Politecnico di Milano Chemical Processes and Technologies (8 CFU) Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015 Distillation sketches
Dec 21, 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Distillation sketches
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Flash
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Binary Distillation
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
nnnnnnnn xLyGxLyG +=+ ++−− 1111
( )xxy
11 −+=
αα
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
nnnnnnnn xLyGxLyG +=+ ++−− 1111
( )xxy
11 −+=
αα
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
•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.
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Binary distillation
QC
QR
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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.
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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 −= +
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Equilibrium diagramsNon-ideal systems
x-y and enthalpy-composition diagrams for the acetone-water mixture
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Equilibrium diagramsNon-ideal systems
x-y diagram for the ethanol-water mixture
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
McCabe-Thiele graphic method
R = const Rmin
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Position of the feed tray
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Position of the feed tray/ 2
DxD
1BxB
FzF
2
3
4
5
6
7
8
Unitary efficiency
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Minimum number of stages (Fenske correlation)
11
→+
∞→==R
RDLRVL
V,yn
L,xn+1
D xD
xD
X
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
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
Politecnico di Milano Chemical Processes and Technologies (8 CFU)Dipartimento CMIC “G. Natta” Prof.ssa Laura Annamaria Pellegrini – AA 2014 / 2015
Gilliland diagram
Molokanove
EduljeeF
FF
FF
1
75.075.01
2.117114.541
5668.0
−
⋅++
−=
−=
φ
φ