13.3 Vapour Compression & Vapour Absorption Refrigeration Systems

Vapour Compression & Vapour Absorption Refrigeration Systems

Refrigeration is the process of removing thermal energy from a low-temperature reservoir and discharging it to a higher-temperature reservoir through the input of mechanical or thermal work. In modern industrial mining operations, massive refrigeration systems provide chilling for underground mine ventilation air (counteracting rock geothermal gradients and equipment heat loads), industrial chiller plants for heavy equipment lubricants, and cooling systems in Coal Handling Plants (CHP).

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1. Thermodynamic Fundamentals & The Ton of Refrigeration

A refrigerator operates on a reversed thermodynamic cycle. The performance index is the Coefficient of Performance (COP):

$$\text{COP}_{\text{Ref}} = \frac{\text{Desired Refrigerating Effect } (Q_L)}{\text{Net Work Input } (W_{\text{net}})} = \frac{Q_L}{Q_H - Q_L}$$

For a Reversed Carnot Cycle operating between low temperature $T_L$ and high temperature $T_H$ (in Kelvin):

$$\text{COP}_{\text{Carnot, Ref}} = \frac{T_L}{T_H - T_L}$$ $$\text{COP}_{\text{Carnot, Heat Pump}} = \frac{T_H}{T_H - T_L} = \text{COP}_{\text{Carnot, Ref}} + 1$$

The Ton of Refrigeration (TR)

The commercial unit of cooling capacity is the Ton of Refrigeration (TR), defined as the steady rate of heat removal required to freeze 1 short ton ($2000\text{ lb} = 907.185\text{ kg}$) of pure water at $0^{\circ}\text{C}$ into ice at $0^{\circ}\text{C}$ in exactly 24 hours:

$$\text{Latent heat of fusion of ice } h_{sf} = 333.55 \ \text{kJ/kg}$$ $$1 \ \text{TR} = \frac{907.185 \ \text{kg} \times 333.55 \ \text{kJ/kg}}{24 \times 3600 \ \text{s}} = \frac{302,601 \ \text{kJ}}{86,400 \ \text{s}} = 3.502 \ \text{kW} \quad (\text{Standard Definition: } 3.51685 \approx 3.517 \ \text{kW})$$ $$1 \ \text{TR} = 3.517 \ \text{kW} = 210 \ \text{kJ/min} = 12,000 \ \text{Btu/hr}$$

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2. Standard Vapour Compression Refrigeration System (VCRS)

The Vapour Compression Refrigeration System (VCRS) is the most widely utilized refrigeration cycle. It eliminates the impractical wet compression and expansion cylinder expansion work of the reversed Carnot cycle by employing dry isentropic compression and an isenthalpic throttling expansion valve.

+-----------------------------------------------------------------------------------------+
|                        STANDARD VCRS SCHEMATIC & CYCLE DIAGRAMS                         |
|                                                                                         |
|   SCHEMATIC:                                                                            |
|               +------------------- [ CONDENSER ] <-------------------+                  |
|               |                     (Q_out = q_c)                     |                 |
|               v                                                       | (State 2: Super-|
|        (State 3: Sat Liquid)                                          |  heated vapor)  |
|        [ EXPANSION VALVE ]                                     [ COMPRESSOR ]           |
|          (h3 = h4 Throttling)                                   (W_in = W_c)            |
|               |                                                       ^                 |
|               v                                                       | (State 1: Sat   |
|               +------------------> [ EVAPORATOR ] --------------------+  vapor)         |
|                                     (Q_in = RE)                                         |
|                                                                                         |
|   PRESSURE-ENTHALPY (P-h) DIAGRAM:            TEMPERATURE-ENTROPY (T-s) DIAGRAM:        |
|   P ^                                         T ^                                       |
|     |       2-3: Condenser                      |         2-3: Condenser                |
|  Pc |--------* 3 <=========== 2 (Superheated)   |          * 3 <========= 2             |
|     |       /|                 \                |         / |            |  (s1 = s2)   |
|     |      / |                  \               |        /  |            |              |
|  Pe |-----*--* 4 -----------> 1 *               |       /   * 4 -------> * 1            |
|     |    /   |   4-1: Evaporator                |      /                  \             |
|     +---+----+--------------------> h           +-----+--------------------> s          |
|         h3=h4                 h1  h2                                                    |
+-----------------------------------------------------------------------------------------+

