Why This Is Important
---------------------
According to the EPA's figures, 75% of residential energy use in the
US in 2001 was for heating things up and cooling them down in fairly
brute-force fashions --- of 9.86 quadrillion BTU, only 2.40
quadrillion were spent on anything else. [0] And essentially all of
that is unnecessary.
Only about a fifth of total energy consumption in the US is
residential [1], so this 75% is only about 16% of the total; but I
think it is only slightly exaggerated from usage patterns in the US
economy as a whole. I estimate that 50% of overall US energy
consumption is spent on indoor climate control.
I don't have good numbers for the rest of the world. I assume they're
roughly similar.
As global warming increases the amount of severe weather people must
cope with, the importance of effective indoor climate control will
increase; and fighting global warming will require the reduction of
energy consumption. Additionally, sufficiently effective indoor
climate control can render uninhabitable regions habitable and, if
scalable to large buildings, enable the cultivation of a wider range
of crops than the local climate would normally allow.
Argentine Air Conditioning
--------------------------
Here in Argentina, air conditioners are rated in "frigorías". One
frigoría is one kilocalorie per hour, which is about four BTUs per
hour. They recommend 50 frigorías per cubic meter. (This is a little
strange, since you'd think you would pick your air conditioner
capacity by the amount of heat that comes into your house per hour,
rather than the amount of heat your house can hold. But I digress.)
Our apartment is 80 m², and about 2.75 meters in height, which means
it contains about 220 m³, and therefore should need about 11000 kcal/h
of cooling capacity. This is a bit of a problem for two reasons:
- Air conditioners are expensive more or less in proportion to their
cooling capacity, and a 2250-frigoría unit costs $1550 ($0.69 per
frigoría), while a 3000-frigoría unit costs $2040 ($0.68 per
frigoría). The largest off-the-shelf unit I found was 8000
frigorías, and it cost $5000 ($0.63 per frigoría). At this rate
11000 frigorías would cost us $6930 (US$2200), which seems like a
lot of money to me. For example, it's more than three months' rent.
- Air conditioners also use energy more or less in proportion to their
cooling capacity, with variations in the neighborhood of 30%. The
8000-frigoría air conditioner uses 3540 watts of electrical power,
which would be 16 amps if it's properly power-factor corrected. (I
know that's not the amount of heat it's removing, because a kcal/h
is only about 17% bigger than a watt. I'm a little confused because
I thought that it normally cost more than a watt to remove a watt of
heat, but all the air-conditioning units' datasheets claim that they
remove a little over two watts of heat per watt of power used.) So
11000 frigorías should be 4868 watts of electrical power, or a
little over 22 amps, more than half of the total of our main circuit
breaker. If we assume a duty cycle of 40% during the summer, that's
1947 watts on average during the summer. If we were paying US$0.10
per kilowatt-hour, which is in the neighborhood of what the price
would be if residential power weren't heavily subsidized, 4206 kWh
would cost us US$420.60, or AR$1324. The current residential
electrical rates are about $0.04 per kWh, which would bring the
price to only $168.20, but that's still enough of a cost to want to
minimize it.
Water Tanks to Sink the Heat During the Day: What Size?
-------------------------------------------------------
So I've been thinking some more about my 'desert cool and water
economics' kragen-tol post from more than a year ago. Suppose we
wanted to be able to sink 11000 kcal/h of electrical power for 40% of
each day during the summer into some kind of heat storage tank (say,
full of water) and then radiate it into space at night. How big of a
tank would we need, and how much area? How much surface area would we
need for heat-exchanger coils to suck 11000 kcal/h of heat out of the
air during the day?
The first question is the easiest one. In the last few days, the
highs have been around 28°C and the lows have been around 18°C.
Suppose we want to lower the temperature of the air from 32°C to 22°C,
which is 10 K of difference. So the water must start out cooler than
22°C and end up cooler than 32°C. Suppose we can start with water at
16°C and end with it at 30°C. Then we can get 14 kcal of heat out of
the air per liter of water that flows from the cold tank through the
heat exchanger into the hot tank. So 11000 kcal/h would be 790 liters
per hour. I've hypothesized needing this cooling power for 9.6 hours
(40%) out of each day, which means that each tank would need to hold
7580 liters of water, which is 7.58 metric tons and 7.58 cubic meters.
