Warm and Fuzzy on Geothermal?

The Earth started its existence as a red-hot rock, and has been cooling ever since. It’s still quite toasty in the core, and will remain so for billions of years, yet. Cooling implies a flow of heat, and where heat flows, the possibility exists of capturing useful energy. Geysers and volcanoes are obvious manifestations of geothermal energy, but what role can it play toward satisfying our current global demand? Following the recent theme of Do the Math, we will put geothermal in one of three boxes labeled abundant, potent, or niche (puny). Have any guesses?

The Physics of Heat

Thermal energy is surprisingly hefty. Consider that putting a room-temperature rock into boiling water transfers to it an equivalent amount of energy as would hurling it to a super-sonic speed! We characterize the amount of heat an object can hold by its specific heat capacity, in Joules per kilogram per degree Celsius (or Kelvin, since one degree of change is the same in either system). Tying some energy concepts together, the definition of a kilocalorie (4184 J) is the amount of energy it takes to raise 1 kg (1 liter) of water 1°C. So we can read the specific heat capacity straight away as 4184 J/kg/K. This is a rather large heat capacity, on the scale of things. As a rule of thumb, 1000 J/kg/K is a marvelously convenient universal number for most substances: it works for wood, air, rock, etc. Liquids tend to be higher (typ. 2000 J/kg/K), and metals tend to be lower (150–500 J/kg/K). Rocks—relevant for geothermal energy—range from about 700–1100 J/kg/K, and although I would be happy enough to use the convenient 1000 J/kg/K for crude analysis, I will be somewhat more refined and use 900 J/kg/K for rock in this post—although I feel silly for it.

As an example, to heat a 30 kg dining room table by 20°C, we need to supply 600,000 J. Just multiply specific heat capacity by the mass and by the temperature change. A 1000 W space heater could do it in ten minutes (600 seconds), if all of its energy could be channeled directly into the table.

The next property to understand is thermal conductivity: how readily heat is transported by a substance. Differing thermal conductivity is why different materials at the same temperature feel like different temperatures to our touch. It’s because high thermal conductivity materials (metals) slurp heat out of our hands much faster than plastic or wooden objects would. Copper has a thermal conductivity of 400 W/m/K, while stainless steel has an abysmally low value (for a metal) around 15 W/m/K—which is one reason why stainless steel is the preferred metal in kitchens: we can tolerate holding the spoon or pot handle even when another part of the item is quite hot. Plastics are around 0.2 W/m/K, and foam insulation tends to be around 0.02 W/m/K. Rock falls between 1.5–7 W/m/K, with 2.5 W/m/K being typical.

How do we apply thermal conductivity? Imagine a flat panel of stuff with area, A, and thickness, t. Using the Greek letter kappa (κ) to represent thermal conductivity, the rate at which thermal energy flows across the panel given a temperature difference ΔT across it is κAΔT/t, which comes out in Watts.

Sources of Heat

Two sources contribute to the Earth’s heat. The first, contributing 20% of the total, derives from gravity. As proto-planetary chunks fell together under the influence of gravity, the kinetic energy they carried (converted gravitational potential energy) ended up heating the clumps that stuck together. If this were the only contributor, Earth’s center would have cooled significantly below its present levels by today. The other 80% of heating is the gift that keeps on giving: long-lived radioactive nuclei given to us by ancient supernovae (as with most of the other elements comprising Earth and ourselves). Specifically—in order of significance to heating—we have 232Th, 238U, 40K, and 235U, with half-lives of 14, 4.5, 1.25, and 0.7 billion years, respectively. Ironically, one can view the radioactive contribution as gravitational in origin also! This is because supernovae result from fusion losing the fight to gravity, and the heavy elements are created in the resulting gravitational collapse.

In total, the radioactive decay produces about 7×10−12 W/kg; in the mantle. The mantle occupies 85% of the volume of the Earth at an average density about 5 times that of water, having a mass of about 4.5×1024 kg. Multiply these together to get 34 TW of heat flow in steady state. If radioactivity is 80% of the story, this implies 42 TW total. Averaging over the area of the Earth, we get 0.08 W/m². Because of the decaying nature of radioactive materials, the heat generation was much higher a few billion years back, making Earth a more geologically active place (e.g., more volcanoes).

