Tímarit Verkfræðingafélags Íslands - 01.02.1984, Blaðsíða 21

Most of Iceland to the west of the ax-
ial zone is also characterized by a high
average heat flow and a considerable
number of low-to-medium temperature
geothermal systems. The activity is con-
centrated on the lowlands of the SW
and the Borgarfjordur region.
There is considerable literature on the
general setting of the geothermal activi-
ty in Iceland. For an overall review, we
will here refer to Bodvarsson (1964) and
Palmason (1974). During the past few
years, a considerable amount of work
has been carried out in the Krafla high-
temperature geothermal area in the
North (Bjornsson et al., 1978). This
work has furnished a great amount of
interesting and important data that
reveals a close relation between active
rift-zone volcanism and geothermal ac-
tivity. The extensive study of the
Deuterium content of natural waters in
Iceland carried out by Arnason (1976) is
another very significant contribution to
the geothermology of Iceland. Finally, a
survey of microearthquake activity in
Iceland (Ward and Bjornsson, 1971) is
of particular interest in the present con-
text.
Turning to the topics of present in-
terest, the results that have been obtain-
ed in Iceland give important data as to
the subsurface circulation of water in a
rift-zone evironment. First, some
borehole temperature profiles indicate
that the axial zone includes local regions
of a very high vertical fluid conductivi-
ty. A borehole that was drilled near to
the city of Reykjavik in the SW (see Fig.
1) gives a direct indication of this situa-
tion. As shown in Fig. 2, this borehole,
although located in a region of con-
spicuous volcanic activity and high heat
flow, is, nevertheless, almost isothermal
at about 5°C down to a depth of 700 m.
This can only be understood on the
basis that adjacent vertical fractures of
substantial conductivity permit a signifi-
cant downward mass flow of surface
water. Moreover, based on some un-
published Deuterium isotope data and
other results from the Krafla area, the
mechanism of, at least, a part of the
high-temperature systems in the axial
zone is best understood on the basis of a
very localized thermal convective flows
in open vertical fractures. In the case of
the Krafla, this circulation is maintained
by magma at a depth of the order of 3
km and there is little doubt that the
water penetrates down to this depth, at
least. It appears very likely that CDM is
in part responsible for the fluid flow
and heat uptake.
A significant result of the microearth-
quake survey of Ward and Bjornsson
(1971) is the concentration of micro-
earthquake foci at depths of 3 to 6 km
below some of the major high-
temperature areas. This is possibly an
indication of hydrothermal activity and
thereby of the penetration of water
down to such depths.
The situation in the many low-to-
medium temperature thermal areas in
the regions west of the axial zone is pro-
bably different. Here, we can, for ex-
ample, consider the Reykholtsdalur
system (see Fig. 1) in the Borgarfjordur
region. This system includes a number
of springs that flow a total of 300 kg/s
and has a base temperature of about
150°C. To account for the supply of the
system, the present writer concludes (see
section (27) above) that the circulating
water flows through a system of
numerous horizontal fracture type
channels covering a total thermal
drainage area of 300 km! and located at
a depth not less than 3 km. The flood
basalt series of Iceland is characterized
by numerous structural features that
permit flow systems of this kind.
ESTIMATES OF THE RATE OF
CONVECTIVE DOWNWARD
MIGRATION OF FRACTURES
In the present context, it is of some
interest to provide estimates of the
possible rate of downward convective
migration of fractures. Here, it must be
underlined that CDM presents some of
the most perplexing problems in
hydrothermal system theory. The
natural setting is notoriously ill-defined.
For example, it is a simple matter to
show that the Rayleigh type problem of
convective stability in narrow vertical
fractures is not well-posed and can
therefore not be discussed along the
same lines as the classical Rayleigh
(1916) method of deriving stability con-
ditions for viscous fluid layers.
Although Murphy (1979) has obtained
important results on fracture fluid
stability this has been achieved by mak-
ing strong assumptions that modify the
problem setting to a substantial degree.
Because of the various difficulties in-
volved, both with regard to the underly-
ing models and the thermomechanical
theory, we will here follow a much
simplified approach to obtain an order
of magnitude estimate of the rate of
CDM of fracture systems in the natural
setting. The method is a modification of
an earlier development along similar
lines (Bodvarsson, 1978). For a number
of the steps taken below, we refer to this
reference.
Consider an upper crustal situation
where there is at some depth a system of
parallel vertical fractures in the process
of CDM. This may take place, for ex-
ample, within major rift or fault zones.
Cold water of surface origin is piped by
natural channels down to the fracture
system where it sinks to the bottom of
the fractures, cools the adjacent forma-
tions and thereby generates the thermal
contraction that is required to migrate
the system downward. The water heated
in the process rises up through the frac-
ture system. On the basis of this model,
we take that there is a steady
temperature differential of AT between
the water at the bottom of the fracture
system and the adjacent formations.
For analytical convenience we con-
sider now a circular fracture of diameter
D in common igneous rock that is clos-
ed because of a contact pressure pc.
Forcing water into this fracture at a
pressure p > pc will open it such that the
width in the center is
w = 1.5xl0'11(p-pc)D, SI (2)
Much the same effect can be achieved
by a thermoelastic contraction of a
volume of the rock around the fracture
such that the resulting tension across the
fracture becomes sufficiently large to
relieve the contact pressure pc. Assum-
ing pressure isotropicity to estimate how
large AT would have to be for this pur-
pose, the following relation
AT > Pc/ok (3)
can be applied where a is the thermal
expansivity and k the bulk modulus of
Ihe rock. Clearly, to obtain the required
effect, the contraction, and thereby the
temperature reduction, has to affect a
certain volume containing the fracture.
Let D be an estimate of the linear
dimension of this volume.
A system of a number of parallel long
fractures in CDM at a rate v can under
rather general circumstances be model-
ed as a cold temperature front moving
downward with the velocity v relative to
the rock. On a one-dimensional heat
conduction theory, the temperature dif-
ferential ahead of the front is given by
T = aTexp(-vx/a) (4)
where x is the distance frorn the front
and a is the thermal diffusivity of the
rock. The expression on the right of (4)
TÍMARIT VFÍ 1984 — 13