Methods for optimizing bunch distance of fractured horizontal wells of shale gas
The present disclosure provides a method for optimizing bunch distance of fractured horizontal wells of shale gas, which relates to the technical field of oil exploration. The method comprises first establishing a stress field distribution model for a single fracture; then establishing an induced stress distribution model of segmented single-bunch fracturing for a horizontal well; later establishing an induced stress distribution model of segmented multi-bunch fracturing for a horizontal well; last optimizing fracturing parameters and fracture distance according to the distribution pattern of the induced stress difference. The method considers the stress barrier, stress interference effects, and the variation of the effective net pressure during the synchronous expansion of fractures, so the calculation model is more in line with the actual working conditions, has higher precision, and can provide more accurate theoretical guidance for the optimization design of segmented multi-bunch fracturing of a horizontal well.
1. A method for optimizing bunch distance of fractured horizontal wells of shale gas, characterized in that, the method comprises
establishing a stress field distribution model for a single fracture;
establishing an induced stress distribution model of multi-segment single-bunch fracturing for a horizontal well;
establishing an induced stress distribution model of multi-segment multi-bunch fracturing for a horizontal well;
calculating the induced stress outside a fracture in a segment adjacent to a previous segment;
calculating the induced stress between fractures inside a segment;
calculating the induced stress outside a fracture in a segment adjacent to a next segment;
calculating the horizontal induced stress difference of segmented multi-bunch fracturing for a horizontal well; and
determining a bunch distance, as an optimal bunch distance, at which the horizontal induced stress difference is at a maximum; and
forming the horizontal well having the optimal bunch distance;
wherein establishing the induced stress distribution model of multi-segment multi-bunch fracturing for a horizontal well comprises calculating an effective net pressure of the first fracture in the segment relative to the previous segment, calculating an effective net pressure of each fracture in the segment relative to neighboring fractures in the segment, and calculating an effective net pressure of the last fracture in the segment relative to the next segment;
wherein each segment has three bunches of fractures, wherein the three bunches of fractures of the Nth segment are sequentially recorded as fractures N 1 , N 2 , and N 3 , fracture N 1 is the fracture nearest the (N-1)th segment, fracture N 3 is the fracture the furthest away from the (N -1)th segment, fracture N 2 is the fracture between fracture N 1 and fracture N 3 ;
wherein the effective net pressure of fracture N 1 relative to the previous segment is
P eni (N 1 )=P n −σ h (n−1) 3 ( N 1 )
wherein σ h (n−1) 3 ( N 1 ) is an induced stress in a minimum horizontal geostress direction generated by the third fracture of the (N−1)th segment to fracture N 1 ;
wherein the induced stress generated at any point between fracture N 1 and fracture N 2 is
{
σ
e
n
h
(
N
1
,
N
2
)
=
P
n
sin
β
n
1
2
(
2
l
n
1
r
n
2
)
3
2
-
P
n
[
r
n
1
cos
β
n
1
(
r
n
1
r
n
2
)
1
2
-
1
]
σ
e
n
H
(
N
1
,
N
2
)
=
2
v
P
n
[
r
n
1
cos
β
n
1
(
r
n
1
r
n
2
)
1
2
-
1
]
wherein σ enh (N 1 , N 2 ) is the induced stress in the minimum horizontal geostress direction generated by fracture N 1 to fracture N 2 ; β n1 is an angle of fracture N 1 to a point in the next segment; l n1 is a total length of fracture N 1 ; r n1 is a half length of Fracture N 1 ; r n2 is a half length of fracture N 2 ; σ enH (N 1 , N 2 ) is the induced stress in the maximum horizontal geostress direction generated by fracture N 1 to fracture N 2 ;
wherein the relationship between fracture N 2 and fracture N 3 is
{
σ
e
n
h
(
N
2
,
N
3
)
=
P
n
sin
β
n
2
2
(
2
l
n
2
r
n
3
)
3
2
-
P
n
[
r
n
2
cos
β
n
2
(
r
n
2
r
n
3
)
1
2
-
1
]
σ
enH
(
N
2
,
N
3
)
=
2
v
P
n
[
r
n
2
cos
β
n
2
(
r
n
2
r
n
3
)
1
2
-
1
]
wherein σ enh (N 2 , N 3 ) is the induced stress in the minimum horizontal geostress direction generated by fracture N 2 to fracture N 3 ; β n2 is an angle of fracture N 2 to a point in the next segment; l n2 is a total length of fracture N 2 ; r n2 is a half length of Fracture N 2 ; r n3 is a half length of Fracture N 3 ; σ enH (N 2 , N 3 ) the induced stress in the maximum horizontal geostress direction generated by fracture N 2 to fracture N 3 ;
wherein the effective net pressure of Fracture N 3 relative to the next segment is
p
enr
(
N
3
)
=
p
n
-
∑
i
=
1
N
-
1
σ
h
i
3
(
N
3
)
wherein P enr (N 3 ) is the effective net pressure of fracture N 3 relative to the next segment.
2. The method according to claim 1 , characterized in that, the stress field distribution model for a single fracture is
{
σ
h
=
p
n
(
1
-
a
2
r
(
a
2
r
)
2
+
1
4
+
a
2
r
4
(
(
a
2
r
)
2
+
1
4
)
3
)
σ
H
=
2
p
n
v
(
1
-
a
2
h
(
a
2
r
)
2
+
1
4
)
wherein σ h is the induced stress in the minimum horizontal geostress direction of a fracture σ H is the induced stress in the maximum horizontal geostress direction of a fracture; P n is an original net pressure in a fracture; α is the distance from the fracture center to a measuring point; r is a half length of a fracture; ν is rock Poisson ratio.
