Method and system for predicting maximum build rate of push-the-bit rotary steering tool
View Patent ↗A method and system for predicting a maximum build rate of a push-the-bit rotary steering tool is provided. In the method, a mechanical mathematical model of a push-the-bit rotary steering device is combined with measured well inclination data of the rotary steering device during actual drilling, a theoretical maximum build rate of a steering tool is calculated by the mechanical mathematical model, and a correction factor is combined with the mechanical mathematical model to predict a maximum build rate of the steering tool during a drilling operation in a same layer of a same block. The method effectively solves the problem of predicting the maximum build rate of the push-the-bit rotary steering device with different parameter changes based on measured data. Therefore, the method and system provide a reliable means for operators to analyze the performance of the push-the-bit rotary steering device, thereby providing technical support for efficient drilling operations.
1. A method for predicting a maximum build rate of a push-the-bit rotary steering tool, comprising the following steps:
step 1: selecting a push-the-bit rotary steering device that has been used in an actual directional well operation;
step 2: calculating, by a mechanical mathematical model, a theoretical maximum build rate of the push-the-bit rotary steering device;
step 3: calculating a measured maximum build rate in a working well depth interval based on measured well inclination data and a record of a steering force used by the push-the-bit rotary steering device in the working well depth interval;
step 4: calculating a correction factor based on the theoretical maximum build rate and the measured maximum build rate; and
step 5: changing a parameter in the mechanical mathematical model based on the correction factor to predict a maximum build rate of the push-the-bit rotary steering device with a different configuration;
step 6: adjusting a structure of the rotary steering tool based on the predicted maximum build rate during operation,
wherein, the mechanical mathematical model is established by: setting a current wellbore curvature of the push-the-bit rotary steering device as k c , mechanically simplifying the push-the-bit rotary steering device by assuming the push-the-bit rotary steering device as being formed by two beam columns, and acquiring a beam column model of the push-the-bit rotary steering device, wherein the push-the-bit rotary steering device is simplified to comprise a drill bit, a stabilizer, and a steering device,
wherein in the calculation by the mechanical mathematical model, parameters are recorded, comprising: an outer diameter D bit of the drill bit, an outer diameter D sta of the stabilizer, a weight on bit WOB, a pushing force F p generated by a pushing pad, maximum pushing force F pmax generated by a pushing pad a distance L AC from the drill bit to the pushing pad, a distance L CB from the pushing pad to the stabilizer, a length L AB of the steering device, an outer diameter D ot of the steering device, an inner diameter D it of the steering device, a bending stiffness EI of the steering device, and a linear weight q t of the steering device, wherein L AB =L AC +L CB , wherein in the beam column model, a displacement y AC of the push-the-bit rotary steering device under a stress between the drill bit and the pushing pad and a displacement y CB between the pushing pad and the stabilizer are expressed as follows:
y
AC
=
c
2
cos
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
c
1
sin
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
x
2
q
t
sec
(
L
AB
k
c
)
2
WOB
+
c
3
x
+
c
4
;
(
1
)
y
CB
=
c
6
cos
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
c
5
sin
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
x
2
q
t
sec
(
L
AB
k
c
)
2
WOB
+
c
7
x
+
c
8
;
(
2
)
wherein, c 1 , c 2 , c 3 , c 4 , c 5 , c 6 , c 7 , and c 8 denote 8 coefficients to be solved, and are calculated by the following boundary conditions:
y
A
C
|
x
=
-
L
AB
=
1
2
×
k
c
×
L
AB
2
+
D
bit
2
(
3
)
y
AC
|
x
=
-
L
CB
=
y
CB
|
x
=
-
L
CB
(
4
)
y
C
B
|
x
=
0
=
D
sta
2
+
(
D
bit
-
D
sta
)
(
5
)
dy
AC
d
x
❘
"\[RightBracketingBar]"
x
=
-
L
AB
=
0
(
6
)
d
y
AC
d
x
❘
"\[RightBracketingBar]"
x
=
-
L
CB
=
dy
CB
d
x
❘
"\[RightBracketingBar]"
x
=
-
L
CB
(
7
)
d
2
y
AC
dx
2
❘
"\[RightBracketingBar]"
x
=
-
L
CB
=
d
2
y
CB
dx
2
❘
"\[RightBracketingBar]"
x
=
-
L
CB
(
8
)
d
2
y
CB
dx
2
❘
"\[RightBracketingBar]"
x
=
0
=
0
(
9
)
-
EI
d
3
y
AC
dx
3
❘
"\[RightBracketingBar]"
x
=
-
L
CB
-
F
c
d
y
AC
dx
❘
"\[RightBracketingBar]"
x
=
-
L
CB
-
EI
d
3
y
CB
dx
3
❘
"\[RightBracketingBar]"
x
=
-
L
CB
-
F
c
dy
CB
dx
=
F
pmax
(
10
)
wherein
,
F
c
=
WOB
×
cos
(
k
c
×
L
AB
)
.
