US 2021/0173976 A1 · SYSTEMS AND METHODS FOR DETERMINING IN-SITU STRESSES BASED ON ORTHOTROPIC ROCK PHYSICS MODEL

A method implemented on a computing device including at least one processor and at least one storage medium, and a communication platform connected to a network, the method comprising:

determining multiple physical parameters of an orthotropic rock by well logging, mud logging, and indoor testing, the multiple physical parameters including compositions of minerals, a content of each of the minerals, compositions of formation fluids, a content of each of the formation fluids, a porosity, and a saturation;
constructing an orthotropic rock physics model;
determining, based on the orthotropic rock physics model, stiffness coefficients;
determining, based on the following relationship formulas between stiffness coefficient and elastic parameter, multiple dynamic elastic parameters of the orthotropic rock,
{
E
1
=
Δ

/

(
c
23
2
-
c
22

c
33
)
E
2
=
Δ

/

(
c
13
2
-
c
11

c
33
)
E
3
=
Δ

/

(
c
12
2
-
c
11

c
22
)


Δ
=
c
33

c
12
2
+
c
22

c
13
2
+
c
11

c
23
2
-
c
11

c
22

c
33
-
2

c
12

c
13

c
23


{
v
12
=
(
c
13

c
23
-
c
12

c
33
)

/

(
c
23
2
-
c
22

c
33
)
v
13
=
(
c
12

c
23
-
c
13

c
22
)

/

(
c
23
2
-
c
22

c
33
)
v
21
=
(
c
13

c
23
-
c
12

c
33
)

/

(
c
13
2
-
c
11

c
33
)
v
23
=
(
c
12

c
13
-
c
11

c
23
)

/

(
c
13
2
-
c
11

c
33
)
v
31
=
(
c
12

c
23
-
c
13

c
22
)

/

(
c
12
2
-
c
11

c
22
)
v
32
=
(
c
12

c
13
-
c
11

c
23
)

/

(
c
12
2
-
c
11

c
22
)


{
E
2

v
12
=
E
1

v
21
E
3

v
13
=
E
1

v
31
E
2

v
32
=
E
3

v
23


{
μ
23
=
c
44
μ
13
=
c
55
μ
12
=
c
66
where c11, c12, c13, c22, c23, c33, c44, c55, and c66 denote the stiffness coefficients of the orthotropic rock, GPa;
E1 denotes a Young's modulus along a direction of a maximum horizontal in-situ stress, GPa;
E2 denotes a Young's modulus along a direction of a minimum horizontal in-situ stress, GPa;
E3 denotes a Young's modulus along a direction of a vertical in-situ stress, GPa;
v12 denotes a Poisson's ratio along the direction of the minimum horizontal in-situ stress and perpendicular to the direction of the maximum horizontal in-situ stress;
v13 denotes a Poisson's ratio along the direction of the vertical in-situ stress and perpendicular to the direction of the maximum horizontal in-situ stress;
v21 denotes a Poisson's ratio along the direction of the maximum horizontal in-situ stress and perpendicular to the direction of the minimum horizontal in-situ stress;
v23 a Poisson's ratio along the direction of the vertical in-situ stress and perpendicular to the direction of the minimum horizontal in-situ stress;
v31 a Poisson's ratio along the direction of the maximum horizontal in-situ stress and perpendicular to the direction of the vertical in-situ stress;
and v32 denotes a Poisson's ratio along the direction of the minimum horizontal in-situ stress and perpendicular to the direction of the vertical in-situ stress;
determining, based on the multiple dynamic elastic parameters of the orthotropic rock, multiple static elastic parameters of the orthotropic rock according to relationships between the multiple dynamic elastic parameters and the multiple static elastic parameters;
determining anisotropy Biot coefficients of the orthotropic rock physics model according to the following formulas:
{
α
11
=
1
-
c
11
dry
+
c
12
dry
+
c
13
dry
c
11
m
+
c
12
m
+
c
13
m
α
22
=
1
-
c
12
dry
+
c
22
dry
+
c
23
dry
c
11
m
+
c
22
m
+
c
23
m
α
33
=
1
-
c
13
dry
+
c
23
dry
+
c
33
dry
c
13
m
+
c
23
m
+
c
33
m

