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 A√CVκω (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 |