View source for Tutorial 2 - 2013

{{OtherSidebar
| due_dates = 21 January 2013
| dates_alt_text = Due date(s)
| questions_PDF = 3K4-2013-Tutorial-week-2.pdf
| questions_text_alt = Tutorial questions
| questions_link = 
| solutions_PDF = 
| solutions_text_alt = Assignment solutions
| solutions_link =
| other_instructions = 
}}

<rst>
<rst-options: 'toc' = False/>
<rst-options: 'reset-figures' = False/>
**Assignment objectives**: math refresher; mol balances; working with conversion

	*	Reminder: always state assumptions in this tutorial, in assignments, midterms and exams.

.. question::
	:grading: 4
	
	Make sure you can do these in a test/exam (i.e. without internet access). Let :math:`X` be conversion; find:
	
	#.	:math:`\displaystyle \int{ \frac{1}{(1-X)^2} \,dX} =`
	#.	:math:`\displaystyle \int_{X_1}^{X_2}{ \frac{1}{(1-X)^2} \,dX} =`
	#.	And in general, what is: :math:`\displaystyle \int{ \frac{a + x}{bx} \,dx} =` 

.. question::
	:grading: 10

	For the question we covered in the end of class last week (see last page of this tutorial), we showed the volume of a PFR required is the area under the curve. The volume required was :math:`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::
	:grading: 20

	The following reaction rate, :math:`-r_A` measured in units of :math:`\left[\dfrac{\text{kmol}}{\text{hr.m}^3}\right]` is observed at a particular conversion, :math:`X`:
	
	.. csv-table:: 
		:header: "Reaction rate", "Conversion"
		:widths: 15, 15

		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 :math:`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 :math:`x`-axis on your plot should be the volume co-ordinate, :math:`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 :math:`x`-axis on your plot should be the volume co-ordinate, :math:`V`.

.. question::
	:grading: 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 :math:`A`, is the only concentration in the rate expression. 
	
	.. math::
	
		-r_A = \frac{5.5C_A}{20+C_A}
		
	where :math:`-r_A` has units of :math:`\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 :math:`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. 



</rst>