# US 12,768,243 B2 · Method and apparatus for controlling temporary plugging construction in perforation boreholes

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- Number: US 12,768,243 B2
- Document ID: US12768243B2
- Status: Granted
- Kind: B2
- Application number: 19/271,778
- Filed: 2025-07-17
- Published: 2026-01-29
- Granted: 2026-10-20
- Earliest claimed: 2025-07-17
- Applicants: China University of Petroleum (Beijing); STenergy LLC
- Inventors: Ben Li; Quanjun Wang; Hui Li
- Web page: https://patentgrep.com/patent/US12768243B2

## CPC

- E21B 33/138: Plastering the borehole wall; Injecting into the formation
- E21B 43/267: reinforcing fractures by propping
- E21B 47/06: Measuring temperature or pressure
- 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
- E21B 2200/20: Computer models or simulations, e.g. for reservoirs under production, drill bits
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS

## Abstract

The present application discloses a method and device for controlling perforation plugging operations. The method comprises: acquiring the pre-plugging fracturing fluid displacement and the target diversion pressure for a perforated interval; invoking a plugging ball quantity model to calculate the target number of plugging balls; computing the theoretical diversion pressure based on the post-plugging displacement and ball quantity; adjusting the post-plugging displacement when the theoretical pressure does not exceed the target pressure until it does; performing the plugging operation using the determined ball quantity and adjusted displacement; determining whether the plugging is effective by comparing the bottomhole pressure difference before and after the operation with the target diversion pressure. This method enables accurate determination of the number of plugging balls and fluid displacement after plugging, thereby ensuring that the fracturing operation meets the designed requirements.

## Claims

### Claim 1

A control method for temporary plugging construction in perforation boreholes, the method comprising:
acquiring, for a target perforation interval, a pre-plugging fracturing fluid displacement, a post-plugging fracturing fluid displacement, a fracturing fluid density, an apparent density of a proppant, a sand ratio, and a target diversion pressure;
retrieving a pre-established model for determining a number of temporary plugging balls for perforation boreholes;
calculating, based on the pre-plugging fracturing fluid displacement, the post-plugging fracturing fluid displacement, the fracturing fluid density, the apparent density of the proppant, the sand ratio, the target diversion pressure, and the pre-established model, a target number of temporary plugging balls;
calculating a theoretical diversion pressure based on the post-plugging fracturing fluid displacement and the target number of temporary plugging balls;
determining whether the theoretical diversion pressure is greater than the target diversion pressure;
in response to determining that the theoretical diversion pressure is not greater than the target diversion pressure, adjusting the post-plugging fracturing fluid displacement until the theoretical diversion pressure exceeds the target diversion pressure, and determining a corresponding adjusted post-plugging fracturing fluid displacement as a target post-plugging fracturing fluid displacement;
performing a temporary plugging fracturing operation for the target perforation interval by injecting the target number of temporary plugging balls and pumping the target post-plugging fracturing fluid displacement;
acquiring a bottomhole pressure at a preset first time before the temporary plugging fracturing operation and a bottomhole pressure at a second time after the temporary plugging fracturing operation; and
determining whether the temporary plugging fracturing operation is effective by comparing a difference between the bottomhole pressure at the second time and the bottomhole pressure at the preset first time with the target diversion pressure.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the pre-established model for determining the target number of temporary plugging balls for perforation boreholes is expressed as:
N
=
ne
(
f
n
-
1
⁢
ln
(
(
Q
2
Q
1
)
-
f
Q
⁢
(
1
-
(
1.31
×
1
⁢
0
-
8
⁢
Q
2
⁢
c
1
2
⁢
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
sz
2
⁢
α
)
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
)
c
2
2
(
P
d
⁢
e
⁢
η
2
⁢
n
2
⁢
d
4
(
1
+
ζ
)
4
⁢
c
1
2
-
Q
2
⁢
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
sz
2
⁢
α
)
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
)
)
)
0.5
)
)
)
where n is the number of perforations in the target perforation interval, e is the base of the natural logarithm, N is the number of temporary plugging balls, fn is the plugging coefficient, fQis the displacement coefficient, Q1 is the pre-plugging fracturing fluid displacement, Q2 is the post-plugging fracturing fluid displacement, c1 is the perforation geometry coefficient, c2 is the plugging perforation geometry coefficient, ρ1 is the fracturing fluid density, ρsz is the apparent density of the proppant, ρsy is the true density of the proppant, α is the sand ratio, pde is the target diversion pressure, η is the perforation open-area ratio, ζ is the perforation expansion ratio, and d is the perforation diameter.

