Jökull - 01.12.1976, Page 22

Hydroelastic Cavity Resonators
GUNNAR BÖÐVARSSON,
SCHOOL OF OCEANOGRAPHY
OREGON STATE UNIVERSITY
CORVALLIS, OREGON 97331, U.S.A.
AXEL BJÖRNSSON,
NATIONAL ENERGY AUTHORITY,
REYKJAVÍK, ICELAND
ABSTRACT
Fluids contained in interconnected systems of
subsurface cavities are capable of oscillations
which we refer to as hydroelastic oscillations.
The simplest type of such systems is represented
by the borehole-cavity oscillator which is analog
to the well known Helmholtz resonator in
acoustics. The restoring force is provided by
the elasticity of the cavity and the oscillating
mass by the fluid column in the borehole.
Temperature observations on a flowing thermal
borehole in the City of Reykjavik appear to
indicate oscillations of this type. A simplified
theory of hydroelastic borehole-cavity oscilla-
tions is given.
INTRODUCTION
Ground water bodies embedded in fractured
rock consist of a system of interconnected fluid-
filled openings with elastic walls. When pro-
perly excited, such systems are capable of oscil-
lations which we will refer to as hydroelastic
oscillations. The fractures act as elastic cavities,
which can expand and contract upon changes
in the fluid pressure, and the oscillating mass
is provided by the fluid. Such systems can be
open or closed depending on whether they are
connected with a free water surface or not. A
particularly simple open system of this type is
represented by a fluid filled cavity at depth
which is connected with a vertical borehole
with a free water level. When the dimensions
of the cavity are substantially greater than the
diameter of the borehole, this system is ana-
20 JÖKULL 26. ÁR
logous to the Helmholtz cavity resonator in
acoustics (see Elmore and Heald, 1969). The
oscillating mass is provided by the water col-
umn in the borehole and the restoring force
results from the elasticity of the cavity.
Simple estimates indicate that open borehole-
cavity oscillators may have resonant frequencies
with periods ranging from a few seconds up to
a few hours, depending on the dimensions of
the elastic cavity and of the water column.
These results indicate that oscillations are not
likely to be excited in large static systems un-
less there is resonance with some component
of the earth tides. Resonances in smaller systems
with a throughflow of fluid may, on the other
hand, be excited by turbulent and other flow
induced pressure fluctuations. Since the reson-
ant frequencies depend heavily on the dimens-
ions of the systems, it may in many cases be of
practical interest to monitor hydroelastic oscil-
lations. The observed frequencies furnish in-
formation on the dimensions of the system
under investigation which may not be obtained
in other ways. Unfortunately, the observation
of oscillations in flowing systems is somewhat
more cumbersome than in open static systems
where a simple recording of water levels may
suffice.
There are principally two ways of recording
oscillations in flowing systems. First, it is pos-
sible to install sensitive pressure transducers
in flowing boreholes or other available open-
ings. Highly sensitive instruments are now
available for this purpose. Second, since pres-
sure oscillations generally induce flow oscilla-
tions, the monitoring of the flow of boreholes