Distillation Course Berlin Summer 2008.
Sigurd Skogestad. Part 1
Introduction to Distillation:
Steady State Design
and Operation
1.
2.
3.
Introduction
Steady-state design
Steady-state operation
BASF Aktiengesellschaft
1. Introduction to distillation

King (Wiley, 1980) on distillation design
Shinskey (McGraw-Hill, 1984) on distillation control
Kister (McGraw-Hill, 1990) on distillation operation

General info: http://lorien.ncl.ac.uk/ming/distil/distil0.htm

I.J. Halvorsen and S. Skogestad, ``Distillation Theory'', In: Encyclopedia of Separation
Science. Ian D. Wilson (Editor-in-chief), Academic Press, 2000, pp. 1117-1134.

S. Skogestad, Dynamics and control of distillation columns - A tutorial introduction.,
Trans IChemE (UK), Vol. 75, Part A, Sept. 1997, 539-562 (Presented at Distillation and
Absorbtion 97, Maastricht, Netherlands, 8-10 Sept. 1997).
More: see home page Sigurd Skogestad http://www.nt.ntnu.no/users/skoge/
http://www.nt.ntnu.no/users/skoge/distillation




Free steady-state distillation software with thermo package
: http://www.chemsep.org/
L
F
V
B
D
I usually number the stages
from the bottom (with reboiler=1),
but many do It from the top
Alternative: Packed column
Vapor-liquid equilibrium (VLE) = Equilibrium line
y=K(x)
Non-ideal
Easy sep.
Difficult separation
(almost az.)
Ideal mixture
less common high-boiling az.
Azeotropes
(non-ideal)
common low-boiling az.
Vi+1
yi+1
The equilibrium stage concept
Stage i+1
Vi
yi
Li+1
Xi+1
Equilibrium (VLE): yi = Ki(xi)
Stage i
Vi-1
yi-1
Material balance stage i (out=in):
Li xi + Vi yi = Li+1xi+1 + Vy-1yi-1
Li
xi
Stage i-1
The equlibrium stage concept is used for both tray and packed columns
• N = no. of equilibrium stages in column
Typical: 0.7
• Tray column:
N = No.trays * Tray-efficiency
• Packed columns:
N = Height [m] / HETP [m]
Typical: 0.5 m
TOP
Simplified energy balance:
Vi = Vi+1 (“constant molar flows”)
VLE: yi = Ki(xi)
Material balance stage i (out=in):
Li xi + Vi yi = Li+1xi+1 + Vi-1yi-1
or (around bottom):
Li+1xi+1 –Vi yi = B xB
Constant molar flows:
xi+1 = (V/L) yi + (B/L) xB
BTM
”Operating line”:
•Straight line giving xi+1 as a function of yi
•Bottom: Goes through point (xB,xB)
McCabe-Thiele: Repeated graphical solution of material balance and VLE:
Equilibrium line (VLE)
TOP
Operating line
(material balance)
BTM
• Bottom (stage 1): start on diagonal (x1,x1)
• Find y1 = K(x1) on equlibrium line
• Find x2 on operating line
• Find y2 on equlibrium line
• Find x3 ........
• ......
When use distillation?


Liquid mixtures (with difference in boiling point)
Unbeatable for high-purity separations because

Essentially same energy usage independent of (im)purity!


Number of stages increases only as log of impurity!