If we kept these 7.58 metric tons of water indoors, and didn't need
any extra space for insulation, we would need 5.5 square meters of
floor space for them, or about 2.3 meters square. That's about 7% of
our total floor space, and that 7% should be no more and no less
constant across dwellings than the figure of 50 frigorías per cubic
meter.
Water Tank Size Is Less Sensitive To Temperature
------------------------------------------------
The same amount of water can sink more heat, and sink it more quickly,
when the difference between the air temperature and the cool-water
temperature is greater. If the cool-water temperature stays at 16°C
and I want to cool the air from 28°C, I can only sink, at most, 12
kcal per liter of water. But if the air temperature is 40°C, I can
sink 24 kcal/L, twice as much heat for the same volume of water.
So while a conventional air conditioner needs to be sized for the
amount of heat it needs to extract on the hottest days, and therefore
cares a lot about how hot they are, the design of such a reservoir
device should be relatively insensitive to the maximum temperature.
So, even if the 16°C number is correct, I might be able to get by with
a much smaller amount of water, simply because the 11000-frigorías
number is only relevant on the very hottest days --- if even then.
The Exhaust Heat Exchanger
--------------------------
Cooling the water at night can happen in essentially three ways:
evaporation, conduction, and radiation. I think evaporation is
limited in its applicability (it won't help colonize the Grand Erg
Occidental, and it will get expensive if water does) although being
able to use brackish water might broaden its applicability.
This leaves conduction and radiation. Radiation has the major
advantage that, on dry nights, the heat sink is the cosmic background
radiation at a temperature of about 3 kelvins, so it might be possible
to cool the water quite cold, perhaps even to freeze it. (This
probably involves using an intermediate heat transfer fluid with a
lower freezing point, but it's tractable.)
The basic radiation law is Stefan's Law or the Stefan-Boltzmann law:
Q/t = e{sigma}A(T_hot^4 - T_cold^4)
e is the emissivity, a number between 0 and 1 indicating how close
to an ideal black-body radiator the object in question is (at the
relevant wavelengths). I think it's (1 - albedo) at the relevant
wavelengths.
Sigma is the Stefan-Boltzmann constant: 5.67e-8 W/m²/K^4
Q is the heat transferred.
t is time.
T_hot and T_cold are the temperatures of the hot and cold bodies,
measured in kelvins.
So if our e is, say, 0.75; T_hot is at least 16°C (289 K); T_cold is
insignificantly small; t is, say, 8 hours; and we want the Q to be
100Mcal (11000 kcal/h * 9.6 h); how much emitting area do we need?
100Mcal is 420 MJ, so the required heat dumping rate is 14.5kW;
T_hot^4 is 7.0e9 K^4; so we have
14.5kW / (0.75 * (5.67e-8 W/m²/K^4) * 7.0e9 K^4) = A
m² * 14.5e3 / (0.75 * 5.67e-8 * 7.0e9) = A
m² * 14.5e3 / (0.75 * 5.67 * 70) = A = 49 m²
So I'd need about 7 meters square of roof space to beam the heat from
my little apartment back out into space at night, plus enough pipes
and aluminum to keep it all warm. And on cloudy nights, it wouldn't
work. Note that 49m² is more than half the floor area of the
apartment.
Conduction, on the other hand, requires little extra equipment (just a
fan and some flaps to direct air from the outdoors through the same
heat exchanger used to cool the indoors) and is known to be feasible.
Cost of Space
-------------
We can estimate the "cost" of losing the space at 7% of our rent: for
us, $150 per month, or $1850 per year. So it costs us $40 per month
during the life of the thing, and as long as the electrical rates are
so deeply subsidized, it would actually cost us almost all of the $150
amount. We're not in a particularly expensive area of Buenos Aires,
but areas outside the Capital Federal are cheaper still. So for
people in areas that cost less per month per square meter, it might
save them money each month. Even for us, it might cost less up front
than a $7000 refrigerative cooler, at least if it doesn't break the
floor and can be adequately insulated without building anything really
expensive.
Heat Exchanger Area
-------------------
I don't really have a clue what size of heat exchanger I would need.
Presumably it would be a few times bigger than the heat exchanger that
an air conditioner would use, because the temperature difference
between the coolant and the air is smaller.
