Method for determining earth stresses in formations surrounding a cased well

An acoustic logging tool traverses a fluid-filled cased well with a monopole acoustic energy source. Pressure waves in the well fluid by the source generate symmetric tube waves in the well casing immediately adjacent the source. At least one spaced-apart receiver detects these tube waves after they have traveled directly to the receiver through the well casing. Asymmetry imparted to said tube waves as they travel along the well casing by the maximum and minimum earth stresses behind the well casing are identified and used to predict the azimuthal direction of subsequent hydraulic fractures.

BACKGROUND OF THE INVENTION 
The present invention relates in general to a method for acoustic well 
logging and, more particularly, to a method for detecting the horizontal 
azimuthal direction of the maximum and minimum earth stresses in 
subsurface formations behind well casing. 
It has long been known to acoustically log open wellbores to determine the 
velocities of compression ("P") waves and shear ("S") waves traveling 
through rock formations located in the wellbore region and tube waves 
("T") traveling along the wellbore interface. Logging devices have been 
used for this purpose which normally comprise a sound source (transmitter) 
and one or more receivers disposed at pre-selected distances from the 
sound source. 
By timing the travel of compression waves, shear waves, and/or tube waves 
between the source and each receiver, it is normally possible to determine 
the nature of surrounding rock formations including natural fracture 
identification. For descriptions of various logging techniques for 
collecting and analyzing compression wave, shear wave, tube wave, and 
secondary wave data, please refer to U.S. Pat. Nos. 3,333,238 (Caldwell); 
U.S. Pat. No. 3,362,011 (Zemanek, Jr.); Reissue No. 24,446 (Summers); 
4,383,308 (Caldwell); 4,715,019 (Medlin et al); and U.S. patent 
application Ser. No. 192,446 (Medlin); and to "The Correlation of Tube 
Wave Events With Open Fractures in Fluid-Filled Boreholes" by Huang and 
Hunter in Geological Survey of Canada, pgs. 336-376, 1981. 
In each of the foregoing references, the acoustic waves are generated in 
the formation in response to an acoustic energy transmission from within 
an open wellbore. However, the teachings of such references are not 
applicable to the identification of earth stress orientation in formations 
which are traversed by well casing, that is, well pipe cement bonded to 
the formation. An acoustic source within the cased well generates tube 
waves which travel along the well casing. These cased well tube waves are 
the predominant mode of wellbore excitation at low frequencies of below 
about 2 kHz. Their amplitudes are orders of magnitude greater than those 
of compressional or shear waves generated in the casing or formation. In 
cemented intervals the cased well tube waves can be sensitive to changing 
conditions behind the casing. 
It is therefore a specific objective of the present invention to provide 
for a method of logging a cased well to detect earth stress orientation in 
the formations surrounding the cased well. 
SUMMARY OF THE INVENTION 
In accordance with the present invention there is provided a method of 
acoustic well logging for detecting earth stress orientation behind well 
casing and more specifically identifying the azimuthal directions of the 
maximum and minimum earth stresses. More particularly, a fluid-filled 
cased well is traversed with a well logging tool comprised of a monopole 
acoustic energy source, a directional gyroscope and a long spaced receiver 
body containing a plurality of directional receivers. The azimuthal 
orientation of the receiver string is given at all times by the gyroscope 
system. The entire configuration is centralized in the wellbore by bow 
springs located well above the source and well below the receiver body. 
The bow springs, gyroscope system, source and receiver body are all 
connected together by rigid steel couplers. Excitation of the monopole 
source produces fluid waves in the fill-fluid within the cased well. These 
fluid waves give rise to tube waves in the cased wellbore. As the tube 
waves propagate along the cased wellbore toward the receiver body they 
interact with the horizontal earth stresses. These stresses are 
characterized by a maximum along some direction and a minimum in the 
orthogonal direction. The interaction between these earth stresses and the 
tube waves produces characteristic patterns in the azimuthal variations of 
tube wave displacement amplitudes. These patterns can be measured by 
rotating the entire receiver string in small angular increments through a 
complete circle. At each angular step the acoustic source is excited and 
the maximum amplitude of the resulting tube waves recorded at each 
receiver. At an appropriate receiver distance, the critical spacing, the 
tube wave amplitude pattern measured consists of a pair of maxima and a 
pair of minima, each separated by 180 degrees. The identified azimuth of 
the pair of maxima represents the direction of minimum earth stress. The 
identified azimuth of the pair of minima represents the orthogonal 
direction of maximum earth stress. 
