Tímarit Verkfræðingafélags Íslands - 01.02.1984, Blaðsíða 22

def'ines the penetration depth d = a/v,
that is, the depth to where the amplitude
of the front has decreased to 1/e of its
full value.
The principal step in the present
development is to identify the penetra-
tion depth d with the linear dimensions
D resulting in the estimate
v v a/D (5)
Thus, we estimate the required
temperature differential AT on the
basis of (4) and the rate of CDM with
help of equation (5).
To proceed with a numerical in-
vestigation we take the possible situa-
tion at the depth of 5 km, for example.
Let a = 2x 10"5/°C and k = 5x 1010 Pa.
The hydrostatic pressure at the depth of
5 km is about 5xl07Pa and the
average minimum horizontal stress will
be of the order of 8 x ÍO7 Pa. The values
will be lower in regions under strain and
we can take that the possible values for
the contact pressure on vertical planes
of discontinuity is then of the order of
ÍO7 Pa. On these premises equation (3)
yields the estimate AT = 10°C. This is a
small value showing that temperature
differentials of a few tens of degrees C
should be sufficient for CDM.
Values for the parameter D are much
more uncertain. Considering, for exam-
ple, the situation in thermally active
fault zones, it would appear reasonable
that the vertical fluid conductivity is
provided by an interconnected system
of fractures of various linear dimen-
sions. Values of the order of a few to a
few tens of meters would appear
reasonable. Inserting a=l0‘6m2/s and
values of d = 3 to 30 m in equation (5)
gives then the estimate of v = l to I0 m.
This result is of the same order as the
results of Lister (1974) for CDM in the
ocean floor that have been obtained on
the basis of a considerably more
elaborate analysis.
Although the above estimates should
be regarded with considerable caution,
the principal result is that as viewed
from the vantage point of geology,
CDM can be a relatively fast process.
Geothermal systems may have active
lives of a few thousand to tens of
thousands of years. CDM over a few
km would probably require only a small
fraction of this time. Considering, on
the other hand, commercial geothermal
energy operations that may span 50 to
100 years only, the possible implications
of the CDM will depend on the local
conditions.
At this end, it is of interest to note
that CDM will probably come to a
standstill when the contact pressure pc
increases beyond certain limits because
of depth and rock compactness.
PRACTICAL CONSIDERATIONS
We have inferred on the basis of
elastomechanics, and also provided
some field evidence, that there may be a
general relation between the state of
stress and fracture fluid conductivity at
depth. The convective penetration of
surface waters down to depths of
several kilometers appears to be possible
only in areas of relatively low horizontal
stress. Obviously, on these premises,
areas of normal to high horizontal stress
would appear to be less attractive as
sources of geothermal fluids. The
general state of stress should thus be
given consideration in geothermal
energy projects involving production
from substantial depths. Two avenues
are available in estimating the stress
situation.
First, global geological features, plate
tectonics, etc. furnish indications as to
the regional state. For example, global
rift zones are generally regions of low
minimum horizontal stress. Zones of
active plates subduction, on the other
hand, generate regions of enhanced
horizontal stress. Second, methods are
now available for direct stress
measurements in boreholes. In par-
ticular, Flaimson (1978) has devoted a
considerable effort to the development
of the hydraulic fracturing technique
and has already provided a number of
interesting and important field data.
Due to thermoelastic processes, the
local stress field is also a factor in
geothermal reservoir evolution during
production, in particular, in cases where
waste fluids are being reinjected for
disposal and pressure maintenance. In
this context, the situation is best il-
lustrated by considering a few total pro-
duction data for a moderately large
geothermal power operation. For exam-
ple, to maintain a production of 200
MW for a period of 20 years at an 80%
load factor from a liquid dominated
reservoir of 250°C base temperature re-
quires the total withdrawal of 1018 J of
heat and 1012 kg of water from the sub-
surface system. The total thermoelastic
contraction associated with the produc-
tion would amount to no less than
I07m\ It is very evident that the general
state of stress has a bearing on the
response of the geothermal system to
the contraction of the rock. In areas of
low minimum horizontal stress, the very
extensive contraction is likely to result
in CDM of existing fractures and also in
the creation of new fractures that can
enhance the water/rock contact area to
a substantial degree and thereby in-
crease the available resources.
It would appear that there is a ra-
tionale for taking up borehole stress
measurements in conjunction with
major geothermal energy projects.
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Acknowledgemcnts
This work was supported by the National Science
Foundation of the U.S.A. under Grant No. EAR
77—23938.
14 — TÍMARIT VFÍ 1984