7.5 Absorption Refrigeration Cycles: Water-Lithium Bromide & Ammonia-Water Systems

7.5 Absorption Refrigeration Cycles: Water-Lithium Bromide & Ammonia-Water Systems

Absorption refrigeration cycles produce cooling through thermal sorption rather than mechanical vapor compression. By substituting the electric motor and compressor with a thermal compressor—composed of an absorber, liquid solution pump, generator (desorber), and solution heat exchanger—absorption chillers utilize low-grade thermal energy such as district steam, engine jacket hot water, industrial waste heat, or direct natural gas firing. On the PE Mechanical exam, understanding the thermodynamic distinctions between Water-Lithium Bromide ($\text{H}_2\text{O}-\text{LiBr}$) and Ammonia-Water ($\text{NH}_3-\text{H}_2\text{O}$) systems, solution concentration balances, crystallization limits, and heat rejection multipliers is critical.

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1. Fundamental Principle of the Thermal Compressor

In a mechanical vapor-compression cycle, compressing low-pressure vapor to high pressure consumes substantial mechanical shaft work because the specific volume of gas is enormous ($w = \int v\,dP$). The absorption cycle bypasses this work penalty by absorbing low-pressure vapor into a liquid solvent and pumping the resulting liquid solution to high pressure.

+-----------------------------------------------------------------------------------------+
| THERMAL COMPRESSOR VS. MECHANICAL COMPRESSOR COMPARISON                                 |
+-----------------------------------------------------------------------------------------+
| Mechanical Compression:  Low-P Vapor ---> [ ELECTRIC COMPRESSOR ] ---> High-P Vapor     |
|                          (Consumes massive shaft work: w = int v_vapor * dP)            |
|                                                                                         |
| Thermal Compression:     Low-P Vapor ---> [ Absorber ] (Refrigerant absorbed in liquid) |
|                                                 |                                       |
|                                                 v                                       |
|                                           [ Solution Pump ] (Negligible work: v_liquid) |
|                                                 |                                       |
|                                                 v                                       |
|                          High-P Vapor <--- [ Generator ] <-- Thermal Heat Input (Q_gen) |
+-----------------------------------------------------------------------------------------+

Because liquid specific volume is roughly $1/1,000\text{th}$ that of refrigerant vapor ($v_{\text{liquid}} \ll v_{\text{vapor}}$), the mechanical pump work accounts for less than 1% to 2% of total cycle energy input. The primary driving potential is thermal energy ($\dot{Q}_{\text{gen}}$) supplied to the generator.

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2. The Two Dominant Working Fluid Pairs

Industrial and commercial absorption systems rely on two primary refrigerant-absorbent fluid pairs:

+-----------------------------------------------------------------------------------------+
| ABSORPTION FLUID PAIRS CLASSIFICATION & CHARACTERISTICS                                 |
+-----------------------------------------------------------------------------------------+
| 1. WATER - LITHIUM BROMIDE (H2O - LiBr):                                                |
|    - Refrigerant: Water (H2O)  |  Absorbent: Lithium Bromide Salt (LiBr)                |
|    - Application: Commercial HVAC Chilled Water (40°F to 45°F / 4.4°C to 7.2°C)         |
|    - Pressure: Deep Vacuum (Evaporator ~0.12 psia / Condenser ~1.0 psia)                |
|    - Minimum Evap Temp: > 32°F (0°C) -> Water freezes at 32°F!                          |
|    - Critical Hazard: Salt Crystallization at high concentration / low temperature      |
|                                                                                         |
| 2. AMMONIA - WATER (NH3 - H2O):                                                         |
|    - Refrigerant: Ammonia (NH3)  |  Absorbent: Water (H2O)                              |
|    - Application: Sub-freezing Industrial Cold Storage & Blast Freezing (-40°F to 20°F) |
|    - Pressure: High Positive Pressure (Evaporator ~20-30 psig / Condenser ~150-250 psig)|
|    - Critical Requirement: Distillation / Rectification Column to purify ammonia vapor  |
+-----------------------------------------------------------------------------------------+

