Divided-Wall Column¶

In this tutorial you will separate a three-component mixture into three products in a single shell with the Divided-Wall Column of the DWSIM Patreon Edition. You will build the column, solve it, read the profiles on both sides of the wall, let the design tools find the wall splits and the side draw stage, and compare the energy it needs with two conventional columns in series.

What you will learn

How a divided-wall column is built from four sections, and which five specifications fix it
How to read the temperature, composition and molecular tracking profiles on both sides of the wall
How the wall split optimizer and the side draw sweep lower the reboiler duty
How much energy the column saves against the direct sequence of two columns

Prerequisites

Completed Distillation Column
DWSIM Patreon Edition, membership level 2 or higher

Patreon feature

The Divided-Wall Column needs a Patreon membership of level 2 or higher. With a lower level the column can be placed and configured, but it does not calculate and the flowsheet cannot be saved with it.

Process Overview¶

A ternary mixture A/B/C is usually split with two columns: the first takes A overhead, the second splits B from C (the direct sequence). In the first column the concentration of B rises to a maximum somewhere below the feed and then falls again, so part of the separation work done on B is undone further down. This remixing is the main inefficiency of the sequence.

A divided-wall column puts a vertical wall in the middle of one shell. The feed side of the wall (the prefractionator) only splits A from C and lets B go both ways; the product side of the wall takes B out as a side draw where it is most concentrated. Above the wall the column is an ordinary rectifying section with one condenser; below the wall, an ordinary stripping section with one reboiler. Thermodynamically it is the fully thermally coupled Petlyuk arrangement, and it typically saves 25 to 35 % of the energy of the conventional sequence, together with one shell, one condenser and one reboiler less.

DWSIM solves all the stages of the four sections and the two condensing and reboiling ends at once, by Newton's method on the full set of MESH equations.

Column Structure¶

graph TB
    C["Condenser"] --> T["Top section (T)<br/>9 stages"]
    T --> P["Prefractionator (P)<br/>23 stages<br/>feed on P14"]
    T --> M["Product side (M)<br/>23 stages<br/>side draw on M14"]
    P --> B["Bottom section (B)<br/>14 stages"]
    M --> B
    B --> R["Reboiler"]
    F["Feed"] -.-> P
    C -.-> D["Pentane"]
    M -.-> S["Hexane"]
    R -.-> W["Heptane"]

Stages are counted from the top of each section. At the top of the wall the liquid leaving the last stage of T is split: part goes down the prefractionator, the rest down the product side. At the bottom of the wall the vapor leaving the first stage of B is split the same way. These two wall splits are what the column adds to an ordinary one.

Degrees of freedom¶

A divided-wall column with one side draw has five specifications:

Where	Specification in this tutorial
Condenser	n-pentane mole fraction 0.99 in the distillate
Reboiler	n-heptane mole fraction 0.99 in the bottoms
Side draw	n-hexane mole fraction 0.92 in the side product
Top of the wall	liquid flow to the prefractionator
Bottom of the wall	vapor flow to the prefractionator

The three purities fix the products. The two wall splits are free: any pair within a feasible region meets the purities, but each pair needs a different reboiler duty. Choosing them well is the main design task, and DWSIM has a tool for it.

Key Design Parameters¶

The case is DTU case 1 from Montonati et al. (2022).

Parameter	Value
Compounds	N-pentane, N-hexane, N-heptane
Property Package	Peng-Robinson (PR)
Feed	100 kmol/h, 40/20/40 mol %, saturated liquid at 2 atm
Sections	9 (top), 23 (prefractionator), 23 (product side), 14 (bottom)
Feed stage	prefractionator stage 14
Side draw	product side stage 14, liquid
Condenser	total, 2 atm, no pressure drop
First guess of the wall splits	45 kmol/h of liquid, 85 kmol/h of vapor to the prefractionator

Step-by-Step in the Classic UI¶

1. Set up¶

File > New Chemical Process Model:

Compounds: N-pentane, N-hexane, N-heptane
Property Package: Peng-Robinson (PR)

2. Create the feed¶

Add a Material Stream Feed: pressure 2 atm, vapor fraction 0 (saturated liquid), molar flow 100 kmol/h, mole fractions 0.4 / 0.2 / 0.4.

