lecture 2 - multi-component distillation
TRANSCRIPT
Multi-Component Distillation
Lecture 2
1
Objectives
�To understand thetheories
theories
theories
theories associated with
multicomponent distillation.
�To be familiar with various methods
various methods
various methods
various methods
multicomponent column design e.g. shortcut
methods, rigorous method.
2
methods, rigorous method.
�Shortcut Method i.e. Smith Brinkley, FUG
�Rigorous Method –Lewis M
atheson (Design Approach)
�Rigorous Method –Thiele Geddes (Rating Approach)
�Some Examples
General Considerations -MCD
�Feed -more than two components
�Not possibleto specify the complete composition of
the top and bottom products independently.
�Separation between the top and bottom products
is specified by setting limits
limits
limits
limitson two ‘key’
two ‘key’
two ‘key’
two ‘key’
components
components
components
components(desired separation)
3
components
components
components
components(desired separation)
�Methods:
1.1.1.1.
Stage
Stage
Stage
Stage- ---bybybyby- ---stage
stage
stage
stagecalculation is too complex
complex
complex
complexand tedious.
2.2.2.2.
Short
Short
Short
Short- ---cut methods
cut methods
cut methods
cut methodsto simplify the task of designing
Multicomponent columns
�Short-cut methods are useful for the preliminary
preliminary
preliminary
preliminary
design work
Short-cut Methods
�Two classes of short-cut methods:
1.1.1.1.
Simplifications
Simplifications
Simplifications
Simplificationsof the rigorous stage-by-stage procedures
–E.g. Hengstebeck(1961) and Smith-Brinkley method
(1960)
2.2.2.2.
Empirical methods
Empirical methods
Empirical methods
Empirical methods, which are based on the perform
ance of
operating columns, or results of rigorous designs
4
operating columns, or results of rigorous designs
–E.g. Gilliland’s correlation, Erbar-M
addoxcorrelation
�Before commencingdesign of multicomponent
distillation, the designer has to choose the two
two
two
two‘keykeykeykey’
components
Shortcut method
1.1.1.1.
Scoping
Scoping
Scoping
Scopingstudies suitable for prelim
inarycosts
2.2.2.2.
Evaluation
Evaluation
Evaluation
Evaluationof operating variables
Separations with coarse purity
coarse purity
coarse purity
coarse purityrequirem
ents (I.e.
5
3.
Separations with coarse purity
coarse purity
coarse purity
coarse purityrequirem
ents (I.e.
contaminants >0.5 wt%)
4.
Detailed designs for approximately idealsystem
s
5.
Design when equilibrium data
equilibrium data
equilibrium data
equilibrium dataare unavailable (minimum
data requirem
ent)
Rigorous Design Procedures
�High
High
High
Highproduct purity is required.
�Non
Non
Non
Non- ---ideal
ideal
ideal
idealsystem
s and good equilibrium data
available.
6
�Relative volatility
Relative volatility
Relative volatility
Relative volatilitybetween key components < 1.3
< 1.3
< 1.3
< 1.3.
�One or more components is near the critical
critical
critical
critical
pressure
pressure
pressure
pressure.
Key Components
�Key componentsare the components between which it is
desired to make the separation
separation
separation
separation
�Light key
Light key
Light key
Light key
at the top
�Heavy key
Heavy key
Heavy key
Heavy key
at the bottom
�Adjacent
Adjacent
Adjacent
Adjacentkeys and Split
Split
Split
Splitkeys
7
�Adjacent
Adjacent
Adjacent
Adjacentkeys and Split
Split
Split
Splitkeys
�Non-keys are non-distributed components
�Non-keys are distributed components
�For complete separation of N components, (N-1) columns
are required
�Order of columnssequence will determine the capital and
operating costs
Heuristic rules –optimum sequencing
�Rem
ove the components one at a time
�Rem
ove any components that are presents in large excess
large excess
large excess
large excessearly in the
sequence
1.
With difficult separations, involving close boiling components
close boiling components
close boiling components
close boiling components,
postpone the most difficult separation to late in sequence
�Difficult separation require many stages, to reduce cost, the column
diameter should be made as small as possible. Since column diameter
8
diameter should be made as small as possible. Since column diameter
depend on flow-rate, the further down the sequence the sm
aller the
amount of material that the column has to handle.
