4 - Binary Distillation

Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015

Distillation sketches










Flash


Binary Distillation




nnnnnnnn xLyGxLyG +=+ ++−− 1111

( )xxy

11 −+=

αα


nnnnnnnn xLyGxLyG +=+ ++−− 1111

( )xxy

11 −+=

αα


•The distillation is defined as a process in which a liquid and/or vapor mixture constituted of two or more species is separated into its components with the desired purity by means of heat supply or removal.

•It is based on the fact that the vapor of a mixture is richer in the most volatile components.

•The distillation is the most used separation technique.

•It requires huge amounts of energy, in terms of both calories and frigories.

•It significantly contributes to the operating costs of the plant.

Distillation is run in trayed (packed) towers.

The standard distillation column presents the following characteristics:

1. only one feed F;

2. withdrawals only at the top and the bottom of the column;

3. a total condenser, ie all the vapor is condensed;

4. a partial reboiler: the operation is not symmetric respect to that at the top of the column;

5. no heat flows along the column.


Binary distillation

QC

QR


The binary mixture (A + B) has to be separated into its components. We can study the problem to define thecriteria for evaluating the reflux ratio (R) (simulation problem) or the number of theoretical plates (N)necessary for the fractionation (design problem). This latter case is the one we deal with in the followingsection.

Since it can be proved that the degrees of freedom of the system are three, 2 specifications of purityand/or recovery at the top and the bottom of the column must be fixed together with the reflux ratio R.Then the global and component material balances and the energy balance are sufficient to define flowrates and compositions of the outlet streams.The balances to be written on the column are:

++=++=

+=

CBDRF

BDF

QBhDhQFhBxDxFz

BDF

The calculation methods for binary columns without the use of simulation programs are :•McCabe-Thiele (graphic and analytical) method ;

•Fenske-Gilliland method ;

•Underwood method (valid also for multicomponent columns);

•Ponchon-Savarit method.


Vn, yn

Ln+1, xn+1

QC

D

McCabe-Thiele method for binary columns

The balances for the upper section of thecolumn are:

++=

+=+=

++

++

+

CDLnn

Vnn

Dnnnn

nn

QDhhLhVDxxLyV

DLV

11

11

1


Balance on the stage n:

n

Vn, yn

Vn-1, yn-1

Ln+1, xn+1

Ln, xn

+=+

+=++=+

++−−

++−−

+−

Lnn

Vnn

Lnn

Vnn

nnnnnnnn

nnnn

hLhVhLhVxLyVxLyV

LVLV

1111

1111

11

LLn

VVn hhhh ==

If:

( ) ( )

−=−

−=−

+−

+−

11

11

nnL

nnV

nnnn

LLhVVhLLVV

VVVLLL

nn

nn

====

−

+

1

1

Countercurrent Equimolar Diffusion


Operating line

Upper section

Dnn xVDx

VLy += +1

DLV +=

1 1

+=+==

RR

VLR

DV

DLR

11 1 ++

+= + R

xxR

Ry Dnn

Lower section

+=

+=

+ Bmm BxyVxLBVL

''''

1

V

L

QC

DxD

BxB

FzF

QR

V’

L’m

n

Bmm xVBx

VLy

'''

1 −= +


Enthalpy factor q

V L

QC

DxD

BxB

F

QR

V’ L’

( ) ( )( ) ( )

−+−=

−+−=

+=++

+=++

VLF

VLVLF

hVVhLLFhVVLLF

VhhLhVLhFhVLVLF

''''

''''

q = fraction of the feed F that is addedto the liquid flow rate L in order to givethe flow rate L’.

qFLL =−′

( )FqVV −=′− 1


LV

FV

hhhh

q−

−=

hF = mole enthalpy of the feed at the feed conditions hV = mole enthalpy of the feed at the saturated vapor conditions at the column pressure hL = mole enthalpy of the feed at the saturated liquid conditions at the column pressure

The following cases can occur:

hF ≡ hL → q = 1 → liquid feed at its boiling pointhF ≡ hV → q = 0 → vapor feed at its dew pointhF > hV → q < 0 → feed at the overheated vapor conditions hF < hL → q > 1 → feed at the subcooled liquid conditionshL < hF < hV → 0 < q < 1 → mixed feed


q - line

Locus of the points of intersection between the operating straight lines (material balances) of the upper and lower section of the column.

