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Archive for the ‘thermodynamics’ Category

Thermodynamics, stars, uranium, life and everything: Part II

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The amount of time necessary to exhaust nuclear energy provided by existing uranium deposits, unused energy in current reserves of used radioactive “waste”, heat produced by the radioactive decay of uranium, thorium and potassium deep inside the Earth (in other words, geothermal energy), and uranium in seawater could indeed last billions of years – approaching the evolution of the sun off the main sequence, and with that, the end of life on this world.

If the energy from the Sun is “renewable”, so too is nuclear energy equally every bit as renewable.

The concentration of uranium in seawater in the world ocean is about 3.3 parts per billion. The total mass of Earth’s hydrosphere is about 1.4×1021 kilograms, therefore putting the total mass of uranium in the world ocean at 4.62 billion tonnes.

Current total world demand for electricity stands at 16,330 TWh per year. Let’s conservatively suppose that, over the millennia to come, the average total world demand for electricity is four times what it is at present, or 65,320 TWh. Conventional LEU fueled light-water reactors and inefficient once-through fuel use in these reactors consume about 200 tonnes of uranium mined per gigawatt-year of electric power generation.

Hence, if we make the assumption that all the nuclear energy generation over these coming millenia is performed with this inefficient once-though LEU fuel chain and no recycling or reprocessing of nuclear fuels is performed, then the world demand for uranium can be expected to be 1.49 million tonnes per year.

Hence, consuming 1.49 million tonnes of uranium per year to supply all the world’s electricity, the 4.62 billion tonnes of uranium presently dissolved in the ocean will supply the world’s electricity for 3100 years.

\mathrm{\frac{4.62 \times 10^{9}\ tonnes}{(200\ tonnes\ per\ GW\cdot year) \cdot (65320\ TWh/year)}\ =\ 3100\ years}

Here we have assumed that no use is made of efficient, advanced reactors or breeder reactors and no use is made of the excess “depleted” uranium-238 or natural thorium, no deuterium is used for nuclear fusion, and no uranium is mined on land. Such assumptions are of course ridiculous, but let’s just be as conservative as possible, for argument’s sake for the purposes of this baseline, worst-case scenario.

If we considered a truly efficient efficient use of nuclear fuel, we may consider an efficient, advanced reactor such as a molten-salt reactor, efficiently transmuting uranium-238 into plutonium-239 in situ to generate energy. We may assume that 200 MeV of energy is released per fission event, and that the efficiency of the 238U transmutation and liberation of useful energy output from these nuclear processes within the reactor is, say, 75% overall. If we assume that this thermal energy is converted in a Brayton-cycle power plant with a thermodynamic efficiency of 50%, then hence we know the amount of natural uranium required to fuel the reactor.

\mathrm{\frac{1\ GW\ \cdot\ 1\ year\ \cdot\ 238\ u\ \cdot\ 1.66 \times 10^{-24}\ grams/u}{200\ MeV\ \cdot\ 75\% \cdot\ 50\%}\ =\ 1.04\ tonnes}

Just over one tonne of natural uranium is required, to generate one gigawatt-year of energy. (That number is basically the same if we’re looking at efficiently burning thorium in a MSR, incidentally, also.) If we utilised nuclear energy efficiently, like this, then the 4.62 billion tonnes of uranium presently dissolved in the ocean would supply the energy we discussed above, 65,320 TWh, for (just under) an astonishing 600,000 years!

\mathrm{\frac{4.62 \times 10^{9}\ tonnes}{(1.038\ tonnes\ per\ GW\cdot year) \cdot (65320\ TWh/year)}\ =\ 597,558\ years}

However, we are not finished yet. Elution of the uranium in the Earth’s crust into the ocean occurs on an ongoing basis, adding 3.24×104 tonnes of uranium to the ocean annually.

It was motivated by Cohen* that we could recover uranium from seawater at perhaps half of that rate; 16,000 tonnes of uranium from seawater per year. This quantity of uranium would supply 15.4 TW of electric power, if used efficiently as outlined above. In order to supply 65,320 TWh of electricity per year, four times the current worldwide demand for electricity, we only require 7750 tonnes of uranium per year, less than half that figure of 16,000 tonnes.

[* Many of you will be familiar with Cohen’s work, but if you are not, that book is highly recommended.]

