Estimating natural fracture properties based on production from hydraulically fractured wells
To estimate natural fracture properties based on production from hydraulically fractured wells, a computer system receives hydrocarbon reservoir production information associated with a naturally fractured hydrocarbon reservoir with entrapped hydrocarbons in which a wellbore has been formed to produce the hydrocarbons. The information includes a wellbore pressure measured over production time. From the wellbore pressure, the computer system determines a time rate of change of the wellbore pressure over the production time. From a plot of a logarithmic time rate of change of the wellbore pressure over logarithmic production time, the computer system identifies multiple plot sections, each representing a respective flow regime of a flow of the hydrocarbons from the reservoir. For each plot section, the computer system determines a corresponding time rate of change of the wellbore pressure intersect value and a reservoir parameter for each corresponding time rate of change of the wellbore pressure intersect value determined for each plot section.
1. A computer-implemented method comprising:
measuring a wellbore pressure (p) over a production time (t) in a wellbore using a pressure gauge;
receiving, by a computer system, hydrocarbon reservoir production information associated with a naturally fractured hydrocarbon reservoir with entrapped hydrocarbons in which the wellbore has been formed to produce the hydrocarbons, the information comprising the wellbore pressure (p) measured over the production time (t), a production rate (q w ), a pressure at standard conditions (p sc ), a temperature at standard conditions (T sc ), a thickness of formation in which the wellbore is formed (h), a radius of the wellbore (r e ), a hydrocarbon viscosity (μ), a reservoir temperature (T), and a reservoir porosity and a compressibility;
determining, by the computer system, from the wellbore pressure measured over the production time, a time rate of change of the wellbore pressure over the production time;
identifying, by the computer system and from a plot of a logarithmic time rate of change of the wellbore pressure (Y-axis) over logarithmic production time (X-axis), a plurality of plot sections, each plot section representing a respective flow regime of a flow of the hydrocarbons from the reservoir, wherein the plurality of plot sections comprises a pseudo-radial plot section having a slope of substantially 0, wherein determining the time rate of change of the wellbore pressure (Y-intersect) value for the pseudo-radial plot section comprises identifying a (Y-axis) intersect value (y i ) of the pseudo-radial plot section on the plot;
determining, by the computer system and for each plot section, a corresponding time rate of change of the wellbore pressure (Y-axis) intersect value; and
determining, by the computer system, a reservoir parameter for each corresponding time rate of change of the wellbore pressure (Y-axis) intersect value determined for each plot section, wherein the reservoir parameter for the pseudo-radial plot section is fracture permeability (k II ) of the reservoir, wherein determining the fracture permeability comprises computationally solving the following equation:
k
II
=
q
w
Tp
s
c
2
π
h
T
s
c
y
i
.
2. The method of claim 1 , wherein the plurality of plot-sections comprises a pseudo-steady state section having a slope of substantially +1, wherein determining the time rate of change of the wellbore pressure Y-intersect value for the pseudo-steady state plot section comprises identifying a Y-axis intersect value (y i ) of the pseudo-steady state plot section on the plot.
3. The method of claim 2 , wherein the reservoir parameter for the pseudo-steady state plot section is matrix permeability (k I ) of the reservoir, wherein determining the matrix permeability comprises computationally solving the following equation:
k
I
=
y
j
π
hr
e
2
T
s
c
μϕ
I
C
t
I
k
II
4
q
w
Tp
s
c
,
where ϕ I C t I is fracture storage.
4. The method of claim 3 , wherein the plurality of plot sections comprises a trough in the time rate of change of the wellbore pressure (Y-axis) over logarithmic production time (X-axis), wherein determining the time rate of change of the wellbore pressure Y-intersect value for the trough comprises identifying a Y-axis intersect value of the trough of the plot.
5. The method of claim 4 , wherein the trough comprises a high point and a low point, wherein the high point comprises a Y-axis intersect value (y max ) and the low point comprises a Y-axis intersect value (y min ), wherein a difference between y max and y min is a time rate of change of pressure of the trough (Δp trough ).
