Tímarit Verkfræðingafélags Íslands - 01.12.1983, Page 8

Resource exploration
by solid earth tidal strain
by Gunnar Bodvarsson, School og Oceanography, Oregon Slale University,
Corvallis, Oregon 97331
ABSTRACT
Solid carth strain generates obser-
vable pressure signals in boreholes that
can be interpreted in terms of formation
parameters. This applies to both frac-
turc dominated and Darcy type flow
situations. The underlying theory is
rather elementary and some details are
presented below. The results are being
applied lo testing of the Raft River
geothermal field in Idaho, U.S.A.
1. RESOURCE EXPLORATION
The techniques of fluid resource ex-
ploration, whether water, petroleum
or geothermal, fall into two main
categories, that is, (1) exploration by
geophysical methods and (2) reservoir
testing. While the geophysical tech-
niques apply a number of physical fields
of different nature to uncover struc-
tural, geometric and such intensive
physical parameters as temperature,
controlled reservoir testing, on the other
hand, consists in producing some fluid
from the reservoir and observing the
response of the system. The test data are
then interpreted in terms of formation
fluid conductivity, capacitivity etc.
Usually, the test load is light as com-
pared to full scale longterm production
and there are severe limitations on the
global and long term relevance of the
test data.
Reservoir exploration or testing on
the basis of solid earth strain is hybrid
with regard to the above classification.
While the strain field applied is of
natural origin and the test load is
ultrasmall as compared with controlled
testing, the target parameters are the
same as in the controlled case, that is,
the fluid conductivity and the capa-
citivity of the reservoir.
The present report has been designed
to evaluate and discuss the applicability
of the tidal test method and to compare
its usefulness with the other methods
available for fluid reservoir exploration.
2. TIDAL STRAIN
Theoretical strain. According to
Takeuchi (1950), the tidal volume dila-
tation at the surface on a spherically
symmetric earth can be taken to be
b = 0.49(W2/Rq) (1)
where W2 is the tidal potential and R the
radius of the earth. Local deviations
from the value given by equation (1) can
be expected at all elastic inhomogeneties
in the crust. In the present context, we
are mainly interested in estimates of the
anomalous dilatation associated with
elastic discontinuities and inhomo-
geneities such as cavities, fractures,
fault zones, in particular, when they are
structural elements of geothermal
systems.
3. CAVITY SYSTEMS
(3.i) Elastance/dilatance. To illustrate
the concepts to be applied in the follow-
ing, we consider a bounded Hookean
elastic body that includes an open inter-
nal cavity of given dimensions. The ex-
ternal dimensions are assumed to be
very large compared to the cavity
dimensions. The body can be deformed
by forces acting on the exterior and/or
the interior surfaces. For the present
purpose it is adequate to consider only
the special case where the surfaces are in
contact with ideal fluids such that the
forces are along the normals and are
uniform over the surfaces. Let V be the
volume of the cavity, p be the pressure
of the cavity fluid and a (stress) be the
Gunnar Böðvarsson lauk f.h. prófi í
vélaverkfrœði frá TH í Miinchen 1936,
verkfræðiprófi í stœrðfræði, kraftfræði
og skipavélfræði frá TH í Berlín 1943.
PhD-próf frá CaUfornia Inst. of
Technology í Bandaríkjunum 1957.
Verkfræðingur hjá vélsmiðjunni Atlas
AS í Khöfn 1943—45, hjá Rafmagnseft-
irliti ríkisins í Rvík 1945—47. Yfirverk-
fræðingur við Jarðboranir rtkisins og
jarðhitadeild Raforkumálaskrifstofunn-
ar 1947-61. Fór á vegum Sþ, til Santa
Lucia í Vestur-Indíum 1951, Mexíkó
1954, Costa Rica 1963, fjölmargar
ferðir til El Salvador, Guatemala og
Nicaragua 1965-76, Chile 1972, íslands
1972 og Kína 1981 til að athuga mögu-
leika á vinnslu jarðvarma. Námsdvöl
við Cal. Inst. of Technology 1955—57.
Meðstofnandi ráðgefandi verkfrœði-
fyrirtækisins Vermis sf. og starfaði við
það 1962-64. Prófessor 1 stærðfræði og
jarðeðlisfrœði við Oregon State Univer-
sity i Bandaríkjunum frá 1964.
negative pressure of the external fluid.
We will then make the following defini-
tions.
Let L be a characteristic dimension of
the cavity. Assuming <7 = 0, the cavity
elastance relative to the length is given
by
El = dL/dp (2)
and the corresponding elasticity
eL = (l/L)dL/dp (3)
Moreover, the cavity dilatance
relative to the same length at p = 0 is
Dl ■ dL/do (4)
and the dilaticity
dL = (l/L)dV/d o (5)
88 — TÍMARIT VFÍ 1983