Cohen argues that given the geophysical cycles of erosion, subduction and uplift, the uranium elution into the oceans would last for five billion years, at a rate of withdrawal of 6500 tonnes per year. At a rate of consumption of 7750 tonnes per year, in the absence of the use of any uranium and thorium mined on the crust, or the use of deuterium for nuclear fusion, the uranium from the oceans alone can be expected to meet world demand for electricity, at 65,320 TWh of electricity per year, for 4.2 billion years. Over a timeframe on the order of 109 years, of course, some non-trivial fraction will be lost, simply due to radioactive decay – however, at the same time, we have not even begun to consider the use of uranium and thorium reserves in the crust, or the use of the vast supply of deuterium as an energy source.

Clearly nuclear energy remains a viable resource on the Earth for a time scale of approximately five billion years – these nuclear fuels will not be consumed or depleted over a timeframe comparable to the life of the sun on the main sequence. Just as the finite hydrogen within the core of the Sun is a “renewable” energy resource, so too is the finite resource of terrestrial nuclear energy an equally renewable energy resource.

However, there is one final point we have overlooked. Even during its life in the main sequence, the Sun is evolving, as with all such stars. The Sun is gradually increasing in luminosity, by about 10% every one billion years, and its surface temperature is correspondingly slowly rising. This increase in the luminosity of the sun is such that in about one billion years, the surface temperature of the Earth will permanently have become too high for liquid water to exist, the oceans will evaporate and a catastrophe of the most immense proportions imaginable will overtake our planet. The Aztecs foretold a time `when the Earth has become tired… when the seed of Earth has ended’. All life on Earth will be extinguished, billions of years before all the nuclear fuels will be depleted.

In the meantime, our descendants will have evolved into something quite different, as far divergent from us in evolutionary terms as we are from the simplest one-celled organisms to have existed on the Earth. If they still inhabit the Earth, our descendants will leave, perhaps to Mars, or to the moons of the gas giants, Europa, perhaps, rich in water and perhaps not dissimilar to Earth if warmed up a little, or perhaps to a younger, more distant world, orbiting a younger star, around which their civilization will flourish once more.

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Written by Luke Weston

October 12, 2008 at 1:12 pm

ThermoGen: When “Green” energy doesn’t add up.

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I’ve been looking at some of the claims on the website of Thermogen recently.

In short, what Thermogen claim is that they can supply a domestic solar thermal energy installation whch provides an electrical power output of 5 kWe, and that that power output is accessible 24 hours a day via energy storage in tanks of high-temperature water.

The Thermogen is designed to supply it’s rated output 24 hours per day, cloudy or sunny weather e.g. a 5kW system will supply 120kW per day. [sic] It has a three day design storage for inclement weather.

Of course, if a 5 kW system can supply 5 kW of power for 24 hours, then that’s 120 kilowatt-hours of energy. I’m a little bit wary of a company selling energy technology when they can’t tell the difference between a unit of energy and a unit of power.

This heated water is then stored in 1000 litre insulated tanks at 150-200 °C. These tanks are a solar energy storage system designed to store enough energy to provide the following services for up to three days without sunshine:

For a 5 kWth system to be able to store energy up for three days, then 360 kWhth of energy must be stored in the system. We’ll come back to that in a minute.

They explain that:

Each panel measures 2.4m wide and 2m up the roof. It is expected that you will need 7 of these panels for the Thermogen system.

That’s a collector area of 33.6 m2. A little less than that, actually, since not 100% of the panel’s dimensions will be usable solar collector area.

For comparison, a standard large two-panel Solahart hot-water system has a collector area of 3.5 square metres.

Now, if we look at BOM’s map of average daily solar exposure across Australia, we see that the average daily solar exposure is, in the sunniest parts of nothern Australia, 21 megajoules of solar energy per square meter per day.

If there is one idea to keep in mind when considering solar energy, that is it. Irrespective of what sort of collector technology you have, there is always a very finite limit to the amount of energy you can collect from a solar collector of a given area. That energy flux is the maximum that there is to be utilised, no matter what technology you use to harvest it.

So, anyhow, we have 21 MJ/m2/day, and a rooftop solar collector of 33.6 m2. We’ll be conservative here and assume (a) you live in Townsville or Alice Springs or Darwin and (b) the entirety of the surface area of those collectors is active area. So, the power output that you get is a maximum of 705.6 megajoules per day.

The most efficient evacuated-tube solar thermal energy collectors, like the ones proposed by Thermogen, manage a gross efficiency of energy collection of about 60%. So, now we’re down to 423.36 MJ per day.

This thermal energy is then converted into electrical energy in a heat engine. In this case, the engine that they’ve pictured on their webpage – without attributing it’s source – is a Freepower 6 [PDF link] 6 MWe Organic Rankine Cycle powerplant.

