Steam

Steam-heated heat exchanger: consumption, steam-space pressure and stall

The steam consumption of a heat exchanger comes from the energy balance: the load on the heated-liquid side, plus losses, divided by the enthalpy difference between the steam entering the control valve and the condensate leaving the steam space (IAPWS-IF97). With U and A — or the design pressure — the calculator finds the steam-space pressure at each load and checks drainage stall.

When to use

Use it for shell-and-tube or plate exchangers in which steam condenses and heats a liquid, with temperature control on the steam side. The calculator gives three levels of answer depending on the data available: consumption only (conservative estimate, condensate assumed saturated at the supply pressure); performance, from the design steam-space pressure (required UA and, with U, the area) or from U and A on the data sheet (required condensing temperature and pressure); and part load with stall, when the minimum operation and the drain back pressure are entered. The results feed the steam network (maximum flow with margin, minimum flow and set point) and the steam trap check (maximum and minimum condensate, steam-space pressure at minimum). Condensate-side control is not covered in this version (D181), and supply steam is limited to 100 bar(a).

What the calculator answers

A steam-heated exchanger with steam-side control has three design questions: how much steam it consumes, at what pressure the steam must sit inside the equipment and whether condensate keeps draining as the load falls. The calculator answers all three in the order the data appear in a project — from consumption, which needs only the process side, to stall, which needs the exchanger performance and the drain back pressure.

Consumption: enthalpy balance, not latent heat

The load comes from the heated-liquid side. For water, the enthalpy change is calculated with IAPWS-IF97 at the process pressure, which is also used to check that the water does not boil at the outlet. For another liquid, the entered mean cp is used (and the density, if the flow is volumetric); in that case non-boiling is not evaluated. Equipment losses are added as a percentage of the load.

The required steam is ṁ_s = Q/(h_inlet − h_condensate). Steam enters the control valve dry saturated (assumption D169: separator with trap ahead of the valve) or superheated, if the temperature is entered; condensate leaves saturated at the steam-space pressure, or subcooled by the entered ΔT.

Performance and part load

Because steam condenses at constant temperature, the relation between load and condensing temperature is closed: T_s = T_out + (T_out − T_in)/(e^NTU − 1). With constant UA, the calculator walks the declared load-reduction trajectory — reduced flow, hotter inlet or both together — and obtains the steam-space pressure at each point. The load of each point is the calculated heat load, never the interpolation parameter.

Checks and honest limits

Stall: steam-space pressure ≤ total back pressure, point found by bisection after a sign check; no trap ΔP added.
Vacuum: warning with drainage guidance (vacuum breaker and gravity, or pump-trap).
Supply above the set point, MAWP (set point and supply), maximum steam-side temperature (steam after the isenthalpic valve) and non-boiling of water.
Out of scope: condensate-side control, desuperheating and subcooling zones in UA, trap capacity and safety valve sizing.

Formulas and fundamentals

Process-side heat load Q = ṁ·(h_out − h_in)·(1 + losses/100)

Q = heat load [kW]; ṁ = liquid mass flow [kg/s]; h_in, h_out = liquid enthalpies at inlet and outlet [kJ/kg]; losses = equipment losses to ambient [% of the process load]. For water, Δh comes from IAPWS-IF97 at the process-side pressure (which is why the process pressure is mandatory); for another liquid, Δh = cp·ΔT with the entered mean cp. Flow in m³/h is converted with the density at the inlet temperature.

Steam consumption from the enthalpy balance ṁ_s = Q / (h_s − h_c)

ṁ_s = steam flow [kg/s]; h_s = enthalpy of the steam at the control valve inlet [kJ/kg] — dry saturated (D169) or superheated, if the temperature is entered; h_c = condensate enthalpy [kJ/kg], saturated liquid at the steam-space pressure or subcooled by the entered ΔT. Latent heat alone is not used (D177): the valve is isenthalpic, so h_s also holds inside the equipment, at the lower pressure.

Number of transfer units NTU = UA / (ṁ·c̄p), c̄p = Δh/ΔT

UA = overall coefficient times area [kW/K]; ṁ·c̄p = heat capacity rate of the process stream [kW/K], with the mean cp taken from Δh itself. It measures the thermal size of the exchanger against the load: a higher NTU allows colder steam (lower pressure) for the same load.

Required condensing temperature (isothermal steam side) T_s = T_out + (T_out − T_in) / (e^NTU − 1) ⇔ UA = ṁ·c̄p·ln[(T_s − T_in)/(T_s − T_out)]

Closed ε–NTU form with one side of infinite capacity: since steam condenses at constant temperature, it holds for any arrangement (shell and tube or plate). With U and A known it gives T_s [°C] and the steam-space pressure P = P_sat(T_s); with the design pressure it gives the required UA (and A = UA/U if U is entered).