### Claim 3 (depends on 1)

The method according to claim 1, wherein calculating the theoretical diversion pressure based on the post-plugging fracturing fluid displacement and the target number of temporary plugging balls comprises:
calculating the theoretical diversion pressure according to the following equation:
P
de
-
Q
2
=
Q
2
⁢
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
sz
2
⁢
α
)
⁢
(
1
.
3
⁢
1
×
1
⁢
0
-
8
⁢
c
1
2
(
c
2
(
1
-
(
Q
2
Q
1
)
f
Q
⁢
(
N
n
)
f
n
)
)
2
+
1
)
η
2
⁢
n
2
⁢
d
4
(
1
+
ζ
)
4
⁢
c
1
2
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
)
where Pde-Q2 represents the theoretical diversion pressure; Q2 is the post-plugging fracturing fluid displacement; ρl is the density of the fracturing fluid; ρsz is the apparent density of the proppant; ρsy is the true density of the proppant; α is the sand ratio; c1 is the geometry coefficient of the perforation hole; c2 is the geometry coefficient of the plugged perforation; Q1 is the pre-plugging fracturing fluid displacement; fQ is the displacement coefficient; N is the number of temporary plugging balls; n is the number of perforations in the target perforation interval; fnis the plugging coefficient; η is the perforation open-area ratio; ζ is the perforation expansion ratio; and d is the diameter of the perforation.

### Claim 4 (depends on 1)

The method according to claim 1, wherein determining whether the temporary plugging fracturing operation is effective comprises:
in response to determining that the difference between the bottomhole pressure at the second time and the bottomhole pressure at the preset first time is greater than or equal to the target diversion pressure, determining that the temporary plugging fracturing operation is effective;
in response to determining that the difference between the bottomhole pressure at the second time and the bottomhole pressure at the preset first time is less than the target diversion pressure, determining that the temporary plugging fracturing operation is ineffective; and
in response to determining that the temporary plugging fracturing operation is ineffective, adjusting the post-plugging fracturing fluid displacement and re-determining the target number of temporary plugging balls and the target post-plugging fracturing fluid displacement until the temporary plugging fracturing operation is determined to be effective.

### Claim 5 (depends on 1)

The method according to claim 1, wherein adjusting the post-plugging fracturing fluid displacement comprises:
adjusting the post-plugging fracturing fluid displacement in increments of 10 percent.

### Claim 6 (depends on 1)

The method according to claim 1, wherein acquiring the bottomhole pressure at the preset first time before the temporary plugging fracturing operation and the bottomhole pressure at the second time after the temporary plugging fracturing operation comprises:
calculating the bottomhole pressure at the preset first time before the temporary plugging fracturing operation according to the following formula:
P
BHP
⁢
1
=
4.505
×
1
⁢
0
-
1
⁢
9
×
4
.
9
⁢
73
-
a
⁢
10
-
m
2
⁢
m
1
⁢
h
m
⁢
d
⁢
Q
pupm
⁢
1
2.5
-
0.25
a
⁢
ρ
l
1.25
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
sz
2
⁢
α
1
)
m
2
d
tub
6
-
0.75
α
⁢
k
0.25
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
1
)
m
2
+
9.8
×
10
-
6
⁢
h
td
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
s
⁢
z
2
⁢
α
1
)
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
1
)
where: PBHP1 is the bottomhole pressure at the preset first time point before the temporary plugging fracturing operation; Qpupm1 is the fracturing fluid displacement at the preset first time point before the temporary plugging fracturing operation; m1 is the density coefficient of the sand-carrying fluid; m2 is the flow regime coefficient of the sand-carrying fluid; k is the consistency coefficient of the fracturing fluid; dtub is the internal diameter of a fracturing string; htd is the true vertical depth of the fracturing interval; hmd is the measured depth of the fracturing interval; α is the flow behavior index of the fracturing fluid; ρl is the density of the fracturing fluid; ρsz is the apparent density of the proppant; ρsy is the true density of the proppant; α1 is the sand ratio at the preset first time point before the temporary plugging fracturing operation;
calculating the bottomhole pressure at the second time after the temporary plugging fracturing operation according to the following formula:
P
BHP
⁢
2
=
4.505
×
1
⁢
0
-
1
⁢
9
×
4
.
9
⁢
73
-
a
⁢
10
-
m
2
⁢
m
1
⁢
h
m
⁢
d
⁢
Q
pupm
⁢
2
2.5
-
0.25
a
⁢
ρ
l
1.25
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
sz
2
⁢
α
2
)
m
2
d
tub
6
-
0.75
α
⁢
k
0.25
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
2
)
m
2
+
9.8
×
10
-
6
⁢
h
td
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
s
⁢
z
2
⁢
α
2
)
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
2
)
where PBHP2 is the bottomhole pressure at the second time point after the temporary plugging fracturing operation; Qpupm2 is the fracturing fluid displacement at the second time point after the temporary plugging fracturing operation; α2 is the sand ratio at the second time point after the temporary plugging fracturing operation.