The Four Thermodynamic Processes

1. Process 1-2 (Isentropic Compression): Saturated vapor at evaporator pressure $P_e$ is compressed isentropically ($s_1 = s_2$) in a mechanical compressor to superheated vapor at condenser pressure $P_c$. Work input: $w_c = h_2 - h_1$.
2. Process 2-3 (Isobaric Heat Rejection): Superheated refrigerant vapor is desuperheated, condensed to saturated liquid, and subcooled inside the condenser at constant pressure $P_c$. Heat rejected: $q_c = h_2 - h_3$.
3. Process 3-4 (Isenthalpic Throttling Expansion): Saturated liquid expands irreversibly through a throttling capillary tube or thermostatic expansion valve (TXV) from $P_c$ down to $P_e$. Throttling is adiabatic with zero work output: $h_4 = h_3$.
4. Process 4-1 (Isobaric Evaporation): Low-quality liquid-vapor mixture absorbs thermal energy from the cold refrigerated space at constant pressure $P_e$ until it reaches saturated vapor (state 1). Refrigerating effect: $\text{RE} = q_e = h_1 - h_4 = h_1 - h_3$.

Mathematical Formulation of Performance

$$\text{Refrigerating Effect (RE)} = h_1 - h_4 = h_1 - h_3 \quad (\text{kJ/kg})$$ $$\text{Compressor Work } (w_c) = h_2 - h_1 \quad (\text{kJ/kg})$$ $$\text{Coefficient of Performance (COP)} = \frac{\text{RE}}{w_c} = \frac{h_1 - h_4}{h_2 - h_1} = \frac{h_1 - h_3}{h_2 - h_1}$$ $$\text{Refrigerant Mass Flow Rate } (\dot{m}_r) = \frac{\text{Plant Capacity (kW)}}{\text{RE}} = \frac{\text{Plant Capacity (kW)}}{h_1 - h_3} \quad (\text{kg/s})$$ $$\text{Compressor Power Input } (P) = \dot{m}_r w_c = \dot{m}_r (h_2 - h_1) \quad (\text{kW})$$ $$\text{Heat Rejection Ratio (HRR)} = \frac{q_c}{\text{RE}} = \frac{h_2 - h_3}{h_1 - h_3} = 1 + \frac{1}{\text{COP}}$$

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3. Influence of Operating Parameters on VCRS Performance

+-----------------------------------------------------------------------------------------+
|                        VCRS OPERATING PARAMETER SENSITIVITY                             |
|                                                                                         |
|   Parameter Modification       RE (kJ/kg)      W_c (kJ/kg)     COP         V_piston     |
|   --------------------------   -------------   -------------   ---------   ---------    |
|   1. Subcooling of Liquid      Increases       Unchanged       Increases   Unchanged    |
|      at Condenser Exit (3->3')                                                          |
|   2. Superheating Vapor        Increases       Increases       Varies      Increases    |
|      in Evaporator (1->1')                                     (R134a +)                |
|   3. Decreasing Evaporator     Decreases       Increases       Decreases   Increases    |
|      Temperature (Te drops)                    sharply         severely    greatly      |
|   4. Increasing Condenser      Decreases       Increases       Decreases   Slight       |
|      Temperature (Tc rises)                                    moderately  increase     |
+-----------------------------------------------------------------------------------------+

+-----------------------------------------------------------------------------------------+
|                         EFFECTS ON P-h DIAGRAM: SUBCOOLING & SUPERHEAT                  |
|                                                                                         |
|   P ^                                                                                   |
|     |           3'    3                                   2      2'                     |
|  Pc |-----------*<----*===================================*=====>*                      |
|     |          /|     |                                    \      \                     |
|     |         / |     |                                     \      \                    |
|  Pe |--------*--*<----*--------------------------------------*----->*                   |
|     |       /   4'    4                                      1      1'                  |
|     +------+----+-----+--------------------------------------+------+--> h              |
|            |<-Delta_h->|                                     |<-Dh->|                   |
|            Subcooling Gain (RE increases)                   Superheating Gain           |
+-----------------------------------------------------------------------------------------+

1. Subcooling of Liquid Refrigerant ($3 \to 3'$)

Cooling liquid refrigerant below saturation temperature before throttling ($T_{3'} < T_{\text{sat}}(P_c)$):

• State 4 shifts left to $4'$ ($h_{4'} < h_4$).
• Refrigerating effect increases: $\text{RE}' = h_1 - h_{4'} > \text{RE}$.
• Compressor work $w_c = h_2 - h_1$ is unaffected.
• $\text{COP}$ always increases.

