Pinch Analysis

You are probably heating and cooling at the same time

Somewhere on your site a stream is being cooled while, a few metres away, another is being heated. Both cost money. The first needs a cooler, water and power; the second needs a burner and fuel. Put them together through an exchanger and both bills fall.

Pinch analysis is how you find out, before designing anything, exactly how much of that is available — and, just as usefully, how much is not.

What the targets are worth

Take the four-stream process this calculator opens with: a reactor feed and a recycle needing heat, a hot product and a flue quench needing cooling.

• Served entirely by utilities: 470 kW of heating and 510 kW of cooling — 980 kW of utility in total.
• Fully integrated at a 10 °C approach: 20 kW of heating and 60 kW of cooling.

That is 450 kW of recovered heat and a 92 % cut in utility demand, from rearranging what you already have. On 6,000 operating hours at 5 p/kWh of gas, the heating side alone is around £135,000 a year.

The number that matters is not the saving, though — it is that 20 kW is a floor. No exchanger network, however clever, beats it. If someone proposes a heat-recovery scheme that claims to get you below it, the proposal is wrong.

How the targets are found

The engine is the Problem Table Algorithm, the standard method.

1. Every stream is shifted onto a common temperature scale — hot streams down by $\Delta T_{min}/2$, cold streams up by the same — so that any hot and cold stream overlapping on the shifted scale is guaranteed a feasible $\Delta T_{min}$ in a real exchanger.
2. The shifted temperatures cut the problem into intervals. In each, the net heat is $(\sum C{P}_{hot}-\sum C{P}_{cold})\times \Delta T$.
3. Heat cascades down the intervals. Where the cascade goes negative it is asking heat to flow uphill, which it will not do, so the whole cascade is lifted by the most negative residual.

That lift is the minimum hot utility. What falls out of the bottom is the minimum cold utility. The interval where the lifted cascade touches zero is the pinch.

Why the pinch is the important answer

The pinch splits your process in two, and the split has three rules that decide whether a retrofit works:

• Do not transfer heat across the pinch. Every kW moved across it adds a kW to both utility bills.
• No cold utility above the pinch. Cooling above the pinch means you paid to heat something and then paid again to cool it.
• No hot utility below the pinch. Heating below the pinch wastes recoverable heat that was already available.

Most disappointing heat-recovery projects break one of these three. The exchanger works exactly as designed, and the site's fuel bill barely moves, because the recovered heat was simply displacing heat that was free anyway.

ΔTmin is a capital decision, not a physical constant

$\Delta T_{min}$ is the smallest approach you allow in any exchanger, and it is the dial between energy and capital:

• Small (5 °C) — more heat recovered, but area goes up sharply as the driving force shrinks, and fouling has less margin to eat into.
• Large (20–30 °C) — cheap, compact exchangers, more utility bought forever.

Typical starting points are 10 °C for liquid–liquid duties, 20–30 °C where a gas is involved, and 3–5 °C in cryogenic service where utility is expensive enough to justify the area. Sweep the value in the calculator and watch the targets move — the shape of that curve is the real answer, and where it flattens is usually where the sensible design sits.

What this does not do

These are targets, and targets are the beginning of a heat-integration study, not its conclusion. The model assumes a constant heat-capacity flowrate per stream and steady state. It does not:

• design the exchanger network, or tell you how many exchangers you need;
• cost anything, or check that the pipework can physically be run;
• handle phase change with a varying CP, streams that only run part of the year, start-up and shutdown, controllability, or the fact that two units may be fifty metres and a road apart;
• know which of your streams are genuinely available for matching.

A target of 450 kW says the prize exists. Whether it is 450, 300 or 180 once layout, operability and capital are real is what the study answers — and a retrofit that ignores those is how heat-recovery projects get a bad name.