−=+=

B

D

BxxLyVDxLxVy

''subtracting the first from the second equation ( ) ( ) ( )DB DxBxxLLyVV +−−=− ''

( ) FFzqFxFyq −=−− 1

11 −−

−=

qzx

qqy F

q=1 q>1

0<q<1

q<0

q=0

x=zF

x=y


Equilibrium diagrams

In the case of ideal mixtures with constant α (for instance the system benzene-toluene) the equilibriumcurve takes the form:

( )xxy

11 −+=

αα

T-x-y and x-y diagrams for the benzene-toluene mixture


Equilibrium diagramsNon-ideal systems

x-y and enthalpy-composition diagrams for the acetone-water mixture


Equilibrium diagramsNon-ideal systems

x-y diagram for the ethanol-water mixture


Minimum reflux ratio

When R = Rmin the column presents a number N of equilibrium stages approaching infinity. It is the “pinch”condition.

“pinch” conditions may occur at the feed point (Fig.1) or in the enriching or stripping sections for non-idealsystems (Fig. 2).

x=zFxB

y

xD x=zFxB

y

xD

Figure 1 Figure 2


Determination of the minimum reflux ratio Rmin

If the equilibrium curve is non-ideal the solution can be graphic or numerical.If the equilibrium curve is ideal the solution is analitical:

( )

−−

−=

−+=

11

11

qzx

qqy

xxy

F

αα

==

i

i

xxyy

iD

iD

xxyx

RR

−−

=+1min

min

( )

−−

−−

=

−−

−−

=

F

D

F

D

F

D

F

D

zx

zxR

zx

zxR

11

11

11

11

min

min

αα

αα

for q = 1

for q = 0


McCabe-Thiele graphic method

R = const Rmin


Position of the feed tray


Position of the feed tray/ 2

DxD

1BxB

FzF

2

3

4

5

6

7

8

Unitary efficiency


McCabe-Thiele analytical method

011 =+++ ++ cbxaxxx nnnn Riccati Equation

nn

ba

bax

bax

++

−=

+++

−

+++

−δδ

δδ

δδ

211

211

0

The general solving formula is:

with:

( ) ( )2

42 cbaba −+±+−=δ

++

−

+++

−

+++

−

=

δδδδ

δδ

ba

bax

bax

n

n

ln

211

211

ln

0


Upper (enriching) section

( )

++

+=

−+=

+ 11

11

1 Rxx

RRy

xxy

Dnn

n

nn α

α011 =+++ ++ cbxaxxx nnnn

( )( )

( )1

11

11

−=

−+

+=

−=

α

αα

α

Rxc

RR

Rxb

a

D

D

For the upper section xn = xD e x0 = xF.. xF is the abscissa corresponding to the intersection of the operating lines or of the q-line with an operating line.

++

−

+++

−

+++

−

=

δδδδ

δδ

ba

bax

bax

N F

D

S

ln

211

211

ln


Connection between the 2 sections

SND

F

ba

baxbax

++

−

+++

−=

+++

−−

δδδδ

δδ2

11

211

To calculate it is necessary to approximate NS to the next higher integer number.

−Fx


Lower (stripping) section

( )

−+−

−+

+=

−+=

+

FBq

FDR

xFB

x

FBq

FDR

qFDR

y

xxy

B

mm

m

mm

1

11 αα

0''' 11 =+++ ++ cxbxaxx mmmm

( )

( )

( )1'

1

1'

11'

−

+

−=

+−

−++−

−=

−=

α

α

αα

α

qFDR

xFB

c

qFDR

FBq

FDRx

FB

b

a

B

B


Minimum number of stages (Fenske correlation)

11

→+

∞→==R

RDLRVL

V,yn

L,xn+1

D xD

xD

X


eavy

1

1hev

lightev

PP

xx

yy

=

−

−=αn

n

n

n

xx

yy

−=

− 11α 1

1

++

=

==

nnnn

xyLxVy

LV

n

n

n

n

N

N

N

N

N

N

D

D

xx

xx

xx

xx

xx

xx

−=

−

−=

−

−=

−

+

+

−

−

11

.

.

.11

11

1

1

1

1

α

α

α at the top yN = xD

( )B

BN

D

D

xx

xx

−=

− 11minα bottomtop ααα ⋅=where

αln

11

ln

min

−⋅

−= B

B

D

D

xx

xx

N

Fenske Correlation


Fenske-Gilliland method for binary mixtures

1. Determine Rmin with the procedure already described for the method of McCabe-Thiele;

2. compute Nmin with the Fenske correlation;

3. compute N by means of the Gilliland diagram that reports on the axes the following ratios:

1)(

1)(

min

min

+−

=

+−

=

RRRRF

eN

NNNφ


Gilliland diagram

Molokanove

EduljeeF

FF

FF

1

75.075.01

2.117114.541

5668.0

−

⋅++

−=

−=

φ

φ

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4 - Binary Distillation