# Dehumidifier Arithmetic

## An Eccentric Anomaly: Ed Davies's Blog

Essentially, the question is which is better: using a dehumidifier or ventilating more? All buildings, particularly those which are occupied, need some ventilation to get rid of CO₂, VOCs and so on but in most cases the gas which requires the most ventilation and so sets the level required is water vapour.

In warm weather it's pretty much a no-brainer: more ventilation is best. When the cold air bought in by the ventilation needs to be heated for comfort, though, a bit more thought might be called for.

Heat-recovery ventilation (in which the outgoing warm air is used to partially pre-warm the incoming air) is the obvious answer but we'll assume it's not practical to retrofit that for whatever reason.

# Example Conditions

Looking on the Amazon UK site finds, for example, the Ecoair ECO DD122FW Desiccant Simple Dehumidifier. Searching, in turn, for that finds the manufacturer's page which says it can extract 7 litres/day from 20 °C air with a relative humidity of 60%. The power consumption range is given as 390 to 620 W and I don't think it's completely unreasonable to assume that the rated extraction rate is at the maximum power.

For the sake of discussion let's assume that the outside conditions are a reasonably damp but borderline chilly UK winter's day with an air temperature of 10 °C and 90% relative humidity.

The rule of thumb for absolute humidity that I remember is that 100% RH corresponds to 20 g/m³ at 20 °C doubling for every 10 °C increase in temperature and halving for every 10 °C decrease. Still, in that Navitron thread Other-Power gives a nice little table which is, conveniently, per kg rather than per m³ and slightly more accurate (or at least more precise) so we'll use that.

For our indoor conditions (20 °C, 60% RH) the absolute humidity would be 15 g/kg * 0.6 = 9 grams of water vapour for each kilogram of dry air. Outdoors it'd be 7.8 g/kg * 0.9 = 6.75 g/kg.

# Ventilation Heat Loss

Assuming we want to remove 7 litres of water vapour per day to match the dehumidifier how much air do we need to change? For each kilogram of air exchanged with the outside we get rid of 9 g of water-vapour and bring in 6.75 g for a net disposal of 2.25 g so we need to exchange 1 / 2.25 ~= 0.444 kg of air for every gram of water we need to get rid of. Our 7 litres of water have a mass of 7 kg so that's 7000 / 2.25 ~= 3111 kg of air per day.

It's worth doing a quick sanity check here. Air has a density of around 1.3 kg/m³ so our 3111 kg/day rate would corresponds with about 2400 m³/day or 100 m³/hour. An 87 m² house (reasonable UK semi-detached) with 2.3 m room heights would have a volume of about 200 m³ so this indicates an air-change rate of 0.5/hour. A commonly recommended figure is 0.4 AC/h so we're in the right area - this dehumidifier perhaps wouldn't need to be run quite all the time in a house of this size (particularly if there's some proper ventilation as well).

The specific heat capacity of air at room-like conditions is about 1 kJ/(kg·K). With our temperature difference between inside and out of 10 °C we'll therefore be losing 31.111 MJ/day (360 W) in the form of sensible heat in the air.

In addition, the water vapour we're so set on expelling has some energy content. At room temperatures the latent heat of evaporation of water is around 2.4 MJ/kg so that's an additional 16.8 MJ/day (190 W) for a total of 550 W lost via ventilation.

This is a bit of a cheat because some ventilation is required even without the need to get rid of water vapour. I'm not sure how much but bear it in mind when reading the following comparisons.

# Dehumidifier Heat Gain

To a very good approximation, all of the 690 W consumed by the dehumifier will go towards heating the house.

In addition, the dehumidifier will actually release more heat than the electrical energy going into it; it also releases the latent heat in the water it condenses. However, that's heat that has been taken up doing evaporation in other parts of the house (in people's lungs, on damp sinks, in the leaves of house plants and so on). Also, we've already considered the latent-heat loss of ventilation and it'd be double counting to also include the gain from condensation here.

If the dehumidifier is actually extracting water vapour which came from outside the house (i.e., ventilation air sent out of the house has a lower absolute humidity than that drawn in) then this caveat wouldn't apply and the dehumidifier would be making a real gain over, for example, a simple resistive heater. It'd be a small gain, though.

Similarly, drying laundry outside is not always practical and wastes the latent heat of evaporation of the water removed. If instead you do it inside and use a dehumidifier instead of resistive heating you'll make a net gain.

# Comparison

In conditions when heating is required we need more heating with ventilation than with a dehumidifier. If no other ventilation was required it'd be 690 + 550 W = 1240 W of additional heating. For easy arithmetic it doesn't seem completely ridiculous to assume the background ventilation actually required even with the dehumidifier results in a heat loss of 190 W so the numbers come out as:

 Gains (+)/losses (-) Ventilation Dehumidifier Net Full ventilation -550 W 0W -550 W Dehumidifier -190 W +640 W +450 W

(Perhaps we should take the water vapour extraction performed by the background ventilation into account by comparing lots of ventilation against dehumidifier with some ventilation for the same total amounts of water extracted. Or perhaps this rough comparison is sufficient to get an idea.)

So, on balance, using the dehumifier saves us 1 kW's worth of heating for the cost 690 W of electricity. If normal heating is via resistive electricity (ordinary electric fires, wall panels or similar) then obviously you'd use a dehumidifier. With gas central heating then ventilation and using a bit more gas is the right answer. With anything in between (night-storage heaters, oil, whatever) you have to look a bit more closely.

Still, the controllability of a dehumidifier vs any but the most sophisticated of ventilation systems seems to me to point to the dehumidifier. It's far too easy to over ventilate on windy days, wasting huge amounts of energy, while the humidistat on the dehumidifier just turns it off when it's not needed.

Whatever, it depends on the circumstances and giving categorical opinions on the things without caveats is not likely to be helpful.