# US 12,180,821 B1 · Method and system for predicting maximum build rate of push-the-bit rotary steering tool

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- Number: US 12,180,821 B1
- Document ID: US12180821B1
- Status: Granted
- Kind: B1
- Application number: 18/664,335
- Filed: 2024-05-15
- Granted: 2024-12-31
- Earliest claimed: 2023-09-08
- Assignees: Chengdu University of Information Technology
- Applicants: Chengdu University of Information Technology
- Inventors: Jiantao Zhang; Hanbing Yan; Dongxing Qin
- Web page: https://patentgrep.com/patent/US12180821B1

## CPC

- E21B 44/00: Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
- E21B 7/06: Deflecting the direction of boreholes
- E21B 2200/20: Computer models or simulations, e.g. for reservoirs under production, drill bits
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS

## Abstract

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.

## Claims

### Claim 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 kc, 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 Dbit of the drill bit, an outer diameter Dsta of the stabilizer, a weight on bit WOB, a pushing force Fp generated by a pushing pad, maximum pushing force Fpmax generated by a pushing pad a distance LAC from the drill bit to the pushing pad, a distance LCB from the pushing pad to the stabilizer, a length LAB of the steering device, an outer diameter Dot of the steering device, an inner diameter Dit of the steering device, a bending stiffness EI of the steering device, and a linear weight qt of the steering device, wherein LAB=LAC+LCB, wherein in the beam column model, a displacement yAC of the push-the-bit rotary steering device under a stress between the drill bit and the pushing pad and a displacement yCB 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, c1, c2, c3, c4, c5, c6, c7, and c8 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
)
.

### Claim 2 (depends on 1)

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, Fd denotes the lateral force on the drill bit.

### Claim 3 (depends on 1)

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:
kmax=FindRoot(Fd=0,kc) (12)
wherein, kmax denotes the maximum build rate; the theoretical maximum build rate is acquired by letting the lateral force Fd on the drill bit be 0 and calculating the wellbore curvature kc in the expression; and FindRoot denotes a root-finding function.

### Claim 4 (depends on 1)

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, Incst denotes an inclination angle at a starting point of a steering command interval, and Azist 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
)
MDst denotes a well depth at the starting point of the steering command interval; Inced denotes an inclination angle at an ending point of the steering command interval; Azied denotes an azimuth angle at the ending point of the steering command interval; MDed 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:
Doglegmax=FilterFun(Doglegmax1,Doglegmax2,Doglegmax3, . . . ,Doglegmaxn) (14)
wherein, FilterFun denotes a filtering function, SFR denotes steering force percentage, and a corresponding filtering method is used as needed.

### Claim 5 (depends on 1)

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, kmax denotes the maximum build rate, and Doglegmax denotes the measured maximum build rate.

### Claim 6 (depends on 1)

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 kRSS of the push-the-bit rotary steering device in the same layer of the same block:
kRSS=α×kmax (16)
wherein, α denotes the correction factor, and kmax denotes the maximum build rate.

### Claim 7 (depends on 1)

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.

### Claim 8 (depends on 7)

The computer system according to claim 7, wherein in the calculation by the mechanical mathematical model, parameters are recorded, comprising: an outer diameter Dbit of the drill bit, an outer diameter Dsta of the stabilizer, a weight on bit WOB, a pushing force Fp generated by a pushing pad, a distance LAC from the drill bit to the pushing pad, a distance LCB from the pushing pad to the stabilizer, a length LAB of the steering device, an outer diameter Dot of the steering device, an inner diameter Dit of the steering device, a bending stiffness EI of the steering device, and a linear weight qt of the steering device, wherein LAB=LAC+LCB.

### Claim 9 (depends on 8)

The computer system according to claim 8, wherein in the beam column model, a displacement yAC of the push-the-bit rotary steering device under a stress between the drill bit and the pushing pad and a displacement yCB 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, c1, c2, c3, c4, c5, c6, c7, and c8 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, Fc=WOB×cos (kc×LAB).

### Claim 10 (depends on 9)

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, Fd denotes the lateral force on the drill bit.

### Claim 11 (depends on 10)

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:
kmax=FindRoot(Fd=0,kc) (12)
wherein, kmax denotes the maximum build rate; the theoretical maximum build rate is acquired by letting the lateral force Fd on the drill bit be 0 and calculating the wellbore curvature kc in the expression; and FindRoot denotes a root-finding function.

### Claim 12 (depends on 11)

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, Incst denotes an inclination angle at a starting point of a steering command interval, and Azist 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
)
MDst denotes a well depth at the starting point of the steering command interval; Inced denotes an inclination angle at an ending point of the steering command interval; Azied denotes an azimuth angle at the ending point of the steering command interval; MDed 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:
Doglegmax=FilterFun(Doglegmax1,Doglegmax2,Doglegmax3, . . . ,Doglegmaxn) (14)
wherein, FilterFun denotes a filtering function, and a corresponding filtering method is used as needed.

### Claim 13 (depends on 12)

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, kmax denotes the maximum build rate, and Doglegmax denotes the measured maximum build rate.

### Claim 14 (depends on 13)

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 kRSS of the push-the-bit rotary steering device in the same layer of the same block:
kRSS=α×kmax (16)
wherein, α denotes the correction factor, and kmax denotes the maximum build rate.