Net Energy and Waste Heat Recovery

[Brian H]

Speaking of onions and photoelectrics, there’s a new development down at the other end of the scale:
http://www.physorg.com/news/2011-03-high-efficiency-infrared-photodetectors-gold.html

Don’t know if the principle would extrapolate from 1500 nm down to 100 or less!

[Brian H]

zapkitty wrote:

Check the total efficiency, fuel therms consumed to therms wasted. I think you’ll find that FF is throwing away far less heat than any competitive energy gen method per MW generated, from shovel or well to output.

Topical example: Each of the units at the afflicted Fukushima plant had to reject 3 times as many megawatts worth of heat as they produced of electricity. 33%.

Just noticed: your ratios are wrong. Rejecting 3X as much as used means 1 unit used, 3 wasted, 4 total; efficiency is thus 1:4, or 25%.

[redsnapper]

25% is actually pretty lousy conversion efficiency for any self-respecting power plant (not that I know typical values for nuclear plants). I noticed the error also, but was more inclined that the error was made going the other way – somebody read 33% efficiency somewhere, and made the common slip of converting that to “1 out of 3” in their head, and simply made the incorrect statement that meant 3x more was thrown away than produced. In other words, they should have said “reject 2 times as many megawatts …. 33%”.

[zapkitty]

It’s not complicated. For the Fukushima Dai ichi reactors each watt of electricity generated also generates about 3 watts of heat that must rejected. At least that’s how the total power and cooling aggregates stack up.

[redsnapper]

So BrianH was right, and it is only 25% efficient, not 33%. Leave it to me to make it complicated. Guess I was trying to give the nuclear industry the benefit of the doubt. 🙂

[Brian H]

redsnapper wrote: So BrianH was right, and it is only 25% efficient, not 33%. Leave it to me to make it complicated. Guess I was trying to give the nuclear industry the benefit of the doubt. 🙂

Of course, efficiency is relative to the nature and size of the power supply. 25% of fission energies is a different beast than 33% of organic fuel combustion. And 45% of fusion energies from pB11 is different from whatever % a Tokamak Deuterium burner + Carnot steam turbine would get. And so on.

[zapkitty]

eerrrr…… isn’t the only figure wanted here the factor of how much waste heat is generated for electrical power delivered?

I.E. watts (thermal) rejected for each watt (electrical) delivered to the grid?

It’s just a version of the energy conversion efficiency equation n=Qout/Qin:

eff = w(e)/w(t)

Now I can’t find the references offhand and could be called on this 🙂 but I found on the web about a week ago the cooling stats together with the electrical output for each of the units at Dai-ichi… and I noted that the thermal stats were all just about 3 times the electrical rating of the particular units. So if you set w(e) at 3 watts and w(t) at 9 watts then 3/9 = .33

[Brian H]

zapkitty wrote: eerrrr…… isn’t the only figure wanted here the factor of how much waste heat is generated for electrical power delivered?

I.E. watts (thermal) rejected for each watt (electrical) delivered to the grid?

It’s just a version of the energy conversion efficiency equation n=Qout/Qin:

eff = w(e)/w(t)

Now I can’t find the references offhand and could be called on this 🙂 but I found on the web about a week ago the cooling stats together with the electrical output for each of the units at Dai-ichi… and I noted that the thermal stats were all just about 3 times the electrical rating of the particular units. So if you set w(e) at 3 watts and w(t) at 9 watts then 3/9 = .33

The power “captured” is 1/3 of the power wasted. It is 1/4 of the total generated. The latter is the crucial figure. If you throw old tomatoes at your favourite politician, and hit with one for every three that miss, you are 25% accurate.

IOW, w(t) is 12 (3+9).

[zapkitty]

nope… in the example w(t) is measured at 9 and w(e) is measured at 3.

