🎓 Lesson 3
D2
Exergy Analysis of Binary Cycle Components
Exergy analysis measures how much useful work a component in a binary geothermal plant *could* produce if it operated perfectly, helping engineers spot where energy is being wasted.
🎯 Learning Objectives
- ✓ Calculate specific exergy flow rates at inlet and outlet of binary cycle components using thermodynamic property tables and dead-state conditions
- ✓ Analyze exergy destruction distribution across the binary cycle to identify the component contributing the largest irreversibility
- ✓ Apply second-law efficiency (exergetic efficiency) to compare performance of organic Rankine cycle (ORC) turbines under varying working fluids and operating conditions
- ✓ Design an improved heat exchanger configuration by evaluating exergy loss sensitivity to pinch-point temperature difference and log-mean temperature difference
📖 Why This Matters
In geothermal binary plants, thermal resource temperatures are often low-to-moderate (80–170°C), making every joule of usable energy precious. Traditional first-law (energy) analysis shows 'how much' energy is conserved—but not 'how well' it’s used. Exergy analysis reveals *where and why* high-value energy degrades into low-value waste—e.g., a 20°C temperature drop across a shell-and-tube heat exchanger may seem small energetically, but it can destroy up to 35% of incoming exergy. For engineers optimizing plant ROI, this insight directly informs decisions on component sizing, fluid selection, and control strategies.
📘 Core Principles
Exergy is the *maximum useful work* obtainable when a system interacts reversibly with a reference environment (dead state: typically 25°C, 101.3 kPa, saturated air). Unlike energy, exergy is not conserved—it is destroyed by irreversibilities. In binary cycles, key exergy carriers are thermal (enthalpy + entropy-driven), kinetic, potential, and chemical (though chemical exergy is negligible for pure ORC fluids like isobutane or R-245fa). Each component has exergy in, exergy out, exergy destruction (Ẇ_destroy = ΣĖ_in − ΣĖ_out − Ẇ_net), and exergetic efficiency (η_II = Ė_useful_out / Ė_in). Critical insights include: (1) Heat exchangers dominate exergy destruction due to large temperature gradients; (2) Turbine isentropic efficiency directly governs both energy and exergy output; (3) Pump work is small in magnitude but critical for net cycle exergy balance due to its role in enabling heat addition.
📐 Specific Flow Exergy and Exergy Destruction
The specific physical exergy of a fluid stream (neglecting kinetic/potential terms) is calculated relative to the dead state (T₀, P₀). For liquid or superheated vapor streams, it combines enthalpy and entropy departures from the dead state. Component-wise exergy destruction is derived from the exergy balance: Ė_destroy = Ė_in − Ė_out − Ẇ_net + Q̇(1 − T₀/T_boundary), where boundary heat transfer must account for ambient temperature ratio.
Specific Physical Exergy (non-reactive, no KE/PE)
e = (h - h₀) - T₀(s - s₀)Calculates specific exergy of a flowing stream relative to dead state conditions.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| e | Specific physical exergy | kJ/kg | Maximum useful work per unit mass obtainable as stream reaches dead state |
| h | Specific enthalpy | kJ/kg | Thermodynamic property at given state |
| h₀ | Specific enthalpy at dead state | kJ/kg | Enthalpy of fluid at T₀, P₀ |
| s | Specific entropy | kJ/kg·K | Thermodynamic property at given state |
| s₀ | Specific entropy at dead state | kJ/kg·K | Entropy of fluid at T₀, P₀ |
| T₀ | Dead-state temperature | K | Reference environmental temperature (typically 298.15 K) |
Typical Ranges:
R-245fa turbine inlet (120°C, 2.8 MPa): 35 – 55 kJ/kg
Isobutane condenser outlet (35°C, saturated liquid): 0.8 – 2.2 kJ/kg
💡 Worked Example
Problem: Calculate specific exergy of R-245fa entering the turbine at 120°C, 2.8 MPa. Dead state: T₀ = 298.15 K, P₀ = 101.3 kPa. From NIST Webbook: h₁ = 272.4 kJ/kg, s₁ = 0.926 kJ/kg·K; h₀ = 125.8 kJ/kg, s₀ = 0.572 kJ/kg·K.
1.
Step 1: Apply specific physical exergy formula: e = (h − h₀) − T₀(s − s₀)
2.
Step 2: Substitute values: e₁ = (272.4 − 125.8) − 298.15 × (0.926 − 0.572)
3.
Step 3: Compute: e₁ = 146.6 − 298.15 × 0.354 ≈ 146.6 − 105.5 = 41.1 kJ/kg
Answer:
The specific exergy is 41.1 kJ/kg, which falls within the typical range of 35–55 kJ/kg for ORC turbine inlets in moderate-temperature geothermal applications.
🏗️ Real-World Application
At the 36 MW Nesjavellir Binary Plant (Iceland), exergy analysis revealed that the plate-type evaporator accounted for 52% of total cycle exergy destruction—primarily due to a 12 K pinch-point temperature difference (ΔT_pp) imposed by conservative fouling margins. Redesigning with enhanced surface geometry and dynamic cleaning reduced ΔT_pp to 6.5 K, increasing net exergy output by 8.3% and raising annual revenue by ~€1.2M—validated via ASME PTC 46-based exergy audit prior to retrofit.
🔧 Interactive Calculator
🔧 Open Geothermal Power Plant Binary Cycle Optimization Calculator📋 Case Connection
📋 Hellisheiði Geothermal Complex ORC Retrofit – Iceland
Low temperature differential limiting efficiency; silica scaling in plate heat exchangers; strict Icelandic environmenta...