Log-mean temperature difference (LMTD) LMTD = (T_out − T_in) / ln[(T_s − T_in)/(T_s − T_out)]

LMTD [K] between steam condensing at T_s and the liquid going from T_in to T_out. With one isothermal side the correction factor F is 1 for any arrangement. This is the physics that decides stall (D184), with constant U across the load range.

Stall condition stall: T_s(load) ≤ T_sat(P_b), P_b = P_return + ρ_l·g·z + ΔP_line

P_b = total drain back pressure — entered directly or summed from the return pressure, the condensate column z after the trap (ρ_l of saturated liquid at the return pressure) and the flow loss in the condensate line (D188). No trap ΔP is added; trap capacity is a separate check against the manufacturer curve.

Standards & methods

IAPWS R7-97(2012) — IAPWS-IF97: enthalpy of steam, condensate and process water; saturation in the steam space
Spirax Sarco, The Steam and Condensate Loop — Block 13, Condensate Removal (technical reference; stall chart used only as a cross-check)
NR-13 (Brazil) — documentation reference and interface with the legally qualified professional (PLH); LOGOS does not perform legal classification nor replace the equipment construction code

Typical reference values

Quantity	Typical range	Note
LMTD correction factor F	1	Isothermal steam side (condensation at constant T): F = 1 for shell and tube or plate. Desuperheating and subcooling zones are not modelled in UA.
Supply steam pressure	up to 100 bar(a)	LOGOS Steam product limit; above it the input is rejected.
Stall load — arithmetic chart × LMTD (Spirax Ex. 13.6.1)	55 % × 51.8 %	Source: Spirax Sarco, Block 13. The arithmetic mean anticipates stall; with constant U the LMTD form is exact and decides the verdict (D184/D222).
Exact consumption × by h_fg (Spirax, selecting the trap, supplier Y)	496.0 kg/h × 497.4 kg/h	With supply above the steam-space pressure, the exact balance needs less steam than Q/h_fg(P_space). Comparison recorded in the LOGOS code.
Back pressure of a vented condensate tank	0 bar(g)	Example from the calculator help for the total back pressure.
Theoretical extension of the stall curve	down to 5 % load	Only in the pure modes (reduced flow or hotter inlet), below the declared minimum. The combined trajectory has no extension.

Worked example

Heating water from 20 to 80 °C in a shell-and-tube exchanger, with U and A from the data sheet

Inputs

Exchanger type: shell and tube -
Steam at the valve inlet (dry saturated): 8 bar(g)
Heated fluid: water, process-side pressure: 3 bar(g)
Maximum / minimum process flow: 20 / 12 m³/h
Inlet / outlet temperature: 20 / 80 °C
Service U × heat-transfer area: 2,000 × 8 W/(m²·K) × m²
Total drain back pressure: 0 bar(g)
Equipment losses / design margin: 2 / 10 %
Steam-space MAWP / max. steam-side T: 10 / 200 bar(g) / °C

Results

Heat load (process + losses): 1,391.8 + 27.8 = 1,419.6 kW
Steam at maximum load: 2,342.0 kg/h
Maximum flow with margin (to the network): 2,576.2 kg/h
Set point at the consumer (T_s): 2.64 (140.4 °C) bar(g)
UA / NTU / LMTD: 16.0 / 0.690 / 87.0 kW/K / - / K
Minimum operation: load, steam-space pressure, steam: 60 % · 0.32 bar(g) · 1,321.2 kg/h
Stall: no stall in the declared range (below 49.7 %) % of load
Status: Meets -

The 20 m³/h of water enter at 998.3 kg/m³, i.e. 19,966.9 kg/h; the IF97 Δh at 3 bar(g) is 250.9 kJ/kg and the process load 1,391.8 kW, which with 2 % losses becomes 1,419.6 kW. Dry saturated steam at 8 bar(g) has h = 2,773.1 kJ/kg, and the real consumption is 2,342.0 kg/h — the network receives 2,576.2 kg/h, because only that flow carries the 10 % margin. With UA = 16 kW/K (NTU 0.690), the steam must condense at 140.4 °C: the valve set point is 2.64 bar(g), well below the 8 bar(g) supply. At minimum (12 m³/h, 60 % load) the steam-space pressure falls to 0.32 bar(g), still above the atmospheric return (T_sat 99.97 °C). Stall would only appear below 49.7 % load, on the theoretical extension below the declared minimum; the Spirax arithmetic chart would indicate 55.3 %, earlier, and is kept only as a reference. The water does not boil (saturation at 143.7 °C on the process side, 63.7 K margin), the throttled steam reaches the equipment at 157.9 °C (below 200 °C), and set point and supply stay below the 10 bar(g) MAWP: all checks were done and passed. If the load can fall below 49.7 % during start-up, shutdown or control failure, drainage must be assessed in that condition.