6. The method of claim 5 , wherein the reservoir parameter for the trough is fracture storage (ϕ I C t I ), wherein determining the fracture storage comprises computationally solving the following equation:
Δ
p
t
r
o
u
g
h
y
max
≈
Ln
10
2
π
Log
1
0
k
II
ϕ
C
t
I
k
I
ϕ
II
C
t
II
,
wherein ϕ II C t II is matrix storage.
7. The method of claim 6 , further comprising computationally solving the following equation:
t
D
=
μ
π
λ
ϕ
I
ϕ
II
C
t
I
C
t
II
k
I
k
II
,
wherein λ is an inter-porosity flow coefficient.
8. The method of claim 6 , wherein the plurality of plot sections comprises a pseudo-linear section having a slope of substantially +½, wherein determining the time rate of change of the wellbore pressure Y-intersect value for the pseudo-linear plot section comprises identifying a Y-axis intersect value (y k ) of the pseudo-linear plot section on the plot.
9. The method of claim 8 , wherein the reservoir parameter is hydraulic fracture half length, wherein determining the hydraulic fracture half length comprises computationally solving the following equation:
dm
(
p
)
dLnt
→
q
w
Tp
s
c
2
h
L
T
s
c
t
πμϕ
II
C
t
II
k
II
,
wherein L is the hydraulic fracture half length.
10. The method of claim 1 , further comprising generating the plot of the time rate of change of the wellbore pressure over the logarithmic production time.
11. A non-transitory, computer-readable medium storing one or more instructions executable by a computer system to perform operations comprising:
measuring a wellbore pressure (p) over a production time (t) in a wellbore using a pressure gauge;
receiving, by a computer system, hydrocarbon reservoir production information associated with a naturally fractured hydrocarbon reservoir with entrapped hydrocarbons in which the wellbore has been formed to produce the hydrocarbons, the information comprising the wellbore pressure (p) measured over the production time (t), a production rate (q w ), a pressure at standard conditions (p sc ), a temperature at standard conditions (T SC ) thickness of formation in which the wellbore is formed (h), a radius of the wellbore (r e ), a hydrocarbon viscosity (μ), a reservoir temperature (T), and a reservoir porosity and a compressibility;
determining, by the computer system, from the wellbore pressure measured over the production time, a time rate of change of the wellbore pressure over the production time;
identifying, by the computer system and from a plot of a logarithmic time rate of change of the wellbore pressure (Y-axis) over logarithmic production time (X-axis), a plurality of plot sections, each plot section representing a respective flow regime of a flow of the hydrocarbons from the reservoir, wherein the plurality of plot sections comprises a pseudo-radial plot section having a slope of substantially 0, wherein determining the time rate of change of the wellbore pressure (Y-intersect) value for the pseudo-radial plot section comprises identifying a (Y-axis) intersect value (y i ) of the pseudo-radial plot section on the plot;
determining, by the computer system and for each plot section, a corresponding time rate of change of the wellbore pressure (Y-axis) intersect value; and
determining, by the computer system, a reservoir parameter for each corresponding time rate of change of the wellbore pressure (Y-axis) intersect value determined for each plot section, wherein the reservoir parameter for the pseudo-radial plot section is fracture permeability (k II ) of the reservoir, wherein determining the fracture permeability comprises computationally solving the following equation:
k
II
=
q
w
Tp
s
c
2
π
h
T
s
c
y
i
.
12. The medium of claim 11 , wherein the plurality of plot-sections comprises a pseudo-steady state section having a slope of substantially +1, wherein determining the time rate of change of the wellbore pressure Y-intersect value for the pseudo-steady state plot section comprises identifying a Y-axis intersect value (y j ) of the pseudo-steady state plot section on the plot.
13. The medium of claim 12 , wherein the reservoir parameter for the pseudo-steady state plot section is matrix permeability (k I ) of the reservoir, wherein determining the matrix permeability comprises computationally solving the following equation:
k
I
=
y
j
π
hr
e
2
T
s
c
μϕ
I
C
t
I
k
II
4
q
w
Tp
s
c
,
where ϕ I C t I is fracture storage.
