# Uranium energy equivalence

One ton of Uranium used at a typical 1 GW reactor is equal to how many tons of coal being burned in a 1 GW coal fired plant?

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mgb_phys
Homework Helper
1 kg of fuel is equivalent to 1000-2000 tons of coal depending on howyou measure it.

vanesch
Staff Emeritus
Gold Member
Indeed. Actually, I'd say, that's the really fissioned fuel.

To run a 1 GW electric plant, with a 33% steam cycle efficiency, you need about 2 800 000 TOE (tons of oil equivalent). Now, taking that per unit of mass, coal is slightly better than oil, we arrive at somewhat more than 2 million tons of coal per year.

Currently, the burnup of fuel in a PWR is around 50 GW-day per ton thermal, and if we take the same steam cycle efficiency, this brings us around 20 tons of enriched uranium that is used up. But actually, only 5% is fissioned (about 3.3% from the original U-235, and about 1.7% from the bred plutonium), so only 1 ton is actually fissioned. To make those 20 tons of enriched uranium, one has usually started with 10 times as much, 200 tons. (one can do better, but then this needs higher separation work).

So we have:

1 GW electric for a year =

more than 2 million tons of coal

200 tons of natural uranium / 20 tons of enriched uranium / 1 ton actually split in a PWR

In a fast breeder, ideally, 1 ton of natural uranium would be entirely split so ideally, 1 ton of natural uranium would also yield 1 GW electric for a year.

mheslep
Gold Member
So we have:

1 GW electric for a year =

more than 2 million tons of coal...
In other terms, 1 GW coal plant requires ~five 100 ton railroad coal cars per hour, every hour. That's typically two 60 car trains a day, every day.

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Andrew Mason
Homework Helper
In other terms, 1 GW coal plant requires ~5 100 ton railroad coal cars per hour, every hour. That's typically two 60 car trains a day, every day.
This is on the low side. And it depends on the quality of the coal and the efficiency of the plant in converting heat into electricity (usually about 30%) The efficiency of a nuclear plant can be higher - as high as 40%.

The energy content of anthracite coal is about 27 GJ/Tonne and of lignite coal is about 15 GJ/Tonne. See the http://en.wikipedia.org/wiki/Heat_of_combustion#Heating_values_of_some_fuels"

A 1 GWe power plant produces 31,536,000,000,000,000 Joules of electrical energy in a year which requires about 105,000,000,000,000,000 Joules of heat (10^8 GJ.). Since the energy from combustion of coal is 15-27 GJ/Tonne, you would need about 4 million tonnes of high grade anthracite or 7 million tonnes of lignite coal.

The http://www.eia.doe.gov/neic/infosheets/coaldemand.html" [Broken] on coal says: "Each ton of coal consumed at an electric power plant produces about 2,000 kilowatt-hours of electricity so a pound of coal can supply enough electricity to light ten 100-watt bulbs for about an hour." That works out to about 4 million tonnes or 4.38 tons of coal for 1 GW year.

By comparison, a LWR 1 GW reactor consumes about 25 tonnes of enriched fuel (which requires 175-200 T of raw U). A Candu 1 GW reactor would use about 200 tonnes of raw (unenriched) Uranium

So the ratio is about 4x10^6/200 = 20,000. That is by mass, a unit of U consumed in a LWR or Candu reactor has the heat equivalent of 20,000 units of the best coal.

But one has to keep in mind that today's reactors use only about 1 percent of the potentially useable energy contained in U. So multiply that by 100 to get the potential useable energy in U and the ratio is 2,000,000:1

AM

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mgb_phys
Homework Helper
In other terms, 1 GW coal plant requires ~five 100 ton railroad coal cars per hour, every hour. That's typically two 60 car trains a day, every day.
The UK's biggest powerstation is 4GW and uses 36,000tons of coal/day.

Wow, I figured it was more efficient but I had no idea it would be so much. Thanks.

mheslep
Gold Member
This is on the low side. And it depends on the quality of the coal and the efficiency of the plant in converting heat into electricity (usually about 30%) The efficiency of a nuclear plant can be higher - as high as 40%.

