Winter office humidification load: mix the outdoor air, heat it, then add the missing moisture
In winter the outdoor air holds so little moisture that ventilation alone dries the room. We work out how many kilograms of water vapour per hour must be added to the mixed air to hold the room humidity, and how the heating coil changes between steam and spray humidification.
Situation
Say a winter office air handler brings in 30 % outdoor air, and by afternoon people complain the room is dry. Outdoor air at -5 °C and 50 % RH looks humid, but its humidity ratio is only 1.24 g/kg. Warm that air to room temperature and its relative humidity falls to a single digit. Three things are worth knowing: how many kilograms per hour the humidifier must produce, whether steam or spray puts more load on the heating coil, and how much the load grows when the room target is raised one step. The conditions are illustrative; a real decision uses the building's outdoor design conditions and its internal moisture gains.
Given conditions
| Item | Value |
|---|---|
| Room RA | 22 °C, 40 % RH (winter office target, example value) |
| Outdoor OA | -5 °C, 50 % RH (winter outdoor air, example value) |
| Supply airflow | 10,000 CMH (at room state), 30 % outdoor air (by dry air mass) |
| Supply S | Dry-bulb 28 °C, humidity ratio equal to the room's (internal moisture gain set to zero, which makes the load larger) |
| Humidifier type | Steam (enthalpy of 100 °C saturated steam 2676 kJ/kg) or spray (adiabatic, constant wet-bulb). Feed water 15 °C |
| Pressure | 101.325 kPa (sea level) |
Reading it on the chart
- Plot outdoor OA and room RA and join them. The 30 % outdoor-air mix M lies 30 % of the way from RA toward OA.
- Supply S is at 28 °C with the room's humidity ratio of 6.56 g/kg. From M, the humidity ratio must rise by 1.60 g/kg to reach S.
- Steam adds moisture without cooling the air much, so heat M to the right to Hs and then inject steam straight up to S.
- Spray follows a constant wet-bulb line, so dry-bulb drops as humidity rises. Follow S back along that line to Hw, and the heating coil must heat the air that much higher first.
Step-by-step calculation
1) States. Room 22 °C / 40 %: WRA = 6.56 g/kg, specific volume 0.8449 m³/kg, dew point 7.8 °C. Outdoor -5 °C / 50 %: WOA = 1.24 g/kg. Dry air mass flow ṁ = 10,000 / 3600 / 0.8449 = 3.2875 kg/s.
2) Mixing. With 30 % outdoor air, WM = 0.3 × 1.24 + 0.7 × 6.56 = 4.96 g/kg, mixed dry-bulb 13.96 °C (enthalpy average 26.58 kJ/kg).
3) Humidification load. Supply humidity ratio WS = WRA = 6.56 g/kg, so ΔW = 1.60 g/kg. The load is mw = ṁ × ΔW = 3.2875 × 0.00160 × 3600 = 18.9 kg/h.
4) Steam. Steam raises the humidity ratio without chilling the air. Taking out the heat the steam brings, ΔW × 2676 kJ/kg, the air before the humidifier, Hs, has enthalpy hS − ΔW × 2676 = 44.92 − 0.00160 × 2676 = 40.65 kJ/kg, which is 27.81 °C. The heating coil takes M to Hs: Q = ṁ(hH − hM) = 3.2875 × (40.65 − 26.58) = 46.2 kW. Making the steam from 15 °C feed water takes (2676 − 62.8) kJ/kg, so 18.9 kg/h is about 13.7 kW. With the coil that is 60.0 kW.
5) Adiabatic spray. The wet-bulb temperature of S is 16.14 °C. The intersection of that wet-bulb line with M's humidity ratio of 4.96 g/kg is Hw, dry-bulb 31.91 °C. The heating coil takes M to Hw: Q = 3.2875 × (44.81 − 26.58) = 59.9 kW. The humidifier itself uses only water, but the coil works 13.7 kW harder than with steam. The saturation efficiency needed is η = (31.91 − 28) / (31.91 − 16.14) = 0.25.
Interpreting the result
The load of 18.9 kg/h is for 10,000 CMH with 30 % outdoor air. Steam uses 46.2 kW at the coil and 13.7 kW to generate steam; spray uses 59.9 kW at the coil. The totals, 60.0 kW and 59.9 kW, are nearly equal. The heat needed to bring the air to the same state does not depend on the method; what changes is whether the heating coil (hot water, steam or electric) or a steam generator (usually electric or boiler-fed) supplies it. The saturation efficiency needed for spray is only 0.25, so the sprayer has some margin, but surfaces in contact with water need hygiene management.