In a more specific aspect, a monopole acoustic energy source, such as a 
Helmholtz resonator, is excited by a tone burst to generate tube wave 
displacements of sufficient amplitude to make the stress-induced asymmetry 
effects large enough to be measured. A receiver string consists of a long 
array of dipole receivers spaced sufficiently close together to provide at 
least one receiver near the critical spacing. Each receiver is made with a 
fundamental resonance matching the fundamental resonance of the source. 
The stress data determined can be used to predict the direction of a 
hydraulically induced fracture because such a fracture always propagates 
in the direction of maximum horizontal earth stress. The method also has 
application to earthquake prediction through repetitive stress 
measurements in cased observation wells over long periods.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIG. 1, there is illustrated an acoustic logging system 
that is used in accordance with the present invention for measuring the 
azimuth of principal earth stresses behind well casing. The logging system 
includes an elongated logging tool 10 which is suspended from a cable 11 
within a cased well 12 which traverses a subsurface formation of interest 
13. The cased well 12 is filled with a liquid such as completion fluid 16. 
The logging tool comprises an acoustic source or transmitter 17, a 
directional gyroscope system 19 and a receiver body 30 containing a 
plurality of directional acoustic receivers 31-38 (i.e. R1-R8) for 
example. The transmitter and directional gyroscope are contained within 
the same rigid steel body. The receiver body is a hollow cylinder 
enclosure filled with silicone oil or other similar liquid. The receiver 
body is connected to the transmitter-gyroscope body by a long, rigid steel 
coupler 18. The entire tool assembly is centralized in the cased wellbore 
by a pair of bow springs 14 and 15. The upper bowspring 14 is attached to 
the steel body containing the transmitter and gyroscope with a long 
spacing between it and the transmitter and the lower bowspring 15 is 
connected to the receiver body by a long rigid, steel coupler 20 with a 
long spacing between it and the lower receiver 38, such spacings being 
effective to minimize acoustic wave diffractions and reflections in the 
fill-fluid which introduce anomalies into the cased well tube waves. The 
steel blades of the bowsprings are acoustically isolated from the wellbore 
casing by rubber pads. The receiver string R1-R8 can be rotated within the 
receiver body. It is rotated upon command in small angular steps of about 
10 degrees each by a stepping motor (not shown) contained in the receiver 
body. The receiver body 30 is made of a material such as aluminum or 
fiberglass which is relatively transparent to the transmission of acoustic 
energy. Its wall thickness is very uniform so as to provide equal 
transparency to acoustic energy in all directions. Signals from the 
logging tool 10 are transmitted uphole by conductors within cable 11 to 
any suitable utilization system at the surface. For example, the 
utilization system is illustrated as comprising an uphole analysis and 
control circuit 22 and recorder 24 in order that the output from circuit 
22 may be correlated with depth. 
Having set forth the well logging system of FIG. 1 for generating and 
receiving acoustic energy within a cased well, the method of the present 
invention for use of such a system to measure the horizontal earth stress 
as a function of azimuth and to thereby determine the azimuthal directions 
of maximum and minimum earth stresses will now be described. 
