Steam

Steam-water mixer: steam flow for in-line direct injection and hot water mixing stations

In direct injection the steam condenses inside the liquid and gives up all its enthalpy, with no heat-transfer surface: consumption follows from the energy balance ṁs·hs + ṁl·hl,in = ṁout·hout, with enthalpies from IAPWS-IF97 and the condensate incorporated into the product as water at the outlet temperature. The calculator covers the in-line injector (liquid flow given) and the hose mixing station (hot water flow given) and checks what limits operation: the pressure for the steam to get in and the outlet saturation for it to condense.

When to use

Use it to estimate the steam for an injector heating a stream of water or another liquid in-line, or for steam-water mixing stations that deliver hot water at a hose. In in-line mode, enter the maximum liquid flow, the pressure at the injection point, the inlet and outlet temperatures and, preferably, the minimum operation — it defines the steam range the injector must control. In station mode, enter the hot water flow per station, the cold water and outlet pressures, and how many stations open at the same time. Manufacturer data (injector minimum ΔP, minimum subcooling, turndown, station minimum steam pressure, maximum steam − water difference) have no default: without them the result is Meets with pending items. The output feeds the Steam line or Steam network with the maximum flow with margin, the minimum flow and the pressure required at the consumer.

What limits a steam-water mixer

In direct injection the steam does not transfer heat through a wall: it condenses inside the liquid and gives up all its enthalpy. That is why the calculation needs no heat-transfer area, UA or steam trap, and consumption follows from an energy balance with IAPWS-IF97 enthalpies. Operation is limited by two pressure conditions: the steam must get in (pressure above the local pressure plus the injector minimum ΔP, with a margin left for the control valve) and must condense (outlet below saturation at the injection-point pressure).

In-line or station

In the in-line injector the liquid flow is given; the calculator returns the steam at maximum and minimum operation, the outlet flow with its condensate share and the steam range to compare with the injector turndown. In the mixing station the hot water flow is given; steam and cold water per station follow, and the network receives the steam of the stations in simultaneous use, with zero minimum flow.

Manufacturer data and status

Minimum ΔP, minimum subcooling, turndown, station minimum steam pressure and maximum steam − water difference come from the catalogue of the selected equipment and have no default. Without them the result is Meets with pending items; with them, each check passes or fails. The design margin multiplies only the flow sent to the steam network.

Formulas and fundamentals

Liquid heat load (in-line) Q = ṁl·(hl,out − hl,in) + Qlosses

Q = load [kW]; ṁl = liquid mass flow [kg/s]; hl,in and hl,out = liquid enthalpies at inlet and outlet [kJ/kg] — for water, from IAPWS-IF97 at the local pressure; for another liquid, cp·(Tout − Tin) with the entered mean cp; Qlosses = optional constant losses [kW]. A volumetric water flow becomes mass flow with the density at the inlet temperature of each scenario.

Injected steam flow (in-line) ṁs = Q / (hs − hc), hc = h_water(Tout, Plocal), ṁout = ṁl + ṁs

hs = steam enthalpy at the valve inlet [kJ/kg] (dry saturated, or the actual value if superheated); hc = enthalpy of the condensed water at the outlet temperature and injection-point pressure [kJ/kg]. There is no isolated h_fg and no steam trap: the condensate leaves in the product, and the outlet flow is liquid plus steam.

Product dilution dilution = ṁs / ṁout · 100%

Share of the outlet flow that came from the steam. For another liquid, the balance takes the product with the entered cp and the condensate as water, with no heat of mixing; the percentage does not validate whether the process accepts the added water.

Mixing station (hose hot water) ṁs = ṁhot·(hhot − hcold) / (hs − hcold), ṁcold = ṁhot − ṁs

ṁhot = hot water flow per station [kg/h]; hcold = cold water enthalpy at the supply pressure (when entered and above the outlet pressure; throttling down to the mixing pressure is isenthalpic); hhot = hot water enthalpy at the outlet pressure. To the network: ṁs,network = ṁs·N_simultaneous·(1 + margin), with zero minimum flow.

Outlet subcooling ΔTsub = Tsat(Plocal) − Tout > 0

Gap between the outlet temperature and saturation at the injection-point pressure (at the station, the outlet pressure). Zero or negative: the mixture boils, steam does not fully condense and consumption is not calculated. The required minimum is manufacturer data; meeting it satisfies their criterion, it does not model condensation inside the injector.

Required pressure and control range (in-line) Preq = Plocal + ΔPmin, Psteam > Preq; range = ṁs,max / ṁs,min ≤ turndown

ΔPmin = injector minimum differential over the local pressure, from the manufacturer [bar]. Preq is at the injector inlet, after the control valve; the supply must be strictly above it to leave a differential across the valve, whose Cv is checked in the Steam line or Steam network. The steam range between maximum and minimum operation is compared with the injector turndown.

