Geoscience Reference
In-Depth Information
signature shown in Figure 5.17 indicates numerous
impulsive events that grow as seal failure progresses.
The hypothesis for the explanation of this data considers
that the epoxy seal failed in a plastic manner beginning
with the onset of failure followed by subsequent repeated
blockage and breakthrough events having a valve-like
behavior until the end of the data acquisition. The seal
failure occurs in the partially epoxy-filled annulus of
the borehole between the steel tube and the cement; as
more fluid contacts the cement walls of the borehole with
higher and higher velocities, the magnitude of the elec-
trical response grows accordingly. The approximate posi-
tion of the fluid contact with the borehole wall can be
determined from the data and will be demonstrated for
Events E2 and E3. The position of the positive anomaly
recorded by the top array is not centered on Hole 9,
but is displaced, from the center of the hole, possibly
because of the position of the electrodes, the electrical
boundary conditions around the borehole, and the spa-
tial interpolation process.
The data from the side face electrical potential array
also contains source location and orientation informa-
tion, indicating that the fluid flow encountered porous
media somewhere well above the bottom of the bore-
hole, also an indication of possible borehole seal failure.
The observations imply that the fluid flow occurred along
a pathway following the borehole and close to the lower
right corner of the top array. The electrical boundary con-
dition in Hole 9 is insulating between the borehole wall
and the stainless steel tubing, causing the reflection of
the electrical potential away from the borehole center.
Generally, these electrical potential measurements are
consistent with the subsequent observations of fluid
leakage at the test block surface near Hole 9 due to com-
plete borehole seal failure. These electrical observations
occurred several minutes before surface fluid leakage
was visually observed on the top surface.
dimension (but still relatively small with respect to the
system geometry), we consider that the centroid of the
electrical current density can still be suitably approxi-
mated by a single electrical dipole. Overall, this argument
establishes the expectation that a relatively compact fluid
leak can be represented by a compact electrical source
current density. Therefore, we can use ideal electrical
dipoles in the numerical inversion process to model the
electrical sources that are postulated to have generated
the signals that were measured during the seal failure.
Thusly, our goal in this section is to apply a dipole-
based inversion process to localize the centroid of the
source of the electrical disturbances in the block for
two of the events discussed earlier. We start by specifying
the physical problem for the occurrence of the quasistatic
electrical potential distribution. Then we introduce and
apply a two-step inversion process as follows: (i) we
apply a gradient-based inversion with reduction of the
volume of support for the source (compactness), fol-
lowed by (ii) a genetic algorithm (GA) localization to
refine the position of the source. We apply a two-step
inversion process that is designed to reduce the compu-
tational resource requirements and computational time
primarily for the kernel matrix computations and
ultimately develop an approach that can be used in a
real-time computational environment.
In the first step, we use a coarse cubical dipole matrix
grid that encompasses the majority of the sample vol-
ume, in an unbiased localization technique that uses a
deterministic algorithm with compactness to locate the
rough area of each of the event dipole sources. The coarse
nature of the dipole grid greatly reduces the time it takes
to compute the kernel matrix relative to a fine grid that
would be needed to locate the source in an equivalently
unbiased and detailed way. This approach is designed to
allow the inversion computations to find the approxi-
mate location for the source within the definition of
the dipole grid points.
In the second step, we use the results of the first step to
bias the localization process by generating a cylindrical
dipole grid point that more than encompasses the dipole
sources located in step one. This dipole matrix has a much
finer spatial resolution, but with about half the points used
in step one. This reduction in points also reduces the size of
the kernel matrix and thereby reduces the computational
resources for that element of the inversion computation.
We use a GA to search through each of the dipole
grid points using a single dipole-based forward model
5.3.5 Source localization algorithms
In this particular situation, an observed electrical signal is
potentially caused by a point fluid leak source. Here, we
consider that the electrical source current density
generated by this type of leak will have a point character-
istic. This point-like current density characteristic can be
simply modeled with a single, ideal electrical dipole.
However, even if the fluid leak has a finite flow dimen-
sion with respect to the measurement system geometry,
generating an electrical current density with a finite
