Steam consumption of a tank or reactor heated by a jacket or coil
The calculator runs the energy balance of a tank or reactor heated by steam in a jacket or coil — in continuous operation (perfect mixing) or in batch (closed-form solution of MC·dT/dt) — and returns the steam flow for the network, the jacket set point, the drainage stall check, the MAWP check and a three-level overall status.
When to use
Use it when an agitated vessel is heated indirectly by steam condensing in a jacket or coil and you need the steam consumption and the steam-side conditions. In continuous mode, the load comes from the feed flow heated to the reactor temperature, plus the reaction heat and the losses, with the jacket pressure set by the control valve. In batch mode, the load comes from the mass to be heated (the contents and, if entered, the vessel metal) between the initial and final temperatures, with the jacket at constant pressure. The result feeds the steam network (maximum flow with margin, minimum flow and set point) and the steam trap (maximum and minimum condensate, minimum steam-space pressure and stall load). Do not use it for direct steam injection into the product, nor to size the steam-side safety valve or the steam trap — those are separate calculations.
What the calculator solves
A tank or reactor heated by steam in a jacket or coil raises two design questions: how much steam it draws from the network and at what pressure the steam sits inside the jacket. The first sizes the valve and the line; the second sets the set point, the MAWP to respect and whether condensate can leave through the steam trap.
The steam flow always comes from the same balance, ṁ_s = Q / (h_s − h_c), with the steam enthalpy at the valve inlet and the condensate enthalpy at the jacket pressure, both from IAPWS-IF97 (D177). What changes between modes is how the load Q and the jacket pressure are obtained.
Continuous and batch
- Continuous. Perfect mixing: all the contents are at the reactor temperature. The load is heating the feed to that temperature, plus the reaction (proportional to flow) and the losses. With U and A, the condensing temperature is closed-form,
T_s = T_reactor + Q/UA. The design load is evaluated at both ends of the declared flow range (D217). - Batch. The contents are uniform and the jacket is held at constant pressure. The equation
MC·dT/dt = UA·(T_s − T) − Lhas a closed-form solution and solves four modes — time only, pressure + time, UA + pressure and UA + time (D193). The network receives the peak at the start of heating; the mean is informative (D178).
What is left out
The calculator does not size the steam trap (its capacity is checked against the manufacturer curve) nor the steam-side safety valve. It does not estimate surface losses or U from the equipment type. Desuperheating of superheated steam is not modelled in UA. For a liquid other than water, non-boiling is not checked and is listed as not evaluated. Jackets and coils under steam pressure are pressure-retaining parts subject to NR-13 classification (Brazil) by the legally qualified professional.
Formulas and fundamentals
ṁ_s = Q / (h_s − h_c) ṁ_s = steam flow [kg/s]; Q = heat load [kW]; h_s = enthalpy of the steam at the control valve inlet [kJ/kg]; h_c = enthalpy of the condensate leaving the jacket or coil, saturated at the steam-space pressure or subcooled by the entered ΔT [kJ/kg]. The latent heat alone is not used: the valve is isenthalpic and the supply enthalpy also holds inside the jacket. Enthalpies from IAPWS-IF97. Without jacket-pressure data, condensate is taken at the supply pressure — a conservative estimate (D187).
Q(f) = f·(ṁ·Δh + Q_reaction) + Q_losses; T_s = T_reactor + Q/UA f = fraction of the maximum feed flow [-]; ṁ = feed mass flow [kg/s]; Δh = liquid enthalpy rise from the feed temperature to the reactor temperature [kJ/kg]; Q_reaction = reaction heat at maximum flow [kW] (+ endothermic, − exothermic), proportional to the flow; Q_losses = constant losses [kW]; UA [kW/K]; T_s = condensing temperature in the jacket [°C]. Perfect mixing: the driving force is T_s − T_reactor, not an LMTD. Since Q(f) is linear in f, the design load lies at one end of the declared range — at minimum flow when the exothermic reaction exceeds the sensible heating.
