CENG 1004: Coursework 1Mass Balances

Professor Eric S Fraga, Chemical Engineering, UCL

Due 12 noon, 18nd October 2013

Answer all the following questions. All have equal weight. Show all work and state all assump-tions made. Cite any sources of data required and used.

1. If the percentage of fuel in a fuel-air mixture falls below a certain value called the lowerflammability limit (LFL), the mixture cannot be ignited. For example, the LFL of propanein air is 2.05 mole% C3H8. If the percentage of propane in a propane-air mixture is greaterthan 2.05 mole%, the gas mixture can ignite if it is exposed to a flame or spark; if thepercentage is lower than the LFL, the mixture will not ignite. (There is also an upperflammability limit, which for propane in air is 11.4%.)A mixture of propane in air containing 4.03 mole% C3H8 (fuel gas) is the feed to a com-bustion 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 notpossible.

(a) Draw and label a flowchart of the fuel gas-dilution air mixing unit, presuming that thegas entering the furnace contains propane at the LFL, and do the degree-of-freedomanalysis.

(b) If propane flows at a rate of 150 mols C3H8 in the original fuel-air mixture, what is the

minimum molar flow rate of the dilution air?

(c) How would the actual dilution air feed rate probably compare with the value calcu-lated in part (b)? (>, <, =) Explain.

2. A liquid mixture contains 60.0 wt% ethanol (E), 5.0 wt% of a dissolved solute (S), andthe balance water. A stream of this mixture is fed to a continuous distillation columnoperating at steady state. Product streams emerge at the top and the bottom of the column.The column design calls for the product streams to have equal mass flow rates and for thetop stream to contain 90.0 wt% ethanol and no S.

(a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions canbe calculated.

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(b) Calculate (i) the mass fraction of S in the bottom stream and (ii) the fraction of theethanol in the feed that leaves in the bottom product stream

kg E in bottom streamkg E in feed stream

if the process operates as designed.

(c) An analyzer is available to determine the composition of ethanol-water mixtures. Thecalibration curve for the analyzer is a straight line on a plot on logarithmic axes ofmass fraction of ethanol, x ( kg E

kg mixture), versus analyzer reading, R. The line passes

through the points (R = 15,x = 0.100) and (R = 38,x = 0.400). Derive an expressionfor x as a function of R (i.e. x= f (R)) based on the calibration, and use it to determinethe value of R that should be obtained if the top product stream from the distillationcolumn were analyzed.

(d) Suppose a sample of the top stream is taken and analyzed and the reading obtainedis not the one calculated in part (c). Assume that the calculation in part (c) is correctand that the plant operator followed the correct procedure in doing the analysis. Givefive significantly different possible causes for the deviation between Rmeasured andRpredicted, including several assumptions made when writing the balances of part(b). For each possible cause, suggest something that the operator could do to checkwhether it is in fact the problem.

3. A liquid mixture containing 30.0 mole% benzene (B), 25.0 mole% toluene (T) and thebalance xylene (X) is fed to a distillation column. The bottoms product stream contains98 mole% X and no B, and 96% of the X in the feed is recovered in this stream. Theoverhead product is fed to a second column. The overhead product from the second columncontains 97.0% of the B in the feed to this column. The composition of this stream is95.0 mole% B and the balance T.

(a) Draw and label a flowchart of this process and do the degree-of-freedom analysis toprove that for an assumed basis of calculation, molar flow rates and compositions ofall process streams can be calculated from the given information. Write in order theequations you would solve to calculate unknown process variables. In each equation(or pair of simultaneous equations), circle the variable(s) for which you would solve.Do not do the calculations!

(b) Calculate (i) the percentage of the benzene in the process feed (i.e. the feed to thefirst column) that emerges in the overhead product from the second column and (ii)the percentage of toluene in the process feed that emerges in the bottom product fromthe second column.

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