# Tutorial 6 RTD

```17 Oct 18
CHEMICAL ENGINEERING
REACTOR TECHNOLOGY FUNDAMENTALS (ENCH3RT)
Tutorial 6
TOPIC: RESIDENCE TIME DISTRIBUTION
TUTORIAL: RESIDENCE TIME DISTRIBUTION
Question 1
i) State and sketch the reactor configuration for the following RTDs:
a)
b)
c)
d)
e)
f)
ii) Sketch cumulative age of each configurations.
1
17 Oct 18
CHEMICAL ENGINEERING
REACTOR TECHNOLOGY FUNDAMENTALS (ENCH3RT)
Tutorial 6
TOPIC: RESIDENCE TIME DISTRIBUTION
Question 2
Consider the following pulse injection tracer data:
t (min)
0.0
C (mol/dm3) 0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.2
16.4
18.0
17.2
15.6
13.2
10.4
6.8
3.2
0.0
a) Plot E(t), stating all required assumptions
b) Calculate the mean residence time and standard deviation
c) Compare the calculated MRTD with the expectations that result from inspecting the E(t)
curve
Question 3
The first order-order reaction
π΄
βΆ
π΅
-1
With k = 0.8 min is carried out in a real reactor with the following RTD function
For 2π ≥ π‘ ≥ 0 then E(t) = √π 2 − (π‘ − π)2 min-1 (hemi circle)
For π‘ &gt; 2π then E(t) = 0
a) What is the mean residence time?
b) What is the variance?
2
CHEMICAL ENGINEERING
REACTOR TECHNOLOGY FUNDAMENTALS (ENCH3RT)
TOPIC: RESIDENCE TIME DISTRIBUTION
17 Oct 18
Tutorial 6
c) What is the conversion predicted by the segregation model?
d) What is the conversion predicted by the maximum mixedness model
Question 4
The second-order reaction is to be carried out in a real reactor which gives the following outlet
concentration for a step input.
For 0 ≤ t ≤ 10 min then CT = 10(1 − e−0.1t )
For t ≥ 10 min then CT = 5 + 10(1 − e−0.1t )
a)
Propose the model and calculate model parameters, α and β?
b) What conversion can be expected in the real reactor?
c)
How would the model and conversion change if the outlet tracer concentration was
For t ≤ 10 min, then CT = 0
For t ≥ 10 min, then CT = 5 + 10(1 − e2(t−10) )
ππ3
ππ3
πππ
π0 = 1
, π = 0.1
, πΆπ΄0 = 1.25
πππ
πππ. πππ
ππ3
Question 5
A computational fluid dynamic study was conducted over a certain real reactor of volume 2.3 m3,
a sketch of the results is shown below:
3
CHEMICAL ENGINEERING
REACTOR TECHNOLOGY FUNDAMENTALS (ENCH3RT)
TOPIC: RESIDENCE TIME DISTRIBUTION
17 Oct 18
Tutorial 6
From the figure, it would appear as if, due to the locations of the entrance and exit points, it is
possible for a large fraction of the inlet stream to simply bypass the reactor (see the long vector
near the top). The mixer is located near the bottom left of the reactor, and the fluid in this vicinity
is fairly well mixed. However, past the mixer, the fluid appears to flow in plug mode to the exit
point.
The study was conducted at a flowrate of 0.5 m3/min; the same flowrate was used in an experiment
during which tracer was pulsed into the reactor and the exist RTD measured; the results are given
in the figure below,
4
CHEMICAL ENGINEERING
REACTOR TECHNOLOGY FUNDAMENTALS (ENCH3RT)
TOPIC: RESIDENCE TIME DISTRIBUTION
a)
17 Oct 18
Tutorial 6
Propose an equivalent reactor network so as to compartmentalise the system. Based on this network,
develop a model of the exit RTD E(θ) and use the experiment data to estimate any unspecified
b)
The fluid flowing through the reactor also contains solid particles of pure component B which reacts
with component A from the liquid phase as it flows. Component A is at a high concentration of 300
mol/min3 and the conversion of A is low enough that the concentration of A can be considered constant
and uniform everywhere inside the reactor. Component B, in the form of the particles, is disappearing
due to the reaction. As B is consumed in each particle, an ash layer (component C) is left behind, as
such, the particle total size does not change with time, but the unreacted core of B is disappearing with
time. It is believed that the transport of component A from the bulk phase to the surface of the particle
(external transfer) is limiting the reaction.
i.
Derive an expression to predict the rate of change of particle radius in terms of initial particle
radius R, surface reaction rate (area-based) constant ks, external mass transfer coefficient kc, molar
density of component B, viz. ρ and bulk concentration of A, viz. CAb.
ii.
If the particles are uniformly suspended in the fluid, what is the mean conversion? Apply the
following numerical values:
R = 1 cm; ks = 1.20 m/min; k = 4.5 m/min; ρ = 62 300 mol/m3; CAb = 35 mol/m3
iii. With regard to consuming component B, what would be the optimal flowrate for this system? In
addition to this, can you suggest any simple/physical means of improving the operation of this
reactor?
5
```