2. Superheating of Suction Vapor ($1 \to 1'$)

Heating vapor above saturation temperature prior to compression ($T_{1'} > T_{\text{sat}}(P_e)$):

• Useful Superheating (inside refrigerated space): Increases $\text{RE}$ ($h_{1'} - h_3 > h_1 - h_3$) while increasing $w_c = h_{2'} - h_{1'}$ due to diverging constant entropy lines at higher temperatures. For R-134a and R-12, COP increases slightly; for Ammonia (R-717), COP decreases.
• Non-Useful Superheating (in connecting pipework outside cold room): $\text{RE}$ remains unchanged while $w_c$ increases, leading to a decrease in COP.

3. Evaporator Temperature Drop

Lowering $T_e$ decreases suction pressure $P_e$:

• Specific volume $v_1$ at compressor suction increases exponentially ($v_1 \propto 1/P_e$).
• Compressor volumetric efficiency drops: $\eta_v = 1 + c - c\left(\frac{P_c}{P_e}\right)^{1/\gamma}$.
• Mass flow rate delivered by a fixed displacement compressor drops drastically.

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4. Multi-Stage Compression with Flash Intercooling

When the overall pressure ratio $r_p = P_c / P_e$ exceeds $6\text{ to }8$ (e.g., low-temperature blast freezing or deep-shaft mine cooling), single-stage VCRS suffers from:

1. Severe deterioration in compressor volumetric efficiency.
2. Extremely high compressor discharge temperatures ($T_2 > 130^{\circ}\text{C}$), which break down lubricating oils and cause valve carbonization.
3. Large throttling irreversibility losses.

+-----------------------------------------------------------------------------------------+
|                        TWO-STAGE COMPRESSION WITH FLASH INTERCOOLER                     |
|                                                                                         |
|   SCHEMATIC:                                                                            |
|                                                                                         |
|               +---------------- [ CONDENSER (Pc) ] <----------------+                   |
|               |                                                     |                   |
|               v                                                     | (HP Compressor)   |
|        [ EXPANSION VALVE 1 ]                                        |                   |
|               |                                                     |                   |
|               v (State 5: Flash Liquid)       (State 3: Saturated)  |                   |
|       +-> [ FLASH CHAMBER (Pi) ] -----------> [ INTERCOOLER ] ------+                   |
|       |       |                                     ^                                   |
|       |       v                                     | (LP Compressor)                   |
|       | [ EXPANSION VALVE 2 ]                       |                                   |
|       |       |                                     |                                   |
|       |       v                                     |                                   |
|       +-------+----------------> [ EVAPORATOR (Pe) ]+                                   |
|                                                                                         |
|   Optimum Intermediate Pressure:   P_i = sqrt( P_e * P_c )                              |
+-----------------------------------------------------------------------------------------+

Optimum Intermediate Pressure ($P_i$)

To minimize total compressor power input for a two-stage system with perfect intercooling between stages:

$$P_i = \sqrt{P_e P_c}$$ $$\text{Pressure Ratio per Stage: } \quad r_{p,1} = r_{p,2} = \sqrt{\frac{P_c}{P_e}}$$

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5. Vapour Absorption Refrigeration System (VARS)

The Vapour Absorption Refrigeration System (VARS) replaces the power-hungry mechanical compressor of the VCRS with a thermal compressor assembly comprising an Absorber, Solution Pump, Generator, and Pressure Reducing Valve. It is driven primarily by low-grade thermal waste heat (steam from mine boilers, exhaust gas from diesel generators, or solar collectors).

