Heat Recovery from Refrigeration

Reference ID: MET-863F | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

Heat recovery from refrigeration systems is a critical process engineering strategy used to improve the overall energy efficiency of industrial facilities. By capturing the thermal energy rejected by the condenser—which would otherwise be dissipated into the atmosphere via cooling towers or air‑cooled condensers—plants can pre‑heat process water for applications such as equipment sanitation, boiler feed, or facility cleaning. A related approach is the aqua‑ammonia cycle for waste heat utilization, which further expands the opportunities to reclaim low‑grade heat.

This calculation is typically employed during the preliminary design phase of heat integration projects. It allows engineers to determine the required heat exchanger surface area, verify thermodynamic feasibility against the Second Law of Thermodynamics, and size the necessary fluid flow rates to meet specific process heating demands, often using a condenser heat load calculation.

Methodology & Formulas

The calculation follows a steady-state energy balance approach. The heat transfer rate (\(\dot{Q}\)) is governed by the sensible heat gain of the water stream and the total enthalpy change of the refrigerant across the condenser. For preliminary design, the refrigerant-side duty is often approximated by its latent heat of condensation (\(h_{fg}\)) alone; however, engineers should be aware that the actual condenser duty also includes desuperheating and subcooling. When these sensible contributions are significant, the total specific enthalpy difference (\(\Delta h_{cond}\)) should replace \(h_{fg}\) in the refrigerant mass flow calculation.

The required mass flow rate of the water (\(\dot{m}_{w}\)) is derived from the energy balance equation:

\[ \dot{m}_{w} = \frac{\dot{Q}}{c_{p,w} \cdot (T_{w,out} - T_{w,in})} \]

To determine the heat exchanger size, the Logarithmic Mean Temperature Difference (\(\Delta T_{lm}\)) is calculated assuming the refrigerant condenses at a constant temperature (\(T_{cond}\)):

\[ \Delta T_{lm} = \frac{(T_{cond} - T_{w,in}) - (T_{cond} - T_{w,out})}{\ln\left(\frac{T_{cond} - T_{w,in}}{T_{cond} - T_{w,out}}\right)} \]

The required heat transfer area (A) is then determined using the overall heat transfer coefficient (U), and understanding the heat recovery efficiency in the regeneration section is essential for accurate sizing; note that  Ė is converted from kW to W by the factor 1000 to maintain unit consistency with U in W/(m²·K).

\[ A = \frac{\dot{Q} \cdot 1000}{U \cdot \Delta T_{lm}} \]

Finally, as a first approximation the refrigerant mass flow rate (\(\dot{m}_{r}\)) is calculated using the latent heat of vaporization (\(h_{fg}\)) at the condensing pressure. For systems with large discharge superheat or significant subcooling, replace \(h_{fg}\) with the total enthalpy difference \((h_{inlet} - h_{outlet})\) for a more accurate result:

\[ \dot{m}_{r} \approx \frac{\dot{Q}}{h_{fg}} \]

Constraint/Regime	Condition	Engineering Significance
Second Law Violation	\(T_{w,out} \geq T_{cond}\)	Heat transfer is physically impossible; outlet water temperature must be lower than the condensing temperature.
Approach Temperature	\((T_{cond} - T_{w,out}) < \Delta T_{min}\)	Insufficient driving force for heat transfer; requires an impractically large heat exchanger area. The minimum approach temperature \(\Delta T_{min}\) is typically 3–5 °C for shell-and-tube condensers.
Water Velocity	\(v_{w} \approx 1.0 - 3.0 \text{ m/s}\)	Recommended range to balance heat transfer efficiency against fouling and pressure drop.

Heat recovery captures the thermal energy typically rejected into the atmosphere by the condenser and repurposes it for secondary processes. This reduces the load on primary heating systems and lowers the total energy intensity of the facility. Key benefits include:

Reduction in natural gas or electricity consumption for water heating.
Lowering the thermal load on cooling towers or evaporative condensers.
Improved system coefficient of performance (COP) by optimizing discharge pressures.

A desuperheater recovers only the sensible superheat from the compressor discharge gas, upstream of the condenser. Integrating a desuperheater requires careful analysis of the refrigerant state and pressure drop. Process engineers should evaluate the following:

Ensuring the desuperheater is installed between the compressor discharge and the condenser inlet.
Maintaining sufficient discharge temperature to prevent refrigerant condensation within the heat recovery unit.
Calculating the impact of additional piping pressure drop on compressor power consumption.
Verifying that the secondary fluid loop is isolated to prevent cross-contamination.