We can work up another estimate of the total geothermal heat flow by observing that the temperature gradient in the crust is 22°C/km. This gradient can be used as the ΔT/t part of the thermal conduction heat flow rate, κAΔT/t. Taking a square meter for A and 2.5 W/m/K for κ, we calculate a geothermal “loading” of 0.055 W/m². Indeed, Wikipedia reports a land-based heat flow of 0.065 W/m² while the ocean (due to thinner crust and thermally greedy water) averages 0.1 W/m².

Compared to Human Use

Using the Wikipedia value of 0.065 W/m² over land, multiplying by land area yields 9 TW. Humans use 13 TW currently. So if we managed to catch every scrap of land-based geothermal flow (and could use it efficiently), we would not fully cover our present demand. Needless to say, we’re not remotely capable of doing this.

Diffuse Use vs. Hotspots

Naturally, some places are better than others for tapping into geothermal energy. A map of the continental U.S. in heat flow (below) reveals that the west has more flow than the east. A similar map for North America (including oceans) can be found on the SMU website. On a large regional basis, some spots in the U.S. dip down to 0.03 W/m², while some of the better regions reach up beyond 0.1 W/m².

Note that Yellowstone, in northwestern Wyoming, is the hottest zone.

Even so, we’re talking thermal gradients that are at most in the neighborhood of 35°C/km. In order to produce electricity in a heat engine, we are stuck with a maximum thermodynamic efficiency of (Th − Tc)/Th, where “h” and “c” subscripts refer to absolute temperatures of the hot and cold reservoirs, respectively. At 1 km depth, this amounts to only 10% (and in practice we tend to only get about half of the theoretical maximum efficiency). One needs to drill at least 3 km down before being able to take advantage of steam (at 27% max efficiency). A depth of 5 km reaches 38% maximum theoretical efficiency—so perhaps 20% practical efficiency. Making a 1 GW electricity plant operating on the steady-state geothermal flow would require canvassing an area 200 km on a side buried 5 km deep even in the better regions having 0.1 W/m². Realizing that we’re stuck with thermodynamic inefficiency, a geothermal network covering every scrap of land area on the globe would get less than 2 TW of power at 20% end-to-end efficiency.

So rather than mess with the pathetically impractical commonplace thermal gradients for the purpose of electricity production, we look to hotspots like the Yellowstone region, or places where hot springs and geysers can be found at the surface. Indeed, The Geysers in California hosts 1.5 GW of installed geothermal electricity, but the power output has declined by almost a factor of two in recent decades (it is possible to draw out heat faster than it is replaced by conduction).

Part of the Geysers plant, in Calif. Source: EERE

The U.S. has about 3 GW of geothermal electricity installed, out of the worldwide total of 10 GW. Surprising to me, Iceland has just 0.6 GW installed, but this is 30% of their national electricity production. Another surprise to me was that the Philippines also derive about 30% of their electricity from geothermal sources, amounting to 1.9 GW.

I don’t have any handy back-of-the-envelope way to estimate the abundance of hotspots. Out of the 9 TW of diffuse land-based heat flow, I might guess that something like 1% (90 GW) may be available in the form of geyser-like surface steam. In short, these are rare beasts.

Direct Use

Rather than try to generate electricity, we could use direct heat from geothermal, or use the thermal mass of the ground as a push-point for heat pumps. The latter should not be called geothermal, since it is not tapping into the geothermal heat flow. As such, I will ignore it here and return to it at some later time together with a discussion of heat pumps for controlled climate applications.

The difficulty with extracting heat from the ground is that the gradient is rather small. For instance, hot water in the home generally wants to be about 45°C. This requires drilling 1.5 km (about a mile) down to get this warm—certainly impractical for individual homes. It could possibly be effective for communities or cooperatives that distribute hot water to a number of houses/businesses. Using geothermal energy for home heating faces similar distribution challenges.

Sustainable Extraction

When drawing heat out of a region in the ground, that region will cool relative to its surroundings if heat is extracted at a rate faster than the nominal flow—leading to a depletion of thermal capacity. The replacement heat must ultimately come primarily from radioactive decay. Let’s ask how much rock volume needs to supply thermal energy for one house on a sustainable basis.

The average American household used 80 thousand cubic feet of natural gas in 2001 (apologies for old data and Imperial units). The gas is predominantly used for heating of one form or another: house, water, and food. 80,000 cf translates to about 800 Therms of energy per year, or 2700 W of continuous thermal power. Using our number from before that the mantle generates 7×10−12 W/kg, the average American home would need a rock mass of 4×1014kg, or a cubic volume 5 km on a side at a crustal density of 3.3 times that of water.

Can you believe this? All that volume for one house! This does not mean that the collection network needs to be this large. After all, heat is flowing from deeper down all the time. In this context, the average house needs to intercept an area 200 meters on a side at 0.065 W/m². Still quite a large outlay of piping 1.5 kilometers deep.

Thermal Depletion

What if we cheat and use a smaller collection network, relying on conduction to fill in with surrounding heat? How long will our resource be useful? I’ll spare you the derivation, but the recharge time via thermal conduction is proportional to density times specific heat capacity divided by thermal conductivity. Most importantly, it scales as the square of the dimension (think radius of the depleted zone). Using numbers for an egg (typical food will have values like: ρ ≈ 1000 kg/m³; κ ≈ 1 W/m/K; cp ≈ 2000 J/kg/K; R ≈ 0.02 m), I get a timescale of 800 seconds, or about 13 minutes. This is how long it would take an egg to cool down (or heat up in boiling water). Not to bad, as estimates go. Using numbers for rock, I get a one year time constant when R ≈ 5 m. Crudely speaking, this means we’d have access to a yearly “sustainable” volume—recharging in summer, for instance—around 500 cubic meters, holding 45 GJ (cpρVΔT) of thermal energy at a ΔT of 30°C. Used over a year, this provides something like 1400 W of average power—about half of the typically desired amount.

The danger is that once you try to go larger scale than this, the depletion volume gets larger, and the time to recharge scales up accordingly. Fundamentally, thermal depletion is a dimensional problem. You can draw out energy according to volume, but it is recharged according to area. So the problem is dimensionally stacked to come up short, leading to thermal depletion. This analysis deals with straight conduction. An underground fluid flow would change the story, and developed geothermal sites usually have this feature.

Damn the Depletion!

Still, if we don’t care about sustainable use of geothermal, we can just keep drilling new holes to deplete one region after the other. In this sense, we could evaluate the thermal endowment in the upper 5 km of crust under land. The average temperature in this layer is about 60°C above the surface value, so that each cubic meter (3300 kg) contains 180 MJ of thermal energy. Summed over 1.4×1014 m², we get about 1026 J. This is 250,000 years of our global appetite. A quarter-million years might seem close enough to indefinite that we’re willing to call it sustainable. Truly it is a substantial endowment. It’s the practical considerations that hold us off from rushing into this resource.

The energy derived is mostly useful for heat, being inefficient at producing electricity. It won’t fly our planes or drive our cars. And it’s buried under kilometers of solid rock, making it very difficult to access. Each borehole only makes available the heat in its immediate surroundings—unlike drilling for oil or natural gas, where a single hole may access a large underground deposit. So my guess is that we’ll burn every tree and fossil fuel on the planet before we start drilling through ordinary rock to stay warm. In other words, there is little incentive to dig deep for heat. By the time we run out of the easier resources—having burned every scrap of wood not bolted down—are we going to be left in a state to drill through rock at a massive scale?

In short, even though the thermal energy sitting under our feet is enormous in magnitude, it does not strike me as a lucky find. No one is racing to dig in.  Perhaps it is simpler to say that it’s economically excluded, at present.  And will it ever be cheaper to drill?  For me, this falls into a category similar to space resources.  Sure, they exist, but getting to them means that they might as well not be there, for practical purposes.

Geothermal In Perspective

Abundant, potent, or niche? Hmmm. It’s complex. On paper, we have just seen that the Earth’s crust contains abundant thermal energy, with a very long depletion time. But extraction requires a constant effort to drill new holes and share the derived heat among whole communities. Consider that two-thirds of our fossil energy goes up as waste heat, and often in cold environments. Waste is an appropriate word, in this context.  But distributing the heat into useful places is a practical challenge to which we seldom rise.