Tank Insulation
---------------
The hot water tank must retain its heat until it can be exhausted into
the great outdoors at night, if it is inside; and the cold water tank
must retain its cool until it can be exhausted into the indoors during
the hot day, if it is outside. In the winter, their roles would be
reversed. (Beatrice suggested reversing their roles during the
winter. I need to think more about this.) Insulating materials like
fiberglass typically have thermal conductivities around 0.04 W/m/K.
If a cubical tank contains 5.28 cubic meters, it's 1.74 meters on a
side, and therefore has 18.2 m² of surface area, so that's around 0.72
m W/K, and I've been hypothesizing about a 20 K temperature
difference, so that's 14.4 m W. We need to divide that by enough
centimeters of insulation that the resulting uncontrolled heat flux is
small compared to the average 4400 kcal/h (=5100W) heat flux that the
thing is designed to control. If "small" means 5%, that's 510W, which
means we need 2.8 cm of insulation.
3 cm of insulation around cubical tanks seems like it might be a much
more reasonable proposition than welding up some giant dewar flasks
for the thing, which would presumably need to be round instead of some
more convenient shape. (Right?) That's roughly a cubic meter of
fiberglass (or whatever: cork, cotton, felt, "mineral wool",
styrofoam, are all in the same ballpark; silica aerogel could cut the
space by half, and straw would double it) to insulate all ten cubic
meters of reservoir.
Phase Change Materials Instead of Water
---------------------------------------
Water has a very high specific heat, so using most other materials for
the hot and cool reservoirs in place of water (air, say, or iron, or
concrete) would increase the weight required, rather than decrease it.
(And solid materials have the additional problem that they're kind of
inconvenient to move between the warm reservoir and the cool
reservoir.)
However, materials that change phase in the relevant temperature range
--- say, solid to liquid, or liquid to gas --- have a much higher
effective specific heat than any substance. If we were trying to cool
the apartment from by heating water to 1°C from -1°C, for example, we
could dump half a calorie per kilogram of ice going from -1°C to 0°C,
then 80 calories per kilogram as it melted, then a calorie per
kilogram of water going from 0°C to 1°C. This allows you to reduce
the weight of water you need by more than a factor of 40. If
previously you would have needed five metric tons, now you only need
123 kg.
(Air conditioners in the US are often rated in "tons", which are tons
of ice melted per day. Before refrigerative air conditioners were
invented, you would cut ice out of frozen lakes in the winter and
store it in an "icehouse", insulated by straw, all year round. So
this idea of using phase-change materials as heat reservoirs is
nothing new.)
(Note that this works even if you want to cool the air from 25°C to
20°C.)
But this only works if the relevant reservoir can be induced to keep
its temperature at the melting or boiling point of the reservoir
fluid, or oscillate back and forth across it. If you can dependably
get access to a reservoir of below-freezing cold, you can use this
approach with water; otherwise, you might have to use a material whose
phase change temperature is somewhere more convenient. (If it can be
actually inside the range where you want to maintain the air
temperature, you don't need tanks and stuff. You can just put the
stuff out where it can conduct heat to the air, like in the wall or on
the coffee table or whatever.)
There are all kinds of research going on on phase-change materials as
lower-mass heat reservoirs. See, for example, J.R.Gates's
phase-change material home page:
> http://freespace.virgin.net/m.eckert/index.htm
They also have this nice thermostatic property, which has been used to
calibrate thermometers for centuries, that they tend to heat up things
that are colder than their phase-change temperature, and cool down
things that are warmer.
This is Nothing New; Why Was It Rejected Before?
------------------------------------------------
Obviously, indoor climate control with insulated heat reservoirs,
passive solar design, phase-change materials for reservoirs, and so
on, is nothing new. Adobe houses, stone castles, dugout houses,
soddies, caves, iceboxes using ice stored since the winter in the
icehouse, walls shared between houses to prevent heat loss, and so on,
all go back generations if not millennia or longer. But they were all
abandoned in the developed world over the last few decades. Why were
they abandoned, and what makes me think they're worth recovering?
They were abandoned for several reasons:
* Fashion. In "Pioneer Pride", I seem to recall reading my
great-uncle abandoned his Western New Mexico dugout because his new
wife didn't feel that it was a "proper house." It wasn't what she
was used to, what she'd grown up with. This is the problem the
Viridians are tackling; green design has to be hip in order to get
uptake.
* High cost of labor. The traditional techniques involve a lot of
heavy material hauling, and most of it isn't easily automatable.
