# Heat Storage Design

The design of our heat storage tank is, like any design, an attempt to balance a number of tradeoffs. The following is a discussion of the main design decisions and the tradeoffs involved. The math is pretty simple but you may want to skip this page if you don't like math. Click here to see pictures of the construction of this tank.

## Tank Size

Our 2500-gallon tank is significantly larger than the tanks used in most
residential solar heating systems. One reason for this is simply a matter of cost, i.e. most systems use less storage in order to keep the cost down,
but our tank actually cost us *less* than many commercially-available solar
storage tanks that are far smaller. Partly this is because we did much of the
work ourselves, such as making the heat exchangers inside the tank from plain
coils of copper tubing. Partly it's because we insulated it with blown-in
cellulose, which is much cheaper than the foam insulation used on
commercially-available heat storage tanks. And largely it's because the tank
itself is poly__eth__ylene,
an inexpensive material even in the heavy-walled industrial-grade tank that we
bought. Its weakness is that it is only rated for 140 degrees F, and even
though it won't melt until it gets much hotter, the tank walls can weaken and
bulge if it's allowed to get hotter than its rated temperature. Many
commercially-produced solar heat storage tanks are made of poly__prop__ylene,
which can take temperatures up to 200 degrees but is far more costly. We have
multiple redundant safety controls to make sure that our tank won't overheat,
but it's not as likely anyway because the vertical orientation of our panels
greatly reduces the heat gain in the summer, and with so much mass the
temperature changes much more slowly than it would in a smaller tank so there's
no danger of it "suddenly" overheating.

If we could ignore the cost, one might think that the tank should be as large as possible. If we doubled the volume of the tank, we could store twice as much energy with the same working temperature range. Or for a given amount of energy collected, the tank's temperature would rise only half as much, and the solar collectors are more efficient when the incoming fluid is at a lower temperature. But there are several reasons why we chose the size we did. For one, industrial grade plastic storage tanks are most economical in this size range. A tank with double the capacity is much more than double the price, probably because of less demand and higher transportation costs etc. And as a practical limitation, the larger tanks tend to be taller. This tank is 88.5 inches tall and we slid it in on 2x6 planks so we had only 6 inches to spare with our 8-foot-high garage door openings. We could have installed a bigger tank before the garage was built but this is much more practical. Conversely a tank with half the volume would be about 2 feet smaller in diameter which doesn't save much space, and the cost isn't much less.

The choice of tank size was also based on our projected heat load and on Michigan's climate. Looking at past climate records, we observed that in the winter we often get sun for 3-5 days followed by clouds for 3-5 days. This is not a predictable pattern and sometimes we go for weeks on end without seeing the sun, but we found a lot of instances where we'd have significant sunshine followed by about 4 days of cloudy weather. So as a very rough guideline, we'd like enough heat storage to last through 4 days of cold cloudy weather. Our calculations of heat loss predict that our superinsulated house will lose about 10,000 BTU/hour under worst-case conditions (cold and dark, no internal gains from cooking etc.). But with four adults and five cats living in the house, internal gains will reduce our heat demand considerably. And even on cloudy days we get some passive solar gain, so under typical winter conditions the house should need only about 5,000 BTU/hour (120,000 BTU/day) for space heating. This is a very rough estimate, but good enough for this purpose.

We also like to bathe now and then, and our low-flow showerheads deliver 1.5 gallons per minute so a 10-minute shower uses 15 gallons or 120 pounds of water. A BTU (British Thermal Unit) is the amount of energy needed to heat one pound of water by one degree Fahrenheit, so heating the well water from 55 degrees to 100 degrees consumes 5,400 BTU for a 10-minute shower. Allowing for other uses of hot/warm water such as laundry, we'll budget 30,000 BTU/day for domestic hot water. That brings our total demand to 150,000 BTU/day.

If we'd like to store 4 days of heat at 150,000 BTU/day, that's a total of 600,000 BTU. If we expect the water to cool from 130 degrees average temperature to 100 degrees, a 30-degree change, we need about 20,000 pounds of water to store 600,000 BTU. At 8 pounds per gallon that's 2500 gallons of water. These calculations are based on very rough estimates but this is how we determined that the tank is a reasonable size for our needs.

