# US 10,872,182 B2 · Method for the development of a fluid deposit traversed by fractures by means of a flow simulation based on an exchange flow and a corrective factor

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- Number: US 10,872,182 B2
- Document ID: US10872182B2
- Status: Granted
- Kind: B2
- Application number: 15/416,646
- Filed: 2017-01-26
- Published: 2017-07-27
- Granted: 2020-12-22
- Earliest claimed: 2016-01-26
- Assignees: Ifp Energies Nouvelles
- Applicants: IFP Energies nouvelles
- Inventors: Bernard Bourbiaux; Didier Yu Ding
- Web page: https://patentgrep.com/patent/US10872182B2

## CPC

- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- E21B 49/00: Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
- G06F 17/11: for solving equations {, e.g. nonlinear equations, general mathematical optimization problems (optimization specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G06F 2111/10: Numerical modelling
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS

## Abstract

The present invention relates to a method for optimizing a fluid deposit traversed by a fracture network. For this method, the deposit is discretized in a meshed representation, a “dual medium” approach is used, and the exchange flows are determined between the meshes, together with corrective factors. The corrective factors are dependent on the initial pressure and the minimum production pressure of the deposit. The fluid flows in the deposit are simulated by means of these flows and these corrective factors.

## Claims

### Claim 1

A method for development of a fluid deposit traversed by a fracture network, based on measurements of properties relating to the fluid deposit and a meshed representation of the fluid deposit which is constructed with each mesh of the representation comprising a matrix medium and a fractured medium, and in which an initial pressure of the fluid deposit and a minimum production pressure of the fluid deposit are known, comprising:
a) determining for each mesh an exchange flow that takes place between the matrix medium and the fractured medium;
b) determining exchange flow corrective factors respectively calculated for longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes for correcting the exchange flow by use of the initial pressure of the fluid deposit and the minimum production pressure of the fluid deposit with the exchange flow corrective factors of the exchange flow being obtained by a formulation of pseudo-pressure by formulation of flow equations of the fluid deposit which are determined for the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes;
c) simulating flows of the fluid in the fluid deposit with a flow simulator, using the exchange flow and the corrective factors and wherein the exchange flow used for the simulation of the flows is multiplied by the exchange flow corrective factors; and
d) optimizing the development of the fluid deposit by use of the simulation of the flows in the fluid deposit with the flow simulator; and wherein
the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes are determined from an initial pressure of the fluid deposit and a final pressure of wells drilled during the development of the fluid deposit and transitioning between the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes which utilizes calculation of an average value of the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes.

### Claim 2 (depends on 1)

The method as claimed in claim 1, wherein the steps a) and b) are performed in order.

### Claim 3 (depends on 1)

The method as claimed in claim 1, wherein the corrective factor of the exchange flow is obtained by a formulation of the pseudo-pressure by flow equations of the fluid deposit.

### Claim 4 (depends on 2)

The method as claimed in claim 2, wherein the corrective factor of the exchange flow is obtained by a formulation of the pseudo-pressure by flow equations of the fluid deposit.

### Claim 5 (depends on 1)

The method as claimed in claim 1, wherein the corrective factor for shorter term transient exchange regimes in one dimension βm-1DST(P) is written as follows:
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
μ
ref
⁢
Z
ref
P
_
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
with
wherein Pref is reference pressure;
μref is viscosity at the reference pressure;
Zref is compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is compressibility factor of the fluid at the pressure P;
mf is pseudo-pressure at a final state;
mi is pseudo-pressure at an initial state of the reservoir;
Pf is pressure of the reservoir at a final state; and
m(P) is an average pseudo-pressure of the matrix block defined by a relationship:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
.

### Claim 6 (depends on 2)

The method as claimed in claim 2, wherein the corrective factor for shorter term transient exchange regimes in one dimension βm-1DST(P) is written as follows:
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
μ
ref
⁢
Z
ref
P
_
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
with
wherein Pref is reference pressure;
μref is viscosity at the reference pressure;
Zref is compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is compressibility factor of the fluid at the pressure P;
mf is pseudo-pressure at a final state;
mi is pseudo-pressure at an initial state of the reservoir;
Pf is pressure of the reservoir at a final state; and
m(P) is an average pseudo-pressure of the matrix block defined by a relationship:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
.

### Claim 7 (depends on 4)

The method as claimed in claim 4, wherein the corrective factor for shorter term transient exchange regimes in one dimension βm-1DST(P) is written as follows:
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
with
wherein Pref is reference pressure;
μref is viscosity at the reference pressure;
Zref is compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is compressibility factor of the fluid at the pressure P;
mf is pseudo-pressure at a final state;
mi is pseudo-pressure at an initial state of the reservoir;
Pf is pressure of the reservoir at a final state; and
m(P) is an average pseudo-pressure of the matrix block defined by a relationship:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
.

