Page 227 - Geothermal Energy Renewable Energy and The Environment

Direct Use of Geothermal Resources 215

Heat loss via convection is

Q = (9.045 × v) × A × dt
cv
2
Q = (9.045 × 1.0 m/s) × 150 m × 17 K
cv
Q = 6,407 J/s.
cv
Heat loss via radiation is

Q = ε × σ × A × (T − T )
4
4
1
2
rd
2
−8
Q = 0.99 × 5.669 × 10 W/m K × 150 m × (300 K − 283 K )
4
4
4
2
rd
Q = 14,191 J/s.
rd
Heat loss via evaporation is
b
Q = a × (P − P ) × H w
ev
w
a
Q = 196.88 × (3.7 kPa − 1.23 kPa) 1.068
ev
Q = 52,575 J/s.
ev
The total heat loss, Q is thus
TL
Q = 37,800 J/s + 6,407 J/s + 14,191 J/s + 52,575 J/s = 110, 973 J/s.
TL
This heat loss value overestimates the average load on the facility for several reasons. The heat
lost by conduction will decrease over time because the thermal gradient driving conduction will
diminish as the ground around the pond heats up. This term will eventually become negligible and
can be ignored for long-term considerations, but must be considered during the start-up phase of the
operation. In addition, the calculation was made for winter conditions and a modest breeze. Neither
of these conditions is likely to be the average condition for the pond. Under average conditions it can
thus be assumed that the actual heat loss will be significantly less than computed.
Managing the flow of water into the pond requires balancing the rate at which fresh water
needs to be added to the facility to keep the stock healthy, and the addition of heat to maintain
temperature. Using the heat loss computed above as the actual rate at which make-up heat must
be added to keep the pond at 27°C, we can compute the inflow rate as a function of the resource
temperature from

F = Q /(C × (T − T ), (11.11)
L
p
G
in
P
where F is the rate at which fluid must be added, in l/s, Q is the total heat loss, C is the constant
p
in
L
pressure heat capacity of water, T is the temperature of the geothermal fluid, and T is the tempera-
G
P
ture of the pond. Plotted in Figure 11.8 is the rate at which fluid must be added to keep the pond at
27°C, as a function of the temperature of the incoming fluid. The curve in the figure indicates that
the amount of geothermal water that needs to be added to the pond is very high if the geothermal
water temperature is within about 15–20° of the pond temperature. Beyond that point, the amount of
make-up fluid that must be added changes at a relatively small rate over a broad range of geothermal
water temperatures. This is often considered a rule of thumb for applications such as this (Rafferty