This test must be completed individually. I will be using tools to check authorship and version histories, equations, and format consistencies, and will be looking for anything suspicious given that this a take-home test given over an extended period.

Academic Integrity and Impact on this Test
This test must be completed individually. I will be using tools to check authorship and version
histories, equations, and format consistencies, and will be looking for anything suspicious given that
this a take-home test given over an extended period. Any academic integrity issues will be fully
pursued, with a recommendation to assign a grade of 0 for the midterm for all involved parties if the
issue is proven. Please save both of us a whole lot of trouble… complete this as best you can, on your
own. If you do discuss this test with your peers, keep it at a VERY high level (process in general).
Do not share parts of solutions, files, or trouble-shoot the excel files/matlab code/solutions of others.
Submission Requirements:
1) Submit a word file containing your responses to the questions (including properly formatted
graphs) with your name and B00 number at the top of each page in the header.
2) Submit a single excel file showing your solution for the problem as given, or your matlab files.
Your excel file must include all of the equations coded in the cells. Do not replace your equations
with Pasted Values! If you are using matlab, it must include the files needed for me to be able to
click “run” and reproduce your results. In excel, use a separate sheet for each question/sub-question,
labelling the sheets (e.g. Question 1C, Question 2A, Question 2B). If using Matlab, include separate,
well-labelled files for each question solution.
IMPORTANT: your excel file must be submitted with the version history/related people/created/last
modified/properties and personal information intact. Removal of this information requires pro-active
steps by a user, so it should be there unless you purposely remove it. If you have opted to use another
software platform for your solution (i.e. matlab), you must submit all your associated files and must
ensure that the code is sufficiently commented to allow for similar testing.
Late Submissions (Important!):
This test is expected to take you between 3 and 5 hours to complete over a 1-week period, during
which time your regular lecture periods and tutorial have been set aside for this. Plan a time to
complete this early.
If you will be late in your submission, you must contact me prior to the due date to make alternate
arrangements and submit the missed work assessment form on the faculty of engineering website.
When contacting me to make alternative arrangements, you MUST INCLUDE a copy of the test
progress to date (word files, excel, pictures of hand-written work if applicable).
This test includes 2 questions. The test is marked out of 75 possible marks.
Question 1 (The Warm-up):{30 marks}
The following reaction is taking place in a batch reactor:
A → B + C ???????? = ???, where k = 5 exp(-4000/T). The units for rforward
are [forward reactions/(m3
s)] or [moles of A consumed/(m3
s)], where CA is in mol/m3
.
For question 1, the reactor is operating adiabatically, and initially contains 300 kg of A and 600
kg of an Inert species.
a) Define the physical properties and initial conditions in your system based on your B00
number (cp, heat of reaction, number of moles of A present, volume of the reactor, state
simplifying assumptions relevant to the problem, etc.): {5 marks}
cp of the entire mixture is assumed to remain constant, with units of [J/(g K)]. The value of cp is
equal to the last 3 digits in your B00 number / middle 3 digits of your B00 number. For
example: B00123456 would have cp = 456/123.
The heat of reaction [J/forward reaction], has a value of ΔHr = the last 3 digits of your B00
number * -5. For example, for B00123456, ΔHr = -5* 456 = -2280 J/forward reaction.
The initial temperature is 400K, density is assumed to be constant at 1000 kg/m3
, and the
molecular weight of A is 60 g/mol.
b) Derive an analytical expression for the temperature as a function of conversion. Your
final expression must have all constants plugged into yield as simple an expression as
possible. Show your work for the derivation. {10 marks}
c) Plot the conversion and temperature vs. time up to a conversion of 50%. How long does it
take to reach this conversion, and what is the temperature at this time? Your solution
must show your derivation steps up to the point where you have the equations you
eventually use in Excel/Matlab to generate your plots (e.g. I should be able to clearly see
the link between the equations you’ve developed and what’s In your excel/matlab files).
{15 marks}
Question 2 (More Complex): {45 marks}
After running the system in question 1, you realize that there is a second, undesirable reaction
occurring…
Desired: A → B + C, ????????,1 = ???, where k = 5 exp(-4000/T) [same units as question 1].
Undesired: B → D, ????????,2 = ???
0.5
, where k = exp(-6000/T) [forward reactions/(m3
s)].
This undesired reaction is not expected to affect the heat capacity of the mixture (i.e. cp for the
mixture is constant).
The heat of reaction for the undesired reaction [J/forward reaction], has a value of ΔHr,2 = the
last 3 digits of your B00 number * 2. For example, for B00123456, ΔHr = 2* 456 = 912
J/forward reaction.
a) For the same initial conditions as Question 1, plot the temperature and concentrations of
A, B, C and D. What is the maximum concentration of B you can achieve for these
initial conditions? What time does this occur at? Don’t forget that your energy balance
and dCB/dt will change now that you have 2 reactions occurring. Show your work in
deriving the equations you use to find your solution in matlab/excel {25 marks}
b) In reality, you initially would start with A and Inerts in the reactor at 300K and heat it up
using an electric heater to your desired temperature, at which point you would turn the
heater off and allow the system to react. Recognize that the reaction is occurring the
entire time you’re heating the reactor contents.
The size of your heater will depend on your cp… in this case, assume the heater’s power
in kW, is equal to 15*cp (for example, if your cp = 0.5 J/(g K), your heater will have a
power of Q = 15 * (0.5) = 7.5 kW).
Modeling this scenario (T0 = 300K at t = 0, Q = 15[kW * (gK/J)]*cp [J/(gK)] until your
desired “reaction temperature” is reached, then Q = 0 as the reaction proceeds)… at what
temperature would you turn off your heater to achieve the maximum possible
concentration of B? Show plots of CB vs. time for different scenarios to justify your
answer. {20 marks – Note this is an iterative design problem}