## Heat Exchangers

Inside the heat storage tank are four coils of copper tubing that function as heat exchangers. Two of them are plumbed in parallel to transfer heat from the solar collectors to the water inside the tank. We chose to use two coils in order to get twice as much surface area for heat exchange, because the solar collectors must transfer heat at a much higher rate (when the sun is shining) compared to the rate at which we remove heat to warm the floors or make hot water. On a really good day we have measured a heat transfer rate of 68,000 BTU/hour from the collectors into the tank, which is equivalent to 20,000 watts! It takes significant surface area to transfer that much power with a reasonable temperature drop of about 20 degrees. By plumbing these two coils in parallel rather than using a single coil twice as long, we can use a smaller pump to move the water through the collectors because there's much less friction in the tubing this way. That saves on electricity, and for this reason the solar heat plumbing is designed to be as smooth as possible (few turns, no sharp elbows) in order to keep the friction loss as low as practical.

The solar heated water enters at the top of the tank and spirals downward, which will create a temperature
*stratification* with hotter water on top and cooler water on the bottom of
the tank.
Our energy records show that the temperature
difference is typically between 5 and 15 degrees. On the other hand the well water enters its exchanger at the bottom and spirals upward through the hottest layer before it exits. If the tank temperature were uniform, the domestic hot water would reach the uniform/average temperature of the tank minus the temperature gradient needed to heat the water through the heat exchanger (roughly 10 degrees, depending on flow rate). But with temperature stratification
we can heat our hot water to a temperature higher than the average temperature of the tank, so stratification is a good thing.
To put it simply, heat energy is more valuable when the medium is at a higher
temperature than you need, and having some very hot water at the top of the tank
makes for nice hot showers. There's also an opposite benefit - just as the stratification raises the temperature of the exiting domestic hot water, it lowers the temperature of the exiting solar fluid headed back to the collectors. That makes them
a bit more efficient because their efficiency goes up as the
incoming fluid temperature
goes down. Most solar heat collection systems are designed to produce
stratification for these reasons.

## Insulation

The tank sits atop rigid foam insulation, inside a compartment that is blown
full of cellulose. How much insulation is enough? There are two main concerns:
unwanted heat loss in the winter, and unwanted heat *gain* in the summer.
In the wintertime, we lose heat from the storage tank into the ground below,
into the attic above, and into the garage. Some heat also moves into the house
through the north/east/south compartment walls but that's not really a loss in
the winter because it helps keep the house warm. In the summer we're mainly
concerned about this heat flow into the house, because instead of a benefit it
becomes an unwanted source of summertime warmth.

Rather than trying to calculate exactly how much insulation would be ideal, we chose practical levels of insulation and calculated the heat flow to determine whether it's reasonable. The tank sits on a concrete pad (isolated from the main floor slab of the house) supported by 6 inches of foam insulation, because we put this amount of foam under the whole house. We added another 3 inches of foam on top of this concrete pad right under the tank because it was easy to do and we had foam left over. So with 9 inches of foam we have an insulation value of about R-45 under the tank. If the bottom of the tank reaches 120 degrees and the ground below is at 60 degrees (an educated guess), we have a temperature difference of 60 degrees. With an insulation value of R-45, that means there's about 1.3 BTU per square foot flowing down into the ground. The tank is 8 feet in diameter so that's about 67 BTU/hour of heat loss through the floor of the tank.

The ceiling of the tank is covered by 4 feet of cellulose insulation, because the tank is 7 feet high and the attic insulation extends 2 feet above the 9-foot ceiling in this area. That works out to a whopping R-170 insulation value! This is not really by design, so much as due to the practical matter of having the tank insulated to the same height as the attic insulation. With an attic temperature of 0 degrees F and the top of the tank at 140 degrees, that works out to about 40 BTU/hour of heat loss through the roof of the tank.

The curved surface of the tank exposed to the garage wall is roughly 60 square feet with an average insulation thickness of 2 feet. If we expect the garage to stay around 40 degrees, we'll lose about 60 BTU/hour into the garage. It's not a total loss since it helps keep the garage from freezing.

Our grand total is about 167 BTU/hour of unwanted heat loss through the tank insulation. This amounts to roughly 3% of the 5,000 BTU/hour that we estimated for the rest of the house, so our tank insulation is only costing us about 3% of our winter heat loss and we think that's reasonable.

The other calculation involves the inside walls of the tank compartment, which transmit heat into the house. These account for about 120 square feet of tank area insulated with 12 inches of cellulose plus 3.5 inches of fiberglass (about R-57 total). In the summer we'll keep the tank cooler since we only need it for domestic hot water, so with an average tank temperature of 120 degrees and a house temperature of 70 (we hope), there's a 50-degree temperature difference across these walls. With an insulation value of R-57, we're getting about 105 BTU/hour of unwanted heat gain into the house in the summer. That's equivalent to a 30-watt light bulb, which we think will be a tolerable level of unwanted heat gain.