MC·dT/dt = UA·(T_s − T) − L; MC = m·c̄p + m_metal·cp_metal MC = heat capacity of the contents plus the metal that follows their temperature [kJ/K]; UA [kW/K]; T_s = condensing temperature at the controlled jacket pressure [°C]; T = contents temperature [°C]; L = losses + reaction [kW] (+ endo, − exo). With the ambient temperature entered, losses become UA_p·(T − T_amb) and the equation stays linear, with UA′ = UA + UA_p. The same equation solves the four modes: time only, pressure + time (required UA), UA + pressure (time) and UA + time (required pressure).
t = (MC/UA)·ln[(T_s,ef − T₁)/(T_s,ef − T₂)], T_s,ef = T_s − L/UA t = time to take the contents from T₁ (initial) to T₂ (final) [s]; T_s,ef = effective equilibrium temperature, net of losses and reaction [°C]. If T_s,ef ≤ T₂ the final temperature is never reached and the calculator flags an error. With proportional losses, UA is replaced by UA′ and T_s,ef = (UA·T_s + UA_p·T_amb − L)/UA′.
Q_peak = UA·(T_s − T₁); Q_end = UA·(T_s − T₂); Q_mean = [MC·(T₂ − T₁) + L·t] / t With the jacket at constant pressure, heat transfer is highest at the start (cold contents) and falls during heating. The peak, with the design margin, is the flow sent to the steam network; the mean and the energy per cycle are informative, for the boiler balance. Without UA the peak is declared not calculable — no multiplier is applied to the mean.
stall: T_s ≤ 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 of height z after the trap and the flow loss of the condensate line. No trap ΔP is added; trap capacity is checked separately against the manufacturer curve. In continuous mode the threshold is closed-form: stall occurs for 0 < Q ≤ UA·(T_b − T_reactor); with Q ≤ 0 there is no steam demand, which is not stall.
Standards & methods
- IAPWS R7-97(2012) — IAPWS-IF97, thermodynamic properties of water and steam (enthalpies, saturation, water density)
- Spirax Sarco, The Steam and Condensate Loop — Block 2 (heating of tanks and vessels), technical cross-check reference
- Spirax Sarco, The Steam and Condensate Loop — Block 13 (condensate removal and stall), technical cross-check reference
- NR-13 (Brazil) — documentation reference and interface with the legally qualified professional; LOGOS does not perform legal classification nor replace the construction code
Typical reference values
| Quantity | Typical range | Note |
|---|---|---|
| Supply steam pressure range | up to 100 bar(a) | LOGOS Steam product limit; inputs above it are rejected. |
| Design margin | 0 to 100 % | Range accepted by the calculator. It multiplies only the flow sent to the network; consumption, set point, condensate and stall use the real load (D185). |
| Total back pressure with an open condensate tank | 0 bar(g) | Example from the screen. A pressurised return, a column after the trap and the line loss raise this value and bring stall forward. |
| Overall heat-transfer coefficient U | from the datasheet | LOGOS criterion: the service U comes from the manufacturer or the design, never estimated from the equipment type. |
| Vessel losses to ambient | entered in kW | No automatic estimate of surface losses in this version (D191). |
| Overall status | 3 levels | Meets; meets with pending items (essential data missing or a warning); does not meet / not viable (a failed check or a non-executable condition) (D199). |
Worked example
Continuous jacketed reactor: water heated from 25 °C to 95 °C with an endothermic reaction
Inputs
- Operation / heated by
- Continuous / jacket -
- Steam at the valve inlet (dry saturated)
- 6 bar(g)
- Contents — water (IF97), vessel pressure
- 3 bar(g)
- Maximum / minimum feed flow
- 2,880 / 1,440 kg/h
- Feed / reactor temperature
- 25 / 95 °C
- Reaction heat at maximum flow (endothermic)
- +20 kW
- Losses to ambient
- 5 kW
- Service U × heat-transfer area
- 800 × 5 W/(m²·K) × m²
- Total drain back pressure
- 0 bar(g)
- Design margin
- 10 %
- Jacket MAWP / max. steam-side temperature
- 6 / 200 bar(g) / °C
Results
- Total heat load (sensible 234.4 + reaction 20 + losses 5)