3. Add the column and connect it¶

From the object palette, under Columns, drag a Divided-Wall Column onto the canvas and name it DWC-101. Add three empty material streams, Pentane, Hexane and Heptane, and two energy streams, Condenser Duty and Reboiler Duty.

Open the DWC-101 editor. On Connections > Inlets, connect Feed to the feed port and Reboiler Duty to the reboiler duty port. On Connections > Outlets, connect Pentane to the distillate, Heptane to the bottoms, Hexane to the first side product and Condenser Duty to the condenser duty.

Connections tab of the divided-wall column

One port per feed and per side draw

The column creates a feed port for each row of the feed table and a side product port for each row of the side draw table (step 5). A new column has one of each, which is what this tutorial needs.

4. Structure, pressure, specifications and wall splits¶

On the Parameters tab:

Structure: Wall position Middle (one condenser, one reboiler); Top section stages 9; Prefractionator stages 23; Product side stages 23; Bottom section stages 14; Condenser Total.
Pressure: Condenser pressure 2 atm (2.0265 bar); both pressure drops 0.
Condenser Specification: Component Mole Fraction, value 0.99, compound N-pentane.
Reboiler Specification: Component Mole Fraction, value 0.99, compound N-heptane.
Wall Splits: Liquid split at the top of the wall Flow to prefractionator, Liquid flow to the prefractionator 45 kmol/h; Vapor split at the bottom of the wall Flow to prefractionator, Vapor flow to the prefractionator 85 kmol/h.

Structure and pressure on the Parameters tab

Reboiler specification and wall splits

Flow or fraction?

A wall split can be given as the fraction of the liquid (or vapor) sent to the prefractionator or as the flow itself. Flows are the usual choice in design studies because they stay meaningful when the reflux changes; the 45/85 kmol/h used here are a deliberately rough first guess that the optimizer will improve in step 8.

5. Feed location and side draw¶

On the Feeds and Side Draws tab, set the feed row to section Prefractionator, stage 14. In the side draw row, set the name to Hexane, section Product side, stage 14, phase Liquid, specification Component Mole Fraction, value 0.92, compound N-hexane.

Feeds and side draws

6. Solve and read the results¶

Press Solve. The column converges in well under a second. The Results tab shows the solution summary, the duties, the reflux and boilup ratios, the interlink flows and a size estimate used for costing:

Result	First guess (45/85 kmol/h)
Condenser duty	1011.5 kW
Reboiler duty	1097.1 kW
Reflux ratio	2.66
Boilup ratio	3.37
Condenser / reboiler temperature	58.4 / 123.6 °C

Results with the first guess of the wall splits

All three purities are met: 40.3 kmol/h of pentane at 99.00 %, 20.9 kmol/h of hexane at 92.00 % and 38.8 kmol/h of heptane at 99.00 %. The wall splits change only how much energy that takes.

7. Read the profiles¶

The Profiles tab has a chart selector and the stage table (temperature, pressure, liquid and vapor flows, side draw flow and the tracking factor β). Each chart has two curves: the product side path (top section, product side of the wall, bottom section) and the prefractionator between the wall ends. The elevation axis counts stages from the top of the column, so both sides of the wall share the same scale.

Temperature Profile: the two sides of the wall run at different temperatures at the same elevation. The prefractionator is cooler around the feed because it still holds a lot of pentane, while the product side, which is richer in hexane, is warmer.

Temperature profile on both sides of the wall

Liquid Composition (Prefractionator Side): follow the feed side path from the condenser to the reboiler. Hexane peaks near the top of the wall and again below the feed. Inside the prefractionator, above the feed, all three compositions are nearly flat: those stages sit in a pinch and do little separation, which is a sign that the feed could move up (see the exercises).

$Liquid composition along the prefractionator side$

8. Optimize the wall splits¶

Open the Design tab and scroll to Wall Split Optimization. Keep Maximum column solutions at 40 and click Optimize Wall Splits. The optimizer runs a Nelder-Mead search on the two split fractions, solving the full column at each point (starting from the last converged profile) and keeping the pair with the lowest reboiler duty that still meets all five specifications. It takes about 10 seconds:

	First guess	Optimized
Liquid to the prefractionator	45.0 kmol/h	33.6 kmol/h
Vapor to the prefractionator	85.0 kmol/h	85.3 kmol/h
Reboiler duty	1097.1 kW	928.4 kW
Condenser duty	1011.5 kW	842.8 kW
Reflux ratio	2.66	2.05

Wall split optimization result

Click Apply the Best Splits and solve again. The reboiler duty drops by 15 % with the same structure and the same products. The optimum agrees with the interlink flows reported by Montonati et al. (33.5 and 84.5 kmol/h, Qr = 898.6 kW with their PR implementation; the duty here is 3 % higher).

