Burning Wood for Heating - The Physics

The Physics of Burning Wood as a Heating Fuel

Nearly everyone has gotten spoiled into the ease and comfort of using fossil-fuels, particularly heating oil (made from petroleum) and natural gas, mostly because of the simplicity of just turning a wall thermostat and not having to worry about anything else (except the heating bill!) However, as people are starting to realize the critical nature of the global warming crisis, and that our burning of fossil fuels is the primary cause of it, there will certainly be coming pressures to reduce our consumption of those fossil fuels in the future. This may show up as actual regulations, but is probably more likely to show up as extremely high taxes on fossil fuels to try to force people to choose other alternatives.

One of those alternatives, which used to be extremely popular, is of burning wood. Even in the 1970s and early 1980s, millions of people burned wood to partially heat their homes. One main reason that happened was that the woodstoves that were then available were fairly simple and inexpensive. For just over $100, people could buy a Franklin Stove, and for $300, some pretty high quality products (including the ones that we invented and manufactured!)

However, in the early 1980s a few giant companies saw the chance to chase nearly all the smaller companies out of the market (in 1979, there were around 2,200 manufacturers of woodstoves in the US, mostly VERY small companies.) In addition, some people concerned about the environment made some incorrect decisions in forcing the enacting of hundreds of laws to essentially try to end woodburning. In many areas, they succeeded. For many years, it was illegal to even consider installing or using a woodburner in Colorado or Oregon or Minnesota or many smaller areas of many States.

Very shortly, out of those 2,200 manufacturers, only 34 still were in business. And soon after that, several very large corporations bought out virtually all of them. There are still several dozen familiar brand names in woodstoves, but they are essentially all now owned by maybe three huge corporations. Between that effect and many extreme efforts at government regulation, virtually no quality woodstove is available today at under $3,000.

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Those giant corporations do not seem to have any problem with that, as they (and their dealers) make huge profits on each one they sell, AND there is essentially no possible way that any new competition could possibly enter the market. Whatever gets sold pretty much invariably benefits one or the other of those corporations.

Long ago (1970s), woodstoves existed in order to actually benefit poor people who needed to try to save on their heating bills! Now, with prices all above $3,000, (plus installation, which also now tends to be extremely expensive, because it is by those very same dealers who sold the stove!) it is nearly unimaginable that any poor people could possibly afford a woodstove! The only people who can really buy them these days are wealthy people who simply want a new toy, and who never think about the cost of heating their house anyway! It is sad, and has been for around 20 years!

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It is sort of darkly amusing to see that, had some older versions of less expensive woodstoves been available and allowable during the past 20 years, THEY would have contributed NOTHING to global warming, and indeed they could have enabled millions of homeowners to have avoided having to burn billions of tons of fossil-fuels. The extreme restrictions on woodburning and woodstoves, has actually GREATLY INCREASED the problem of global warming! I wonder when lawmakers will finally figure that out? And maybe then again allow the manufacture and sale of things like Potbellies and Franklins and Fisher stoves? Hard to say! Cast iron Potbelly stoves might realistically sell today at around $200. But only $3,000 and up woodburners are allowed to be manufactured or sold! Think many Potbellies might sell? You bet! Think those millions of new buyers might reduce their consumption of fossil-fuels in heating their homes? You bet! No, potbellies and Franklins were NOT really sophisticated! They were actually quite simple and crude. And even though their thermal efficiency was not spectacular, they generally did the job!

Now, with the new concerns regarding global warming and fossil-fuel it figures that there may be renewed interest in burning wood. For this reason, this presentation is being provided so that a background of the actual Physics behind what occurs in burning wood can be better understood.

First, absolutely anything you could burn initially started out by a single process, photosynthesis, where energy from sunlight is applied to carbon dioxide from the atmosphere and water from the ground (and water vapor from the air) by chlorophyll in plants, to form a single compound, called glucose.

It is actually pretty impressive that the simple CO2 and H2O molecules can be combined to form the fairly complex C6H12O6 organic molecule of glucose! Glucose is the ONLY molecule that photosynthesis can create! A plant uses the (previously sunlight) energy in these molecules to modify them to make all the other organic molecules on which lifeforms depend. Specifically, plants often remove one water from the glucose and use that bond to chain together long and strong molecules of C6H10O5, which is called cellulose. This is important here because cellulose is what nearly all of wood is made of!

Because we know the molecular composition of cellulose, we know its molal composition. What this means is that if we multiply each type of component (C, H, and O) by the known atomic weights, we can immediately know the WEIGHT composition of the cellulose. You can confirm that this is therefore 44.5% Carbon, 6.2% Hydrogen, and 49.3% Oxygen.

If ALL wood was always completely cellulose, this would be the exact composition of every piece of wood. But that is not quite the case. All plants and trees also manufacture other organic molecules then need, not just cellulose for the structure. So, even though every piece of wood is primarily cellulose, the actual percentage composition varies a little. Actual wood generally varies within the following ranges: 49.5%-53.1% Carbon, 5.8%-6.7% Hydrogen, and 39.8%-43.8% Oxygen.