�For tall columns, it may be necessary to split a column into two
separate columns to reduce the height of the column. Alternatively,
reduce the column pressure
Details: Douglas (1988), Conceptual Design of Chem
ical Processes.
Details: Douglas (1988), Conceptual Design of Chem
ical Processes.
Details: Douglas (1988), Conceptual Design of Chem
ical Processes.
Details: Douglas (1988), Conceptual Design of Chem
ical Processes.
Smith-Brinkley method
()
()
()
()
()
11
11
11
+−
−
−
−+
−+
−
−+
−=
ss
rs
r
sr
N s
NN r
r
NN r
r
NN r
SG
SS
RS
SR
S
fb
feed
t
he
abo
ve
st
ages
m
equ
ilib
riu
o
fn
um
ber
bo
tto
m
and
fe
ed e
bet
wee
n t
hco
mp
on
ent
t
he
of
spli
t
frac
tio
nal
Nfb
r
===
9
con
dit
ion
fe
ed
on
th
e
dep
end
s
se
ctio
n
st
rip
pin
g
fact
or,
st
rip
pin
g
se
ctio
n
re
ctif
yin
g
fact
or,
st
rip
pin
g
feed
t
he
bel
ow
st
ages
m
equ
ilib
riu
o
fn
um
ber
G
'L
/'
V'
KS
L/
VK
SN
is
ir
s
==
===
isr
ii
iSS
'L
K
L'
KG
−−=
11
isr
iSS
'LL
G
−−=
11
Main
ly l
iqu
id:
Main
ly v
ap
or:
Smith-Brinkley Procedures
1.
Estimate the flow rates L, V and L’, V’
L, V and L’, V’
L, V and L’, V’
L, V and L’, V’from the specified
component separations and reflux ratio.
2.
Estimate the top
top
top
topand bottom
bottom
bottom
bottomtemperatures by calculating
the dewdewdewdew
and bubble
bubble
bubble
bubblepoints for assumed
assumed
assumed
assumed
top and bottom
compositions
compositions
compositions
compositions.
10
compositions
compositions
compositions
compositions.
3.
Estimate the feed
feed
feed
feed
temperature
4.
Estimate the average component K values
K values
K values
K valuesin the stripping
and rectifying sections
5.
Calculate the values of
values of
values of
values of S SSSr,i
r,i
r,i
r,ifor the rectifying section and S SSS
s,i
s,i
s,i
s,i
for the stripping section
Smith-Brinkley Procedures…
6.
Calculate the fractional split
fractional split
fractional split
fractional splitof each component, and
hence the top and bottom compositions
top and bottom compositions
top and bottom compositions
top and bottom compositions.
7.7.7.7.
Compare the calculated
Compare the calculated
Compare the calculated
Compare the calculatedwith the
with the
with the
with the assumed values
assumed values
assumed values
assumed valuesand
check the overall column
overall column
overall column
overall column material balance.
material balance.
material balance.
material balance.
8.
Repeat the calculation until a
calculation until a
calculation until a
calculation until a satisfactory material balance
satisfactory material balance
satisfactory material balance
satisfactory material balance
is obtained
is obtained
is obtained
is obtained.
11
is obtained
is obtained
is obtained
is obtained.
•The usual procedure is to adjust the feed tem
perature up
adjust the feed tem
perature up
adjust the feed tem
perature up
adjust the feed tem
perature up
and down
and down
and down
and downtill asatisfactory
satisfactory
satisfactory
satisfactorybalance is obtained.
�Note:
Note:
Note:
Note:This is a rating approach
rating approach
rating approach
rating approach, suitable for determining
the perform
ance
perform
ance
perform
ance
perform
ance
of an existing
existing
existing
existingcolumn, rather than a
design method
design method
design method
design method.
