Question 2 of 5: Heat Integration – Pinch Analysis & Heat Exchanger Network

Question 2: Heat Integration – Pinch Analysis & Heat Exchanger Network (24 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

ΔT_min = 10°C. Utilities: LPS (≈160°C condensing, 2000 kJ/kg), HPS (≈250°C condensing, 1700 kJ/kg), CW (30→45°C, 63 kJ/kg sensible).

Find. (a) Utility type and flow rate per stream with no integration. (b) Pinch temperature and minimum hot/cold utility duties via the problem-table (temperature-interval) method. (c) A feasible heat exchanger network achieving those minimum utility targets.

Approach. Compute each stream's duty CP·ΔT; without integration each stream is served by whichever utility is both hot/cold enough and cheapest, sized by Q = ẓ·ΔH. With integration, shift hot streams down and cold streams up by ΔT_min/2, tabulate the net CP imbalance in each temperature interval between consecutive shifted stream temperatures, cascade the heat downward from zero at the top, and add the minimum heat needed at the top to make every cascade value ≥0 — the point where the cascade first reaches exactly zero is the pinch. A network is then built stream-by-stream honouring the pinch-matching feasibility rule (CP_hot ≤ CP_cold for any match touching the pinch from above).

1. (a) Utility duties without heat integration. Each stream's total duty: $$Q_{H101}=20.0\times(190-50)=2800\ \text{kW},\quad Q_{C102}=27.0\times(165-95)=1890\ \text{kW},\quad Q_{C103}=28.0\times(135-50)=2380\ \text{kW}$$ C102's target (165°C) exceeds the practical ceiling of LPS (≈160°C condensing — too close to 165°C to leave a 10°C approach), so it must be served by HPS; C103's target (135°C) is comfortably below LPS's ceiling, so the cheaper LPS serves it; H101 needs only sensible cooling well within the CW range, so CW serves it. Sizing each from ẓ = Q/|ΔH|: $$\dot m_{HPS}=\frac{1890}{1700}=\boxed{1.112\ \text{kg/s}},\qquad \dot m_{LPS}=\frac{2380}{2000}=\boxed{1.190\ \text{kg/s}},\qquad \dot m_{CW}=\frac{2800}{63}=\boxed{44.44\ \text{kg/s}}$$
2. (b) Shifted temperatures and the problem-table cascade. Shift the cold streams up 5°C and the hot stream down 5°C (half of ΔT_min) onto a common scale: H101*: 185→45°C; C102*: 100→170°C; C103*: 55→140°C. The six distinct shifted temperatures (185, 170, 140, 100, 55, 45) bound five internal intervals; in each interval, net = (ΣCP_hot − ΣCP_cold)×ΔT of the streams spanning it: $$[185,170]:\ (20-0)(15)=+300 \quad [170,140]:\ (20-27)(30)=-210 \quad [140,100]:\ (20-55)(40)=-1400$$ $$[100,55]:\ (20-28)(45)=-360 \quad [55,45]:\ (20-0)(10)=+200$$ Cascading from Q=0 at the top gives running totals 0, 300, 90, −1310, −1670, −1470 — the most negative value is −1670 kW, so adding Q_H,min = 1670 kW at the top makes every value ≥0. The re-cascaded values are 1670, 1970, 1760, 360, 0, 200 — the cascade hits exactly zero at shifted T*=55°C, which is the pinch (actual hot-stream pinch temperature 60°C, actual cold-stream pinch temperature 50°C), and the final value, Q_C,min = 200 kW, is the minimum cold utility. $$Q_{H,min}=\boxed{1670\ \text{kW (above pinch)}}\qquad Q_{C,min}=\boxed{200\ \text{kW (below pinch)}}$$
3. Energy-balance check. Total process heating demand minus total cooling demand (1890+2380−2800 = 1470 kW) must equal Q_H,min−Q_C,min = 1670−200 = 1470 kW — confirmed. Heat integration recovers 2600 kW of process-to-process exchange (versus 4270+2800 = 7070 kW of total utility duty with no integration at all), a 73.6% reduction in total utility load.

4. (c) Heat exchanger network design. Above the pinch there is one hot stream (H101, CP=20) and two cold streams (C102, CP=27; C103, CP=28); since N_hot (1) ≤ N_cold (2) above the pinch, no stream split is required — a single hot stream may simply serve both cold streams in series. C103's cold inlet (50°C) sits exactly at the cold-pinch temperature, so it forms the pinch match (the pinch-design "tick-off" heuristic starts here): running H101 down from the pinch (60°C) while heating C103 fully from 50 to 135°C uses $$Q_{E2}=28\times(135-50)=2380\ \text{kW}\ \Rightarrow\ H101: 179^\circ\text{C}\rightarrow60^\circ\text{C}$$ which fully satisfies C103 (no utility needed for this stream) and is feasible throughout (10°C approach at the pinch end, 44°C at the top end — both ≥ΔT_min). The remaining H101 capacity above the pinch (190→179°C) is then matched against the hot end of C102: $$Q_{E1}=20\times(190-179)=220\ \text{kW}\ \Rightarrow\ C102: 156.85^\circ\text{C}\rightarrow165^\circ\text{C}$$ (feasible: 25°C approach at the hot end, 22.15°C at the cold end). C102's remaining duty down to its 95°C supply, $$Q_{E3}=1890-220=\boxed{1670\ \text{kW}}=Q_{H,min},$$ must be supplied by HPS: the heater has to deliver C102 at 156.85°C, which with a 10°C approach needs steam condensing at ≥166.85°C — above LPS's 160°C — confirming the same Q_H,min found by the cascade. Below the pinch, only H101 remains (60→50°C), cooled by CW: $$Q_{E4}=20\times(60-50)=\boxed{200\ \text{kW}}=Q_{C,min}$$ Utility flow rates for the integrated network: $\dot m_{HPS}=1670/1700=\boxed{0.982\ \text{kg/s}}$, $\dot m_{CW}=200/63=\boxed{3.17\ \text{kg/s}}$. This 4-exchanger network (E1, E2, E3-heater, E4-cooler) achieves both minimum utility targets exactly, with no LPS required at all in the integrated design.