Fróðskaparrit - 01.07.2004, Blaðsíða 137

NÝTT INNAN VÍSINDI 2004
135
based on general fracturing theory. This
also includes measurements of induced
borehole fractures on the borehole wall.
The general cubic equation is investigat-
ed both as a full solution, and, for several
ways of linearization. The solution takes
the form of a not valid elliptical solution,
and hyperbolic and parabolic solutions that
are investigated further. Coherent solu-
tions are obtained between the magnitude
and the directions of the in-situ stresses,
and the trace of the induced fracture on the
borehole wall. A dimensionless stress
function and a dimensionless variable are
also introduced to develop the general so-
lution.
The work is based on the linear inversion
technique developed by Aadnøy in 1990.
The present work has developed analytical
theories in two directions. One is a further
development of the linear inversion tech-
nique by approximating the general equa-
tion of fracture to a system of asymptotes.
By applying a dimensionless stress func-
tion, the other developed direction of the
linear technique is to choose the effective
in-situ stress ratio as a regional constant,
resulting in the so-called k-theory.
Using the k-theory with the effective
stress ratio, the circumferential borehole
angle is eliminated from the general frac-
turing equation, providing a simpler model
of the fracturing pressure, the fracture an-
gle and the fracture trace angle for the dif-
ferent stress fault regimes. Of particular in-
terest is the observation that for given bore-
hole inclination and azimuth, the relative
magnitude of the in-situ stresses and their
orientation is independent of borehole frac-
Boriveskan verður eisini nýtt til at smyr-
ja boriholið, og til flyta knúst grót upp úr
boriholinum.
Úrslitið verkætlanini kann geva jarð-
frøðingum eitt gott støddfrøðisligt amboð,
at nýta til ætlan av veskutyndgini í kom-
andi oljuboringum.
turing pressure, that is, dependent on
geometry alone.
It is established that there are many pos-
sible values of the in-situ stresses that are
solutions to the same problem (over deter-
mined system of equations). This makes
comparison between the various models
difficult. However, it is shown that the sim-
ple linear model usually is nearly as accu-
rate as the approach using asymptotes.
However, the k-theory is more robust for
numerical simulations.
Finally, data from the Snorre field in the
North See has been used to compare the
various stress methods, and to assess the
accuracy.