For the rest of this presentation, we are going to assume that the wood we are considering will be 51% Carbon, 6% Hydrogen and 43% Oxygen.

This analysis is of the actual wood itself, that is wood that is totally without any moisture in it. It is not practical to try to dry pieces of wood to that condition. Rather, a reasonable drying is generally done.

While part of a tree, each piece of wood was filled with water. Many cells are hollow in order to be able to provide pipelines for water collected by the roots to be sent up to the branches and the leaves, where it is needed for photosynthesis and other needs. So a piece of wood cut immediately from a tree that was just alive contains massive amounts of water in it. Actually, nearly always far too much water for the piece to burn. Such wood is generally called GREEN. The main reason it cannot burn is because all that moisture has to be evaporated first before the actual wood could possibly heat up enough in order to catch fire. With so much water to evaporate, nearly all the heat produced in an attempt to start a fire gets used up for that evaporation and none goes to heating the wood up. It NEVER works!

Therefore, firewood is always stacked and left for many months, even a year, so that dry winds can blow through the pile, and more importantly, through the hollow cell pipelines, to dry out the wood.

There appears to have early developed two different ways of describing how much moisture is in a piece of wood. Say you have a piece, just cut, which weighs 50 pounds on a scale. But we will later find that there is actually 30 pounds of wood in it. The less desirable way of describing the moisture content is to use the weight of the actual wood as a basis, and say that the wood initially had 67% moisture [(50 - 30)/30]. The more correct and useful way to describe the moisture content is to use the weight of the full piece as a basis, and say it initially had 40% moisture [(50-30)/50]. In either case, there is a lot of moisture! We are going to use the second, more common and more useful description here.

After a year of drying the already cut lengths of wood (so the insides of the cells are exposed to the drying winds) in that stack, the moisture content has usually dropped down to between 18% and 25%, what is then called Seasoned wood. In our discussion, to keep things as simple as possible, we will assume that our wood has 20% moisture.

We are getting close to being able to do some calculating! Say we start out with 100 pounds of wood. Twenty percent of this, or 20 pounds, is water that we were not able to remove. That leaves 80 pounds of wood. Actually, slightly less, because all pieces of wood contain small amounts of materials that cannot burn, which will create ash content after burning. That unburnable material is rarely much over 1%, and we are going to assume exactly 1% here. So we actually have 79 pounds of actual wood, which has the composition we described above. That means we have 79 * 0.51 or 40.3 pounds of Carbon, 79 * 0.06 or 4.7 pounds of Hydrogen and 79 * 0.43 or 34.0 pounds of Oxygen in it. We are starting to get somewhere!

First, we can now determine the total chemical heat in that wood. Each pound of Carbon will generate 14,100 Btu of heat energy if it is able to completely oxidize into carbon dioxide. Since we have 40.3 pounds of Carbon, that means 568,000 Btus. Each pound of Hydrogen will generate 61,000 Btu of heat energy if allowed to completely oxidize into water, so our 4.7 pounds of Hydrogen contains another 287,000 Btus. The Oxygen is already oxygen so it cannot oxidize and therefore it has no chemical energy content in it. Therefore our absolute total chemical energy in the Carbon and Hydrogen is 855,000 Btus. No actual process is perfect! In actual measurements, the combustion process falls well short of this theoretical value. Around 720,000 Btus for our hundred pounds of seasoned (20% moisture) firewood is more realistic.

This is for 100 pounds of wood, so we can say that each pound of wood contains around 7,200 Btus of chemical energy in it. Absolutely dry wood contains around 8,660 Btu/pound in it a quantity that is generally referred to as the HHV (high heat value) of the wood, which you can confirm from many published sources.

Next, we need to consider the fact that we have to heat up and evaporate water from three main sources. One: the 20% of water still remaining in the seasoned wood pieces. Two: the water newly created by the combustion of the Hydrogen. And three, humidity in the air brought in for the combustion. We need to first total up the weights of water involved. We know that there are 20 pounds of the water that remained in the wood. As to the water generated by the combustion of the Hydrogen in the wood, that is a little more complicated to calculate! We know that the chemical reaction is (2) H2 + O2 gives (2) H2O. If we look at this by molal amounts, we have 4 H + 2 O = 2 H2O. Since we know the atomic weights of each, we can see that by weight, we have 4 + 32 = 36. We will do this sort of thing again later, but for now we just want to see that there has to be nine times the weight of water produced for the weight of the Hydrogen which is oxidized. In our problem, that means 4.7 * 9 or 42.3 pounds of water produced.

There is also the humidity (moisture) in the air that is brought in for the fire, which greatly depends on the outdoor humidity at that moment. We are going to assume here that the 644 pounds of air (calculated below) brought in will contain 10 pounds of humidity used by the fire. Therefore, in our problem we have a total of 72.3 pounds of water.