Going from 1% to 0.001% (1 ppm) impurity in one product increases
required number of stages only by factor 2
Well suited for scale-up


Going from 1% to 0.0001% (1 ppm) impurity in one product increases
energy usage only by about 1%
Columns with diameters over 18 m
Examples of unlikely uses of distillation:


High-purity silicon for computers (via SiCl3 distillation)
Water – heavy-water separation (boiling point difference only 1.4C)
2. Steady-state Design


Given separation task
Find




configuration (column sequence)
no. of stages (N)
energy usage (V)
”How to design a column in 5 minutes”
Multicomponent and binary mixtures

We will mostly consider separation of binary mixtures

Multicomponent mixtures: For relatively ideal mixtures this is almost the
same as binary - if we consider the “pseudo-binary” separation between
the key components
L = light key component
H = heavy key component


The remaining components are almost like “dead-weight”
“Composition”: The impurity of key component is the important
Relative volatility, 
• Distillation is based on difference in relative volatility
• Vapor-liquid equilibrium (VLE). Component j: fjV=fjL,or
• Ideal gas (j=1) and ideal liquid (i=1): Raoult’s law:
Relative volatility between components L and H:
Note:  is constant for ideal mixture with similar heat of vaporization
Ideal mixture:
Estimate of relative volatility
IDEAL VLE (constant α)
Estimate of relative volatility (2)

Example. iso-pentane (L) – pentane (H)

Example. Nitrogen (L) – Oxygen (H)
Separation factor for column
or column section

Example: Binary separation with purities: 90% light in
top and 90% heavy in bottom:

Example: Binary separation with purities: 99.9% light in
top and 98% heavy in bottom:
Minimum no. of stages
Total reflux = Infinite energy
Total reflux:
Vi = Li+1
yi = xi+1
Stage i+1
Li+1
xi+1
Vi
yi
Stage i
Vi-1
yi-1
O
Li
xi
Operating line:
xi+1 = yi
(diagonal)
IDEAL VLE
MIXTURE
(constant α)
Minimum no. of stages, Nmin
(with infinite energy)

Infinity energy ) Total reflux. Stage i:

Repeat for all N stages

Fenske’s formula for minimum no. of stages
Assumption: Constant relative volatility

Applies also to column sections
Minimum energy (minimum
pinch
reflux)
(a) IDEAL VLE
(b) NON-IDEAL VLE
Infinite number of stages in pinch region
IDEAL VLE
MIXTURE
(constant α)
Minimum energy, Vmin
(with infinite no. of stages)

Feed liquid (King’s formula, assuming pinch at feed):
feed vapor: delete the D
 NOTE: Almost independent of composition!!
split (rLD=1, rHD=0), feed liquid:
For sharp
Assumption: Ideal mixture with constant relative
volatility and constant molar flows.
IDEAL VLE
MIXTURE
(constant α)
Examples design
• =1.5. xL,top = 0.99, xH,btm=0.99
–
–
–
–
Separation S = (0.99/0.01)2 = 9801
Nmin = lnS/ln = 9.19/0.405 = 22.7
Vmin/F = (0.99-0.01)/(1.5-1) + 0.5 = 2.46
Column A: N=40 (a bit small) gives V=1.3 Vmin
• =1.5. xL,top = 0.9999, xH,btm=0.9999
– Separation S = (0.9999/0.0001)2 = 9.99 e7
– Nmin = lnS/ln = 18.42/0.405 = 45.4
– Vmin/F = (0.9999-0.0001)/(1.5-1) + 0.5 = 2.50
Design: How many stages?
Number of stages
Energy (V) vs. number of stages (N)
• Trade-off between number of stages and
energy
• Actual V approaches Vmin for N
approximately 2 x Nmin or larger,
typically:
Nmin
Vmin
Energy
2Nmin 
3Nmin 
4Nmin 
+ 25% Vmin
+ 3 % Vmin
+ 0.3 % Vmin
Design: How many stages?
Conclusion: Select N > 2 Nmin (at least)

1.
2.
Many stages reduce energy costs
Many stages is good for control

Can overfractionate (tight control is then not critical)
or

Get less interactions between top and bottom (because of
pinch zone around feed)
IDEAL VLE
MIXTURE
(constant α)
Real well-designed column

Recall:

Choose N ≈ 2 Nmin:
Get V ≈ 1.25 Vmin and Q ≈ 1.25 ¢ Vmin ¢  Hvap
N = 3-4 Nmin gives V very close to Vmin


feed liquid
(0 for feed vapor)
Important insights:

Vmin is a good measure of energy usage Q
Vmin is almost independent of purity
Vmin is weakly dependent on feed comp. (feed liquid: get vaporization term D/F≈ zF)
Design: To improve purity (separation): Increase N
N and Vmin both increase sharply as  → 1








Example. Decrease  from 2 to 1.1:
Nmin increases by a factor 7.3
Vmin increases by a factor 10
( =ln 2/ln1.1)
( =(2-1)/(1.1-1))
NON-OPTIMAL
Feed stage location
with “extra” stages in top:
“Pinch” above feed stage
(mixture on feed stage is “heavier” than feed)
OPTIMAL:
•No pinch
•or: pinch on both
sides of feed stage
(mixture on feed stage has
same composition as feed)
feed line (q-line):
vertical for liquid feed;
horizontal for vapor feed
NON-OPTIMAL
with “extra” stages in bottom:
“Pinch” below feed stage
Note: Extra stages (and pinch) is NOT a problem,
because it implies lower energy usage.
Preferably, the pinch should be on both side of the feed.
(mixture on feed stage is “lighter” than feed)
“Pinch”: Section of column where little separation occurs
IDEAL VLE
MIXTURE
(constant α)
Simple formula for feed stage
location (Skogestad, 1987)
Example. C3-splitter. zFL=0.65, xDH= 0.005, xBL=0.1, =1.12.
IDEAL VLE
MIXTURE
(constant α)
Example: “5 min column design”




Design a column for separating air
Feed: 80 mol-% N2 (L) and 20% O2 (H)
Products: Distillate is 99% N2 and bottoms is 99.998% O2
Component data




Nitrogen: Tb = 77.4 K,  Hvap=5.57 kJ/mol
Oxygen: Tb = 90.2 K,  Hvap=6.82 kJ/mol
Problem: 1) Estimate . 2) Find split D/F. 3) Stages: Find
Nmin and 4) suggest values for N and NF. 5) Energy usage:
Find Vmin/F for a) vapor feed and b) liquid feed.
Given: For vapor feed and sharp sep. of binary mixture: Vmin/F = 1/(-1)
IDEAL VLE
MIXTURE
(constant α)
Solution “5-min design”
Also see paper (“Theory of distillation”)
IDEAL VLE
MIXTURE
(constant α)
IDEAL VLE
MIXTURE
(constant α)
Column profiles

Binary separation. Typical composition profile
Example column A
(binary, 41 stages,
99% purities, =1.5)
1
0.9
Typical:0.8
Flat profile at column ends
0.7
0.6
xi =
mole fraction
of light
component
0.5
0.4
Here: No pinch (flat profile) around feed
because we have “few” stages
compared to required separation
0.3
0.2
0.1
0
0
5
BTM
10
15
20
25
30
35
stage no.
40
45
TOP
Binary distillation: Typical column profiles
pinch below feed
(have extra stages in
bottom compared to
required separation)
Note: here with composition on x-axis
“More linear profile with log. compositions”:
Proof for infinite reflux and constant relative volatility
Check of feed location





It is the separation of key components that matters!
Plot X = ln(xL/xH) versus stage no.
Feed is misplaced if “pinch” (no change in X) only
on one side of feed stage
Feed is OK if no pinch or pinch on both sides of
feed
If misplaced feed location: May get better purity or
save energy by moving it (if possible)
Temperature profiles
•
Temperature gives information about composition
–
Crude estimate: T ¼ xi Tbi (avg. of boiling points)
–
–
Binary mixture. T ¼ xH TbH + xL TbL = TbH - (TbH – TbL )xL
“In theory”, temperature tells us everything about the separation for a binary mixtures. BUT two problems:
–
–
•
pressure variations
measurement noise for temperature
–
Both these make temperature “useless” for high purity (column ends for binary separation)
–
Multicomponent: Non-key components influence temperature. Thus, “even in theory” temperature does not
tell us about column separation.
Temperature is important for control
We may maintain the right split D/F by keeping a column temperature constant.
Rule for closing “stabilizing” temperature loop:
“Control most sensitive temperature” =
“control where gradient of temperature is steepest”
Rule applies to both binary and multicomponent mixtures
Temperature profiles
BTM
TOP
Binary distillation:
Typical temperature profiles
T
Flat around feed when pinch
(turned around with T on y-axis)
Flat temperature profile
toward column end
(because of high purity)
Stage no. !
LT ¼ -X
Again profile is much more linear
in terms of logarithmic temperatures:
342K
Stage no. !
355K
Pinch: region of little change (no separation) because of “extra” stages
Example using Chemsep





