Friends, Happy New Year! Over the Christmas break I have managed to get back to doing some experiments – playing with candles, weighing scales, and gas cylinders. And in doing experiments I have remembered the pleasure of experimental “play”, free from the tyranny of having to produce results.
I have been experimenting with estimating the rate of air change in my home, by use of a carbon dioxide concentration monitor. I wrote about this previously, but was stimulated to re-visit the topic by a comment from a Twitter friend: (Peter Miller) who suggested using candles as a quantifiable source of CO2.
Regular readers, may know that I love candles, and it seemed delightfully quixotic to be able to do some actual measurements by ‘dosing’ CO2 into the home at a known and measurable rate by burning candles. Someone else then suggested using cartridges of CO2 that are available for rapid re-inflation of bicycle tyres.
So I began a series of experiments using candles and CO2 canisters and a CO2 meter which records readings every 5 seconds onto a micro-SD card. But 10 days in, I have realised that I have proverbially “bitten off more than I chew“. And so rather than plough on, I am going to pause my experiments, and summarise what I have learned so far. And hopefully by writing the summary, the future of the experimental program at Podesta Towers will become clearer to me.
Why Air Changes per Hour (ACPH) matters
Everyone knows that a draughty home is not a comfortable home. The number of Air Changes per Hour (ACPH) quantifies this effect. And knowing the ACPH for a dwelling is useful for making a retrofit plan.
Let’s suppose a dwelling has a volume of (say) 200 cubic metres and has 1 ACPH. This means that every hour, 200 m^3 of air from outside (at maybe 0 °C) enters the house and has to be heated up to (say) 20 °C. The heat capacity of air is around 840 joules per cubic metre, so this represents a heating load of 200 m^3 × 20 °C × 840 J/m^3 = 3.36 MJ per hour or about 930 W – just under a kilowatt. With 3 ACPH this becomes 2.8 kW which is a very significant heat load – and financial burden.
At the same time, if the number of air changes per hour is low, then the concentration of CO2 can build up to levels around 2,000 ppm at which level people will likely feel drowsy. And air quality – in terms of particulates and unpleasant smells – will likely suffer.
I designed a spreadsheet to show the balance of these two effects.
Click on the image for larger version. This is a screenshot from the spreadsheet for calculating CO2 concentrations in homes of different volumes, different occupancy and different numbers of air changes per hour (ACPH).
But despite being very important, ACPH is a difficult quantity to measure, and consequently in practice it is never measured! Instead, in the few cases where people make any measurements, they measure a different quantity which is related to ACPH by an unknown factor, which may be between 20 and 50.
Really? Yes. The most common measurement is a so-called door blower test in which people attach a giant fan to the door of a dwelling which sucks (or blows) air out of (or into) the dwelling, recording the rate at which the pressure inside the dwelling falls (or rises). From the air flow at 50 pascals of pressure difference between the inside and outside of a dwelling, the number of ACPH is inferred by dividing by a factor 20. [Aside:In case you are not familiar with the pascal unit, 50 Pa is a very low pressure difference – the difference between the air pressure at the ground and the air pressure at a height of 5 m].
The door-blower test is a good way of comparing the air-tightness of one dwelling with another, but simply does not measure the thing one wants to know! A more modern so-called ‘Pulse’ technique achieves a similar measurement more quickly by exploding an “air bomb” inside a house and measuring the transient changes in pressure. Once again this is a good way of comparing the air-tightness of one dwelling with another, but simply does not measure the thing one wants to know!
As Persily & de Jonge point out in their landmark paper, simply measuring the concentration of carbon dioxide in the air has been recognised since the time of Lavoisier as an indicator of indoor air quality. The idea is simple: as people go about their usual business in a dwelling, they breathe out carbon dioxide, increasing the concentration of carbon dioxide in the indoor air. As the air is exchanged with outside air, the concentration of carbon dioxide in the indoor air decreases. If the rate at which people produce CO2 is known (the subject of Persily & de Jonge’s paper) then the ACPH can be estimated.
This was the subject of my last article on this subject and I thought I had said all I had to say: but then Peter Miller suggested using candles.
Candles and Canisters
Persily & de Jonge’s paper addresses the variability of the rate of human carbon dioxide emissions with age, gender and activity level. So unless one characterises the age, gender and activity level of all the people in one’s home, it can be hard to estimate the ACPH.
However, as this excellent paper on the physics of candles makes clear, a candle burns steadily for many hours and produces carbon dioxide at a rate of 1.71 litres of pure CO2 per gram of wax burned. So a candle can become a standardised source which releases CO2 at a known rate – around 10 litres per hour for a typical candle – not so different from the roughly 14 litres per hour that a lightly-active adult creates.
Alternatively, a canister of CO2 containing 16 g of carbon dioxide (stored in liquid form at almost 60 atmospheres!) can be used to rapidly inject about 8.7 litres of CO2 into a dwelling.