Once we move to the steady flow regime, we get 9 TW across all land. This might qualify it as potent, except that practical utilization of the resource fails to deliver. For one thing, the efficiency with which we can produce electricity dramatically reduces the cap to the 2 TW scale. And for heating a home, we saw that we would need to capture zones well over 100 meters on a side. Recall that in similar fashion, the 1200 TW scale for wind dissipation was knocked way down to a handful of terawatts to account for the practically extractable portion—but still leaving it in the potent category. So realistically, steady-state geothermal fails to deliver, and lands in the “niche” box.

Clearly, geothermal energy works well in select locations (geological hotspots). But it’s too puny to provide a significant share of our electricity, and direct thermal use requires substantial underground volumes/areas to mitigate depletion. All this on top of requirements to place lots of tubing infrastructure kilometers deep in the rock (do I hear EROEI whimpering?). Even dropping concerns about depletion, the practical/economic challenges do not favor extraction of geothermal heat on a large scale.  So geothermal is not giving me that warm, fuzzy feeling I seek. It’s certainly not riding to the rescue of the imminent liquid fuels crunch.

We’ll see nuclear fusion next week.

29 thoughts on “Warm and Fuzzy on Geothermal?

  1. Tom, thanks again for an excellent analysis.

    When you’ve finished this whirlwind tour of energy sources, I’d love to see one more, where you add up all the niche players and see if, combined, they amount to something. I’d especially be interested in how well they complement each other. Can they be combined in a way that each makes up for the shortcomings of another?

    (I’ll bet you a cup of coffee that the answer is, “Not in a big way,” but I’d still like to see the analysis.)

    Cheers,

    b&

  2. Wow.

    I wasn’t really expecting geothermal to ride to the rescue, but neither was I expecting it to be so pathetic. When supposedly moderately well informed people (google re<c guys) associate themselves with phrases like 'geothermal sleeping giant' I'd thought there might be something to it. To say nothing of these numerous, funded companies trying to exploit it's "incredible untapped potential".

    What a joke. Thanks for the numbers!

    • Well, there truly is a sleeping giant of thermal energy below our feet. Sustainable use of the flow is on the pathetic side, but depletion-extraction opens up a vast store. But it’s primarily useful for direct heat, and I personally judge it to be highly impractical—even if the numbers are large.

      • Why limit to 5km though, if depletion occurs at 5 km why not go down 10+km as well. It May not be more efficient (delta T) energy extraction but as we can drill down that far, see Kola Super deep Borehole, it would take longer to deplete and recharge faster no?

        • The idea of sucking all warmth out of the earth strikes me as a potential environmental catastrophe. Changing the earths climate on a massive scale is a BAD idea.

          • Yeah – precisely. It’d be a shift from one massively unsustainable fossil fuel source to another somewhat less unsustainable (perhaps) but still pretty stupid one. And if we really had to go that deep to tap large reserves of heat I find it hard to imagine it’ll be economic either.

            I’m happy, actually. I devote most of my energy to solar/wind development, so there’s always this nagging sense in the back of my mind that maybe I should be looking more into some others (geothermal, nuclear, algae based Gen IV biofuels). Every time something comes off that list it gives me that little bit more certainty.

            Though I guess even that has two possible paths. The optimistic one is that I’m working on the right thing to save us from a crash. The pessimistic one is that there’s one less thing to potentially save us from a crash at a time when we need every advantage we can get.

      • Yup, fair point, but as you say it’s only conceivably useful as low grade direct heat even if we DO accept that we’ll deplete it. I don’t really see low grade heat being of significant value to us in the next 100 years – today it’s interesting for space heating, sure, but if we haven’t shifted to passive house/building-in-general designs and materials a century from now then we really would need to be fairly thick. I guess such an assumption means that our energy load will drop, which is nice, but it means that when looking for solutions we need solutions that provide high grade energy for tools/toys rather than low-grade energy potentially for space heating. I guess there’s still hot water.