The energy content of anthracite coal is about 27 GJ/Tonne and of lignite coal is about 15 GJ/Tonne. See the http://en.wikipedia.org/wiki/Heat_of_combustion#Heating_values_of_some_fuels"

A 1 GWe power plant produces 31,536,000,000,000,000 Joules of electrical energy in a year which requires about 105,000,000,000,000,000 Joules of heat (10^8 GJ.). Since the energy from combustion of coal is 15-27 GJ/Tonne, you would need about 4 million tonnes of high grade anthracite or 7 million tonnes of lignite coal...
That is running 100% capacity, which no electric plant does, not even nuclear and nuclear has the highest capacity factor. A well run nuclear plant runs ~93% online in the US, coal much lower, 50-75% if I recall. Its on EIA somewhere. The reason is mostly economic I expect - once the expensive outlay has been made for nuclear, it is practically 'too cheap to meter' for the producer as the operational costs are 2-3 cents/kWh, and thus the operator wants to run it not stop, but no so for coal, for the reasons we've outlined here (two+ train loads a day.) Thus if one has nuclear, run the odd coal plant in the summer to handle the high cooling loads, but idle the ravenous beast in the winter.

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mgb_phys
Homework Helper
You are thinking like an engineer not a politician.
The real trick is to close the old nuclear power stations while stalling on building new ones.
Then you privatise the generation capcity in such a way that first past the post wins, and since gas is the quickest station to build, you end up with the majority of your power generated by the only fossil fuel more expensive than coal.
That leaves you with coal as the baseline load - the fun bit in Europe is that your peak load is in winter when the atmospheric conditions are worst for putting out smoke.

Putting my oar in:

Coal and gas have a better thermal efficiency than PWR. Decently recent coal and gas power stations have about 42% heat-to-electricity efficiency. PWR stick to some 33% because they produce a low temperature vapour and because, as they only produce vapour, combined cycle (gas followed by vapour) is impossible.

In Western Europe, coal power plants don't inject fumes in the atmosphere, as fumes are filtered out, as well as nitrous and sulphur oxides. CO2 is a huge concern but underground storage could be a solution. Germany works in this direction. If this works properly (...see that in 10.000 years) then we may go on burning coal.

Nukes run at full capacity because they can't be throttled down easily. So countries with a high proportion of nuclear power plants use other plants to adjust the production - thus letting coal plants work at an economically bad load factor.

Morbius
Dearly Missed
Nukes run at full capacity because they can't be throttled down easily. So countries with a high proportion of nuclear power plants use other plants to adjust the production .
Enthalpy,

There's nothing that prevents a nuclear power plant from throttling to meet demand. The reactor and
steam generator combo is just a boiler. From there on the nuclear plant looks like a fossil fueled plant.

The reason one operates the nuclear plant at full throttle is because that is most economical. You use
your least cost power plants to baeload. That is you use the cheapest plants first - and then the more
expensive ones.

Addtitionally, most of the cost of a nuclear power plant is fixed cost - the facility itself - rather than fuel.

The way you best amortize the fixed cost is to operate the plant at full throttle. You don't save much
money throttling back a nuclear plant - as you do with a fossil fuel plant where a good fraction of the
expense is fuel.

However, countries like France which is on the order of 85% nuclear may well have to throttle back the
nuclear power plants when the load on the grid drops below 85% of the grid capacity. They have no
problem doing that.

You can operate a reactor at whatever power level you want - up to its maximum capacity.

Dr. Gregory Greenman
Physicist

mgb_phys
Homework Helper
However, countries like France which is on the order of 85% nuclear may well have to throttle back the nuclear power plants when the load on the grid drops below 85% of the grid capacity.
The French (being anti-capitalist with no word for entrepreneur) just sell it to their neighbours for a profit.
They are busy building a whole new set of stations to make up for the UK failing to build anything in the last 10years.

Morbius
Dearly Missed
The French (being anti-capitalist with no word for entrepreneur) just sell it to their neighbours for a profit.
mgb_phys,

Yes - if they can sell it - they do. However, if the case arises where they have more capacity than
demand - either domestic or foreign - they can throttle back.

You are correct that is a more remote happenstance lately, With France's nearest neighbors of
Denmark and Germany going "green" with windmills and solar arrays; the opportunities for France
to sell nuclear power to Denmark and Germany abound - when the wind and solar installations don't
live up to expectations.

Dr. Gregory Greenman
Physicist

CO2 is a huge concern but underground storage could be a solution.

Which isn't any different from what we do (or in some cases are planning to do) with nuclear waste.

Yes - if they can sell it - they do. However, if the case arises where they have more capacity than
demand - either domestic or foreign - they can throttle back.
Probably not going to happen for some time, since now they are the only western european country without any real power problems.

With France's nearest neighbors of
Denmark and Germany going "green" with windmills and solar arrays; the opportunities for France
to sell nuclear power to Denmark and Germany abound - when the wind and solar installations don't
live up to expectations
Already happening. I really don't know what those guys were thinking when they tried to replace a stable, high energy density power source with an intermittent, low energy density power source. Germany is already having to start building more coal power plants to make up the difference, with the green party (who pushed to get rid of nuclear) reluctantly approving it.

vanesch
Staff Emeritus