How large a tank to keep from freezing in zone 4b Wisconsin?

My plan is to have a large underground tank to store water.  Obviously, if I can get it in the ground deep enough, it won't freeze.  My question is, if I have the tank above ground, how large would it need to be to keep it from freezing over the winter?  January is our coldest month and average low is 3 F, with a record low of -43 F.  It often hits -20 F. here in the winter, with -30 F. not at all unheard of.  The tank could be insulated if need be.  I have access to fairly large amounts of sheet insulation for free so I could pretty easily put a box around the tank with 4-6 inches of it.

Hi Todd, sorry to start with questions, but they could affect the answer...
1.  Would the tank be in intimate contact with the ground (to get a bit of heat transfer)?
2.  Would you be adding/removing water during the winter?
3.  Can part of the tank freeze and it still be ok?
4.  What's your average temperature (not high or low) in January?

My initial guess is that there isn't a size that will keep from freezing up on you.  All lakes around here are buried fairly deep and still freeze the top couple of feet  I know a guy who runs the water department for a decent sized city in central WI.  I asked him how they keep water towers from freezing.  They do it by periodically changing the height of the water to break the ice that forms and in the process introduce new "warm" 45 degree water to the tower.  

Insulating the tank would resist the flow of heat out of the tank but not prevent it.  So day after day the temperature will drop to meet some ratio of the ground temp under the tank and the air temp around the tank.  IE, if the average air temp is 10 and the ground temp is 40 and 75% of the tank is exposed to air and 25% is exposed to ground, the tank should eventually reach around 17.5 degrees.  Insulation would help but I don't think the amount of slightly warm heat from the ground would overcome the loss out the sides.

Side Note:  Water towers only have one pipe going up them.  Water can flow either up or down.  So the water plant just pumps extra water into the main and it forces water back up into the tower.  When they slow down the pumps, the water starts to leave the tower as the city uses it.

Mike Jay wrote:Hi Todd, sorry to start with questions, but they could affect the answer...
1.  Would the tank be in intimate contact with the ground (to get a bit of heat transfer)?
2.  Would you be adding/removing water during the winter?
3.  Can part of the tank freeze and it still be ok?
4.  What's your average temperature (not high or low) in January?

My initial guess is that there isn't a size that will keep from freezing up on you.  All lakes around here are buried fairly deep and still freeze the top couple of feet  I know a guy who runs the water department for a decent sized city in central WI.  I asked him how they keep water towers from freezing.  They do it by periodically changing the height of the water to break the ice that forms and in the process introduce new "warm" 45 degree water to the tower.  

Insulating the tank would resist the flow of heat out of the tank but not prevent it.  So day after day the temperature will drop to meet some ratio of the ground temp under the tank and the air temp around the tank.  IE, if the average air temp is 10 and the ground temp is 40 and 75% of the tank is exposed to air and 25% is exposed to ground, the tank should eventually reach around 17.5 degrees.  Insulation would help but I don't think the amount of slightly warm heat from the ground would overcome the loss out the sides.

Side Note:  Water towers only have one pipe going up them.  Water can flow either up or down.  So the water plant just pumps extra water into the main and it forces water back up into the tower.  When they slow down the pumps, the water starts to leave the tower as the city uses it.

My initial thoughts were to build it directly on the soil on a gravel base.  I was thinking that if I circulated the water somewhat, I could keep it from freezing all the way down, but that may not be realistic.  It wouldn't matter if I got an ice layer on top of the water as long as there was enough room for the water to expand so the container wasn't damaged, but it seems like a better idea is just put it at least 8 feet into the ground.  Average temp here can't be more than 10-15 F in January.  I only want the tank for an emergency water supply.  It seems that easiest answer may be to sink it into the ground and use a frost-free hand pump.

