Water Heating Using Steam Calculator

Detailed Description

This calculator estimates the benefit of using vent steam for water heating applications. The calculation uses steam and water properties, flow rates, pressures, temperatures, and system efficiencies. The method is based on standard industrial practice for waste heat recovery in steam systems.

Water Heating Using Steam Diagram

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The calculation follows a top-down approach:

1. Steam and Water Properties - Determine steam enthalpies at inlet conditions and saturation properties, boiling point temperature, and makeup water enthalpy
2. Outlet Water Temperature - Calculate heated water outlet temperature based on energy balance
3. Boiling Point Check - Verify outlet water temperature is below safe boiling point threshold
4. Bypass Steam Flow - Calculate bypass steam flow if boiling point is exceeded (conditional)
5. Heat Gain Rate - Determine the rate of heat transfer to the water
6. Energy Saved in Domestic Water Heater - Calculate annual energy savings in the water heating system
7. Energy Saved in Boiler - Calculate annual energy savings from reduced boiler makeup water heating
8. Water Saved - Calculate annual water savings from condensate return

Relevant formulas and symbol definitions are documented below.

Outlet Water Temperature

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Outlet water temperature based on energy balance between steam and water.

The outlet water temperature is calculated by adding the temperature rise to the inlet water temperature. The temperature rise is determined by the energy transferred from the condensing steam (enthalpy difference) divided by the heat capacity of the water. Water specific heat is physics::si::kSpecificHeatWater (4.1796 kJ/(kg·K)).

\begin{equation}\label{eq:water-heating-steam-outlet-temp} T_{w,out} = T_{w,in} + \frac{(h_{s,in} - h_{s,out}) \cdot \dot{m}_{steam}}{C_{p,w} \cdot 1000 \cdot \dot{V}_{water}}\end{equation}

Symbols

\(T_{w,out}\)	Outlet water temperature \([\unit{ \kelvin}]\)
\(T_{w,in}\)	Inlet water temperature \([\unit{ \kelvin}]\)
\(h_{s,in}\)	Inlet steam specific enthalpy (saturated vapor) \([\unit{ \kilo\joule\per\kilogram}]\)
\(h_{s,out}\)	Outlet steam specific enthalpy (saturated liquid/condensate) \([\unit{ \kilo\joule\per\kilogram}]\)
\(\dot{m}_{steam}\)	Steam mass flow rate \([\unit{ \kilogram\per\hour}]\)
\(C_{p,w}\)	Water specific heat - see physics::si::kSpecificHeatWater \([\unit{ \kilo\joule\per\kilogram\kelvin}]\)
\(\dot{V}_{water}\)	Water volumetric flow rate \([\unit{ \meter\cubed\per\hour}]\)

Safe Boiling Point Temperature

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Safe operating temperature threshold to prevent boiling.

The safe boiling point temperature is calculated as 96.328% of the saturation temperature at the outlet water pressure. This safety margin prevents the outlet water from reaching the boiling point, which could cause operational issues in the heat exchanger. The saturation temperature is determined from steam tables based on the outlet water pressure.

\begin{equation}\label{eq:water-heating-steam-safe-boiling-point} T_{bp,safe} = 0.96328 \cdot T_{sat}(P_{w,out})\end{equation}

Symbols

\(T_{bp,safe}\)	Safe boiling point temperature \([\unit{ \kelvin}]\)
\(T_{sat}\)	Saturation temperature at outlet pressure \([\unit{ \kelvin}]\)
\(P_{w,out}\)	Outlet water pressure \([\unit{ \mega\pascal\abs}]\)

Heat Gain Rate

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Rate of heat transfer from steam to water (normal operation).

The heat gain rate is calculated as the product of the steam mass flow rate and the enthalpy difference between inlet steam (saturated vapor) and outlet condensate (saturated liquid). This represents the latent heat of condensation transferred to the water. This formula is used when the outlet water temperature is below the safe boiling point.

\begin{equation}\label{eq:water-heating-steam-heat-gain-rate} \dot{Q}_{gain} = (h_{s,in} - h_{s,out}) \cdot \dot{m}_{steam}\end{equation}

Symbols

\(\dot{Q}_{gain}\)	Heat gain rate \([\unit{ \kilo\joule\per\hour}]\)
\(h_{s,in}\)	Inlet steam specific enthalpy (saturated vapor) \([\unit{ \kilo\joule\per\kilogram}]\)
\(h_{s,out}\)	Outlet steam specific enthalpy (saturated liquid/condensate) \([\unit{ \kilo\joule\per\kilogram}]\)
\(\dot{m}_{steam}\)	Steam mass flow rate \([\unit{ \kilogram\per\hour}]\)

Adjusted Heat Gain Rate (If Boiling Point Exceeded)

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Rate of heat transfer when boiling point is exceeded.