Transmitter 17 is a monopole acoustic energy source which emits acoustic 
energy equally in all directions in a plane perpendicular to the wellbore 
axis. The acoustic receivers 31-38 are directional devices which have a 
peak sensitivity in only one direction. All of the directional receivers 
in the receiver string are aligned with respect to their direction of peak 
sensitivity. The orientation of this peak sensitivity, with respect to 
magnetic north, is given by the gyroscope system 19 which is rigidly 
attached to the receiver string through the steel coupler 18. The 
transmitter and all of the receivers are matched so as to have fundamental 
resonances at the same frequency, preferably in the range 1-5 kHz. 
The transmitter is excited by a sine wave tone burst of 3-5 cycles at the 
frequency corresponding to the fundamental resonance of the transmitter 
and receivers. The source excitation generates fluid waves in the 
fill-fluid within the cased well. These fluid waves give rise to tube 
waves in the cased wellbore. As the tube waves propagate along the cased 
wellbore they interact with the horizontal earth stresses. They are then 
detected by each of the directional receivers in the receiver body. The 
response of each receiver typically consists of a simple wavelet of 10-15 
cycles duration. The maximum amplitude of the envelope of this wavelet can 
be used as a measure of the tube wave amplitude. Alternatively, the total 
area under all of the cycles making up the wavelet can be taken as another 
measure of tube wave amplitude. As yet another alternative, the Fourier 
transform of the entire wavelet can be generated and the area under the 
peak corresponding to the transmitter resonance can be taken as a measure 
of the tube wave amplitude. 
Interactions between the horizontal earth stresses and the tube waves 
propagating along the wellbore have an effect on the amplitude of tube 
wave vibration. The earth stresses are characterized by a pair of 
orthogonal principal stress directions. Along one of these directions the 
earth stress is a maximum and along the other orthogonal direction it is a 
minimum. This stress asymmetry produces a corresponding asymmetry in the 
amplitude of tube wave displacements measured as a function of azimuth in 
a horizontal plane. This asymmetry can be detected by using a directional 
receiver to measure tube wave amplitudes as the receiver is rotated 
through 360 degrees while centralized in the wellbore at fixed depth. 
The difference between the maximum and minimum earth stresses is typically 
very small, of the order of 100-200 pounds per square inch. When the 
stress difference is small the tube wave asymmetry effects are also small 
and therefore difficult to detect. The methods set forth in this invention 
provide ways to enhance the detection of these effects. Interactions 
between the tube waves and other modes of wellbore vibration produce 
additional effects which are mixed with the stress asymmetry effect. This 
mixing produces different asymmetry patterns when the receiver is rotated 
at different spacings from the transmitter. At the appropriate spacing, 
(i.e., the critical spacing) the asymmetry pattern consists of a pair of 
amplitude maxima separated by exactly 180 degrees and a pair of amplitude 
minima also separated by exactly 180 degrees. This pattern is used to 
determine the directions of maximum and minimum horizontal earth stress. 
To make a logging measurement the tool is lowered to a selected depth. The 
orientation of the directional receiver string is sensed by the gyroscope 
system. The monopole source is excited by a tone burst and the response of 
each receiver recorded. For enhancement of data quality the source can be 
excited repetitively and the receiver signals stacked. The stepping motor 
then rotates the receiver string by a small angular increment, such as 10 
degrees, and the procedure is repeated. This procedure is continued until 
the receiver string has been rotated through at least 360 degrees. The 
logging tool is then moved to a new depth and the entire procedure 
repeated. 
