Jökull - 01.12.1982, Page 25

mostly volcanic tufFs. According to seismic results of
Palmason (1971), the total integrated thicknessofthe
flood basalt formation varies from 3 to 9 kilometers.
The basalt plateau is heavily eroded, faulted, in-
truded by a number of central volcano structures
and transsected by an enormous number of basaltic
dikes. Dense swarms ofdikes radiatingout from the
volcano cores are a frequent occurrence.
Although the hydrological properties of the plat-
eau are not well known, a few main features appear
quite clear. There is concentrated horizontal per-
meability or íluid conductivity along many contacts
of lava beds and/or tuffs. The bulk of the individual
lava beds is, on the other hand, apparently ofa very
low conductivity. Concentrated vertical fluid con-
ductivity is mainly up along the walls of dikes or
possibly through dikes of a sufficiently open colum-
nar structure. The role of faults is much less clear.
I he open interbed contacts and the open dikes thus
appear to be the major fluid conductors of the flood
basalt series.
Superimposed on the system of major conductors
there may be a more dispersed fluid conductivity
through smaller fractures and openings. Little is
known about this type of conductivity, and it
appears to be of less importance for the develop-
ment ofgeothermal systems.
To attempt at quantifying rock/water heat trans-
fer in the above scenario, it is useful to introduce
typical idealized fluid conducting elements that can
provide simple models of the heat transfer processes
m the real situations. In this respect pipe-like and
sheet-like elements are of particular interest. The
pipe elements carry concentrated currents ofwater
with a small cross section over long distances. Many
such elements can form pipe-grids. The sheets are
fracture type elements having a large rock/water
contact area but a very small aperture. Clearly,
there can be systems of interconnected sheets form-
tng one- or two-dimensional networks. Moreover,
the orientation of sheets is important. Open forma-
tion contacts generate horizontal flow-sheets while
openings along the walls of dikes represent vertical
flow sheets. Of particular interest is that the latter
type of sheets can harbor convective íluid move-
ments that transfer heat vertically up. The cooling
of the formations at the lower end leads to thermo-
elastic contraction that increases the local aperture
and opens up new fracture space. The open vertical
flow sheet can thus migrate downward by such a
process that we shall refer to as convective down-
ward migration (CDM). The process has been dis-
cussed elsewhere by the present writer (Bodvarsson
1979, 1982a) and involves concepts that have been
advanced earlier by Bodvarsson (1951), Palmason
(1976), White (1968), Bodvarsson and Lowell (1972)
and Lister (1972, 1974, 1976). The heat transfer in
the above type of elements will now be discussed in
little more detail.
Thesinglepipe. The pipe-like conductors represent
the simplest case. Although a variety of irregular
cross section can be envisioned, rather elementary
potential theoretical arguments indicate that on a
sufficiently long time scale, apipe afany meaningful
cross section can be approximated by a pipe of a
circular cross section with a properly chosen equi-
valent diameter d. Since a discussion of the argu-
ments involved would not be too useful here, we will
refrain from entering into details.
Consider now a horizontal pipe of diameter d that
is buried at a depth D below the surface ofa homo-
genous/isotropic half-spaceofthermal conductivity
k and dilfusivity a. Let the temperature of the half-
space away from the pipe be T and the pipe surface
have a temperature zero. An elementary potential
theoretical argument shows that in a steady state
situation, the rate of heat uptake by conduction
per unit length of the pipe is (Bodvarsson 1949)
H = 277kT/ln(4D/d) (1)
Carslaw and Jaeger (1959) furnish the appropriate
relations for a transient situation. Let the pipe be
emplaced at time t = 0. For times t in the interval
250 d2/a <t < D2/4a, the rate of heat uptake is
approximately
H = 4xrkT/ln(1.2N) (2)
whereN = 4at/d2 is theFouriernumberofthepipe.
Grid ojpipes. The transient heat uptake by a grid
of parallel pipesofspacing s that were embedded at
time t = 0 in a homogeneous conducting space of
initial temperatureThas been discussed by Bodvars-
ronand Reislad (1982). In thesamesettingand using
the same notation as above, the rate of heat uptake
per unit length of each pipe is given by
H = T/R ' (3)
where R is the conduction resistance which for t >
250 d2/a is
R = ((7rat)l/2/2ks) + (ln(1.2N)/47Tk). (4)
The horizontal sheet in steady state. Let the sheet be
buried at a depth D, and, íör convenience, be rec-
tangular of dimensions B X L where B>>D,
L>>D and have an aperture that is negligible as
compared to D. There is a uniform/unidirectional
flow of water along L and of magnitude m per unit
JÖKULL 32. ÁR 23