If the calculated outlet water temperature exceeds the safe boiling point, the heat gain rate is recalculated based on the temperature rise limited to the safe boiling point. The adjusted heat gain rate uses the water heat capacity, temperature difference, and volumetric flow rate. The factor of 1000 converts the water density from kg/m³ to proper units.

\begin{equation}\label{eq:water-heating-steam-adjusted-heat-gain-rate} \dot{Q}_{gain,adj} = 1000 \cdot C_{p,w} \cdot (T_{bp,safe} - T_{w,in}) \cdot \dot{V}_{water}\end{equation}

Symbols

\(\dot{Q}_{gain,adj}\)	Adjusted heat gain rate \([\unit{ \kilo\joule\per\hour}]\)
\(C_{p,w}\)	Water specific heat - see physics::si::kSpecificHeatWater \([\unit{ \kilo\joule\per\kilogram\kelvin}]\)
\(T_{bp,safe}\)	Safe boiling point temperature \([\unit{ \kelvin}]\)
\(T_{w,in}\)	Inlet water temperature \([\unit{ \kelvin}]\)
\(\dot{V}_{water}\)	Water volumetric flow rate \([\unit{ \meter\cubed\per\hour}]\)

Bypass Steam Flow

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Excess steam flow that must be bypassed to prevent boiling.

When the outlet water temperature would exceed the safe boiling point, some steam must be bypassed around the heat exchanger to limit the heat transfer. The bypass steam flow is calculated as the difference between the total steam flow and the steam flow required to achieve the safe boiling point temperature. This is only calculated when the boiling point warning flag is triggered.

\begin{equation}\label{eq:water-heating-steam-bypass-steam-flow} \dot{m}_{bypass} = \dot{m}_{steam} - \frac{\dot{Q}_{gain,adj}}{h_{s,in} - h_{s,out}}\end{equation}

Symbols

\(\dot{m}_{bypass}\)	Bypass steam flow \([\unit{ \kilogram\per\hour}]\)
\(\dot{m}_{steam}\)	Total steam mass flow rate \([\unit{ \kilogram\per\hour}]\)
\(\dot{Q}_{gain,adj}\)	Adjusted heat gain rate \([\unit{ \kilo\joule\per\hour}]\)
\(h_{s,in}\)	Inlet steam specific enthalpy (saturated vapor) \([\unit{ \kilo\joule\per\kilogram}]\)
\(h_{s,out}\)	Outlet steam specific enthalpy (saturated liquid/condensate) \([\unit{ \kilo\joule\per\kilogram}]\)

Energy Saved in Domestic Water Heater

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Annual energy savings in the domestic water heating system.

The energy saved in the domestic water heater (DWH) is calculated by multiplying the heat gain rate by the annual operating hours and dividing by the water heater efficiency. The division by efficiency accounts for the fuel energy that would have been required to provide the same amount of useful heat. This represents the primary energy savings from using waste steam instead of conventional water heating.

\begin{equation}\label{eq:water-heating-steam-energy-saved-dwh} E_{saved,DWH} = \frac{\dot{Q}_{gain} \cdot t_{op}}{\eta_{heater}}\end{equation}

Symbols

\(E_{saved,DWH}\)	Annual energy saved in domestic water heater \([\unit{ \kilo\joule\per\year}]\)
\(\dot{Q}_{gain}\)	Heat gain rate \([\unit{ \kilo\joule\per\hour}]\)
\(t_{op}\)	Operating hours per year \([\unit{ \hour\per\year}]\)
\(\eta_{heater}\)	Water heater efficiency (fraction) \([\unit{ \unitless}]\)

Energy Saved in Boiler

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Annual energy savings in the boiler from condensate return.

The energy saved in the boiler is calculated from the condensate returned to the boiler system. By returning hot condensate instead of using cold makeup water, less energy is needed to generate steam. The calculation multiplies the net steam flow (excluding bypass), the enthalpy difference between condensate and makeup water, and the operating hours, then divides by the boiler efficiency. The net steam flow accounts for the usable condensate that can be returned to the boiler.

\begin{equation}\label{eq:water-heating-steam-energy-saved-boiler} E_{saved,boiler} = \frac{(\dot{m}_{steam} - \dot{m}_{bypass}) \cdot (h_{s,out} - h_{makeup}) \cdot t_{op}}{\eta_{boiler}}\end{equation}

Symbols

\(E_{saved,boiler}\)	Annual energy saved in boiler \([\unit{ \kilo\joule\per\year}]\)
\(\dot{m}_{steam}\)	Steam mass flow rate \([\unit{ \kilogram\per\hour}]\)
\(\dot{m}_{bypass}\)	Bypass steam flow \([\unit{ \kilogram\per\hour}]\)
\(h_{s,out}\)	Outlet steam specific enthalpy (saturated liquid/condensate) \([\unit{ \kilo\joule\per\kilogram}]\)
\(h_{makeup}\)	Makeup water specific enthalpy \([\unit{ \kilo\joule\per\kilogram}]\)
\(t_{op}\)	Operating hours per year \([\unit{ \hour\per\year}]\)
\(\eta_{boiler}\)	Boiler efficiency (fraction) \([\unit{ \unitless}]\)

Water Saved

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Annual water savings from condensate return.