- 259.4 kW
- UA
- 4.0 kW/K
- Condensing temperature / jacket pressure (set point)
- 159.9 / 5.15 °C / bar(g)
- Steam at maximum load (real consumption)
- 447.3 kg/h
- Flow sent to the network (with 10 % margin)
- 492.1 kg/h
- Minimum flow — load 51.0 %, jacket at 1.54 bar(g)
- 214.0 kg/h
- Stall
- below 7.7 % of load outside the declared range
- Steam temperature in the jacket (≤ 200 °C)
- 162.1 °C
- Overall status
- Meets -
The 259.4 kW load sits at maximum flow, because the reaction is endothermic (+20 kW) and adds to the sensible heating. With UA = 4.0 kW/K and perfect mixing, the steam must condense at 159.9 °C, which gives a jacket set point of 5.15 bar(g) — below the 6 bar(g) supply, so the valve has pressure to control. The real consumption is 447.3 kg/h and only the flow sent to the network carries the margin: 492.1 kg/h. At minimum flow the load drops to 132.2 kW (51.0 %) and the jacket falls to 1.54 bar(g), still above the 0 bar(g) back pressure; stall would only occur below 7.7 % of load (168.6 kg/h of feed), outside the declared range — so it is reported as information, as a reminder to assess start-up and shutdown. Water at 95 °C is 48.7 K below saturation at the vessel pressure (143.7 °C). Downstream of the isenthalpic valve the steam reaches the jacket at 162.1 °C, below the 200 °C limit. The supply equals the MAWP (6 bar(g)) and the set point is below it, so the MAWP check passes without relying on a safety valve; with the supply above the MAWP, the status would drop to a pending item or a failure.
Common mistakes
- Sizing the batch control valve and line on the mean consumption. With the jacket at constant pressure, heat transfer is highest at the start, with cold contents; that peak is what the network must deliver (D178). On the mean, heating is slower than required.
- Dividing the load by the latent heat at the jacket pressure. The correct balance is Q/(h_s − h_c), with the steam enthalpy at the valve inlet: the valve is isenthalpic and the steam reaches the jacket with the supply enthalpy (D177).
- Confusing the supply pressure with the jacket pressure. The heating pressure is the controlled pressure inside the jacket or coil, downstream of the valve; the supply must stay above it for the valve to control (D193).
- Assuming the maximum load of a continuous reactor is always at maximum flow. With an exothermic reaction larger than the sensible heating, the steam load rises as the flow falls, because the losses do not decrease; without the minimum flow, the peak is not evaluated (D217).
- Checking the jacket MAWP only against the set point. If the control valve fails open, the jacket sees the supply pressure; above the MAWP a steam-side safety valve is required, and declaring it does not demonstrate its sizing — the result stays with a pending item (D198, D230).
- Leaving the condensate line loss out of the back pressure. Without it the total back pressure is underestimated and stall is predicted optimistically (D188).
- Ignoring the vessel metal in batch mode. Vessel, jacket and agitator follow the contents temperature and enter the heat capacity MC when entered, with the user's cp (D195).
Frequently asked questions
Why does the network receive the peak, not the mean, in batch mode?
Because with the jacket or coil at constant pressure, heat transfer is highest at the start, with cold contents, and falls during heating (D178). In the calculator's batch example — 12 m³ of a liquid with cp 3.9 kJ/(kg·K) and ρ 1,000 kg/m³ heated from 8 °C to 60 °C in a coil with U = 650 W/(m²·K), A = 7 m² and 1.1 bar(g), plus 3,885 kg of metal with cp 0.5 kJ/(kg·K) and 15 kW of losses — heating takes 113.3 min (within the 120 min requested). The peak is 840.4 kg/h and the mean 628.5 kg/h: a ratio of 1.34. The network receives the peak with the margin, 924.4 kg/h; the mean and the cycle energy (about 2,637 MJ) are for the boiler balance. This case reports 'meets with pending items' because, for a liquid other than water, non-boiling is not checked.
