Reference ID: MET-FE8E | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The condenser heat‑load calculation determines the amount of thermal energy that must be removed from a vapor stream to convert it to liquid. This is a fundamental step in the design of heat exchangers, refrigeration cycles, and distillation columns. Accurate sizing of the condenser and its cooling‑water system ensures reliable operation, prevents fouling, and optimizes energy consumption in process plants.
Methodology & Formulas
The calculation follows a straightforward energy‑balance approach:
Convert the vapor mass‑flow rate from a per‑hour basis to a per‑second basis:
\[
\dot{m}_v = \frac{\dot{m}_{v,\;{\rm kg/h}}}{3600}\;{\rm (kg/s)}
\]
Compute the condenser heat load (the rate of latent heat removal):
\[
Q_{\rm cond} = \dot{m}_v \; L_v \;\;{\rm (kW)}
\]
where \(L_v\) is the latent heat of vaporization.
Determine the required cooling‑water mass‑flow rate using the water heat‑capacity equation:
\[
\dot{m}_w = \frac{Q_{\rm cond}}{c_{p,w}\,\Delta T_w}\;\;{\rm (kg/s)}
\]
with \(c_{p,w}\) the specific heat of water and \(\Delta T_w\) the allowable temperature rise of the cooling water.
Optionally, express the water flow rate in more convenient units (e.g., L/s) by dividing by the density of water (≈ 1 kg/L).
Validity Checks & Design Criteria
Parameter
Acceptable Range / Condition
Action if Violated
\(\Delta T_w\) (Cooling‑water temperature rise)
10 °C ≤ \(\Delta T_w\) ≤ 15 °C
Issue a warning; consider redesigning the water‑side flow.
\(\dot{m}_{v,\;{\rm kg/h}}\) (Vapor mass flow)
\(\dot{m}_{v,\;{\rm kg/h}} > 0\)
Terminate calculation with an error.
\(L_v\) (Latent heat)
\(L_v > 0\)
Terminate calculation with an error.
\(c_{p,w}\) (Specific heat of water)
\(c_{p,w} > 0\)
Terminate calculation with an error.
After performing the calculations, the results are typically presented as:
Condenser heat load, \(Q_{\rm cond}\), in kilowatts (kW).
Cooling‑water mass‑flow rate, \(\dot{m}_w\), in kilograms per second (kg/s) or liters per second (L/s).
These values feed directly into the selection of condenser surface area, tube diameter, and pump capacity for the cooling‑water circuit.
Use the latent heat of condensation at the saturation temperature of the vapor entering the condenser. Multiply the total vapor mass flow rate by this latent heat value: Q = m · λ. This gives a conservative heat load in kW or BTU/h that is usually within 5–10 % of the rigorous value for pure components or narrow-boiling mixtures.
Determine the mole fraction of non-condensables in the inlet vapor; this sets the partial pressure of the condensable species.
Adjust the condensation temperature by the dew-point depression caused by the non-condensables.
Calculate the condensable vapor flow that actually condenses; subtract the uncondensed vent flow.
Apply the latent heat to the condensable portion only, then add any sensible heat removed from both gas and liquid phases.
Latent heat of condensation at operating pressure.
Specific heat capacities for vapor and liquid phases.
Thermal conductivity and viscosity of the condensate film.
Vapor–liquid equilibrium data if the mixture is wide-boiling or azeotropic.
Missing any of these can introduce errors >15 % in duty and subsequent exchanger sizing.
Use latent-heat-only when the vapor enters at saturation and the condensate leaves within 2–3 °C of that temperature. Switch to a full enthalpy balance (sensible + latent) when:
There is significant superheat (>10 °C) in the inlet vapor.
Sub-cooling of the condensate is required.
The mixture has a wide boiling range (>30 °C) or multi-component fractionation occurs.
Worked Example – Condenser Heat Load
A small pilot plant condenses 200 kg·h⁻¹ of saturated steam at 100 °C. The latent heat released is removed by cooling water that enters at 20 °C and leaves at 30 °C. Determine the condenser duty and the required cooling-water flow rate.
