Introduction

A course about undoing mixing

Mixing is free. Pour cream into coffee and it disperses on its own; leave a bottle of nitrogen open in a room and it is gone. Nature does this without being asked, because a mixture has more entropy than its separated parts. Everything in this course is the reverse operation, and the reverse operation is never free.

That single asymmetry is the reason separation processes exist as a discipline, the reason they consume as much energy as they do, and the reason a chemical plant usually looks like a small reactor surrounded by a great deal of separation equipment. It is worth taking seriously before we start drawing diagrams.

1.1 Where this course sits

CH E 316 is a Term 6 course, and it is a genuine confluence: it takes thermodynamics from CH E 243 and CH E 343, transport from CH E 314, and mass balances from CME 265, and turns them into equipment you can size. It runs alongside CH E 318 Mass Transfer, which supplies the rate description that this course's equilibrium description deliberately leaves out. Downstream, essentially every unit you place in the design courses will be a separator.

1.2 Why separations matter

Start with the number that should reframe the subject for you. Separation processes account for roughly half of all industrial energy use in the United States, and something like 10–15 % of the country's total energy consumption. Distillation alone is of the order of half of that. No other single class of unit operation comes close.

That is not because engineers have been careless. It is because separations are performed on enormous throughputs, and because the dominant technology — distillation — boils and re-condenses the entire mixture many times over to exploit a property difference that is often small. Later chapters will make that statement quantitative: relative volatility2a §2.7 near unity is exactly what forces a tall column and a large reboiler duty.

The reach is wider than the chemical industry:

Every one of those is a property difference being exploited: volatility, solubility, molecular size, charge, affinity for a surface.

The 2025 Nobel Prize in Chemistry

In October 2025 the Nobel Prize in Chemistry went to Susumu Kitagawa, Richard Robson and Omar M. Yaghi for the development of metal–organic frameworks — crystalline solids built from metal nodes and organic linkers, with pores so regular and so numerous that a gram of the material can have the internal surface area of a football pitch. You can tune the pore size and its chemistry deliberately.

That is a separations prize in everything but name. A designed pore is a designed property difference: it distinguishes molecules by size, by shape, by polarity, by how strongly they stick. MOFs are being developed for carbon capture, for water harvesting from desert air, for separating gases that distillation can only separate cryogenically. You will meet the engineering of exactly this in the adsorption chapter8 §8.3 — the equilibrium isotherm, and the fact that a solid adsorbent is a separating agent that must itself be regenerated.

Separations in Alberta

You do not have to go far to find the units in this course. Every one of these operates within a few hundred kilometres of this classroom:

• Upgraders and refineries along the Industrial Heartland northeast of Edmonton run atmospheric and vacuum distillation columns on bitumen-derived crude — the largest, most energy-intensive separation equipment in the province. Chapters 3 to 5.
• Oil-sands tailings and produced water are a separation problem in solid–liquid and liquid–liquid form: settling, flocculation, and the recovery of process water for reuse.
• CO₂ capture. Shell's Quest facility near Fort Saskatchewan captures roughly a megatonne of CO₂ a year from hydrogen production using amine absorption — the unit operation of Chapter 66 §6.1 — and stores it two kilometres down.
• Natural-gas processing. Sour gas sweetening (H₂S and CO₂ removal by amine absorption), glycol dehydration, and turboexpander plants recovering ethane and heavier components. Chapters 5 and 6.
• Lithium from formation brines. Alberta's deep saline aquifers carry lithium at tens of milligrams per litre, and several companies are working on direct lithium extraction using sorbents and membranes. It is a textbook dilute-feed problem — App 1 below will tell you why it is hard.
• Air separation. Industrial gas plants supplying oxygen to upgraders and nitrogen to just about everyone, by cryogenic distillation of air.

1.3 The plant view

Draw any chemical plant at the block level and the same shape appears. Raw materials arrive impure and must be cleaned up before they meet the catalyst. The reactor converts only part of the feed, and makes by-products. What leaves the reactor must therefore be split: product to specification, unconverted reactant back to the front, by-product to sale or disposal.

Two consequences are worth committing to memory. First, separations typically account for 50–80 % of the capital cost of a plant. Second, the recycle loop couples the separator to the reactor: a poorer separation means more unconverted material going round again, which means larger equipment everywhere. You cannot design the two independently, which is why the design courses put them in the same flowsheet.

1.4 Why a separation costs work

Mix two ideal components and the Gibbs energy falls. For one mole of an ideal mixture,

Unmixing must therefore climb back up that hill, and the least work you could conceivably do is the height of the hill. For a complete separation of a mixture into its pure components at constant temperature and pressure:

Real separations do not go to completion. We want a product of some purity , recovering some fraction of what came in, and we are content to leave the rest behind in a waste stream of composition . The general statement is the Gibbs energy of the products minus that of the feed:

per mole of feed. Three things about this expression matter more than the algebra.