What does the calculator do without the jacket U and A?
In continuous mode, without U and A or the jacket design pressure, it calculates consumption only, with condensate assumed saturated at the supply pressure — a conservative estimate, not a prediction (D187); set point and stall are not evaluated. In batch mode, with only the heating time, the mean consumption is returned; the steam peak, which is what goes to the network, is declared not calculable, with no invented multiplier. With the jacket design pressure (and the time, in batch), the calculator returns the required UA and, if U is entered, the area.
How is an exothermic reactor handled?
The reaction heat is proportional to the flow (constant conversion and composition, D192), while the losses are constant. If the exothermic reaction exceeds the sensible heating, the steam load rises as the flow falls, and the design load — flow to the network, set point, MAWP and required UA — is the one at minimum flow (D217). If the reaction covers the feed and the losses, there is no steam demand: the flow is zero, never negative, and the reactor may need cooling. No demand is not stall.
What is stall and how is it checked here?
With control on the steam side, the jacket pressure falls as demand falls. When it reaches or drops below the total drain back pressure, condensate does not leave through a conventional steam trap and the jacket floods. In continuous mode, the calculator plots jacket pressure against load and gives the stall load in closed form, stating whether it falls inside or outside the declared range; in batch mode, it checks heating and holding at the final temperature. The usual remedies are a pump-trap, gravity drainage with the jacket always at or above atmospheric pressure, or a control strategy that keeps the pressure above the back pressure.
How is the jacket or coil MAWP checked?
The MAWP is compared with the set point and with the supply pressure, which reaches the jacket if the control valve fails open (D198). The limits are entered separately for jacket and coil, according to the equipment data (D190). A supply above the MAWP without declared protection fails. With a steam-side safety valve declared, the calculation proceeds, but as a pending item: the declaration does not demonstrate the valve sizing, which is done separately (D230).
What if the jacket has to run below atmospheric pressure?
It is a physically possible condition and is reported as a warning, not a calculation error (D221). With the jacket declared vacuum-rated, equipment, control and drainage remain to be checked. Otherwise, the guidance follows the return back pressure: at or below atmosphere, a vacuum breaker with gravity drainage; above it, a pump-trap. The air admitted by the vacuum breaker reduces heat transfer and takes this range out of the pure-steam model.
How are losses handled in batch mode?
Losses are entered in kW, with no automatic estimate (D191). Without the ambient temperature, they are held constant throughout heating — conservative when the entered value is the loss at the final temperature. With the ambient temperature, the entered value is the one at the final temperature and during heating the losses fall with the colder contents, Q_losses = UA_p·(T − T_amb), keeping the closed-form solution (D218).
Glossary
- Jacket and coil
- Indirect heating surfaces of the vessel: the jacket surrounds the shell, the coil is immersed in the contents. Steam condenses at constant temperature inside them; the steam-side limits are entered for each one (D190).
- Perfect mixing
- Assumption of continuous mode: all the contents and the outlet are at the reactor temperature, so the driving force is T_s − T_reactor, with no LMTD.
- UA
- Product of the overall heat-transfer coefficient U and the area A of the jacket or coil [kW/K]. With steam at constant temperature, it fixes the heat transfer for each temperature difference.
- Jacket pressure (set point)
- Steam pressure inside the jacket or coil, downstream of the control valve. In continuous mode, the pressure needed for the design load; in batch mode, the controlled pressure during heating.
- Steam peak
- In batch mode, the steam flow at the start of heating, with cold contents — when heat transfer is highest. It is the flow sent to the network (D178).
- Heat capacity MC
- Energy to raise the contents and the metal that follows them by 1 K: MC = m·c̄p + m_metal·cp_metal [kJ/K].
- Stall
- Condition in which the jacket pressure is at or below the total drain back pressure: condensate stops leaving through the conventional steam trap and the jacket floods.
- MAWP
- Maximum allowable working pressure of the jacket or coil, compared with the set point and with the supply pressure (control valve failing open).