Mass Transfer - Lecture No 5- 2006

8/10/2019 Mass Transfer - Lecture No 5- 2006

1/45

Distillation


2/45

Topics

Types of Distillation

Action on an Ideal Plate

Mass Balance in a Distillation Column

Determination of Ideal Number ofPlates McCabe Thiele Analysis


3/45

The methods of distillation

Differential or batch distillation

Flash or equilibrium distillation

Continuous Rectification Binarysystems


4/45

Differential distillation The simplest examples of batch distillation at a

single stage. Starting with a still pot, initially full, heated at a

constant rate. In this process the vapour formedon boiling the liquid is removed at once from the

system. Since this vapour is richer in the more volatile

component, with this result the composition ofthe product progressively alters.

Thus, whilst the vapour formed over a shortperiod is in equilibrium with the liquid At the end of the process the liquid, which has

been vaporized, is removed as the bottomproduct.


5/45

Differential Distillation

Let S be the number of mols of material inthe still and x be the mol fraction ofcomponent A.

Suppose an amount dS, containing a molfraction y of A, be vaporised.

Then a material balance on component A

gives:ydS = d (Sx)

= S dx + x dS


6/45

Differential Distillation

The integral on then right-hand sidecan be solved graphically if the

equilibrium relationship between y andx is available.

Thus, if over the range concerned the

equilibrium relationship is a straightline of the form y= m x + c


7/45

Differential distillation

This process consists of only a singlestage, a complete separation is

impossible unless the relativelyvolatility is finite. Application isrestricted to conditions where apreliminary separation is to befollowed by a more rigorousdistillation, where high purifies is notrequired, or where the mixture is very

easily separated


8/45

Flash vaporisation

or Equilibrium Distillation This method is frequently carried out as a

continuos process. Consist of vaporizing a definite fraction of liquid

feed in such a way that the vapour evolved is inequilibrium with the residual liquid. The feed is usually pumped through a fired heater

and enters the still through a valve where thepressure is reduced.

The still is essentially a separator in which theliquid and vapour produced is reduced byreduction in pressure with sufficient time to reachequilibrium. The vapour is removed from the topof the separator and is then usually condensed,while the liquid leaves from the bottom.


9/45

Flash or Equilibrium

Distillation It is used in petroleum refining, in

which petroleum fractions are heated

in pipe stills and the heated fluidflashed in to vapour and residualstreams, each containing many

components.


10/45

Continuous Distillation

with Reflux Flash distillation is used most for

separating components that boil at

widely different temperatures. It is not effective separating

components of comparable volatility,

which requires the use of distillationwith reflux


11/45

Action on an Ideal Plate

By definition a vapour leaving a plate arebrought into equilibrium.

\Assume that the plates are numberedserially from top down and that the plateunder consideration is the nth plate fromthe bottom.

Then the immediately above plate n is platen-1, and the immediately below is n+1.


12/45

Material Balance diagram for plate n

Plate n

Plate n+1

Plate n-1

Vn,yn

Ln-1,Xn-1

Vn-1,yn-1

Ln-2,Xn-2

Vn+1,yn+1

Ln,xn


13/45

For example if two fluid enter plate n and two leave it,the liquid, Ln-1mol/h, from plate n-1and the stream ofvapour, Vn+1mol/h, from plate n+1are brought into

intimate contact. A stream of vapour, Vnmol/h, rises to plate n-1and a

stream of liquid, Lnmol/h, descends to plate n+1.

Since the vapour streams are the V phase, their

considerations are denoted byy; the liquid streams arethe L phase and their concentrations are denoted byx.Then the concentrations of the streams entering andleaving the nth plate are as follows:

Vapour leaving plate, yn

Liquid leaving plate, xn Vapour entering plate, yn+1

Liquid entering plate, xn-1


14/45

Boiling-Point Diagram showing

rectification on ideal plate

xn

xn-1

yn+1

yn


15/45

Number of Plates Required in

a Distillation Column To develop a method for the design of distillation units

to give the desired fractionation, it is necessary todetermine the numbers of trays.

Before that the heat and material flows over the trays,the condenser and the reboiler must be established

Thermodynamic data is required to establish how muchmass transfer is needed to establish equilibriumbetween the stream leaving each tray.

The diameter of the column will be dictated by the

necessity to accommodate the desired flow rates, tooperate within the available drop in pressure, while atthe same time affecting the desired degree of mixing ofthe stream on each tray.


16/45

Summary of the materialbalances for two

components systems Let the process be analysed simply for

a binary mixture of A and B as follows:

Let F be the number of mols per unitof feed of mol fraction xfof A.

D be the number of mols per unit time

of vapour formed with y the molfraction of A and


17/45

B be the number of mols per unit time of liquidwith x the mol fraction of A. Then an overall

mass balance gives:F = D + B

ComponentAbalance

FxF= D xD+ B xB Eliminating B and D from these equations give

the follow:

BD

FD

BD

BF

xx

xx

F

B

xx

xx

F

D


18/45

Net flow rates. Quantity D is the differencebetween the flow rates of the streams entering

and leaving the top of the column. A materialbalance around the condenser and accumulatorin the gives:

The difference between the flow rates of vapourand liquid anywhere in the upper section of thecolumn is also equal to D. This surface includes

the condenser and all plates above n+1. A totalmaterial balance around this control surfacegives:

D V La a

D V Ln n

1


19/45

Similar material balances for A give the followingequations:

Quantity D xDis the net flows rate of the

component A upward in the upper section of thecolumn. It too is constant throughout this part ofthe equipment. In the lower section of thecolumn the net flow rates are also constant but,

are in a downward direction.

