After reflecting on my solar dehumidifier idea (from August 2016 or maybe earlier) and the current air-conditioner-less state of my new bedroom, I did some calculations on making a desiccant-based air conditioner powered by the sun.
The basic idea is that you cool air by evaporating water, like a swamp cooler. But because swamp coolers work poorly or not at all when the air is already humid, you dehumidify the air before cooling it. And because the high-humidity output is undesirable in climates that aren’t dry, you transfer the cool through a recuperative heat exchanger without transferring the humidity; this is known as “indirect evaporative cooling”.
Standard swamp coolers use a recirculating pump to dribble water over wood wool (“excelsior”) pads to evaporate it, but a mister might work just as well, and might reduce the available habitat for bacteria. WP says a high-pressure pump and 5-micron mist orifices are effective.
To dehumidify the air, you pass it over a desiccant, a hygroscopic substance which absorbs some of the moisture from the air — potentially nearly all of it, depending on the desiccant and how dry it is. The desiccant will eventually be saturated with moisture and stop absorbing it from the air; at this point it needs to be regenerated, normally by heating, normally by running hot air through it, then dumping the hot, moist air into the environment.
This design uses a large quantity of a cheap, inefficient desiccant, such as wood wool, rather than a more reasonable quantity of a more mainstream desiccant, such as calcium chloride. As a result, most of the heat from the regeneration air is deposited as sensible heat in the desiccant; only a fraction is used to drive out the water. In order to prevent this heat from leaking into the intake air to be desiccated, two more air circuits are needed: a closed circuit of dry air to remove the heat from the desiccant, and an open circuit of hot dry air to remove the heat from the closed circuit.
So there are five separate, isolated air circuits: a cool wet circuit running through the desiccant, the evaporator, and a heat exchanger; a cool dry circuit running through that heat exchanger; a hot wet circuit running through a solar heater and used to regenerate the desiccant; a closed dry circuit (half hot, half cold) to cool the desiccant; and a hot dry circuit to cool the air in the closed dry circuit down to ambient, transferring the heat to the outside air. Only the cool dry circuit connects to the indoor air.
Swamp coolers typically achieve 70% to 90% relative humidity on their output side; I think it should be possible for relatively simple desiccants (wood wool itself, for example) to get the relative humidity of the air going into the evaporator below 20% see calculations below), but I haven’t performed experiments to show this yet. As long as it’s below 20%, we have a minimum swing of 50% relative humidity, which achieves half of the total theoretically achievable temperature swing. WP says, “Most efficient systems can lower the dry air temperature to 95% of the wet-bulb temperature, the least efficient systems only achieve 50%.”
I am estimating that my new bedroom might receive 4 kilowatts of solar heat during the day (3400 frigories per hour, a bit over a “ton”) that it might be necessary to extract. Converting this sensible heat adiabatically into latent heat by evaporating water consumes 1 g of water per 2260 J, which is to say (4000/2260) g/s of water: 1.8 g of water per second, or 6.4 kg (= 6.4 ℓ) per hour. And let’s suppose that the desiccant can be recycled every 30 minutes.
Let’s suppose that it is adequate to reduce the temperature of the humid air in the evaporation stage to 15° — indeed, the cool air output will probably need to be mixed with enough warm air to avoid being uncomfortably cold. At 15°, the vapor pressure of water is about 1.7 kPa or about .017 atm; at about a 18:28 molar mass ratio of air to water vapor, that works out to .0109 g of water per g of air; air’s density of 1.2 g/ℓ means that our 1.8 g/s of water will need 165 g/s of air occupying 138 ℓ/s to carry it along.
But wait, how much cooling can we get out of .0109 g of water per g of air? Will it cool it enough? Air holds 1.005 kJ/kg/K of sensible heat. 2260 J/g * .0109 g/g / (1.005 kJ/kg/K) is about 24.5 kelvins of ΔT, so we should be fine as long as the incoming air is below 15° + 24.5K ≈ 40°. Checking the psychrometric chart, that seems about right; the 15° diagonal wet-bulb line hits the horizontal 0% RH line at a dry-bulb temperature of 41°. 40° or 41° is fine. It never gets that hot here.
