other hand we try to suck a flux bigger than 5 W/m2, we should expect that
we’ll be shifting the temperature of the ground significantly away from its
natural value, and such fluxes may be impossible to demand.

The population density of a typical English suburb corresponds to
160 m2 per person (rows of semi-detached houses with about 400 m2 per
house, including pavements and streets). At this density of residential
area, we can deduce that a ballpark limit for heat pump power delivery is

5 W/m2 × 160 m2 = 800 W = 19 kWh/d per person.

This is uncomfortably close to the sort of power we would like to deliver
in winter-time: it’s plausible that our peak winter-time demand for hot air
and hot water, in an old house like mine, might be 40 kWh/d per person.

This calculation suggests that in a typical suburban area, not everyone
can use ground-source heat pumps
, unless they are careful to actively dump
heat back into the ground during the summer.

Let’s do a second calculation, working out how much power we could
steadily suck from a ground loop at a depth of h = 2 m. Let’s assume that
we’ll allow ourselves to suck the temperature at the ground loop down
to ΔT = 5 °C below the average ground temperature at the surface, and
let’s assume that the surface temperature is constant. We can then deduce
the heat flux from the surface. Assuming a conductivity of 1.2 W/m/K

thermal
conductivity
κ
(W/m/K)
heat
capacity
CV
(MJ/m3/K)
length-scale

z0
(m)
flux

ACVκω
(W/m2)
Air 0.02 0.0012
Water 0.57 4.18 1.2 5.7
Solid granite 2.1 2.3 3.0 8.1
Concrete 1.28 1.94 2.6 5.8

Sandy soil
dry 0.30 1.28 1.5 2.3
50% saturated 1.80 2.12 2.9 7.2
100% saturated 2.20 2.96 2.7 9.5

Clay soil
dry 0.25 1.42 1.3 2.2
50% saturated 1.18 2.25 2.3 6.0
100% saturated 1.58 3.10 2.3 8.2

Peat soil
dry 0.06 0.58 1.0 0.7
50% saturated 0.29 2.31 1.1 3.0
100% saturated 0.50 4.02 1.1 5.3
Table E.18. Thermal conductivity and heat capacity of various materials and soil types, and the deduced length-scale z0 = √2κ/(CVω) and peak flux ACVκω associated with annual temperature variations with amplitude A = 8.3 °C. The sandy and clay soils have porosity 0.4; the peat soil has porosity 0.8.