14. The medium of claim 13 , wherein the plurality of plot sections comprises a trough in the time rate of change of the wellbore pressure (Y-axis) over logarithmic production time (X-axis), wherein determining the time rate of change of the wellbore pressure Y-intersect value for the trough comprises identifying a Y-axis intersect value of the trough of the plot.
15. The medium of claim 14 , wherein the trough comprises a high point and a low point, wherein the high point comprises a Y-axis intersect value (y max ) and the low point comprises a Y-axis intersect value (y min ), wherein a difference between y max and y min is a time rate of change of pressure of the trough (Δp trough ).
16. The medium of claim 15 , wherein the reservoir parameter for the trough is fracture storage (ϕ I C t II ) wherein determining the fracture storage comprises computationally solving the following equation:
Δ
p
t
r
o
u
g
h
y
max
≈
Ln
10
2
π
Log
1
0
k
II
ϕ
C
t
I
k
I
ϕ
II
C
t
II
,
wherein ϕ II C t II is matrix storage.
17. The medium of claim 16 , the method further comprising computationally solving the following equation:
t
D
=
μ
π
λ
ϕ
I
ϕ
II
C
t
I
C
t
II
k
I
k
II
,
wherein λ is inter-porosity flow coefficient.
18. The medium of claim 17 , wherein the plurality of plot sections comprises a pseudo-linear section having a slope of substantially +½, wherein determining the time rate of change of the wellbore pressure Y-intersect value for the pseudo-linear plot section comprises identifying a Y-axis intersect value (y k ) of the pseudo-linear plot section on the plot.
19. The medium of claim 18 , wherein the reservoir parameter is hydraulic fracture half length, wherein determining the hydraulic fracture half length comprises computationally solving the following equation:
dm
(
p
)
dLnt
→
q
w
Tp
s
c
2
h
L
T
s
c
t
πμϕ
II
C
t
II
k
II
,
wherein L is the hydraulic fracture half length.
20. The medium of claim 11 , the method further comprising generating the plot of the time rate of change of the wellbore pressure over the logarithmic production time.
21. 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:
measuring a wellbore pressure (p) over a production time (t) in a wellbore using a pressure gauge;
receiving, by a computer system, hydrocarbon reservoir production information associated with a naturally fractured hydrocarbon reservoir with entrapped hydrocarbons in which the wellbore has been formed to produce the hydrocarbons, the information comprises production rate (q w ), pressure at standard conditions (p sc ), temperature at standard conditions (T sc ), thickness of formation in which the wellbore is formed (h), radius of the wellbore (r e ), hydrocarbon viscosity (μ), reservoir temperature (T), and reservoir porosity and compressibility;
determining, by the computer system, from the wellbore pressure measured over the production time, a time rate of change of the wellbore pressure over the production time;
identifying, by the computer system and from a plot of a logarithmic time rate of change of the wellbore pressure (Y-axis) over logarithmic production time (X-axis), a plurality of plot sections, each plot section representing a respective flow regime of a flow of the hydrocarbons from the reservoir, wherein the plurality of plot sections comprises a pseudo-radial plot section having a slope of substantially 0, wherein determining the time rate of change of the wellbore pressure (Y-intersect) value for the pseudo-radial plot section comprises identifying a (Y-axis) intersect value (y i ) of the pseudo-radial plot section on the plot;
determining, by the computer system and for each plot section, a corresponding time rate of change of the wellbore pressure (Y-axis) intersect value; and
determining, by the computer system, a reservoir parameter for each corresponding time rate of change of the wellbore pressure (Y-axis) intersect value determined for each plot section, wherein the reservoir parameter for the pseudo-radial plot section is fracture permeability (k II ) of the reservoir, wherein determining the fracture permeability comprises computationally solving the following equation:
k
I
I
=
q
w
T
p
s
c
2
π
h
T
s
c
y
i
.