Top
Flo
wra
te:
L &
V
Bott
om
Flo
wra
te:
L’
& V
’
Sp
ecif
y C
om
pon
ents
&
Ref
lux R
ati
o
Dew
Poin
t -
Top
Bu
bb
le P
oin
t -
Bott
om
Ass
um
e: T
op
&
Bott
om
Com
posi
tion
Est
imate
: K
i&
Fee
d T
(1)
Com
pare
: A
ssu
med
&
12
Calc
ula
te:
Sr,
i&
Ss,
i
Calc
ula
te:
Fra
ctio
nal
Sp
lit
(b/f
)
Calc
ula
te:
Top
& B
ott
om
Com
posi
tion
s
(1)
Com
pare
: A
ssu
med
&
Calc
ula
ted
Valu
es –
Top
&
Bott
om
Com
posi
tion
s
(2)
Ch
eck
–O
ver
all
Mate
rial
Bala
nce
Sto
p:
Ass
um
ed =
Calc
ula
ted
&
Over
all
Mate
rial
Bala
nce
is
met
Shortcut Method -Fenske Equation
�Calculation of multicomponent separation at total reflux
total reflux
total reflux
total reflux
�Stage equilibrium assumption
�Partial condenser and reboiler
Dx
Dx
)/
(
x
x
AB
RB
A
dis
tB
A
Bx
Bx
Dx
Dx
Nα
ln
)/
(
)/
(ln
min
=
()
()
()
()
()
()
AB
bo
tB
dis
tA
bo
tB
dis
tA
FR
FR
FR
FR
Nα
ln
11
ln
min
−−
=
13
AB
RBA
dis
tBA
xx
xx
Nα
ln
/ln
min
=
----
----
----
-(A
)
Fenske Equation…
()
Ad
ist
AA
Fz
FR
Dx
=
()
()
()
min
min
1
N CB
bo
tBb
ot
B
N CB
dis
tC
FR
FR
FR
α
α
+−
=
----
----
--(B
)
[]
[]
2/1
1
/1
12
1m
in..
.R
N
NN
AB
αα
αα
αα
α≈
=−
0
,,
,=
=b
ot
LN
KL
NK
dis
tL
NK
xF
zD
x
14
Ass
um
e non-d
istr
ibuti
ng n
on-k
eys: 0
,,
,=
=d
ist
HN
KH
NK
bo
tH
NK
xF
zB
x
Stage calculation at Total Reflux
1.
Calculate average relative volatility
average relative volatility
average relative volatility
average relative volatility
2.
Calculate N NNN
min
min
min
minfrom eqn(A)
3.
Calculate fractional recovery of non-key component C
component C
component C
component C
with eqn
eqn
eqn
eqn(B)
(B)
(B)
(B)based on key component A.
4.
Calculate fractional recovery
fractional recovery
fractional recovery
fractional recoveryof non-key component C
component C
component C
component C
15
4.
Calculate fractional recovery
fractional recovery
fractional recovery
fractional recoveryof non-key component C
component C
component C
component C
with eqn
eqn
eqn
eqn(B)
(B)
(B)
(B)based on key component B
component B
component B
component B.
5.
If fractional recovery of C in (3) and (4) are similar then
calculation is consistent (valid assumption)
Note:
Note:
Note:
Note:A
ccuracy of Fenske calculation depends on accurate
estimation of relative volatility
relative volatility
relative volatility
relative volatility.
Underwood Equation-Minimum Reflux
∑ =
−=
C ii
dis
ti
iDx
V1
,
min
φα
α
HK
KV
L
min
min
=φ
Rec
tify
ing s
ecti
on
----
----
-(9
.29)
∑ =
−=
−C i
i
bot
iiB
xV
1
,m
in
φαα
HK
KV
L
min
min
=φ
16
Str
ippin
g s
ecti
on
----
----
-(9
.30)
Underwood equation…
Assume CMO and constant relative volatilities, there are
common values Ø ØØØof that satisfy both equations (9.29 and
9.30):
∑ =
−+
−=
−=
∆C i
i
bot
ii
i
dis
ti
i
feed
Bx
Dx
VV
V1
,,
min
min
φαα
φα
α--
-(9.3
1)
17
feed
feed
V
calc
ula
te
to
feed
at
the
n
calc
ula
tio
flas
h
U
sed
stag
e.
feed
at
the
ra
te
flow
in v
apor
ch
ange
- V
∆
∆
=
−
−i
ii
1φ
αφ
α
()
qF
V
Fz
V
feed
C ii
ii
feed
−=
∆
−=
∆∑ =
1
1φ
αα--
----
---(
9.3
3)
----
----
-(9.3
4)
Underwood equation -Case A
Case A
Case A
Case A
�Assume all non
all non
all non
all non- ---keys do not distribute.
keys do not distribute.
keys do not distribute.
keys do not distribute.
