Power Plants

I was reading the comments following a column in a Very Famous Newspaper and came across a good comment about how conservation is preferable to fossil fuel extraction.  However, the commenter attempted to figure out how much natural gas would be needed to supplant the coal we currently use for electrical generation, and things kind of off track, but got me wondering what the answer was and what the ramifications were.

Some background:

Using rough numbers, power plants are approximately 33% efficient.  In other words, to deliver 1 kilowatt-hour of electricity to your house, the plant must burn 3 kilowatt-hour’s worth of fuel.  Basically, 2/3 of the heat just goes up the stack and vanishes, while 1/3 of the energy actual does the work to turn a generator and produce electricity.

You might think that capturing some of that stack heat would make sense, and you would be right.  Stack heat economizers allow plants to pre-heat the incoming combustion air and boiler make-up water, which can  give them a percent or two higher efficiency.

Far more effective, and far more common overseas, is to take the stack heat and use it to provide district heating to nearby homes and businesses, generally by heating water and pumping around the district with below-grade piping.  However, in the U.S., power plants are often at a good remove from facilities that might be able to use their waste heat, so district heating, while not exactly rare, is not exactly common, either.

Anyway, I did a bit of Googling and it looks like we generate about 2 trillion kilowatt-hours of electricity with coal every year.  That’s a lot of kilowatt-hours: 2,000,000,000,000 if you like to look at big numbers.

Actually, if you consider that there are about 350,000,000 people in the U.S. that’s 5,700 kWh per per year for every man, woman and child in the country.  Which is amazing.

According to the Energy Information Agency (a GREAT resource, by the way), the average energy content of coal is about 19,583,000 Btu per ton, or 9,792 Btu per pound.  I was surprised it was this low, but our average coal quality may not be that good.  In any event, we can approximate how much coal was burned pretty easily:

(2,000,000,000,000 kWh * 3,412 Btu-per-kWh) / (33% efficient * 19,583,000 Btu-per-Ton) = 1,056,000,000 tons of coal.

Man, that’s a lot of coal.  A billion tons!  And remember from our earlier posts, coal is mostly carbon by weight, and CO2 weights 3.7 times more than carbon.  So we’re talking of carbon emissions in the neighborhood of 3+ billions of tons of CO2 that enters the atmosphere each year from electrical generation.

I see that coal prices vary quite a bit from region to region, but if we use $50/ton as an average price, that means fuel for coal fired generation costs about $50 billion dollars annually.

Natural gas is generally measured in units of volume (normally 100’s of cubic feet [or CCF]) or in units of energy (Therms at 100,000 Btu, or Decatherms at 1,000,000 Btu.  Gas is purchased in bulk in unit of Decatherms, but most customer bills are in therms or CCF.)  Fortunately for us,  the energy content of a CCF of natural gas is about the same as a Therm, so they can  be used more or less interchangeably without introducing undue error.  Also, from the above we see that a cubic foot of gas is about 1,000 Btu and that a decatherm is equivalent to about 1,000 cubic feet.

We can now readily calculate how much natural gas would be required to supplant coal at our power plants:

(19,583,000 Btu-per-ton-coal * 1,056,000,000 tons/year) / 1,000,000 Btu-per-Decatherm = 20,679,648,000 DTh.

That’s a hell of a lot of natural gas.  By the way, delivered gas might cost $5 a DTh.  So the cost for this much natural gas would be about $100 billion dollars.  Each year!  Note that this is roughly twice the cost of coal for the same electrical generation – there’s one reason why coal is a hard habit to quit.

Now, the Energy Information Agency (EIA) reports natural gas production in millions of cubic feet, so I am going to do a rough conversion by multiplying our Dth number by 1,000 – recall that a Dth is about 1,000 cubic feet.  We’re now talking roughly 20 trillion cubic feet of natural gas (or as EIA would state it, 20,000,000 million cubic feet)

US Natural Gas Consumption

via: http://www.eia.gov/dnav/ng/hist/n9140us2a.htm

Given that the U.S. consumes about 25,000,0000 million cubic feet for all end uses today, we would need to almost double our production capability to convert our coal burning power plants to natural gas.

You may recall from an earlier post that natural gas puts almost 50% less CO2 in the atmosphere than coal.  So converting to natural gas would reduce our annual carbon dioxide emissions by somewhere in the neighborhood of 1.5 billion tons.

