Chapter 11

Case Studies

Ten chapters have each covered one piece — a flash, a column, a reactor, a heat exchanger. Real processes chain many of these together to solve a problem no single unit can. This chapter walks four such flowsheets end to end, each a genuine running MaximaLabs example, not a narrated screenshot from someone else's simulator.

11.1 Breaking an azeotrope: extractive distillation

Chapter 5 (§5.6) showed the wall a plain column hits: ethanol-water can't be pushed past its ~89 mol% azeotrope by ordinary distillation, no matter how many stages you add. Here's the fix in practice — a reference case from Luyben (Ind. Eng. Chem. Res. 2006, 45, 4625). An 85 mol% ethanol feed enters an extractive column alongside a heavy, high-boiling entrainer (ethylene glycol) fed a few stages below the top:

EXTCOL — 16 stages, two feeds (the ethanol-water mixture on stage 12, the glycol entrainer on stage 3). The glycol raises water's relative volatility enough to pull the overhead ethanol past the azeotrope in a single pass — nothing about the MESH equations from Chapter 5 changes, only that a third, non-volatile component reshapes the vapor-liquid equilibrium enough to open a path the binary system didn't have.
RECOVCOL — an 8-stage column that strips the water back overhead from the EXTCOL bottoms (glycol + water), regenerating clean glycol as bottoms for recycle.

This is why entrainer selection matters as much as stage count: the entrainer has to be heavy enough to stay in the bottoms of the first column (so it doesn't contaminate the ethanol product) yet volatile enough relative to water to be strippable in the second. Run it and compare the EXTCOL distillate composition against the plain-column azeotrope ceiling from Chapter 5 — this is a genuinely different equilibrium surface, computed by the same NRTL package (Chapter 2), not a workaround bolted onto the solver.

11.2 Reaction, separation, and a second reaction: ethylene oxide to glycol

A single flowsheet chaining reaction, phase separation, a second reaction, and distillation — the shape of a real petrochemical train. Ethylene and oxygen feed two competing reactors over a silver catalyst: the desired epoxidation (ethylene → ethylene oxide) and an undesired total combustion side reaction (ethylene → CO₂ + water), modeled here as two sequential conversion reactors sharing the same ethylene — a deliberately low 8% per-pass conversion on the first reactor, because pushing per-pass conversion higher is exactly what favors the combustion side reaction in a real EO plant:

C_2H_4 + \tfrac12 O_2 \longrightarrow C_2H_4O \qquad(\text{epoxidation, desired})

C_2H_4 + 3\,O_2 \longrightarrow 2\,CO_2 + 2\,H_2O \qquad(\text{combustion, undesired})

A cooled flash (CONDENSE) then does the separation job Chapter 3 covers: condensing ethylene oxide and reaction water out of the unreacted ethylene/oxygen/CO₂, which vents for purge (real plants would recycle the unreacted ethylene at high ratio — left out here as a stated simplification, not a hidden one). The condensed EO stream mixes with fresh water and hydrates to monoethylene glycol in a second reactor:

C_2H_4O + H_2O \longrightarrow C_2H_6O_2 \qquad(\text{hydration, 99\% conversion here})

A final distillation column (COL) then separates the water byproduct from the glycol product — the exact same rigorous MESH solve as the ethanol-water column, just purifying a different pair. Four unit types from four different chapters (reactor, flash, reactor, distillation), one flowsheet, one converged solve.

The two competing reactors together decide what actually matters commercially: how much of the fed ethylene ends up as EO rather than burned to CO₂. With

X_1

the epoxidation reactor's conversion (on the fresh ethylene feed) and

X_2

the combustion reactor's conversion (on what's left after epoxidation), the overall selectivity to EO is:

S = \frac{X_1}{X_1 + (1-X_1)\,X_2}

$X_1$: Epoxidation-reactor conversion — fraction of fresh ethylene converted to EO in the first reactor.
$X_2$: Combustion-reactor conversion — fraction of the remaining ethylene (after epoxidation) burned to CO₂ + water in the second reactor.
$S$: Overall selectivity to EO — moles of ethylene that became EO ÷ total moles of ethylene reacted (both pathways).

Worked example — this flowsheet's selectivity

With the flowsheet's

X_1 = 0.08

and

X_2 \approx 0.0217

S = \frac{0.08}{0.08 + 0.92\times0.0217} \approx 0.80

About 80% of the ethylene reacted ends up as EO, 20% burned — the deliberately low 8% per-pass conversion on EPOXRX is what keeps that ratio favorable (§11.6's exercise derives this same result from first principles).

11.3 A continuous polymerization reactor

The reference book's resin-reactor case study asks a different kind of question than the others: not just conversion and duty, but the molecular-weight distribution of the product itself — the number a specialty-polymer plant actually sells against. MaximaLabs' polymerization unit op is a continuous free-radical CSTR solved by an Arrhenius rate law closed with the method of moments, reporting the number- and weight-average molecular weights and the polydispersity index directly:

PDI = \frac{M_w}{M_n} \qquad(\text{a measure of chain-length spread, not just average size})

$M_n$: Number-average molecular weight — the simple mean chain length (total polymer mass ÷ total number of chains).
$M_w$: Weight-average molecular weight — the mean weighted by each chain's own mass, so longer chains count more; always ≥ M_n.
$PDI$: Polydispersity index M_w/M_n — 1.0 is a perfectly uniform chain length; larger values mean a broader spread of chain lengths.

Two reactors can hit the identical monomer conversion and still ship a very different product if their

PDI

differs — a broader distribution means more short chains (weaker mechanical properties) and more very-long chains (harder to process) than a narrow one at the same average. Honest scope: the example flowsheet below runs the polymerization kinetics on a generic monomer/solvent pair rather than nylon-6,6's actual step-growth condensation chemistry (the book's specific case is a different polymerization mechanism entirely — batch step-growth, not continuous free-radical) — what transfers is thereactor-design question the book is really asking: given a CSTR, what molecular- weight distribution comes out, and how does it move with residence time and initiator concentration.

11.4 Economic evaluation

A converged flowsheet answers "does it work"; a cost estimate answers "is it worth building." MaximaLabs' capital-cost estimator (Turton-style correlations — purchased equipment cost from a size attribute per unit, escalated by material, location, and CEPCI, then multiplied by a bare-module installation factor) runs the same role as Aspen Icarus in the book's own case study, without a separate application: purchased cost by unit type comes from a power-law correlation on that unit's real solved size —

C_{purchased} = a\,(\text{size})^{\,b} \qquad(\text{e.g. compressor: } 7900\,(\text{kW})^{0.62})

C_{installed} = C_{purchased}\cdot F_{BM}\cdot\frac{\text{CEPCI}_{now}}{\text{CEPCI}_{base}}\cdot(\text{location}\times\text{material}\times\text{year})

$C_{purchased}$: Base purchased-equipment cost, from the correlation alone (no installation labor/piping/instrumentation).
$a,\; b$: Correlation constants fit per unit type (e.g. a=7900, b=0.62 for a compressor) — b<1 is the "six-tenths rule": cost rises slower than size (see the worked example below).
$\text{size}$: The unit's own solved sizing attribute driving cost — duty for a compressor/heater, area for a heat exchanger, diameter×height for a column.
$F_{BM}$: Bare-module factor — installed cost ÷ purchased cost (e.g. 4.0 for a column/reactor, 2.2 for a heater), covering piping, instrumentation, and installation labor.
$\text{CEPCI}_{now},\;\text{CEPCI}_{base}$: Chemical Engineering Plant Cost Index at today's date vs. the correlation's original publication date — escalates a decades-old correlation to current cost levels.
$\text{location}\times\text{material}\times\text{year}$: Further multipliers for build location (e.g. Gulf Coast vs. Asia), construction material (carbon steel vs. stainless), and project year — all applied on top of the CEPCI escalation.

with the bare-module factor

F_{BM}

(installed cost ÷ purchased cost, e.g. 4.0 for a column or reactor, 2.2 for a heater) carrying the piping/instrumentation/labor allowance a purchased-equipment quote alone doesn't. Run it against any of this chapter's flowsheets — the compressor from Chapter 9, the reactors and column from §11.2 — and every installed-cost number traces back to that unit's own solved duty or flow, not a lookup table keyed on "distillation column."

Worked example — why one big compressor beats two small ones

Take the compressor correlation

C = 7900\,(\text{kW})^{0.62}

and split one unit's duty into two equal units in series, each at half the total kW. Purchased cost scales as

(\text{size})^{0.62}

, so two half-size units together cost

2\times2^{-0.62}\approx 1.30

times the single full-size unit — ~30% more in total purchased cost for the same total duty. The sub-linear exponent

b<1

is exactly why plants default to one train and only split equipment when something else forces it (§11.6's exercise works this out in full).

Honest scope (stated directly in the tool, not buried): these are AACE screening-level (order-of-magnitude) correlations from a published textbook, not a live vendor quote — the same caveat the book itself makes about Icarus's own accuracy class.

11.5 Try it

Reproduce these in your browser

1Open extractive distillation and Run — check the EXTCOL distillate composition against the ~89 mol% ceiling from Chapter 5's plain ethanol-water column.
2Open ethylene oxide to glycol and Run — click EPOXRX vs. COMBRX to see the two competing reactors' duties and conversions side by side.
3Open free-radical polymerization and Run — the POLY node's Theory tab reports Mn, Mw, and PDI. Raise the initiator concentration and re-run to see the distribution shift.
4On any solved flowsheet, open Analysis & reports ▸ Cost estimator to get an installed-capital breakdown by unit, with the location/material/year adjustment factors from §11.4.

11.6 Exercises

Practice

Work each problem yourself first, then reveal the solution to check it. Where a problem says so, reproduce it live in MaximaLabs — the solver is the answer key.

1
warm-up
In §11.2's ethylene-oxide reactors, the desired epoxidation and the undesired combustion reaction both consume ethylene. Write the overall selectivity expression (moles of ethylene to EO ÷ total moles of ethylene reacted) in terms of the two reactors' individual conversions $X_1$ (epoxidation, on the fresh feed) and $X_2$ (combustion, on the epoxidation reactor's outlet).
2
core
Explain, using §11.1's physics, why the entrainer (ethylene glycol) has to be fed above the main feed stage in the extractive column rather than at the same stage or below it.
3
challenge
§11.4's compressor cost correlation is $C = 7900\,(\text{kW})^{0.62}$ . A plant is considering replacing one large compressor with two smaller ones in series, each doing half the total duty. Using the correlation's exponent alone (ignoring bare- module and installation factors), is the two-compressor option cheaper or more expensive in purchased-equipment cost, and by roughly what factor? What does this imply about why plants don't always split equipment into many small parallel/series units?

Open the ethylene oxide example →← Chapter 10 The Handbook