7/27/2019 221-04.pdf

1/18

7/27/2019 221-04.pdf

2/18

51

Simple Batch (differential) Distillation

1. Liquid is charged to aheated kettle

2. The liquid charge is boiled slowly

3. The vapors arewithdrawn as quickly asthey form to acondenser

4. The condensed vapor (distillate) is collected

The first portion of vapor condensed will be richest inthe more volatile component A. As vaporization

proceeds, the vaporized product becomes leaner in A.i.e., the composition changes with time.

The total mole amount in the liquid is L with the mololfraction of A being x. Assume a small amount of dL isvaporized so that the composition of the liquid changesfrom x to (x-dx) and the amount of liquid from L to (L-dL). Let y be the composition of A in the vapor.

The material balance of A givesxL = (x-dx)(L-dL) + ydL (5)

Expanding the right side, we havexL = xL xdL Ldx +dxdL +ydL (6)

52

Ignoring the double derivative term dxdL andrearranging,

Integrating,

ln where L 1 is the original moles charged, L 2 the moles leftin the still, x 1 the original composition, and x 2 the final

composition of liquid. Equation (8) is known as the Rayleigh equation .

The equilibrium curve gives the relationship between yand x. Then the integration of Rayleigh equation can bedone numerically or graphically between x 1 and x 2.

The average composition of total material distilled, y av,can be obtained using the material balance:

L1x1 = L 2x2 + V y av (9)V = L 1 L 2 = moles distilled (10)

Example D1 : A mixture of 100 mol containing 50

mol % n-pentane and 50 mol % n-heptane is distilledunder differential conditions at 101.2 kPa until 40 mol isdistilled. What is the average composition of the totalvapor distilled and the composition of the liquid left?The equilibrium data are as follows, where x and y aremole fractions of n-pentane: x 1 0.867 0.594 0.398 0.254 0.145 0.059 0 y 1 0.984 0.925 0.836 0.701 0.521 0.271 0

7/27/2019 221-04.pdf

3/18

53

Solution : The given values for the Rayleigh equation areL1 = 100 mol, x 1 = 0.50, L 2 = 60 mole, V = 40 mol.

ln100600.510

.

The unknown is x 2. To solve this by numericalintegration, the equilibrium relationship is converted tothe function of 1/(y-x) vs x as the following figure.

x 1 0.867 0.594 0.398 0.254 0.145 0.059 0 y 1 0.984 0.925 0.836 0.701 0.521 0.271 0

1/(y-x) 8.547 3.021 2.283 2.237 2.660 4.717

The integration is done graphically from x 1 = 0.5 to x 2 such that the integral (shaded area) = 0.510. Hence x 2 =0.277. Substituting into Eq. (5) to solve for the averagecomposition of the 40 mol distilled,

100(0.50) = 60(0.277) + 40 y av

yav = 0.835

54

Flash (single stage, continuous) Distillation

Flash distillation vaporizes a definite fraction of the

liquid, the evolved vapor is in equilibrium with theresidual liquid, the vapor is separated from the liquid andcondensed.

Plant for flash distillation.

Consider 1 mole of a binary mixture fed to the above

equipment. By a material balance for the more volatilecomponent, we have

x fy f xF D B ( )1 (11)where

xF = concentration (mole fraction) of A in the feedyD and x B = concentrations of A in the vapor and

liquid

7/27/2019 221-04.pdf

4/18

55

f = V/F = the molal fraction of the feed to bevaporized

V = moles per hour of vapor

F = moles per hour of feedL = F V = moles per hour of liquid

Both y D and x B are unknown, but they are on theequilibrium curve.

In general we have the following operating equation for flash distillation by rearranging eq. (11):

yf

f x

xf F1 (12)

which passes the point (x F, xF).

56

Example D2 : A mixture of 50 mole percent benzeneand 50 mole percent toluene is subjest to flashdistillation at a separator pressure of 1 atm. The vapor-

liquid equilibrium curve and boiling-point diagram aregiven below.

Boiling-point diagram (system of benzene-toluene at 1atm).