+-----------------------------------------------------------------------------------------+
|                        VAPOUR ABSORPTION SYSTEM (VARS) SCHEMATIC                        |
|                                                                                         |
|                      Heat In (Q_g at T_g)                                               |
|                               v                                                         |
|                     +-------------------+                                               |
|                     |   GENERATOR       |                                               |
|                     | (Vapor Separated) |                                               |
|                     +-------------------+                                               |
|                       | High-P Vapor      ^ Weak Solution (Rich in Refrigerant)         |
|                       v                   |                                             |
|               [ CONDENSER (Pc) ]     [ SOLUTION PUMP ] (Work input W_p ~ 0)             |
|                       |                   ^                                             |
|                       v                   |                                             |
|               [ EXPANSION VALVE ]   +-------------------+                               |
|                       |             |   ABSORBER        | ---> Heat Out (Q_a at T_a)    |
|                       v             | (Vapor Absorbed)  |                               |
|               [ EVAPORATOR (Pe) ]-> +-------------------+                               |
|                       ^                                                                 |
|                       |                                                                 |
|                 Cooling Load (Q_e at T_e)                                               |
+-----------------------------------------------------------------------------------------+

Maximum Theoretical COP of VARS (Carnot Analysis)

A VARS can be modeled as a combined system: a reversible Carnot Heat Engine operating between generator temperature $T_g$ and ambient/absorber temperature $T_a$, producing mechanical work $W$ that directly drives a reversible Carnot Refrigerator operating between $T_e$ and $T_a$.

$$\eta_{\text{Carnot, HE}} = \frac{W}{Q_g} = \frac{T_g - T_a}{T_g}$$ $$\text{COP}_{\text{Carnot, Ref}} = \frac{Q_e}{W} = \frac{T_e}{T_a - T_e}$$ $$\text{COP}_{\text{max, VARS}} = \frac{Q_e}{Q_g} = \eta_{\text{Carnot, HE}} \times \text{COP}_{\text{Carnot, Ref}} = \left(\frac{T_g - T_a}{T_g}\right) \left(\frac{T_e}{T_a - T_e}\right)$$

Where all temperatures ($T_g, T_a, T_e$) must be expressed in Kelvin.

Comparison of Commercial Absorption Systems

The Three-Fluid Electrolux (Platen-Munters) System

Designed for domestic refrigerators where electricity or mechanical pumps are unavailable:

• Working Fluids: Ammonia (Refrigerant), Water (Absorbent), Hydrogen (Inert Auxiliary Gas).
• Eliminates Solution Pump: Operates at uniform total pressure ($P_{\text{total}} \approx 15\text{ bar}$) throughout the system.
• Evaporator Principle: Dalton's law of partial pressures: $P_{\text{total}} = P_{\text{NH}_3} + P_{\text{H}_2}$. Hydrogen gas introduced into the evaporator lowers the partial pressure of ammonia ($P_{\text{NH}_3} \approx 2\text{ bar}$), allowing liquid ammonia to evaporate at low temperature ($-15^{\circ}\text{C}$) without requiring a mechanical throttling valve or compressor.
• Zero Moving Parts: Circulation occurs entirely via natural thermosiphon buoyancy.

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6. Refrigerant Chemistry, Nomenclature & Environmental Protocols

ASHRAE Standard Refrigerant Nomenclature

For halogenated hydrocarbons with chemical formula $\text{C}_m \text{H}_n \text{F}_p \text{Cl}_q$ where $2m + 2 = n + p + q$:

$$\text{Refrigerant Number: } \quad \text{R-}(m-1)(n+1)(p)$$

• Inorganic Compounds: Numbered as $\text{R-}(700 + \text{Molecular Weight})$:
  • Ammonia ($\text{NH}_3$, $M = 17$): $\text{R-717}$
  • Water ($\text{H}_2\text{O}$, $M = 18$): $\text{R-718}$
  • Carbon Dioxide ($\text{CO}_2$, $M = 44$): $\text{R-744}$
  • Air ($M = 29$): $\text{R-729}$

Environmental Impact Metrics & Global Treaties

1. Ozone Depletion Potential (ODP): Relative index measuring damage to the stratospheric ozone layer compared to trichlorofluoromethane ($\text{R-11}$, baseline $\text{ODP} = 1.0$).
2. Global Warming Potential (GWP): Index measuring thermal radiation trapped in the atmosphere over 100 years relative to carbon dioxide ($\text{CO}_2$, baseline $\text{GWP} = 1.0$).