### Claim 7 (depends on 6)

The method according to claim 6, wherein the density coefficient and the flow regime coefficient of the sand-carrying fluid are determined by:
taking a proppant used during the temporary plugging fracturing operation as a target proppant;
acquiring a type and a mesh size of the target proppant;
measuring a bulk density and an apparent density of the target proppant based on the type and the mesh size of the target proppant;
obtaining a target sand ratio and a target displacement;
calculating a sand-carrying fluid density under the target sand ratio based on the bulk density and the apparent density of the target proppant;
calculating a frictional gradient based on friction experiments conducted at the target displacement and under the target sand ratio; and
fitting the density coefficient and the flow regime coefficient of the sand-carrying fluid based on a relationship among the frictional gradient, the sand-carrying fluid density under the target sand ratio, the density coefficient, and the flow regime coefficient of the sand-carrying fluid.

### Claim 8 (depends on 7)

The method according to claim 7, wherein calculating the sand-carrying fluid density under the target sand ratio based on the bulk density and the apparent density of the target proppant comprises:
calculating the sand-carrying fluid density under the target sand ratio according to the following formula:
ρ
ls
-
α
=
(
ρ
l
⁢
ρ
s
⁢
v
+
ρ
sz
2
⁢
α
)
(
ρ
s
⁢
v
+
ρ
s
⁢
z
⁢
α
)
where ρls-α is the sand-carrying fluid density;
the frictional gradient is calculated according to the following formula:
G
ls
-
α
=
P
/
L
where Gls-α is the frictional gradient, P is the frictional resistance, and L is the length of the target conduit;
the relationship among the frictional gradient, the sand-carrying fluid density coefficient, the sand-carrying fluid flow regime coefficient, and the sand-carrying fluid density under the target sand ratio is expressed by the following formula:
G
ls
-
α
=
m
1
⁢
ρ
ls
-
α
m
2
.

### Claim 9

A control apparatus for temporary plugging construction in perforation boreholes, comprising:
one or more processors; and
one or more non-transitory computer-readable storage media storing instructions that, when executed by the one or more processors, cause the apparatus to:
acquire, for a target perforation interval, a pre-plugging fracturing fluid displacement, a post-plugging fracturing fluid displacement, a fracturing fluid density, an apparent density of a proppant, a sand ratio, and a target diversion pressure;
retrieve a pre-established model for determining a number of temporary plugging balls for perforation boreholes;
calculate, based on the pre-plugging fracturing fluid displacement, the post-plugging fracturing fluid displacement, the fracturing fluid density, the apparent density of the proppant, the sand ratio, the target diversion pressure, and the pre-established model, a target number of temporary plugging balls;
calculate a theoretical diversion pressure based on the post-plugging fracturing fluid displacement and the target number of temporary plugging balls;
determine whether the theoretical diversion pressure exceeds the target diversion pressure;
in response to determining that the theoretical diversion pressure does not exceed the target diversion pressure, adjust the post-plugging fracturing fluid displacement until the theoretical diversion pressure exceeds the target diversion pressure, and determine a corresponding adjusted post-plugging fracturing fluid displacement as a target post-plugging fracturing fluid displacement;
perform a temporary plugging fracturing operation for the target perforation interval by injecting the target number of temporary plugging balls and pumping the target post-plugging fracturing fluid displacement;
acquire a bottomhole pressure at a preset first time before the temporary plugging fracturing operation and a bottomhole pressure at a second time after the temporary plugging fracturing operation; and
determine whether the temporary plugging fracturing operation is effective by comparing a difference between the bottomhole pressure at the second time and the bottomhole pressure at the preset first time with the target diversion pressure.

### Claim 10 (depends on 1, 2, 3, 4, 5, 6, 7, 8)

An electronic device, comprising one or more processors and a memory storing instructions that, when executed by the one or more processors, cause the electronic device to perform the method according to any one of claims 1-8.

### Claim 11 (depends on 1, 2, 3, 4, 5, 6, 7, 8)

A non-transitory computer-readable storage medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method according to any one of claims 1-8.