Estimating annual fuel usage

Mike T., Swampeast MO

You cannot play with the delta-t number in the denominator because it is <I>already</I> relative to your design outdoor temperature and heat load based on standard conditions in your numerator.

Keith Cappuccio

annual fuel consumption

I was putting together some numbers from John Siegenthaler's awesome book "Modern Hydronic Heating" and wanted to get some input on something.

On page 34 he gives a formula for estimating annual fuel usage: (It helps to write this out on paper)

Annual fuel required=(design heating load x annual degree days x 24 hrs x unitless correction factor)/(1,000,000 x design delta T)

For my area, I put together this simple estimate of an average house:

Annual fuel required= (100,000 btu x 5219 x 24 x .63)/(1,000,000 x 70 degrees delta T) = 113 MMBtu per heating season

That MMBtu means one million btu. Anyway, it's a great formula and hopefully shows a few of you how great the book really is and how much you should buy it. Anyway, I started plugging a few different numbers into the equation, and got some startling results. Try it yourself.

Predictably, if you were to increase the heating load of the building, the result would be that you need more energy per heating season to heat the building. So, if you change the design heating load to 150,000 btu/hr input, your annual consumption would increase to 169 MMBtu per season. That makes perfect sense, right?

If one were to plug in different delta T's for indoor design temperature, the results are a little less intuitive. By increasing the delta T between indoor and outdoor, that is by increasing the indoor temperature without moving the house, we find that there is LESS energy required per season!

So in our first equation, the one with 70 degree delta T, we came up with 113 MMBtu per season required. With all numbers remaining the same, we find that a 75 degree delta T requires 105 MMBtu per season. An 85 degree delta T requires 93 MMBtu per season. This implies that increasing the indoor air temperature will require less fuel input for each increase!

The reason for this is because the equation takes the form of the reciprocal function, that is, the function Y=1/X. When this happens, as the denominator increases, the output, or Y must decrease. The function is simple enough to plot on a graph when there is only one variable.

The question that I have is, well, am I correct in my findings? It is counterintuitive to state that a higher delta T would result in lower energy costs.

The answer, of course is that the indoor design temperature is intimately related to the design heating load of the building. In order to estimate the design heating load, the indoor/outdoor delta T is calculated in, because a higher difference in temperatures between two objects will result in a greater rate of heat transfer.

As a result of that, the denominator can only increase at the same pace as the coefficient in the numerator that represents design heating load. One number cannot change without the other following suit. When we change both numbers, the estimate of energy required becomes correct.

Anyway, I hope that I'm right about all of this. Any thoughts, suggestions? The reason that I set up the spreadsheet is because we're doing a huge number of oil to gas conversions right now. It's been a critical part of our success to be able to use math and solid numbers to make faithful estimates to our customers as to what they can expect from their new systems. I suggest that you pick up the book and do the same.

Thanks for listening,

Keith

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Peter Zelchenko_2

There is an error in the formula. As the Delta T rises, fuel usage rises.

jp_2

got it backwards

as delta T increases, so will energy requirements in a nonlinear fashion. it will take more and more energy for each increase in temp.