| Case | mDot (kg/s) | Cp (kJ/kg-K) | Tin -> Tout (degC) | Hvap (kJ/kg) | xvap | Loss (kW) | Eff (%) | LHV (MJ/kg) |
|---|---|---|---|---|---|---|---|---|
| Heater A | 2.5 | 2.1 | 60 -> 320 | 0 | 0.00 | 150 | 80 | 48 |
| Reboiler B | 1.8 | 2.4 | 90 -> 170 | 2250 | 0.25 | 120 | 78 | 50 |
| Preheater C | 4.0 | 1.9 | 25 -> 180 | 0 | 0.00 | 220 | 85 | 42 |
This calculator estimates the heat transferred to the process stream and the fired duty required from the furnace.
Q_useful = mDot * Cp * (Tout - Tin) + mDot * xvap * Hvap
Fired duty required (kW):
Q_fired = (Q_useful + Q_loss) / eta
Fuel rate (kg/h):
mFuel = (Q_fired / 1000) * 3600 / LHV
Where mDot is mass flow (kg/s), Cp is kJ/kg-K, Hvap is kJ/kg, eta is efficiency as a fraction, and LHV is MJ/kg.
- Enter mass flow rate, inlet temperature, and target outlet temperature.
- Provide an average heat capacity for the temperature range.
- If vaporization occurs, enter latent heat and vaporized fraction.
- Add estimated furnace losses and overall thermal efficiency.
- Enter fuel LHV to estimate fuel consumption rate.
- Press Calculate to view results above the form.
For multi-component or strongly temperature-dependent Cp, use a weighted or integrated Cp and treat results as an engineering estimate.
- Assumes steady state and constant average Cp.
- Latent heat term applies to the fraction that changes phase.
- Losses include stack, casing, and auxiliary losses as a single kW input.
- Efficiency represents overall conversion from fired heat to useful transfer.
- Fuel rate uses LHV and does not include excess air corrections.
Heat Duty Scope and Boundaries
This calculator targets steady heating in fired equipment where a stream enters at Tin and leaves at Tout. Useful duty is computed in kW from mass flow and average Cp, then augmented by any vaporization term. Losses are entered as a fixed kW allowance to represent casing radiation, convection, and stack energy not recovered by process coils.
Sensible Heating and Temperature Lift
Sensible duty equals mDot×Cp×ΔT. For example, 2.5 kg/s, Cp 2.1 kJ/kg-K, and a 260 K rise produces about 1365 kW. Negative ΔT indicates cooling service and should be flagged because furnace duty becomes misleading for that case. Maintain consistent Cp units and treat Cp as an averaged property across the temperature range.
Phase Change Contribution
Latent duty is mDot×xvap×Hvap. With 1.8 kg/s, xvap 0.25, and Hvap 2250 kJ/kg, latent heat adds roughly 1013 kW. This term is commonly used for reboilers and partial vaporization heaters. If no phase change occurs, set Hvap and xvap to zero to avoid overstating total duty.
Efficiency and Fired Duty
Fired duty scales inversely with efficiency, Qfired=(Quseful+Qloss)/eta. A 10 percentage-point drop in efficiency from 80% to 70% increases fired duty by about 14.3%. Track efficiency using stack oxygen, flue temperature, and burner tuning data so that duty estimates remain aligned with actual fuel firing rates.
Fuel Rate from Heating Value
Fuel rate is estimated using LHV: mfuel=(Qfired/1000)×3600/LHV. If Qfired is 2000 kW and fuel LHV is 48 MJ/kg, fuel use is near 150 kg/h. This is an approximation; real plants should adjust for excess air, moisture, and fuel composition variability.
Operational Use and Validation
Use the results to compare scenarios, not to replace detailed heater simulations. Validate against coil inlet/outlet temperatures, flow measurements, and fuel flow meters. When losses are uncertain, bracket them with low and high values and observe the fired duty spread. Combine this tool with trending to detect fouling, control drift, or efficiency deterioration. For quick screening, run the calculator at minimum, normal, and maximum throughput. Record Quseful, Qfired, and fuel rate as baseline KPIs. During turnarounds, recalibrate Cp and losses with test runs, and update efficiency assumptions to reflect burner and air-preheater changes so projected firing stays consistent with measured plant performance.
1) What does “useful heat” represent?
Useful heat is the energy transferred into the process stream for sensible heating plus any latent duty. It excludes casing and stack losses that do not raise the process enthalpy.
2) Why can I use degC for temperature?
The calculation uses only the temperature difference (Tout − Tin). A change of 1 degC equals a change of 1 K, so the delta is consistent for sensible duty.
3) How should I choose Cp?
Use an average Cp over the operating temperature range, preferably from property data or simulation. For mixtures, use a mass-weighted Cp and update it if composition changes materially.
4) What is a reasonable efficiency value?
Overall heater efficiency varies by design and operation, often 70–90%. Use plant test results when available. If uncertain, run sensitivity cases to see how efficiency shifts affect fired duty.
5) How accurate is the fuel rate estimate?
Fuel rate uses LHV and assumes the fired duty is fully supplied by the fuel. It does not model excess air, moisture, or variable composition, so treat it as an estimate for screening and comparison.
6) Can I include multiple phase changes?
This tool includes a single latent term based on a vaporized fraction and Hvap. For multiple phase changes or wide boiling ranges, approximate with an effective Hvap and validate using a detailed heat balance.