So using a combination of candles and canisters, might it be possible to characterise the ACPH of a dwelling by measuring the carbon dioxide levels, but with no uncertainty from the number, age, gender and activity level of the occupants? The answer is definitely “Yes”, but the optimum procedure is not obvious. Let me show you results from some of my experiments and then I’ll discuss possible sources of uncertainty, and my difficulty in working out what a workable procedure might look like.
Click on image for a larger version: The tools of the trade: candles, CO2 cylinders, discharge device, weighing scales, and a CO2 meter.
#1: Candles in a room
One of the first tests involved burning a candle in a room with dimensions 4.0 × 3.1 × 2.9 m i.e. a volume of 28.9 cubic metres or 28,900 litres. I positioned the CO2 meter on the other side of the room from the candle and set it to record overnight. The next day I lit the candle, let it burn for a few hours and then extinguished it. The data looked like I anticipated it might – but rather better than I had hoped for!
Click on image for a larger version. Graph showing the measured concentration of CO2 (ppm CO2) in a room versus time (hours). The concentration of CO2 fell overnight, rose when the candle was lit, and fell when it was extinguished.
The overnight fall in CO2 concentration arises from air changes with the outside air and with air in the rest of the house.
After igniting the candle, one expects the CO2 concentration to at first rise linearly. Then, as the concentration rises, one expects the natural air changes with the rest of the house and the outside to replace some of the CO2-rich air with air at the background concentration – causing the initial linear rise to slow down. Eventually, the concentration will stabilise when the rate of emission of CO2 from the candles is just matched by the rate of removal of CO2-rich air. The expected trajectory of the concentration has a well-known form. By matching the standard form to the data one can estimate the rate of emission of CO2 (litres/hour) and the rate of exchange of air (ACPH). I’ve described the mathematics at the end of the article.
Click on image for a larger version. Detail from the previous graph showing the time around the ignition and extinguishing of the candle. The graph shows the measured concentration of CO2 (ppm CO2) versus time (hours).
Based on the rate of loss of wax (established by weighing the candles) I anticipated that the concentration of CO2 would initially rise at about 350 ppmCO2/hour. When I analysed the CO2 concentration data I found that the initial rate of rise of CO2 concentration was 346 ppmCO2/hour. This level of agreement (within ±1%) is remarkable given that one prediction is based on weighing and analysis of the chemistry of candles, and the other is based on readings from a device measuring the transmission of infrared light through the air. It suggests to me that CO2 meter is reading at least roughly correctly, and that CO2 from the candle is mixing reasonably well in the room. It suggests that the technique might be capable of giving estimates of ACPH with low uncertainty.
The data looked like I expected it to: a linear rise, curving over, peaking when I extinguished the candle, and then falling in a similar fashion. Based on the analysis, it seemed that the number of ACPH in our front room was around 0.28. But I noticed that the initial rise had a small delay: I thought this might be because it took a few minutes for the CO2 from the candle to mix in the room. And I noticed that after I extinguished the candle, the CO2 concentration fell immediately – perhaps I left the door open too long?
Click on image for a larger version. Graph showing the time around the ignition and extinguishing of two candles in our front room. The graph shows the measured concentration of CO2 (ppm CO2) versus time (hours).
The next day I tried the same experiment with two candles and obtained similar results. This time the data suggested that the number of ACPH was 0.22, slightly different from the value of 0.28 from the previous day.
The following day I tried using a single night-light candle which I knew would self-extinguish after about 3 hours. There was good agreement between predicted and measured initial rates of rise of CO2 concentration, but now the ACPH appeared to be 0.60 – much higher than estimated previously. Additionally, I could also estimate ACPH from the nearly steady state concentration being 244 ppm higher than background just before the night-light self-extinguished. This analysis suggested ACPH of around 0.75.
I thought these larger estimates might be an artefact of the fitting because I took the measurements at what were initially higher CO2 concentrations than the background level – and so the baseline concentration was probably falling at the same time as the candle was burning.
Click on image for a larger version. Graph showing the time around the ignition and extinguishing of a single “night-light” candle in our front room. The graph shows the measured concentration of CO2 (ppm CO2) versus time (hours).
At this point I thought that the analysis was valuable – but it was taking a long time to make the measurements, I was leaving a lighted flame unattended, and the results showed a higher variability (between 0.22 and 0.75) than I thought was really the case.
#2: Canister in a room
So after a suggestion on Twitter, I tried some experiments discharging 16 g CO2 capsules. These capsules are remarkable, storing the CO2 as a liquid under approximately 60 atmospheres of pressure! Devices are available which can pierce the sealed canister and discharge the gas – which emerges rapidly and is very cold – with relative safety.
In the first experiment I discharged a single CO2 canister in the front room. By weighing the canister before and after discharge, I calculated that the cylinder had contained 15.1 g of gas (rather than the nominal 16g), which corresponds to 8.25 litres of pure CO2.