Taking into account the finite efficiencies of evaporative coolers mentioned earlier, a 60%-efficient evaporative cooler (justified below) would only lower the air temperature by 14.7°, which gets us to 15° for temperatures of 29.7° and below, and even at 38° still gets us to a quite tolerable 23.3°.
Common high-capacity desiccants include Glauber’s salt (sodium sulfate, mirabilite), plaster of Paris, silica gel, calcium chloride, and sodium bentonite. But many other hygroscopic substances could potentially be used, including Play-Doh, pot shards, coffee beans, cocoa husks, shredded PET bottles, wood wool, straw, or palo borracho fibers. But let’s consider wood wool, since it’s probably pretty typical of many of these substances, and relatively cheap.
Let’s suppose that by heating wood wool or a similar cheap hygroscopic substance after saturation with outdoor air we can easily drive out 5% of its mass in water.
5% is a conservative estimate for wood, because dry wood normally has about 12% moisture content, says WP, compared to its mass after being oven-dried at 103° for 24 hours. The fiber saturation point, which wood in a 99% relative-humidity atmosphere, is typically 25% or 30% moisture content; equilibrium moisture content ranges from 0% at 0% relative humidity through that 25% or 30%, hitting about 7% moisture content at 40% relative humidity and 12% moisture content at 60% relative humidity. (Buenos Aires summer usually ranges from 30% to 60% relative humidity.) Wood outdoors in Miami ends up with 13% to 15% moisture; in Phoenix, it’s more like 5% to 10%.
Wood drying is normally a very slow process, taking days for hardwoods at tens of millimeters of thickness, roughly proportional to the 1.52th power of the wood thickness, according to the Simpson-Tschernitz wood drying model. At 500 microns (a typical thickness for wood wool), this should be several hundred times faster, needing only 15 to 30 minutes to come near equilibrium, or less for softwoods.
To me, the above implies that exposing air to a sufficiently large quantity of wood with, say, 7% moisture content, will result in reducing its relative humidity to 40%, like Phoenix, and if the incoming air has 60% relative humidity, the wood will stop removing water from it once the wood reaches 12% moisture content. So I think 5% moisture content swing is a reasonable estimate for wood. But can we do better? Like 10%?
Wood starts to char above about 200°, and sugar starts to caramelize at 170°. Let’s say we heat our desiccant up to just 150° to give a good margin of safety. What will the air’s relative humidity be? And what will it leave in the wood?
If we take some incoming air at 35° (a worst case scenario in Buenos Aires!) and 65% relative humidity, the psychrometric chart shows that it contains .022 g of water per g of air, I guess because water’s vapor pressure at 35° is 5.63 kPa = .0556 atmospheres, 65% of that is .0361 atmospheres, and water vapor is only about 18/28 of nitrogen’s density, which gives a fraction of .0232 grams per gram — close enough. If we then use a solar oven to heat it up to 150°, water’s vapor pressure goes from 5.63 kPa to 476 kPa, so the relative humidity falls by the same factor of 84.5, to 0.77%. This should leave the wood’s equilibrium moisture content at about 0.1%; the EMC chart in the WP page I linked above has wood at 120° reaching 5% EMC at 60% RH, a ratio of about .08 between the two percentages.
That is to say, heating wood up to 150° should be sufficient to remove over 99% of its moisture content from ordinary levels of air humidity once it reaches equilibrium, a process whose speed depends on the thickness of the wood but should only take a few minutes for the thicknesses I’m talking about here.
This means that we probably can get 10% of the wood’s weight in water, and perhaps more importantly, we can use it to reduce the relative humidity of the air being desiccated down below 20% or so, at the expense of a lower moisture load in the wood. Indeed, using countercurrent regenerator principles — where the air being desiccated runs through progressively dryer and dryer wood — perhaps we can reduce its relative humidity down below 5% or even 1% in this way.
Wood has a specific heat typically between 2 and 3 kJ/kg/K, with white pine being in the middle at about 2.5. The energy used to heat up the wood to the drying temperature is essentially wasted, so it would be nice to minimize it; going from 20° to 150°, it’s about 390 kJ/kg of wood, or about 3900 kJ per kg of moisture absorbed in the wood. Additionally, we need energy to evaporate the water, which is the same 2260 J/g or 2260 kJ/kg of moisture, for a total of about 6200 kJ/kg of moisture removed by the dehumidifier.