where c11dry, c12dry, c13dry, c22dry, c23dry, and c33dry denote stiffness coefficients of a dry orthotropic (ORT) rock, GPa;
c11m, c12m, c13m, c22m, c23m, and c33m denote stiffness coefficients of a dry vertical transverse isotropy (VTI) rock, GPa;
and α11, α22, and α33 denote the anisotropy Biot coefficients;
determining a formation pore pressure based on longitudinal wave time differences according to an Eaton method described as the following formula:
Pp=σv−(σv−pw)(ACn/AC)c
where σv denotes the vertical in-situ stress, MPa;
pw denotes a formation hydrostatic column pressure, MPa;
ACn denotes a longitudinal wave time difference of trend line at normal pressure, μs/ft;
AC denotes an actual longitudinal wave time difference, μs/ft;
and Pp denotes the formation pore pressure, MPa;
and
determining the maximum horizontal in-situ stress and the minimum horizontal in-situ stress of the orthotropic rock according to the following formulas:
{
σ
H
=
v
13
+
v
12

v
23
1
-
v
12

v
21

(
σ
v
-
α
33

P
p
)
+
α
11

P
p
+
E
1
1
-
v
12

v
21

ɛ
H
+
E
1

v
21
1
-
v
12

v
21

ɛ
h
σ
h
=
v
23
+
v
13

v
21
1
-
v
12

v
21

(
σ
v
-
α
33

P
p
)
+
α
22

P
p
+
E
2
1
-
v
12

v
21

ɛ
h
+
E
1

v
21
1
-
v
12

v
21

ɛ
H
where σH denotes the maximum horizontal in-situ stress, MPa;
σh denotes the minimum horizontal in-situ stress, MPa;
εH denotes a maximum horizontal strain corresponding to the direction of the maximum horizontal in-situ stress;
and εh denotes a minimum horizontal strain corresponding to the direction of the minimum horizontal in-situ stress.

577 more elements

A system of comprising:

at least one storage device storing executable instructions, and
at least one processor in communication with the at least one storage device, wherein when executing the executable instructions, the at least one processor is directed to cause the system to perform operations including:
determining multiple physical parameters of an orthotropic rock by well logging, mud logging, and indoor testing, the multiple physical parameters including compositions of minerals, a content of each of the minerals, compositions of formation fluids, a content of each of the formation fluids, a porosity, and a saturation;
constructing an orthotropic rock physics model;
determining, based on the orthotropic rock physics model, stiffness coefficients;
determining, based on the following relationship formulas between stiffness coefficient and elastic parameter, multiple dynamic elastic parameters of the orthotropic rock,
{
E
1
=
Δ

/

(
c
23
2
-
c
22

c
33
)
E
2
=
Δ

/

(
c
13
2
-
c
11

c
33
)
E
3
=
Δ

/

(
c
12
2
-
c
11

c
22
)


Δ
=
c
33

c
12
2
+
c
22

c
13
2
+
c
11

c
23
2
-
c
11

c
22

c
33
-
2

c
12

c
13

c
23


{
v
12
=
(
c
13

c
23
-
c
12

c
33
)

/

(
c
23
2
-
c
22

c
33
)
v
13
=
(
c
12

c
23
-
c
13

c
22
)

/

(
c
23
2
-
c
22

c
33
)
v
21
=
(
c
13

c
23
-
c
12

c
33
)

/

(
c
13
2
-
c
11

c
33
)
v
23
=
(
c
12

c
13
-
c
11

c
23
)

/

(
c
13
2
-
c
11

c
33
)
v
31
=
(
c
12

c
23
-
c
13

c
22
)

/

(
c
12
2
-
c
11

c
22
)
v
32
=
(
c
12

c
13
-
c
11

c
23
)

/

(
c
12
2
-
c
11

c
22
)