Standards & methods

IAPWS R7-97(2012) — IAPWS-IF97: enthalpies, saturation and density of water and steam
Spirax Sarco, The Steam and Condensate Loop — Block 2 (direct steam injection; technical cross-check reference)
NR-13 (Brazil) — documentation reference and interface with the legally qualified professional; LOGOS does not perform legal classification

Typical reference values

Quantity	Typical range	Note
Outlet subcooling	> 0 K	Physical condition checked by LOGOS: zero or negative is an error and consumption is not calculated. The minimum comes from the injector or station manufacturer, with no default (D204).
Steam pressure at the valve inlet (in-line)	> Plocal + ΔPmin	Strictly above, to leave a differential across the control valve (D205). Without the manufacturer minimum ΔP, the pressure required for the network is not defined.
Steam range max/min (in-line)	≤ injector turndown	Turndown entered from the manufacturer, ≥ 1 (D206). Above it, consider two injectors in parallel or another operating range.
Steam − cold water difference (station)	\|Psteam − Pwater\| ≤ manufacturer maximum	The mixing valve only controls with both pressures close to each other (D207). Cold water must also arrive above the outlet pressure.
Design margin	0% to 100%	Multiplies only the flow sent to the steam network; consumption and balances use the real load (D185, D208).
Steam pressure	up to 100 bar(a)	LOGOS Steam product limit; superheated steam cannot be below saturation.
Minimum flow to the network (station)	0 kg/h	Intermittent consumption: the station only consumes while the hose is open.

Worked example

In-line injector heating 20 m³/h of water from 15 °C to 75 °C with steam at 8 bar(g)

Inputs

Application / liquid: In-line / water (IF97) -
Steam pressure at the valve inlet: 8 (dry saturated) bar(g)
Pressure at the injection point: 3 bar(g)
Maximum / minimum liquid flow: 20 / 8 m³/h
Inlet / outlet temperature: 15 / 75 °C
Design margin: 10 %
Manufacturer data (min. ΔP, min. subcooling, turndown): not entered -

Results

Liquid mass flow (maximum) / Δh: 19,985 / 250.9 kg/h / kJ/kg
Heat load (maximum / minimum): 1,392.8 / 557.1 kW
Steam / condensed water at outlet enthalpy: 2,773.1 / 314.3 kJ/kg
Steam at maximum / minimum operation: 2,039.3 / 815.7 kg/h
Outlet flow (maximum operation): 22,024 kg/h (condensate 9.3%)
Outlet subcooling: 68.7 K (Tsat 143.7 °C at 3 bar(g))
Steam range max/min: 2.5:1 -
Maximum flow to the network (with margin): 2,243.2 kg/h
Status: Meets with pending items -

Saturated steam at 8 bar(g) enters at 2,773.1 kJ/kg and leaves as water at 75 °C at 314.3 kJ/kg; each kilogram of steam gives the difference to the liquid. The 20 m³/h of water (19,985 kg/h) need 1,392.8 kW, hence 2,039.3 kg/h of steam at maximum operation and 815.7 kg/h at minimum. The outlet stream grows to 22,024 kg/h: 9.3% of it is incorporated condensate — irrelevant for water, decisive if the product were another liquid. Since the inlet temperature is the same in both scenarios and there are no losses, the steam range (2.5:1) follows the ratio of the liquid flows. With 3 bar(g) at the injection point saturation is 143.7 °C, and the 75 °C outlet has 68.7 K of subcooling: the mixture does not boil. The network receives 2,243.2 kg/h (2,039.3 kg/h + 10%) and 815.7 kg/h at minimum. The result is Meets with pending items because the three manufacturer data are missing: without the minimum ΔP the pressure required for the network is not defined, and the subcooling and the 2.5:1 range are not compared with the injector limits.

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Common mistakes

Entering the steam network pressure as the local pressure. The local pressure is the liquid pressure at the injection point: it sets the outlet saturation and the pressure the steam has to overcome.
Forgetting that the steam needs a differential for the control valve. The supply must be strictly above the local pressure plus the injector minimum ΔP; equality leaves no ΔP for the valve.
Asking for an outlet too hot for the injection-point pressure. With an open hose (0 bar(g)) saturation is close to 100 °C; without subcooling the mixture boils, with noise and hammer, and consumption is not calculated.
Treating injection as if it added no mass. The condensate becomes product: the outlet flow is larger than the liquid flow, and for another liquid that dilution has to be acceptable to the process.
Not entering the minimum operation. Without it the steam range is not calculated and the injector turndown is not checked — exactly where an oversized injector stops controlling.
At a station, sizing the network for a single station when several open together. The network receives steam per station times the stations in simultaneous use.
Expecting a default catalogue value. Minimum ΔP, minimum subcooling, turndown, station minimum pressure and steam − water difference belong to the selected equipment; without them the result has pending items.