�Solve eqn(9.33) for one value of Ø ØØØbetween the relative
volatilities of the two keys, α
HK< Ø ØØØ
< α
LK.
�Use the value of Ø ØØØto calculate V
minusing eqn(9.29)
�Calculate L
min= V
min-D
�Note: Non-distributing non-keys assumption is probably invalid
�Note: Non-distributing non-keys assumption is probably invalid
for sloppy separations or when a sandwich component is present.
With sandwich component, two value of Ø ØØØ
between α
HKand
αLK
()
[]
HK
bo
tH
Kd
ist
HK
LK
dis
tL
Kd
ist
LK
LN
Kd
ist
LN
Kd
ist
HN
K
Fz
FR
Dx
Fz
FR
Dx
Fz
Dx
Dx
)(
1
an
d 0
,,
,,
−==
==
18
----
----
---(
9.3
6)
----
----
---(
9.3
7)
Underwood Equation –Case B
Case B
Case B
Case B
�Assume non
non
non
non- ---distributing non
distributing non
distributing non
distributing non- ---keys
keys
keys
keysdetermined from
Fenske equation at total reflux is valid at minimum
minimum
minimum
minimum
reflux.
reflux.
reflux.
reflux.
�Dx N
K,distvalues obtained from Fenske Eqn.
�Solve eqn(9.33) for Ø ØØØvalue between relative volatilities
19
�Solve eqn(9.33) for Ø ØØØvalue between relative volatilities
of two keys.
�Use eqn(9.36) and (9.37) to obtain LK and HK in the
distillate
�Solve eqn(9.29) to find V
min
�Calculate L
min= V
min+ D
Underwood Equation –Case C
Case C
Case C
Case C
�Exact solution without further assumption
Exact solution without further assumption
Exact solution without further assumption
Exact solution without further assumption–solve the polynomial
eqn(9.33)
�Solve eqn(9.33) for all values of Ø ØØØlying between the relative
volatilities of all component
�αLNK,1< Ø ØØØ
1< α
LNK,2< Ø ØØØ
2< α
LK< Ø ØØØ
3< α
HK < Ø ØØØ
4< α
HNK,1
�C-1 valid roots
20�C-1 valid roots
�Write eqn(9.29) C-1 times, for each value of Ø ØØØ
�C-1 equations and C-1 unknowns
�Solve the simultaneous equations
�Note:
Note:
Note:
Note: A
ccuracy
Accuracy
Accuracy
Accuracydepends on
depends on
depends on
depends on relative volatility
relative volatility
relative volatility
relative volatilityand CMO
and CMO
and CMO
and CMO
Gilliland Correlation
1.
Calculate N
minfrom Fenske eqn
2.
Calculate (L/D) m
infrom Underwood eqn
3.
Choose actual (L/D); usually multiplication of (L/D) m
inby
a factor between 1.05 to 3.0
4.
Calculate the abscissa [(L/D)-(L/D)
]/[(L/D)+1]
21
4.
Calculate the abscissa [(L/D)-(L/D) m
in]/[(L/D)+1]
5.
Determine the ordinate value (N-N
min)/(N+1)
6.
Calculate the actual number of stages, N
Note:
Note:
Note:
Note:G
illiland correlation is only for rough estimates
rough estimates
rough estimates
rough estimates. C
alculated number
of stages can be off by ±30%,
30%,
30%,
30%,but norm
ally within ±7%.
7%.
7%.
7%.
Gilliland Correlation
00
27
43
.0
N-
N
0.0
1x
0fo
r
57
1.
18
0.1
1N
N-
Nm
in
<<
+−
=
≤≤
−=
+x
22
1.0
x0
.90
for
16
59
5.
01
65
95
.0
1N
N-
N
0.9
0x
0.0
1fo
r
00
27
43
.0
59
14
22
.0
54
58
27
.0
1N
N-
N
min
min
≤≤
−=
+
<<
+−
=+
x
xx
Feed Stage –Gilliland criteria
1+
≤
≤
fH
K
LK
FE
ED
HK
LK
fH
K
LK
xx
xx
xx
23
HK
LK
HK
LK
dis
tH
K
LK
zz
xx
−
=α
/ln
N
stag
e
feed
t
he
wh
ere
esti
mat
e
eqn
to
F
ensk
e
Use
min
F,
FUG
Approach
Fenske
Equation
To
tal R
efl
ux -
Nm
in
24
Underwood
Equation
Case A
Case B
Case C
To
ob
tain
r min
Gilliland
Correlation
To
ob
tain
actu
al
N
Kirkbride empirical equation
N NNNand N
and N
and N
and N
are the number of theoretical stages above
20
60
2.