### Claim 8 (depends on 4)

The method as claimed in claim 4, wherein the corrective factor for shorter term transient exchange regimes in one dimension is written as follows:
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
with
wherein Pref is reference pressure;
μref is viscosity at the reference pressure;
Zref is compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is compressibility factor of the fluid at the pressure P;
mf is pseudo-pressure at a final state;
mi is pseudo-pressure at an initial state of the reservoir;
Pf is pressure of the reservoir at a final state; and
m(P) is an average pseudo-pressure of the matrix block defined by a relationship:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
.

### Claim 9 (depends on 1)

The method as claimed in claim 1, in which the corrective factor for shorter term transient exchange regimes in two dimensions βm-2DST(P) is written as follows:
βm-2DST(P)=SC·βm-1DST(P) with
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
and
SC
=
1
+
(
1
L
eq
0
2
1
-
1
L
eq
LT
2
)
⁡
[
m
-
m
f
+
m
i
2
m
i
-
m
f
+
m
i
2
]
with
formula of the type: βm-2DST(P)
Pref is a reference pressure;
μref is viscosity at the reference pressure;
Zref is a compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is a compressibility factor of the fluid at the pressure P;
mf is a pseudo-pressure at a final state;
mi is a pseudo-pressure at an initial state of the reservoir;
Pf is a pressure of the reservoir at the final state;
m(P) is an average pseudo-pressure of the matrix block defined as:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
,
wherein
Leq 0 is an equivalent length of a matrix block of one dimension at the initial time of a transient regime; and
LeqST is an equivalent length of a matrix block of one dimension at a final time of a transient regime.

### Claim 10 (depends on 2)

The method as claimed in claim 2, in which the corrective factor for shorter term transient exchange regimes in two dimensions βm-2DST(P) is written as follows:
βm-2DST(P)=SC·βm-1DST(P) with
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
and
SC
=
1
+
(
1
L
eq
0
2
1
-
1
L
eq
LT
2
)
⁡
[
m
-
m
f
+
m
i
2
m
i
-
m
f
+
m
i
2
]
with
formula of the type: βm-2DST(P)
Pref is a reference pressure,
μref is viscosity at the reference pressure,
Zref is a compressibility factor of the fluid at the reference pressure,
P is an average pressure of a matrix block of the matrix medium,
μ is viscosity of the fluid at a pressure P
Z is a compressibility factor of the fluid at the pressure P,
mf is a pseudo-pressure at a final state
mi is a pseudo-pressure at an initial state of the reservoir,
Pf is a pressure of the reservoir at the final state,
m(P) is an average pseudo-pressure of the matrix block defined as:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
,
wherein
Leq0 is an equivalent length of a matrix block of one dimension at the initial time of a transient regime; and
LeqST is an equivalent length of a matrix block of one dimension at a final time of a transient regime.

### Claim 11 (depends on 3)

The method as claimed in claim 3, in which the corrective factor for shorter term transient exchange regimes in two dimensions βm-2DST(P) is written by as follows:
βm-2DST(P)=SC·βm-1DST(P) with
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
and
SC
=
1
+
(
1
L
eq
0
2
1
-
1
L
eq
LT
2
)
⁡
[
m
-
m
f
+
m
i
2
m
i
-
m
f
+
m
i
2
]
with
formula of the type: βm-2DST(P)
Pref is a reference pressure;
μref is viscosity at the reference pressure;
Zref is a compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is a compressibility factor of the fluid at the pressure P;
mf is a pseudo-pressure at a final state;
mi is a pseudo-pressure at an initial state of the reservoir;
Pf is a pressure of the reservoir at the final state;
m(P) is an average pseudo-pressure of the matrix block defined as:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
,
wherein
Leq0 is an equivalent length of a matrix block of one dimension at the initial time of a transient regime; and
LeqST is an equivalent length of a matrix block of one dimension at a final time of a transient regime.

### Claim 12 (depends on 4)

The method as claimed in claim 4, in which the corrective factor for shorter term transient exchange regimes in two dimensions βm-2DST(P) is written as follows:
βm-2DST(P)=SC·βm-1DST(P) with
β
m
-
1
⁢
⁢
D
ST
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
8
π
3
⁢
(
m
f
-
m
i
)
2
[
P
f
-
P
_
]
⁡
[
m
⁡
(
P
_
)
-
m
i
]
and
SC
=
1
+
(
1
L
eq
0
2
1
-
1
L
eq
LT
2
)
⁡
[
m
-
m
f
+
m
i
2
m
i
-
m
f
+
m
i
2
]
with
formula of the type:
Pref is a reference pressure;
μref is viscosity at the reference pressure;
Zref is a compressibility factor of the fluid at the reference pressure;
P is an average pressure of a matrix block of the matrix medium;
μ is viscosity of the fluid at a pressure P;
Z is a compressibility factor of the fluid at the pressure P;
mf is a pseudo-pressure at a final state;
mi is a pseudo-pressure at an initial state of the reservoir;
Pf is a pressure of the reservoir at the final state;
m(P) is an average pseudo-pressure of the matrix block defined as;
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
,
wherein
Leq0 is an equivalent length of a matrix block of one dimension at the initial time of a transient regime; and
LeqST is an equivalent length of a matrix block of one dimension at a final time of a transient regime.