Plot the following quantities, all as functions of f, thefractional vaporization:(a) the temperature in the separator (b) the composition of the liquid leaving the separator

(c) the composition of the vapor leaving the separator

7/27/2019 221-04.pdf

5/18

57

Solution :For each value of f, the corresponding quantity of [(f-1)/f] is calculated, which is the slope of the operating

line. By using this slope and the point (x F, xF), onestraight operating line can be drawn on the x-y diagram.

Equilibrium curve, system of benzene-toluene.

The coordinate of the intersection of the equilibrium andoperating lines gives the compositions of the leavingliquid and vapor as (x, y). From the value of x or y thetemperature in the separator can be obtained from the

boiling-point diagram. By doing this procedure for

58

different values of f, the solutions can be found. Theresults are given in the following figure and table.

7/27/2019 221-04.pdf

6/18

59

Continuous Distillation with Reflux (Rectification) Flash distillation is not effective in separatingcomponents of comparable volatility, or in obtainingnearly pure components.

Rectification on an ideal plate .

Vapor leaving plate n = y n Liquid leaving plate n = x n Vapor enterrng plate n = y n+1 Liquid entering plate n = x n-1

yn+1 is in contact (same position) with x n For an ideal plate, y n is in

equilibrium with x n

Distillation Trays Allows efficientmixing of vapor andliquid enabling

rapid equilibrationCombination of rectification and stripping .If we want to obtain both near pure top and bottom

products, the feed plate has to be in the central portion of the column. The bottom is called the reboiler .Rectification in the section below the feed plate is calledstripping, the bottom product can be nearly pure B.

60

Rectifying (enriching) section: all plates above the feed.Stripping section: all plates below the feed, including the

feed plate itself .

Liquid flows down by gravity to reboiler. The bottom product is withdrawn from the pool of liquid on the

downstream side of the weir and flows through thecooler G.

7/27/2019 221-04.pdf

7/18

61

The vapors rising through the rectifying section arecompletely condensed in condenser C , and thecondensate is collected in accumulator D .

A portion of liquid from the accumulator is returned tothe top plate, which is called reflux . It provides thedownflowing liquid. Without the reflux, no rectificationwould happen in the rectifying section and theconcentration of the overhead product would be thesame as that of the vapor rising from the feed plate.

Condensate not returned to the top plate is cooled in heatexchange E , called the product cooler , and withdrawn asthe overhead product.

Overal material balance for binary systems

Total material balance: F = D + B (13)Component A balance: Fx F = Dx D + Bx B (14)

Eliminating B gives

Eliminating D gives

Net flow rate in the rectifying sectionThis is the overhead product, D = V a - L a = difference

between the flow rates of vapor and liquid anywhere in

the upper section above n+1 .62

Distillation in the Enriching Section of Tower

Material balances D LV nn 1 (15)

V y L x Dxn n n n D 1 1 (16)

By rearranging Eq. (16) we obtain the operating line

D L Dx

x D L

LV Dx

xV L

yn

Dn

n

n

n

Dn

n

nn

111 (17)

This is the operating line in the rectifying section.

The reflux ratio, R = L n/D. If R is constant, the operatingline will be straight on the y-x plot.

111 R x

x R

R y Dnn

(18)

7/27/2019 221-04.pdf

8/18

63

The slope is L n/Vn+1 or R/(R+1). It intersects the y = xline (45 o diagonal line) at x = x D. The intercept of theoperating line at x = 0 is y = x D /(R+1).

The theoretical stages are determined by starting at theoperating line at x D and moving horizontally to intersectthe equilibrium line at x 1. Then y 2 is the composition of the vapor passing the liquid x 1. Similarly, other theoretical trays are stepped off down the tower in theenriching section to the feed tray.

64

Distillation in the Stripping Section of Tower

Material balances L V Bm m 1 (19) L x V y Bxm m m m B 1 1 (20)

so that the operating line is

B L Bx x

B L L

V Bx x

V L y

m

Bm

m

m

m

Bm

m

mm

111 (21)

This is the operating line in the stripping section.

If equimolal flow is assumed, L m = L N = constant andVm+1 = V N = constant, Eq. (21) is a straight line when

plotted as y vs x, with a slope of L m/ V m+1 . It intersectsthe y = x line at x = x B.The intercept at x =0 is y=-B x B/ V m+1 .