You could consider this a fairly appallingly terrible level of efficiency, but solar thermal energy has been very cheap for the last several billion years, and will probably remain so until at least 2030. So we can afford to “waste” an enormous amount of such low-grade thermal energy.
The air output from the desiccant, at 20% humidity or less, then gets humidified by the evaporator to 80% or more, so we can get at least 60% of the theoretical 24.5K temperature reduction, as long as the output is at or above 15°.
Above I’ve talked about a 30-minute cycle time, 65% input humidity (at up to 35°, thus involving up to .022 g/g of moisture), 20% output humidity from the desiccant, and 138 ℓ/s of airflow for the cool, wet air circuit. The amount of water absorbed in the desiccant should be somewhat less than the 1.8 g/s evaporated in the evaporator, because the input humidity is lower than the evaporator’s output humidity. 0.022 g/g of water vapor in air of 1.2 g/ℓ is .0183 g/ℓ of water vapor, which, at 138 ℓ/s, works out to 2.5 g/s. XXX this is clearly wrong. Over 30 minutes, 2.5 g/s works out to 4.5 kg of moisture; our equilibrium moisture content is only 10%, since we’re using an inefficient cheap desiccant, so that works out to 45 kg of desiccant.
This is clearly a manageable quantity of stuff to put on the roof of your bedroom — it’s not 4500 kg or something clearly impractical like that — but at Lowe’s they sell “excelsior blankets” for landscaping at [US$183 for 65 pounds, US$6.20/kg], so we’re talking about almost US$300 of material.
2.5 g/s by 6200 kJ/kg gives us an estimate of how much thermal power we need: about 15.5 kW, which is about, say, 20 m² of sunlight, and about 4× the amount of thermal power we’re trying to reject.
15.5 kW of thermal power at 150° with a ΔT of 130 K in air carrying 1.005 kJ/kg/K is 119 g/s of hot wet air, or 99 ℓ/s, a bit lower than the other circuits.
The 138 ℓ/s of cool wet air can be used to cool a somewhat larger quantity of cool dry air to, perhaps, a somewhat higher temperature. If the cool dry air temperature is to be 20°, you could perhaps have 200 ℓ/s or more of cool dry air.
If we compromise at, say, 160 ℓ/s, we still need to figure out how we move this air around, ideally somewhat quietly. If the ducting is a generous 400mm in diameter, this works out to about 1.3 m/s of air velocity, which is going to be somewhat noisy, but tolerable and easily achievable.
The 3900 kJ/kg deposited as sensible heat to raise the desiccant from 20° to 150° must be removed somehow; otherwise it will heat the intake air rather than desiccating it. My friend Mina suggests perhaps separating the desiccant from the outside air with only a very thin moisture barrier, such as aluminum flashing, so that it can absorb the ambient temperature in a rest period after being regenerated; if this is workable, it is clearly simpler than what I propose here, which I am certain is workable.
The desiccant passes through three stages: desiccation, regeneration, and cooling. The cooling stage passes cooling air in a closed circuit through it, heating the air; that air then passes through a recuperative heat exchanger to cool it so that it can return to cool the desiccant further.
This air is at, I think, an average temperature of 85°, thus transferring 65 K of ΔT, and holding 65 K · 1.005 kJ/kg/K = 65 kJ/kg of air. The sensible heat involved is 2.5 g/s · 3900 kJ/kg = 9.7 kW. Consequently this circuit must circulate 149 g/s of air, 124 ℓ/s; I think a similar quantity is needed on the hot dry circuit, although maybe it’s twice as much air due to a lower ΔT.
160 ℓ/s is 340 cubic feet per minute. For comparison, a US$24 6" (152 mm) duct fan pumps 240 cfm on 37 watts and supposedly makes 68 dB of noise. This works out to US$0.21 and 330 mW per ℓ/s; the five air circuits of 138, 160, 99, 124, and 248 ℓ/s add up to 770 ℓ/s, US$160, and 250 W. This is less than 2% of the power needed to regenerate the desiccant. It could be reduced further by using wider ducts like the 400mm ducts I suggested above; perhaps it could be provided by solar heat as well, rather than by electricity, particularly since Buenos Aires is prone to power outages at the hottest times. At 1 m/s, 250 W is 250 N, the weight of about 25 kg, which gives some idea of how much work this device requires.