This water must first be heated from the wood/air initial temperature (say 35°F) up to 212°F, which takes 177 Btu/pound, evaporated, which takes 1050 Btu/pound, and then heated further as a gas (water vapor) up to the final smoke exit temperature (we will assume the best possible value, of around 240°F, where the absolute temperature is 700°R), which takes another 7 Btu/pound or so. Therefore, we need a total of around (177 + 1050 + 7) * 72.3 or 89,000 Btu. This energy must come out of the 720,000 Btus of chemical energy in the wood, now leaving around 631,000 Btus.

The carbon dioxide generated by the burning must also be heated up to the final smoke temperature. We will see below that 187 pounds of carbon dioxide will be created, and each pound will require 30 Btu, or an additional usage of 6,000 Btus. We now have left around 625,000 Btus.

Finally, we have that air that was used for combustion, which also must all be heated up. We will calculate below that the complete combustion of that wood would require 184 pounds of oxygen. We had 34 pounds of oxygen in the wood itself, so we actually need just 150 actual pounds of oxygen to be provided in the air. Since air is around 23.15% oxygen, this means that 644 pounds of air is absolutely needed.

That situation would require remarkably smart oxygen molecules, to always go to exactly where needed for the combustion. In reality, additional air is always provided, called EXCESS AIR. We will assume here a common amount of excess air, 40%. This means that we need to provide 901 pounds of air. Each pound requires around 31 Btus of heat, or an additional 28,000 Btus.

In other words, we have now calculated all the amounts of energy losses if smoke leaves an amazingly efficient woodstove (over 80% overall thermal efficiency, essentially unheard of) at around 240°F. We therefore have remaining, the 597,000 Btus of energy which might actually be considered useful. Again, dividing by the 100 pounds, we see this is around 6,000 Btu/pound. This is generally considered the USABLE heat from a pound of wood commonly used for calculations of the LHV (low heat value) for wood.

Even the theoretical flame temperature can be estimated from these calculations! We know that it is experimentally proven that something like 8,600 Btus (HHV) is created in the flame of a perfectly dry piece of wood. If we would apply really good mixing fans, we should be able to avoid having to add Excess air, and therefore would only need the theoretical needed amount of air. We would need oxygen of 0.48 pound (0.06 * 8) for the Hydrogen present and 1.36 pound (0.51 * 2.667), or a total of 1.84 pounds of oxygen. The wood contains 0.43 pound of oxygen in it, so the externally needed extra oxygen would be 1.41 pound. This is provided in 6.1 pounds of air.

We now know the amount of heat that will exist and the amount of air and we already know how to calculate the amounts of carbon dioxide and water vapor that also must be heated up, as directly participating in the combustion process. We probably already dumped enough math on you here, so we will just say that it is pretty easy to determine the enthalpy (energy content) of all those gases (as we already have been doing, using enthalpy charts for each gas), and then simply look to see what temperature corresponds to the amount of energy we are creating. That temperature generally turns out to be pretty close to 2500°F.

Just a little more!

Above, we needed to know how much air was going to be needed for the combustion. Here are the fairly simple calculations of that.

We already learned above that we can figure out how many pounds of Carbon and Hydrogen and Oxygen we have from a pound of wood (or any other fuel), by just using a molal analysis, that is, using the chemical formulas to first learn how many moles of each are involved in a reaction, and then multiplying each by the atomic weight of that element. Let's do that again, but now for two simpler problems!

C + O2 gives CO2.

By atomic weights, this is

12 + 32 = 44.

That is the same as actual weights.

That means that if we divide everything by 12, we have:

1 + 2.667 = 3.667

Therefore, one pound of Carbon in the wood (or any other fuel) requires 2.667 pounds of Oxygen (whether from also inside the fuel or from air or from any other source), and it produces 3.667 pounds of carbon dioxide. Simple!

The same problem regarding Hydrogen (we pretty much did this one up above):

[2] H2 + O2 gives [2] H2O.

By atomic weights, this is

4 + 32 = 36.

That is again the same as actual weights.

That means that if we divide everything by 4, we have:

1 + 8 = 9

Therefore, one pound of Hydrogen in the wood (or any other fuel) requires 8.0 pounds of Oxygen (whether from also inside the fuel or from air or from any other source), and it produces 9.0 pounds of water vapor. Simple again!

We used these results in the calculations above, where we had calculated known amounts of carbon (40.3 pounds) and hydrogen (4.7 pounds) and then needed to calculate the total amount of oxygen needed for the combustion of all if it (184 pounds) and the rest, all previously calculated above. We also needed these calculations to know how much new carbon dioxide and water vapor had been created, to be able to figure how much heat we would have to use up to heat them up, too.

IF you made it this far, and understand ANY of it, you have essentially learned a massive amount of Thermodynamics and Organic Chemistry! Congratulations! Otherwise, you probably now hate me!

This presentation was first placed on the Internet in June 2007.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago