Jökull - 01.12.1966, Síða 48

k = heat conductivity of the rock
c = specific heat of the rock
e = density of the rock
t = time since the opening of the contact
q = total amount of hot water produced
per unit area of the contact during
the time t
s = specific heat of the water.
The interesting fact about this result is that
the quantity u is proportional to the ratio
\/ t/q. That is, the total amont of thermal
water which can be produced per unit area, in
a given temperature interval, is proportional to
the square root of the time since the produc-
tion was initiated. For example, let us consider
a system of this kind with a rock temperature
of T0 = 100° C and a total flow rate of one
Mton/year* which can produte a total of
10 Mton in 10 years before the outlet tem-
perature drops below 80° C. The above result
indicates. that at a production rate of V2 Mton/
year the same system could produce a total
of 20 Mton of thermal water in the period of
40 years before the temperature drops below
the 80° C level. Thus, the half rate leads to
the double total production.
We have here the first indication that the
total useful life of a geothermal system may
depend substantially on the rate of produc-
tion, and that an optimum production rate
may exist. The unfortunate fact is that it
appears very difficult to obtain sufficient data
to derive the optimum rate. This question will
be discussed below.
(2.3) The hydrological conditions. Water is
the heat carrier in all geothermal systems, and
an adequate flow niust be available in order
to make an exploitation possible. In fact, the
maximum total available flow of water from
boreholes limits the power that can be drawn
from a geothermal area. The hydrological con-
ditions are, therefore, of primary importance.
In order to give a quantitative idea about
the flows involved, we can state that the total
output of the boreholes connected to the
Reykjavik district heating system is of the
order of 15 Mton/year at an average tempera-
ture of 115° C. The boreholes at Wairakei,
New Zealand, have a total output of the order
*) one Mton = 108 tons.
202 JÖKULL
of 50 Mton/year of water at 250° C. Of course,
a part of this water flashes to steam in the
boreholes.
The problems encountered in geothermal
areas are quite similar to those encountered
in ground-water hydrology in general, although
there may be additional complications in high-
temperature areas due to two-phase flow, that
is, the flow of steam-water mixtures. However,
the steam phase is usually present only in a
relatively shallow zone and the heat carrier is
probably in its liquid state throughout most of
the hydrothermal systems.
Unfortunately very little is known about the
hydrology of the hydrothermal systems. In many
ways this is the most discouraging fact in geo-
thermal engineering. Until very recently the
only available set of hydrological data was de-
rived on the basis of the pressure-flow charac-
teristics of boreholes. But in most cases the test
periods are very short, and it is no secret that
geothermal plants have been built rather on
faith in good luck than on the results of a
comprehensive test program. A well producing
at a constant rate and constant temperature
for a period of a few months is generally re-
garded as good enough. Of course, the basis
of this procedure is that geothermal plants in
general are so economically healthy that even
a very short useful life can be tolerated. More-
over, experience lias shown that the constancy
of sorne geothermal wells is quite remarkable.
There appears no doubt that the hydrological
systems involved are very extensive.
But it is very much desirable to obtain more
reliable data on the structure of the systems.
Progress can be achieved on the basis of more
comprehensive hydrological work, and also
through a better evaluation of the well-test
data. A few words will be devoted to the latter
subject.
The subsurface hydrological network consists
of capacitors and resistors. In general we are
confronted with distributed parameters, but we
may in the first approximation use the methods
which electrical engineers have used with great
success for a long time. We can approximate
the real systems by lumped parameter models
and try to derive the the parameters that best
fit the observed data. The simplest lumped
model is the chain of capacitors and resistors
shown in Fig 3 below.