Pinch analysis finds the minimum external heating and cooling a process needs once hot and cold streams are allowed to exchange heat directly, and the single "pinch" temperature that limits how much recovery is possible. It uses the problem table algorithm:
Shift temperatures by half the minimum approach:
hot streams: T* = T − ΔTmin/2
cold streams: T* = T + ΔTmin/2
For each interval between consecutive shifted
breakpoints, sum the heat-capacity flow rates
CP [kW/°C] of every stream spanning it:
netCP = ΣCP(hot) − ΣCP(cold)
ΔH = netCP × ΔT(interval)
Cascade ΔH from the hottest interval down.
If the running total ever goes negative, the
process needs Qh_min = −min(cascade) added at
the top to become feasible. The pinch is the
temperature where the corrected cascade first
hits exactly zero; the leftover at the bottom
of the cascade is Qc_min.
- ΔTmin — the closest two streams may approach in any exchanger. Raising it wastes less capital on exchanger area but always raises both utility targets and can shift the pinch.
- H2 flow rate — scales that hot stream's CP, which changes how much heat is available in each temperature interval and can move the pinch temperature entirely.
- Heat Integration toggle — ON shows the optimal Qh,min/Qc,min after cross-exchanging streams (the diagonal recovery flow above the pipes); OFF shows what utilities alone would cost with no stream-to-stream recovery at all — every cold stream heated fresh, every hot stream cooled fresh.
This is the core method behind industrial heat-exchanger-network design (refineries, chemical plants, paper mills): a plant that ignores its pinch temperature and adds a cooler above it, or a heater below it, is provably wasting energy no matter how the rest of the network is built.