My girlfriend’s bedroom is cold in winter, so we sleep with the door closed and the electric heater turned on, which pretty much eliminates air circulation. But sometimes we wake up out of breath, perhaps because so much CO₂ has accumulated in the air. Recent research suggests that this is a problem for a lot of modern sleeping arrangements, but it doesn’t usually rise to levels that cause perceptible discomfort. This note explores the possibilities for solving this problem.
(See Notes and calculations on building luxury underground arcologies for whoever wants them for more information on the air changes per hour needed for clean air.)
The bedroom is 3 m × 3 m × 4 m, and pretty much at sea level, where the density of air is 1.2 g/ℓ (at STP, according to Millikiln), so it contains about 43 kg of air. The window seals pretty well. We are two people, and we commonly spend 12 hours straight in there; at 2000 kcal/day/person that’s 4000 kcal/day or 2000 kcal without opening the door.
Carbohydrates, our normal energy source, are about 5 kcal/g (21 MJ/kg), and carbohydrates all have the empirical formula CH₂O, thus the name. (Glucose, for example, is C₆H₁₂O₆.) Multiplying by the atomic weights, that’s 12 parts carbon, 2 parts hydrogen, and 16 parts oxygen, so carbohydrate is 12/30 carbon by mass. (Protein is similar; fat is about twice as high in carbon and also about twice as high in energy, so the result is approximately the same.) So that’s about 12.5 kcal per gram of carbon (52 MJ/kg). CO₂ is 12 parts carbon to 32 parts oxygen, so that’s about 3.4 kcal per gram of CO₂ (14.3 MJ/kg).
So 2000 kcal is 590 g of CO₂, which would amount to 14000 ppm by mass, 1.4% of the air, 35 times the concentration in the outside air. No wonder we get uncomfortable!
If we wanted to use ventilation to limit the CO₂ to only 2½ times the 400 ppm in the outside air, we’d need to have only an extra 600 ppm in the air, or 26 g CO₂, or 370 kJ, or, in archaic units, 88 kcal, which our two human bodies emit every half-hour. This would require roughly two or three air changes per hour.
If you put houseplants in your bedroom to keep the CO₂ levels down when you sleep, you may be disappointed if you are one of those people who sleep at night, rather than during the day. Plants convert CO₂ to oxygen (and sugar) through photosynthesis, which only happens when the sun is shining on them. At night, plants oxidize sugar to survive, just like the humans do.
Plants using crassulacean acid metabolism are commonly recommended to help with this; these are typically succulent desert plants. Normal land plants keep their pores (“stomata”, literally “mouths”) open during the day, allowing water to evaporate from their leaves and keeping the plants cool. CAM plants instead tolerate the high temperatures, keeping their stomata tightly closed during the day. But, like normal plants, they need sunlight and CO₂ for photosynthesis. So the motherfuckers open their stomata at night, releasing the excess oxygen from photosynthesis, and store the CO₂ as malic acid until daylight comes around.
Cacti, aloe, and pineapples are among the crassulacean acid metabolism plants, although none of those are actually Crassulacea. Because most CAM plants are specialized to very dry climates, they grow very slowly, prioritizing surviving over thriving. This means, I suspect, that they tend to photosynthesize very slowly. Aloe vera might be the best choice of CAM plant for this kind of thing.
The amount of CO₂ consumed is dependent on the amount of sunlight and the photosynthetic efficiency of the plant. Typical photosynthetic efficiency is 3%–6% at 114 kcal per mole of CO₂, which is to say, it instead takes 1900–3800 kcal of sunlight (8–16 MJ in SI units) falling on typical plants to reduce a mole of CO₂ (44 g).
So how much aloe do you need, or how much sunlight do your aloes need to soak up during the day, in order to suck up 590 g of CO₂ per night? Well, 590 g · 12 MJ/44 g = 161 MJ, and divided by a day, that’s 1900 W. But how much sunlight is that?
Let’s figure that the “capacity factor” of photosynthesis is close to the capacity factor for utility-scale solar photovoltaic energy in the US, which is about 25% — that is, for every 100 watts peak of installed solar photovoltaic generation capacity, you get on average 25 watts, due to things like the sun being on the wrong side of the Earth half the time, and clouds, and a suboptimal sunlight angle on your panels. Or leaves.
The “solar constant” against which those theoretical numbers are calibrated is 1000 W/m², which is about how much sunlight gets to the bottom of Earth’s atmosphere where the humans live. At a 25% capacity factor, this is 250 W/m². So you need almost 8 square meters of aloe plants. (And 8 square meters of sunlight to put them in. You might want to put them in some Radio-Flyer-style wagons so you can trundle them out onto the patio in the daytime.)
So basically this approach can work, but it requires on the order of 4 m² of sunlit leaves per person, so you kind of have to design your house around it. I can’t do it here in my apartment (not enough sunlit area) and neither can she.
If we had that much sunlight available, we might be able to store much of its energy thermally (see Household thermal stores) which would reduce our desire to keep the door closed.
I’ve written previously in Notes on a possible household air filter and House scrubber about mechanical means of removing CO₂ from the air in your house; I will not go into more details here except to mention that it does seem feasible, and could be retrofitted to existing sun-poor housing.
