Energy and Human Ambitions on a Finite Planet, 2021a

16 Small Players 277
engineering challenges that may limit us to half the theoretical
efficiency, we would have to capture 36 TW of theoretical flow to end
up at 18 TW. Now we need a theoretical efficiency of 82%, 6 translating 6: 36 out of 44
to T h of 1,600 K, which would be about 50 km down: deeper than the
earth’s crust is thick.
For context, the deepest mine is less than 4 km deep, <strong>and</strong> the deepest
drill hole is about 12 km. 7 So outfitting 100% of Earth’s surface—
including under the oceans—with a dense thermal collection grid
50 km down sounds like pure fantasy.
7: Drilling stopped because technical challenges
prevented going deeper. The project
goal was 15 km.
16.1.2 Geothermal Depletion
The previous section was framed in the context of accessing the 44 TW
steady geothermal flow, sustainable for billions of years—finding that
we cannot expect to satisfy dem<strong>and</strong> by that route. But when did we
ever exhibit collective concern for long-term sustainable solutions? The
human way is more about exploiting a resource fully, not worrying about
consequences even decades down the line. In that sense, geothermal
energy has more to offer—at least on paper.
A one-time extraction of thermal energy under out feet—not worrying
about replenishment—amounts to mining thermal energy, in much the
same way that we mine copper, or fossil fuels. Using a rock density
of 2,500 kg/m 3 <strong>and</strong> a specific heat capacity of 1,000 J/kg/ ◦ C (Sec. 6.2;
p. 85), each cubic meter of rock has an extra 60 MJ of thermal energy
for each kilometer deeper we go—based on a gradient of 25 ◦ C/km, as
before. Is that a lot? It’s about the same as the energy in 2 L of gasoline.
The energy density works out to 0.006 kcal/g, to put in familiar units
(see Table 16.1).
So it’s no screaming-good deal, but it’s still energy, <strong>and</strong> the earth’s crust
has a heck of a lot more rock than it does oil. To appreciate the scale,
the l<strong>and</strong> area of the lower-48 states is approximately 10 13 m 2 . A 1-meterthick
slice of earth under the U.S. at a depth of 1 km therefore contains
60 MJ/m 3 times 10 13 m 3 ,or6 × 10 20 J of energy. It’s a big number, but
recall that 1 qBtu is about 10 18 J, so we’re talking about ∼600 qBtu. The
U.S. uses about 100 qBtu per year of energy, but at an average efficiency
of 35% in heat engines, so that we seek about 35 qBtu of useful energy.
As we saw, the geothermal resource, at lower temperature, is less potent
in terms of efficiency. If achieving half of the theoretical 8% efficiency
for the 1 km ΔT of 25 ◦ C, a one-meter-thick slice would provide about
Reaching the 35 qBtu goal would require a slice
about 1.5 m thick, at 24 qBtu per meter.
Table 16.1: <strong>Energy</strong> densities of familiar energy
substances. For hydroelectricity, a 50 m
dam is assumed, <strong>and</strong> for geothermal, the
depth is 1 km.
Substance
kcal/g
Gasoline 11
Fat (food) 9
Carbohydrates 4
TNT explosive 1
Li-ion battery 0.15
Alkaline battery 0.11
Lead-acid battery 0.03
Geothermal (1 km) 0.006
Hydroelectric (50 m) 0.0001
24 qBtu of useful work. 8 8: . . . 4% efficiency times 600 qBtu thermal
To summarize, we would need to completely remove all the heat from all
the rock 1 km below our feet in a 1.5 m-thick layer every year. Once we
cool the underground rock, it will take a long time for the surrounding
resource for one meter
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.