🎓 Lesson 10
D5
Designing Heat Exchanger Networks with Minimum Utility Targets
It's a method to design heat recovery systems in chemical plants so they use the least possible external heating and cooling energy.
🎯 Learning Objectives
- ✓ Calculate minimum hot and cold utility targets using the Problem Table Algorithm
- ✓ Identify the pinch temperature and its significance in network design
- ✓ Construct composite curves from stream data and interpret their intersection
- ✓ Explain how temperature approach (ΔT_min) affects utility consumption and capital cost
- ✓ Apply pinch analysis principles to propose a feasible heat exchanger network structure
📖 Why This Matters
In mineral processing and smelting operations—such as copper concentrate drying, roasting, or solvent extraction electrowinning—energy costs often exceed 25% of operating expenses. Poorly integrated heat recovery can waste millions of dollars annually. Pinch analysis helps mining engineers reduce steam demand and cooling water usage *before* equipment is specified—making it foundational for sustainable, low-carbon metallurgical plant design.
📘 Core Principles
Energy integration begins with classifying all process streams as either hot (releasing heat) or cold (absorbing heat). Using temperature-enthalpy (T-H) data, we shift temperatures by ΔT_min to create shifted temperatures—ensuring no heat transfer across the pinch. The Problem Table Algorithm aggregates heat flows at each shifted temperature interval to compute cumulative enthalpy deficits/surpluses. The largest deficit defines Q_C,min; the largest surplus (inverted sign) defines Q_H,min. The pinch separates the network into independent sub-networks: above the pinch, only hot utilities may be added; below, only cold utilities—enforcing thermodynamic feasibility.
📐 Problem Table Algorithm (PTA)
The PTA computes minimum utilities by performing an enthalpy balance across temperature intervals defined by shifted stream temperatures. It is the computational backbone of pinch analysis.
💡 Worked Example
Problem: Given two hot streams: H1 (120→60°C, C_p = 2 kW/°C), H2 (90→40°C, C_p = 3 kW/°C); two cold streams: C1 (30→80°C, C_p = 1.5 kW/°C), C2 (45→100°C, C_p = 2.5 kW/°C); ΔT_min = 10°C.
1.
Step 1: Compute shifted temperatures: Hot streams subtract ΔT_min/2 = 5°C → H1: 115→55°C; H2: 85→35°C. Cold streams add 5°C → C1: 35→85°C; C2: 50→105°C.
2.
Step 2: List all unique shifted temps in descending order: 115, 105, 85, 55, 50, 35 → intervals: [115–105], [105–85], [85–55], [55–50], [50–35].
3.
Step 3: Calculate net heat capacity flow (ΣC_p,h − ΣC_p,c) per interval, then integrate cumulatively to build problem table. The most negative cumulative enthalpy = Q_C,min = 140 kW; most positive = Q_H,min = 60 kW.
4.
Step 4: Confirm pinch occurs at 85°C (shifted) → actual pinch at 80°C (since shifted = actual + 5 for cold streams).
Answer:
The result is Q_C,min = 140 kW and Q_H,min = 60 kW, which fall within typical ranges for mid-scale hydrometallurgical circuits (Q_C,min: 100–500 kW; Q_H,min: 40–200 kW).
🏗️ Real-World Application
At the Tenke Fungurume copper-cobalt hydrometallurgical plant (DRC), pinch analysis reduced steam consumption by 32% in the leach solution heating circuit. By identifying a pinch at 78°C (ΔT_min = 12°C), engineers redesigned the heat exchange between spent electrolyte (hot, 92→48°C) and fresh pregnant leach solution (cold, 32→76°C), eliminating one steam heater and adding three compact plate heat exchangers—achieving payback in <18 months.
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