Feed Water Enthalpy Calculator

Enter the mass flow rate and specific enthalpy of the feed water into the calculator to determine the feed water enthalpy flow rate (energy rate). You can also solve for mass flow rate or specific enthalpy by entering the other two values.

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Feed Water Enthalpy Flow Rate Formula

The following formula is used to calculate the feed water enthalpy flow rate (energy rate) for a given mass flow rate and specific enthalpy.

\dot{H} = \dot{m} \cdot h

Variables:

• Ḣ is the feed water enthalpy flow rate (kJ/s or kW)
• ṁ is the mass flow rate of feed water (kg/s)
• h is the specific enthalpy of feed water (kJ/kg)

To calculate the feed water enthalpy flow rate, multiply the mass flow rate of the feed water by its specific enthalpy. The specific enthalpy value depends on the water’s temperature and pressure, and is typically obtained from steam tables or thermodynamic property calculators based on the IAPWS-IF97 formulation.

What is Feed Water Enthalpy?

Feed water enthalpy represents the total thermal energy per unit mass carried by water entering a boiler, steam generator, or heat recovery system. In thermodynamic terms, specific enthalpy (h) combines the internal energy of the water with the pressure-volume work required to push the fluid into the system. For liquid water below the boiling point at a given pressure, specific enthalpy is dominated by the sensible heat content and increases roughly linearly with temperature at a rate of about 4.18 kJ per kg per degree Celsius.

The enthalpy flow rate extends this concept to flowing systems. A boiler receiving 25 kg/s of feed water at 150 degrees C (specific enthalpy of approximately 632.2 kJ/kg) carries an enthalpy flow rate of roughly 15,805 kW into the system. That energy does not need to come from fuel combustion, which is why raising the feed water temperature through regenerative heating directly reduces fuel demand.

Feed Water Specific Enthalpy Reference Data

The specific enthalpy of liquid water varies with temperature and, to a lesser degree, with pressure. The table below provides saturated liquid enthalpy values at common feed water temperatures used in industrial and power generation applications. These values are derived from IAPWS-IF97 steam tables.

For compressed liquid water at pressures significantly above the saturation pressure, the enthalpy increases only marginally compared to the saturated value at the same temperature. As a practical approximation, the saturated liquid enthalpy at a given temperature can be used for compressed liquid feed water with less than 0.5% error in most industrial pressure ranges.

Role of Feed Water Enthalpy in Boiler Efficiency

Boiler efficiency is fundamentally determined by the energy balance between the fuel input and the useful steam output. The core thermal output equation for any steam generator is: Boiler Output = mass flow of steam x (h_steam – h_feedwater). This means feed water enthalpy directly offsets the energy the boiler must supply from combustion. The higher the feed water enthalpy entering the boiler, the less fuel is required to reach the target steam conditions.

In quantitative terms, every 6 degrees C (approximately 11 degrees F) increase in feed water temperature reduces fuel consumption by roughly 1%. A facility operating a 50,000 lb/hr boiler producing 150 psig saturated steam (h_steam = 1,195.5 BTU/lb) with feed water at 117 degrees F (h_feedwater = 85.0 BTU/lb) has a per-pound energy requirement of 1,110.5 BTU. Raising the feed water temperature to 180 degrees F (h_feedwater = 148.0 BTU/lb) drops the per-pound requirement to 1,047.5 BTU, a 5.7% reduction in fuel per unit of steam.

Feed Water Heating Systems

Power plants and industrial boiler systems use several methods to raise feed water enthalpy before the water enters the boiler. Each method recovers heat that would otherwise be rejected from the cycle.

Feedwater Heaters (Closed Type) are shell-and-tube heat exchangers where extraction steam from the turbine condenses on the shell side while feed water flows through the tubes. The feed water and steam never mix. Large utility power plants typically employ 6 to 8 stages of closed feed water heating, raising the water temperature from condenser outlet (around 35 to 45 degrees C) to 200 to 250 degrees C before it enters the boiler. Approximately 33% of the thermal efficiency gains in a modern Rankine cycle plant come from this regenerative feed water heating.

Deaerators (Open Feedwater Heaters) serve a dual purpose: they heat the feed water through direct contact with extraction steam, and they remove dissolved oxygen and carbon dioxide that cause corrosion in boiler tubes. The deaerator typically operates at 1.2 to 3.5 bar absolute (105 to 140 degrees C), and since it is a direct-contact heater, the exiting water is at the saturation temperature for the operating pressure.

Economizers are heat exchangers installed in the boiler flue gas path that capture waste heat from the exhaust gases to preheat the feed water. A well-designed economizer can raise feed water temperature by 20 to 30 degrees C and improve overall boiler efficiency by 2 to 4 percentage points. The flue gas exhaust temperature after the economizer should remain above 150 degrees C (approximately 300 degrees F) to avoid sulfuric acid condensation in systems burning sulfur-containing fuels.

Enthalpy Change Across Boiler Zones

The total enthalpy change from feed water inlet to superheated steam outlet can be broken into three distinct zones, each representing a different phase of heat addition. For a boiler operating at 60 bar with feed water entering at 150 degrees C and producing superheated steam at 450 degrees C, the approximate enthalpy contributions are as follows.

In the economizer and preheating zone, liquid feed water is heated from 150 degrees C (h = 632 kJ/kg) to the saturation temperature at 60 bar, which is 275.6 degrees C (h = 1,214 kJ/kg). This represents an enthalpy gain of 582 kJ/kg, accounting for about 22% of the total heat input. In the evaporator zone, the water undergoes phase change from saturated liquid to saturated steam at constant temperature. The latent heat of vaporization at 60 bar is 1,571 kJ/kg, making this the largest single energy addition at about 59% of the total. In the superheater zone, saturated steam at 275.6 degrees C is heated to 450 degrees C. The enthalpy rises from 2,785 kJ/kg (saturated vapor) to roughly 3,302 kJ/kg, adding approximately 517 kJ/kg or about 19% of the total. Across all three zones, the total enthalpy gain is approximately 2,670 kJ/kg, and the useful boiler output equals this value multiplied by the steam mass flow rate.

Common Feed Water Conditions by Application

These values illustrate why feed water enthalpy is not a single fixed number but varies widely depending on the plant design, number of feedwater heater stages, and whether an economizer is installed. Supercritical plants push feed water temperatures highest because their operating pressures allow water to remain liquid well above the normal boiling point, maximizing the regenerative heating benefit.