Detailed Analysis: Water-Lithium Bromide ($\text{H}_2\text{O}-\text{LiBr}$)

• Deep Vacuum Operation: Because water is the refrigerant, the system operates at sub-atmospheric pressures. At an evaporating temperature of $40^\circ\text{F}$, water saturation pressure is only $P_{\text{evap}} = 0.1217\text{ psia} = 6.3\text{ mmHg} = 0.84\text{ kPa}$. At a condensing temperature of $104^\circ\text{F}$, $P_{\text{cond}} = 1.07\text{ psia} = 55.3\text{ mmHg} = 7.38\text{ kPa}$. The entire machine is a hermetically sealed vacuum vessel; non-condensable gas purge units are essential.
• Crystallization Phenomenon: Lithium bromide is a solid salt dissolved in water. On a Dühring equilibrium diagram, if the solution mass fraction ($x = m_{\text{salt}} / (m_{\text{salt}} + m_{\text{water}})$) exceeds the solubility limit (typically $65\%\text{ to }68\%\text{ LiBr}$ by mass) or if the solution is overcooled in the Solution Heat Exchanger (SHX), solid salt crystals precipitate out, completely plugging the piping and heat exchanger tubes. Systems incorporate automatic dilution cycles and J-tube overflow bypasses to dissolve crystals.

Detailed Analysis: Ammonia-Water ($\text{NH}_3-\text{H}_2\text{O}$)

• Sub-Freezing Capability: Because ammonia freezes at $-108^\circ\text{F}$ ($-77.7^\circ\text{C}$), it can operate at low industrial evaporating temperatures ($-40^\circ\text{F}$ to $10^\circ\text{F}$).
• The Distillation/Rectification Column: Both ammonia and water are volatile liquids (unlike non-volatile LiBr salt). When the generator boils the strong solution, the resulting vapor contains approximately $90\%\text{ to }95\%\text{ ammonia}$ and $5\%\text{ to }10\%\text{ water vapor}$. If water vapor enters the condenser and evaporator, it raises the boiling temperature and causes water accumulation (water logging) in the evaporator. A vertical fractionating column (analyzer and rectifier) is installed above the generator to condense out residual water vapor, ensuring $99.5\%+\text{ pure ammonia vapor}$ enters the condenser.

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3. The Single-Effect Absorption Cycle Architecture

A complete single-effect absorption cycle consists of two interconnected circulation loops: the Refrigerant Loop and the Solution Loop.

+-----------------------------------------------------------------------------------------+
| COMPLETE SINGLE-EFFECT ABSORPTION CHILLER CYCLE (H2O - LiBr)                            |
+-----------------------------------------------------------------------------------------+
|                                   GENERATOR (DESORBER)                                  |
|                          +-------------------------------------+                        |
|   Heat Input: Q_gen ---> | Strong solution boiled by steam/gas | ---> Refrigerant Vapor |
|                          +-------------------------------------+      (State 7: High-P) |
|                                 |                       ^                     |         |
|                   Strong Sol'n  |                       | Weak Sol'n          v         |
|                   (Conc. LiBr)  |                       | (Dilute LiBr)  [ CONDENSER ]  |
|                   State 4       v                       | State 3        (Rejects Q_c)  |
|                          +-------------------------------------+              |         |
|                          |    SOLUTION HEAT EXCHANGER (SHX)    |              | State 8 |
|                          | (Preheats weak sol / cools strong)  |              v         |
|                          +-------------------------------------+        [ EXP VALVE ]   |
|                                 |                       ^                     |         |
|                                 v                       |                     v State 9 |
|                          [ Sol'n Exp ]            [ Sol'n Pump ]        [ EVAPORATOR ]  |
|                                 |             (Work: W_pump ~ 0)|       (Chills Water:  |
|                                 v                       |       |        Q_evap)        |
|                          +-------------------------------------+              |         |
|                          |              ABSORBER               | <------------+         |
|                          | (Absorbs vapor, rejects Q_absorber) |   Low-P Vapor (State 1)|
|                          +-------------------------------------+                        |
+-----------------------------------------------------------------------------------------+