Again the theoretical stages for the stripping section aredetermined by starting at x B, going up to intersect theequilibrium line at y

B, and then across to the operating

line at x N, and so on.

7/27/2019 221-04.pdf

9/18

65

Condenser and top plateThe material balance diagram for the top plate andcondenser is shown in the figure.

At the top plate, the composition is (x C, y1). The simplestcase is a total condenser, which condense all the vapor so that the liquid has the same composition as the vapor.Hence, x C = x D = y 1. The enriching line starts with (x D,

xD), which is in the diagonal line. Triangle abc in thefigure represents the top plate.

66

Bottom plate and reboilerThe material balance diagram for the top plate andcondenser is shown in the figure.

The lowest point on the operating line for the column isthe bottom plate (x b, y r ), which are the liquidconcentration leaving the bottom plate and the vapor concentration leaving the reboiler. However, as shown inthe stripping section, the operating line can be extendedto cross the diagonal at point (x B, xB).

In a commonreboiler, the vapor leaving the reboiler is inequilibrium with the

liquid leaving as bottom product.Then x B and y r are in equilibrium curve,and the reboiler acts asan ideal plate. Trianglescde and abc are thereboiler and bottom

plates.

7/27/2019 221-04.pdf

10/18

67

Effect of feed conditionsThe condition of the feed stream F entering the tower determines the relation between the vapor V m in thestripping section and V n in the enriching section as wellas between L m and L n. If the feed is part liquid and partvapor, the vapor will add to V m to give V n, and the liqudwill add to L n to give L m.We define

1

1(22)

Where H V is the enthalpy of the feed at the dew point,HL the enthalpy of the feed at the boiling point (bubble

point), and H F the enthalpy of the feed at its entranceconditions.

Feed conditions:(a) cold liquid, q>1(b) at bubble point

(saturated liquid),q=1(c) partial vapor,0

7/27/2019 221-04.pdf

11/18

69

Lacation of the feed tray in a tower and number of ideal plates; McCabe-Thiele method

To determine the number of theoretical trays needed in atower, the stripping and enriching lines are drawn tointersect on the q line as follows.

1. Starting from the top at x D, the trays are stepped off

along the enriching line.2. It is important to switch to the stripping line when thetriangle first passes the q line (intersection of the 2operating lines), which is tray 2 in this case.

3. The trays are continued to step off along the strippingline.

4. The number of theoretical trays required is 3.7 withthe feed on tray 2.

70

In the above figure, the feed is part liquid and part vapor,since 0

7/27/2019 221-04.pdf

12/18

71

Example D3. Rectification of a benzene-toluenemixtureA liquid mixture of benzene-toluene is to be distilled in afractionating tower at 101.3 kPa pressure. The feed of 100 kmol/h is liquid, containing 45 mol % benzene and55 mol % toluene, and enters at 327.6 K. A distillatecontaining 95 mol % benzene and 5 mol % toluene and a

bottoms containing 10 mol % benzene and 90 mol %toluene are to be obtained. The reflux ratio is 4:1. Theaverage heat capacity of the feed is 159 kJ/(kmol K) and

the average latent heat is 32099 kJ/kmol. Equilibriumdata for this system are given in the table below.Calculate the distillate and bottoms in kmol/h, and thenumber of theoretical trays needed.

Vapor-Pressure and Equilibrium-Mole-Fraction Data for

Benzene-Toluene SystemT (K)

Vapor pressure (kPa) Mole fraction of benzene at 101.325 kPa

Benzene Toluene x A yA 353.3 101.32 - 1.000 1.000358.2 116.9 46.0 0.780 0.900363.2 135.5 54.0 0.581 0.777368.2 155.7 63.3 0.411 0.632373.2 179.2 74.3 0.258 0.456378.2 204.2 86.0 0.130 0.261383.8 240.0 101.32 0 0

72

F = 100 kmol/h, x F = 0.45, x D = 0.95, x B = 0.1,R = L n/D = 4.Overall material balance

F = D + B100 = D + B

Benzene balanceFxF = Dx D + Bx B

100(0.45) = D(0.95) + (100-D)(0.10)D = 41.2 kmol/h B = 58.8 kmol/h

The enriching operating line is19.080.0

1495.0

144

111 nn D

nn x x R x

x R

R y

The q line is

1 1

1 The value of H V H L = latent heat = 32099 kJ/kmol.

HL H F = c pL(TB T F)where the heat capacity of the liquid feed c

pL= 159

kJ/(kmol K), T B = 366.7 K (boiling point of feed), andTF = 327.6 K (inlet feed temperature).

