RE-401

RE-401

Residence Time Distribution

GROUP : A12-b

Date of Experiment: 14/08/2015

Date of Presenting: 18/08/2015

Aakash Rajwani (120020021) Chirag Jha (120020015)

Rupansh Goyal (120020011) Nikhil Sharma (120020058)

Aim of the experiment

u  To determine the residence time distribution in the given configuration for pulse and step inputs

Theory

u  Residence Time Distribution - Different atoms take different time to come out of the reactor, the distribution of the various atoms coming out of the reactor with respect to time is called the residence time distribution

u  The residence time distribution (RTD) or more precisely the E(t) function may be looked upon as a correction factor to account for the non-ideality

u  RTD can be determined experimentally by injecting an inert chemical, molecule, or atom, called tracer, into the reactor at some time t = 0 and then measuring the tracer concentration 'C' in the exit stream as a function of time

u  Pulse and Step inputs are the two commonly used methods of injection.

Pulse Input - u  An amount of tracer No is suddenly injected in one shot into the feed stream

in as short a time as possible

u  The outlet concentration is then measured as a function of time

u  The effluent concentration-time curve is referred to as the C curve in the RTD analysis

u  We select ∆ t sufficiently small that the concentration of tracer, C(t), exiting between time t and t+ ∆ t is essentially constant

u  Then the amount of tracer material ∆ N, leaving the reactor between time t and t + ∆ t is

∆N = C (t) v ∆t

∆N/No = C(t) v ∆t / No

u  represents the fraction of the material that has a residence time in the reactor between time t and t +∆t

u  For a pulse injection we define,

E(t) = v C(t)/ No

u  therefore,

∆N / No = E(t) ∆ t

dN = v C(t) dt

u  and integrating, we obtain

No = 0∫∞ v C(t) dt

u  volumetric flow rate v is constant,

E(t) = C(t) / 0∫∞C(t)dt

Step Input - u  A constant rate of tracer is added to the feed at time t = 0

u  Thus, we have

C0(t) = 0 t < 0 C0(t) = C0 t ≥ 0

u  The concentration of the tracer in the feed to the reactor is kept at this level until the concentration in the effluent is indistinguishable from that in the feed

Cout(t) = ∫ Cin (t-t') E(t’) dt'

u  Therefore,

[Cout/Co] = 0∫t E(t’) dt’

u  normalized concentration vs. time profile gives the F curve dF(t)/dt = E(t)

u  For a laminar flow reactor, the velocity profile is parabolic with the fluid in the center of the tube spending the shortest time

u  By using a similar analysis as shown above, we obtain the complete RTD function for a laminar flow reactor as,

E(t) = 0 t < τ/2

E(t) = τ2/2t3 t ≥ τ /2

u  For pulse input (CSTR) E(t) = (1/τ) exp(-t/τ)

u  the mean residence time:

u  variance of residence time is defined as,

u  The Dispersion number is defined as D/uL and is given by,

Apparatus

Apparatus

Given Data

Pulse

Pulse

Step

Step

Graphs

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 500 1000 1500 2000 2500 3000

Cond

ucti

vity

C(t

)

Time (s)

C vs t (STEP LFR)

y = 0.0004x - 0.0924

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 500 1000 1500 2000 2500 3000

Ftheo vs t (STEP LFR)

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 500 1000 1500 2000 2500 3000

Fexp vs t (STEP LFR)

0

0.01

0.02

0.03

0.04

0.05

0.06

0 500 1000 1500 2000 2500 3000

E(t) vs t (STEP LFR)

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800

E vs t (PULSE CSTR)

E(t) E(theo)(t)

0

200

400

600

800

1000

1200

1400

1600

0 200 400 600 800 1000 1200 1400 1600 1800

C vs t (PULSE CSTR)

CSTR (Pulse) LFR (Step)

Variance 193158 512551.2

Scaled Variance 0.789 0.222

Space time 269.39 s 220 s

Mean Residence Time 495.26 s 1518.58 s

D/uL - 0.126

Final Values