Steam heating theory - physics

michael_15 · March 2005

So I've been sitting here thinking about the theoretical aspects of steam heat (I'm sort of strange that way). . .

We've all heard the comments about water expanding to 1700x its size when it turns into steam and latent heat and all that good stuff, so I thought I'd see how the math really worked out. The math, however, results in some awfully funny conclusions I can't explain. What's wrong here?

Assumptions: "High quality" dry steam is about 1700x the volume of water at 212F and 0 psi; it's about 1500x at 2 psi. We also know that 1 pound of steam has about 970 BTU of latent heat. Let's assume some sensible heat comes out too (that is, the condensate loses temperature) and say that 1 pound of steam releases 1000 BTU before returning to the boiler, roughly speaking.

More assumptions: I've determined that my system (pipes and radiators) is about 6 cubic feet in air volume. My radiators total 160 sq feet EDR, or around 38400 BTU/hour when hot. This means a properly sized boiler would be rated for gross output of, say, 51000 BTU (1.33 pickup). The total weight of my pipes and radiators is about 1250 lbs cast iron+steeel.

It takes 21500 BTU to heat 1250 lb of cast iron+steel from 65 degrees to 215 degrees, assuming no heat is lost in the process. To get the metal this hot, it also has to be full of steam, but I'll ignore that for now. 21500 BTU for a 51000 BTU boiler. . . Conclusion #1: The absolute theoretical top speed at which the boiler can heat all the radiators and pipes (with no air resistance and no loss of heat during heating, and so forth) is 21500/51000 = 25 minutes. In practice, it is always longer than this because the air vents aren't arbitrarily large, you lose energy during the process, and you also have a bunch of hot steam you need to heat up. I've got a lot of thin-tube, so I have comparatively little metal (and air) for my EDR; big column radiators would theoretically take longer.

At 0 psi, 6 cubic feet of steam equals 3.5 ounces of water. That's less than half a cup. Conclusion #2: Given how far the boiler water line drops, that's an awful lot of condensate in the pipes at any given time.

At 2 psi, 6 cubic feet of steam equals 4.0 ounces of water. At 1 psi, 6 cubic feet of steam equals, well, around 3.75 ounces of water. Conclusion #3: If the boiler is off (on pressure) and not making steam, the difference between 2 psi and 1 psi is 0.25 ounces of steam (3 gallons worth at 1 psi).

But, 0.25 ounces of steam only holds a whopping 16 BTU of heat energy. My radiators are fully hot and giving off 38400 BTU of heat energy per hour, or 640 BTU/minute, or 11 BTU per second. I only need 16 BTU of steam condensation to drop the pressure from 2 psi to 1 psi, though, so Conclusion #4: After turning off on pressure at 2 psi, it should take roughly 1.5 seconds of non-steam-generation before the pressure drops back to 1 psi.

=================

Now, obviously the math comes up with some awfully funny results, especially Conclusion#4 above. But I'm not sure I can see where the flaws are. There must of course be something more than just steam going up, condensing, and rolling back down going on in the system, but simplifying it as such should get pretty decent results. Besides, what type of simplification is so erroneous that we would have 1.5 second pressure cycling?

Let me know what you think!

-Michael

bob_44 · March 2005

Mike

I took the time to run through your numbers and I think they are close enough for the problem. I see your point good question. The only thing I can think of is maybe there is a bunch of compressed air traped somewhere that doesn't get vented, this would make the pressure drop more slowly. As for warm-up I doubt that you are heating all the iron from 65F each cycle. Your method makes sense, "I think". I'd like to hear some other opinions. bob

Unknown · March 2005

Steam Theory

Factor that was overlooked.

For every cubic foot of steam there is .10 cubic feet of air mixwd with the steam.

Air is heavier than the steam so it will travel along the lower portion of horizontal pipes. The air take up some space and moves a bit slower than the steam as it flows to the radiators.

Steam condenses in the radiators and flows (1 pipe steam)down the same pipe the steam flowed in. The water meets both the steam and air on its way back to the boiler and return to the boiler is slightly retarded. When the steam meets the cooler air and water some of the latent heat is removed from the steam.

Add these quantifyable factors to the numbers you used and some of the didparity goes away.

Be mindful of this fact: The math that we use and the constants (specific heat, specific gravity, densities and types of materials are all estimates within a five percent range.

Problems:

What kind of steel pipe are we calculating, Steel is an alloy and there are many variations to the pipe. Each manufacturer makes make thete piping a bit different.

Cast iron. How much sand, silica, carbon is in the iron. are all the sections of a radiator the same weight as the sections of a radiator are from anothe manufacturer.

These numbers that we use are our best guess based on the information we have gotten from other reputable sources.