Frequently asked questions

How does the calculator find the steam flow of an injector?

With the direct-injection energy balance: steam condenses in the liquid and leaves as water at the outlet temperature and local pressure, so ṁs = (ṁl·Δhl + Qlosses)/(hs − hc). Enthalpies come from IAPWS-IF97. Steam arrives dry saturated (assumption D169: separator with trap ahead of the valve) unless a superheat temperature is entered — then all the superheat goes into the liquid. Losses are optional, in constant kW.

Why is the outlet flow larger than the liquid flow?

Because with direct injection the condensate becomes part of the product: ṁout = ṁl + ṁs. In the example, 19,985 kg/h of water leave as 22,024 kg/h, with 9.3% condensate. For another liquid the calculator shows this dilution as a warning, but does not evaluate whether the process accepts the added water. The injected steam does not return as condensate either: in the plant balance it appears as boiler make-up water.

What is outlet subcooling and why does it block the calculation?

It is Tsat(Plocal) − Tout. If it is zero or negative, the outlet water would be at or above saturation: steam does not fully condense, with flashing, noise and hammer, and the calculator does not calculate consumption. With a positive margin, it still compares the value with the manufacturer minimum subcooling; without that data, the check stays pending. The manufacturer margin is a check criterion, not a model of condensation inside the injector.

What steam pressure does an in-line injector need?

The required pressure is the local pressure plus the injector minimum ΔP, at the injector inlet and after the control valve. The steam pressure at the valve inlet must be strictly above it, to leave a differential across the valve. Steam below the local pressure itself is an error. This is a preliminary check: the valve Cv is checked in the Steam line or Steam network, which receive this required pressure.

How does the mixing station mode work?

You enter the hot water flow per station, and steam and cold water follow from the mass and energy balances. Example: 30 L/min of water at 65 °C from cold water at 20 °C and 4 bar(g), dry saturated steam at 5 bar(g) and an outlet at 0 bar(g) need, per station, 124.0 kg/h of steam and 1,641 kg/h of cold water for 1,765 kg/h of hot water (85.6 kW). With 2 simultaneous stations the network receives 248.1 kg/h, or 272.9 kg/h with a 10% margin, and the minimum flow is zero. The outlet at 0 bar(g) saturates at 100.0 °C, leaving 35.0 K of subcooling; the 1 bar steam − water difference stays pending until the manufacturer maximum is entered.

Does the calculator work for liquids other than water?

Yes, in in-line mode only, with an entered mean cp (and density, if the flow is volumetric). The product uses that cp and the condensate enters as water, with no heat of mixing; this assumes a product compatible with water, complete mixing and properties unchanged by dilution. Subcooling is calculated with water saturation at the local pressure; boiling of the product itself is not checked, because the calculator does not have its vapour pressure.

What does this calculator not do?

It estimates consumption and checks pressure, outlet saturation, turndown and steam − water difference against manufacturer data. It does not select the injector, the mixing valve, the thermal safety device or the hose; it does not calculate the valve Cv (that is done in the Steam line or Steam network); it does not model condensation inside the injector; and it does not cover sparger injection into a tank, which is outside this version. Supply steam is limited to 100 bar(a).

Glossary

Direct steam injection: Heating in which steam is introduced into the liquid itself and condenses there, giving up all its enthalpy; there is no heat-transfer surface, UA, steam trap or stall.
In-line injector: Mixer installed in the pipe that heats a given liquid flow; steam is controlled by a temperature control valve ahead of the injector.
Mixing station: Assembly that mixes steam and cold water through a mixing valve and delivers hot water at a hose; intermittent consumption, only while the hose is open.
Outlet subcooling: Tsat at the injection-point pressure minus the outlet temperature. It must be positive for the steam to condense; the required minimum is manufacturer data.
Dilution (incorporated condensate): Percentage of the outlet flow that came from condensed steam. It does not indicate whether the process accepts the added water.
Injector minimum ΔP: Minimum pressure differential over the local pressure required by the manufacturer; added to the local pressure, it gives the required pressure at the injector inlet.
Injector turndown: Maximum ratio between the maximum and minimum steam flow the injector controls, per the manufacturer; compared with the range between maximum and minimum operation.
Meets with pending items: Status in which consumption was calculated but essential manufacturer data is missing or there is a point of attention; a failed check leads to Does not meet / not viable.