D,H
K
B,L
K
FL
K
HK
sr
DB
xx
xx
NN
=
25
�N NNN
r rrrand N
and N
and N
and N
s sssare the number of theoretical stages above
(rectifying section) and below (stripping section) the feed
plate respectively.
�Match as closely as possible the composition of the feed
composition of the feed
composition of the feed
composition of the feed
and
that of the appropriate stream
(vapor or liquid) leaving the
leaving the
leaving the
leaving the
feed stage
feed stage
feed stage
feed stage.
Rigorous MCD Methods
�Lewis
Lewis
Lewis
Lewis- ---M
atheson
Matheson
Matheson
Mathesonmethod (LM) is rigorous analog of FUG
rigorous analog of FUG
rigorous analog of FUG
rigorous analog of FUG
shortcut method.
�Number of stages is determined from specified split between
two key components.
Basis of LM method:
26�Basis of LM method:
()
()
() D
in
in
ix
VDx
VLy
+=
+1
()
()
() B
im
im
x'
V
'B
x'
V
'L
y−
=+
11
Rec
tify
ing s
ecti
on
Str
ipp
ing
sec
tio
n
Thiele-Geddes method (TG)
�Rating method which is analog to SB shortcut
analog to SB shortcut
analog to SB shortcut
analog to SB shortcut.
�Distribution of components
Distribution of components
Distribution of components
Distribution of componentsbetween distillate and bottom is
calculated for a specified number of stages.
�Approach starts with an assumed number of stages
assumed number of stages
assumed number of stages
assumed number of stagesand
reflux ratio, and provides as output the separation
output the separationthat can
27
reflux ratio, and provides as output the separation
output the separation
output the separation
output the separationthat can
be made.
�It rates a given column instead of designing it.
�Has convergence advantages
convergence advantages
convergence advantages
convergence advantages, hence norm
ally used for
computer solutions to multicomponent, multi-tray
distillation systems.
LM Method –Design Approach
�Starts with a given separation and reflux ratio
given separation and reflux ratio
given separation and reflux ratio
given separation and reflux ratioand
determines the number of theoretical stages
number of theoretical stages
number of theoretical stages
number of theoretical stagesrequired to
make the separation.
�Stage
Stage
Stage
Stage- ---bybybyby- ---stage calculations
stage calculations
stage calculations
stage calculationsstarting at thebottom
bottom
bottom
bottomup
up
up
up the
28
�Stage
Stage
Stage
Stage- ---bybybyby- ---stage calculations
stage calculations
stage calculations
stage calculationsstarting at thebottom
bottom
bottom
bottomup
up
up
up the
column, or from the top down
top down
top down
top downthe column.
�Difficulty is the distribution of components
distribution of components
distribution of components
distribution of componentsbetween the
distillate and the bottoms will not be known until the
calculation is completed.
LM method –Design Procedure
1.
Estimate reflux ratio
reflux ratio
reflux ratio
reflux ratio, product compositions
compositions
compositions
compositions, tem
perature
temperature
temperature
temperature
profile,
2.
And number of theoretical trays
theoretical trays
theoretical trays
theoretical traysand feed location
feed location
feed location
feed location(by
various shortcut methods).
3.
Check the number of theoretical trays, feed trays, feed tray
location and tem
perature profile by LM method
4.
Calculate the product composition by TG method
294.
Calculate the product composition by TG method
Note:
Note:
Note:
Note:
LM -design method. TG -rating method. LM does not give accurate
product compositions
product compositions
product compositions
product compositions, but provides a better check for fixing the
better check for fixing the
better check for fixing the
better check for fixing the
specification
specification
specification
specificationof tower design (number of theoretical stages required
at a given reflux ratio).
TG allows the designer to rate the perform
ance
rate the perform
ance
rate the perform
ance
rate the perform
ance
of a given design by
checking the theoretical product compositions.