Unless we can weigh the material ourslves we have to allow 10% one way of the other.

As far as the exact correct sized boiler being able to provide the BTUH in give time frame we have to do one tjing a bit better.

If we use atandard air valves on the system all air can be vented in seven to ten minutes. If the boiler cannot reach proper operating pressure in ten to fifteen minutes we have lost the ability to control some of the confort in a building.

Typically, a good practice would be to increase the boilers capacity 1.5 times the standing Heat Load (raditors) plus the piping pick up factor.

When we factor in the combustion efficiency loss we will have oversized boiler 25 to 30%.

That extra energy will get the boiler up to operating pressure in about 12 minutes.

I have done all the math before and have always had questions about where is the missing water, where did the all the steam go and above all why are there problems in the building.

Unfortunatelly we are not given the time or the pay to find out the answers to all the questions on the job.

I have been lucky in a few projects where I had to find the answers and I got paid for it in two ways, a stipend to do the work and a 20% share of fuel savibgs for 10 years.

Those jobs turned out to be slam dunks.

Jake

t. tekushan · March 2005

steam stuff

This may not be as thorough as is necessary but its late. So there:-)

You say 25 minutes to fully preheat the iron. This is true, but since all that iron happens to be in your home, its going to begin transferring heat to its environment immediately. Even before the convection currents can begin, the radiant component of the radiator begins at once (same with pipes- pipe insulation is seldom more than 80% efficient).

I look at the pick-up load as the 3 "P's" -Piping, purging (of air) and preheating of the iron radiators. The initial purging is not assisted by the condensation of steam within the radiator creating its own vacuum, as air is one of the non-condensables. This purging is done with steam pressure (the heating medium) rather than with a pump (hot water) or fan (forced air). Once the purging is complete and condensation is in full swing at the radiators (and vacuum created through the heat releasing process), the distribution load is little more than the frictional losses in the system (pressure drop). These things account for the higher initial heating times beyond the theoretical.

Of course, this isn't enough fun unless you throw in a few wild cards! Lets forget about the proportion of boiler heating capacity versus pick-up load. In the first minute after the onset of steaming, you have no heating so the piping load consumes steam at a rate of 51,000 btu per hour. After the main and risers are filled and the steam reaches the radiators, the proportion of heating to pick-up shifts in a linear fashion towards heating, until you reach the radiator saturation level and boiler shut-down on pressure. At this point, the heating component of the boiler's output is approaching 51,000 btu! The piping arrangements,lengths and size affect the time it takes to do this.
Want another wild card? I'll assume you said yes. Piping losses also include the return piping, which is why any piping that goes through unheated spaces has to be well insulated -both supply AND return. When the system starts, that condensate that returns to the boiler is ice cold, affecting the actual steam output. Cold return water hinders the development of the rated steam output of the boiler. This also increases the heating time.

The pressure drop across the system should be factored in too. The furthest radiator will be at a lower pressure than the boiler gage pressure would indicate. The lower that pressure, the larger the volume of steam per pound. Of course, that means there are fewer pounds of steam in the radiator, but the latent heat per pound is higher (check out your steam saturation tables). Typically, the system equalizes as those radiators reach saturation.

Now, the reason the water level drops in the boiler is that the condensate is delayed in returning. While the steam is breezing into the system at a healthy velocity, the condensate is trickling back. You only have to look at how long the condensate takes to return after shut-down to see how slowly it moves in comparison to steam.

With regard to the time it takes for the boiler to restart after shutting off on pressure: Something interesting happens when the system is pressurized and the boiler shuts down. First, the steam source (boiler) is substantially removed from the equation initially so that higher pressure areas close to the boiler and lower pressure areas away from the boiler do the pressure shuffle and equalize (the expansion at the high pressure end can outweigh the contraction due to condensation, as the condesation rate is lowest when the radiator's at saturation in a warm room in addition to the fact that you can't have a pressure drop without velocity). Second, the lowering pressure simultaneously increases the steam volume everywhere in the system while decreasing the boiling temperature, so that condensate and boiler water at,say, 218 degrees will re-evaporate as the pressure drops, delaying the pressure drop. Don't forget the heat stored in the cast iron of the boiler will find its way to the water. Finally, as contraction continues, any air re-entering the system will also expand due to the heat within the system. All of these things conspire to lengthen the actual time it takes for the boiler to cut in.

I hope these ramblings put a few more pieces into the puzzle. I remain intrigued with steam heat because the more I learn, the more amazing it is to me.

-Terry

Boiler Guy · March 2005

As Arte Johnson would say:

> Factor that was overlooked.

>

> For every cubic

> foot of steam there is .10 cubic feet of air

> mixwd with the steam.