{
E
2

v
12
=
E
1

v
21
E
3

v
13
=
E
1

v
31
E
2

v
32
=
E
3

v
23


{
μ
23
=
c
44
μ
13
=
c
55
μ
12
=
c
66
where c11, c12, c13, c22, c23, c33, c44, c55, and c66 denote the stiffness coefficients of the orthotropic rock, GPa;
E denotes a Young's modulus along a direction of a maximum horizontal in-situ stress, GPa;
E2 denotes a Young's modulus along a direction of a minimum horizontal in-situ stress, GPa;
E3 denotes a Young's modulus along a direction of a vertical in-situ stress, GPa;
v12 denotes a Poisson's ratio along the direction of the minimum horizontal in-situ stress and perpendicular to the direction of the maximum horizontal in-situ stress;
v13 denotes a Poisson's ratio along the direction of the vertical in-situ stress and perpendicular to the direction of the maximum horizontal in-situ stress;
v21 denotes a Poisson's ratio along the direction of the maximum horizontal in-situ stress and perpendicular to the direction of the minimum horizontal in-situ stress;
v23 a Poisson's ratio along the direction of the vertical in-situ stress and perpendicular to the direction of the minimum horizontal in-situ stress;
v31 a Poisson's ratio along the direction of the maximum horizontal in-situ stress and perpendicular to the direction of the vertical in-situ stress;
and v32 denotes a Poisson's ratio along the direction of the minimum horizontal in-situ stress and perpendicular to the direction of the vertical in-situ stress;
determining, based on the multiple dynamic elastic parameters of the orthotropic rock, multiple static elastic parameters of the orthotropic rock according to relationships between the multiple dynamic elastic parameters and the multiple static elastic parameters;
determining anisotropy Biot coefficients of the orthotropic rock physics model according to the following formulas:
{
α
11
=
1
-
c
11
dry
+
c
12
dry
+
c
13
dry
c
11
m
+
c
12
m
+
c
13
m
α
22
=
1
-
c
12
dry
+
c
22
dry
+
c
23
dry
c
11
m
+
c
22
m
+
c
23
m
α
33
=
1
-
c
13
dry
+
c
23
dry
+
c
33
dry
c
13
m
+
c
23
m
+
c
33
m

where c11dry, c12dry, c13dry, c22dry, c23dry, and c33dry denote stiffness coefficients of a dry orthotropic (ORT) rock, GPa;
c11m, c12m, c13m, c22m, c23m, and c33m denote stiffness coefficients of a dry vertical transverse isotropy (VTI) rock, GPa;
and α11, α22, and α33 denote the anisotropy Biot coefficients;
determining a formation pore pressure based on longitudinal wave time differences according to an Eaton method described as the following formula:
Pp=σv−(σv−pw)(ACn/AC)c
where σv denotes the vertical in-situ stress, MPa;
pw denotes a formation hydrostatic column pressure, MPa;
ACn denotes a longitudinal wave time difference of trend line at normal pressure, μs/ft;
AC denotes an actual longitudinal wave time difference, μs/ft;
and Pp denotes the formation pore pressure, MPa;
and
determining the maximum horizontal in-situ stress and the minimum horizontal in-situ stress of the orthotropic rock according to the following formulas:
{
σ
H
=
v
13
+
v
12

v
23
1
-
v
12

v
21

(
σ
v
-
α
33

P
p
)
+
α
11

P
p
+
E
1
1
-
v
12

v
21

ɛ
H
+
E
1

v
21
1
-
v
12

v
21

ɛ
h
σ
h
=
v
23
+
v
13

v
21
1
-
v
12

v
21

(
σ
v
-
α
33

P
p
)
+
α
22

P
p
+
E
2
1
-
v
12

v
21

ɛ
h
+
E
1

v
21
1
-
v
12

v
21

ɛ
H
where σH denotes the maximum horizontal in-situ stress, MPa;
σh denotes the minimum horizontal in-situ stress, MPa;
εH denotes a maximum horizontal strain corresponding to the direction of the maximum horizontal in-situ stress;
and εh denotes a minimum horizontal strain corresponding to the direction of the minimum horizontal in-situ stress.

579 more elements

A non-transitory computer readable medium, comprising executable instructions that, when executed by at least one processor, direct the at least one processor to perform a method, the method comprising:

determining multiple physical parameters of an orthotropic rock by well logging, mud logging, and indoor testing, the multiple physical parameters including compositions of minerals, a content of each of the minerals, compositions of formation fluids, a content of each of the formation fluids, a porosity, and a saturation;
constructing an orthotropic rock physics model;
determining, based on the orthotropic rock physics model, stiffness coefficients;
determining, based on the following relationship formulas between stiffness coefficient and elastic parameter, multiple dynamic elastic parameters of the orthotropic rock,
{
E
1
=
Δ

/

(
c
23
2
-
c
22

c
33
)
E
2
=
Δ

/

(
c
13
2
-
c
11

c
33
)
E
3
=
Δ

/

(
c
12
2
-
c
11

c
22
)


Δ
=
c
33

c
12
2
+
c
22

c
13
2
+
c
11

c
23
2
-
c
11

c
22

c
33
-
2

c
12

c
13

c
23


{
v
12
=
(
c
13

c
23
-
c
12

c
33
)

/

(
c
23
2
-
c
22

c
33
)
v
13
=
(
c
12

c
23
-
c
13

c
22
)

/

(
c
23
2
-
c
22

c
33
)
v
21
=
(
c
13

c
23
-
c
12

c
33
)

/

(
c
13
2
-
c
11

c
33
)
v
23
=
(
c
12

c
13
-
c
11

c
23
)

/

(
c
13
2
-
c
11

c
33
)
v
31
=
(
c
12

c
23
-
c
13

c
22
)

