Workshop 11: Distribution of residence time
Lecture notes for chemical reaction engineering
Solutions to these problems are uploaded at Workshop 11 solutions
Try following problems from Fogler 5e (Fogler (2016)) P 16-3, P 16-6, P 16-11
We will go through some of these problems in the workshop.
P 16-3
Consider the E(t) curve below.
Mathematically this hemi circle is described by these equations:
For 2\tau >= t >= 0, then E(t) = \sqrt{\tau^2 - (t - \tau)^2} min–1 (hemi circle)
For t > 2\tau, then E(t) = 0
What is the mean residence time?
What is the variance?
P 16-6
An RTD experiment was carried out in a nonideal reactor that gave the following results:
| E(t) = 0 | for | t < 1 \, min |
| E(t) = 1.0 \, min^{-1} | for | 1 <= t <= 2 \, min |
| E(t) = 0 | for | t > 2 \, min |
What are the mean residence time, t_m, and variance \sigma^2?
What is the fraction of the fluid that spends a time 1.5 minutes or longer in the reactor?
What fraction of fluid spends 2 minutes or less in the reactor?
What fraction of fluid spends between 1.5 and 2 minutes in the reactor?
P 16-11
The volumetric flow rate through a reactor is 10 dm3/min. A pulse test gave the following concentration measurements at the outlet:
| t (min) | c \times 10^5 | t (min) | c \times 10^5 |
|---|---|---|---|
| 0 | 0 | 15 | 238 |
| 0.4 | 329 | 20 | 136 |
| 1.0 | 622 | 25 | 77 |
| 2 | 812 | 30 | 44 |
| 3 | 831 | 35 | 25 |
| 4 | 785 | 40 | 14 |
| 5 | 720 | 45 | 8 |
| 6 | 650 | 50 | 5 |
| 8 | 523 | 60 | 1 |
| 10 | 418 |
Plot the external-age distribution E(t) as a function of time.
Plot the external-age cumulative distribution F(t) as a function of time.
What are the mean residence time t_m and the variance, \sigma^2 ?
What fraction of the material spends between 2 and 4 minutes in the reactor?
What fraction of the material spends longer than 6 minutes in the reactor?
What fraction of the material spends less than 3 minutes in the reactor?
Plot the normalized distributions E(\Phi) and F(\Phi) as a function of (\Phi).
What is the reactor volume?
Plot the internal-age distribution I(t) as a function of time.
What is the mean internal age \alpha_m ?
References
Citation
@online{utikar2024,
author = {Utikar, Ranjeet},
title = {Workshop 11: {Distribution} of Residence Time},
date = {2024-03-24},
url = {https://cre.smilelab.dev//content/workshops/10-distribution-of-residence-time},
langid = {en}
}