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I have a boiler (oil) with integrated water heater (3.5 gallon). I don't have problems with running out of hot water but I do wonder if having a tempering tank before the boiler would save money on heating the water. (I'm in the Boston area so the cold supply is really cold in winter.) Are there any rules of thumb, etc. for figuring out if this is a worthwhile thing to do?

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You're basically thinking of a tank near/above the boiler that pre-warms the cold feed from waste heat (the warmth of the boiler room) - If installation cost was no object, hand-wavingly it will help. So if you can do it at a fairly low cost, it should save a bit.

Getting to hard numbers is fairly difficult, or very easy if you knew some unknowable things.

A gallon of #2 fuel oil is roughly 138,000 BTUs - if we give your boiler the benefit of the doubt and say it's 85% efficient (a few might be more, a fair number will be 80 ) that means you'll get 117,000 BTUs from each gallon burned.

1 BTU heats one pound of water one degree Farenheit. 117,000 will heat 1800 lb of water from a "cold but not frozen" 34F to "might be a warm shower" 99F - that's roughly 225 gallons. If you prefer a "very hot" 120F shower, 170 gallons.

That's the easy part. The hard part (or mass of made-up fudge-factors) is "and what will the tempering tank do for the input water temperature" - to the extent that it directly sucks heat, it will make no difference (you're still burning fuel to heat your house and water, you're just shifting it around a bit) but to the extent that it "scavenges" heat that would otherwise be wasted, there is a savings. If the input water temperature was raised 21 degrees to 55, you'd get 225 gallons of very hot shower from your gallon of oil. If we make the ballpark assumption that you use 17 gallons per shower, you'd get 3 "free" showers (13 for the price of 10) Which is 25% savings looked at one direction, 30 the other. But "garbage in, garbage out" rules here - while I'm trying to speculate reasonably, it's just speculating. what the actual effect on your water heating will be is essentially unknown until you try it, though you can possibly make more educated guesses by considering things like the average temperature in the place you'd be putting the tank, your actual shower times and shower flow-rate, actual water temperatures in and as you shower, etc...

If you can fit the appropriate drain pipe below your shower, there is a neat widget that plumbs the cold-water to the shower around a copper drain pipe from the shower, pre-warming the cold water to the shower as you shower, so you can use less hot for the same shower temperature.

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The answer completely depends on where the heat comes from. As with the answer from @Ecnerwal if it simply scavenges heat that otherwise would go into the home, it's just shuffling deck chairs. In Boston you might find the tank does more good in summer, when air temperature is well above ground temperature, thus providing a true source of free pre-heat. Solar is possible, but difficult and not so great in winter. It's possible your boiler has excess flue energy, but this is tricky to extract because if you take too much you get all sorts of combustion and buildup problems.

Website http://www.greenbuildingadvisor.com/ is a good place to go for energy advice, but you won't find tempering tanks among people's top ten best list. There's a list of drain water heat recovery units at my website http://obviously.com/6/drain-water-heat-recovery-units-dwhr (but keep in mind they only really work for showers as for many good reasons they don't store water).

You may have more total energy savings by focusing on summer: is the boiler the right solution for heating water in that season?

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