2. The method for predicting the maximum build rate of the push-the-bit rotary steering tool according to claim 1 , wherein
after the 8 coefficients to be solved are calculated, a lateral force on the drill bit is calculated:
F
d
=
EI
d
3
y
A
C
dx
3
❘
"\[LeftBracketingBar]"
x
=
-
L
AB
+
F
c
dy
AC
d
x
❘
"\[RightBracketingBar]"
x
=
-
L
AB
-
WOB
×
sin
(
k
c
×
L
AB
)
(
11
)
wherein, F d denotes the lateral force on the drill bit.
3. The method for predicting the maximum build rate of the push-the-bit rotary steering tool according to claim 1 , wherein after the lateral force on the drill bit is calculated, the theoretical maximum build rate of the push-the-bit rotary steering device is calculated:
k max =FindRoot( F d =0, k c ) (12)
wherein, k max denotes the maximum build rate; the theoretical maximum build rate is acquired by letting the lateral force F d on the drill bit be 0 and calculating the wellbore curvature k c in the expression; and FindRoot denotes a root-finding function.
4. The method for predicting the maximum build rate of the push-the-bit rotary steering tool according to claim 1 , wherein after predicting the theoretical maximum build rate, measured well inclination data of a rotary steering tool with a same parameter during a drilling operation in a certain layer of a certain block is processed, and a measured maximum build rate of the rotary steering tool during drilling in the layer is calculated as follows:
a series of steering commands during the operation in the layer are assumed as comprising different steering force percentages and steering orientations, a starting well depth and an ending well depth of each steering command in an action period are defined, and a measured maximum build rate in a well depth interval under the action of the command is calculated:
wherein, Inc st denotes an inclination angle at a starting point of a steering command interval, and Azi st denotes an azimuth angle at the starting point of the steering command interval;
Dogleg
mac
i
=
DoglegFun
(
Inc
si
,
Azi
st
,
Inc
ed
,
Azi
ed
)
(
MD
ed
-
MD
st
)
×
SFR
100
(
13
)
MD st denotes a well depth at the starting point of the steering command interval; Inc ed denotes an inclination angle at an ending point of the steering command interval; Azi ed denotes an azimuth angle at the ending point of the steering command interval; MD ed denotes a well depth at the ending point of the steering command interval; and DoglegFun denotes a dogleg calculation function for a trajectory formed in the steering command interval; and
a set of measured maximum build rates for different steering commands during the operation in the layer is calculated, and a representative measured maximum build rate from n measured maximum build rates of the set is selected by using different filtering methods comprising a median taking method or an average taking method:
Dogleg max =FilterFun(Dogleg max 1 ,Dogleg max 2 ,Dogleg max 3 , . . . ,Dogleg max n ) (14)
wherein, FilterFun denotes a filtering function, SFR denotes steering force percentage, and a corresponding filtering method is used as needed.
5. The method for predicting the maximum build rate of the push-the-bit rotary steering tool according to claim 1 , wherein the correction factor α is calculated based on the measured maximum build rate and the theoretical maximum build rate:
α
=
Dogleg
max
k
max
(
15
)
wherein, k max denotes the maximum build rate, and Dogleg max denotes the measured maximum build rate.
6. The method for predicting the maximum build rate of the push-the-bit rotary steering tool according to claim 1 , wherein after the correction factor α is calculated, different parameters are substituted into the mechanical mathematical model expressed by Eqs. (1) to (12) to predict the maximum build rate k RSS of the push-the-bit rotary steering device in the same layer of the same block:
k RSS =α×k max (16)
wherein, α denotes the correction factor, and k max denotes the maximum build rate.
7. A computer system, comprising a processor and a memory, wherein the memory is configured to store a computer program executable on the processor; and the processor is configured to execute the computer program to implement steps of the method for predicting the maximum build rate of the push-the-bit rotary steering tool according to claim 1 .
8. The computer system according to claim 7 , wherein in the calculation by the mechanical mathematical model, parameters are recorded, comprising: an outer diameter D bit of the drill bit, an outer diameter D sta of the stabilizer, a weight on bit WOB, a pushing force F p generated by a pushing pad, a distance L AC from the drill bit to the pushing pad, a distance L CB from the pushing pad to the stabilizer, a length L AB of the steering device, an outer diameter D ot of the steering device, an inner diameter D it of the steering device, a bending stiffness EI of the steering device, and a linear weight q t of the steering device, wherein L AB =L AC +L CB .
