Tímarit Verkfræðingafélags Íslands - 01.12.1983, Page 15

ticular, when there is a stress-pore fluid
coupling as may be expected in cases of
fairly large porosities. Not much atten-
tion can be given to the subject within
the confines of the present project. A
few remarks are made in section (13)
below.
9. VARIOUS FIELD SITUATIONS
The development above has been bas-
ed on the assumption of ideal condi-
tions such as homogeneous/isotropic
formation etc. Obviously, the real field
situation may deviate considerably from
the simple model. It is of interest to
make a few remarks about such cases,
and present estimates of the resulting ef-
fects that may affect tidal testing.
We consider the model presented in
section (7) above. Assuming a spherical
cavity of radius R and placing the origin
at the center, the solution of the
homogeneous form of equation (59) for
an infinite homogeneous and isotropic
space is
p = (B/r)expt-(l+i)r/dsi (94)
where ds is the skin depth of the forma-
tion and B is an integration constant.
Obviously, for distances r<3Cds, the ex-
ponential factor is close to unity and we
can then resort to the steady state solu-
tion. The steady state pressure field
around a point source of mass flow
strength q is
p = q/4ncr (95)
We will now consider the following
cases on the basis of (94) and (95).
(9.i) Non-sperical cavities. Consider a
cavity that has the largest dimension L
and is embedded in an infinite space.
Based on equation (95) we can easily
show that the first order effects of non-
sphericity are of the order of (L/2r)2.
The pressure field will thus be sperical
within less that one percent at distances
r>5L. At such distances, the non-
spherical cavity can be approximated by
a spherical one with an equivalent
radius
Re = A/4nC (96)
where A is the admittance of the non-
spherical cavity.
As a matter of course, the above
result does not apply to axisymmetric
cases where we have very well known
solutions.
(9.ii) Layered spaces. The next step is
to consider layered spaces where the in-
dividual layers are both homogeneous
and isotropic. Of particular interest is
the infinite two-layer space where the
spherical cavity of radius R is located at
a distance (L/2) from the boundary. We
assume that ds»L. The admittance of
the cavity A is affected by the boun-
dary, and on a first order theory, we ob-
tain with the help of (95) above that
A = Aq[1 + C (R/L) 1 (97)
where A0 is the admittance of the cavity
in a homogeneous/isotropic space and
f is the reflection coefficient* of the
boundary. In the extreme case of a fluid
conductivity jump by an order of
magnitude or more across the boundary
we find that e = 1 and in the reverse
case of a decrease by an order of
magnitude e =-l.
(9.iii) Multi-hole situation. In tidal
testing there is a capacitive interaction
between boreholes that are spaced suffi-
ciently close that their pressure fields in-
teract. The formation skin depth ds is
the proper measure of the dimension of
the sphere of influence.
To estimate the borehole/borehole
interaction, we will consider the simple
model set forth in section (7.i) and re-
main with the assumption that
R/ds»l. In the case of a non-
spherical cavity R = Re as defined by
(96). Moreover, we will only consider a
twohole situation where the hole spac-
ing is D, and carry out a first order per-
turbation estimate. Under these circum-
stances, the borehole interaction
manifests itself in that the driving
pressure around one of the holes is
reduced because of the presence of the
other one. Placing a coordinate system
at the center of one of the cavities, the
surrounding pressure field obtained by
solving (59) is found to be
p = (B/r)exp[-(l+i)r/dsl (98)
where r is the radial coordinate and B is
an integration constant, that is given by
(77) such that
B = - (öb/ s) RT / (1+T) (99)
Abbreviating the exponential factor in
(98) by E(r), the driving pressure field at
the center of each of the holes is reduced
by
* q = (ag - a^)/(»2 + al1
4p = -(ðfa/s)RE(D)T/D(l+T) (100)
and hence equation (77) has to be
replaced by
h = -(ðb/pgs) (l-a)T/(l+T) (101)
where
a = (R/D)E(D)T/ (1+T) (102)
This procedure is easily extended to
multi-hole situations. Obviously, the in-
teraction effect is dominated by the
ratios (R/D) and (D/ds) and is small
when (R/D) « 1 and /or (D/Ds)»l.
10. GEOTHERMAL SYSTEMS
(10.i) Basic data. It is important to con-
sider the implications of the geological/
physical structure of geothermal
systems for the applicability and
usefulness of tidal testing in the explora-
tion of such systems. It is well known
that geothermal systems are of many
types and display a considerable
amount of individuality. Moreover, it
should be emphasized that the struc-
tural/physical details of no major
geothermal system have been uncovered
to such an extent that we can claim to
have a detailed model at hand. As a
matter of fact, most of the major
systems, even those that have been in
production for decades, are only poorly
known.
In spite of this situation, we are,
nevertheless, able to work out a useful
classification of a number of system
types and establish some of their major
characteristics. A thorough discussion
of the various types of systems would
not be within the confines of the present
report, and we will therefore resort to
considering mainly a specific type of
system that appears to be associated
witli the geological environment in the
Great Basin of North America. As a
matter of fact, this is probably the most
common type liquid dominated geother-
mal system, in the USA. We will refer to
them as the BR (Basin and Range) type.
For a discussion of some aspects of the
flow/thermophysics of these systems,
we refer mainly to a report by the pre-
sent writer (Bodvarsson, 1978).
Considering the structure of the
Great Basin and the location of most of
the BR systems, it is quite obvious that
most, if not all, of the systems are con-
trolled by the master faults of the horst/
graben structure in the region. In fact,
TÍMARIT VFÍ 1983 — 95