CENG0002 Coursework 1

Mass Balances

Question 1

If the percentage of fuel in a fuel-air mixture falls below a certain value called the lower flammability  limit  (LFL),  the  mixture  cannot be ignited.   For  example,  the  LFL  of propane in air is 2.05 mole% C3 H8 .  If the percentage of propane in a propane-air mixture is greater than 2.05 mole%, the gas mixture can ignite if it is exposed to a flame or spark; if the percentage is lower than the LFL, the mixture will not ignite.  (There is also an upper flammability limit, which for propane in air is 11.4%.)

A mixture of propane in air containing 4.030 mole% C3 H8  (fuel gas) is the feed to a combustion furnace.  If there is a problem in the furnace, a stream of pure air  (dilution air) is added to the fuel mixture prior to the furnace inlet to make sure that the ignition is not possible.

a)  Draw and fully label a flowchart of the fuel gas-dilution air mixing unit, presuming that the gas entering the furnace contains propane at the LFL. Do the degree of freedom analysis for this process given the information given above.                            [10]

b)  If propane flows at a rate of 150 mol s-1  C3H8  in the original fuel-air mixture, what is the minimum molar flow rate of the dilution air to ensure ignition is not possible?   [10]

c) How would the actual dilution air feed rate probably compare with the value calculated in part (b)? (>, <, =) Explain. [5]

Question 2

Figure 1 is a sketch  (not a fully detailed process diagram) which describes the shirt-

cleaning process used by the Floods of Suds  One-Day Laundry Services plc.  The shirts

are soaked in an agitated tub containing Whizzo, the Wonder Detergent, and are then

wrung out and sent to a rinse stage.  The dirty Whizzo is sent to a filter in which most of

the dirt is removed, and the cleaned detergent is recycled back to join a stream of pure

Whizzo, with the combined stream serving as the feed to the washtub.                                 [40]

Figure 1: Sketch of the Whizzo process where Wh denotes the Whizzo detergent in  a stream.

Data: (1) Each 100 kg of dirty shirts contains 2 kg of dirt; (2) The washing removes 95% of the dirt;  (3) For each 100 kg of dirty shirts, 25 kg of Whizzo leaves with the clean shirts, of which 22 kg is wrung back into the tub; and (4) The detergent that enters the tub contains 97% Whizzo and that which enters the filter contains 87%.  The wet dirt that leaves the filter contains 8% Whizzo.

Analyse this process so as to provide the answers to these two questions:

a)  How much pure Whizzo must be supplied per 100 kg of dirty shirts?

b) What is the composition of the recycled stream?

The majority of the marks will be for the analysis required to answer the two sub- questions, not the answers themselves.  The analysis must include a fully labelled process diagram including any system boxes used  (10 marks), the degree of freedom analysis for each system box you must analyse to answer these questions (15 marks), and clear description of the steps taken to solve this problem (10 marks for algebra; 5 marks for answers to above questions).

Question 3

At low to moderate pressures, the equilibrium state of the water-gas shift reaction

is approximately described by the relation

where T is the reactor temperature in Kelvin, Ke(T) is the reaction equilibrium constant which is a function of the temperature, and yi  is the mole fraction of species i in the reactor contents at equilibrium.

The feed to a batch shift reactor contains 20.0 mole% CO, 10.0% CO2, 40.0% water, and the balance an inert gas. The reactor is maintained at T=1123 K.

a) Assume a basis of 1 mol feed and draw and label a flowchart. Carry out a degree-of-freedom analysis of the reactor based on extents of reaction and use it to prove that you have enough information to calculate the composition of the reaction mixture at equilibrium. Write no equations down and do no calculations beyond calculating the degrees of freedom. [5]

b) Without performing any calculations, what is the total moles of gas in the reactor at equilibrium and why? [5]

c) Determine the equilibrium mole fraction of hydrogen in the product using an extents of reaction mass balance approach. [10]

d) Suppose a gas sample is drawn from the reactor and analysed shortly after startup and the mole fraction of hydrogen is significantly different from the calculated value. Assuming that no calculation mistakes or measurement errors have been made, what is a likely explanation for the discrepancy between the calculated and measured hydrogen yields? [5]

e) Write a spreadsheet to take as input the reactor temperature and the feed component mole fractions y1,CO, y1,H2O, and y1,CO2 (assume no hydrogen is fed) and which calculates the mole fraction y2,H2 in the product gas when equilibrium is reached. The spreadsheet column headings should be

Columns between Ke  andyH2    (indicated by ···) may contain intermediate quanti- ties required for the calculation of yH2 .

First test your spreadsheet for the conditions given in part  (a) and verify it is correct.  Then try a variety of values of the input variables and draw conclusions about the conditions (reactor temperature and feed composition) that maximize the equilibrium yield of hydrogen.

The solution should be an exported table of the spreadsheet with all the rows corresponding to the different sets of values you have considered and which lead to your conclusions and with an explanation of the calculations performed by the spreadsheet.  The first row after the column headings, if any, should be the base case from part (a).                      [10]