A flat valley with steep walls

Near the optimum the duty hardly changes: 30/80 kmol/h gives 932 kW. Away from it the duty climbs fast: 25/95 kmol/h needs 1540 kW. A divided-wall column run with badly chosen splits can lose most of its advantage over the conventional sequence, which is why the splits are worth optimizing.

9. Check the side draw stage with molecular tracking¶

Select the Molecular Tracking chart on the Profiles tab. It plots β = K·V / (K·V + L) for the middle compound (hexane) on every stage: the probability that a hexane molecule on that stage leaves upward with the vapor. Where β is below 0.5 hexane tends to move down, where it is above 0.5 it tends to move up, so hexane accumulates where β crosses 0.5. That is where the side draw belongs (Montonati et al., 2022).

Molecular tracking chart

On the product side path β crosses 0.5 near stage M13. The jumps at the wall ends come from the interlink flows and are ignored. On the Design tab, Molecular Tracking reports the crossing and lets you check it: set the sweep range (for example 7 to 19) and click Sweep Side Draw Stage. The column is solved with the side draw on each stage and the reboiler duty is listed:

Side draw stage	M8	M10	M12	M13	M14	M16	M19
Reboiler duty (kW)	934.3	929.9	927.9	927.8	928.4	933.3	977.2

Side draw stage sweep

The minimum is at M12-M13, where β crosses 0.5, and it is shallow: the stage used in this tutorial (M14) costs 0.6 kW more. Moving the side draw toward the bottom of the wall costs much more. Use the Lowest-Duty Stage moves the side draw to the best stage of the sweep.

10. Compare with the conventional sequence¶

To see what the wall buys, build the same products with two ordinary Distillation Columns in series: C-1 (30 stages, feed on stage 15) takes pentane overhead at 99 % with 1 % pentane in its bottoms; C-2 (30 stages, feed on stage 15) splits that bottoms into hexane at 92 % and heptane at 99 %. The Python script in the next section builds this flowsheet too.

	Direct sequence	Divided-wall column
Columns / condensers / reboilers	2 / 2 / 2	1 / 1 / 1
Stages	60	69 (46 in height)
Reboiler duty	686.8 + 724.7 = 1411.5 kW	928.4 kW
Saving		34 %

Giving each conventional column 40 stages lowers its total to 1340 kW; the divided-wall column still needs 31 % less heat.

Divided-wall column flowsheet

Results and Validation¶

Variable	Value
Pentane	40.3 kmol/h, 99.00 mol %
Hexane (side draw)	20.9 kmol/h, 92.00 mol %
Heptane	38.8 kmol/h, 99.00 mol %
Optimized wall splits	33.6 / 85.3 kmol/h
Reboiler duty	928.4 kW (paper: 898.6 kW)
Condenser duty	842.8 kW (paper: 815.8 kW)
Reflux ratio	2.05 (paper: 1.95)
Best side draw stage	M12-M13

Expected results

All five specifications met, a reboiler duty about 930 kW after the optimization, and about a third less heat than the direct sequence.

Designing a Column from Scratch¶

This tutorial started from a known structure. For a new separation, the Shortcut Design box on the Design tab proposes one. Pick the light key (distillate), the middle compound (side product) and the heavy key (bottoms), their recoveries and the ratio of the operating vapor to the minimum vapor, then click Run Shortcut Design. The design follows Triantafyllou and Smith (1992): the column is treated as a prefractionator and a main column split into an upper and a lower part; Underwood gives the minimum vapor flows (the Vmin diagram), and Fenske, Gilliland and Kirkbride size each part.