http://www.chemsep.org/
Written by Ross Taylor, Clarkson University
Lite version: max 50 stages and 5 components
Lite version is free and extremely simple to use
Example:





25% nC4(1), 25% nC5(2), 25% nC6(3), 25% nC7(4)
Key components C5 (L) and C6 (H)
Relative volatility varies between 2.5 (bottom) and 3.5 (top)
Assume we want about 99% of C5 in top and 99% of C6 in bottom
How many stages (N) and approx. L/F?
IDEAL VLE (constant α)
Shortcut analysis

Nmin = ln S / ln  = ln (1/(0.01*0.01)) / ln 3 = 8.4
(this no. does not depend on neon-keys)
Lmin/F ¼ 1/(-1) = 1/(3-1) = 0.5
(but non-keys change this...)
Let us try N = 20 and L/F=0.6

Now run detailed stage-to-stage simulation...


Data input... components
... column configuration
... thermodynamics
Correction: Use Soave-RK also here
... feed data
TOP: Specify L/F = 0.6
BTM: Specify B/F = 0.5
L/F = 0.6 gives 99.9 % recovery of
keys
recovery keys = 99.9 %
Profiles 99.9% recovery
Liquid phase composition
99.9 % recovery
TOP
light non-key
(butane)
light key
(pentane)
Stage
heavy non-key
(heptane)
BTM
x
heavy key
(hexane)
Vapor phase composition
99.9% recovery
TOP
Stage
BTM
y
Flow profile
99.9% recovery
TOP
L
Stage
BTM
Flows
V
Temperature profile
99.9% recovery
TOP
Stage
BTM
Temperature [K]
Turn profile around
Temp.
TOP
BTM
Stage
Log (xL/xH)-plot (“key ratio profile”):
Use to check feed location
TOP
Stage
log(xL/xH) straight line:
Feed placement OK
BTM
With feed moved from stage 10 to 15
TOP
5
Stage
10
15
BTM
log(xL/xH) has pinch above feed:
Too many stages above feed
Relative volatility
(Feed back to stage 10)
TOP
2.5
3.0
3.5
4.0
Stage
BTM

McCabe-Thiele diagram
99.9% recovery
TOP
y’C5
BTM
x’C5
3. Steady-state operation
The column is now given!
Operational degrees of freedom:


1.
2.




Get right split = cut (“external flows” e.g. D/F) !!!
Adjust separation = fractionation (“internal flows” L/V)
Column (temperature) profiles
Multicomponent mixtures
...other factors...
Optimal operation (in a plantwide setting)
Given feed (F) and pressure (p):
2 steady-state degrees of freedom, e.g. L and V.
Can use for (for example): Control one composition for each product (xD, xB)
Operation conventional column

2 steady-state degrees of freedom
1.
“External flows” (product split D/F).



