How close can two streams get?

In heat integration, one number decides almost everything: the minimum temperature approach, written dT_min. Drag it and watch the energy bill trade against the exchanger area. The interesting part is how little the total moves.

This is a teaching problem, not plant data. The four streams are the published example from Linnhoff and Hindmarsh (1983), the founding paper of pinch analysis. Using it means the utility targets and the pinch location have published values to check against, which a self-invented stream table could not offer. Every stream is assumed to have a constant heat capacity flowrate.

The tradeoff

Minimum temperature approach, dT_min

20.0°C

Hot utility 107.5 kW

Cold utility 40.0 kW

Pinch, hot / cold 90 / 70 °C

Heat recovered 380.0 kW

Area target 88.2 m²

Total annualized 53,779

energy annualized capital total within 2% of the optimum

Why the curve is flat

Composite curves

The two curves are fixed by the stream table. Sliding dT_min pulls them apart horizontally. The overlap is heat recovered inside the process. What sticks out at each end is what the utilities must supply.

hot composite cold composite pinch

Grand composite curve

The same cascade seen as net heat flow against shifted temperature. Where the curve touches the axis, heat flow is zero: that is the pinch. The opening at the top is the hot utility, the opening at the bottom the cold.

Checked against the published paper

At the frozen design point the engine has to reproduce the values printed in Linnhoff and Hindmarsh (1983). This is the whole reason for using a published problem, so the check is shown rather than asserted.

Quantity	Published	Computed	Status

The stream table

Stream	Type	T supply	T target	CP	Duty

Temperatures in °C, CP in kW/°C, duty in kW. Four streams, Linnhoff and Hindmarsh (1983).

The designed network

These seven exchangers exist only at dT_min = 20 °C. The slider retargets the problem, which is arithmetic. Designing a network that hits a new target is engineering judgment, and it was done by hand once, at the frozen design point. The table below does not move with the slider, and nothing here claims it would.

Unit	Type	Duty	Hot in	Hot out	Cold in	Cold out	Area

What this does not tell you

Limitations, stated plainly

Teaching problem. Four streams from a 1983 paper, not a plant. Real problems have dozens of streams, forbidden matches, and layout constraints none of which appear here.
Constant CP. Every stream is assumed to have a heat capacity flowrate that does not vary with temperature. Phase change and strongly temperature-dependent CP both break this.
Targets, not a design. Away from 20 °C the page shows what is thermodynamically achievable, not a network achieving it. A target nobody can build is still just a target.
Two cost bases. The sweep prices the Bath area target split evenly across seven units. It does that because there is no designed network at an arbitrary dT_min. The committed report prices the seven real exchanger areas. The two differ, and the figures name which is which.
Screening economics. Utility prices and the capital correlation are published typical values, not quotes.
A regime change the slider can cross. This stream table needs more cold duty than it has hot duty. So below roughly 12.7 °C it becomes a threshold problem with no genuine pinch. The page says so when you get there. The committed study sweeps only down to 5 °C, so it never had to describe this. The interactive version surfaces it and the static report does not.