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Common mistakes

Entering the steam-space pressure in the supply field. The field asks for the pressure arriving at the control valve INLET (from the network or the line); the steam-space pressure is a result — or the design value from the data sheet, on the Performance tab.
Computing consumption from latent heat alone. The correct balance is Q/(h_inlet − h_condensate) with IAPWS-IF97 enthalpies: the enthalpy of the supply steam, which arrives at a higher pressure, is not that of saturated steam in the steam space.
Guessing U from the exchanger type. U depends on fouling, velocity and geometry and must come from the data sheet. Without U and A, use the design steam-space pressure or the consumption-only mode.
Leaving the condensate line loss out of the back pressure by components. The back pressure is underestimated and stall appears to occur at a lower load than the real one.
Applying the design margin to the set point or the stall. The margin multiplies only the flow sent to the network (valve and line sizing); consumption, set point, condensate and stall use the real load (D185).
Forgetting that the control valve can fail open. The steam-space MAWP is also compared with the supply pressure; supply above the MAWP is accepted only with a declared steam-side safety valve set at or below the MAWP (D198).
Using a plate exchanger without the manufacturer limits. Gaskets and brazing limit steam-side pressure and temperature: enter the MAWP and the maximum temperature so the calculator checks them.

Frequently asked questions

Why isn't consumption simply the load divided by the latent heat?

Because steam reaches the control valve at a higher pressure than the steam space, and the valve is isenthalpic: the enthalpy entering the exchanger is that of the supply, not that of saturated steam at the internal pressure. LOGOS uses ṁ_s = Q/(h_inlet − h_condensate) with IAPWS-IF97 enthalpies (D177). In the Spirax trap-selection example (supplier Y), the exact balance gives 496.0 kg/h against 497.4 kg/h by h_fg.

What is stall and when does it happen?

With steam-side control, the valve closes as the load falls and the steam-space pressure falls with it. When it is equal to or below the total drain back pressure, condensate does not leave through a conventional trap: waterlogging, hammer and unstable control. The calculator classifies the result as stall already at maximum load, stall inside the operating range, or no stall in the declared range (with the point below the minimum reported as a theoretical extension). Without back pressure or performance data, stall is not evaluated.

What is the difference between entering U and A or the design steam-space pressure?

With U and A from the data sheet the calculator finds the temperature and pressure the steam needs inside the equipment at each load. With the design steam-space pressure it returns the required UA (and the area, if U is entered). With neither, only consumption is calculated, with condensate assumed saturated at the supply pressure — a conservative estimate — and set point, part load and stall are not evaluated. U is never inferred from the exchanger type.

The Spirax stall chart gives a different number. Which one applies?

The Spirax Sarco chart (Block 13, Ex. 13.6.1) uses the arithmetic mean of temperatures and tends to anticipate stall (in that example, 55 % against 51.8 %). With constant U the logarithmic (LMTD) form is exact and decides the verdict (D184); the chart is shown as a reference only on the reduced-flow trajectory (D222). A large divergence calls for attention to part-load drainage.

What does Meets with pending items mean?

The overall status has three levels (D199). Meets: all mandatory checks done and passed. Meets with pending items: essential data is missing — MAWP, maximum temperature, back pressure, minimum operation — or there is a warning. Does not meet / not viable: a check failed or a condition is not executable. Supply above the MAWP with a safety valve that is only declared falls into pending items, never into a full pass (D230), because that valve is not sized here.

Can the steam space run under vacuum?

Yes. When the required condensing temperature is below saturation at the local atmospheric pressure, the calculator issues a vacuum warning and gives drainage guidance based on the return back pressure (D221): with the return at or below atmosphere, a vacuum breaker and gravity drainage; above it, a pump-trap. Air admitted by the vacuum breaker reduces heat transfer and takes that range out of the pure-steam model: capacity must be confirmed with the manufacturer.

Does the calculator size the steam trap and the safety valve?

No. It passes to the trap the maximum and minimum condensate, the steam-space pressure at minimum and the stall load; trap capacity is checked against the manufacturer curve, at the real differential. For the safety valve it only records whether protection was declared; sizing it for the fully open control valve flow is done separately.

Glossary

Steam space: The side of the exchanger where steam condenses, downstream of the control valve. Its pressure is the saturation pressure at the condensing temperature required by the load.
Set point at the consumer: Required steam-space pressure at maximum load — the pressure at the control valve outlet. The supply must be above it, with room for the valve to regulate.
UA: Overall heat-transfer coefficient U times area A [kW/K]. With the steam side at constant temperature, it fixes the relation between load and condensing temperature.
NTU: Number of transfer units: UA divided by the heat capacity rate of the process stream (ṁ·c̄p).
LMTD: Log-mean temperature difference between condensing steam and the liquid. With one isothermal side, F = 1 for any arrangement.
Stall: Condition in which the steam-space pressure falls to or below the total drain back pressure and condensate no longer leaves through a conventional trap.
Total back pressure: Pressure against which the trap discharges: entered directly or summed from the return, the condensate column after the trap and the line loss.
MAWP: Maximum allowable working pressure of the steam space, from the manufacturer; compared with the set point and with the supply pressure (control valve failing open).