Jökull - 01.12.1961, Blaðsíða 42

er references. A wealth of descriptive material
is given by Barth (1950). Data on utilization and
economical aspects are given by Bodvarsson and
Zoéga (1961).
2. THEORETICAL liEMARKS.
The temperature of the earth increases with
depth. A part of the associatecl heat flow is gen-
eratecl by radioactive decay and a part may be
due to general cooling of the earth. The tempera-
ture field is no simple function of the depth as
complications may arise because of the follow-
ing factors:
(1) Non-uniform distribution of the radioactive
sources.
(2) Possible local generation of heat by the
dissipation of mechaniccal energy and by
chemical processes.
(3) Non-uniform thermal properties of the mat-
erial.
(4) Movement of fluids, gases and magmas.
(5) Tectonic movements.
(6) Irregular topography and surface changes
due to erosion ancl sedimentation.
(7) Long-period variations of the surface
temperature.
be illustrated on the basis of the following simple
considerations.
Thermal areas are the outlets for extensive
circulations of water in geological bodies. The
water after being heated at depth moves upward
and is issued in the thermal areas. The clepth
of the circulation base will here be called the
base depth, ancl the temperature of the water as
it enters the upward movement will be called
the base temperature. The latter quantitv is an
important physical characteristic of the individ-
ual thermal areas.
The upflowing water looses heat because of
the conduction of heat froni the channels of flow
and sometimes because of intermixture with
colder water. Moreover, the water may loose
teinperature because of flashing if the base
temperature is above 100° C.
Suppose that the water flows vertically up
through a rock of a uniform permeability and
heat conductivity and that flow is uniform over
a large area. In case of stationary conditions and
no heat sources or flashing in the upflow zone
the heat transport equation reduces to the follow-
ing simple equation
kd2T/dx2 + sqdT/dx = 0 (2)
These factors have to be taken into account in
any evaluation of observational temperatures.
The equation for the temperature field, the heat
transport equation, can be written as follows:
V • (kVT - S) + h = pc y*- , (1)
where T = temperature,
k = heat conductivity,
S = vector of mass transport of heat per
unit surface and time,
h = generation of heat per unit volume
and time,
p = density of the material,
c = heat capacity of the material.
where s is the specific heat of the water and q
the upward mass flow per unit surface. The qu-
antity x represents the depth. With a base depth
D and a base temperature Tb the followins solu-
tion is obtained
T
: T„
(1 _ e-sqx/k)
(1 e-saD/kj
(3)
In general, the base cleptli is a relatively large
quantity and the seconcl term in the denominator
negligible. The simplified solution is in this
case
T = Tb (1 — e-s(ix/k) (4)
The heat transport equation is quite com-
plicated if all of the above factors have to be
taken into account. However, in the study of
natural heat resources most are of minor impor-
tance with the exception of the mass trans-
port of heat by fluids, gases and magmas which
is one of the main factors causing thermal acti-
vity. The implications of the mass transport can
This relation, although obtained by means of
great simplifications, is of conceptual import-
ance. It illustrates in a qualitative manner the
temperature-depth relation in thermal areas.
As a matter of course, the permeability and
the specific flow are never uniform. This leads
to cleviations which have to be discussed in the
indiviclual casses.
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