        Did you take a look at that google paper on thermal energy resources in the US? The one thing I missed in your assessment above (I may have just read too quickly) is the potential of high grade heat with replenishment from fluid flow.

        The conclusions you’ve drawn seem to be that:
        1. Sustainable resource is trivial
        2. Depletion resource is large, but difficult to access if we assume upper-crust thermal gradient and replenishment only by conduction through rock.

        There is still a possibility I guess that there is a large (depletion based) resource of deep-crust high-grade heat that’s made readily accessible by natural fluid flows; ‘sleeping giant’ comments might be justified if this is the case (and my scorn therefore unjustified… which I think it is, they are for sure smart guys).

        The SMU/Google work (here: http://www.google.org/egs/) mentions 3TW technical capacity, and offers a really awesome google earth overlay with technical recoverable potential. Still doesn’t seem remotely like a universal panacea, but would perhaps bump geothermal up out of the niche category at least on a ~1000 year basis (assuming that the replenishment flows aren’t screwed up).

    • From an investment standpoint geothermal could be a “sleeping giant” insofar as 15 or 20 companies could triple or quadruple in values while supplying “millions and millions” of homes with energy from geothermal sources. But that wouldn’t mean it has a significant effect on total global energy supply.

  3. Totally niche.

    I saw a special once about Iceland where they were showing their use of geothermal and how they used it to make H2 for vehicles. I thought this was brilliant since as an Island without bridges, they can play the niche markets since they do not have to worry too much about large drives across country like the US or Europe does.

    I also thought that places like Hawaii could use the same concept or go with EV.The price of gasoline on islands has to be pretty high.

    Like the whole food thing, we need to start thinking locally about energy generation. Use what you have.

    However, I think the next topic of fusion will solve all of our problems, including space travel. Now if I could just get a better explanation of why a matter / anti-matter reaction needs to be regulated by di-lithium crystals? LOL

  4. [shortened by moderator]

    I think geothermal is a good source of energy for heating small and/or densely used spaces, such as domestic, institutional and (some) commercial buildings. I think it is a good option especially when combined with passive solar heating/cooling (because the flow of energy can be used for both) and efficient insulation (and why not some PV for powering the pump and other uses?).

    Up to now DtM posts bore on two main subjects : energy for transportation, and energy for producing electricity. The focus has been on the physical possibility, scalability and economic practicalities of various sources of energy and storage schemes. I would like to see a post dedicated to the heating of small/densely used spaces. I think it is one of the few energy sectors (if not the only one) where small is indeed beautiful.

    To sum up this point, it seems crystal-clear to me that life-style changes are required in this age of energy crisis. However, individuals can only do so much. This is why we need urban, industrial and agricultural (amongst other things) planning to achieve transportation, heating and fertilizing (e.g.) efficiency/sustainability.

    Last point, I wonder if thermal depletion is such a problem. In nordic countries such as Québec, geothermal energy is used in summer for cooling and in the winter for heating. We could talk about a positive thermal flow (ptf) in the winter and a negative thermal flow (ntf) in the summer (relative to the house; inverse the attributes for the ground). Wouldn’t the ptf and ntf cancel each other out over the course of a year? Wouldn’t that depend on average temperatures? I guess there’s a risk that the flows would not be equivalent everywhere. But in some regions of the world, it may balance out and therefore be and adequate solution for controlling indoor temperature.

    Of course, geothermal remains in the niche category. However, I thought these reflections were of some interest.

    • What you’re talking about in the last paragraph here is energy storage, not an energy source. I definitely agree that ground source heat pumps have a lot of potential (and Tom mentioned early in this post he’ll look into them sometime). But that’s only a thermal reservoir – you have to put energy into it in order to be able to take it out later, and there will be significant losses. It’s absolutely not an energy source, which is what we need when looking at the 30TW etc conundrums.

      • aka GeoExchange, and it does have huge potential — when conditions are right. It works best when annual heating and cooling loads are _roughly_ equal in size. In an overwhelmingly hot (Las Vegas) or cold (Buffalo) climate, a thermal plume forms over time, reducing the efficiency of the system. The exception to this would be when there water flowing either above or underground to/from which the system can sink or source, though that could be viewed as another kind of depletion.