Rating method
�Input
�Number of stages
�Feed stage number
�Feed rate
�Feed composition
�Output
�Distillate composition
�Bottom composition
30
�Feed composition
�Feed enthalpy
�Reflux ratio
�Distillate to feed ratio
�Pressure
Design method
�Input
�Distillate composition
�Bottom composition
�Feed rate
�Feed enthalpy
�Output
�Number of stages
�Feed stage
�Reflux ratio
�Distillate rate
31
�Feed enthalpy
�Design/m
inimum reflux
ratio
�Optimum feed stage
�Pressure
�Distillate rate
TG method-Rating Approach
�Assume a temperature profile throughout
temperature profile throughout
temperature profile throughout
temperature profile throughoutthe column
(number of stages given).
�Starting at either end and working along the profile, arrive at
a composition at the other end.
32
a composition at the other end.
�If the calculated split
calculated split
calculated split
calculated splitdoes meet material balance
material balance
material balance
material balance
requirem
ent, the temperature profile is varied
temperature profile is varied
temperature profile is varied
temperature profile is varied
through
successive iterations.
TG method
�Assume number of theoretical plates, reflux ratio, temperature
on each plate.
�Procedure:
�Obtain V VVV- ---L distribution coefficient
L distribution coefficient
L distribution coefficient
L distribution coefficientas a function of T and P for
each component
�Perform
plate
plate
plate
plate- ---to tototo- ---plate calculations
plate calculations
plate calculations
plate calculationsfrom reflux condenser AND
from reboiler to fed plate
33
Perform
plate
plate
plate
plate- ---to tototo- ---plate calculations
plate calculations
plate calculations
plate calculationsfrom reflux condenser AND
from reboiler to fed plate
�Match results at feed plate
Match results at feed plate
Match results at feed plate
Match results at feed plate, calculate distillate and bottom
compositions
�With the obtained compositions, check the assumed T
�Adjust T and repeat until convergence.
Note:
Note:
Note:
Note:See Dr. M
artynRay note, pp 1.17-1.18 for mathem
atical operation of TG method.
Problem Specification
�C+6 variables must be specified, and C+2 are always
specified:
�Feed composition (C-1)
�Feed rate (1)
�Feed enthalpy (1)
34
�Feed enthalpy (1)
�Pressure (1)
�What are other four variables?
TG method –rating approach
1.
Number of stages
2.
Feed stage number
3.
Reflux ratio
4.
Distillate to feed ratio
Alternatively
Alternatively,
35
�Alternatively
Alternatively
Alternatively
Alternatively,
1.
Rectifying stages and Stripping stages or
2.
Number of stages and Feed stages
3.
Fractional recovery of LK in distillate
4.
Concentration of LK in distillate
Design Approach –LM method
1.
Distillate composition
2.
Bottom composition
3.
Design/m
inimum reflux ratio
4.
Feed location (usually at optimum)
�Alternatively,
Alternatively,
Alternatively,
Alternatively,
36
�Alternatively,
Alternatively,
Alternatively,
Alternatively,
1.
Composition of LK in distillate
2.
Composition of LK in bottom
3.
Reflux ratio
4.
Feed location (usually at optimum)
Other Methods
1.
Underwood’s Group M
ethod, A.J.V., Trans. Inst. Chem
. Eng. (London), Vol.10, p.112 (1932); and J. Inst. Petrol.,
Vol.31, p.111 (1945); Vol.32, p.598 and p.614 (1946)
2.
Tridiagonal-M
atrix Algorithm, (see Perry 6
thed, pp.13.44
to 13.47 for further detail)
37
to 13.47 for further detail)
3.
Matrix Techniques for Multicomponent Distillation
•Mathem
atical models for multicomponent equilibrium
separation systems in matrix notation (see Dr. M
artynRay,
pp1.22 –1.23 for further detail).
Summary
�FUG
FUG
FUG
FUG- ---method
method
method
methodto estimate the number of theoretical stages at
a given reflux ratio.
�Operating reflux ratio is usually chosen to be between 1.05
1.05
1.05
1.05
to 3 times that of minimum value
to 3 times that of minimum value
to 3 times that of minimum value
to 3 times that of minimum value.
38
�LM method is a design approach
LM method is a design approach
LM method is a design approach
LM method is a design approach(output are number of
stages, feed stage, reflux ratio, distillate).
�TG is a rating approach
TG is a rating approach
TG is a rating approach
TG is a rating approach(output are distillate composition
and bottom composition).