Some of the images on the Thermogen site appear to depict the FreePower 6 organic Rankine cycle engine / generator as well as a Rotartica absorption chiller, with no credit given to the peope responsible for these components.

(An organic Rankine cycle is simply a Rankine cycle engine using an organic chemical as the engine’s working fluid, such as a fluorocarbon liquid, a fluorocarbon gas like a refrigerant type material, or some type of liquid with a lower boiling point than water, as the engine’s working fluid. Such engines are commonly used to recover low-grade heat from industrial processes, and as geothermal electricity generators, since they’re designed to operate with low temperatures.)

Now, let’s look at the specs of the FreePower 6 engine. It requires a heat source of 180 °C, returns the cooled oil at 123 °C, and requires a thermal power input of 70 kWth, to generate an electrical power output of 6 kWe. Since the Thermogen system is supposed to generate 5 kWe, I presume 1 kWe is consumed to drive the hot water pumps.

Therefore, the engine only has an efficiency of 8.6% – seemingly very low efficiency indeed. That seems like a terribly low efficiency, but the maximum efficiency – as per Carnot’s theorem – at these temperatures is only 11.6%, so the efficiency realised in practice isn’t too bad. At least these guys aren’t trying to flog off a perpetual motion machine.

Now, if we’re putting 423.36 MJ into the engine, and our electricity output is uniform day and night, then at this efficiency, we have a thermal input power of 4.9 kW, and we’re getting an electrical power output of 421.4 Watts.

I suppose that might be where they’re getting their claimed of “5 kW” from, given that they’re putting an average power of about 5 kW thermal into the engine?

Furthermore, cooling water is required to dissipate the engine’s 60 kWth of waste heat, at a flow rate of up to about 0.8 L/s and a maximum outlet temperature of 55 °C. I’m afraid that yes, in this house, we obey the laws of thermodynamics. Perhaps you need to build an artificial pond next to it or something? But that’s good, right? Lake Anna attracts lots of tourists, doesn’t it? 😉

So, we’re left with 421.4 Watts. Jump for joy; your energy needs are solved forever.
That’s, what, enough energy to run a handful of incandescent light bulbs?

We have an electricity output of 10.11 kWh per day, then.

The energy requirement for an average home is 10kW per day (See Synergy website), so the additional 110kWhrs of electricity may be supplied to the grid.

For example, a 5kW Thermogen system will generate 120kW per day while the average Australian home uses between 10kW to 30kW per day.

Average Australian household electricity consumption is about 15 GJ per household per annum – 11.4 kWh per day.

If you have a small household, or an energy-efficient household, then such an installation can realistically meet all your household electricity needs. Probably. If you live in northern Australia. If you live in Melbourne, Sydney or Adelaide, forget about it. Even if you could supply all household demand for electricity, however, there will be little or none left to sell into the grid.

They claim that the power generated from a domestic Thermogen installation “will supply a revenue stream of up to $20,000 per annum at current rates which will pay the mortgage on most homes in Australia”.

It won’t.

If we really did want to generate 120 kWh of electricity per day, what would be required? You’d simply need 400 square meters of collector panels. That won’t fit on your roof. It would be the kind of system that lives up to what they’re claiming, though.

This is before we even start thinking about the energy storage tanks of a couple of thousand litres of water at 150 to 250 °C – superheated water at pressures exceeding 200 psi. If you’re standing around the tank and it ruptures, it will cook you to death. Do you really want this engineered and installed in homes by people who can’t tell the difference between power and energy?

For a 5 kW system to be able to store energy up for three days, then 360 kWh of energy must be stored in the system.

If the initial temperature of the water is 180 °C, and the final temperature of the water is 123 °C, then the storage of 360 kWhth to supply three days worth of energy requires 360 kWh / (4.184 Jg-1K-1 * 57 K * 1 g cm-3) = 5434 L; 6 quite large 1000 L storage tanks.

How much does all this cost, anyway? There is not one word of it on the site thus far.

There’s nothing especially malicious or ill-intentioned about Thermogen – although I would not invest in them under any circumstances. They simply appear to be another trendy, hopeful “Green” enterprise that simply can’t count.

The illustrious Dan Rutter has more in a similar vein, here.

Written by Luke Weston

October 11, 2008 at 11:55 am

Water and cooling requirements for large thermal power plants.