### Claim 13 (depends on 1)

The method as claimed in claim 1, in which the corrective factor for longer term pseudo-permanent exchange regimes in one dimension βm-1DLT(P) or in two dimensions βm-2DLT(P) is written:
by a formula of the type:
β
m
-
1
⁢
⁢
D
LT
⁡
(
P
_
)
=
β
m
-
2
⁢
⁢
D
LT
⁡
(
P
_
)
=
P
ref
/
μ
ref
⁢
Z
ref
P
_
/
μ
⁢
⁢
Z
⁢
[
m
f
-
m
⁡
(
P
_
)
]
[
P
f
-
P
_
]
with
Pref is a reference pressure;
μref is viscosity at said reference pressure;
Zref is a compressibility factor of said fluid at said reference pressure;
P is an average pressure of a matrix block of said matrix medium;
μ is viscosity of said fluid at the pressure P;
Z is a compressibility factor of said fluid at the pressure P;
mf is pseudo-pressure at a final state;
m is pseudo-pressure at an initial state of the reservoir;
Pf is pressure of the reservoir at a final state; and
m(P) is an average pseudo-pressure of said matrix block defined by the equation:
m
⁡
(
P
_
)
=
μ
ref
⁢
Z
ref
P
ref
⁢
∫
P
ref
P
_
⁢
P
_
μ
⁢
⁢
Z
⁢
d
⁢
P
_
.

### Claim 14 (depends on 1)

The method as claimed in claim 1, in which prior to step a) a plurality of values of the corrective factors are determined and stored, and in step b), the corrective factor is determined from the stored values.

### Claim 15 (depends on 2)

The method as claimed in claim 2, in which prior to step a) a plurality of values of the corrective factors are determined and stored, and in step b), the corrective factor is determined from the stored values.

### Claim 16 (depends on 1)

The method as claimed in claim 1, wherein the exchange flow fp is calculated by from a relationship: fp=CPmpΔϕp, with C being a geometric coefficient defined by C=ΔA·ΔB·ΔC·IV(X), with ΔA, ΔB, ΔC being the dimensions of the mesh, IV(X) being a shape factor, Δϕp being a the potential difference and Pmp being a property relating to the fluids and to the matrix medium.

### Claim 17

A computer program product stored non transiently on computer readable medium which is executed by a processor, which performs a method used for developing a fluid deposit traversed by a fracture network based on measurements of properties relating to the fluid deposit, a meshed representation of the fluid deposit is constructed with each mesh of the representation comprising a matrix medium and a fractured medium, and in which an initial pressure of the fluid deposit and a minimum production pressure of the fluid deposit are known, comprising;
a) determining for each mesh an exchange flow that takes place between the matrix medium and the fractured medium;
b) determining exchange flow corrective factors respectively calculated for longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes for correcting the exchange flow by use of the initial pressure of the fluid deposit and the minimum production pressure of the fluid deposit with the exchange flow corrective factors of the exchange flow being obtained by a formulation of pseudo-pressure by formulation of flow equations of the fluid deposit which are determined for the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes;
c) simulating flows of the fluid in the fluid deposit with a flow simulator, using the exchange flow and the corrective factors and wherein the exchange flow used for the simulation of the flows is multiplied by the exchange flow corrective factors; and
d) optimizing the development of the fluid deposit by use of the simulation of the flows in the fluid deposit with the flow simulator; and wherein
the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes are determined from an initial pressure of the fluid deposit and a final pressure of wells drilled during the development of a fluid deposit and transitioning between the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes which utilizes calculation of an average value of the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes.

### Claim 18

A method for the development of a fluid deposit traversed by a fracture network based on measurements of properties relating to the fluid deposit, a meshed representation of the fluid deposit being constructed with each mesh of the representation comprising a matrix medium and a fractured medium, and an initial pressure of the fluid deposit and a minimum production pressure of the fluid deposit being known comprising steps of:
a) determining for each mesh an exchange flow that takes place between the matrix medium and the fractured medium;
b) determining exchange flow corrective factors respectively calculated for longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes for correcting the exchange flow by use of the initial pressure of the fluid deposit and the minimum production pressure of the fluid deposit with the exchange flow corrective factors of the exchange flow being obtained by a formulation of pseudo-pressure by formulation of flow equations of the fluid deposit which are determined for the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes;
c) simulating flows of the fluid in the fluid deposit with a flow simulator, using the exchange flow and the corrective factors and wherein the exchange flow used for the simulation of the flows is multiplied by the exchange flow corrective factors; and
d) optimizing the development of the fluid deposit by use of the simulation of the flows in the fluid deposit with the flow simulator; and wherein
the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes are determined from an initial pressure of the fluid deposit and a final pressure of wells drilled during the development of a fluid deposit and transitioning between the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes which utilizes calculation of an average value of the longer term pseudo-permanent exchange regimes and shorter term transient exchange regimes.

### Claim 19 (depends on 1)

The method as claimed in claim 1 wherein steps a) and b) are performed simultaneously.

### Claim 20 (depends on 18)

The method as claimed in claim 18 wherein steps a) and b) are performed simultaneously.