Click on image for a larger version. Graph showing the time around the injection of CO2 from small gas canister into the front room. The graph shows the measured concentration of CO2 (ppm CO2) versus time (hours).
Based on the volume of the room (28,900 litres), I expected the CO2 concentration to rise almost immediately by 285 ppm to about 835 ppm. But in fact the concentration increased to 890 ppm – which suggests that the ‘cloud’ of CO2 rich gas reached the sensor before fully mixing with the total volume of air in the room. Analysis of the decay curve suggested that there were 0.76 ACPH.
#3: The whole house?
In general, people want to know the ACPH for an entire dwelling, and not just a single room. But how to distribute a CO2 dose uniformly to an entire dwelling? I tried an experiment in which I lit 6 candles for a period of 2 hours and distributed the CO2 around the house by using an array of 4 fans positioned to make sure ‘dead ends’ of the house were exposed to the CO2.
However I didn’t have enough fans to distribute the CO2-enriched air into and out-of the 3 bedrooms and the loft. So I closed all the upstairs doors to roughly exclude them from the experiment. The resulting volume was approximately 200 m^3 and I lit 6 candles to produce a sizeable signal in this larger volume.
Click on image for a larger version. Graph showing the time around the ignition and extinguishing of six candles with the resulting CO2 ‘plume’ being distributed around the whole of the ground floor by four fans. The graph shows the measured concentration of CO2 (ppm CO2) versus time (hours).
The data looked more or less as I expected. Based on weighing the candles, I expected that the CO2 concentration would rise at approximately 293 ppmCO2/hour, but the CO2 meter registered an initial rate of rise about 20% higher than this (348 ppmCO2/hour). This suggests that the volume estimate and the CO2-mixing strategy are almost, but not quite, right.
The fit to the data suggested 0.53 ACPH and extrapolation to the limiting value suggested 0.45 ACPH, a pleasingly low discrepancy.
In the graph above, the ACPH is estimated by analysing data in just the rising part of the curve. But the time constant of that fit also describes well the first part of the declining curve after the candles were extinguished. But after four hours, my biggest fan (my wife 🙂 ) returned to the house and the background level of CO2 increased.
I then thought I would try recording data over a long period, and try to model all of the changes – due to people entering and leaving the house – and any candle-burning or canister-bursting experiments.
Click on image for a larger version. Graph showing the 20 hours of CO2 concentration measurements (ppm CO2) in the house. The red dotted lines show attempts to analyse the data. The sharp peak at 14 hours is due to the release of 2 CO2 cartridges – this is shown in detail in the next figure.
The results from Test 7 show a recording of CO2 concentration on the ground floor of Podesta Towers over 20 hours starting roughly at midnight. They show the decline in CO2 concentration on the ground floor as my wife & I slept upstairs. Then there is a rise as first my wife and then I got up, and then a decline after my wife left for work. Then at 12-ish I discharged a CO2 cylinder, and then just before 14 elapsed hours, I discharged two CO2 cylinders in quick succession. After 16 hours, I left the house and returned later.
My aim had been to model all these changes – as shown by a dotted red line – assuming a single value of ACPH. But I became overwhelmed by the complexity of the process. For example, the first cylinder discharge barely shows up on the data. The second double-discharge (see below) shows up, but the back ground levels before and after the discharge are clearly not the same.
Click on image for a larger version. Detail from the graph above. Notice that the CO2 levels change before and after the pulse for reasons that are not obvious.
Summary
My experiments have convinced me that there must be a way to use measurements of CO2 concentration in homes to meaningfully assess ACPH. But I am not sure of the best way to proceed: these are the things on my mind at the moment.
- The number of actual ACPH will likely change with external factors such as wind speed and direction. It may also vary with internal factors such as the use of fans.
- Ideally a measurement would not inconvenience people living in a house. This favours measurements made either (1) quickly, or (2) overnight when living areas of a dwelling are likely unoccupied or (3) while people are present. Each option has advantages and disadvantages.
- This might involve a canister discharge and CO2 measurement at multiple locations to ensure the dose of CO2 is uniformly distributed.
- This technique uses the occupants to ‘dose’ the living areas of the house, and the overnight decline in CO2 could be used to estimate ACPH if the sleeping areas are separated from the living areas.
- Perhaps the statistical parameters of CO2 measurements: Average, Peak, Minimum, Maximum and minimum rate of change – could be used to estimate ACPH.
- Candles should really be inside a fire-proof candle holder.
- The technique is limited by the need to have CO2 uniformly distributed around the volume being assessed. Usefully, this can be restricted to just a single room, but it is difficult to extend the technique over multiple floors.
So I have lots of things on my mind – but I have written 3,000 words already, and so for now, I just need to stop! Please do share any suggestions you have!
Mathematics
The image below shows the functional form used to model the transient changes in CO2 concentration.