US2014350860A1PendingUtilityA1
Systems, methods, and computer-readable media for continuous capillary pressure estimation
Est. expiryMay 24, 2033(~6.9 yrs left)· nominal 20-yr term from priority
E21B 49/008E21B 49/00G01V 11/00
39
PatentIndex Score
0
Cited by
0
References
0
Claims
Abstract
Provided are methods, systems, and computer-readable media for determining capillary pressure in a basin/reservoir. Well log data is obtained that includes permeability log data, porosity log data, water saturation log data, and oil saturation log data. Thomeer parameters for a multi-pore system of a Thomeer model are determined by evaluating an objective function that measures the mismatch between the well log data and modeled data having the Thomeer parameters as input. The objective function is iteratively evaluated using linear equality constraints, linear inequality constraints, and nonlinear equality constraints until convergence criteria are met.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A computer-implemented method for determining capillary pressure in a reservoir, the method comprising:
accessing well log data from a well log for a well, the well log data comprising permeability log data, porosity log data, water saturation log data, and oil saturation log data; determining Thomeer parameters from the permeability log data, the porosity log data, the water saturation log data, and the oil saturation log data, the Thomeer parameters comprising a fractional bulk volume, a pore geometrical factor, and a minimum entry pressure, the determining comprising:
determining a modeled permeability;
determining a modeled porosity;
determining a modeled water saturation, and
evaluating an objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints, the objective function comprising:
F
(
T
)
=
w
2
(
1
-
Sw
FAL
)
-
So
(
T
)
2
+
(
1
-
w
)
2
T
-
T
^
2
wherein T is the Thomeer parameters,
Sw FAL is the value of the water saturation data,
So(T) is a modeled oil saturation;
the one or more linear equality constraints comprising:
∑
i
=
1
n
Bv
i
(
Pc
)
=
α
*
φ
FAL
wherein Bv i is a fractional bulk volume occupied by mercury,
Pc is an applied capillary pressure;
α is the conversion factor from mercury-air to oil-water,
n is the number of pore systems in the reservoir,
φ FAL is the porosity data;
the one or more linear inequality constraints comprising:
Bv i min ≦Bv i ( Pc )≦ Bv i max for 1≦1 ≦n
G i min ≦G i ≦G i max for 1 ≦i≦n
wherein G i is the pore geometrical factor,
Pd i min ≦Pd i ≦Pd i max for 1 ≦i≦n
wherein Pd i is a minimum entry pressure,
If Bv i ( Pc )≠0 then Bv i+1 ( Pc ) Bv i ( Pc ) for 1 ≦i≦n− 1,
Pd i ≦Pd i+1 for 1 ≦i≦n− 1, and
the one or more nonlinear equality constraints comprising:
K ( T )= K FAL
wherein K(T) is the modeled permeability,
K FAL is the permeability log data; and
determining the capillary pressure of the reservoir using a Thomeer model having the determined Thomeer parameters.
2 . The computer-implemented method of claim 1 , wherein the modeled permeability comprises:
K
(
T
)
=
506
*
∑
i
=
1
n
Bv
i
(
Pc
)
Pd
i
2
exp
(
-
4.43
G
i
)
.
3 . The computer-implemented method of claim 1 , wherein the modeled porosity comprises:
φ
(
T
)
=
α
∑
i
-
1
n
Bv
i
.
4 . The computer-implemented method of claim 1 , wherein the modeled oil saturation comprises:
So
i
(
G
i
,
Pd
i
)
=
Bv
∞
*
exp
(
-
G
i
log
(
Pc
)
-
log
(
Pd
i
)
)
;
and
So
(
T
)
=
1
φ
∑
i
=
1
n
Bv
i
*
So
i
(
G
i
,
Pd
i
)
.
5 . The computer implemented method of claim 1 , wherein the Thomeer model comprises:
B
v
(
P
c
)
≈
{
φ
·
exp
(
-
G
log
(
P
c
)
-
log
(
P
d
)
)
for
P
c
>
P
d
0
elsewhere
}
6 . The computer-implemented method of claim 1 , wherein evaluating the objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints comprises iteratively evaluating the objective function until convergence criteria are met.
7 . The computer-implemented method of claim 1 , wherein evaluating the objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints comprises iteratively evaluating the objective function evaluating the objective function using sequential quadratic programming (SQP).
8 . The computer-implemented method of claim 1 , wherein the well log comprises a fluid analysis log.
9 . The computer-implemented method of claim 1 , wherein the reservoir comprises an oil reservoir.