+-----------------------------------------------------------------------------------------+
|                        REFRIGERANT ENVIRONMENTAL CLASSIFICATION                         |
|                                                                                         |
|   Class        Examples           ODP        GWP (100-yr)    Regulatory Status          |
|   ---------    ----------------   --------   -------------   ------------------------   |
|   CFC          R-11, R-12, R-115  0.6 - 1.0  4,500 - 10,000  BANNED (Montreal Protocol) |
|   HCFC         R-22, R-123        0.02-0.05  700 - 1,800     PHASED OUT (Montreal)      |
|   HFC          R-134a, R-410A     0.00       1,300 - 4,000   PHASE DOWN (Kigali Amend.) |
|   HFO          R-1234yf, R-1234ze 0.00       < 1             Modern Low-GWP Standard    |
|   Natural      R-290 (Propane)    0.00       3               Eco-friendly Hydrocarbons  |
|   Refrigerants R-600a (Isobutane) 0.00       3               Zero ODP, Ultra-low GWP    |
|                R-717 (Ammonia)    0.00       0               High efficiency, toxic     |
|                R-744 (CO2)        0.00       1               Transcritical cycle        |
+-----------------------------------------------------------------------------------------+

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7. Step-by-Step Worked Problems: VCRS Cycle & VARS Thermal Efficiency

Worked Example 1: Standard Industrial VCRS Chiller Performance

A 10 TR R-134a industrial water chilling plant operates on a standard VCRS cycle between an evaporator temperature of $-10^{\circ}\text{C}$ ($P_e = 2.01\text{ bar}$) and a condenser temperature of $+40^{\circ}\text{C}$ ($P_c = 10.17\text{ bar}$). Saturated vapor leaves the evaporator and saturated liquid leaves the condenser. The refrigerant enthalpy values are:

• Saturated vapor at $-10^{\circ}\text{C}$: $h_1 = 392.8\text{ kJ/kg}$, $s_1 = 1.733\text{ kJ/kg}\cdot\text{K}$
• Superheated vapor after isentropic compression at $P_c$: $h_2 = 425.8\text{ kJ/kg}$
• Saturated liquid at $+40^{\circ}\text{C}$: $h_3 = 256.4\text{ kJ/kg}$

Calculate the COP, mass flow rate of refrigerant (kg/s), and compressor power input (kW).

+-----------------------------------------------------------------------------------------+
|                        VCRS CHILLER CALCULATION STEPS                                   |
|                                                                                         |
|   STEP 1: Identify Enthalpies at Key State Points                                       |
|           h1 = 392.8 kJ/kg (Evaporator Exit)                                            |
|           h2 = 425.8 kJ/kg (Compressor Exit)                                            |
|           h3 = 256.4 kJ/kg (Condenser Exit)                                             |
|           h4 = h3 = 256.4 kJ/kg (Expansion Valve Exit, Isenthalpic)                     |
|                                                                                         |
|   STEP 2: Calculate Refrigeration Effect (RE) and Compressor Work (Wc)                  |
|           RE = h1 - h4 = 392.8 - 256.4 = 136.4 kJ/kg                                    |
|           w_c = h2 - h1 = 425.8 - 392.8 = 33.0 kJ/kg                                     |
|                                                                                         |
|   STEP 3: Calculate Coefficient of Performance (COP)                                    |
|           COP = RE / w_c = 136.4 / 33.0 = 4.133                                         |
|                                                                                         |
|   STEP 4: Calculate Total Plant Capacity in kW                                          |
|           Capacity = 10 TR * 3.517 kW/TR = 35.17 kW                                     |
|                                                                                         |
|   STEP 5: Calculate Refrigerant Mass Flow Rate                                          |
|           m_dot_r = Capacity / RE = 35.17 kW / 136.4 kJ/kg = 0.2578 kg/s                |
|                                                                                         |
|   STEP 6: Calculate Compressor Power Input                                              |
|           Power = m_dot_r * w_c = 0.2578 kg/s * 33.0 kJ/kg = 8.507 kW                   |
+-----------------------------------------------------------------------------------------+