Ground storage without walls

OK, we’ve established the size of a useful ground store. But is it difficult to
keep the heat in? Would you need to surround your rock cuboid with lots
of insulation? It turns out that the ground itself is a pretty good insulator.
A spike of heat put down a hole in the ground will spread as

where κ is the conductivity of the ground, C is its heat capacity, and ρ is
its density. This describes a bell-shaped curve with width

for example, after six months (t = 1.6 × 107 s), using the figures for granite
(C = 0.82 kJ/kg/K, ρ = 2500 kg/m3, κ = 2.1 W/m/K), the width is 6 m.

Using the figures for water (C = 4.2 kJ/kg/K, ρ = 1000 kg/m3, κ =
0.6 W/m/K), the width is 2 m.

So if the storage region is bigger than 20 m × 20 m × 20 m then most
of the heat stored will still be there in six months time (because 20 m is
significantly bigger than 6 m and 2 m).

Limits of ground-source heat pumps

The low thermal conductivity of the ground is a double-edged sword.
Thanks to low conductivity, the ground holds heat well for a long time.
But on the other hand, low conductivity means that it’s not easy to shove
heat in and out of the ground rapidly. We now explore how the conductivity
of the ground limits the use of ground-source heat pumps.

Consider a neighbourhood with quite a high population density. Can
everyone use ground-source heat pumps, without using active summer re-
plenishment (as discussed on p152)? The concern is that if we all sucked
heat from the ground at the same time, we might freeze the ground solid.
I’m going to address this question by two calculations. First, I’ll work out
the natural flux of energy in and out of the ground in summer and winter.

water 0.6
quartz 8
granite 2.1
earth's crust 1.7
dry soil 0.14
Table E.15. Thermal conductivities. For more data see table E.18, p304.
Figure E.16. The temperature in Cambridge, 2006, and a cartoon, which says the temperature is the sum of an annual sinusoidal variation between 3 °C and 20 °C, and a daily sinusoidal variation with range up to 10.3 °C. The average temperature is 11.5 °C.