As David MacKay (RIP) pointed out in Without Hot Air, Section III, chapter E, the humans’ nose is a heat exchanger which reduces heat and humidity losses to your breath, and they can install a countercurrent heat exchanger on their houses, with the same purpose of transporting air in and out without transporting the precious heat along with it. (Or, in the summer, the odious heat.)
Countercurrent heat exchangers (“recuperators”) have a couple of major differences from the “regenerator” design used in Stirling engines and the noses of the humans. One is that, for the same efficiency, they must be much larger, because the two working fluids in a recuperator are in much less intimate contact than the fluid and reservoir in a regenerator. (However, see Heat exchangers modeled on retia mirabilia might reach 4 TW/m³ for a design that fixes this.) The other is that regenerators transfer not only heat but also material between the two directions of flow. For example, water condenses in your nose as you exhale, then evaporates again as you inhale. For some applications, such as your nose, this mass transport is essential; for others, such as transferring heat from a sodium coolant loop to a steam coolant loop, mass transport would be fatal. (Regenerators also have a third difference, which is that their flow is unidirectional and alternating rather than continuous, which is somewhat awkward for rigid structures such as most human bedrooms; often they are used in pairs to compensate for this.)
Ventilating your house is an intermediate case: it’s not essential for the water vapor that condenses from the outgoing air to be infused into the incoming air, but it would be desirable, because otherwise an aqueous human is going to want a humidifier in the bedroom. (Maybe hundreds of kilograms of aloes would solve this problem as well.) This suggests that regenerators would be a better choice for this application than recuperators.
Suppose we want to achieve 10 air changes per hour, a relatively normal number of air changes for spaces designed for the humans, and one which in this case would exceed the two or three air changes per hour computed above. This is 100 liters per second in the bedroom I described. If we want to keep air speeds below about 10 m/s to avoid thunderous wind noise, we need to use a duct of at least about 100 mm × 100 mm in each direction.
This presumably means that the regenerators themselves, the pebble beds, will be somewhat wider than 100 mm in order to have comparable air resistance despite being full of chunks, but perhaps not much wider:
| |
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| air |
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| /**********/|
| /**********/ |
| /**********/ |
| /**********/ |
| /**chunks**/ |
| /**********/ |
| /**********/ |
| /**********/ |
|/**********/ |
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| air |
| ↓ |
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To prevent infestations like Legionnaires’ Disease, some kind of anti-bacterial and anti-fungal treatment might need to be applied to the chunks. For example, you could use steel ball bearings plated with nickel and then with copper, or (at the risk of deliquescence) rock salt. Some kind of gravel — say, non-clumping clay kitty litter — that’s been somehow copper-plated or infused with blue vitriol would also work. Maybe chunks of portland cement would be natively sufficiently alkaline to keep mold or bacteria from growing. (The specific heat of portland cement is 0.880 J/kg/K. Probably the specific heat of clay kitty litter is the same as brick: 0.84 J/kg/K.)
(Shah and Sekulić tell me that paper, wool, hygroscopic nylon, and polypropylene are common materials for such regenerators in HVAC applications, and that the cycle time is frequently measured in seconds.)
How small could we make the pebble beds?
The total thermal mass of each regenerator needs to be much larger than the thermal mass of the air sent through it between reversals of direction. The amount of air sent between reversals of direction needs to be much larger than the amount in the duct, which can be reduced to just over the amount of air in the regenerator pebble beds themselves by doing the reversals of direction close to those beds. This way, if the air ducts from the regenerator to the bedroom has to run a long distance through the house, the air in those ducts can continue moving in the same direction.
Air’s specific heat of 1.01 kJ/kg/K is a bit higher than steel’s specific heat of 0.47 kJ/kg/K, but steel’s density of 7.9 g/cc is much higher than air’s 0.0012 g/cc. So if the volumes of air and steel in the pebble bed were equal, the thermal mass of the steel would be about 3100 times greater.
So, presumably, whatever their size, you could send air through them in one direction until you had sent through 150 times their volume of air, then reverse. So far this isn’t getting me any closer to conclusions about how big or small the pebble beds have to be if they’re just serving to transfer heat and humidity from outgoing air to incoming air.
To take a particular size, suppose one pebble bed is 100 mm × 400 mm in cross-section and 400 mm long, and it’s mostly full of steel shot plated as above, close-packed as spheres, which means the spheres occupy π/(3√2) or 74% of the space. This is 11.9 ℓ of steel, weighing 94 kg, and holding 44 kJ/K, the same thermal mass as 44 kg of air, roughly the entire bedroomfull. If ΔT = 22°-10° = 12 K, this is 530 kJ, equivalent to running the 2 kW electric heater for four or five minutes. So this is probably overkill, by at least one and possibly three orders of magnitude.
Making the regenerator matrix finer increases airflow resistance but also increases heat conduction between the mass of the matrix and the air passing through. Probably using parallel fins, as in corrugated cardboard, improves this tradeoff. Actual corrugated cardboard itself may be a reasonable material; its specific heat should be close to that of wood, 1–3 kJ/kg/K.
Sometimes we might have the heater turned off, for example because we’re not there, and then want to turn it on.