/

(
c
12
2
-
c
11

c
22
)
v
32
=
(
c
12

c
13
-
c
11

c
23
)

/

(
c
12
2
-
c
11

c
22
)


{
E
2

v
12
=
E
1

v
21
E
3

v
13
=
E
1

v
31
E
2

v
32
=
E
3

v
23


{
μ
23
=
c
44
μ
13
=
c
55
μ
12
=
c
66
where c11, c12, c13, c22, c23, c33, c44, c55, and c66 denote the stiffness coefficients of the orthotropic rock, GPa;
E1 denotes a Young's modulus along a direction of a maximum horizontal in-situ stress, GPa;
E2 denotes a Young's modulus along a direction of a minimum horizontal in-situ stress, GPa;
E3 denotes a Young's modulus along a direction of a vertical in-situ stress, GPa;
v12 denotes a Poisson's ratio along the direction of the minimum horizontal in-situ stress and perpendicular to the direction of the maximum horizontal in-situ stress;
v13 denotes a Poisson's ratio along the direction of the vertical in-situ stress and perpendicular to the direction of the maximum horizontal in-situ stress;
v21 denotes a Poisson's ratio along the direction of the maximum horizontal in-situ stress and perpendicular to the direction of the minimum horizontal in-situ stress;
v23 a Poisson's ratio along the direction of the vertical in-situ stress and perpendicular to the direction of the minimum horizontal in-situ stress;
v31 a Poisson's ratio along the direction of the maximum horizontal in-situ stress and perpendicular to the direction of the vertical in-situ stress;
and v32 denotes a Poisson's ratio along the direction of the minimum horizontal in-situ stress and perpendicular to the direction of the vertical in-situ stress;
determining, based on the multiple dynamic elastic parameters of the orthotropic rock, multiple static elastic parameters of the orthotropic rock according to relationships between the multiple dynamic elastic parameters and the multiple static elastic parameters;
determining anisotropy Biot coefficients of the orthotropic rock physics model according to the following formulas:
{
α
11
=
1
-
c
11
dry
+
c
12
dry
+
c
13
dry
c
11
m
+
c
12
m
+
c
13
m
α
22
=
1
-
c
12
dry
+
c
22
dry
+
c
23
23
c
11
m
+
c
22
m
+
c
23
m
α
33
=
1
-
c
13
dry
+
c
23
dry
+
c
33
dry
c
13
m
+
c
23
m
+
c
33
m
where c11dry, c12dry, c13dry, c22dry, c23dry, and c33dry denote stiffness coefficients of a dry orthotropic (ORT) rock, GPa;
c11m, c12m, c13m, c22m, c23m, and c33m denote stiffness coefficients of a dry vertical transverse isotropy (VTI) rock, GPa;
and α11, α22, and α33 denote the anisotropy Biot coefficients;
determining a formation pore pressure based on longitudinal wave time differences according to an Eaton method described as the following formula:
Pp=σv−(σv−pw)(ACn/AC)c
where σv denotes the vertical in-situ stress, MPa;
pw denotes a formation hydrostatic column pressure, MPa;
ACn denotes a longitudinal wave time difference of trend line at normal pressure, μs/ft;
AC denotes an actual longitudinal wave time difference, μs/ft;
and Pp denotes the formation pore pressure, MPa;
and
determining the maximum horizontal in-situ stress and the minimum horizontal in-situ stress of the orthotropic rock according to the following formulas:
{
σ
H
=
v
13
+
v
12

v
23
1
-
v
12

v
21

(
σ
v
-
α
33

P
p
)
+
α
11

P
p
+
E
1
1
-
v
12

v
21

ɛ
H
+
E
1

v
21
1
-
v
12

v
21

ɛ
h
σ
h
=
v
23
+
v
13

v
21
1
-
v
12

v
21

(
σ
v
-
α
33

P
p
)
+
α
22

P
p
+
E
2
1
-
v
12

v
21

ɛ
h
+
E
1

v
21
1
-
v
12

v
21

ɛ
H
where σH denotes the maximum horizontal in-situ stress, MPa;
σh denotes the minimum horizontal in-situ stress, MPa;
εH denotes a maximum horizontal strain corresponding to the direction of the maximum horizontal in-situ stress;
and εh denotes a minimum horizontal strain corresponding to the direction of the minimum horizontal in-situ stress.

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Systems and methods for determining in-situ stresses based on orthotropic rock physics model

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Systems and methods for determining in-situ stresses based on orthotropic rock physics model

Life of this patent

Abstract

Claims20