3. The method according to claim 1 , wherein the effective net pressure of a fracture in the Nth segment is
p
en
(
N
)
=
p
n
-
∑
i
=
1
N
-
1
σ
h
i
(
N
)
wherein P n is an original pressure in the fracture of the N th segment; σ h i (N) is the induced stress in the minimum horizontal geostress direction generated by the fracturing of the ith segment in the fracture of the N th segment;
wherein the horizontal induced stress in the formation around the fracture of the N th segment is
{
σ
h
N
=
p
en
(
N
)
(
1
-
a
2
r
(
a
2
r
)
2
+
1
4
+
a
2
r
4
(
(
a
2
r
)
2
+
1
4
)
3
)
σ
H
N
=
2
p
en
(
N
)
v
(
1
-
a
2
r
(
a
2
r
)
2
+
1
4
)
wherein σ h n is the induced stress in the minimum horizontal geostress direction generated by the fracturing of the N th segment to formations around the N th segment σ H N is the induced stress in the maximum horizontal geostress direction generated by the fracturing of the N th segment to the formations around the N th segment;
wherein after the fracturing of the N th segment, the total induced stress in the formation around the segment is
{
σ
h
′
=
∑
i
=
1
N
σ
h
i
σ
H
′
=
∑
i
=
1
N
σ
H
i
wherein σ′ h is the induced stress in the formation around the segment in the minimum horizontal geostress direction after the fracturing of the N th segment; σ′ h is the induced stress in the formation around the segment in the maximum horizontal geostress direction after the fracturing of the N th segment; σ h i is the induced stress in the minimum horizontal geostress direction generated by the fracturing of the ith segment; σ H i is the induced stress in the maximum horizontal geostress direction generated by the fracturing of the ith segment.
4. The method according to claim 1 , characterized in that, the said multi-segment is segments of natural numbers equal to or greater than 3.
5. The method according to claim 1 , characterized in that, the specific calculation of the induced stress outside a fracture in a segment adjacent to previous fractured segment is as follows:
the induced stress outside a fracture inside the N th segment adjacent to the previous fractured segment is:
{
σ
h
N
1
=
∑
i
=
1
N
-
1
σ
h
i
+
σ
h
N
1
[
p
enl
(
N
1
)
]
σ
H
N
1
=
∑
i
=
1
N
-
1
σ
H
i
+
σ
H
N
1
[
p
enl
(
N
1
)
]
wherein σ h N 1 is the total induced stress in the minimum horizontal geostress direction; σ H N 1 is the total induced stress in the maximum horizontal geostress direction; σ h i is the induced stress in the minimum horizontal geostress direction generated by the fracturing of the ith segment; σ H i is the induced stress in the maximum horizontal geostress direction generated by the fracturing of the ith segment; σ h N 1 [P enl (N 1 )] is the induced stress in the minimum horizontal geostress direction generated by the fracture at the first perforated bunch of the N th segment to the previous fractured segment; σ h N 1 [P enl (N 1 )] is the induced stress in the maximum horizontal geostress direction generated by the fracture at the first perforated bunch of the N th segment to the previous fractured segment;
wherein the induced stress between fractures of the N th segment comprises the induced stress between Fracture N 1 and N 2
{
σ
h
1
=
∑
i
=
1
N
-
1
σ
h
i
1
+
σ
e
n
h
(
N
1
,
N
2
)
σ
H
1
=
∑
i
=
1
N
-
1
σ
H
i
1
+
σ
e
n
H
(
N
1
,
N
2
)
wherein σ h 1 is the induced stress in the minimum horizontal geostress direction generated between Fracture N 1 and N 2 ; σ h i1 is the induced stress in the minimum horizontal geostress direction generated by the fracture at the first perforated bunch of the ith fractured segment; σ H 1 the induced stress in the maximum horizontal geostress direction generated between Fracture N 1 and N 2 ; σ H i1 is the induced stress in the maximum horizontal geostress direction generated by the fracture at the first perforated bunch of the ith fractured segment;
wherein the induced stress between Fracture N 2 and N 3 is
{
σ
h
2
=
∑
i
=
1
N
-
1
σ
h
i
1
+
σ
e
r
ι
h
(
N
1
,
N
2
)
+
σ
e
n
h
(
N
2
,
N
3
)
σ
H
2
=
∑
i
=
1
N
-
1
σ
H
j
1
+
σ
e
n
H
(
N
1
,
N
2
)
+
σ
e
n
H
(
N
2
,
N
3
)
wherein σ h 2 is the induced stress in the minimum horizontal geostress direction generated between Fracture N 2 and N 3 ; σ H 2 the induced stress in the maximum horizontal geostress direction generated between Fracture and N 2 and N 3 ;
wherein the induced stress outside a fracture in N th segment adjacent to next fractured segment is
{
σ
h
N
3
=
∑
i
=
1
N
-
1
σ
h
i
+
σ
h
N
3
[
p
e
n
r
(
N
3
)
]
σ
H
N
3
=
∑
i
=
1
N
-
1
σ
H
i
+
σ
H
N
3
[
p
e
n
r
(
N
3
)
]
wherein σ h N 3 is the total induced stress in the minimum horizontal geostress direction at the point; σ H N 3 is the total induced stress in the maximum horizontal geostress direction at the point.
6. The method according to claim 5 , characterized in that, the horizontal induced stress difference Δσ of segmented multi-bunch fracturing for a horizontal well is
σ H =σ H N 1 +σ H 1 +σ H 2 +σ H N 3
σ h =σ h N 1 +σ h 1 +σ h 2 +σ h N 3
Δσ=σ H −σ h
wherein σ h is the induced stress in the minimum horizontal geostress direction generated by formation; σ H the induced stress in the maximum horizontal geostress direction generated by formation.
7. The method according to claim 6 , characterized in that, the position with the maximum induced stress difference is the optimal bunch distance.