      • 30TW? Where does that come from, a future projection? World consumption rate is 14-15 TW primary energy.

  5. Very informative post.

    I did not realise the CA geysers were depleting so fast.

    I don’t know if any communities in the US use direct geothermal heat the way they do in Iceland, but if they did Northern Nevada, Southern Idaho, or Western Oregon would seem like a good place for them.

    I eagerly await your analysis of heat pumps.

  6. The only application for geothermal that I see as being generally useful are earth-source heat pumps for conditioning buildings. Those only work on the efficiency side of the equation, though.

  7. Hello, and thank you for an interesting and informative post, as well as blog!

    I agree on your numbers but I must say I disagree on your conclusions. As you point out, geothermal “mining” or depletion-extraction as you refer to it will last longer than the human race, especially if depths down to 10 km are included. Apart from that, geothermal possess a combination of attributes that I find extremely beneficial and that no other renewable energy source can compete with. With EGS-technology it is almost deployable anywhere on the planet, it will always be available regardless of time or day or weather and it has the ability to provide both electricity and heat. This combination might make it worth the trouble drilling for it, diffuse as it might be. Sure EROEI is low for electricity generation but considerably better for CHP-applications.

    One might also consider hybrid systems of for instance geothermal and solar thermal, where geothermal steps in during nighttime and extended periods of bad weather. Not only would this provide the ability for the system to provide base load power and heat, it would also prevent the geothermal resource from premature depletion. One would have to take the different working temperatures into consideration of course, but it could be a possible way to go.

    I’ve been writing for a while about energy issues myself on http://www.hoglundaberg.se/energibloggen, unfortunately it’s in Swedish :)

    Regards,
    Johan

  8. Certainly the geothermal resource has some thermal depletion limit, but I doubt the Geysers in California is not an example of thermal depletion, not yet. The operation has been taking out substantially more water (as steam) than has been pumped in.
    http://en.wikipedia.org/wiki/File:Geysers_annual_steam_production.jpg

    According to the NREL the geothermal plant has seen a power drop because of *water depletion*, and suggests the effort underway to recharge the ground water should increase power production substantially.
    http://www.nrel.gov/docs/fy04osti/36317.pdf, page 4.

    • Water depletion at geysers. not conduction.

      huge omission i would say.

  9. I’m curious about the the portion discussion which calculates power per total surface area, returning to it several times, and similarly stating average temperature gradients, as if the sphere were solid. I’ve seen the geothermal problem framed this way before by others so perhaps I am missing something as to why it should be so done.

    Certainly this is a valid approach for solar and wind as they are intrinsically tied to a patch of surface, more or less independent of what may be collected elsewhere. But, and as described in the later part of the article, heat *flows*, conveniently as it happens for geothermal, to where the heat is being depleted.

    Calculating average heat flux at the surface is like calculating the heat flux of a steam boiler at the surface before discovering, aha, we can install an expansion valve, or embed a heat exchanger, to draw real power. Indeed, mass transfer via magma risers appear to have built ‘valves’ (high heat flux collection points) into the system as a common occurrence, not a rarity:
    http://en.wikipedia.org/wiki/Mantle_(geology)#Movement

    It seems to me, having achieved the solid figure of merit of 42 GWth, corrected for thermal dynamic efficiency (and using a delta T closer to 8-900C, amply obtained, not 150C), that the physics of limits should have stopped this time, leaving the rest to the ingenuity of drilling engineers, with no guarantees either way.

  10. I think your final analysis is flawed. Hot dry rock or enhanced geothermal eople aren’t looking at the whole upper 5 km and an average temperature delta of 60 C; they’re looking at 3-5km depths and temperatures of 140 to 300 C, with a definite eye to electricity production.
    http://geoheat.oit.edu/bulletin/bull22-4/art4.pdf

    Above this is extracting heat from magma reservoirs, which are definitely hot enough, or maybe from unusually hot plutons.

  11. This is well outside my engineering knowledge but has anyone done a calculation on how much water all this would take. Sounds like truly immense amounts even allowing for the idea of pumping some back which might reduce efficiency of the system.. The areas of hotter rocks appear to uncomfortably coincide with all the driest regions of the planet. Is the return fluid corrosive and cause further environmental damage.

