This question paper consists of 6 printed pages, each of which is identified by the Code Number PEME330101
Graph paper required
© UNIVERSITY OF LEEDS
School of Proc ss, Environmental and Materials Engine ring
January 2011 Examinations
PEME330101 SEPARATION PROCESSES Time allowed: 3 hours
Answer two qu questi ns from Section A and two qu questions from Section B PLEASE SHOW ALL W RKIN RKING GS IN ANSW ANSWER ERS S TO TO NUM NUMER ERIC IC L QUESTIONS. SECTION A
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(a)
Explain the following concepts (5 marks each): (i) (ii) (iii) (iv) (iv)
(b) (b)
Equilibrium rium stage stage Differentia tial distilla illattion ion Bubble point point and dew point Raou Raoult’ lt’s law
(v) (vi) (vii) (viii)
Henry’ Henry’s law Equilibrium K-value Relative volatility Azeotr pe [40 marks]
Figu Figure re A belo below is the the T-xy T-xy diag diagra ram m for for a bina binary ry mixt mixt re of A and B in equilibrium. If the mole fraction of B in the liquid phase is 0.8, what is the compo compositi sition on o B in the vapour phase above the liquid? What will be the [20 marks] reading on the thermometer at this point?
Figure A: T-xy diagram f a bina binary ry mixtu mixture re of of A and and B at at equilib equilibriu riu
(Question 1b) Continued over
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PEME330101
(c)
Figure B shows a schematic diagram of a flash distillation process to separate a binary mixture of A and B. The process is continuous a nd the flowrates of feed (F), top p oduct (V) and bottom product (S) are respe tively 1000 mol/s, 800 mol/s and 00 mol/s. Show that the following relations ip holds: 1 5 y = − x + x f 4 4
where y is the ole fraction of A in the vapour phase, x is the mole fraction of [20 marks] A in the liquid phase, subscript f denotes the feed.
Figure B (Question 1c)
2
(d)
Explain the principles of, and assumptions used in, (i) the (ii) the Poncho -Savarit methods.
(a)
Table A belo gives the vapour pressures of compone ts A and B as a function of te perature. Assume that mixing of the two components forms an ideal solution so that the Raoult’s law is applicable.
o
Temperature, C Vapour pressure of A, mmHg Vapour pressure of B, mmHg (i)
(ii) (iii) (iv)
Table A Question 2(a) 98.4 105 110 760 940 1050 333 417 484
115 1200 561
cCabe-Thiele and [20 marks]
120 1350 650
125.6 1540 760
Calcul te the mole fractions of component A in oth the liquid and vapour phases at temperatures listed in Table A for a constant pressure [15 marks] of 1 standard atmosphere (760 mmHg). Calcul te the relative volatility at the temperatures l sted in Table A. [15 marks] What onclusions can you draw from the values of the relative [5 marks] volatili y? Based on the conclusion of (iii) above, obtain an approximate x-y relationship and plot the relationship to give the x-y diagram. [15 marks] Continued over
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PEME330101
(b)
Minimum refl x ratio can be calculated by using the Underwood method as follows: α A x fA α B x fB α C x fC + + + ... = 1 − q α A − θ α A xdA α A − θ
α B − θ
+
α B xdB
α C − θ
+
α B − θ
α C xdC α C − θ
+ ... = Rm + 1
where x fA , x fB , fC , x dA , x dB , x dC etc. are the mole fractions o components A, B, and C etc. in the feed and distillate; A is the light key and B is the heavy key; q is the ratio of the heat required to vaporise 1 mole of th feed to the molar latent heat of he feed; α A , α B and α C are the volatilities with respect to the least volatile c mponent; θ is the root of the first equation that lies between α A and α B; Rm is t e minimum reflux ratio. (i) (ii)
(iii)
Explai the conditions under which the above meth d is applicable. [10 marks] Consid r a mixture of hexane, heptane and octane to be separated to give th products as given in Table B (below). Calculate the minimum [25 marks] reflux ratio if the feed is liquid at its boiling point. If the f ed is not at the boiling point, discuss qualit atively what would [15 marks] happen. Table B (Question 2b)
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(a)
Figure C on t e following page shows a continuous dist llation column for separating a bi ary mixture under a non-equimolal overflo condition. [40 marks]
(i)
Derive both bottom and top operating lines.
(ii)
Show that the top operating line goes through a ommon point ( x D, H D’), hile the bottom operating line goes through a common point ( x B, H B’) in the enthalpy-concentration graph. Here, x D is the mole fractio of the light component in the distillate (top product), x B is the mole raction of the light component in the bottom product, L L H D' = D + Qc / D with H D the specific enthalpy of the top product, D the flowrate of the top product and QC the heat duty of the L condenser, and H B' = H B L − Q B / B with H B the specific enthalpy of the bot om product, B the flowrate of the bottom roduct and Q B the [20 marks] heat du y of the reboiler. Continued over
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PEME330101
Figure C (Question 3a) (b)
A multi-comp nent mixture containing A, B, C, D, … is in equilibrium in a closed vessel. The mole fractions of the components in t e liquid phase are respectively x , xB, xC, x D, …, and that in the vapour ph se are respectively yA, yB, yC, yD, . (i)
Show t at the following relationship holds α AB
xA xB
+ BB
xB xB
+ CB
xC xB
+ DB
xD xB
+ ... =
1 yB
and y B =
x B
(α iB xi ) i = A, B ...
the relative volatility of components i and j.