Some kind of wacked-out dude has made a solar Stirling engine of “probably about 100 to 150 W” or “an estimated 70–100 watts” at about 400 mm diameter, “from the ‘Andy Ross Stirling’ design,” with the two cylinders at right angles (“V-position”). At a typical 25% Carnot efficiency and 800 W/m² insolation, 250 W would require a solar concentrator of some 1.25 m². It looks like the nutbag is using a Fresnel lens of about 1 m² for his somewhat smaller engine.
At a minimum, even with a perfect system, to get to 0° with evaporative cooling, you need to start with dry air at 9°; to get to 9° with evaporative cooling, you need to start with dry air at 27°; but to get to 27° with evaporative cooling, you can start with dry air at any livable temperature whatsoever. So a cascade of two or three such desiccant-based coolers could cool food or whatever down below freezing.
6.4 ℓ/h is probably 30 ℓ/day, which is probably an acceptable cost. I can’t think of a way to condense either the water from the desiccant or from the evaporator.
There are a few process parameters that need to be controlled to keep the system working properly.
If the cool wet air circuit runs too fast, the desiccant could be overloaded, leading to air still moist as it enters the evaporator, and thus output air not as cool as it should be.
If the cool wet air circuit runs too slow, it may not be able to evaporate enough water — it will be the right temperature, but there won’t be as much cool air as there should be.
If the evaporator water runs too slowly, output air will not be as cool as it should be.
If the evaporator water runs too quickly, it could accumulate. Swamp coolers normally use a float valve to prevent this.
If the hot wet air circuit runs too fast, it might not be as hot as it should be, and so the desiccant might be less regenerated than intended, leading to diminished cooling capacity; however, unless this is super extreme, the diminution should be minimal, because the drying process is an exponential decay already close to its asymptote at this point.
If the hot wet air circuit runs too slowly, it might be too hot, which could set fire to the desiccant or melt other parts of the machinery, maybe including the solar heater itself. This would be disastrous. Some kind of thermostatic control on the solar heater seems essential.
If the cool dry air circuit runs too fast, it won’t be as cool as it could be, while if it runs too slow, some of the cool will escape up the chimney with cool wet air.
If the desiccant rotates too slowly, it will become saturated with moisture in the cool wet air circuit, diminishing cooling performance; if the regeneration air is properly temperature-controlled, there should be no further risk, but if the regeneration air is too hot, then the desiccant rotating quickly enough be the only thing preventing it from overheating.
If the desiccant rotates too quickly, assuming a countercurrent configuration, I think the only bad thing that will happen is that it will leak more heat from the hot wet circuit into the cool dry circuit, mildly degrading performance.
XXX what about the desiccant cooling circuits?
With electronics, of course, it’s very simple to monitor and compensate for all of these problems. But one of the appealing benefits of this design is that, at least in theory, you should be able to construct and repair it with Stone Age materials and tools.
So it should be possible to make it work reliably under varying conditions with the following feedback and safety mechanisms:
Perhaps of use is the fact that most species of flat grain wood will change size 1% for every 4% change in moisture content, but only crosswise, so you can make humidistats out of wood.
The desiccant could be either in the form of a single, slowly rotating wheel, physically rotating through the three phases it needs, or it could be three or more separate pebble beds, controlled using valves.
Suppose we just want to see if the idea can work. It should be possible to scale it down:
wait, how much thermal input?
Any kind of fire, including a propane or wood fire, should serve to heat the air to regenerate the desiccant. With a coke or charcoal fire, you could pass the combustion exhaust directly through the desiccant, but other common kinds of fires probably produce too much water and other contaminants which could damage the desiccant in several ways: directly hydrating it, clogging pores in it, coating its surface with waterproof coatings, catalyzing pyrolysis at lower temperatures, and supporting fire. So this involves using another heat exchanger in place of the solar heater.
Air has some significant advantages as a coolant: it can withstand temperatures from cryogenic to red-hot, it isn’t combustible, it’s readily available anywhere in the world, it has low viscosity, and it’s compatible with a wide variety of materials (at least at ordinary temperatures). But it also has very low density, which means that transferring significant heat flows with it requires very large pipes and large heat exchangers.