Logging data obtained by this procedure are illustrated in FIG. 2 which 
shows sequences of amplitude plots obtained by a plurality of four spaced 
apart receivers such as R1-R4, designated by 31-34 in FIG. 1. In this case 
the receivers are spaced apart from the transmitter by distances of 183, 
210, 237 and 264 inches, respectively. The plot for each receiver was 
obtained by rotating the complete receiver string in small angular 
increments through more than 360 degrees at a fixed depth of 2200 ft. Tube 
waves were generated in the cased wellbore by exciting a Helmholtz 
resonator source with a 3-cycle tone burst at a frequency of 3.0 kHz. The 
amplitudes plotted in FIG. 2 represent the maximum amplitudes of the 
envelopes of the received wavelets. In the FIG. 2 plots receiver R3 is at 
the critical spacing. The R3 plot shows the characteristic pattern of a 
pair of maxima separated by 180 degrees and a pair of minima also 
separated by 180 degrees. The pair of minima at 55 and 235 degrees 
correspond to the vertical plane of maximum horizontal earth stress where 
magnetic north corresponds to 0 or 360 degrees. In this plane the 
horizontal earth stresses provide the greatest resistance to wellbore 
displacements associated with tube wave vibration. The pair of maxima at 
145 and 325 degrees correspond to the vertical plane of minimum horizontal 
earth stress. In this plane the horizontal earth stresses provide the 
least resistance to wellbore displacements associated with tube wave 
vibrations. The R2 plot in FIG. 2 is slightly skewed with separations 
between maxima and minima different from 180 degrees. The R1 plot is 
skewed to an even greater degree. At receiver spacings closer to the 
transmitter than R1 the pattern becomes progressively more skewed, 
degenerating finally into a single cycle with only one maximum and one 
minimum. The R4 plot in FIG. 2 is skewed in a reverse sense. At spacings 
beyond R4 the skewedness becomes progressively exaggerated, degenerating 
finally into a single cycle. The maximum and minimum in this case are 
reversed from those of the single cycle produced at spacings close to the 
transmitter. The interval between 180 degrees and 225 degrees in FIG. 2 
represents an overlap in which the receiver string has started on a second 
revolution around the wellbore. The small discrepancies between the two 
sets of points for the various receivers are due to small differences in 
centering of the tool in the wellbore. 
The critical spacing varies with wellbore conditions. It is also sensitive 
to the lithology of the formation rock behind the casing. It can be 
determined for any set of wellbore conditions by using a long string of 
closely spaced receivers, such as R1-R8 in FIG. 1. This provides a way to 
recognize the sequence of skewed patterns and also insures that one of the 
receivers will be at or very close to the critical spacing as in FIG. 2. 
The stress data illustrated in FIG. 2 provide a way to predict the 
azimuthal direction of a hydraulically induced vertical fracture. Such a 
fracture will always propagate in the direction of maximum horizontal 
earth stress. Thus, in the case corresponding to FIG. 2, the azimuthal 
direction of fracture propagation is predicted to be 55 degrees where 
magnetic north is 0 or 360 degrees. In the aforementioned U.S. patent 
application there is described another method for identifying the 
azimuthal direction of a hydraulically induced vertical fracture. In this 
method acoustic logging measurements similar to the ones described here 
are made after the fracture has been created. In this method the azimuth 
of the fracture cannot be determined until after the fracture is in place. 
This requires that logging measurements be made in the fractured interval 
after the hydraulic fracturing treatment is completed. This procedure 
introduces a number of difficulties. After a hydraulic fracturing 
treatment formation gas may flow into the wellbore, making it impossible 
to obtain acoustic logs because of the excessive compressibility of the 
gas bubbles. To avoid this problem it is necessary to circulate the 
gas-laden fluid out of the wellbore and replace it with a higher density 
fluid which prevents further gas flow into the wellbore. The density of 
this fluid must be high enough to produce a downhole pressure in excess of 
the formation gas pressure. Under these conditions the wellbore fluid 
flows into the fracture producing detrimental effects in the stimulation 
characteristics of the fracture. The present invention can be used to 
predict fracture azimuth before fracturing, thus avoiding these problems 
and offering valuable advance information for proper planning of well 
patterns, spacings, etc. 
FIG. 3 shows tube wave amplitude plots obtained at depths of 450, 300 and 
180 ft in the same well. All three plots were produced by the same 
receiver with the same gain settings, located at the critical spacing. 
