🎓 Lesson 9
D5
Composite Curves and Grand Composite Curve Construction
Composite curves are graphs that show how much heating and cooling energy a process needs at different temperatures, helping engineers find the most efficient way to reuse heat.
🎯 Learning Objectives
- ✓ Construct hot and cold composite curves from stream data using enthalpy interval analysis
- ✓ Identify the pinch temperature and calculate minimum hot and cold utility requirements
- ✓ Design a Grand Composite Curve including utility placement and temperature-dependent heat recovery limits
- ✓ Analyze trade-offs between capital cost (more heat exchangers) and operating cost (less utilities) using GCC slope interpretation
- ✓ Apply temperature shift (ΔT_min) sensitivity analysis to evaluate robustness of energy integration design
📖 Why This Matters
In mining and mineral processing, energy-intensive operations like ore drying, roasting, autoclaving, and smelting consume up to 30–40% of site-wide energy. Poor heat integration leads to excessive steam generation (via boilers) and cooling water use—increasing emissions, OPEX, and carbon footprint. Composite curves reveal *where* and *how much* heat can be recovered—turning waste heat from tail gas or leach solutions into preheating feed streams. For example, a copper SX-EW facility reduced low-pressure steam demand by 22% after GCC-guided retrofit—proving this isn’t theory: it’s ROI in kilowatts and tonnes of CO₂ avoided.
📘 Core Principles
Composite curve construction begins with stream data (flow rate, specific heat, inlet/outlet temperatures). Streams are discretized into temperature intervals bounded by all unique stream temperatures, adjusted by the minimum approach temperature (ΔT_min)—typically 5–20°C depending on fouling risk and economics. Within each interval, net heat flow is calculated: positive net flow indicates excess heat (to be exported upward), negative indicates deficit (to be imported from above). The hot composite curve is built by cumulatively summing heat surplus starting from the highest temperature; the cold composite curve sums heat deficit from the lowest temperature upward. The vertical separation between curves at any temperature reflects unrecoverable heat—minimum utilities occur where the curves are closest (the pinch). The Grand Composite Curve adds utility lines (e.g., steam at 180°C, cooling water at 30°C) and shows residual heat availability *across* the full temperature range, enabling optimal utility selection and cascade design.
📐 Enthalpy Change per Interval & Composite Enthalpy
The enthalpy change of a stream across a temperature interval determines heat surplus/deficit. Cumulative enthalpy defines the composite curve ordinate. ΔT_min governs interval resolution and sets the theoretical limit for heat recovery.
💡 Worked Example
Problem: A hot stream: 50 kg/s, Cp = 3.2 kJ/kg·K, Tin = 160°C, Tout = 70°C. Cold stream: 85 kg/s, Cp = 4.1 kJ/kg·K, Tin = 35°C, Tout = 110°C. Use ΔT_min = 10°C. Calculate net heat flow in the 100–110°C interval.
1.
Step 1: Determine active streams in [100,110]°C — Hot stream cools from 160→70, so present; cold stream heats from 35→110, so present only up to 110°C → fully active in this interval.
2.
Step 2: Calculate heat capacity flow rates: C_hot = 50 × 3.2 = 160 kW/K; C_cold = 85 × 4.1 = 348.5 kW/K.
3.
Step 3: Net heat flow in interval = (C_hot − C_cold) × ΔT = (160 − 348.5) × 10 = −1885 kW (i.e., deficit — requires external heating).
Answer:
The net heat flow is −1885 kW (cooling required), confirming this interval lies below the pinch and contributes to cold utility demand. This value feeds into cumulative cold composite enthalpy calculation.
🏗️ Real-World Application
At Newmont’s Boddington Gold Mine (Western Australia), pinch analysis using composite curves identified 12.4 MW of recoverable low-grade heat (65–95°C) from autoclave vent gases and thickener underflows. The GCC revealed that installing a dedicated organic Rankine cycle (ORC) unit at 85°C was more economical than upgrading existing steam systems. Post-implementation, the ORC supplies 4.8 MW of baseload power, reducing grid draw by 19% and cutting annual CO₂ emissions by ~14,000 t. Crucially, GCC slope analysis showed diminishing returns beyond 88°C — validating the selected expander inlet temperature and avoiding overcapitalization.
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