The Solution Heat Exchanger (SHX)

The counter-flow Solution Heat Exchanger preheats the cool, dilute (weak) solution traveling from the absorber to the generator while precooling the hot, concentrated (strong) solution returning from the generator to the absorber. This delivers a dual energy benefit:

1. Reduces required thermal heat input ($\dot{Q}_{\text{gen}}$) at the generator.
2. Reduces required heat rejection ($\dot{Q}_{\text{abs}}$) at the absorber, improving overall cycle COP by up to 50%.

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4. Single-Effect vs. Double-Effect Absorption Chillers

The Double-Effect Cycle Principle

A double-effect absorption chiller features two generators in series: a High-Temperature Generator (HTG) and a Low-Temperature Generator (LTG). High-temperature heat drives the HTG, boiling off high-pressure refrigerant vapor. Instead of routing this vapor directly to the condenser, it is routed through condensing tubes inside the LTG, where its latent heat of condensation boils off a second batch of refrigerant vapor from intermediate solution. This reuses the thermal energy twice, nearly doubling thermal COP from $0.70$ to $1.25$.

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5. Thermodynamic Equations & Mass/Concentration Balances

1. Thermal Coefficient of Performance ($\text{COP}_{\text{thermal}}$)

$$\text{COP}_{\text{thermal}} = \frac{\dot{Q}_{\text{evap}}}{\dot{Q}_{\text{gen}} + \dot{W}_{\text{pump}}} \approx \frac{\dot{Q}_{\text{evap}}}{\dot{Q}_{\text{gen}}}$$

2. Maximum Theoretical Carnot Absorption COP

An absorption cycle can be conceptualized as a reversible Carnot heat engine driving a reversible Carnot refrigerator between three temperature levels: generator heat source ($T_{\text{gen}}$), ambient heat rejection sink ($T_0 = T_{\text{absorber}} = T_{\text{condenser}}$), and refrigerated load ($T_{\text{evap}}$). All temperatures in Rankine (${}^\circ\text{R}$) or Kelvin ($\text{K}$):

$$\mathbf{\text{COP}_{\text{Carnot, abs}} = \eta_{\text{Carnot, engine}} \times \text{COP}_{\text{Carnot, refrig}} = \left( \frac{T_{\text{gen}} - T_0}{T_{\text{gen}}} \right) \times \left( \frac{T_{\text{evap}}}{T_0 - T_{\text{evap}}} \right)}$$

3. Mass & Solute (LiBr) Conservation Equations

Let $\dot{m}_w$ be weak solution mass flow rate, $\dot{m}_s$ be strong solution mass flow rate, and $\dot{m}_r$ be pure refrigerant mass flow rate:

• Total Mass Balance: $\dot{m}_w = \dot{m}_s + \dot{m}_r$
• Solute (LiBr Salt) Conservation Balance: $\dot{m}_w \cdot x_w = \dot{m}_s \cdot x_s$

Where $x_w$ is weak solution mass fraction and $x_s$ is strong solution mass fraction.

$$\dot{m}_s = \dot{m}_w - \dot{m}_r \quad \Longrightarrow \quad \dot{m}_w x_w = (\dot{m}_w - \dot{m}_r) x_s$$ $$\mathbf{\dot{m}_w = \dot{m}_r \left( \frac{x_s}{x_s - x_w} \right)} \qquad \mathbf{\dot{m}_s = \dot{m}_r \left( \frac{x_w}{x_s - x_w} \right)}$$