You are basically correct that if you bury it partially, it won't all freeze - IF you get "enough" of it down below frost line.
Then you're getting contact with earth temps that will not go much below 50 degrees even in the dead of winter.
You'll probably get a layer of ice on the top, like the lakes someone mentioned already - and, those lakes don't freeze solid, just a layer on top.
The warmth from under frost line will counteract exterior cold and prevent freezing solid.

How much of your tank below frost line, I'm not equipped to calculate specifically. More is better until you're "deep enough," at which point you are wasting energy going deeper.
You can berm up around the tank with earth if you have the material, to reduce excavation - use the material you excavate for the partial burial.

You could use manufactured materials PAHS (Passive Annual Heat Storage) methods as well - a ground level insulation perimeter layer around the tank, same as one would do for a dwelling using PAHS. Basically just raises the frost line under the insulated area around the structure/tank. But the main "easy" & durable way to do that is using petroleum materials (rigid foam board etc.), and if you excavate some and berm some and stick with good old earth you can avoid that mostly externalized cost.

Also, a little circulation can go a long way to reducing freezing. Observe winter-flow inlets and/or outlets in "frozen" lakes/watercourses - even very slow ones...the old-timers (the ones that didn't fall in and die that is) will warn you not to go walking on those areas, even when other areas are safe as houses.
So circulation is an option to consider also, as you mentioned - but that's not a passive method, you'll have to provide some power input and industrial infrastructure.

Note that whatever the tank is, it needs to be structurally able to not cave in (the buried part) when empty.

Why not insulate the tank?

Lay your gravel pad.

Put down 4" of styrofoam insulation. (2 layers of 2" with overlapping.

Make your tank.  

Wrap your tank in strawbales.

Top the tank with bales.

Put a roof on it to keep the top bales dry.

Wrap the whole thing, or put a traditional render on it.

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calculations:  Wisconsin, zone 4, I'm guessing has about 6000 degree heating days.  Adjusting that from 68 F to 32 F would take off about 180 * 36 or about 2000 degree days.  So call it 4000 degree heating days.  You can get a better estimate by looking up how many frost degree days you have.

That's 100,000 degree heating hours.  So each square foot of exposed tank will lose 100,000 BTU/I per year, where I is the insulation value.  E.g. If it's just 6 inches of concrete that's about R2 so 50,000 btu/year/ft2

Water has a latent heat of 334 BtU/pound.  This is so much larger than the heat from whatever you put into it, that we will consider it only.  That's 3 pounds per 1000 BTU.

So if you insulate to R20 each square foot loses 5000 btu per year it takes a tank that holds 5 pounds of water per square foot of surface.   At R2 it's 50 lbs of water per square foot.  By this figuring a 3 foot cube would have a total surface of 6 * 3^2 =54 square feet, and would contain about 3000 pounds of water.


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Tricks:

The tank doesn't have to freeze solid to get you in trouble.  So float about 3 inches of styrofoam peanuts on top of the water in the tank.  This slows down the ice formation on top, which means as the ice freezes in and compresses the water, the top is the weakest point, and the water bursts through there.  I do this in the cool house for my tree storage, doing it in barrels.

Be generous with the rebar in the bottom.  It has to be stronger that the styrofoam in the top.

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You can be more dynamic if you make a 'pool heater' coil on a south facing wall, filled with propylene glycol (non-poisonous) with a heat exchange loop in the tank.  use a 12v boat sump pump to circulate the water whenever the sun is hitting the coil, and the coil temp is above 50 F.  This will keep the water in the tank reasonably warm.

If you run a loop in the trench that goes from the tank to the house, you can have water year round.  You have to make all your water lines to drain to a particular point so that you can winterize by opening a single valve.

Can you also pick up some passive solar gain for the tank?  Maybe as simple as a dark surface.  Perhaps a windbreak too!

Phil Gardener wrote:Can you also pick up some passive solar gain for the tank?  Maybe as simple as a dark surface.  Perhaps a windbreak too!

If you want to go this route google "nick pine" solar heating.  He goes through a lot of design calcs.