2.
Adjust by changing D/F
Moves “profile” up and down
Large effect on operation
“Internal flows” (L/V).





Increase L and V with D/F constant
Stretches profile
Improves separation factor S, but costs
energy and limits capacity
Small effect
Why small effect? Recall design: Purity
(separation) mainly influenced by no. of
stages (N), which is fixed during operation
SPLIT (CUT)
Operation conventional column
2 steady-state degrees of freedom
“External flows” (product split D/F).
1.
•
•
•
Adjust by changing D/F
Moves “profile” up and down
Large effect on operation
“Internal flows” (L/V).
2.
•
•
•
•
•
Increase L and V with D/F constant
Stretches profile
Improves separation factor S, but costs
energy and limits capacity
Small effect
Why small effect? Recall design: Purity
(separation) mainly influenced by no. of
stages (N), which is fixed during
operation
FRACTIONATION
(SEPARATION)

Split D/F (external
flows):




Moves entire composition
profile up or down.
One product gets purer and
the other less pure
Large effect
Internal flows (L/V):



“Stretches profile”
Both products get purer if
we increase internal flows
Smaller effect
Composition profiles for column A (F=1).
Change in external flows: D = -0.02 with V=0
Change in internal flows: V = 1
with D=0
TOP
BTM
“Less pure”:
Breakthrough of light component in bottom
Implication for control
Important to get the right split (D/F)




avoid breakthrough of light components in bottom
avoid breakthrough of heavy components in top
How can this be done?
1. Measure feed composition (zF) and adjust D/F ¼ zF (feedforward
control).
NO! Does not work in practice because of uncertainty
2. Keep “column profile” in place by measuring and “fixing” it
somewhere in the column (feedback control)


Simplest in practice: Control temperature
To minimize movement of profile:
Control temperature at most sensitive location
Implication for control
D
LIGHT
TC
F
HEAVY
B
Idea: The column is a “tank” filled with heavy and light component
Need to adjust the split (D) to keep constant holdups of light and heavy
Simplest: “Profile feedback” using sensitive temperature
Temperature profile multicomponent
360
Feed:
25% C4
25% C5 (L)
25% C6 (H)
25% C7
350
340
Temp.
L/F=0.6:
99.9% recovery
of L and H
330
320
20 stages
D/F = 0.5
Vary L/F
L/F=0.3:
99% recovery
of L and H
310
300
STEEP PROFILE TOWARDS COLUMN ENDS
BECAUSE OF NON-KEYS
290
280
0
2
TOP
4
6
8
10
Stage
12
14
16
18
20
BTM
Control: Use temperature about here
(large sensitivity)
Summary. Steady-state operation of
given column




If split is wrong then one end will be too pure (overpurified), while the
other end does not meet spec. (underpurified)
Assume now split is right (e.g. control column profile)
If column has too few stages, then it may difficult to obtain desired
purities (even with maximum heat input): may need to give up one end
 You may try lowering the pressure, but usually limited effect
 You may consider moving the feed location (look at profile), but usually
has limited effect
 Normally the only “fix” is to get more stages in your column
If it has many stages, then you have two options:
 Overpurify one or both ends: Won’t cost much in terms of energy, and
makes control easier (no pinch in column)
 Keep specifications and save energy: Get pinch in column
Steady-state design and simulation
of real columns

Commercial software: Hysys, Aspen, …

Most important: Use right thermodynamics (VLE). SRK or PR works
surprisingly well for most mixtures (especially at high pressures and for
gases)

Design (given products): Use shortcut method to estimate required no. of
stages + feed location.

Operation (given column): First get no. of stages in each section by
matching data for composition and temperature profiles. Adjust holdups
by matching with dynamic responses
Trays vs. packings

Packings:
+ Much smaller pressure drop (typically 1/10)
+ Usually: More stages for given column height
- Problems with liquid distribution in larger columns (can use structured packings,
but more expensive)

Trays:
+ More easy to clean
+ Better for large capacity columns
+ Larger holdup (typically, 2 times larger): Advantage for control (“have more time”)
- Can have inverse response in bottom of column (- effect - difficult to predict)

Overall: Differences are surprisingly small – also for control
Conclusion steady-state distillation

Understanding the steady-state behavior brings you
a very long way towards understanding the control