Interesting stuff.

Combustion #2 – The Ratio of Weights and Calculating Emissions

To figure out how much carbon you’re dumping into the air, you need to examine the molecular weight of the fuel and the carbon content of the fuel.  For energy calculations, the following atomic weights are pretty much all you need to know:

Molecular Weights

  •  C             12
  • H                1
  • H2             2
  • O              16
  • O2            32
  • CO           28
  • CO2         44
  • H20         18
  • CH4         16
  • C2H4       28
  • C2H6O    46
  • S               32
  • NO           30
  • NO2         46
  • SO2          64
  • C8H18    114 (typical gasoline)

Don’t forget to refer to the Combustion #1 post to get heat of combustion values for various fuels.

Note that carbon burned in the air will preferentially create carbon dioxide and release heat.  Observe that a molecule of carbon has a weight of 12, whereas a molecule of CO2 has a weight of 44.  Therefore, burning 1 unit of carbon (it can be pounds, tons, etc) will generate 3.7 units of carbon dioxide.

Let’s take a look at the combustion analysis for natural gas and oil.

For our purposes, we will assume that natural gas consists of only CH4 (methane.)  In fact, natural gas often contains some butane, propane. ethane, nitrogen and other elements.

The combustion equation is pretty simple.  The corresponding molecular weights are to the right in parentheses.

CH4 + 2O2 = CO2 + 2H2O     (16 lb + 64 lb = 44 lb + 36 lb)

This tells us that burning 16 pounds of natural gas will generate 44 pounds of CO2.  The 36 pounds of water vapor can be ignored because it is benign, which is why hydrogen is such a great fuel.

The weight ratio of natural gas to carbon dioxide is 2.75.  So burning a ton of natural gas will release 2.75 tons of carbon dioxide.

You may recall from my earlier post that burning a pound of methane results in a release of 23,875 Btu.  From this we can conclude that methane delivers 8,682 Btu heat per pound of CO2 generated.

Let’s see how that compares with a generic fuel oil.  The combustion equation (ignoring the hydrogen products) and pertinent molecular weights are:

2 C14H30 (396) combines with 43 O2 => 28 CO2 (1,232) + 30 H2O

We observe that the weight ratio of fuel to CO2 is 3.1.  So burning a ton of fuel oil will release 3.1 tons of carbon dioxide.  You may find it surprising that the carbon dioxide emissions are not that much higher than natural gas, since natural gas is widely cited as a “cleaner” form of energy than oil.

What we need to keep in mind is that fuel oil delivers less heat per pound than natural gas.  If we figure a fuel oil energy content of 20,000 Btu per pound, we see that fuel oil delivers only 6,430 Btu heat per pound of CO2 generated.

To put this another way, 100,000 Btu of heat will result in CO2 emissions of 11.5 pounds if you are burning natural gas, 15.6 pound if burning fuel oil.  That difference is significant.

Coal is even more striking.  While the carbon content of coal varies, let’s figure it to be about 75% by weight.  It has negligible other combustibles, though there is other stuff in there like sulfur and mercury that can cause problems.

Well, we know the ratio of carbon to carbon dioxide is 3.7 to 1.  So with 75% carbon content, burning a ton of coal will emit about 2.8 tons of carbon dioxide (75% of 3.7.)

Coal contains roughly 13,500 Btu per pound, so coal delivers about 4,820 Btu heat per pound of CO2 generated.  And 100,000 But of heat from coal will result in CO2 emissions of roughly 20.8 pounds of CO2.  Let’s summarize this:

Carbon Dioxide Emissions per 100,000 Btu Liberated Heat

  • Hydrogen                  0
  • Natural Gas          11.5 pounds
  • Generic Fuel Oil  15.6 pounds
  • Generic Coal        20.8 pounds

So there you have it.  Once you know the chemical makeup of your particular fuel, calculating the carbon emissions is pretty simple.

Combustion #1 – Fuels

Hey, it’s going to be increasingly important that you can link reduced carbon emissions to energy savings.  So let’s learn how to calculate this.

I’m going to start by listing typical raw materials and fuels.  Fuels contain energy that is released when the chemical bonds holding hydrogen and carbon in the fuel are broken and these elements are able to recombine with free oxygen from the atmosphere, which results in the release of heat and the production of carbon dioxide.  The list below also shows the approximate amount of energy that is released when a pound (technically a pound-mass, which weighs a pound here on good old earth) of the material is burned.