1 c T T 1 159 366.7 3232099 1.195 So the q line is

7/27/2019 221-04.pdf

13/18

73

1.1950.195 0.195 6.128 5.128 The enriching and q lines are plotted in the figure below.Their intersection identifys one point in the strippingline. Linking this point to the bottom point y = x = x B =0.1, we obtain the stripping line. The number of theoretical steps is 7.6, or 7.6 steps minus a reboiler,which gives 6.6 theoretical trays. The feed is introducedon tray 5 from the top.

74

Total reflux ratioIn distillation of a binary mixture A and B, the feedconditions, distillate and bottoms compositions areusually specified and the number of theoretical trays areto be calculated. The number of theoretical trays dependson the operating lines. To fix the operating lines, thereflux ratio R = L n/D at the top must be set.

One limiting case is total reflux, R = , or D = 0. Thematerial balance becomes

Vn+1 = L n Vn+1yn+1 = L nxn

Hence, the operating lines of both sections are on the 45 o line, y n+1 = x n.

Total reflux

is an extremecase, thenumber of theoreticaltraysrequired is atits minimumto obtain thegivenseparation of xD and x B.However, inreality we

have no product at all, and the twoer diameter is infinite.

7/27/2019 221-04.pdf

14/18

75

Minimum reflux ratioAnother limiting case is the minimum reflux ratio, Rm,that will require infinite number of trays for the givenseparation of x D and x B. This corresponds to theminimum vapor flow in the tower, and hence theminimum reboiler and condenser sizes.

If the reflux ratio R decreases, the slope of the enrichingline R/(R+1) decreases, the intersection of this line andthe stripping line with the q line moves farther from the

45o

line and closer to the equilibrium line. The number of steps required to give a fixed x D and x B increases. Atthe extreme case, the two operating lines touch theequilibrium line, a pinch point at y and x occurs,where the number of steps required is infinite. The slopeof enriching line in this case is

1 76

In some cases, where the equilibrium line has aninflection in it as shown below, the operating line atminimum reflux will be tangent to the equilibrium line.

The minimum reflux ratio refers to the situation that wecan have the maximum products (D and B) but thenumber of trays required is infinite. Both total reflux andminimum reflux are impossible in actual operation.

7/27/2019 221-04.pdf

15/18

77

Operating and optimum reflux ratioThe actual operating reflux ratio lies between the twolimits. To select the proper value of R requires acomplete economic balance on the fixed costs of thetower and operating costs. By experience, the optimumreflux ratio has been shown to be between 1.2R m and1.5R m.

Example D4: Minimum reflux ratio and total refluxratioFor the rectification in Exanple D3, where a benzene-toluene feed is being distilled to give a distillatecomposition of x D = 0.95 and a bottom product of x B =0.10, calculate the following:

(a) Minimum reflux ratio R m (b) Minimum number of theoretical plates at a total

reflux78

Solution:(a) First draw the equilibrium line and the q line as wedid in Example D3. The operating line for minimumreflux ratio is plotted as a dashed line and intersects theequilibrium line at the same point the q line intersects.Reading the values of x = 0.49 and y = 0.702, we have

1

0.95 0.7020.95 0.49 0.539

Hence, the minimum reflux ratio is Rm = 1.17.

(b) The theoretical steps are drawn as shown between theequilibrium line and the 45 o line. The minimum number of theoretical steps is 5.8, which gives 4.8 theoreticaltrays plus a reboiler.

7/27/2019 221-04.pdf

16/18

79

Special case for rectification1. Stripping-column distillation .In some cases the feed is added at the top of the strippingcolumn because we would like to have bottoms productonly. The feed is usually a saturated liquid at the boiling

point, and the overhead product V D is the vapor risingfrom the top plate, which goes to a condenser with norelux returned to the tower.