Shortcut design

For this feed (relative volatilities 5.71 / 2.24 / 1), recoveries 0.99 / 0.95 / 0.99 and 1.2 times the minimum vapor, the shortcut proposes 8 / 26 / 26 / 9 stages, the feed on P13, the side draw on M12, a reflux ratio of 2.14 (minimum 1.61) and interlinks of 33.7 and 79.0 kmol/h, close to the structure used above. Apply to the Column copies the structure and the splits into the parameters; tick the option above it to copy the purity specifications too. A shortcut design is a starting point: solve the rigorous column, then refine it with the optimizer and the sweep as in steps 8 and 9.

Going Further¶

Secondary specifications: the Secondary Specs tab adjusts a primary specification until a product property reaches a target, for example a D86 95 % point, a flash point or a density. The Divided-Wall Column - Secondary Specifications on D86 Cut Points sample runs a naphtha splitter to two D86 cut points this way.
Four products (Kaibel column): add a second side draw on the product side. The Divided-Wall Column - Kaibel Column, Pentane to Octane sample splits four normal alkanes in one shell.
Wall at the top or the bottom: Wall position Top runs the wall up to the top of the column and gives each side its own condenser and distillate; Bottom runs it down to the bottom and gives each side its own reboiler and bottoms product. Each extra end brings its own specification.
Heat through the wall: a real wall conducts heat from the hotter side to the cooler one. Give an overall coefficient and the wall area under Heat Transfer Through the Wall to include it; zero in either keeps the wall adiabatic.
Costing: the size estimate on the Results tab (diameter, height, shell and wall weight) feeds the Techno-Economic Analysis, so you can compare the capital cost of the two arrangements as well as the energy.

Automating This Tutorial¶

Files in this repository

Python script: examples/advanced/08_divided_wall_column.py
In DWSIM: Samples list on the welcome screen, Divided-Wall Column - Pentane, Hexane, Heptane (the same column with the optimized splits)

FluentAPI (Python)LLM Prompt

import os
import sys

import pythonnet
pythonnet.load("netfx")              # DWSIM is a .NET Framework application
import clr  # noqa: E402

DWSIM_BIN = os.environ.get("DWSIM_BIN")
if not DWSIM_BIN:
    raise SystemExit("Set DWSIM_BIN to the DWSIM installation folder before running.")
for sub in ("", "unitops", "ppacks", "extenders"):
    sys.path.append(os.path.join(DWSIM_BIN, sub))
# In a source tree the Plus unit operations live in a separate DistPackages folder;
# an installed Patreon edition already has them under DWSIM_BIN.
PLUS = os.environ.get("DWSIM_PLUS", "")
if PLUS:
    for sub in ("unitops", "extenders"):
        sys.path.append(os.path.join(PLUS, sub))
clr.AddReference("DWSIM.Automation")
clr.AddReference("DWSIM.Automation.FluentAPI")

from DWSIM.Automation.FluentAPI import Flowsheet, License, PropertyPackages, Q  # noqa: E402

key = os.environ.get("DWSIM_PATRON_KEY")
if not key:
    raise SystemExit("The Divided-Wall Column is a DWSIM Patreon operation: set DWSIM_PATRON_KEY to your Patreon key.")
if not License.CheckLicense(key):
    raise SystemExit("The Patreon key was not accepted.")

clr.AddReference("DWSIM.UnitOperations.DividedWallColumn")
from System import Array, Int32  # noqa: E402
from DWSIM.UnitOperations.DividedWallColumn import DwcSection, DwcEndSpecType, DwcSideSpecType  # noqa: E402
from DWSIM.UnitOperations.DividedWallColumn.Design import InterlinkOptimizer, MolecularTracking  # noqa: E402

COMPOUNDS = ("N-pentane", "N-hexane", "N-heptane")


def add_feed(fs):
    # 100 kmol/h of saturated liquid at 2 atm, 40/20/40 mol %; compound flows in mol/s
    return (fs.AddMaterialStream("Feed").WithPressure(Q.Atm(2.0)).WithVaporFraction(0.0)
            .SetCompoundMolarFlow("N-pentane", 100.0 / 9.0)
            .SetCompoundMolarFlow("N-hexane", 50.0 / 9.0)
            .SetCompoundMolarFlow("N-heptane", 100.0 / 9.0))