>

> Air is heavier than the

> steam so it will travel along the lower portion

> of horizontal pipes. The air take up some space

> and moves a bit slower than the steam as it flows

> to the radiators.

>

> Steam condenses in the

> radiators and flows (1 pipe steam)down the same

> pipe the steam flowed in. The water meets both

> the steam and air on its way back to the boiler

> and return to the boiler is slightly retarded.

> When the steam meets the cooler air and water

> some of the latent heat is removed from the

> steam.

>

> Add these quantifyable factors to the

> numbers you used and some of the didparity goes

> away.

>

> Be mindful of this fact: The math that

> we use and the constants (specific heat, specific

> gravity, densities and types of materials are all

> estimates within a five percent

> range.

>

> Problems:

>

> What kind of steel pipe

> are we calculating, Steel is an alloy and there

> are many variations to the pipe. Each

> manufacturer makes make thete piping a bit

> different.

>

> Cast iron. How much sand, silica,

> carbon is in the iron. are all the sections of a

> radiator the same weight as the sections of a

> radiator are from anothe manufacturer.

>

> These

> numbers that we use are our best guess based on

> the information we have gotten from other

> reputable sources.

>

> Unless we can weigh the

> material ourslves we have to allow 10% one way of

> the other.

>

> As far as the exact correct sized

> boiler being able to provide the BTUH in give

> time frame we have to do one tjing a bit

> better.

>

> If we use atandard air valves on the

> system all air can be vented in seven to ten

> minutes. If the boiler cannot reach proper

> operating pressure in ten to fifteen minutes we

> have lost the ability to control some of the

> confort in a building.

>

> Typically, a good

> practice would be to increase the boilers

> capacity 1.5 times the standing Heat Load

> (raditors) plus the piping pick up

> factor.

>

> When we factor in the combustion

> efficiency loss we will have oversized boiler 25

> to 30%.

>

> That extra energy will get the

> boiler up to operating pressure in about 12

> minutes.

>

> I have done all the math before and

> have always had questions about where is the

> missing water, where did the all the steam go and

> above all why are there problems in the

> building.

>

> Unfortunatelly we are not given the

> time or the pay to find out the answers to all

> the questions on the job.

>

> I have been lucky in

> a few projects where I had to find the answers

> and I got paid for it in two ways, a stipend to

> do the work and a 20% share of fuel savibgs for

> 10 years.

>

> Those jobs turned out to be slam

> dunks.

>

> Jake

Boiler Guy · March 2005

As Arte Johnson would say:

"Velly intellestink" you guys got too much time on your hands!

I too am fascinated by steam and am completely "absorbed" by your theories. I shall bookmark this thread to follow it further.

michael_15 · March 2005

Good stuff

Just warning you now: I have a habit of being excessively verbose.

With respect to the 25 minute heating time, there are certainly a lot of arguments that say it won't heat that fast; all of the ones you state are true. This is more to say that the results seem to oppose the idea of having built pressure and being comfortable in 20 minutes or whatever, which, in some cases, is reality, which means we need to take another look at the accuracy of our theory.

With respect to the pressure drop after the boiler shuts off, I've distilled your comments into a few ideas:

(A) There's some air left in the radiator at all times.

(B) The steam/water is hotter than 212 because it's under pressure.

(C) There is air re-entering the system through the radiator.
(D) Frictional pressure losses - pressure is perhaps up to 1 psi higher at the boiler than at the radiators.

With respect to (A), I think this actually hurts. I believe we can quantify this. Let's say that the system is 17% air when complete. (This is hopefully reasonable, plus, it makes the math easy.) My 6-cubic-feet of steam is now really 5 cubic feet of steam and 1 cubic foot of air. The air just sits there and doesn't condense. At 2 psi, 5 cubic feet of steam+1cubic foot of air is 3.33 ounces of water. At 1 psi, it's 3.13 ounces of water. Now we only have 0.2 ounces of pressure drop instead of the old 0.25. I'll ignore this for now.

With respect to (B), this is an interesting point I didn't consider. I think this is most significant in the boiler, where all the water is. At 2 psi, the boiling point of water is 219 degrees; at 1 psi, it's 215 degrees. Heating steam from 212 degrees to 219 degrees takes an insignificant amount of energy. Let's say your boiler has 5 gallons of water. While allowing a drop to 1 psi, you suddenly have 5 gallons (around 40 lbs) of water with a bonus 4 degrees of energy beyond boiling. 40 lbs * 4 degrees = 160 BTU = another 2.6 ounces of steam will be generated after the boiler shuts off. Since my system emits around 640 BTU/minute, this adds 15 seconds to the pressure cycle. I know, it's not much, but it'll become important later on.