In this case, I don’t think there is a reasonable alternative to air for any of the five circuits. The cold wet circuit and the hot wet circuit need water to evaporate into them, so they need to be air;
Wood scraps, paper scraps, and such things may be a cheaper alternative to such freshly manufactured materials. In some places, soil containing a substantial amount of clay, or maybe organic matter, might be cheaper and work adequately. Watts, Bilanski, and Menzies show adsorption “isotherms” for various bentonite clays showing about 100–200 mg adsorbed water per gram of dried clay at 0.6 “relative vapour pressure”, which I think means 60% relative humidity. (They never explain the terms in the paper.) US patent 4,254,565 from 1981 says that bentonite left out to dry in the sun for a few weeks to months typically ends up with 10% to 18% moisture content.
So a porous soil mixture that’s half sodium bentonite and half, say, sand, might perform similarly to wood as a desiccant. It would also have has the safety advantage that it’s not combustible.
Perhaps the second cheapest alternative, following dirt itself, is agricultural crop residues like straw or bagasse. It turns out there are a number of studies of equilibrium moisture content of straw, because moisture absorption is crucial for, among other things, straw-bale construction.
Kymäläinen and Pasila published an experiment in 2000 on flax and hemp fiber “moisture regain”, typically 12% in flax or hemp at 21° and 65% RH, but only 7% in cotton, because most of the sorption is not from cellulose. They found curves quite similar to wood — 5% EMC at 15% RH, 10–15% EMC at 76% RH, and 25 or 30% EMC at 97% RH, depending on harvest time, all dry basis. They also say, “Pectins and hemicellulose absorb more moisture from the air than does cellulose,” which sounds intriguing.
Farmers discussing online say you normally bale straw at 15% moisture content, though sometimes you can get away with 20% (at which point hay will rot, posing a fire risk, but straw may not), and if you leave it out long enough it gets down to 8–10%. Farmers won’t buy hay with over 16% moisture. For construction, anything below 20% is OK.
Some anonymous Canadians at CMHC in maybe 1996 measured straw bale equilibrium moisture content and found a similar curve to that of wood: 5% EMC at 20% RH, 10% EMC around 50% RH, and 15% EMC around 80% RH, all dry basis.
Duggal and Muir measured EMC of wheat straw in 1981 and found 7–9% EMC at 35% RH, 7–12% EMC at 55% RH, and about 10%–14% EMC at 70% RH, all wet basis, all depending on temperature.
Taha Ashour et al. in 2010 measured EMC of some plasters used for straw-bale buildings, finding EMCs mostly in the 2%–4% range, even when the plasters were 75% reinforcing fibers made of wood or straw and 25% made of soil (which was 31% clay). The article doesn’t mention the fact that these EMCs are like five times lower than the EMCs of the incorporated fibers, so I don’t know if the author has any idea why this large discrepancy exists, or even if they know there is a discrepancy.
Heath and Walker in 2009 measured EMC of straw bale walls and found a fairly straight line from 2% EMC at 4% RH up to 13% EMC at 70% RH, followed by a sharp upward turn to 50% EMC (!!) at 93% RH, all dry basis.
Alfalfa hay bales currently cost AR$35 per 25-kg bale, which would reduce the desiccant cost from US$300 to AR$70, which is about US$5. (Actually there are some shipping costs which almost double the cost, but whatever.) Wheat straw bales cost AR$70.
Hay can spontaneously combust due to thermophilic bacteria if wet. At 200°F (93°) farmers are advised, “Most likely, a fire will occur.”, but even as low as 160°F (71°) it can happen. So it's possible that straw, being in many ways similar to hay, might not withstand temperatures as high as 150° without catching fire.
You might reasonably ask why not simply use a normal cooling tower to cool some water (or oil or propylene glycol or whatever), then run that water through a heat exchanger in your house. That is a much simpler approach, and it also avoids raising the humidity in the house. However, more or less by definition, it can only cool the air down to the wet-bulb temperature of the outside air, and usually it can’t quite make it that far. On an unpleasant summer day in Buenos Aires, when the temperature reaches 35° and the relative humidity 60%, the wet-bulb temperature is 27° — still unbearable. Worse, on simply cooling that air to 27° without dehumidifying it, you would raise its relative humidity to 90%, which is very unpleasant indeed. (Air conditioners generally reduce this problem by dehumidifying air by cooling it even further, then allowing it to mix. XXX maybe I should tackle that by a different approach)