10 . The computer-implemented method of claim 1 , comprising providing the capillary pressures to a reservoir modeling system, a reservoir simulation system, or a combination thereof.
11 . A non-transitory tangible computer-readable storage medium having executable computer code stored thereon for determining capillary pressure in a reservoir, the computer code comprising a set of instructions that causes one or more processors to perform the following operations:
accessing well log data from a well log for a well, the well log data including permeability log data, porosity log data, water saturation log data, and oil saturation log data; determining Thomeer parameters from the permeability log data, the porosity log data, the water saturation log data, and the oil saturation log data, the Thomeer parameters comprising a fractional bulk volume, a pore geometrical factor, and a minimum entry pressure, the determining comprising:
determining a modeled permeability;
determining a modeled porosity;
determining a modeled water saturation, and
evaluating an objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints, the objective function comprising:
F
(
T
)
=
w
2
(
1
-
Sw
FAL
)
-
So
(
T
)
2
+
(
1
-
w
)
2
T
-
T
^
2
wherein T is the Thomeer parameters,
Sw FAL is the value of the water saturation data,
So(T) is a modeled oil saturation;
the one or more linear equality constraints comprising:
∑
i
=
1
n
Bv
i
(
Pc
)
=
α
*
φ
FAL
wherein Bv i is a fractional bulk volume occupied by mercury,
Pc is an applied capillary pressure;
α is the conversion factor from mercury-air to oil-water,
n is the number of pore systems in the reservoir,
φ FAL is the porosity data;
the one or more linear inequality constraints comprising:
Bv i min ≦Bv i ( Pc )≦ Bv i max for 1 ≦i≦n
G i min ≦G i ≦G i max for 1 ≦i≦n
wherein G i is the pore geometrical factor,
Pd i min ≦Pd i ≦Pd i max for 1 ≦i≦n
wherein Pd i is a minimum entry pressure,
If Bv i ( Pc )≠0 then Bv i+1 ( Pc )≦ Bv i ( Pc ) for 1 ≦i≦n− 1,
Pd i ≦Pd i+1 for 1 ≦i≦n− 1, and
the one or more nonlinear equality constraints comprising:
K( T )= K FAL
wherein K(T) is the modeled permeability,
K FAL is the permeability log data; and
determining the capillary pressures of the reservoir using a Thomeer model having the determined Thomeer parameters.
12 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein the modeled permeability comprises:
So
i
(
G
i
,
Pd
i
)
=
Bv
∞
*
exp
(
-
G
i
log
(
Pc
)
-
log
(
Pd
i
)
)
;
and
So
(
T
)
=
1
φ
∑
i
=
1
n
Bv
i
*
So
i
(
G
i
,
Pd
i
)
.
13 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein the modeled porosity comprises:
φ
(
T
)
=
α
∑
i
-
1
n
Bv
i
.
14 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein the modeled oil saturation comprises:
K
(
T
)
=
506
*
∑
i
=
1
n
Bv
i
(
Pc
)
Pd
i
2
exp
(
-
4.43
G
i
)
.
15 . The computer implemented method of claim 1 , wherein the Thomeer model comprises:
B
v
(
P
c
)
≈
{
φ
·
exp
(
-
G
log
(
P
c
)
-
log
(
P
d
)
)
for
P
c
>
P
d
0
elsewhere
}
16 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein evaluating the objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints comprises iteratively evaluating the objective function until convergence criteria are met.
17 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein evaluating the objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints comprises iteratively evaluating the objective function evaluating the objective function using sequential quadratic programming (SQP).
18 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein the well log comprises a fluid analysis log.
19 . The non-transitory tangible computer-readable storage medium of claim 12 , wherein the reservoir comprises an oil reservoir.