…. if ;w(t) were to be forced to w(t) = 12 then w(e) would = ~4 and then your method would add 12+4 for 16 w(t) and then w(e) = 5.3 and then 16+5.3… oh… no wonder the reactors kept exploding…

Fly + corned beef is much safer even with the containment issues…

[Brian H]

zapkitty wrote: nope… in the example w(t) is measured at 9 and w(e) is measured at 3.

…. if ;w(t) were to be forced to w(t) = 12 then w(e) would = ~4 and then your method would add 12+4 for 16 w(t) and then w(e) = 5.3 and then 16+5.3… oh… no wonder the reactors kept exploding…

Fly + corned beef is much safer even with the containment issues…

What’s measured is the energy lost.
Assume a perfect fission/generation system: 100% efficient. That implies all the energy would leave as electricity, with no nasty entropy losses or heat generated.

A 50% efficient system would split the difference, ½ leaving as electric current, ½ heating up the rig and coolants.

A 25% efficient system would have ¼ leaving as current, and 3/4 heating the local universe.

The ratio of ¼ to 3/4 is 1:3, or a 33% ratio of output to WASTE.

Waste is not represented in your formula. w(t) is total energy, ¼ + 3/4 = 1.

[zapkitty]

Brian H wrote:
Waste is not represented in your formula. w(t) is total energy, ¼ + 3/4 = 1.

Ah. I understand what you want to do now and it can be applicable to a problem with more given parameters… but in this case you’ve made an erroneous assumption regarding the basic data.

Viewed from outside, as a black box, the plant actually has only two factors that would concern us: its thermal output and its electrical output. w(t) and w(e)… and that’s all. What happens inside the plant is not a concern from an external point of view.

Of course the plant may be generating electricity at less than capacity and may be running cooler than it needs to… but for our example it’s close enough and in real life plant owners don’t tend to run plants at half power or build in much more cooling than they need.

And that would be why the comparison of the Dai-ichi units nominal ratings for w(t) and w(e) happens to hew fairly closely to the expected efficiency of those types of reactors.

Does it represent an actual reading of the efficiency of the plant? Within limits, a varying set of parameters, the answer is that it does if it is stipulated that the purpose of the plant is to provide power, not heat.

If one claims that one is using some of the heat produced by the plant for useful work in addition to the electrical output then certainly one can legitimately claim higher efficiencies than straight w(e)/w(t)… dividing w(t) into useful and rejected heat might get you eff = w(e)+w(tu)/w(tr) or something like that… but in our example here we are assuming that the heat is unwanted and is thus rejected.

So, from an external point of view you must assume that the w(t) accounts for all the losses in getting the w(e) to the grid. You need not make, and actually can not make, any other assumptions with the data that is given.

So the efficiency given by 3 w(e) and 9 w(t) in the example is indeed .33

[Brian H]

Uh-huh. Soooo… to take my second hypothetical, where half the energy went out as electricity, w(e), (and, of course, in the inevitable normal course of thermodynamic entropic things ends up as heat somewhere), and half is “waste” heat variously distributed about the rig and housing, which you assiduously measure and call w(t), the ratio would be w(e) = w(t), and therefore the “efficiency” would be 100%!!

Nice work if you can get it. (That’s a physics pun, BTW 😉 )!

[zapkitty]

It gets better… at 9 w(e) and 3 w(t) the efficiency equals 300%!

🙂

[Brian H]

zapkitty wrote: It gets better… at 9 w(e) and 3 w(t) the efficiency equals 300%!

🙂

Or, in reality, 75% (9/12 x 100%). :coolgrin:

[zapkitty]

Brian H wrote:

It gets better… at 9 w(e) and 3 w(t) the efficiency equals 300%!

🙂

Or, in reality, 75% (9/12 x 100%). :coolgrin:

… but what if the quantities measured were in numbers of bananas and aardvarks instead of two different varieties of watts? Would your denominator measure bananvarks or would your denominator measure aardnanas?

[Author]

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