Methods for diagnosing control effectiveness of fracture heights in hydraulic fracturing by combining monitoring pressure signals
The embodiments of the present disclosure provide a method for diagnosing control effectiveness of a fracture height in hydraulic fracturing by combining monitoring a pressure signal, comprising: obtaining engineering data and geological data; calculating a fracture slit fluid pressure, a double-logarithmic slope of the fracture slit fluid pressure, and a bedding fracture pressure; updating a growth time of the fracture height and a reference pressure based on the fracture height in hydraulic fracturing; based on determining whether a fracturing construction operation ends, updating the cumulative fracturing time or calculating a ratio of the growth time of the fracture height to the total time of hydraulic fracturing.
1. A method for diagnosing control effectiveness of a fracture height in hydraulic fracturing by combining monitoring a pressure signal, comprising:
S1: obtaining engineering data and geological data of a target oil and gas well, denoting a cumulative fracturing time as t, and setting a time step for simulation computation as Δt, setting a reference pressure p r in an initial state as 0 Pa, and a growth time t p of the fracture height in the initial state as 0 s;
S2: calculating a fracture slit fluid pressure p frac at the cumulative fracturing time t and a double-logarithmic slope n of the fracture slit fluid pressure at the cumulative fracturing time, and calculating a bedding fracture pressure p e based on a bedding dip angle;
wherein the fracture slit fluid pressure p frac at the cumulative fracturing time t is calculated by a following equation:
p
frac
=
p
s
-
8
ρ
q
2
π
2
m
2
d
p
4
(
1
)
where p frac denotes the fracture slit fluid pressure at the cumulative fracturing time t in Pa; p s denotes a pressure inside a wellbore of a target fracturing section in Pa; ρ denotes a density of fracturing fluid in kg/m 3 ; q denotes a displacement of fracturing fluid of a perforation cluster in m 3 /s; m denotes a perforation number of the perforation cluster, which is dimensionless; and d p denotes a perforation diameter of the perforation cluster in m;
the double-logarithmic slope n of the fracture slit fluid pressure at the cumulative fracturing time is calculated by a following equation:
n
=
log
10
(
p
frac
-
p
r
1000000
)
log
10
(
Δ
t
)
(
2
)
where n denotes the double-logarithmic slope of the fracture slit fluid pressure, which is dimensionless; p r denotes the reference pressure in Pa; and Δt denotes the time step s;
the bedding fracture pressure p e is calculated by a following equation:
p
e
=
σ
min
+
σ
h
2
+
σ
min
-
σ
h
2
cos
(
π
-
2
α
)
+
R
t
(
3
)
where p e denotes the bedding fracture pressure in Pa; σ min denotes a minimum horizontal principal stress in Pa; σ h denotes a vertical stress in Pa; α denotes the bedding dip angle in rad; and R t denotes a bedding tensile strength in Pa;
S3: determining whether the fracture height in hydraulic fracturing grows at the cumulative fracturing time t based on the fracture slit fluid pressure p frac , the double-logarithmic slope n of the fracture slit fluid pressure, and the bedding fracture pressure p e :
in response to p frac >pe and |n|<0.1, determining the fracture height in hydraulic fracturing not growing at the cumulative fracturing time t; and
in response to p frac ≤pe or |n|≥0.1, determining the fracture height in hydraulic fracturing growing at the cumulative fracturing time t, updating the growth time t p of the fracture height to t p +Δt, and updating the reference pressure p r to p frac ;
S4: determining whether a fracturing construction operation ends based on the cumulative fracturing time t and a total time of hydraulic fracturing T a :
in response to t<T a , determining the fracturing construction operation not ending, updating the cumulative fracturing time t to t+Δt, and repeating step S2 to step S4; and
in response to t≥T a , determining the fracturing construction operation ending and proceeding to S5; and
S5: calculating a ratio G of the growth time t p of the fracture height to the total time of hydraulic fracturing T a , and diagnosing the control effectiveness of the fracture height based on the ratio G, wherein the smaller the ratio G is, the better the control effectiveness of the fracture height is.
2. The method of claim 1 , wherein the step S3 further includes:
in response to determining the fracture height hydraulic fracturing not growing at the cumulative fracturing time t, determining an acquisition frequency of a pressure sensor based on a current fracture height in hydraulic fracturing and controlling the pressure sensor to reacquire a pressure at a wellhead based on the acquisition frequency.
