Experiment no. 5 of Advance Reaction Engineering. The work submitted in vishwakarma government Engineering college, Ahmedabad, Gujarat

1. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
Experiment No. 5
Residence Time Distribution for Plug Flow Reactor (PFR)
5.1 Objective
• To construct ‘C’ and ‘E’ curve for delta function input.
• To calculate the dispersion number for different flow rates.
5.2 Apparatus
1. One tubular flow reactor with inlet and outlet flow arrangement.
2. Tracer injection system
3. Stop watch and test tubes
4. Titration set
5.3 Chemical
1. Oxalic acid ((CO2H)2(aq)) 0.05 N
2. Sodium Hydroxide (NaOH(aq)) 0.5 N
3. Hydrochloric Acid (HCl(aq)) 0.1 N
4. Indicator: Phenolphthalein
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2. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
5.4 Theory
According to the dispersion model; and by Fick’s law for molecular diffusion in x
direction the differential equation is
∂C
∂t
= D
∂2C
∂x2
Where, D = longitudinal or axial dispersion coefficient showing the degree of back
mixing during the flow. Introducing the dimensionless variables,
Z =
x
L
,θ =
t
t
= u
L
t
The basic differential equation becomes:
∂C
∂θ
=
D
uL
∂2C
∂z2
−
∂C
∂z
Where D/uL is called the dispersion number. For plug flow through reactor,
D
uL
→ 0
For mixed flow through reactor,
D
uL
→ ∞
The variance,
σ2
=
∑t2
i Ci
∑Ci
−t2 =
∑t2
i Ci
∑Ci
−
∑tiCi
∑Ci
2
For closed vessel (variance based on dimensionless time units)
σ2
θ =
σ2
t2
σ2
θ =
σ2
t2
= 2
D
uL
−2
D
uL
2
1−e−uL
D
5.5 Procedure
1. Standardize the Sodium hydroxide (NaOH) and Hydrochloric acid (HCl) solu-
tions by using 0.05 N Oxalic acid solutions before titration.
2. Start the circulation of a fluid through PRF and adjust the flow rate in range of
200 cm2/min to 1000 cm2/min.
Chemical Engineering Department, VGEC, Ahmedabad 22

3. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
3. First inject the dummy tracer and see how long the dummy tracer molecule
stays within the reactor. Divide that time into equal time interval and then
inject 5 N Sodium Hydroxide (NaOH) and start the stopwatch. Collect the
sample at a regular time interval. Collect number of samples that cover a total
time period that spent by dummy tracer molecule within the reactor. Titrate the
sample against 0.1 N Hydrochloric acid (HCl)) solutions.
4. Repeat the same procedure for another 3 different flow rates.
5.6 Calculation
• First of all plot the graph of concentration C (t) versus time (t) and find out
R ∞
0 C(t)dt either trapezoidal method or Simpson 1/3 rule or Simpson 3/8 rule
or area under the curve. One another approach of curve fitting and integration
of the curve is also suitable.
• Calculation of E(t):
E(t) =
C(t)
R ∞
0 C(t)dt
• Calculation of F(t):
F(t) =
Z t
0
E(t)dt
• Calculation of tm:
tm =
Z ∞
0
tE(t)dt
• Calculation of σ2:
σ2
=
Z ∞
0
(t −tm)2
E(t)dt
• Calculation of D/uL:
σ2
t2
m
= 2
D
uL
−2
D
uL
2
1−e−uL
D
Chemical Engineering Department, VGEC, Ahmedabad 23

4. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
Table 5.1: Observation table (Set 2)
Property Value Unit
Volumetric flow rate of water 0.54 L/min
Volume of PFR 3 L
N1=Conc. of NaOH 1 N
Residence time 5.5556 min
V1=volume of NaOH 5 mL
N2=Conc. Of HCl 1.1 N
Table 5.2: Experimental readings and calculation of various parameters (Set 2)
Sr. No.
Time=ti
(s)
V2=burette
reading
(mL)
N1=Ci=Conc. of
NaOH remained
(N)
Ei Fi
tiEi
(s)
(t-tm)2Ei
(s2)
1 0 0 0 0 0 0 0
2 30 0.5 0.5500 0.0009 0.0086 0.0259 13.2821
3 60 1.2 1.3200 0.0021 0.0462 0.1243 18.3208
4 90 2 2.2000 0.0035 0.1373 0.3109 14.1580
5 120 3.5 3.8500 0.0060 0.2878 0.7253 6.9972
6 150 4.2 4.6200 0.0073 0.4792 1.0880 0.1175
7 180 3.7 4.0700 0.0064 0.6758 1.1502 4.3115
8 210 2.1 2.3100 0.0036 0.8392 0.7616 11.3634
9 240 1.5 1.6500 0.0026 0.9441 0.6217 19.1483
10 270 0.6 0.6600 0.0010 0.9896 0.2798 13.9371
11 300 0.2 0.2200 0.0003 1.0000 0.1036 7.3600
12 330 0.1 0.1100 0.0002 1.0090 0.0570 5.3480
13 360 0 0 0 1.0218 0 0
Figure 5.1: C(t) Curve (Set 2)
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5. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
Figure 5.2: E(t) Curve (Set 2)
Figure 5.3: F(t) Curve (Set 2)
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6. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
Figure 5.4: tE(t) Curve (Set 2)
Figure 5.5: (t-tm)2E(t) Curve (Set 2)
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7. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
Table 5.3: Polynomial coefficients of various curve fitted curve and area under the curve (Set 2)
Polynomial
coefficients1 C(t) Curve E(t) Curve F(t) Curve t E(t) Curve (t-t2)2E(t) Curve
A -2.40E-13 -3.77E-16 -8.73E-15 -9.05E-14 1.66E-12
B 2.26E-10 3.55E-13 1.17E-11 9.38E-11 -1.40E-09
C -6.97E-08 -1.09E-10 -5.60E-09 -3.42E-08 3.36E-07
D 6.79E-06 1.07E-08 1.08E-06 4.99E-06 2.96E-06
E 6.28E-05 9.86E-08 -5.88E-05 -2.27E-04 -9.16E-03
F 4.90E-03 7.69E-06 1.44E-03 3.47E-03 7.84E-01
G 5.49E-02 8.62E-05 -1.37E-03 5.99E-03 -5.46E-01
Area under
the curve between
t=0 and t=300 s
636.9532 1 147.4034 154.0241 3275.9568
Table 5.4: Volumetric flow rate and dispersion number for all sets of experiments
Set
Volumetric flow rate
(L/min)
tm
(s)
σ2
(s2)
D/uL
1 0.55 156.0407 2962.477 1.7817
2 0.54 154.0241 3275.957 1.7785
3 0.5 152.5807 3461.348 1.7777
4 0.49 151.9576 3532.372 1.7795
Figure 5.6: Volumetric flow rate and dispersion number plot for all sets of experimets
5.7 Conclusion
Dispersion number initially decreases, then after reaching the minimum value of
around 1.7777, again increase with volumetric flow rate, but compare to CSTR it’s
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8. Laboratory Manual - ADVANCE REACTION ENGINEERING, Subject Code: 3723024 (Core-IV),
Enrollment No.: 200170730007
nature is not strong decrease and increase (U shape in PRF, rather than V shape of
CSTR).
Chemical Engineering Department, VGEC, Ahmedabad 28