1BDIST-ss.ppt

Introduction to Distillation:
Steady State Design
and Operation
Distillation Course Berlin Summer 2008.
Sigurd Skogestad. Part 1
1. Introduction
2. Steady-state design
3. Steady-state operation

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/

I usually number the stages
from the bottom (with reboiler=1),
but many do It from the top

Vapor-liquid equilibrium (VLE) = Equilibrium line
Ideal mixture
Difficult separation
(almost az.)
Azeotropes
(non-ideal)
common low-boiling az.
less common high-boiling az.
Easy sep.
Non-ideal
y=K(x)

Stage i
Stage i+1
Stage i-1
Vi
yi
Vi-1
yi-1
Li+1
Xi+1
Li
xi
Equilibrium (VLE): yi = Ki(xi)
Vi+1
yi+1
Material balance stage i (out=in):
Li xi + Vi yi = Li+1xi+1 + Vy-1yi-1
The equilibrium stage concept
The equlibrium stage concept is used for both tray and packed columns
• N = no. of equilibrium stages in column
• Tray column: N = No.trays * Tray-efficiency
• Packed columns: N = Height [m] / HETP [m]
Typical: 0.7
Typical: 0.5 m

McCabe-Thiele: Repeated graphical solution of material balance and VLE:
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
”Operating line”:
•Straight line giving xi+1 as a function of yi
•Bottom: Goes through point (xB,xB)
• 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 ........
• ......
Equilibrium line (VLE)
Operating line
(material balance)
BTM
TOP
TOP
BTM
Simplified energy balance:
Vi = Vi+1 (“constant molar flows”)

When use distillation?
 Liquid mixtures (with difference in boiling point)
 Unbeatable for high-purity separations because
 Essentially same energy usage independent of (im)purity!
 Going from 1% to 0.0001% (1 ppm) impurity in one product increases
energy usage only by about 1%
 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
 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

Estimate of relative volatility (2)
 Example. iso-pentane (L) – pentane (H)
 Example. Nitrogen (L) – Oxygen (H)
IDEAL VLE (constant α)

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
O
Operating line: xi+1 = yi (diagonal)
Stage i
Stage i+1
Vi
yi
Vi-1
yi-1
Li+1
xi+1
Li
xi
Total reflux:
Vi = Li+1
yi = xi+1

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
IDEAL MIXTURE

Minimum energy (minimum
reflux)
Infinite number of stages in pinch region
pinch
(a) IDEAL VLE (b) NON-IDEAL VLE

Minimum energy, Vmin
(with infinite no. of stages)
 Feed liquid (King’s formula, assuming pinch at feed):
NOTE: Almost independent of composition!! For sharp
split (rL
D=1, rH
D=0), feed liquid:
Assumption: Ideal mixture with constant relative
volatility and constant molar flows.
feed vapor: delete the D
IDEAL MIXTURE

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
IDEAL MIXTURE

Design: How many 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:
2Nmin  + 25% Vmin
3Nmin  + 3 % Vmin
4Nmin  + 0.3 % Vmin
Energy
Number
of
stages
Vmin
Nmin

Design: How many stages?
 Conclusion: Select N > 2 Nmin (at least)
1. Many stages reduce energy costs
2. 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)

 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
 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 ( =ln 2/ln1.1)
 Vmin increases by a factor 10 ( =(2-1)/(1.1-1))
Real well-designed column
feed liquid
(0 for feed vapor)
IDEAL MIXTURE

Feed stage location
feed line (q-line):
vertical for liquid feed;
horizontal for vapor feed
•No pinch
•or: pinch on both
sides of feed stage
(mixture on feed stage has
same composition as feed)
with “extra” stages in top:
“Pinch” above feed stage
(mixture on feed stage is “heavier” than feed)
with “extra” stages in bottom:
“Pinch” below feed stage
(mixture on feed stage is “lighter” than feed)
“Pinch”: Section of column where little separation occurs
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.
OPTIMAL:
NON-OPTIMAL
NON-OPTIMAL

Simple formula for feed stage
location (Skogestad, 1987)
Example. C3-splitter. zFL=0.65, xDH= 0.005, xBL=0.1, =1.12.
IDEAL MIXTURE

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 MIXTURE

Solution “5-min design”
Also see paper (“Theory of distillation”)
IDEAL MIXTURE

IDEAL MIXTURE

Column profiles
 Binary separation. Typical composition profile
stage no.
Example column A
(binary, 41 stages,
99% purities, =1.5)
0 5 10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Here: No pinch (flat profile) around feed
because we have “few” stages
compared to required separation
xi =
mole fraction
of light
component
BTM TOP
Typical: Flat profile at column ends

Binary distillation: Typical column profiles
Note: here with composition on x-axis
pinch below feed
(have extra stages in
bottom compared to
required separation)

“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

Binary distillation:
Typical temperature profiles
(turned around with T on y-axis)
Again profile is much more linear
in terms of logarithmic temperatures:
T
Stage no. !
Stage no. !
LT ¼ -X
342K
355K
Flat around feed when pinch
Pinch: region of little change (no separation) because of “extra” stages
Flat temperature profile
toward column end
(because of high purity)

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?

 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...
Shortcut analysis

... thermodynamics
Correction: Use Soave-RK also here

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 %

Liquid phase composition
99.9 % recovery
x
Stage
TOP
BTM
light key
(pentane)
heavy key
(hexane)
heavy non-key
(heptane)
light non-key
(butane)

Vapor phase composition
99.9% recovery
Stage
y
BTM
TOP

Flow profile
99.9% recovery
Stage
Flows
V
L
BTM
TOP

Temperature profile
99.9% recovery
Temperature [K]
Stage
TOP
BTM

Turn profile around
Stage
Temp.
TOP BTM

Log (xL/xH)-plot (“key ratio profile”):
Use to check feed location
log(xL/xH) straight line:
Feed placement OK
Stage
BTM
TOP

With feed moved from stage 10 to 15
Stage
TOP
BTM
log(xL/xH) has pinch above feed:
Too many stages above feed
15
10
5

Relative volatility
(Feed back to stage 10)
Stage

2.5 3.0 3.5 4.0
BTM
TOP

McCabe-Thiele diagram
99.9% recovery
y’C5
x’C5
BTM
TOP

3. Steady-state operation
 The column is now given!
 Operational degrees of freedom:
1. Get right split = cut (“external flows” e.g. D/F) !!!
2. 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): 2steady-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).
 Adjust by changing D/F
 Moves “profile” up and down
 Large effect on operation
2. “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
1. “External flows” (product split D/F).
• Adjust by changing D/F
• Moves “profile” up and down
• Large effect on operation
2. “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 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
“Less pure”:
Breakthrough of light component in bottom
BTM
TOP

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).
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
NO! Does not work in practice because of uncertainty

Implication for control
LIGHT
HEAVY
F
D
B
TC
Need to adjust the split (D) to keep constant holdups of light and heavy
Simplest: “Profile feedback” using sensitive temperature
Idea: The column is a “tank” filled with heavy and light component

Temperature profile multicomponent
0 2 4 6 8 10 12 14 16 18 20
280
290
300
310
320
330
340
350
360
Stage
TOP BTM
Temp.
L/F=0.6:
99.9% recovery
of L and H
L/F=0.3:
99% recovery
of L and H
Feed:
25% C4
25% C5 (L)
25% C6 (H)
25% C7
20 stages
D/F = 0.5
Vary L/F
STEEP PROFILE TOWARDS COLUMN ENDS
BECAUSE OF NON-KEYS
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

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