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I was involved in a bit of discussion recently about the cooling of large thermohydraulic (i.e. heat engine) generatng stations, their use of water, and the like. I was thus inspired to to a bit of thinking, research and writing about the issue. The little essay or discussion piece that I’ve put together can be found here, and I encourage you to please have a read if you’re interested and tell me what you think. I’ll keep it online in that PDF since it’s a little long, and I’ve used a little math typesetting which is a hassle to transcribe across to the blog post.

Written by Luke Weston

September 5, 2008 at 4:54 pm

Genepax “Water Energy System”: Redux

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An update on the latest “breakthrough car that runs on water!”:

http://techon.nikkeibp.co.jp/english/NEWS_EN/20080616/153301/

Kiyoshi Hirasawa, president of Genepax Co Ltd, unveiled part of the reaction mechanism of the company’s new fuel cell system called “Water Energy System” in an interview with Nikkei Electronics.

The system, which is capable of generating power with water and air, was first presented June 12, 2008. As reported in our previous article, the system produces hydrogen through a chemical reaction between water and a metal (or a metal compound) on the fuel electrode side (See related article).

Genepax uses a metal or a metal compound that can cause an oxidation reaction with water at room temperature, the company said. Metals that react with water include lithium, sodium, magnesium, potassium and calcium. The main feature of the Water Energy System is that it can be operated for a longer period of time by controlling the reaction of the metal or the metal compound, the company said.

According to Genepax, the metal or the metal compound is supported by a porous body such as zeolite inside the fuel electrode of the membrane electrode assembly (MEA). The products of the hydrogen generation reaction dissolves in water, and the water containing them will be discharged with water inside the system. Upon the completion of the reaction, the generation of hydrogen and power stops.

There is nothing revolutionary here – nothing that violates the laws of physics. Rather than “running on water” the device if fuelled with chemical potential energy in the form of a reactive chemical – such as lithium metal – that will spontaneously reduce water to hydrogen gas on contact, consuming the lithium. Energy is “stored” in such a material, which requires considerable energy input to create, and does not occur in the free metallic form in nature.

This is essentially nothing more than a non-rechargeable chemical battery. When its chemical “fuel” is depleted, it doesn’t work, and the chemical material must be replenished.

Written by Luke Weston

July 14, 2008 at 5:21 am

Looking into Solar Thermal power systems.

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Atomic Insights has an interesting recent post asking some pertinent questions about solar thermal energy systems:

What are the steam cycle parameters? What is the overall thermal efficiency?

What is the cooling medium for your condensers?

How much water will the plant consume per unit of power?

Are the mirrors steered so that they track the sun?

What is the installation cost per unit of energy produced each year?

These are good questions – they’re worth asking. I’m very interested in learning the answers to these questions too – so I’ve done a little bit of, well, Google-ing (it seems unfair to call it “research” when it’s so fast and easy, doesn’t it?) and found some interesting information from solar thermal manufacturers. Admittedly, much of what I’ve found doesn’t really come as a surprise.

The Abengoa Solar corporation has several large-scale solar thermal systems in operation and on the drawing board, including this 280 MW (nameplate) plant which will be built near Phoenix, Arizona.

http://www.abengoasolar.com./sites/solar/en/nproyectos_eeuu_arizona.jsp

The schematic diagram on that page clearly shows that a fairly conventional water-based cooling tower is proposed as the basis of the condenser heatsink.

The Arizona system is based on the 50 MW Solnova 1 installation, in Spain. This installation does include a mechanical single-axle drive mechanism for steering the trough collectors.

Solnova 1 has a design power rating of 50 MW. Based on the local solar resource, the plant is predicted to deliver 114.6 GWh of clean energy per year.

That’s a capacity factor of 26%.

Here’s what Adams had to say about the thermal efficiency expected from such a system:

Based on my back of the envelope computations it appears that the steam conditions will be roughly equivalent to those found in the second generation nuclear plants operating today. That implies a thermal efficiency of about 33%, and a condenser cooling water requirement that is comparable to a nuclear power plant on a per unit power basis.

Here’s what the company says:

At peak conditions, the plant converts available solar radiation into heat at an efficiency near 57%. Combined with the efficiency of the steam cycle, the overall plant efficiency is approximately 19%.

The efficiency of the steam cycle based on the manufacturer’s official claims, then, must be 19% divided by 57%, or 33%.

Well, that’s really all that needs to be said on that question!

In terms of efficiency of the energy conversion in these solar-thermal systems, there’s nothing particular special about them – the efficiency, and therefore the condenser water cooling requirement, is comparable to any other typical Rankine-cycle steam power plant.