9. The computer system according to claim 8 , wherein in the beam column model, a displacement y AC of the push-the-bit rotary steering device under a stress between the drill bit and the pushing pad and a displacement y CB between the pushing pad and the stabilizer are expressed as follows:
y
AC
=
c
2
cos
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
c
1
sin
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
x
2
q
t
sec
(
L
AB
k
c
)
2
WOB
+
c
3
x
+
c
4
;
(
1
)
y
CB
=
c
6
cos
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
c
5
sin
(
x
WOB
cos
(
L
AB
k
c
)
EI
)
+
x
2
q
t
sec
(
L
AB
k
c
)
2
WOB
+
c
7
x
+
c
8
;
(
2
)
wherein, c 1 , c 2 , c 3 , c 4 , c 5 , c 6 , c 7 , and c 8 denote 8 coefficients to be solved, and are calculated by the following boundary conditions:
y
AC
❘
"\[LeftBracketingBar]"
x
=
-
L
AB
=
1
2
×
k
c
×
L
AB
2
+
D
bit
2
(
3
)
y
AC
❘
"\[LeftBracketingBar]"
x
=
-
L
CB
=
y
CB
❘
"\[LeftBracketingBar]"
x
=
-
L
CB
(
4
)
y
CB
❘
"\[LeftBracketingBar]"
x
=
0
=
D
sta
2
+
(
D
bit
-
D
sta
)
(
5
)
dy
AC
dx
❘
"\[LeftBracketingBar]"
x
=
-
L
AB
=
0
(
6
)
dy
AC
dx
❘
"\[RightBracketingBar]"
x
=
-
L
CB
=
dy
CB
dx
❘
"\[RightBracketingBar]"
x
=
-
L
CB
(
7
)
d
2
y
AC
dx
2
❘
"\[RightBracketingBar]"
x
=
-
L
CB
=
d
2
y
CB
dx
2
❘
"\[RightBracketingBar]"
x
=
-
L
CB
(
8
)
d
2
y
CB
dx
2
❘
"\[RightBracketingBar]"
x
=
0
=
0
(
9
)
-
EI
d
3
y
AC
dx
3
❘
"\[RightBracketingBar]"
x
=
-
L
AB
-
F
c
dy
AC
dx
❘
"\[RightBracketingBar]"
x
=
-
L
CB
-
EI
d
3
y
CB
dx
3
❘
"\[RightBracketingBar]"
x
=
-
L
CB
-
F
c
dy
CB
dx
=
F
pmax
(
10
)
wherein, F c =WOB×cos (k c ×L AB ).
10. The computer system according to claim 9 , wherein
after the 8 coefficients to be solved are calculated, a lateral force on the drill bit is calculated:
F
d
=
EI
d
3
y
AC
dx
3
❘
"\[RightBracketingBar]"
x
=
-
L
AB
+
F
c
dy
AC
dx
❘
"\[RightBracketingBar]"
x
=
-
L
AB
-
WOB
×
sin
(
k
c
×
L
AB
)
(
11
)
wherein, F d denotes the lateral force on the drill bit.
11. The computer system according to claim 10 , wherein after the lateral force on the drill bit is calculated, the theoretical maximum build rate of the push-the-bit rotary steering device is calculated:
k max =FindRoot( F d =0, k c ) (12)
wherein, k max denotes the maximum build rate; the theoretical maximum build rate is acquired by letting the lateral force F d on the drill bit be 0 and calculating the wellbore curvature k c in the expression; and FindRoot denotes a root-finding function.
12. The computer system according to claim 11 , wherein after predicting the theoretical maximum build rate, measured well inclination data of a rotary steering tool with a same parameter during a drilling operation in a certain layer of a certain block is processed, and a measured maximum build rate of the rotary steering tool during drilling in the layer is calculated as follows:
a series of steering commands during the operation in the layer is assumed as comprising different steering force percentages and steering orientations, a starting well depth and an ending well depth of each steering command in an action period are defined, and a measured maximum build rate in a well depth interval under the action of the command is calculated:
wherein, Inc st denotes an inclination angle at a starting point of a steering command interval, and Azi st denotes an azimuth angle at the starting point of the steering command interval;
Dogleg
max
i
=
DoglegFun
(
Inc
st
,
Azi
st
,
Inc
ed
,
Azi
ed
)
(
MD
ed
-
MD
st
)
×
SFR
100
(
13
)
MD st denotes a well depth at the starting point of the steering command interval; Inc ed denotes an inclination angle at an ending point of the steering command interval; Azi ed denotes an azimuth angle at the ending point of the steering command interval; MD ed denotes a well depth at the ending point of the steering command interval; and DoglegFun denotes a dogleg calculation function for a trajectory formed in the steering command interval; and
a set of measured maximum build rates for different steering commands during the operation in the layer is calculated, and a representative measured maximum build rate from n measured maximum build rates of the set is selected by using different filtering methods comprising a median taking method or an average taking method:
Dogleg max =FilterFun(Dogleg max 1 ,Dogleg max 2 ,Dogleg max 3 , . . . ,Dogleg max n ) (14)
wherein, FilterFun denotes a filtering function, and a corresponding filtering method is used as needed.
13. The computer system according to claim 12 , wherein the correction factor α is calculated based on the measured maximum build rate and the theoretical maximum build rate:
α
=
Dogleg
max
k
max
(
15
)
wherein, k max denotes the maximum build rate, and Dogleg max denotes the measured maximum build rate.
14. The computer system according to claim 13 , wherein after the correction factor α is calculated, different parameters are substituted into the mechanical mathematical model expressed by Eqs. (1) to (12) to predict the maximum build rate k RSS of the push-the-bit rotary steering device in the same layer of the same block:
k RSS =α×k max (16)
wherein, α denotes the correction factor, and k max denotes the maximum build rate.