Hello! Thanks for coming!
Is it possible to check and help me for this exercise, please?
This is the exercise I have been given:
A liquid mixture contains 60.0 wt% ethanol (E), 5.0 wt% of a dissolved solute (S), and the balance water. A stream of this mixture is fed to a continuous distillation column operating 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 the top stream to contain 90.0% ethanol and no solute S.
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 can be calculated.
My basis of calculation is m1=100 Kg/h (100 Kg/h of feed)
I have 15 equations and 15 unknows, therefore there I found there is 0 degree of freedom.
I found with this basis:
m2 (top stream) = m3 (bottom stream) = 50 Kg/h
X1.W = 0.35 Kg/Kg
X2.W = 0.1 Kg/Kg
X3,E = 0.3 Kg/Kg
X3,W = 0.6 Kg/Kg
X3,S = 0.1 Kg/Kg
Is this correct?
b) Calculate (i) the mass fraction of S in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream
kg E in bottom stream / kg E in feed stream
if the process operates as designed
I don't understand what is (i) but it might be this ? :
(i)=m3,S/m3 = (5 Kg/h)/(50 Kg/h) = 0.1 Kg/Kg
(ii)=m3,E/m1,E = (15 Kg/h)/(60 Kg/h) = 0.25 Kg/Kg d
Are those correct or completely wrong?
I neither do not understand the "if the process operates as designed"...
c) An analyzer is available to determine the composition of ethanol-water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol. x[(kg E)/(kg mixture)], versus analyzer reading, R. The lines passes through the points (R=15, x=0.100) and (R=38, x=0.400). Derive an expression for x as a function of R (i.e. x=f(R)) based on the calibration, and use it to determine the value of R that should be obtained if the top product stream from the distillation column were analyzed.
d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in part c). Assume that the calculation in part c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between Rmeasured and Rpredicted, including several assumptions made when writing the balances of part b). For each possible cause, suggest something that the operator could do to check whether it is in fact the problem.
Unfortunately, I do not understand c) and d) could you please help me :S ?