The water saved is calculated from the condensate that can be returned to the boiler instead of being discharged. This is the net steam flow (excluding bypass) converted to volumetric flow and multiplied by the operating hours. The division by 1000 converts the mass flow (kg/hr) to volumetric flow (m³/hr) assuming water density of 1000 kg/m³. Returning condensate reduces the need for makeup water and provides both water conservation and energy savings benefits.

\begin{equation}\label{eq:water-heating-steam-water-saved} V_{saved} = \frac{(\dot{m}_{steam} - \dot{m}_{bypass}) \cdot t_{op}}{1000}\end{equation}

Symbols

\(V_{saved}\)	Annual water saved \([\unit{ \meter\cubed\per\year}]\)
\(\dot{m}_{steam}\)	Steam mass flow rate \([\unit{ \kilogram\per\hour}]\)
\(\dot{m}_{bypass}\)	Bypass steam flow \([\unit{ \kilogram\per\hour}]\)
\(t_{op}\)	Operating hours per year \([\unit{ \hour\per\year}]\)

Modules
	Outlet Water Temperature Formula
	Outlet water temperature based on energy balance between steam and water.
	Safe Boiling Point Temperature Formula
	Safe operating temperature threshold to prevent boiling.
	Heat Gain Rate Formula
	Rate of heat transfer from steam to water (normal operation).
	Adjusted Heat Gain Rate Formula
	Rate of heat transfer when boiling point is exceeded.
	Bypass Steam Flow Formula
	Excess steam flow that must be bypassed to prevent boiling.
	Energy Saved in Domestic Water Heater Formula
	Annual energy savings in the domestic water heating system.
	Energy Saved in Boiler Formula
	Annual energy savings in the boiler from condensate return.
	Water Saved Formula
	Annual water savings from condensate return.

Files
file	water_heating_using_steam.h
	Water heating using vent steam calculations for process heating systems.

Namespaces
namespace	water_heating_using_steam
	Water heating using vent steam calculations for process heating systems.

Classes
struct	water_heating_using_steam::WaterHeatingUsingSteamResults
	Results of the water heating using steam calculation. More...

Functions
WaterHeatingUsingSteamResults	water_heating_using_steam::waterHeatingUsingSteam (double pressure_steam_in, double flow_steam_rate, double temperature_water_in, double pressure_water_out, double flow_water_rate, double temp_makeup_water, double pres_makeup_water, double eff_water_heater, double eff_boiler, double operating_hours)
	Calculates energy savings from using vent steam to heat water using a steam to liquid heat exchanger.

Function Documentation

waterHeatingUsingSteam()

WaterHeatingUsingSteamResults water_heating_using_steam::waterHeatingUsingSteam	(	double	pressure_steam_in,
		double	flow_steam_rate,
		double	temperature_water_in,
		double	pressure_water_out,
		double	flow_water_rate,
		double	temp_makeup_water,
		double	pres_makeup_water,
		double	eff_water_heater,
		double	eff_boiler,
		double	operating_hours
	)

Uses process parameters to estimate the benefit of using vent steam for water heating and boiler operation.

Parameters

[in]	pressure_steam_in	Inlet steam pressure \([\unit{MPaa}]\)
[in]	flow_steam_rate	Steam flow rate \([\unit{kg/hr}]\)
[in]	temperature_water_in	Inlet water temperature \([\unit{K}]\)
[in]	pressure_water_out	Outlet water pressure \([\unit{MPaa}]\)
[in]	flow_water_rate	Water flow rate \([\unit{m3/hr}]\)
[in]	temp_makeup_water	Makeup water temperature \([\unit{K}]\)
[in]	pres_makeup_water	Makeup water pressure \([\unit{MPaa}]\)
[in]	eff_water_heater	Water heater efficiency (fraction)
[in]	eff_boiler	Boiler efficiency (fraction)
[in]	operating_hours	Operating hours \([\unit{hr}]\)

Returns

WaterHeatingUsingSteamResults struct with all calculated outputs.