Model Featuring N-Porosity
The subject matter of this specification can be embodied in, among other things, a method for determining leak-off rate includes receiving a collection of geological data descriptive of a well path through a predetermined geographical area, the geological data comprising fracture density and fracture distribution data obtained from offset wellbore image and wellbore nuclear magnetic resonance logs, determining a hydraulic fracturing fluid leak-off rate based on the received collection of geological data, and providing the determined hydraulic fracturing fluid leak-off rate.
1 . A method for determining leak-off rate, comprising:
receiving a collection of geological data descriptive of a well path through a predetermined geographical area, the geological data comprising fracture density and fracture distribution data obtained from offset wellbore image and wellbore nuclear magnetic resonance logs;
determining a hydraulic fracturing fluid leak-off rate based on the received collection of geological data; and
providing the determined hydraulic fracturing fluid leak-off rate.
2 . The method of claim 1 , further comprising:
determining an amount of hydraulic fracturing fluid based on the provided hydraulic fracturing fluid leak-off rate; and
providing the determined amount of hydraulic fracturing fluid to the predetermined geographical area.
3 . The method of claim 1 , wherein the hydraulic fracturing fluid leak-off rate is further based on an N-porosity N-permeability media model.
4 . The method of claim 1 , wherein the hydraulic fracturing fluid leak-off rate is further based on an average leak-off velocity value.
5 . The method of claim 4 , wherein the average leak-off velocity value is given by the equation:
q=Σ i=1 N v i q i ,
where:
q
i
(
t
)
=
-
k
i
μ
∂
p
i
∂
x
(
x
=
0
,
t
)
=
-
2
L
∑
m
=
0
∞
k
i
μ
(
2
m
+
1
)
π
2
b
(
C
im
e
γ
m
t
-
2
bD
i
(
T
f
-
T
0
)
(
2
m
+
1
)
π
e
-
λ
ρ
C
v
(
2
m
+
1
)
2
π
2
4
b
2
t
)
cos
(
2
m
+
1
)
π
2
b
.
6 . The method of claim 1 , wherein the hydraulic fracturing fluid leak-off rate is given by the equation:
Q= 2 qΣ j=1 n h j l j .
7 . The method of claim 1 , wherein the hydraulic fracturing fluid leak-off rate is given by the equation:
Q
=
-
4
L
∑
j
=
1
n
∑
i
=
1
N
∑
m
=
0
∞
h
j
l
j
v
i
k
i
μ
(
2
m
+
1
)
π
2
b
(
C
im
e
γ
m
t
-
2
bD
i
(
T
f
-
T
0
)
(
2
m
+
1
)
π
e
-
λ
ρ
C
v
(
2
m
+
1
)
2
π
2
4
b
2
t
)
cos
(
2
m
+
1
)
π
2
b
.
8 . The method of claim 1 , further comprising:
receiving permeability data descriptive of the well path; and
determining the collection of geological data based on the permeability data.
9 . A computer-implemented system, comprising:
one or more processors; and
a non-transitory computer-readable storage medium coupled to the one or more processors and storing programming instructions for execution by the one or more processors, the programming instructions instructing the one or more processors to perform operations comprising:
receiving a collection of geological data descriptive of a well path through a predetermined geographical area, the geological data comprising fracture density and fracture distribution data obtained from offset wellbore image and wellbore nuclear magnetic resonance logs;
determining a hydraulic fracturing fluid leak-off rate based on the received collection of geological data; and
providing the determined hydraulic fracturing fluid leak-off rate.
10 . The system of claim 9 , the operations further comprising:
determining an amount of hydraulic fracturing fluid based on the provided hydraulic fracturing fluid leak-off rate;
controlling, based on the determined amount, an actuator; and
providing, based on the controlling, the determined amount of hydraulic fracturing fluid to the predetermined geographical area.
11 . The system of claim 9 , wherein the hydraulic fracturing fluid leak-off rate is further based on an N-porosity N-permeability media model.
12 . The system of claim 9 , wherein the hydraulic fracturing fluid leak-off rate is further based on an average leak-off velocity value.
13 . The system of claim 12 , wherein the average leak-off velocity value is given by the equation:
q=Σ i=1 N v i q i ,
where:
q
i
(
t
)
=
-
k
i
μ
∂
p
i
∂
x
(
x
=
0
,
t
)
=
-
2
L
∑
m
=
0
∞
k
i
μ
(
2
m
+
1
)
π
2
b
(
C
im
e
γ
m
t
-
2
bD
i
(
T
f
-
T
0
)
(
2
m
+
1
)
π
e
-
λ
ρ
C
v
(
2
m
+
1
)
2
π
2
4
b
2
t
)
cos
(
2
m
+
1
)
π
2
b
.
14 . The system of claim 9 , wherein the hydraulic fracturing fluid leak-off rate is given by the equation:
Q= 2 qΣ j=1 n h j l j .
15 . The system of claim 9 , wherein the hydraulic fracturing fluid leak-off rate is given by the equation:
Q
=
-
4
L
∑
j
=
1
n
∑
i
=
1
N
∑
m
=
0
∞
h
j
l
j
v
i
k
i
μ
(
2
m
+
1
)
π
2
b
(
C
im
e
γ
m
t
-
2
bD
i
(
T
f
-
T
0
)
(
2
m
+
1
)
π
e
-
λ
ρ
C
v
(
2
m
+
1
)
2
π
2
4
b
2
t
)
cos
(
2
m
+
1
)
π
2
b
.
16 . The system of claim 9 , the operations further comprising:
receiving permeability data descriptive of the well path; and
determining the collection of geological data based on the permeability data.
17 . A non-transitory, computer-readable medium storing one or more instructions executable by a computer system to perform operations comprising:
receiving a collection of geological data descriptive of a well path through a predetermined geographical area, the geological data comprising fracture density and fracture distribution data obtained from offset wellbore image and wellbore nuclear magnetic resonance logs;
determining a hydraulic fracturing fluid leak-off rate based on the received collection of geological data; and
providing the determined hydraulic fracturing fluid leak-off rate.
18 . The system of claim 9 , the operations further comprising:
determining an amount of hydraulic fracturing fluid based on the provided hydraulic fracturing fluid leak-off rate; and
providing the determined amount of hydraulic fracturing fluid to the predetermined geographical area.
19 . The system of claim 9 , wherein the hydraulic fracturing fluid leak-off rate is further based on an N-porosity N-permeability media model.
20 . The system of claim 9 , wherein the hydraulic fracturing fluid leak-off rate is further based on an average leak-off velocity value.