As the outdoor air gets colder the load grows (room 22 °C / 40 %, 30 % outdoor air, outdoor RH fixed at 50 %).
| Outdoor dry-bulb | Outdoor W (g/kg) | Mixed dry-bulb | Mixed W (g/kg) | Load (kg/h) |
|---|---|---|---|---|
| -10 °C | 0.80 | 12.5 °C | 4.83 | 20.5 |
| -5 °C | 1.24 | 14.0 °C | 4.96 | 18.9 |
| 0 °C | 1.88 | 15.4 °C | 5.16 | 16.6 |
| 5 °C | 2.69 | 16.9 °C | 5.40 | 13.8 |
Raising the room target grows the load even more (outdoor -5 °C / 50 %, room held at 22 °C).
| Room RH | Room W (g/kg) | Room dew point | Load (kg/h) |
|---|---|---|---|
| 30 % | 4.91 | 3.6 °C | 13.1 |
| 35 % | 5.73 | 5.9 °C | 16.0 |
| 40 % | 6.56 | 7.8 °C | 18.9 |
| 45 % | 7.39 | 9.5 °C | 21.8 |
| 50 % | 8.22 | 11.1 °C | 24.7 |
Going from 30 % to 50 % RH takes the load from 13.1 kg/h to 24.7 kg/h, a factor of 1.9. The dew point also rises from 3.6 °C to 11.1 °C, so condensation starts on colder surfaces as well. Before raising the winter room humidity, check the coldest surface with Winter exterior wall condensation check.
For a quick estimate, here is the moisture needed to bring 1,000 CMH of outdoor air all the way to the room condition, by outdoor temperature (room 22 °C / 40 %, outdoor RH 50 %).
| Outdoor dry-bulb | Outdoor W (g/kg) | 1,000 CMH outdoor air = dry air (kg/s) | Load (kg/h) |
|---|---|---|---|
| -10 °C | 0.80 | 0.372 | 7.7 |
| -5 °C | 1.24 | 0.365 | 7.0 |
| 0 °C | 1.88 | 0.358 | 6.0 |
| 5 °C | 2.69 | 0.351 | 4.9 |
What the calculation leaves out
The calculation sets internal moisture gain (breathing, perspiration) to zero; in practice it lowers the load. Dry outdoor air infiltrating through the building envelope and moisture moving through windows and walls raise it. Treat the result as close to an upper bound, and give the humidifier some headroom without oversizing it, because an oversized unit cycles on and off and the control becomes unstable.
Steam injected into a duct needs some distance to be fully absorbed, and before that it can condense on duct walls. Leave an absorption distance after the humidifier and keep elbows, dampers and filters out of the zone where the air is close to saturation. For spray, water quality and Legionella control are part of the design. The numbers here cover the psychrometric heat and moisture balance only.
Common mistakes
- Judging dryness by outdoor relative humidity. Outdoor -5 °C / 50 % looks humid but holds only 1.24 g/kg. Warmed to room temperature its RH collapses.
- Sizing the load from a difference in RH. The load is the humidity ratio difference times the dry air mass flow. You cannot subtract RH of air at different temperatures.
- Forgetting the steam generation heat in the coil sizing. Steam humidification needs 46.2 kW at the coil and a separate 13.7 kW to make the steam.
- Treating spray as free. The latent heat comes out of the air, so the air must be heated to 31.9 °C before the sprayer.
- Raising only the room humidity. A higher RH target raises the dew point and puts condensation on cold surfaces. Set the humidification target together with the condensation check.
Try this calculation on the site
Open the heating and humidifying on the chart
The chart link plots outdoor -5 °C / 50 %, room 22 °C / 40 %, the mixed point, the pre-steam point and the supply point, with heating and humidifying process cards that give the heating kW and the humidification rate. A calculator that solves the same problem in one step, heating and humidifying for winter, is in the calculation menu on the home screen. For condensation see the dew point tool, for plotting see How to read a psychrometric chart, and for outdoor-air decisions see Economizer changeover.
References
- ASHRAE Handbook Fundamentals 2017 (SI), chapter 1 Psychrometrics: humidity ratio, enthalpy, specific volume, wet-bulb temperature and saturation vapour pressure (Hyland-Wexler). The psychrometric numbers here were computed with this site's engine, which implements those equations at 101.325 kPa.
- ASHRAE Handbook HVAC Systems and Equipment, Humidifiers chapter: the heat balance of steam humidification (steam enthalpy added to the air balance), the constant wet-bulb process of adiabatic spray humidification, and saturation efficiency. The steam enthalpy of 2676 kJ/kg is the 100 °C saturated steam value (IAPWS-IF97 2675.6), and the feed water heating uses a specific heat of 4.186 kJ/kg·K.
- Room 22 °C / 40 %, outdoor -5 °C / 50 %, supply 28 °C, airflow and outdoor-air fraction are example values. A real design uses the local outdoor design conditions and the building's humidity target.