Apparatus and method using measurements taken while drilling cement to obtain absolute values of mechanical rock properties along a borehole
An innovative apparatus and computer implemented methods to obtain values for a set of scalars corresponding to each force and displacement, which may be obtained from acoustical signals captured by sensors of a drill bit while drilling, in a material of known mechanical properties, such as a cement from casing the well, such that the application and use of the scalars in relation to measurements of the mechanics while drilling, such as the acceleration of the bit and motion of the bit captured by sensors such as accelerometers, allow for absolute values of mechanical rock properties to be obtained in rock formations, being drilled through, with otherwise unknown mechanical properties prior to drilling.
1. A method of characterizing rock properties comprising:
receiving, at a processor, a first set of acoustical signals obtained from one or more sensors, the acoustical signals generated from a drill bit interacting with a rock formation while drilling a wellbore, wherein the acoustical signals include an axial acceleration of the drill bit and a lateral or a rotary acceleration of the drill bit;
processing, at the processor, the first set of acoustical signals to obtain forces acting on the drill bit interacting with the rock formation while drilling the wellbore and to obtain displacements of the drill bit interacting with the rock formation while drilling the wellbore;
applying, at the processor, scalars to the obtained forces acting on the drill bit interacting with the rock formation while drilling the wellbore and the obtained displacements of the drill bit interacting with the rock formation while drilling the wellbore to obtain information representative of stresses and strains of the rock formation, the scalars obtained from processing a second set of acoustical signals to obtain forces acting on the drill bit interacting with a sample with known mechanical rock properties and to obtain displacements of the drill bit interacting with the sample with known mechanical rock properties, the second set of acoustical signals obtained from the one or more sensors positioned on a component of a bottom hole assembly, the second set of acoustical signals generated from the drill bit interacting with the sample with known mechanical rock properties, and processing the obtained forces acting on the drill bit interacting with the sample and the obtained displacements of the drill bit interacting with the sample to obtain the scalars that conform to a stress strain relationship of the sample with known mechanical rock properties; and
processing, at the processor, the scaled forces and the scaled displacements to obtain at least one set of data values representative of a mechanical rock property of the rock formation along the wellbore created by the drill bit interacting with the rock formation for a period of time.
2. The method of claim 1 wherein the stress strain relationship is:
[
-
a
1
0
0
d
1
C
11
d
2
C
12
d
3
C
12
0
-
a
2
0
d
1
C
12
d
2
C
11
d
3
C
12
0
0
-
a
3
d
1
C
12
d
2
C
12
d
3
C
11
]
[
A
B
C
D
E
F
]
=
[
0
0
0
]
where:
the a values are forces or accelerations acting on the drill bit interacting with the sample;
the d values are displacements the drill bit interacting with the sample;
where C 11 and C 12 are populated with known rock properties of the sample; and
A-F are the at least one set of scalars being obtained.
3. The method of claim 2 where the stress strain relationship is:
[
-
a
1
0
0
d
1
C
11
d
2
C
12
d
3
C
13
0
-
a
2
0
d
1
C
12
d
2
C
11
d
3
C
13
0
0
-
a
3
d
1
C
13
d
2
C
13
d
3
C
33
]
[
A
B
C
D
E
F
]
=
[
0
0
0
]
where:
the a values are forces or accelerations acting on the drill bit interacting with the sample with respect to an axis of material symmetry of the sample;
the d values are displacements the drill bit interacting with the sample with respect to the axis of material symmetry of the sample;
where the Cijs are populated with known rock properties of the sample; and
A-F are the at least one set of scalars being obtained.
4. The method of claim 2 wherein:
the first set of acoustical signals are captured at the one or more sensors as axial accelerations of the drill bit generated from the drill bit interacting with the rock formation while drilling the wellbore and a lateral or rotary acceleration of the drill bit generated from the drill bit interacting with the rock formation while drilling the wellbore; and
the second set of acoustical signals are captured at the one or more sensors as axial accelerations of the drill bit generated from the drill bit interacting with the sample and a lateral or rotary acceleration of the drill bit generated from the drill bit interacting with the sample.
