1. Fundamental Thermodynamic Principles
Absorption refrigeration using CaBr₂-H₂O operates on a heat-driven thermodynamic cycle that substitutes mechanical compression with chemical absorption. The key thermodynamic processes include:
- Evaporation (cooling effect at low pressure)
- Absorption (exothermic vapor uptake by CaBr₂ solution)
- Desorption/Generation (heat-driven refrigerant separation)
- Condensation (heat rejection)
2. Property Diagrams for CaBr₂-H₂O System
The system is typically analyzed using two primary diagrams:
A. Dühring Plot (Pressure-Temperature-Concentration)
- Illustrates the vapor-liquid equilibrium of CaBr₂-H₂O mixtures
- Shows how boiling point elevation occurs with increasing CaBr₂ concentration
- Critical parameters:
- At 50% CaBr₂ concentration:
- Saturation pressure ≈ 0.7 kPa at 25°C
- Boiling point ≈ 115°C at atmospheric pressure
- At 50% CaBr₂ concentration:
B. Enthalpy-Concentration (h-ξ) Diagram
- Plots specific enthalpy (kJ/kg) vs. CaBr₂ mass fraction
- Key features:
- Lower enthalpy region: Concentrated solution (strong absorbent)
- Upper enthalpy region: Dilute solution (after absorption)
- Crystallization boundary at high concentrations (~60% CaBr₂ at 25°C)
3. Energy Balance Analysis
The thermodynamic performance is evaluated through energy balances at each component:
| Component | Energy Equation | Typical Values |
|---|---|---|
| Evaporator | Qₑ = mᵣ(h₆ – h₅) | 200-300 kJ/kg refrigeration effect |
| Absorber | Qₐ = mₐh₄ + mᵣh₂ – mₛh₁ | Heat rejection ≈ 1.3×Qₑ |
| Generator | Q₉ = mₛh₃ – mₐh₄ – mᵣh₇ | Heat input ≈ 1.5×Qₑ |
| Condenser | Q_c = mᵣ(h₇ – h₈) | Heat rejection ≈ Qₑ + Q₉ – Qₐ |
Where:
- mᵣ = refrigerant (water) mass flow
- mₐ = absorbent (CaBr₂ solution) mass flow
- h = specific enthalpy at state points
4. Performance Metrics
A. Coefficient of Performance (COP)COP=QevapQgen+Wpump≈0.6−0.75COP=Qgen+WpumpQevap≈0.6−0.75
Typical values for CaBr₂ systems are lower than LiBr systems (COP~0.8) due to:
- Higher solution circulation ratios
- Greater heat of dilution
B. Circulation Ratio (f)f=mstrongmrefrigerant=ξweakξstrong−ξweakf=mrefrigerantmstrong=ξstrong−ξweakξweak
Where ξ is CaBr₂ mass fraction. Typical f ≈ 10-15 for CaBr₂ vs. 5-8 for LiBr.
5. Comparison with LiBr-H₂O Systems
| Parameter | CaBr₂-H₂O | LiBr-H₂O |
|---|---|---|
| Max Concentration | ~60% | ~70% |
| Crystallization Risk | Lower | Higher |
| Absorption Efficiency | Moderate | Higher |
| Corrosivity | More corrosive | Less corrosive |
| Operating Pressure | 0.6-7 kPa | 0.8-10 kPa |
6. Advanced Thermodynamic Considerations
- Solution Heat Exchanger Effectiveness: Crucial for improving COP by recovering heat between strong/weak solutions
- Non-Ideal Behavior: Activity coefficients deviate from ideality at high concentrations
- Triple Point Effects: Phase behavior becomes complex near crystallization boundaries
7. Optimization Strategies
- Concentration Control: Maintain optimal ξ_strong (~50-55%) to balance absorption capacity and crystallization risk
- Temperature Management: Keep generator temp <130°C to prevent thermal decomposition
- Additives: Corrosion inhibitors (e.g., LiOH) can improve longevity without significantly altering thermodynamics
8. Practical Limitations
- Lower Cooling Capacity: Compared to LiBr systems due to higher circulation ratios
- Temperature Lift Constraints: Limited to ~40K temperature lift between evaporator/condenser
- Material Compatibility: Requires nickel-based alloys for long-term operation
This thermodynamic analysis demonstrates that while CaBr₂-H₂O systems have slightly lower performance than LiBr systems, they offer advantages in crystallization stability and lower maintenance requirements, making them suitable for specific applications where these factors are prioritized.
