pinch-analysis

name	pinch-analysis
description	Pinch analysis — composite curves, pinch point, minimum utility targets (Q_H_min, Q_C_min), heat exchanger network (HEN) design, ΔT_min, stream matching rules, Linnhoff methodology, energy integration.
metadata	{"priority":7,"promptSignals":{"phrases":["pinch analysis","pinch technology","composite curve","heat exchanger network","HEN design","minimum utility","energy integration"],"minScore":3}}

Pinch Analysis — Complete Skill

Fundamentals (Linnhoff, 1978)

Purpose: identify minimum energy targets for process before designing heat exchanger network (HEN) Key principle: process-to-process heat exchange reduces external utility requirements Pinch: bottleneck temperature in heat exchange; determines minimum heating and cooling utilities

Stream Data Collection

For each process stream, collect:

• Supply temperature T_s [°C]: starting temperature
• Target temperature T_t [°C]: required ending temperature
• Heat capacity flow rate CP = ṁ × c_p [kW/°C]
• Heat duty Q = CP × |T_t - T_s| [kW]

Hot stream: requires cooling (T_s > T_t) Cold stream: requires heating (T_s < T_t)

Composite Curves

Hot composite curve: overlap of all hot streams on H-T diagram Plot heat content H vs. T for all hot streams superimposed

Cold composite curve: similarly for all cold streams

Construction:

1. Extract T intervals where stream populations change
2. Sum CP values of all hot (or cold) streams in each T interval
3. Integrate ΔH = CP_sum × ΔT across each interval
4. Plot cumulative ΔH vs. T for both curves

Minimum approach temperature ΔT_min: Horizontal distance between composite curves where they are closest Typical: ΔT_min = 10°C (oil refinery); 20°C (chemical plant); 3–5°C (refrigeration)

Pinch temperature: At ΔT_min overlap → hot pinch T_pinch,hot; cold pinch T_pinch,cold = T_pinch,hot - ΔT_min

Minimum Utility Targets

From composite curve overlay: Q_H_min = area of cold composite curve NOT covered by hot composite (left overhang) Q_C_min = area of hot composite curve NOT covered by cold composite (right overhang)

Energy conservation rule: Q_H_actual = Q_H_min + Q_extra [extra = cross-pinch heat transfer] Every kW of heat transferred across pinch costs 1 kW more hot utility AND 1 kW more cold utility

Three golden rules of pinch analysis:

1. Do not transfer heat across the pinch
2. Do not use hot utility below the pinch
3. Do not use cold utility above the pinch

Targeting Method (Temperature Interval Method)

Problem table algorithm:

1. Shift temperatures: hot stream T → T - ΔT_min/2; cold stream T → T + ΔT_min/2
2. Divide into temperature intervals
3. Within each interval: heat available = Σ(CP_hot - CP_cold) × ΔT_interval
4. Cascade heat from hot to cold intervals (waterfall)
5. Pinch = interval with zero cumulative surplus (after adding minimum hot utility)

Algebraic result: Q_H_min = minimum hot utility required Q_C_min = Q_H_min + ΣQ_process (energy balance)

Heat Exchanger Network Design

Above Pinch

Driving force: hot streams enter above T_pinch,hot; cold streams exit above T_pinch,cold Rule: CP_hot ≤ CP_cold (to prevent ΔT violation) Minimum units: U_above = N_streams_above - 1 (Euler's graph theorem for connected network)

Below Pinch

Rule: CP_hot ≥ CP_cold Minimum units: U_below = N_streams_below - 1

Total minimum units: U_min = N_hot + N_cold + N_utilities - 1 [for one connected graph; ignoring multiple utilities]

Network with loops: can reduce units but increases cross-pinch heat transfer

Matching Streams (Tick-off Heuristic)

Above pinch:

1. Match largest CP_hot with largest CP_cold (if CP_hot ≤ CP_cold)
2. Exhaust one stream (tick off)
3. Repeat until all hot streams cooled to pinch T

Below pinch:

1. Match largest CP_cold with largest CP_hot (if CP_hot ≥ CP_cold)
2. Exhaust one stream
3. Repeat until all cold streams heated to pinch T

Capital vs. Energy Trade-off

Total annual cost (TAC): TAC = Q_H × C_hot + Q_C × C_cold + Σ(annualized capital cost of each HX)

Optimize ΔT_min: Smaller ΔT_min → lower utility cost; more/larger heat exchangers → higher capital Typical optimal ΔT_min found by plotting TAC vs. ΔT_min → curve minimum

Payback period for energy-saving retrofits: n = (C_HX_added) / (annual utility savings)

Multiple Utilities and Temperature Levels

Multiple hot utilities: steam at different pressures + furnace Use highest-quality utility (furnace, HP steam) only where needed (highest T above pinch) Multiple cold utilities: air cooling (free) vs. refrigeration (expensive) Use cheapest cooling (air) first at highest T; refrigeration only at lowest T

Grand Composite Curve (GCC): Plots shifted surplus vs. temperature from problem table Shows "pockets" where process self-sufficient in energy → use internally available heat

Retrofit vs. New Design

New design: target first; then design network Retrofit: identify inefficiencies in existing network Cross-pinch exchangers → candidates for modification

Retrofit strategy:

1. Identify cross-pinch matches → reroute to avoid crossing
2. Identify closest temperatures for new matches → add HX there
3. Reduce utility by adding HX upstream of current first utility input

Process Integration Beyond Heat

Water pinch: minimize freshwater use (analogous to heat, using contaminant mass as currency) Hydrogen pinch: oil refinery hydrogen management Carbon pinch: CO₂ allocation (Tan and Foo methodology)

ASPEN Hysys / Aspen Plus / HINT / SuperTarget

Software tools for pinch analysis: Aspen Energy Analyzer: attached to Aspen Plus; automated composite curves, HEN design HINT: standalone; early commercial tool SuperTarget (KBC): commercial; integrated with economics

Output

Provide: minimum hot utility Q_H_min [kW or MW], minimum cold utility Q_C_min [kW or MW], pinch temperature (hot/cold) [°C], recommended ΔT_min [°C], number of HX units above and below pinch (U_min), stream matching pairs with heat duty and area for each match, energy recovery potential vs. current design [kW and %], and annual utility cost saving at current utility prices [$/yr].