A plant that heats itself
Every plant has streams that need heating and streams that need cooling. Buy steam for one and cooling water for the other and you pay twice for heat you already had. Let them heat each other instead and the only question left is how much of it you can do — and the answer fits on one graph.
Stack every hot stream into one curve. Stack every cold stream into another. Slide them together until the closest vertical gap is your minimum approach temperature. That point is the pinch. What sticks out past each end is the least utility the process can run on: 20 kW of steam and 60 kW of cooling water here, with 450 kW recovered in the middle.
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Build the curves
Split the temperature axis at every stream start and target. Inside each interval, add up the CP of every stream present and accumulate ΔH = ΣCP × ΔT from the cold end up. Do it once for the hot streams and once for the cold ones and you have two composite curves: 510 kW of heat available, 470 kW of heat wanted.
| Stream | Type | Ts (°C) | Tt (°C) | CP (kW/°C) | |ΔH| (kW) |
|---|---|---|---|---|---|
| 1 | cold | 20 | 135 | 2.0 | 230 |
| 2 | hot | 170 | 60 | 3.0 | 330 |
| 3 | cold | 80 | 140 | 4.0 | 240 |
| 4 | hot | 150 | 30 | 1.5 | 180 |
Slide them to ΔTmin
Move the cold curve along the enthalpy axis until the smallest vertical gap between the two equals your minimum approach — 10 °C here, 10 to 20 °C in most designs. The gap between two piecewise-linear curves is smallest at a kink of one of them, so you only have to check the kinks. The answer is exact, not sampled.
That lands the pinch at 90 °C on the hot side and 80 °C on the cold side. Read the overhangs and you have your utility targets before you have drawn a single exchanger: steam 20 kW, cooling water 60 kW. Both balances close — 450 + 20 = 470 into the cold streams, 450 + 60 = 510 out of the hot ones.
The three rules that fall out of it
Above the pinch the process is a net heat sink; below it, a net source. Everything else follows from that one fact.
- 01Do not transfer heat across the pinch. Move 1 kW down across it and the region above is 1 kW short, so it buys 1 kW more steam, while the region below has 1 kW too much and rejects it. Steam 20 → 21, cooling water 60 → 61. You pay for it twice.
- 02No cold utility above the pinch. Cooling above the pinch is heat you then have to buy back as steam.
- 03No hot utility below the pinch. Steam below the pinch is heat the process already has too much of.
Why it is worth the afternoon
When ICI applied this to processes its own engineers considered optimised, the savings averaged about 30 percent. Across sectors the range usually quoted is 10 to 35 percent, with refining at 10 to 25. Worth being precise about what the method gives you: pinch analysis sets the minimum utility your process can run on. It is a target, not zero. A plant that heats itself is the idea; the number on the overhang is the promise.
Sources: Natural Resources Canada, Pinch Analysis: For the Efficient Use of Energy, Water and Hydrogen (2003). Towler & Sinnott, Chemical Engineering Design 2e, ch. 3. Kemp, Pinch Analysis and Process Integration 2e, ch. 1 — the ICI result (Linnhoff & Turner, 1981) and the stream table used above.
The graph is the easy part. Building the model under it is not.
Getting to those two curves on a real plant means a converged simulation with every stream, every duty and every CP in it — which is the week nobody enjoys. Reflux drives the simulator you already have from plain English, takes the setup grind, and reads back every change it makes before it reports it. That is the part I am shortcutting.
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Nathan Ruberto · Co‑Founder, CEO
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