The feasibility of heat recovery is heavily dependent on the thermodynamic properties of the refrigerant, specifically the discharge temperature and the critical point. Engineers must monitor:

The temperature glide of the refrigerant, which affects the heat exchanger approach temperature.
The discharge gas temperature, which determines the maximum grade of heat available for recovery.
The compatibility of the refrigerant with heat exchanger materials to prevent corrosion or degradation.

To estimate the available heat, you must perform a mass and energy balance on the discharge side of the compressor. Use the following methodology:

Determine the mass flow rate of the refrigerant using the compressor capacity and enthalpy change.
Calculate the enthalpy difference between the compressor discharge state and the saturation state at the condensing pressure.
Apply the heat exchanger effectiveness factor to account for thermal losses.
Verify the result against the secondary fluid flow rate and temperature rise requirements.

Worked Example: Heat Recovery from an Ammonia Refrigeration Condenser

A food plant uses an ammonia (R717) refrigeration system. The condenser operates at a condensing temperature of 35 °C and rejects 500 kW of heat. The plant intends to pre-heat cleaning water from 15 °C to 30 °C using a counterflow shell-and-tube heat exchanger. The overall heat transfer coefficient is 1500 W/(m²·K). The following calculations determine the required water flow rate, heat transfer area, and refrigerant mass flow. Note: For this preliminary estimate, the total heat rejected is assumed to come entirely from latent condensation (neglecting desuperheating and subcooling). The approach temperature of 5.0 °C exactly equals the specified minimum (\(\Delta T_{min} = 5.0\) °C); this is at the boundary of feasible design and may require a larger area or a slightly lower water outlet setpoint in practice.

Known parameters
\(\dot{Q}\) = 500.0 kW
\(T_{cond}\) = 35.0 °C
\(T_{w,in}\) = 15.0 °C
\(T_{w,out}\) = 30.0 °C
\(c_{p,w}\) = 4.18 kJ/(kg·K)
\(U\) = 1500.0 W/(m²·K)
\(h_{fg}\) = 1140.0 kJ/kg (ammonia at 35 °C)
Conversion factor: 1 L/min water ≈ 0.0167 kg/s
Minimum approach temperature, \(\Delta T_{min}\): 5.0 °C

Determine required water flow rate.
From the heat balance on the water side: \[ \dot{m}_{w} = \frac{\dot{Q}}{c_{p,w} \cdot (T_{w,out} - T_{w,in})} \] Using the given values, the water temperature difference \(\Delta T_{w}\) = 15.0 °C. The mass flow rate is \[ \dot{m}_{w} = 7.974\ \text{kg/s}. \] Converting to volumetric flow: \[ \dot{m}_{w,\text{L/min}} = 477.514\ \text{L/min}. \]
Calculate log-mean temperature difference.
For counterflow with pure condensation, the terminal temperature differences are: \[ \Delta T_{1} = T_{cond} - T_{w,in} = 20.0\ \text{°C}, \quad \Delta T_{2} = T_{cond} - T_{w,out} = 5.0\ \text{°C}. \] The log-mean temperature difference is \[ \Delta T_{lm} = \frac{\Delta T_{1} - \Delta T_{2}}{\ln(\Delta T_{1} / \Delta T_{2})} = 10.820\ \text{°C}. \]
Estimate required heat transfer area.
The heat transfer equation is: \[ \dot{Q} = U \cdot A_{req} \cdot \Delta T_{lm}. \] Rearranging for area and converting \(\dot{Q}\) to watts (×1000): \[ A_{req} = \frac{\dot{Q} \times 1000}{U \cdot \Delta T_{lm}} = 30.807\ \text{m}^{2}. \]
Check refrigerant mass flow (latent-heat approximation).
Assuming all heat rejected is due to condensation at constant temperature: \[ \dot{m}_{r} \approx \frac{\dot{Q}}{h_{fg}} = 0.439\ \text{kg/s}. \]

Final Summary

Water flow rate: 7.974 kg/s (477.514 L/min)
Log-mean temperature difference: 10.820 °C
Required heat transfer area: 30.807 m²
Refrigerant mass flow (latent-heat approx.): 0.439 kg/s

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

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