Tutorial 2 - 2013
Due date(s): | Selected questions will be in assignment 2 |
(PDF) | Tutorial questions |
Assignment objectives: math refresher; mol balances; working with conversion
- Reminder: always state assumptions in this tutorial, in assignments, midterms and exams.
Question 1 [4]
Make sure you can do these in a test/exam (i.e. without internet access). Let \(X\) be conversion; find:
- \(\displaystyle \int{ \frac{1}{(1-X)^2} \,dX} =\)
- \(\displaystyle \int_{X_1}^{X_2}{ \frac{1}{(1-X)^2} \,dX} =\)
- And in general, what is: \(\displaystyle \int{ \frac{a + x}{bx} \,dx} =\)
Question 2 [10]
For the question we covered in the end of class last week (see last page of the PDF for this tutorial), we showed the volume of a PFR required is the area under the curve. The volume required was \(2.16\,\text{m}^3\) to obtain 80% conversion.
If we used 4 CSTRs in series:
- What would be the size of each reactor if we wanted 20% conversion in each reactor?
- What is the total volume of these 4 reactors?
- How does this total CSTR volume compare with (a) the single CSTR volume and (b) the single PFR volume?
- What is the reaction rate in each reactor?
Question 3 [20]
The following reaction rate, \(-r_A\) measured in units of \(\left[\dfrac{\text{kmol}}{\text{hr.m}^3}\right]\) is observed at a particular conversion, \(X\):
Reaction rate | Conversion |
---|---|
78 | 0.0 |
106 | 0.2 |
120 | 0.4 |
70 | 0.6 |
We showed in class that the area under this curve is related to volume of the plug flow reactor.
- Start from the general mol balance and derive the equation that shows the area is equal to the plug flow reactor's volume; clearly state all assumptions used in your derivation.
- Assuming these assumptions are all met, calculate the plug flow reactor's volume to achieve a 60% conversion given a feed rate of \(15\,\text{mol.s}^{-1}\) to the reactor.
- If there is zero conversion at the entry to the PFR and 60% at the exit; what is the conversion half-way along the reactor?
- What is the conversion at 25% of the way along the reactor?
- Now plot a graph a graph of conversion throughout the reactor, from start to end. The \(x\)-axis on your plot should be the volume co-ordinate, \(V\).
- What is the reaction rate at the entry of the reactor?
- And at the midpoint?
- And at the exit?
- Plot a curve that shows the reaction rate throughout the reactor, from start to end. The \(x\)-axis on your plot should be the volume co-ordinate, \(V\).
Question 4 [12]
A new drug is being prototyped in a batch reactor; as is becoming common-place now, this drug is grown inside a cell as a by-product of the regular cellular processes. So far, experiments have shown the rate of consumption of the starting material, an animal-derived cell \(A\), is the only concentration in the rate expression.
where \(-r_A\) has units of \(\left[\dfrac{\text{mol}}{\text{day.m}^3}\right]\)
- Why is a batch reactor suitable for this type of testing?
- 30 mols of cellular material are added to a batch reactor of \(0.5\,\text{m}^3\); the liquid food source is added at the same time to the reactor, in excess. Calculate the amount of cellular material remaining in the tank after 10 days.
- How many days are required to convert 80% of the starting cellular material.
- Show a plot of the concentration in the tank over time until there is essentially 100% conversion.
Note: in tutorial 1 you solved a similar problem, but for a CSTR and PFR.