[20 marks]
Discus the case when the relative volatility is const ant.
[20 marks]
where (ii)
ij is
SECTION B 4
Consider the case of a sorption of a solute in an inert gas by a liquid solvent in a mass transfer operation. (a)
Show typical c ncentration profiles of the solute in both gas and liquid phases. [10 marks]
(b)
Outline the W itman two-film theory of mass transfer by first describing the mass transfer process, followed by listing the underlying as umptions. [15 marks]
(c)
Show the concentration profiles of solute A accor ing to Whitman schematically in a graph, identify the driving forces and define the mass [10 marks] transfer coefficients. Continued over
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PEME330101
(d)
Using the general equation of diffusion for a binary mixture N A = −cDAB
dx A dz
+ x A ( N A + N B )
show that for the case of equimolar counter diffusion, the mass transfer cD coefficient, k x′ is given by k x′ = AB , where N A = k x′ ( xAi − xAL ) , c is the total δ L
concentration, D AB is the diffusion coefficient and δ L is the mass film thickness [20 marks] in the liquid side. (e)
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In an absorption process CO2 is absorbed in water at a very low concentration -1 in a packed column where the mass transfer coefficient is 0.001 ms . -8 2 -1 Calculate the associated mass transfer film thickness, if D AB = 10 m s . -3 Density of water is 1000 kg m and its relative molar mass is 18. [45 marks]
A packed absorption column is used to remove a solute at a very low concentration (less than 1 vol%) from a gas stream by contacting it with a liquid stream which flows counter-currently. The liquid contains a reagent which reacts instantaneously with the solute in the liquid phase. The reagent’s concentration is sufficiently high so that its depletion by reaction is negligible. (a)
Show the concentration profile of the solute on the gas side schematically and discuss why, according to Whitman film theory, the flux across the interface is given by: N A=k y×y A where k y is the mass transfer coefficient of the gas side and y A is the mol [10 marks] fraction of the solute in the gas phase.
(b)
By making a differential mass balance on the solute on the gas side, show that the packing height may be obtained from: dz =
Gm k y a
×
dy A y A
where Gm is the molar flux of the gas and a is the specific interfacial area. [30 marks] (c)
Integrate the above equation between the top and bottom end of the column and show that: G Z = m × n( y AB / y AT ) k y a where y AB and y AT are the mol fractions of the solute in the gas at the bottom [20 marks] and top of the column, respectively.
Continued over
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PEME330101
(d)
An absorption column operates on the above basis to remove a low -1 -2 concentration solute from air flowing at the rate of 5000 kg h m . The partial pressure of solute gas in the inlet stream is 5000 Pa and this is to be reduced to 500 Pa. Water containing a suitable reagent which reacts instantaneously with the solute in the liquid phase is used as the wash liquid. 5 The column operates at 1.5 ×10 Pa pressure. Determine the packing height [40 marks] required for this duty. -1
-3
The gas film mass transfer coefficient, k ga = 10 mol h m Pa Relative molar mass of air: 29 kg/kmol
6
-1
A dilute mixture of ammonia in air (1 vol%) flows in a vertical tube at a superficial -1 velocity, U , of 10 m s , and is contacted counter-currently with a falling film of water flowing under gravity on the internal surface of the tube. The tube is of internal diameter D = 40 mm and 10 m long. (a)
Sketch a diagram of the tube, and show that the molar flow rate ammonia is UAC , where A is column cross sectional area and C is ammonia concentration [5 marks] in air at height z.
(b)
Consider the absorption of ammonia by the falling film using The Whitman Two Film Theory and show that the flux across the falling film interface is given by N A = k cC , where k c is the mass transfer coefficient. State your [15 marks] assumptions clearly.
(c)
By making a material balance across a differential element of the height of the falling film and integrating it, show that the profile of ammonia concentration is given by: - 4k c Z ( ) UD C = C 0 e where Z is the distance from the entrance to the tube, C 0 is the solute [40 marks] concentration at z = 0.
(d)
Estimate the concentration of the ammonia in the exit air stream in terms of -3 -1 kmol m and vol% and calculate the rate of absorption in the column in kmol s . The gas side mass transfer coefficient may be obtained from the correlation of Gilliland: Sh = 0 .023 Re 0 .83 Sc 0 .44
where Sh = k c D/D AB; Re = DU g / g; Sc = g /(D AB g); k c is mass transfer -1 2 -1 coefficient, m s , D AB is diffusivity, m s ; U is superficial gas velocity; g and g are gas density and viscosity, respectively. Ammonia is highly soluble [40 marks] in water. Data: -5 2 -1 -3 -5 -1 -1 D NH3-air = 10 m s ; g = 1 kg m ; g = 2×10 kg m s ; -1 -1 R = 8314 J kmol K ; T = 333 K; P = 1 bar.
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