Fracture apertures from electrical borehole scans
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Transcript of Fracture apertures from electrical borehole scans
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GEOPHYSICS, VOL. 55, NO JULY 1990 ;P. 821-833, 15FIGS.
Fracture apertures from electrical borehole scans
S
M
Luthi and P ouh itet
ABSTRACT
Three-dimensional finite-element modelingwas per
formed to investigate the response to fractures of the
Formation MicroScanner Mark of Schlumberger ,
which records high-resolution electrical scans of the
borehole wall. is found that the equation
W
c A R ~ R o b
describes, over two orders of magnitude of resistivity
contrasts between borehole mud and the formation,
the relationship between fracture width W in mm ,
formation resistivity R
xo
mud resistivity R
m
and the
additional current flow caused by the presence ofthe
fracture. is the additional current which can be
injected into the formation divided by the voltage,
integrated along a line perpendicular across the frac
ture trace. Coefficient c and exponent b are obtained
numerically from forward modeling. Tool standoffs of
up to 2.5 mm and fracture dips in the range from 0 to
40 were found to have an insignificant effect on the
above relation.
INTRODUCTION
Fluid flow rates through fractures with smooth surfaces
are proportional to the cube of the aperture, but decrease
with increasing roughness such as found on natural fracture
surfaces Brown,
1987;
Jones et al., 1988 . The estimation of
fracture apertures in wellbores penetrating fractured reser
voirs is, therefore, of paramount importance for assessing
reservoir productivity. Reflections of the Stoneley wave
measured by an array sonic tool Hornby et al., 1989 have
recently been proposed as an in-situ measurement of frac
ture aperture. The technique presented in this paper ad
dresses the same problem, albeit with an entirely different
downhole geophysical measurement principle.
The Formation MicroScanner is a wireline device produc-
A three-step approach to detect, trace,and quantify
fractures is used. Potential fractures in Formation
MicroScanner images are detected as locations where
conductivity exceeds the local matrix conductivity by
a statistically significant amount. Integration over a
circular area is performed around these locations to
gather all excessive currents; this integral is then
geometrically reduced to approximate the line integral
Line sharpening and neighborhood connectivity
tests are done to trace the fractures, and apertures are
computed for all fracture locations.
Results from a well into basement in Moodus Con
necticut show that the method successfully traces
fractures seen on Formation MicroScanner images.
The resulting fracture apertures range from 10urn to 1
mm. For the wider fractures there is acceptable agree
ment with apertures obtained from Stoneley wave
reflection measurements. This unique and novel tech
nique for characterizing fractures in wellbores has a
very low detection threshold of around 10 urn and
resolves fractures as little as I em apart. Furthermore,
it provides azimuthal orientation of the fractures.
ing electrical scans of the borehole wall Ekstrom et al.,
1987 .
The scans are achieved by arrays of small electrodes
mounted on pads held at a known potential with respect to a
return electrode in the upper part of the tool Figure
1 .
Currents emitted from these electrodes are recorded at a
high sampling rate typically 0.1 inches, or 2.5 mm , and are
used to produce conductance images of the part of the
borehole wall covered by the pads while traveling upward.
These images can be oriented with respect to geographic
north through continuous downhole measurement of the
sonde orientation by a triaxial fluxgatemagnetometer. Thus,
dip and azimuth of fractures and bedding planes can be
measured if the electrical images are displayed in an azi
muth-depth plot Plumb and Luthi,
1986;
Pezard and Luthi,
1988;
Luthi, 1990 .
Manuscript received by the Editor August 22, 1989;revised manuscript received December 8, 1989.
*Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT
06877 4108.
*Etudes et Productions Schlumberger, rue de la Cavee, Clamart, France.
e 1990Society of Exploration Geophysicists. All rights reserved.
82
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822 Luthi and souhalte
Open fractures are among the most prominent features
seen on electrical images because of the large conductivity
contrasts between the fluid in the fracture-typically as
sumed to be the drillingmud nd the surrounding rock. In
many boreholes drilled with water-based mud this contrast
may be several orders of magnitude. Examples of open
fractures on electrical images are documented by Plumb and
Luthi
1986 ,
Ekstrom et al. 1987), and Pezard and Luthi
1988 .
They show up as conductive streaks exhibiting a
large variety of morphologies ranging from short, irregular
shapes to planar. Fractures typically affect several adjacent
samples because the electrode diameter is approximately
twice the sampling distance, accounting for some vertical
and horizontal overlap, and also because the electrical flow
lines are severely distorted in the vicinity of the fracture. It
is, therefore, of interest to find a relationship between the
Button
Trajectory
I
I
I
I
I
I
I
I
I
Fracture
MODELING OF ELECTRICAL FRACTURE RESPONSE
Technique
electrical signal produced by the fracture and fracture pa
rameters such as aperture, dip angle, resistivity of the fluidin
the fracture, resistivity of the rock, and the distance from the
tool to the borehole wall tool standotl). We address this
problem through forward modeling of the electrical field
using a three-dimensional 3-D) finite-element modeling
code. To invert electrical borehole scans for fracture param
eters, we then present a statistical method to identify and
trace fractures on Formation MicroScanner images and a
technique to compute fracture apertures for each sample
located on the fracture trace.
The finite-element method has been used successfully by
Chang and Anderson
1984
to model electromagnetic bore
hole devices such as the induction tool. In our approach,
which is closely related to the technique of Chang and
Anderson
1984 ,
the current emitted by a single Formation
MicroScanner button in front of a fracture Figure 2) is
simulated using the finite-element method which solves
Laplace s differential equation for the electrical field over an
adaptive three-dimensional grid in and around the borehole.
Grid node spacing is very close in the vicinity of the
electrode button, covering at least 20 nodes in the sensitive
area along a line across the fracture and increases progres
sively away from this area with a minimum of 10more nodes
in each direction. The total number of grid points is about
70000; the progressive variation in element size away from
the sensitive area avoids discontinuities which may be
detrimental to the computational accuracy. The fracture is
modeled as a thin-sheet element with a uniform resistivity
equal to the mud resistivity. Current densities are computed
on the nodes covering the tool pad, and button currents are
obtained by multiplying current densities with their corre
sponding area. All computations assume planar, parallel
fractures of infinite extent. The dip of the fracture, i.e., the
4
R
SONDE
TELEMETRY
HYDRAULICS
INCLINOMETER
INSULATING SUB
PREAMPlIFICATION
CARTRIDGE
AMPLIFICATION
CARTRIDGE
INSULATING
SLEEVE
FLEX JOINT
FIG. 1. Sketch of the Formation MicroScanner tool config
uration discussed in this paper after Ekstrom et aI., 1987 .
Two of the four pads are equipped with the array of imaging
electrodes shown on the left. A newer tool design has fewer
electrodes on all four arms.
Borehole
FIG. 2. The modeled situation of an electrode button crossing
a fracture on the borehole wall.
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Fracture Apertures from Electrical Scans
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