4. Circulation Ratio ($\lambda$)

The ratio of weak solution pumped per unit mass of refrigerant generated:

$$\lambda = \frac{\dot{m}_w}{\dot{m}_r} = \frac{x_s}{x_s - x_w}$$

5. Cooling Tower Heat Rejection Multiplier

Unlike vapor-compression chillers where heat is rejected only at the condenser, absorption chillers reject heat from both the condenser and the absorber:

$$\dot{Q}_{\text{tower}} = \dot{Q}_{\text{cond}} + \dot{Q}_{\text{abs}} = \dot{Q}_{\text{gen}} + \dot{Q}_{\text{evap}} + \dot{W}_{\text{pump}} \approx \dot{Q}_{\text{gen}} + \dot{Q}_{\text{evap}}$$

Exam Sizing Impact: For a single-effect chiller with $\text{COP}_{\text{thermal}} = 0.70$, $\dot{Q}_{\text{gen}} = \dot{Q}_{\text{evap}} / 0.70 = 1.43 \dot{Q}_{\text{evap}}$. Total heat rejection to the cooling tower is $\dot{Q}_{\text{tower}} = 1.43 \dot{Q}_{\text{evap}} + 1.0 \dot{Q}_{\text{evap}} = \mathbf{2.43 \times \dot{Q}_{\text{evap}}}$ ($2.43\text{ Tons of Heat Rejection per Ton of Cooling}$). Cooling towers for absorption chillers must be sized roughly twice as large as cooling towers for electric chillers!

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6. NCEES Reference Handbook Navigation Tactics

• Carnot Absorption COP Formula: Search "Absorption Refrigeration" or "Carnot Absorption" in Section 7 to locate the product equation $[(T_g - T_0)/T_g] \times [T_e / (T_0 - T_e)]$.
• Mass Balance Formulas: Locate solution mass balance equations $\dot{m}_w x_w = \dot{m}_s x_s$ and circulation ratio definition $\lambda = x_s / (x_s - x_w)$.
• Dühring Plot Navigation: Read solution equilibrium temperatures and concentration lines from the $\text{LiBr}-\text{H}_2\text{O}$ chart.

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7. Worked Computational Examples

Example 1: 100-Ton Single-Effect $\text{H}_2\text{O}-\text{LiBr}$ Mass & Energy Balance

A single-effect $\text{H}_2\text{O}-\text{LiBr}$ absorption chiller provides $100\text{ Tons}$ of chilled water cooling ($1,200,000\text{ Btu/hr}$). The evaporator produces $40^\circ\text{F}$ saturated vapor ($h_v = 1,079.3\text{ Btu/lbm}$) and the condenser produces $100^\circ\text{F}$ saturated liquid ($h_l = 68.0\text{ Btu/lbm}$).

• Weak solution leaving absorber: $x_w = 58\%\text{ LiBr}$ ($0.58$), enters generator at enthalpy $h_{\text{weak, in}} = 42.0\text{ Btu/lbm}$
• Strong solution leaving generator: $x_s = 64\%\text{ LiBr}$ ($0.64$), exits at enthalpy $h_{\text{strong, out}} = 98.0\text{ Btu/lbm}$
• Superheated water vapor leaves generator at $180^\circ\text{F}$ with enthalpy $h_{\text{vapor}} = 1,140.0\text{ Btu/lbm}$

Calculate: (a) Refrigerant water mass flow rate ($\dot{m}_r$), (b) Circulation ratio ($\lambda$) and solution flow rates ($\dot{m}_w, \dot{m}_s$), (c) Generator thermal heat input ($\dot{Q}_{\text{gen}}$), (d) Thermal $\text{COP}_{\text{thermal}}$, and (e) Total heat rejection rate to the cooling tower.

Solution:

1. Refrigerant Mass Flow Rate ($\dot{m}_r$):

   $$q_{\text{evap}} = h_v - h_l = 1,079.3 - 68.0 = 1,011.3\text{ Btu/lbm}$$ $$\dot{m}_r = \frac{\dot{Q}_{\text{evap}}}{q_{\text{evap}}} = \frac{1,200,000\text{ Btu/hr}}{1,011.3\text{ Btu/lbm}} = \mathbf{1,186.60\text{ lbm/hr}}$$