# --- build the divided-wall column -----------------------------------------
fs = (Flowsheet.Create("DividedWallColumn")
      .WithCompounds(*COMPOUNDS)
      .WithPropertyPackage(PropertyPackages.PengRobinson))
feed = add_feed(fs)
pentane, hexane, heptane = (fs.AddMaterialStream(n) for n in ("Pentane", "Hexane", "Heptane"))
qc, qr = fs.AddEnergyStream("Condenser Duty"), fs.AddEnergyStream("Reboiler Duty")

# 9 stages above the wall, 23 on each side of it, 14 below; feed and side draw on stage 14 of their sides.
# The wall splits start from a first guess (45 kmol/h of liquid and 85 kmol/h of vapor to the feed side).
dwc = (fs.AddDividedWallColumn("DWC-101")
       .WithSections(9, 23, 23, 14)
       .WithPressures(Q.Atm(2.0))
       .WithFeed(feed, DwcSection.Prefractionator, 14)
       .WithDistillate(pentane)
       .WithBottoms(heptane)
       .WithSideProduct(hexane, DwcSection.Main, 14, DwcSideSpecType.ComponentMoleFraction, 0.92, "N-hexane")
       .WithCondenserDuty(qc)
       .WithReboilerDuty(qr)
       .WithCondenserSpec(DwcEndSpecType.ComponentMoleFraction, 0.99, "N-pentane")
       .WithReboilerSpec(DwcEndSpecType.ComponentMoleFraction, 0.99, "N-heptane")
       .WithSplitFlows(Q.KmolPerHour(45.0), Q.KmolPerHour(85.0)))
uo = dwc.Object
uo.Config.SideDraws[0].Name = "Hexane"


def report(title):
    r = uo.Results
    print(f"\n{title}")
    print(f"  converged in {r.Iterations} Newton iterations")
    print(f"  condenser duty = {r.CondenserDuty:8.1f} kW   reboiler duty = {r.ReboilerDuty:8.1f} kW   reflux ratio = {r.RefluxRatio:.3f}")
    print(f"  wall splits: liquid {uo.Config.LiquidSplitFlow * 3.6:.1f} kmol/h, vapor {uo.Config.VaporSplitFlow * 3.6:.1f} kmol/h to the feed side")
    for name, flow, x in (("Pentane", r.DistillateFlow, r.DistillateComposition[0]),
                          ("Hexane", r.SideProducts[0].Flow, r.SideProducts[0].Composition[1]),
                          ("Heptane", r.BottomsFlow, r.BottomsComposition[2])):
        print(f"  {name:8s} {flow * 3.6:6.2f} kmol/h, purity {x * 100:.2f} mol %")


fs.Solve()
report("First guess of the wall splits")

# --- optimize the wall splits (minimum reboiler duty at the specifications) --
opt = InterlinkOptimizer.Optimize(uo, 40)
best = opt.Best
print(f"\nWall split optimization: {opt.Evaluations.Count} column solutions, {opt.Message}")
print(f"  best liquid {best.LiquidFlow * 3.6:.2f} kmol/h, vapor {best.VaporFlow * 3.6:.2f} kmol/h, reboiler duty {best.ReboilerDuty:.1f} kW")
InterlinkOptimizer.Apply(uo.Config, best)
fs.Solve()
report("Optimized wall splits")

# --- molecular tracking: where does hexane accumulate on the product side? --
print(f"\nMolecular tracking suggests the side draw on product side stage(s) {list(MolecularTracking.SuggestSideStages(uo.Results))}")
sweep = MolecularTracking.Sweep(uo, Array[Int32](list(range(8, 20))))
for p in sweep:
    print(f"  side draw on M{p.Stage:<2d}: reboiler duty {p.ReboilerDuty:7.1f} kW" + ("" if p.Converged else " (not converged)"))
fs.Solve()                           # back to the configured stage (sweeping does not change it)
qr_dwc = uo.Results.ReboilerDuty

# --- the same products from two conventional columns (direct sequence) -----
seq = (Flowsheet.Create("DirectSequence")
       .WithCompounds(*COMPOUNDS)
       .WithPropertyPackage(PropertyPackages.PengRobinson))
feed2 = add_feed(seq)
d1, b1, d2, b2 = (seq.AddMaterialStream(n) for n in ("Pentane", "C6-C7", "Hexane", "Heptane"))
qc1, qr1, qc2, qr2 = (seq.AddEnergyStream(n) for n in ("Qc1", "Qr1", "Qc2", "Qr2"))
(seq.AddDistillationColumn("C-1").WithNumberOfStages(30).WithTopPressure(Q.Atm(2.0)).WithFeed(feed2, 15)
    .WithDistillate(d1).WithBottoms(b1).WithCondenserDuty(qc1).WithReboilerDuty(qr1)
    .WithCondenserSpec("Component_Fraction", 0.99, "", "N-pentane")
    .WithReboilerSpec("Component_Fraction", 0.01, "", "N-pentane")
    .WithSolvingMethod("Napthali-Sandholm"))
(seq.AddDistillationColumn("C-2").WithNumberOfStages(30).WithTopPressure(Q.Atm(2.0)).WithFeed(b1, 15)
    .WithDistillate(d2).WithBottoms(b2).WithCondenserDuty(qc2).WithReboilerDuty(qr2)
    .WithCondenserSpec("Component_Fraction", 0.92, "", "N-hexane")
    .WithReboilerSpec("Component_Fraction", 0.99, "", "N-heptane")
    .WithSolvingMethod("Napthali-Sandholm"))
seq.Solve()
qr_seq = qr1.EnergyFlowKW + qr2.EnergyFlowKW
print("\nDirect sequence (two columns of 30 stages)")
print(f"  C-1 reboiler {qr1.EnergyFlowKW:.1f} kW, C-2 reboiler {qr2.EnergyFlowKW:.1f} kW, total {qr_seq:.1f} kW")
print(f"  the divided-wall column needs {qr_dwc:.1f} kW: {(1 - qr_dwc / qr_seq) * 100:.0f} % less heat")

# --- save --------------------------------------------------------------------
HERE = os.path.dirname(os.path.abspath(__file__))
OUT = os.path.normpath(os.path.join(HERE, "..", "saved", "divided_wall_column.dwxmz"))
fs.OrthogonalLayout()
fs.Save(OUT)
print(f"\nSaved: {OUT}")

Output may vary

Results depend on the LLM's reasoning quality and tool-use accuracy. Always verify the simulation matches your intent before relying on the numbers.

In the DWSIM Assistant, build the following simulation:

- Compounds N-pentane, N-hexane and N-heptane; property package Peng-Robinson
- A material stream "Feed": 100 kmol/h of saturated liquid (vapor
  fraction 0) at 2 atm, mole fractions 0.4 / 0.2 / 0.4
- A Divided-Wall Column "DWC-101" with 9 top section stages, 23
  prefractionator stages, 23 product side stages and 14 bottom section
  stages, a total condenser at 2 atm and no pressure drop
- Feed on prefractionator stage 14; distillate "Pentane", bottoms
  "Heptane", a liquid side draw "Hexane" on product side stage 14 with
  an n-hexane mole fraction of 0.92
- Condenser specification: n-pentane mole fraction 0.99 in the
  distillate; reboiler specification: n-heptane mole fraction 0.99 in
  the bottoms
- Wall splits: 33.5 kmol/h of liquid and 84.5 kmol/h of vapor to the
  prefractionator
- Solve, then report the condenser and reboiler duties, the reflux
  ratio and the flow and purity of the three products

Exercises

The prefractionator stages above the feed sit in a pinch (step 7). Move the feed to P10, optimize the splits again and compare the reboiler duty. How few prefractionator stages can you use before the duty rises?
Relax the side product purity to 0.90 and then tighten it to 0.95. How do the reboiler duty and the optimal splits change?
Add a second side draw to turn the column into a Kaibel column and take part of the heptane out above the reboiler. What purity can the second side product reach?
Set a wall heat transfer coefficient of 500 W/m²·K and a wall area of 50 m². Which side of the wall loses heat, and what does it do to the reboiler duty?

Next Steps¶

Congratulations! You have completed the advanced tutorial track in the Classic UI. You have built complete simulations of:

Vapor-compression refrigeration
Ammonia synthesis (Haber-Bosch)
Aromatic distillation
Natural gas processing
Bioethanol fermentation
Reverse osmosis desalination
Methanol synthesis
A divided-wall column

Continue with Distillation Curves and Secondary Specifications to check refinery products against their pools and converge a column on product qualities, or with the Features Track to explore TEA, LCA, and the AI Assistant.