 0.0065

24 0.00215 0.0053

26 0.00133 0.0033

28 0.001 0.0025

30 0.00075 0.0018

32 0.00059 0.0015

34 0.00051 0.0013

36 0.00043 0.0011

38 0.00043 0.0011

40 0.00034 0.0008

42 0.00034 0.0008

44 0.00026 0.0006

46 0.00026 0.0006

48 0.00026 0.0006

Table 2: The concentration and E(t) for each time is tabulated

3. From the trend of RTD, suggest prevailing issues. Determine whether the reactor is an
ideal CSTR?

6
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

Figure 3: Graph of E(t) versus time

From Figure 3, we can see that E(t) is decreasing with time. According to Werner at el, the
graph should produce a narrow peak and moves closer to unity afterwards if it is an ideal CSTR.
However, our graph is exponential graph, so we can assume that the reactor is a non-ideal
reactor. This is probably due to the less effective of mixing the NaCl. This is because when the
mixed NaCl is introduce into the re3actor it might be mix with other materials inside. Some
residue from every time experiment was done will remain in the tank as all the residue is
impossible to remove from the reactor at one time. Hence, this affect the performance of the
reactor. However, this can be overcome by increasing the stirrer speed, decreasing the solution
viscosity or bio catalyst concentration more effective reactor baffling. (Chaplin, 2004).

4. Conclusion and recommendations

In a conclusion, the conductivity or the concentration of the solution is decreasing and
slowly achieved equilibrium point throughout the reaction time. This happened as the solution
is being diluted with the pure water. The tabulated results show that conductivity significantly
decreases from 7.2 mS/cm to 0.19m S/cm within 34 minutes’ time frame and slowly decreases
the equilibrium point at 0.16 mS/cm at 48 minutes. This has turned out the fact that the
concentration of the solution is inversely proportional to time. From the trend of RTD obtained,
the existed CSTR reactor is not performed as an ideal condition where we obtain an exponential
graph.

For the recommendations, to make an improvement in the accuracy and safety of the
experiment, make sure that the conductivity meter is well calibrated before used to reduce the
instrumentation error. Besides, the conductivity meter must also be rinsed with the water after
taking each reading. In addition, the reactor must first be purged with the pure water to remove
(wash) and flash out the impurity which might contribute to the conductivity reading.
Furthermore, the CSTR water pump must be kept the same throughout the experiment as it may
cause the tracer happens to be flow out at the higher rate which is more than 150mL/min set,

7
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

and the flowrate is not constant. This can be done by adjusting the value of the flow rate. Lastly,
in order for the CSTR reactor to perform in a nearly perfect and ideal condition the stirrer speed
need to be increased and the solution viscosity should be decreased.

Reference
[1] Fogler, H. S., (2006). Elements of Chemical Reaction Engineering. New Jersey: Pearson Education, Inc
[2] Fogler, H. S. (2011). Elements of Chemical Reaction Engineering. New Jersey: Pearson Education.
[3] Fogler, H. (2008). Distribution of residence times for chemical reactors. In H. Fogler, Elements of Chemical
Reaction (p. 867). Pearson.
[4] Chaplin, M. (6 August, 2014). Continuous Flow Stirred Tank Reactor. Retrieved from Enzyme technology:
http://www1.lsbu.ac.uk/water/enztech/cstr.html

8
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

Appendix
Preparation of Solution for Calibration Curve

Volume of the solution = 1.5 L

Molar mass = 58.44 g/mol
Number of moles = Mass/ Molar Mass
Example = 5 /58.44 = 0.08556 mol

Concentration = Number of moles

Volume of solution
0.08556
= = 0.057
1.5

Mass of
Concentration(mol/L) Conductivity(mS/cm)
Nacl(g)

0 0 0.06

0.5 0.0057 0.76

1 0.0114 1.61

1.5 0.0171 2.22

2 0.0228 2.97

2.5 0.0285 3.62

3 0.0342 4.28

3.5 0.0399 4.98

4 0.0456 5.65

4.5 0.0513 6.36

5 0.057 7.05

Table 3: Mass, Concentration and Conductivity

9
BKF3741 Chemical Reaction Engineering Laboratory
SEMESTER 2 SESSION 2020/2021

Experiment Results

Time Conductivity (mS/cm)

0 7.22
2 5.42
4 3.70
6 3.02
8 2.45
10 1.91
12 1.54
14 1.19
16 0.99
18 0.78
20 0.57
22 0.45
24 0.39
26 0.29
28 0.25
30 0.22
32 0.20
34 0.19
36 0.18
38 0.18
40 0.17
42 0.17
44 0.16
46 0.16
48 0.16
Table 4: Time and Conductivity

10