US 8,301,428 B2Granted

Modeling the nonlinear hysteresis response of reservoir media

AssigneeSchlumberger Technology Corporation

InventorsAlexander Lukyanov, Ali Fadili, David Browning, Mark Wakefield

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Abstract

A method of modeling a nonlinear hysteresis response of reservoir media involves obtaining measurements of core samples from the reservoir to generate a multitude of bounding curves representing primary drainage and primary imbibition characteristics of a reservoir, generating, using a processor, a plurality of constitutive equations based on the multitude of bounding curves and a multitude of material functions, the multitude of material functions determined based on material properties associated with the reservoir, generating, using the processor, an output in a form of capillary-pressure scanning curves based on the multitude of constitutive equations, the capillary-pressure scanning curves representing drainage and imbibition behaviors of the reservoir during an oilfield operation, and storing the output.

Claims17

Dependent claims

A method of modeling a nonlinear hysteresis response of reservoir media comprising:

obtaining measurements of core samples from the reservoir to generate a plurality of bounding curves representing primary drainage and primary imbibition characteristics of a reservoir;
generating, using a processor, a plurality of constitutive equations based on the plurality of bounding curves and a plurality of material functions, the plurality of material functions determined based on material properties associated with the reservoir, and wherein the plurality of constitutive equations comprises:
pc=(1−α)pcd+αpci,αε[0,1],
dα/dS=η(α)[sgn({dot over (S)})(χ(S,{dot over (S)})−α)+γ(S,{dot over (S)}),αε[0,1]
where pc is capillary pressure, pcd is a primary drainage curve, pci is a primary imbibition curve, α is a hysteretic function parameter, S is fluid saturation, sgn( ) is sign function, {dot over (S)}=dS/dt is a rate of the fluid saturation, and χ(S,{dot over (S)}), γ(S,{dot over (S)}) and η(α) are at least a portion of the plurality of material functions;
generating, using the processor, an output in a form of capillary-pressure scanning curves based on the plurality of constitutive equations, the capillary-pressure scanning curves representing drainage and imbibition behaviors of the reservoir during an oilfield operation;
and
storing the output.

5 more elements

A non-transitory computer readable medium for modeling a nonlinear hysteresis response of reservoir media, the computer readable medium storing instructions when executed by the processor comprising functionality for:

obtaining a plurality of bounding curves representing primary drainage and primary imbibition characteristics of a reservoir;
generating, using a processor, a plurality of constitutive equations based on the plurality of bounding curves and a plurality of material functions, the plurality of material functions determined based on material properties associated with the reservoir, wherein the plurality of constitutive equations comprise:
p
c
=
(
1
-
α
)
⁢
p
c
d
+
α
⁢
⁢
p
c
i
,
α
∈
[
0
,
1
]
,
⁢
ⅆ
α
ⅆ
S
=
η
⁡
(
α
)
[
sgn
⁡
(
S
.
)
⁢
(
χ
(
S
,
S
.
)
-
α
)
+
γ
(
S
,
S
.
)
]
,
α
∈
[
0
,
1
]
where pc is capillary pressure, pcd is a primary drainage curve, pci is a primary imbibition curve, α is a hysteretic function parameter, S is fluid saturation, sgn( ) is sign function, {dot over (S)}=dS/dt is a rate of the fluid saturation, and χ(S,{dot over (S)}), γ(S,{dot over (S)}) and η(α) are at least a portion of the plurality of material functions;
obtaining, using the processor, an analytical solution of the plurality of constitutive equations as capillary-pressure scanning curves, the capillary-pressure scanning curves representing drainage and imbibition behaviors of the reservoir during an oilfield operation;
and
storing the output.

78 more elements

A computer system for modeling a nonlinear hysteresis response of reservoir media, the system comprising:

a processor,
memory storing instructions when executed by the processor comprising functionality for:
obtaining a plurality of bounding curves representing primary drainage and primary imbibition characteristics of a reservoir;
generating a plurality of constitutive equations based on the plurality of bounding curves and a plurality of material functions, the plurality of material functions determined based on material properties associated with the reservoir, wherein the plurality of constitutive equations comprises:
p
c
=
(
1
-
α
)
⁢
p
c
d
+
α
⁢
⁢
p
c
i
,
α
∈
[
0
,
1
]
,
⁢
ⅆ
α
ⅆ
S
=
η
⁡
(
α
)
[
sgn
⁡
(
S
.
)
⁢
(
χ
(
S
,
S
.
)
-
α
)
+
γ
(
S
,
S
.
)
]
,
α
∈
[
0
,
1
]
where pc is capillary pressure, pcd is a primary drainage curve, pci is a primary imbibition curve, α is a hysteretic function parameter, S is fluid saturation, sgn( ) is sign function, {dot over (S)}=dS/dt is a rate of the fluid saturation, and χ(S,{dot over (S)}), γ(S,{dot over (S)}) and η(α) are at least a portion of the plurality of material functions;
obtaining a numerical solution of the plurality of constitutive equations as capillary-pressure scanning curves, the capillary-pressure scanning curves representing drainage and imbibition behaviors of the reservoir during an oilfield operation;
and
displaying the output.

80 more elements

Dependencies are inferred from the claim text.

Facts

Application: 12/491,316Filed 25 Jun 2009 · us provisional application
Priority: 1 Jul 2008
Published: US 2010/0004914 A17 Jan 2010
Granted: 30 Oct 2012
Term ends: Not estimatedThe source records don’t support an estimate.

Classification9 codes

G06F 30/20
Computer-aided design [CAD]: design optimisation, verification or simulation
E21B 43/00
Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials
G01V 11/00
Prospecting or detecting by methods combining techniques covered by two or more
G01V 20/00
Geomodelling in general