The bottoms product W usually has a high concentrationof the less volatile component B. Hence, the column

operates as a stripping tower, with the vapor removingthe more volatile A from the liquid as it flowsdownward. Assuming constant molar flow rates, amaterial balance of the more volatile component Aaround the dashed line gives,

111

m

W m

m

mm

V

Wx x

V

L y

80

This stripping line is the same as that for a completetower. It intersects the y = x line at x = x W, and the slopeis constant at L m/Vm+1 .

If the feed is saturated liquid, then L m = F. This is shownin the figure. Starting at x F, the steps are drawn down thetower.

If the feed is cold liquid below the boiling point, the qline should should be used and q > 1: L m = qF.

Example D5: Number of trays in stripping towerA liquid feed at the boiling point of 400 kmol/hcontaining 70 mol % benzene (A) and 30 mol % toluene(B) is fed to a stripping tower at 101.2 kPa pressure. The

bottoms product flow is 60 kmol/h containing only 10mol % A and the rest B. Calculate the kmol/h overheadvapor, its composition, and the number of theoreticalsteps required.

SolutionF = 400 kmol/hxF = 0.70W = 60 kmol/hxW = 0.10Plot the equilibriumand diagonal lines.Overall material

balance gives

F = W + V D

7/27/2019 221-04.pdf

17/18

81

400 = 60 + V D VD = 340 kmol/h

Component A balance givesFxF = Wx W + V DyD 400(0.70) = 60(0.10) + 340y D yD = 0.806

For a saturated liquid, q=1, the q line is vertical. Theoperating line is plotted through the point y = y W = 0.10and the intersection of y D = 0.806 with the q line.

Alternatively, the slope of L m/Vm+1 = 400/340 = 1.176can be used. Stepping off the trays from the top, 5.3theoretical steps or 4.3 theoretical trays plus a reboiler are needed.

2. Enriching-column distillationEnriching towers are also used at times, where the feedenters the bottom of the tower as a vapor. The overheaddistillate is produced in the same way as in a completefractionating tower and is usually quite rich in the morevolatile component A. The liquid bottoms is usuallycomparable to the feed in composition, slightly leaner inA. If the feed is saturated vapor, the vapor in the tower Vn = F.

82

Plate Efficiency

To translate ideal plates into actual platesApplicable to both distillation & absorption

1 Types of plate efficiency

1.1 overall efficiency

platesactualof number

platesidealof number

0

for the entire columnsimple but the least fundamental

1.2 Murphree efficiency

M nn n

y y y y

n 1

1*

whereyn = actural concentration of vapor leaving plate n yn+1 = actural concentration of vapor entering plate n yn

* = concentration of vapor in equilibrium with liquid

concentration xn leaving downpipe from plate n

for a single platein reality samples are taken of the liquidon the plates, and the vapor compositions aredetermined from a McCabe-Thiele diagram.

7/27/2019 221-04.pdf

18/18

83

1.3 Local or point efficiency

'' '' '

y y y y

n n

en n

1

1

wherey'n = concentration of vapor leaving a specific point in

plate n y'n+1= concentration of vapor entering plate n at the

same location y'en = concentration of vapor in equilibrium withliquid

at the same point (x' n)

for a specific location in a plate

2. Relationship between efficiencies

2.1 Murphree & local efficienciesIn small columns, good mixing can be achieved so thatthe concentration is uniform in the tray.y'n = yn, y'n+1 =yn+1 , and y'en = yn*. Therefore, ' M .

84

In large columns, incomplete mixing of the liquid occursin the tray. M is the integration of ' over the entiretray.

2.2 Murphree & overall efficiencies

01 1 ln ( / )

ln /M mV LmV L

where m is the slope of equilibrium line. WhenmV/L=1.0 or M 1.0, M = 0.

This relationship depends on the relative slopes of equilibrium and operating lines.

M < 0 (stripping section)

M > 0 (enriching section)

M 0 for the whole column if the feed plate is near

the middle

3. Use of Murphree efficiencyDraw an effective equilibrium line.Use McCable and Thiele method between theeffective equilibrium line and the operating line.

4. Factors influencing plate efficiencyAdequate and intimate contact between liquid andvapor can enhance the efficiency; any excessivefoaming or entrainment, poor distribution, or short-circuiting, weeping, or dumping of liquid, lowersthe plate efficiency.

Rate of mass transfer between liquid and vapor.