    There has also be a definite spike in small tremors when water injection of any type is attempted deep down. Might want of be careful with this technology.

  12. Thanks Tom for another interesting article. You said you would cover heat pumps another time, but I wanted to mention ‘Air-ground pipes’. Not much used in the U.S. but has been around for centuries in the Middle East. A tremendous amount of our electrical generation, ( and thus CO2 emissions) are for air conditioning. While Air-ground pipes are often used in conduction with a heat exchanger system (larger more profitable installation sale), in it’s simplest form it is just a hundred foot of 6″ pipe buried 6 or more feet down with one end with an air inlet, and another into the building space. Convection alone can draw a substantial draft through the pipe and bring in 10C air for cooling. No electricity required. http://export.rehau.com/construction/civil.engineering/ground.heat…geothermal.energy/awadukt.thermo.shtml as an example.
    It would be nice if you could consider this when you look into heat pumps. In light of something so simple, it seems incredibly stupid to be running millions of air conditioners. (OK, not so simple for a high rise, but you know what I mean.)

    • I like these simple and yet effective remedies. Like solar water heating, passive solar design, solar cookers, etc. They can have a tremendous impact on human well-being, don’t require a high capital investment and don’t create dependency. These small-scale low-tech solutions will prove an important part of any transition towards energy sustainability.

  13. Hi Tom,

    Yes, thermal energy is surprisingly hefty.

    Even more amazing is the latent heat of vaporization. This is nicely described by a graph at the following website:
    http://www.kentchemistry.com/links/Energy/HeatVaporization.htm

    Note that 2.26 MegaJoules are required to vaporize a kg of water once it has been brought up to 100 degrees at standard pressure. Far more energy than the 400 or so kiloJoules required to raise said kg from room temperature. This is why the old steam engines which exhausted the steam to atmosphere were significantly less efficient than a modern powerplant outfitted with steam generator, turbine, condenser and reheat exchange. These efficient facilities recover some of the latent heat of condensation.

    A modern steam turbine rotor is a beautiful thing, and the assembled turbine includes stator blades between each rotor stage:
    http://www.flickr.com/photos/cheesy42/4018182996/

  14. This might be a stretch right now, but making the most out of the type of energy begin used; it should be evaluated as well.
    Not all technologies and forms of energy are used in the most efficient way. Hydroelectric plants using potential energy to produce electricity is one thing, nuclear or fossil energy to produce electricity has always been a stretch. My point being, using geothermal energy for heating sounds a strong proposition. Tag to that, if we ensure its being used in the areas of greater demand. That would add to the benefits of it.
    Anyone has done entropy analysis on these models? Would be interesting to review…

  15. Tom,

    Great post. A couple small points of clarification, that don’t really change your conclusions at all:

    1) Radiogenic heat production is significantly higher in the crust than in the mantle, because radiogenic minerals typically don’t fit well in the crystal lattices of typical mantle minerals, and escape quickly into the melt when a body of mantle rock undergoes partial melting–this is how the crust formed. A typical granite (what much of the crust is made of) has a radiogenic heat production of 2-5 E-6 W/ m^3, or ~7E-10 to 2 E-9 W/kg (given a typical density of 2700 kg/m^3) (e.g., http://cat.inist.fr/?aModele=afficheN&cpsidt=15131658). This is significantly higher than the mantle values and proportionally affect the volume of rock required for household sustenance; However, it probably doesn’t really affect global heat flow values.

    2) As some other posters have commented, geothermal power plants are basically reliant upon (super)heated groundwater to derive their power. They divert it and capture energy through various techniques involving steams turning turbines or releasing latent heat through condensation. Therefore, geothermal plants go offline because the groundwater is pumped out too fast, not because the bedrock itself has cooled appreciably. The basic heat collection is done by water in the subsurface, generally traveling along faults and other fractures in the rock (igneous rocks are not very permeable otherwise), and overpumping and earthquakes (seismicity correlates well with surface heat flow; let’s not get into causation on that topic) can change the groundwater flow patterns and increase or decrease productivity at the power plant. Both of these have been observed at the Coso plant in Owens Valley.

Comments are closed.