3. The method of claim 1 , wherein the step S5 further includes:
in response to determining the control effectiveness of the fracture height being less than a preset effectiveness threshold value, determining an updated injection rate; and
pumping the fracturing fluid to the wellbore at the updated injection rate by controlling a fracturing device to regulate a pumping pressure.
4. The method of claim 1 , wherein in the step S1, the engineering data includes a length of the wellbore L w between an oil and gas wellhead and the target fracturing section, a hydrostatic pressure p g between the oil and gas wellhead and the target fracturing section, an inner diameter D of the wellbore, a number N of a perforation cluster of the target fracturing section, a perforation number m of the perforation cluster, and a perforation diameter d p of the perforation cluster, a total displacement Q of the fracturing fluid, a viscosity of μ the fracturing fluid, a density ρ of the fracturing fluid, a concentration G c of a thickening agent, a concentration G p of a proppant, and the total time of hydraulic fracturing T a ; and
the geological data includes the minimum horizontal principal stress σ min , the vertical stress σ h , the bedding dip angle α, and the bedding tensile strength R t .
5. The method of claim 1 , wherein the pressure inside the wellbore of the target fracturing section p s is calculated by a following equation:
p s =p o −p f +p g (4)
where p o denotes a pressure monitored at a wellhead in Pa; p f denotes a frictional resistance of the fracturing fluid flowing along the wellbore in Pa; and p g denotes the hydrostatic pressure p g between an oil and gas wellhead and the target fracturing section in Pa.
6. The method of claim 5 , wherein the frictional resistance p f of the fracturing fluid flowing along the wellbore is calculated by a following equation:
p f =σp c (5)
where σ denotes a drag reduction ratio, which is dimensionless; and p c denotes a frictional resistance of clear water flowing along the wellbore in Pa.
7. The method of claim 6 , wherein the drag reduction ratio σ is calculated by a following equation:
ln
(
1
σ
)
=
2.20323
-
2.4457
u
-
0.6016
G
c
u
-
0.1639
ln
G
c
-
2.3367
*
10
-
4
G
p
e
0.11983
G
c
(
6
)
where u denotes a flow rate of the fracturing fluid in the wellbore in m/s; G c denotes a concentration of a thickening agent in kg/m 3 ; and G p denotes a concentration of a proppant in kg/m 3 ; and
the frictional resistance p c of the clear water flowing along the wellbore is calculated by a following equation:
p
c
=
2
f
ρ
u
2
L
w
2
D
(
7
)
where f denotes a Fanning friction factor, which is dimensionless; u denotes the flow rate of the fracturing fluid in the wellbore in m/s; L w denotes a length of the wellbore between the oil and gas wellhead and the target fracturing section in m; and D denotes an inner diameter of the wellbore in m.
8. The method of claim 7 , wherein the Fanning friction factor f is calculated by a following equation:
f
=
0.046
Re
-
0.2
(
8
)
Re
=
ρ
uD
μ
(
9
)
where Re denotes Reynolds number of flow of the fracturing fluid, which is dimensionless; and μ denotes a viscosity of the fracturing fluid in Pa·s.
9. The method of claim 7 , wherein the flow rate u of the fracturing fluid in the wellbore is calculated by a following equation:
u
=
1.2732
Q
D
2
(
10
)
where Q denotes the total displacement of the fracturing fluid in m 3 /s.
10. The method of claim 1 , wherein the displacement q of the fracturing fluid of the perforation cluster is calculated by a following equation:
q
=
Q
N
(
11
)
where Q denotes the total displacement of the fracturing fluid in m 3 /s; and N denotes a number of the perforation cluster of the target fracturing section, which is dimensionless.
11. The method of claim 1 , wherein in the step S5, when diagnosing the control effectiveness of the fracture height based on the ratio G, setting a threshold value of the control effectiveness of the fracture height, including a threshold value I and a threshold value II which is greater than the threshold value I, and specific diagnostics criteria are as follows:
in response to determining that G is less than or equal to the threshold value I, determining the control effectiveness of the fracture height is effective;
in response to determining that G is greater than the threshold value I and less than or equal to the threshold value II, determining the control effectiveness of the fracture height is moderate; and
in response to determining that G is greater than the threshold value II, determining the control effectiveness of the fracture height is less effective.