These plots show that the ratio of maximum to minimum tube wave amplitude 
decreases significantly approaching the surface. This is consistent with 
the expected decrease in earth stresses approaching the surface. With 
proper calibration, absolute values of horizontal earth stresses can be 
estimated. Proper calibration can be obtained from hydraulic fracturing 
data. The so called instantaneous shut-in pressure measured at the end of 
a hydraulic fracturing treatment provides an absolute value of the minimum 
horizontal earth stress. By combining this measurement with a tube wave 
amplitude plot, absolute earth stresses can be estimated for all 
directions in the horizontal plane and at other depths in the same well. 
Since the above described method provides a way to detect changes in 
horizontal earth stress conditions, it has application to earthquake 
prediction. In this application stress measurements are made in cased 
observation wells at regular intervals, such as weekly or monthly. 
Significant changes in stress conditions in a particular area can then 
serve as a warning of an impending earthquake. This method of earthquake 
prediction can be steadily improved through the experience. 
Because the asymmetry effects used are very weak it is necessary to 
generate wellbore tube waves of the largest possible amplitude. A monopole 
source of the Helmholtz type generates tube waves of much larger amplitude 
than those generated by a dipole source of the bender type and is 
therefore a more preferable source for this application. Helmholtz 
resonator principles are well known for use in the generation of sound as 
described in Fundamentals of Acoustics, by L. E. Kinsler and A. R. Frey, 
Wiley and Sons, New York (1962), pg. 186. The use of Helmholtz resonators 
as sources for acoustic logging is described in U.S. Pat. No. 4,674,067 to 
Zemanek, Jr., the teaching of which is incorporated herein by reference. A 
suitable Helmholtz resonator consists of a hollow ceramic sphere with 
apertures at opposite ends. The apertures are of such diameter as to 
produce a strong fundamental resonance at a selected frequency in the 
range 1-5 kHz. The sphere is enclosed in a rubber boot and mounted in the 
transmitter body with the apertures directed along the vertical tool axis 
so as to produce the strongest possible tube waves in the wellbore. A more 
preferable source is made by stacking two or more Helmholtz spheres in 
such a way as to align all of the apertures with the vertical axis of the 
transmitter body. Such a source produces stronger tube wave energy than a 
source containing a single sphere. One such source employing stacking of 
resonator shells is described in U.S. Pat. No. 4,890,687 to Medlin, the 
teaching of which is incorporated herein by reference. 
Directional receivers 31-38 preferably take the form of a dipole receiver 
of the bender-disc-type. The bender disc is highly directional with peak 
sensitivity in the direction perpendicular to the disc face. In the method 
of this invention it is mounted with its face centered in the receiver 
body 30 of FIG. 1 and parallel to the body axis. Mounted in this way, the 
bender disc is an excellent directional receiver for detection of tube 
waves. As a tube wave detector it is moderately sensitive to wellbore 
centering. Therefore, the bow spring centralizers, 14 and 15 of FIG. 1, 
are needed to avoid errors due to non centeredness. Dipole receivers of 
the bender-bar-type are described in U.S. Pat. Nos. 4,516,228 to Zemanek, 
Jr.; and 4,649,525 to Angona and Zemanek, Jr., the teachings of which are 
incorporated herein by reference. Bender-disc-type receivers are supplied 
by Actran, Incorporated, Orlando, Fla. Each bender disc receiver is made 
with a fundamental resonance matching that of the monopole transmitter and 
preferably in the range 1-5 kHz. 
The gyroscope system 19 preferably takes the form of a directional 
gyroscope which delivers a DC voltage whose magnitude is proportional to 
the angular rotation from a pre-selected direction determined from a 
magnetic compass setting at the surface. One example is a DC voltage 
increasing from 0 to 3.60 V as the tool is rotated clockwise through 360 
degrees starting from an azimuth of magnetic north. A commercial device 
which functions in this way is Model DG 29-0700 directional gyroscope 
supplied by Humphrey, Inc., 9212 Balboa Avenue, San Diego, Calif. 
Having now described a preferred embodiment of the present invention, it 
will be apparent to those skilled in the art of acoustic well logging that 
various changes and modifications may be made without departing from the 
spirit and scope of the invention as set forth in the appended claims.