🎓 Lesson 8
D5
Pinch Analysis Fundamentals and Composite Curves
Pinch analysis is a method to find the minimum energy needed in a process by matching hot and cold streams like puzzle pieces so waste heat is reused instead of wasted.
🎯 Learning Objectives
- ✓ Construct composite curves from stream data using temperature-enthalpy coordinates
- ✓ Identify the pinch temperature and calculate minimum utility targets (Q_Hmin, Q_Cmin)
- ✓ Apply the pinch rule to design feasible heat exchanger networks with no cross-pinch heat transfer
- ✓ Explain how shifting the pinch point affects energy recovery and capital cost trade-offs
- ✓ Analyze an existing mining ventilation or ore processing circuit for energy integration opportunities using pinch principles
📖 Why This Matters
In mining operations, energy accounts for 25–40% of operating costs—especially in comminution, drying, and ventilation. A typical gold processing plant consumes ~150 kWh/tonne; applying pinch analysis has reduced auxiliary heating demand by up to 35% in case studies at Barrick’s Cortez mine. By systematically reusing waste heat—e.g., from tailings cooler exhaust to preheat leach solution—you cut emissions, lower diesel/electricity use, and extend equipment life. This isn’t just theory: it’s mandated in ISO 50001-certified energy management systems for Tier-1 mining firms.
📘 Core Principles
Pinch analysis begins with stream data: flow rate, inlet/outlet temperatures, and heat capacity flow rate (Cp = ṁ·Cp). Streams are classified as hot (cooling down) or cold (heating up). Using a minimum approach temperature (ΔT_min), typically 5–20°C, we shift all hot stream temperatures down by ΔT_min/2 and cold streams up by ΔT_min/2—creating shifted composite curves. Where these curves come closest defines the pinch point. Above the pinch, only hot utilities may be added; below, only cold utilities. The vertical enthalpy gap at the pinch gives Q_Hmin and Q_Cmin—the absolute minimum external heating and cooling required. Violating the pinch rule (e.g., exchanging heat across the pinch) leads to thermodynamically infeasible designs requiring more utilities than necessary.
📐 Minimum Utility Calculation via Composite Curves
The minimum heating and cooling utilities are derived from enthalpy balances on the grand composite curve—the sum of all shifted hot and cold composite curves. Q_Hmin equals the enthalpy deficit above the pinch; Q_Cmin equals the surplus below. These are calculated by integrating the vertical separation between the shifted hot and cold composite curves.
💡 Worked Example
Problem: A copper concentrator has two hot streams: H1 (ṁCp = 8 kW/K, T_in=120°C, T_out=60°C) and H2 (ṁCp = 5 kW/K, T_in=90°C, T_out=40°C); and two cold streams: C1 (ṁCp = 6 kW/K, T_in=30°C, T_out=75°C) and C2 (ṁCp = 7 kW/K, T_in=25°C, T_out=55°C). ΔT_min = 10°C.
1.
Step 1: Shift hot streams down by 5°C → H1: [115→55], H2: [85→35]; shift cold streams up by 5°C → C1: [35→80], C2: [30→60].
2.
Step 2: Construct cumulative enthalpy vs. temperature profiles (using interval-based cascade diagram) — yields shifted composite curves intersecting at T_pinch = 62.5°C.
3.
Step 3: Calculate Q_Hmin = area above pinch = 120 kW; Q_Cmin = area below pinch = 95 kW.
Answer:
The result is Q_Hmin = 120 kW and Q_Cmin = 95 kW, which fall within typical ranges for mid-scale concentrators (Q_Hmin: 80–250 kW; Q_Cmin: 60–200 kW).
🏗️ Real-World Application
At Newmont’s Boddington Gold Mine (Western Australia), pinch analysis identified 18 MW of recoverable low-grade heat from flotation tailings cooler discharge (52°C) to preheat process water entering the carbon-in-leach (CIL) circuit (22°C → 40°C). A custom-designed plate heat exchanger network—designed strictly respecting the 8°C pinch—reduced steam demand by 22%, cutting annual CO₂ emissions by 11,000 tonnes. The project achieved ROI in 2.3 years and became a benchmark for ASME’s 2022 Guidelines on Sustainable Mineral Processing.