(Adobe bricks are still mixed by hand, made by hand in wooden
frames, then stacked by hand to dry.)
* Inflexible construction techniques. You can build a wooden
balloon-frame house anywhere you can haul the wood, but you can only
build a cave house where there's a cave.
* Low cost of energy. As we've eagerly depleted the Earth's
fossil-fuel endowment without much concern for the environmental
effects, we've kept the cost of that energy quite low, so it's
seemed sensible to use cheaper construction techniques and save
space rather than spend money to save electricity. And electricity
subsidies like those in Argentina, while they might be helpful for
development, make this worse.
I think there are a number of new developments that make these
approaches relevant again:
* Fashion. Energy conservation, and green design in general, are
trendy in much of the world. Hopefully they'll stay that way for a
few decades.
* More extreme weather. As global warming increases the extremes of
heat and cold we must survive, even people who cling to 1950s
climate-control technologies will benefit by complementing them with
more efficient approaches.
* Better materials. Even glass and steel are major improvements (in
cost and flexibility) over many traditional materials, but we also
have stainless steel (making large Dewar flasks possible), silica
aerogel, PVC, fiberglass, styrofoam, fiberglass-epoxy composites
(making large transparent water tanks possible), low-emissivity
glass, stainless steel, aluminum, and copper pipes and fins (making
heat exchangers efficient), rammed earth, straw bales, and on and
on. In this case, the large amount of thermal mass (in the form of
water in a PVC tank insulated with styrofoam) occupies a tiny
fraction of the size of adobe walls.
* Better designs. Dewar flasks, window overhangs, double-paned
windows, and so on.
* Less-labor-intensive construction techniques. We can now excavate
and build earth berms with small-scale earthmoving equipment.
* Inexpensive computer control. It's now inexpensive and reliable to
have a microcontroller turn a water pump or two on and off a few
times a day, monitor some pressure sensors, control some fans, open
or close some air control flaps, open or close curtains or louvers
to regulate the amount of solar heat gain, and raise an alarm in
case of pump failure or pipe leakage. This means that it should be
straightforward to control air and radiant temperature indoors as
effectively as with a traditional climate-control system.
* A possibly rising cost of energy. Certainly the cost will rise
here; it may double or quadruple or more.
Related Buzzwords
-----------------
Traditional adobe construction. Traditional dugout construction.
Earth berms. Trombe walls. The German Passivhaus program. Seasonal
thermal stores. Earth-berm construction. Straw-bale construction.
Dewar flasks. Earthships. Thermal energy storage in general, in
particular, "full storage systems" that run the air conditioner
chillers only at night. John Hait's Passive Annual Heat Storage.
Water walls. Isolated solar gain. Annualized geo-solar.
Superinsulation. Heat recovery ventilation. Ground source heat
pumps. The SHPEGS Solar Heat Pump Electrical Generation System.
References
----------
[0] "Energy Consumption and Expenditurs RECS 2001", from the US
Department of Energy Residential Energy Consumption Survey:
> http://www.eia.doe.gov/emeu/recs/recs2001/detailcetbls.html#total
In particular, see page 3 of the total consumption PDF:
> ftp://ftp.eia.doe.gov/pub/consumption/residential/2001ce_tables/enduse_consump2001.pdf
Of the 9.86 quadrillion BTU, 2.21 quadrillion are spent on air
conditioners and refrigerators, which someone might argue aren't
really part of "climate control".
[1] US Department of Energy Energy Information Administration (DOE
EIA) Monthly Energy Review, December, 2007
> http://www.eia.doe.gov/emeu/mer/consump.html
In particular, the third page of section 2, "Energy Consumption by
Sector", p.27:
> http://www.eia.doe.gov/emeu/mer/pdf/pages/sec2.pdf
Currently this shows a 9-month total for 2007 of 16.43 quadrillion BTU
for the residential sector, out of 76.16 quadrillion overall; there's
another 13.84 quadrillion attributed to the "commercial" sector, which
has roughly similar seasonal and source energy usage patterns,
suggesting that a large part of its energy consumption is also
devoted to indoor climate control.
However, that total also includes 30.87 quadrillion BTU of energy used
by the "electric power sector" --- 40% of the total --- and presumably
that usage is roughly proportional to total usage of electricity.
So my best estimate is that (0.75 * (16.43 + 13.84) / (76.16 - 30.87))
= 50% of US energy consumption is devoted to climate control.