You’ll sometimes hear this argument about water consumption put forward by the anti-nuclear-power set. It uses so much water, they say. The fact is, the condenser cooling requirements for a typical Rankine-cycle steam power system are all pretty much comparable, per unit of electrical energy output, irrespective of what the heat source is – the heat source might be solar thermal, it might be nuclear fission, it might be coal, it might be oil – it doesn’t matter!

The laws of thermodynamics certainly don’t show any prejudice against nuclear fission heat sources, or against solar thermal heat sources, or anything else.

Some power plants, particularly the common coal-fired power plants, can achieve higher temperatures – and higher efficiency – utilizing supercritical water as the working fluid. A supercritical coal-fired plant, for example, might be able to achieve improved efficiency – and therefore a reduced condenser cooling water demand per unit electrical energy output – compared to a non-supercritical nuclear generating unit. However, the same concept can be applied to nuclear generating units, too. Supercritical light-water nuclear power systems are under serious development.

(Note that that does not mean supercritical in the nuclear physics sense of that word!)

Now, how much will it cost?

http://www.azcentral.com/arizonarepublic/news/articles/0221biz-solar0221.html

Estimated build cost for the Solana project: 1 billion dollars.

Nameplate capacity of 280 MWe. Since it’s using molten-salt thermal energy storage, it’s fair to expect a capacity factor that is superior to the Solnova 1 installation discussed above. But, of course, they just have to be difficult, and not provide any mention of the actual capacity factor expected (or the actual energy output per year), and instead only providing this difficult “supply energy to n homes” stuff.

Solnova 1: 50 MW / 25,700 = 1946 W of nameplate capacity per home

Solana: 280 MW / 70,000 = 4000 W of capacity per home.

Obviously there’s something missing here – the efficient thermal-storage Solana installation should be expected to require less capacity for a given number of homes supplied, but instead it requires twice as much. I guess they assume, maybe, that Americans are going to use more electricity than the people of Spain?

Unfortunately, at this point, without some basis to make reasonable estimates of capacity factor for the thermal-storage solar thermal plant, it’s almost impossible to make any meaningful comparison of the cost.

Almost impossible. We could make the most unrealistically conservative, optimistic, renewable-energy-is-infalliable estimate conceivable. We could estimate, just for argument’s sake, that a thermal-storage solar plant like the Solana facility has a capacity factor of 100%.

Then, the installation cost comes to 3.6 billion dollars per gigawatt of “real” average power output. It’s proportionately higher if you factor in some realistic capacity factor.

And finally, here’s something else that’s interesting – but perhaps not too surprising.

That is enough to supply 25,700 homes and to reduce CO2 emissions by more than 31,200 tons per year. To supplement power generation under conditions of low solar radiation, Solnova 1 is equipped to burn natural gas. This can be used to deliver 12-15% of the plant output.

Emphasis is mine. Obviously this clean, green, greenhouse gas emissions free energy is clearly so much more preferable to any kind of nuclear energy. I’m sure Amory Lovins would be proud of them.

Anti-nuclear quote of the day…

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http://www.theoildrum.com/node/3877#comment-334713

With concentrated solar, high temperature electrolysis of hydrogen is more than 100% efficient. Nuclear reactors for making hydrogen have temperature limitations.

Emphasis is mine. I’m sure there have to be a few TOD readers who aren’t going to let that stand unchallenged.

Written by Luke Weston

April 25, 2008 at 7:54 am

Anti-nuclear Quote of the Day.

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“Of course it [nuclear energy] isn’t sustainable. When finite resources are consumed, the amount decreases. Clearly consumption of the resource is unsustainable. Didn’t we learn that with fossil fuels and fossil water?”

There’s no such thing as an infinite energy resource.

That’s the second law of thermodynamics.

In a thermodynamically isolated system, there’s no such thing as “renewable energy”.

Sooner or later the uranium runs out, sooner or later the radiological geothermal heat in the Earth runs out, sooner or later the hydrogen in the sun runs out… and sooner or later, the free energy of the universe runs out, and everything in existence ends.

There are no renewable energy resources, and there are no infinite energy resources – there are only those energy resources which are sustainable in practical terms over the foreseeable future of human civilisation on this planet.

In about 2.5 billion years time, the Andromeda galaxy and our own Milky Way galaxy are going to collide with each other and merge together. My astrophysics is a little bit rusty, but suffice to say that things could get a little interesting gravitationally for our solar system.

Planning things out regarding resource sustainability on Earth beyond such a timescale is impossible, and arguably, irrelevant.