2. Circulation Ratio & Solution Flow Rates:

   $$\lambda = \frac{x_s}{x_s - x_w} = \frac{0.64}{0.64 - 0.58} = \frac{0.64}{0.06} = \mathbf{10.667}$$ $$\dot{m}_w = \lambda \cdot \dot{m}_r = 10.667 \times 1,186.60\text{ lbm/hr} = \mathbf{12,657.1\text{ lbm/hr}}$$ $$\dot{m}_s = \dot{m}_w - \dot{m}_r = 12,657.1 - 1,186.60 = \mathbf{11,470.5\text{ lbm/hr}}$$

3. Generator Heat Input Rate ($\dot{Q}_{\text{gen}}$): Energy balance around generator:

   $$\dot{Q}_{\text{gen}} = \dot{m}_r h_{\text{vapor}} + \dot{m}_s h_{\text{strong, out}} - \dot{m}_w h_{\text{weak, in}}$$ $$\dot{Q}_{\text{gen}} = (1,186.60 \times 1,140.0) + (11,470.5 \times 98.0) - (12,657.1 \times 42.0)$$ $$\dot{Q}_{\text{gen}} = 1,352,724 + 1,124,109 - 531,598 = \mathbf{1,945,235\text{ Btu/hr}}$$

4. Thermal COP:

   $$\text{COP}_{\text{thermal}} = \frac{\dot{Q}_{\text{evap}}}{\dot{Q}_{\text{gen}}} = \frac{1,200,000}{1,945,235} = \mathbf{0.6169} \quad (\approx 0.62)$$

5. Cooling Tower Heat Rejection:

   $$\dot{Q}_{\text{tower}} = \dot{Q}_{\text{gen}} + \dot{Q}_{\text{evap}} = 1,945,235 + 1,200,000 = \mathbf{3,145,235\text{ Btu/hr}}$$ $$\text{Tons of Heat Rejection} = \frac{3,145,235}{12,000} = \mathbf{262.10\text{ THR}} \quad (2.62\text{ THR / Ton of Cooling})$$

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Example 2: Carnot Upper Limit for Direct-Fired Double-Effect Chiller

A direct-fired natural gas double-effect absorption chiller operates with a high-temperature generator driving temperature $T_{\text{gen}} = 340^\circ\text{F}$, an evaporating temperature $T_{\text{evap}} = 40^\circ\text{F}$, and an ambient heat rejection temperature (absorber/condenser) $T_0 = 95^\circ\text{F}$. The actual machine achieves a thermal $\text{COP}_{\text{thermal}} = 1.22$.

Calculate: (a) The theoretical maximum Carnot absorption COP, and (b) The Second Law efficiency ($\eta_{\text{II}}$).

Solution:

1. Convert all temperatures to absolute Rankine: $$T_{\text{gen}} = 340^\circ\text{F} + 459.67 = 799.67^\circ\text{R}$$ $$T_{\text{evap}} = 40^\circ\text{F} + 459.67 = 499.67^\circ\text{R}$$ $$T_0 = 95^\circ\text{F} + 459.67 = 554.67^\circ\text{R}$$
2. Evaluate Carnot Heat Engine & Refrigeration Terms: $$\eta_{\text{Carnot, engine}} = \frac{T_{\text{gen}} - T_0}{T_{\text{gen}}} = \frac{799.67 - 554.67}{799.67} = \frac{245.0}{799.67} = 0.30638 \quad (30.64\%$$ $$\text{COP}_{\text{Carnot, refrig}} = \frac{T_{\text{evap}}}{T_0 - T_{\text{evap}}} = \frac{499.67}{554.67 - 499.67} = \frac{499.67}{55.0} = 9.0849$$
3. Carnot Absorption COP: $$\text{COP}_{\text{Carnot, abs}} = 0.30638 \times 9.0849 = \mathbf{2.783}$$
4. Second Law Efficiency: $$\eta_{\text{II}} = \frac{\text{COP}_{\text{actual}}}{\text{COP}_{\text{Carnot, abs}}} = \frac{1.22}{2.783} = 0.4384 = \mathbf{43.84\%}$$