Later on being now. Consider that the metal also drops in temperature. We'll pretend (D) isn't the case (in mine, it isn't, I simply don't have that much piping for so much pressure loss). Thus, all my metal is, let's say, 219 degrees as well. Cast Iron/steel varies in specific heat, but not much and we're rounding anyway, so what the heck -- it takes about 11.5% as much energy to heat the metal than it does water. So 1250 lbs * 11.5% * 4 degrees = 575 BTU of heat available, or 54 seconds.

Since the boiler itself is several hundred pounds, this factors in as well. Let's just rough out some numbers and say the boiler sections total 400 lbs of metal, which adds about 17 seconds. Again, I'm estimating, but heck, if I'm within 10%, or even 25%, that's plenty good enough. I'm just trying to reason out why pressure cycles aren't 1.5 seconds.

With respect to (C), this is potentially a big deal. It wasn't when I had a pressure drop time in the 1-2 second ballpark, but now that it's over a minute, maybe. To some extent, of course, air will not re-enter the system unless there is negative pressure, and since going from 2 psi to 1 psi is positive pressure, air wouldn't re-enter the system. However, we have to hope for a local anomaly of negative pressure upon steam condensation in the radiators, that is, upon condensation, the radiator manages to pull air in through the vent before it pulls steam in through the piping. Let's make it up and say it pulls 50% of from the air vent and 50% from the piping. But the air pulled in is 70 degrees, so it expands about 25% in heating to 212 degrees. So of the 3 gallons worth of steam condensation, we get 1.5+25% = 1.875 gallons of air inflow. But we need to get rid of the equivalent of 3 gallons of gas to reduce the system pressure from 2psi to 1psi. Since the air inflow makes my original 3 gallon estimate only 1.125 gallons, I multiply my result by 2.7.

With respect to (D), well, I don't think this matters. I'll also ignore the idea of the boiler quickly dropping in pressure as the system pressure equalizes when the boiler shuts off. I'm not sure it actually does this.

Here's a tally:

Original Estimate: 1.5 seconds for system pressure to drop. Let's round to 2.

Adjustment #1: The water is hotter than 212 degrees, so water re-boils upon condensation. Adds 15 seconds to pressure cycle (for 5 gallons of water), more if you have more water.

Adjustment #2: The pipes and radiator are hotter than 212 (215) degrees, so it will re-boil water upon depressurization. Adds 54 seconds.

Adjustment #3: The boiler itself is hotter than 212 (215) degrees, so it will re-boil water upon depressurization. Adds 17 seconds (assuming a 400 lb metal boiler).

Adjustment #4: Air reenters the system. I'm assuming that that radiator condensation will pull in equal amounts from the outside and from the piping, which is a slight overestimation. (The radiator vent hole, after all, isn't that big.) This is a 2.7x multiplier.

(2 + 15 + 54 + 17) seconds * 2.7 = 240 = 4 minutes for the pressure drop from 2 psi to 1 psi.

I've made some estimates, but you can add plus or minus however many percent you want from that result. I think that I've overestimated the air re-entry effect, so the pressure drop time should be less than 4 minutes (again, these are estimates!). On my system in real life, it's probably around 2 minutes if I set it to 1psi cut in and 2psi cut out.

I hope whoever bothered to read this far down found it at least interesting. I just think about things (when I'm supposed to be working) and I think the physics is much more complex (and interesting) than we usually think about -- i.e., I thought of pressure cycling just having to do with steam condensing and hence resulting in a drop in pressure. If the calculations are done correctly in spirit (even if not in value), who knew that the excess heat in the metal over boiling temperature was so significant? Just a few degrees, after all. . .

-Michael

Steamhead · March 2005

For those reading this who don't understand steam

read this thread again!

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Mark Hunt · March 2005

Excellent post

The assumption here is that the rads are only "heating" when they are 200+ degrees. That is for convective heat transfer, but radiant heat transfer comes much quicker.

Remember that rads were painted to reduce the radiant side.

Good thread though!

Fun with math!!!!!!

Mark H

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t. tekushan · March 2005

this was fun and informative

Thanks for giving me something to get my mind around. I, too was avoiding working on an electronic design problem that's been driving me crazy. Avoiding something frustrating=time on your hands! BTW, I'm keeping your analysis since the methodology may come in handy for solving boiler sizing problems. Its nice to come closer to an accurate prediction of warm-up time.

Thanks-

Terry

bob_44 · March 2005

Mike&Terry

Great stuff. bob

michael_15 · March 2005

true about early radiant loss

Which is why I've only referred to the 25 minutes (or whatever I came up with) as a theoretical limit, assuming the radiator gives off no heat until its fully hot. The point was more to dispel the idea that your house should be warm in 15 minutes than to establish a speed to try to reach in heating -- my system never makes it by the 25 minutes, either.

-Michael

Steam heating theory - physics

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