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**Introduction to Distillation: Steady State Design and Operation**

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

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**BASF Aktiengesellschaft**

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**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: I.J. Halvorsen and S. Skogestad, ``Distillation Theory'', In: Encyclopedia of Separation Science. Ian D. Wilson (Editor-in-chief), Academic Press, 2000, pp S. Skogestad, Dynamics and control of distillation columns - A tutorial introduction., Trans IChemE (UK), Vol. 75, Part A, Sept. 1997, (Presented at Distillation and Absorbtion 97, Maastricht, Netherlands, 8-10 Sept. 1997). More: see home page Sigurd Skogestad Free steady-state distillation software with thermo package :

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F V L B D

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**I usually number the stages**

from the bottom (with reboiler=1), but many do It from the top

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**Alternative: Packed column**

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**Vapor-liquid equilibrium (VLE) = Equilibrium line**

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

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**The equilibrium stage concept**

Vi+1 yi+1 Stage i+1 Material balance stage i (out=in): Li xi + Vi yi = Li+1xi+1 + Vy-1yi-1 Li+1 Xi+1 Vi yi Stage i Equilibrium (VLE): yi = Ki(xi) Li xi Vi-1 yi-1 Stage i-1 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

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**TOP BTM TOP BTM Simplified energy balance:**

Vi = Vi+1 (“constant molar flows”) BTM TOP BTM

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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 % (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)

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**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”

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**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

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Relative volatility,

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**Ideal mixture: Estimate of relative volatility**

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**Estimate of relative volatility (2)**

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

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**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:

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**Minimum no. of stages Total reflux = Infinite energy Stage i+1**

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

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**Minimum no. of stages, Nmin (with infinite energy)**

IDEAL VLE (constant α) IDEAL MIXTURE 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

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**Minimum energy (minimum reflux)**

pinch (a) IDEAL VLE (b) NON-IDEAL VLE Infinite number of stages in pinch region

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**Minimum energy, Vmin (with infinite no. of stages)**

IDEAL MIXTURE IDEAL VLE (constant α) 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 (rLD=1, rHD=0), feed liquid: Assumption: Ideal mixture with constant relative volatility and constant molar flows. feed vapor: delete the D

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IDEAL VLE (constant α) IDEAL MIXTURE Examples design

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**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 % Vmin

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**Design: How many stages?**

Conclusion: Select N > 2 Nmin (at least) 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)

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**Real well-designed column**

IDEAL VLE (constant α) IDEAL MIXTURE 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 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 ( =ln 2/ln1.1) Vmin increases by a factor ( =(2-1)/(1.1-1)) feed liquid (0 for feed vapor)

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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 (mixture on feed stage is “lighter” than feed) 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. “Pinch”: Section of column where little separation occurs

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**Simple formula for feed stage location (Skogestad, 1987)**

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

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**Example: “5 min column design”**

IDEAL VLE (constant α) 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 % 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)

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**Solution “5-min design”**

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

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IDEAL VLE (constant α) IDEAL MIXTURE

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IDEAL VLE (constant α) IDEAL MIXTURE

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**Column profiles Binary separation. Typical composition profile**

Example column A (binary, 41 stages, 99% purities, =1.5) Typical: Flat profile at column ends xi = mole fraction of light component Here: No pinch (flat profile) around feed because we have “few” stages compared to required separation TOP BTM stage no.

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**Binary distillation: Typical column profiles**

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

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**“More linear profile with log. compositions”:**

Proof for infinite reflux and constant relative volatility

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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)

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Temperature profiles

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Temperature profiles BTM TOP

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**Typical temperature profiles T**

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

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**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?

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**Shortcut analysis Nmin = ln S / ln = ln (1/(0.01*0.01)) / ln 3 = 8.4**

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...

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Data input... components

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... column configuration

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

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... feed data

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**TOP: Specify L/F = 0.6 BTM: Specify B/F = 0.5**

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**L/F = 0.6 gives 99.9 % recovery of keys**

recovery keys = 99.9 %

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Profiles 99.9% recovery

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**Liquid phase composition 99.9 % recovery**

TOP light non-key (butane) light key (pentane) Stage heavy non-key (heptane) heavy key (hexane) BTM x

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**Vapor phase composition 99.9% recovery**

TOP Stage BTM y

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**Flow profile 99.9% recovery**

TOP V L Stage BTM Flows

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**Temperature profile 99.9% recovery**

TOP Stage BTM Temperature [K]

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Turn profile around Temp. TOP BTM Stage

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**Log (xL/xH)-plot (“key ratio profile”): Use to check feed location**

TOP Stage log(xL/xH) straight line: Feed placement OK BTM

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**With feed moved from stage 10 to 15**

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

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**Relative volatility (Feed back to stage 10)**

2.5 3.0 3.5 4.0 TOP Stage BTM

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**McCabe-Thiele diagram 99.9% recovery**

TOP y’C5 BTM x’C5

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**3. Steady-state operation**

The column is now given! Operational degrees of freedom: 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)

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**Given feed (F) and pressure (p): 2 steady-state degrees of freedom, e**

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)

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**Operation conventional column**

2 steady-state degrees of freedom “External flows” (product split D/F). 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)

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**Operation conventional column**

2 steady-state degrees of freedom “External flows” (product split D/F). 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 FRACTIONATION (SEPARATION)

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**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 = with V=0 Change in internal flows: V = with D=0 TOP BTM “Less pure”: Breakthrough of light component in bottom

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**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? 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: NO! Does not work in practice because of uncertainty Control temperature at most sensitive location

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**Implication for control**

LIGHT HEAVY F D B TC 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

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**Temperature profile multicomponent**

Feed: 25% C4 25% C5 (L) 25% C6 (H) 25% C7 20 stages D/F = 0.5 Vary L/F L/F=0.6: 99.9% recovery of L and H Temp. L/F=0.3: 99% recovery of L and H STEEP PROFILE TOWARDS COLUMN ENDS BECAUSE OF NON-KEYS BTM TOP Stage Control: Use temperature about here (large sensitivity)

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**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

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**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

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**Trays vs. packings Packings: Trays:**

+ 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

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**Conclusion steady-state distillation**

Understanding the steady-state behavior brings you a very long way towards understanding the control

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