5. The method of claim 4 wherein:
processing the obtained forces acting on the drill bit interacting with the sample and the obtained displacements of the drill bit interacting with the sample to obtain the scalars that conform to a stress strain relationship of the sample with known mechanical rock properties comprises applying a first stress strain relationship of:
[
-
a
1
0
0
d
1
C
11
d
2
C
12
d
3
C
12
0
-
a
2
0
d
1
C
12
d
2
C
11
d
3
C
12
0
0
-
a
3
d
1
C
12
d
2
C
12
d
3
C
11
]
[
A
B
C
D
E
F
]
=
[
0
0
0
]
where:
d 1 , d 2 , and d 3 are any one of axial, centripetal, or lateral displacement of the drill bit,
a 1 , a 2 , a 3 may be any one of axial, centripetal or lateral acceleration of the drill bit,
C 11 and C 12 are known values for the sample, and
A-F are the obtained at least one set of scalars
further wherein:
scaling the obtained forces acting on the drill bit interacting with the rock formation while drilling the wellbore and the obtained displacements of the drill bit interacting with the rock formation while drilling the wellbore to obtain information representative of stresses and strains of the rock formation; and processing the scaled forces and the scaled displacements to obtain at least one set of data values representative of a mechanical rock property of the rock formation along the wellbore created by the drill bit interacting with the rock formation for a period of time comprises applying a second stress strain relationship of:
[
Dd
1
′
(
Ed
2
′
+
Fd
3
′
)
Ed
2
′
(
Dd
1
′
+
Fd
3
′
)
Fd
3
′
(
Ed
2
′
+
Fd
3
′
)
]
[
C
11
′
C
12
′
]
=
[
Aa
1
′
Ba
2
′
Ca
3
′
]
where:
A-F are the obtained scalars of the first stress strain relationship,
d′ 1 , d′ 2 , and d′ 3 are any one of axial, centripetal, or lateral displacement of the drill bit as applied in the first stress strain relationship to the rock formation by the drill bit during the period of time,
a′ 1 , a′ 2 , a′ 3 are any one of axial, centripetal or lateral acceleration of the drill bit as applied in the first stress strain relationship to the rock formation by the drill bit during the period of time, and
C′ 11 and C′ 12 are the obtained at least one set of data values representative of the mechanical rock property of the rock formation along the wellbore.
6. The method of claim 4 wherein:
processing the first set of acoustical signals comprises obtaining a root mean square of the axial acceleration of the drill bit generated from the drill bit interacting with the rock formation while drilling the wellbore and a root mean square of at least one of the lateral and rotary acceleration of the drill bit generated from the drill bit interacting with the rock formation while drilling the wellbore, and obtaining an axial displacement of the drill bit generated from the drill bit interacting with the rock formation while drilling the wellbore and at least one of a lateral and rotary displacement of the drill bit generated from the drill bit interacting with the rock formation while drilling the wellbore; and
processing the second set of acoustical signals comprises obtaining a root mean square of the axial acceleration of the drill bit generated from the drill bit interacting with the sample and a root mean square of at least one of a lateral and rotary acceleration of the drill bit generated from the drill bit interacting with the sample, and obtaining an axial displacement of the drill bit and at least one of a lateral and rotary displacement of the drill bit generated from the drill bit interacting with the sample.
7. The method of claim 1 wherein the sample is cement used to set a casing of the wellbore.
8. The method of claim 1 wherein the sample is a rock formation with known mechanical rock properties.
9. The method of claim 1 wherein the known mechanical rock properties of the sample are obtained from at least one of sonic measurements, core measurements, cutting measurements, seismic measurements, wireline log measurements, and a mineralogical model.
10. The method of claim 1 wherein the set of data values include at least one absolute Cij value.
11. An apparatus comprising:
a hardware processor in communication with a non-transitory computer readable media including computer executable instructions to perform a method of:
accessing a first set of acoustical signals obtained from one or more sensors, the acoustical signals generated from a drill bit interacting with a rock formation while drilling a wellbore, wherein the acoustical signals include an axial acceleration of the drill bit and a lateral or rotary acceleration of the drill bit;
processing the first set of acoustical signals to obtain forces acting on the drill bit interacting with the rock formation while drilling the wellbore and to obtain displacements of the drill bit interacting with the rock formation while drilling the wellbore;
obtaining scalars by:
receiving a second set of acoustical signals obtained from the one or more sensors wherein the one or more sensors are positioned on a component of a bottom hole assembly, the second set of acoustical signals generated from the drill bit interacting with a sample with known mechanical rock properties;
processing the second set of acoustical signals to obtain forces acting on the drill bit interacting with the sample and to obtain displacements of the drill bit interacting with the sample; and
processing the obtained forces acting on the drill bit interacting with the sample and the obtained displacements of the drill bit interacting with the sample to obtain the scalars that conform to a stress strain relationship of the sample with known mechanical rock properties;
applying the scalars to the obtained forces acting on the drill bit interacting with the rock formation while drilling the wellbore and the obtained displacements of the drill bit interacting with the rock formation while drilling the wellbore to obtain information representative of stresses and strains of the rock formation; and
processing the scaled forces and the scaled displacements to obtain and store in a tangible memory at least one set of data values representative of a mechanical rock property of the rock formation along the wellbore created by the drill bit interacting with the rock formation for a period of time.
12. The apparatus of claim 11 wherein the stress strain relationship is:
[
-
a
1
0
0
d
1
C
11
d
2
C
12
d
3
C
12
0
-
a
2
0
d
1
C
12
d
2
C
11
d
3
C
12
0
0
-
a
3
d
1
C
12
d
2
C
12
d
3
C
11
]
[
A
B
C
D
E
F
]
=
[
0
0
0
]
where:
the a values are forces or accelerations acting on the drill bit interacting with the sample;
the d values are displacements the drill bit interacting with the sample;
where C 11 and C 12 are populated with known rock properties of the sample; and
A-F are the at least one set of scalars being obtained.