Heat of Combusion for Raw Materials

Carbon                         C                      14,093 Btu/lb

Hydrogen                     H2                   61,095 Btu/lb

Carbon Monoxide        CO                     4,347 Btu/lb

Methane                       CH4                 23,875 Btu/lb

Ethane                         C2H4               22,323 Btu/lb

Propane                       C3H8               21,669 Btu/lb

n-Butane                      C4H10             21,271 Btu/lb

Ammonia                     NH3                   9,667 Btu/lb

Gasoline                      C8H18             19,000 Btu/lb (approx)

Heating value of fuel oil runs as follows:

Kerosene         134,000 Btu/gal

No. 2               134,000 Btu/gal   (138,000 Btu/gal to MGH)

No. 4               144,000 But/gal

No. 5               150,000 Btu/gal

No. 6               143,800 Btu/gal – low sulfur (0.3%)

No. 6               152,000 Btu/gal – high sulfur (2.7%)

Gasoline          109,000 to 125,000 Btu/Gal  – 114,000 average.

Gasoline weighs approximately 6 pounds per gallon.  Heavy oil (No. 6) weighs approximately 8 pounds per gallon.  The lighter oils run in between.  This means that gasoline and fuel oils run in the neighborhood of about 20,000 Btu per pound, similar to the other hydrocarbons listed above.

I find having a list like this to be very handy.

An upcoming post will show how the combustion equations can be used to determine the energy release and carbon dioxide emissions associated with burning different kinds of fuels.

I’m probably wrong

I hope I’m wrong.

But I have this sneaking suspicion that some of the people who question climate change partially base this on a belief that burning fossil fuel does not necessarily add carbon dioxide to the atmosphere.  That this is somehow speculative or a matter of debate.

There is no debate on this matter.

Coal, oil and natural gas liberate heat when the carbon in their composition combines with free oxygen in the air to produce CO2.  There is no way around this fact. (Okay, it’s true that the combusted hydrogen in hydrocarbons also liberates heat, but we aren’t going to worry about that for our present purposes since the combustion byproduct of hydrogen is just water vapor.)

So, while you may not believe that rising carbon dioxide levels contribute to climate change, and while you may even be treated with deference when expressing this opinion, to assert that mankind is not contributing to the elevated CO2 levels seen in the atmosphere is a preposterous claim that denies fundamental facts about combustion.

We’re putting CO2 up there in the atmosphere without question.

A couple of interesting facts.

The atomic weight of carbon is 12.  The atomic weight of oxygen is 16. (you may be asking, 12 and 16 what? ounces? pounds?  butterfly wings?  Turns out it doesn’t matter for our purposes, as I will show…)

What that means is that when fuel is burned and converts from carbon to carbon-dioxide, the weight of the carbon dioxide is almost 4 times heavier than the carbon that was burned.  Why?  Look at the atomic weight ratios

Carbon (12) + 2 Oxygen (16+16) ==> Carbon Dioxide (12+16+16)

Ratio of CO2 weight divided by the weight of the burned carbon is 44/12 = 3.7

What this means is that a ton of coal (which is mostly carbon) will result in about 3.7 tons of carbon dioxide emissions when burned.  This is not a theory.  This is not just possible.  This is non-negotiable.

You may be wondering about the hydrogen in fuels such as natural gas or petroleum. If you look at natural gas, the chemical composition is mostly CH4.  The combustion equation is pretty simple:

CH4 + 2O2 ==> CO2 + 2H2O + liberated heat (about 22,000 Btu per pound of natural gas)

Note that the H2O combustion product is just  water vapor, which is benign.  This makes pure hydrogen a very attractive fuel, at least in theory.

Also note that when we discuss fuels, we are discussing something different from energy or power.  Fuels are repositories of stored energy, and the rate at which we burn fuels determines how much power is generated.  Some common combustion fuels include:

  • Fuel Oil
  • Coal
  • Natural Gas
  • Petroleum
  • Peat
  • Wood

Note that the energy content of fuels is pretty well defined.  For instance, coal might house 25 million Btu of energy per ton, depending on the coal type.   Somewhere along the line I will provide more detailed fuel energy content data and show how the combustion calculation are performed.

Right now I’m just getting some preliminary stuff out of the way as I try to figure out if this blog is going to have any value to me, let alone anyone else.