It is a lower bound and nothing more. It assumes a reversible process, and reversible processes take infinite time and infinite equipment. Real separations consume roughly 3 to 20 times it — equivalently, they run at a second-law efficiency of about 5–35 %. The gap is not waste in any simple sense — it is what you pay for finite size and finite time.

It is independent of the mechanism. Distillation, adsorption, a membrane and a magic demon are all subject to the same bound. That makes equation 1.3 the honest yardstick against which any proposed process should be measured, including the ones in press releases.

And it is logarithmic in composition, which turns out to be both a mercy and a trap. The app below is built around exactly that point.

The dilution penalty — and where it really bites

For a trace species at mole fraction , equation 1.3 collapses to a memorable limit. Per mole of the species you recover,

At room temperature kJ/mol, so going from a 10 % feed to a 1 ppm feed — a hundred-thousandfold dilution — multiplies the minimum work by less than five. Thermodynamics is remarkably forgiving about dilution.

The equipment is not. To recover one mole of product you must handle at least moles of feed, and that is linear, not logarithmic. Direct air capture needs of the order of a million cubic metres of air pushed through the contactor per tonne of CO₂; gold at its natural seawater concentration would need hundreds of cubic kilometres of ocean per tonne of metal. Nobody is defeated by the thermodynamics there. They are defeated by the pumps, the pressure drop and the vessel.

1.5 Three kinds of separation task

Before choosing equipment, name the job. The three tasks look similar on a flowsheet and behave very differently.

The distinction changes which specification is binding. A purification is judged by how little impurity is left; a concentration by how much of the target you captured; a fractionation by both, on both products at once. Notice that these map exactly onto the two knobs in App 1 — purity and recovery — and that pushing either one towards its limit is what makes a separation expensive.

1.6 Five ways to make a separation happen

A separation needs a second phase, a barrier, or a field. Something has to give the species somewhere different to go. There are only five generic ways to arrange that, and every technique in this course is one of them.

Energy separating agent or mass separating agent?

Cutting across those five is a choice with real consequences. A energy separating agent (ESA) creates the second phase with heat or work — the reboiler of a distillation column, the compressor of a refrigeration cycle. A mass separating agent (MSA) creates it by adding something: a solvent, an adsorbent, a stripping gas.

The ESA route is thermodynamically clean and its cost is visible as a utility bill. The MSA route can be far more selective — you can choose a solvent that loves one component and ignores the other — but it comes with a debt: the agent must itself be separated from the product and recycled, which is a second separation problem you have just created. That is why an absorber is almost always drawn next to a stripper6 §6.1, and why an adsorption process spends half its cycle regenerating.

1.7 Choosing a process

Given several candidates, what decides? In rough order of how often it is the deciding factor:

• Cost, capital and operating together, over the life of the plant. Everything below is really an input to this.
• Feed and product condition — phase, temperature, pressure, and how far you are from where the separation naturally wants to happen. A feed already at 40 bar is an argument for a membrane; a feed already boiling is an argument for distillation.
• Purity required. The last decade of impurity removal often costs more than the first 99 %, and may force a different technology entirely — this is why ethanol is distilled to the azeotrope and then dried on a molecular sieve.
• The size of the property difference. A relative volatility of 1.02 and one of 4 are not the same design problem; they are barely the same technology.
• Scale. Chromatography is unbeatable for a kilogram of a monoclonal antibody and unthinkable for a megatonne of ethylene. Distillation is the reverse.
• Utilities available. Cheap steam favours distillation; cheap electricity and no steam favours membranes and mechanical vapour recompression. Cooling water temperature sets the condenser pressure and therefore the whole column.
• Maturity and risk. Which brings us to the most useful single diagram in this chapter.

Read the diagram two ways. As a practitioner: the top right is where the risk is low, the design methods are reliable and the vendors are many — which is why, when in doubt, industry distils. As a researcher: the interesting space is the bottom left, where a technique is real but not yet routine. Almost the entire research literature on separations lives in that corner, and the 2025 Nobel Prize was awarded for a material that will move part of it up and to the right.

Notice also what the diagram implies about this course. We spend most of our time in the top right — distillation, absorption, extraction — because that is where the design methods are mature enough to teach properly, and because those methods are the vocabulary in which the newer techniques are described.

1.8 Where to read more

Think about it

No marks, no answer boxes — this chapter is orientation. But these are worth sitting with for a minute each before opening the reveal.

The rest of the course

Each chapter answers one question. It is worth knowing where you are going.

Summary & key equations