US 11,106,843 B2Granted

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

AssigneeSouthwest Petroleum University

InventorsTianshou Ma, Junchuan Gui, Ping Chen, Yang Liu, Jianhong Fu

Life of this patent

Estimating the term…

Abstract

The present disclosure provides systems and methods for determining in-situ stresses based on an orthotropic rock physics model. The method may include obtaining multiple physical parameters of a rock; constructing an orthotropic rock physics model based at least in part on the multiple physical parameters; determining multiple stiffness coefficients based on the orthotropic rock physics model; and determining one or more in-situ stresses of the orthotropic rock based on the multiple stiffness coefficients.

Claims20

Dependent claims

A method comprising:

acquiring, by an inductive device, measurement signals of an orthotropic rock by well logging, mud logging, or indoor testing;
collecting, by a ground recording instrument vehicle, the measurement signals from the inductive device in real time;
determining, by one or more processors, multiple physical parameters of the orthotropic rock based on the measurement signals, 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, by the one or more processors, an orthotropic rock physics model based on the multiple physical parameters;
determining, by the one or more processors based on the orthotropic rock physics model, stiffness coefficients;
determining, by the one or more processors 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, 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;
v<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;
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, by the one or more processors 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, by the one or more processors, 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;
c11 m,2, c12m, c13m, c22m, c23m and c33m denote stiffness coefficients of a dry vertical transverse isotropy (VTI) rock, GPa;
and α11, α22, and α33denote the anisotropy Biot coefficients;
determining, by the one or more processors, 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;
pwdenotes 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, by the one or more processors, 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.

559 more elements

A system comprising:

an inductive device configured to acquire measurement signals of an orthotropic rock by well logging, mud logging, or indoor testing;
a ground recording instrument vehicle configured to collect the measurement signals from the inductive device in real time;
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:
obtaining the measurement signals from the one or more storage devices or the ground recording instrument vehicle;
determining multiple physical parameters of the orthotropic rock based on the measurement signals, 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 based on the multiple physical parameters;
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;
v12 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;
v13 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, chd 12m, c13m, c22m, c23, and c23 m 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.

582 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:

causing an inductive device to acquire measurement signals of an orthotropic rock by well logging, mud logging, or indoor testing;
causing a ground recording instrument vehicle to collect the measurement signals from the inductive device in real time;
obtaining the measurement signals of the orthotropic rock from the ground recording instrument vehicle;
determining multiple physical parameters of the orthotropic rock based on the measurement signals, 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 based on the multiple physical parameters;
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 c33hu m 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

Dependencies are inferred from the claim text.

Facts

Application: 17/106,270Filed 30 Nov 2020
Priority: CN 201911239424.26 Dec 2019
Published: US 2021/0173976 A110 Jun 2021
Granted: 31 Aug 2021
Term ends: Not estimatedThe source records don’t support an estimate.

Classification13 codes

G06F 30/20
Computer-aided design [CAD]: design optimisation, verification or simulation
E21B 49/00
Testing the nature of borehole walls
G01N 33/24
Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00: earth materials
G01V 1/42
Specially adapted for well-logging: using generators in one well and receivers elsewhere or vice versa

Family

US 2021/0173976 A1Pre-grant publication · published 10 Jun 2021
US 11,106,843 B2This patent

From the US filing history. Foreign family members aren’t listed.

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Abstract

A method comprising:

acquiring, by an inductive device, measurement signals of an orthotropic rock by well logging, mud logging, or indoor testing;
collecting, by a ground recording instrument vehicle, the measurement signals from the inductive device in real time;
determining, by one or more processors, multiple physical parameters of the orthotropic rock based on the measurement signals, 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, by the one or more processors, an orthotropic rock physics model based on the multiple physical parameters;
determining, by the one or more processors based on the orthotropic rock physics model, stiffness coefficients;
determining, by the one or more processors 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, 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;
v<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;
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, by the one or more processors 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, by the one or more processors, 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;
c11 m,2, c12m, c13m, c22m, c23m and c33m denote stiffness coefficients of a dry vertical transverse isotropy (VTI) rock, GPa;
and α11, α22, and α33denote the anisotropy Biot coefficients;
determining, by the one or more processors, 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;
pwdenotes 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, by the one or more processors, 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.

559 more elements

Facts

Application

17/106,270Filed 30 Nov 2020

Priority

CN 201911239424.26 Dec 2019

Published

US 2021/0173976 A110 Jun 2021

Granted

31 Aug 2021

Term ends

Not estimatedThe source records don’t support an estimate.

Classification13 codes

G06F 30/20
Computer-aided design [CAD]: design optimisation, verification or simulation
E21B 49/00
Testing the nature of borehole walls
G01N 33/24
Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00: earth materials
G01V 1/42
Specially adapted for well-logging: using generators in one well and receivers elsewhere or vice versa