20 . A system for determining capillary pressure in a basin and reservoir, the system comprising:
well log data, the well log data comprising permeability log data, porosity log data, water saturation log data, and oil saturation log data; one or more processors; a tangible non-transitory computer-readable memory having executable computer code stored thereon for determining capillary pressure in a reservoir, the computer code comprising a set of instructions that causes the one or more processors to perform the following operations:
determining Thomeer parameters from the permeability log data, the porosity log data, the water saturation log data, and the oil saturation log data, the Thomeer parameters comprising a fractional bulk volume, a pore geometrical factor, and a minimum entry pressure, the determining comprising:
evaluating an objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints, the objective function comprising:
F
(
T
)
=
w
2
(
1
-
Sw
FAL
)
-
So
(
T
)
2
+
(
1
-
w
)
2
T
-
T
^
2
wherein T is the Thomeer parameters,
Sw FAL is the value of the water saturation data,
So(T) is a modeled oil saturation;
the one or more linear equality constraints comprising:
∑
i
=
1
n
Bv
i
(
Pc
)
=
α
*
φ
FAL
wherein Bv i is a fractional bulk volume occupied by mercury,
Pc is an applied capillary pressure;
α is the conversion factor from mercury-air to oil-water,
n is the number of pore systems in the reservoir,
φ FAL is the porosity data;
the one or more linear inequality constraints comprising:
Bv i min ≦Bv i ( Pc )≦ Bv i max for 1 ≦i≦n
G i min ≦G i ≦G i max for 1 ≦i≦n
wherein G i is the pore geometrical factor,
Pd i min ≦Pd i ≦Pd i max for 1 ≦i≦n
wherein Pd i is a minimum entry pressure,
If Bv i ( Pc )≠0 then Bv i+1 ( Pc )≦ Bv i ( Pc ) for 1 ≦i≦n− 1,
Pd i ≦Pd i+1 for 1 ≦i≦n− 1, and
the one or more nonlinear equality constraints comprising:
K ( T )= K FAL
wherein K(T) is the modeled permeability,
K FAL is the permeability log data; and
determining the capillary pressures of the reservoir using a Thomeer model having the determined Thomeer parameters.
21 . The system of claim 20 , tangible non-transitory computer-readable memory storing a modeled permeability, a modeled porosity, and a modeled water saturation.
22 . The system of claim 21 , wherein the modeled permeability comprises:
K
(
T
)
=
506
*
∑
i
=
1
n
Bv
i
(
Pc
)
Pd
i
2
exp
(
-
4.43
G
i
)
.
23 . The system of claim 21 , wherein the modeled porosity comprises:
φ
(
T
)
=
α
∑
i
-
1
n
Bv
i
.
24 . The system of claim 21 , wherein the modeled oil saturation comprises:
So
i
(
G
i
,
Pd
i
)
=
Bv
∞
*
exp
(
-
G
i
log
(
Pc
)
-
log
(
Pd
i
)
)
;
and
So
(
T
)
=
1
φ
∑
i
=
1
n
Bv
i
*
So
i
(
G
i
,
Pd
i
)
.
25 . The system of claim 20 , the tangible non-transitory computer-readable memory storing a the Thomeer model, the Thomeer model comprising:
B
v
(
P
c
)
≈
{
φ
·
exp
(
-
G
log
(
P
c
)
-
log
(
P
d
)
)
for
P
c
>
P
d
0
elsewhere
}
26 . The system of claim 20 , wherein evaluating the objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints comprises iteratively evaluating the objective function until convergence criteria are met.
27 . The system of claim 20 , wherein evaluating the objective function based on one or more linear equality constraints, one or more linear inequality constraints, and one or more nonlinear equality constraints comprises iteratively evaluating the objective function evaluating the objective function using sequential quadratic programming (SQP).
28 . The system of claim 20 , wherein the well log comprises a fluid analysis log.
29 . The system of claim 20 , wherein the reservoir comprises an oil reservoir.
30 . The system of claim 20 , comprising a network coupled to the one or more processor.
31 . The system of claim 20 , comprising providing, over the network, the capillary pressures to a reservoir modeling system, a reservoir simulation system, or a combination thereof.
32 . A computer-implemented method for determining capillary pressure in a reservoir, the method comprising:
accessing well log data from a well log for a well, the well log data comprising permeability log data, porosity log data, water saturation log data, and oil saturation log data; evaluating an objective function measuring the different between the permeability log data and a modeled permeability, the porosity log data and a modeled porosity, and the oil saturation log data and a modeled oil saturation, the modeled permeability, the modeled porosity, and the modeled oil saturation each a function of Thomeer parameters; and determining the capillary pressures of the reservoir using a Thomeer model having the Thomeer parameters, the Thomeer parameters comprising a fractional bulk volume, a pore geometrical factor, and a minimum entry pressure for each pore system.
33 . The computer-implemented method of claim 32 , wherein evaluating the objective function measuring the different between the permeability log data and a modeled permeability, the porosity log data and a modeled porosity, and the oil saturation log data and a modeled oil saturation comprises evaluating the objective function based on a linear equality constraint dependent on the porosity log data, a linear inequality constraint, and a nonlinear equality constraint dependent on the permeability log data.Cited by (0)
No later patents cite this yet.
References (0)
No backward citations on record.