Dx V Y L x V y L xD a a a a n n n n 1 1


20/45

The net flow of total material equals B; thatof the component A is BxB. The following

equations apply:B L L L V

Bx L x V y L x V y

b b m m

B b b b b m m m m

1

1 1


21/45

Operating lines There are two sections in the column; there

are also two operating lines, one for therectifying section and other for the strippingsection.

For the first section (rectifying section) the

operation line is represented by:

11

1

n

aaaan

n

nn

VxLyVx

VLy

DL

Dxx

DL

Ly

n

Dn

n

nn

1


22/45

Substituting for DxDin the equation above andeliminating Vn+1

For the section below the feed plate, a material balanceover control surface II gives

Rearranging this equation and taking into account thatthe slope is the ratio of liquid flow to the vapour flow,

and also eliminating Vm+1

Bmmmm BxxLyV 11

BL

Bxx

BL

Ly

m

Bm

m

mm

1

DLDxx

DLLy

n

Dn

n

nn

1


23/45

Feed Line

The conditions of the vapour rate orthe liquid rate may change depending

of the thermal condition of the feed. It is related to the heat to vaporise

one mole of feed divided by molar

latent heat (q)


24/45

Various type of feed

conditions Cold feed, q>1

Feed at bubble point (saturated

liquid), q=1

Feed partially vapour, 0


25/45

Feed Line


26/45

Feed Line

Cold feed : It is assumed that the entirefeed stream adds to the liquid flowing downthe column.

Feed at bubble point: no condensation isrequired to heat the feed.

Feed partial vapour: the liquid portion of thefeed becomes part of the L and the vapourportion becomes part of V


27/45

Feed Line

Feed saturated vapour the entire feedbecomes part of the V

Feed superheated: part of the liquidfrom the rectifying column is vaporizedto cool the feed to a state of saturated

vapour.


28/45

Feed Line Equation

If xq= xF, and yq=xFthen;

The point of intersection of the two

operating lines lies on the straight line ofslope (q/q -1) and intercept (xF, yF)

11

q

xx

q

qy F

qq


29/45

Reflux Ratio The analysis of fractionating columns is

facilitated by the use of a quantity called refluxratio.

Two ratios are used, one is the ratio of the refluxto the overhead product and the other is theratio of the reflux to the vapour.

Both ratios refer to quantities in the rectifying

section. The equations for those ratios are

DL

L

V

LRand

D

DV

D

LR VD


30/45

Reflux Ratio

If the operation lines equations are divided D,the result is, for constant molar overflow,

This equation is an operation line of therectifying section

111

D

Dn

D

Dn

Rxx

RRy


31/45

Reflux Ratio

The y intercept of this line is xD/(RD+1). The concentration xDis set by the

conditions of the design. RD, the reflux ratio, is an operating

variable that can be controlled at willby adjusting the split between reflux

and overhead product or by changingthe amount of vapour formed in thereboiler for a given flow rate of theoverhead product.


32/45

Reflux Ratio

A point at the upper end of theoperating line can be obtainedby setting xnequal to xDin theequation above.


33/45

Reflux Ratio

A point at the upper end of the operating linecan be obtained by setting xnequal to xDin theprevious equation.

The operating line for the rectifying section thenintersects the diagonal at point (xD, xD)

Dn

D

DD

D

DD

D

Dn xyor

R

Rx

R

xx

R

Ry

11

1

1

11


34/45

Reflux Ratio

The operation lines represented by thosetwo equations are plotted with theequilibrium curve on the x-y diagram.

Those equations also show that unless Lnand Lm are constant, the operating lines arecurved.

The lines can be plotted only if the changein these internal streams with concentrationis known.


35/45

Reflux Ratio

a

e

b

xF

MinimumReflux

Total

(Maximum)Reflux


36/45

Influence of the Number of

Reflux Ratio Any change in

R will

thereforemodify theslope of theoperation line

as can beseen from theFigure

b

a

f

e

d

g


37/45

Maximum or Total Reflux

If no product is withdrawn from thestill (D=0), the column is said to

operate under conditions of totalreflux and, as seen from equation ,the top operating line has its

maximum slope of unity, and coincideswith the line x=y.


38/45

The step become very close to theplate above, these conditions are

known as minimum reflux and Rmdenotes the reflux ratio.

Any small increase in R beyond Rm

will give a workable system, though alarge numbers of plate will berequired.


39/45


40/45

Calculation of Minimum

Reflux Ratio Rm Based on the previous figure, the slope of

the line ad is given by

1

m D F D F m

m D F F F

R x x x yor R

R x x y x


41/45

McCabe - Thiele

Construction the operation lines:

Locate the feed line

Calculate the y-axis intercept xD/(RD+ 1)of the rectifying line and plot that linethrough the intercept and the point

(xD, xD)

Draw the stripping line through point(xB,xB) and the intersection of therectifying line with the feed line.


42/45

Effect the feed condition onfeed line

If the feed is a cold liquid, the feed line slopeswill be upward and to the right;

if the feed is a saturated liquid, the line isvertical;

if the feed is a mixture of liquid and vapour,the lines slopes upward and to the left andthe slope is the negative of the ratio of theliquid to the vapour;

if the feed is saturated vapour the line ishorizontal and

if the feed is superheated vapour. The linesslope downward and to the left.


43/45

McCabe - Thiele

Feed Plate location

After the location of the feed plate

the construction of the number ofideal trays is found by the usualstep-by-step construction.

The process can begin at the top andalso a total condenser is used.


44/45

McCabe - Thiele


45/45

END

Summary

Documents

Mass Transfer - Lecture No 5- 2006