Methods and systems for determining reservoir properties of subterranean formations
Methods and systems are provided for evaluating subsurface earth oil and gas formations. More particularly, methods and systems are provided for determining reservoir properties such as reservoir transmissibilities and average reservoir pressures of a formation layer or multiple layers using fracture-injection/falloff test methods. The methods herein may use pressure falloff data generated by the introduction of an injection fluid at a pressure above the formation fracture pressure in conjunction with a fracture-injection/falloff test model to analyze reservoir properties. The fracture-injection/falloff test model recognizes that a new induced fracture creates additional storage volume in the formation and that a fracture-injection/falloff test in a layer may exhibit variable storage during the pressure falloff, and a change in storage may be observed at hydraulic fracture closure.
1. A method of determining a reservoir transmissibility of at least one layer of a subterranean formation having a reservoir fluid comprising the steps of:
(a) isolating the at least one layer of the subterranean formation to be tested;
(b) introducing an injection fluid into the at least one layer of the subterranean formation at an injection pressure exceeding the subterranean formation fracture pressure for an injection period;
(c) shutting in the wellbore for a shut-in period;
(d) measuring pressure falloff data from the subterranean formation during the injection period and during a subsequent shut-in period; and
(e) determining quantitatively the reservoir transmissibility of the at least one layer of the subterranean formation by analyzing the pressure falloff data with a fracture-injection/falloff test model.
2. The method of claim 1 wherein step (e) is accomplished by transforming the pressure falloff data to equivalent constant-rate pressures and using type curve analysis to match the equivalent constant-rate pressures to a type curve to determine quantitatively the reservoir transmissibility.
3. The method of claim 1 wherein step (e) is accomplished by:
transforming the pressure falloff data to obtain equivalent constant-rate pressures;
preparing a log-log graph of the equivalent constant-rate pressures versus time; and
determine quantitatively the reservoir transmissibility of the at least one layer of the subterranean formation by analyzing the variable-rate pressure falloff data using type-curve analysis according to a fracture-injection/falloff test model.
4. The method of claim 2 wherein the reservoir fluid is compressible; and wherein the transforming of the pressure falloff data is based on the properties of the compressible reservoir fluid contained in the reservoir wherein the transforming step comprises:
determining a shut-in time relative to the end of the injection period;
determining an adjusted time; and
determining an adjusted pseudopressure difference.
5. The method of claim 4 wherein the transforming step comprises:
determining a shut-in time relative to the end of the injection period: Δt=t−t ne ;
determining an adjusted time:
t
a
=
(
μ
_
c
_
t
)
∫
0
Δ
t
ⅆ
Δ
t
(
μ
c
t
)
w
;
and
determining an adjusted pseudopressure difference: Δp a (t)=p aw (t)−p ai where
p
a
=
μ
_
g
z
_
p
_
∫
0
p
p
ⅆ
p
μ
g
z
;
wherein:
t ne is the time at the end of the injection period;
μ is the viscosity of the reservoir fluid at average reservoir pressure;
(μc t ) w is the viscosity compressibility product of wellbore fluid at time t;
(μc t ) 0 is the viscosity compressibility product of wellbore fluid at time t=t ne ;
p is the pressure;
p is the average reservoir pressure;
p aw (t) is the adjusted pressure at time t;
p ai is the adjusted pressure at time t=t ne ;
c t is the total compressibility;
c t is the total compressibility at average reservoir pressure; and
z is the real gas deviator factor.
6. The method of claim 5 further comprising the step of preparing a log-log graph of a pressure function versus time: I(Δp a )=f(t a );
where
I
(
Δ
p
a
)
=
∫
0
t
a
Δ
p
a
ⅆ
t
a
.
7. The method of claim 5 further comprising the step of preparing a log-log graph of a pressure derivative function versus time: Δp a ′=f(t a );
where
Δ
p
a
′
=
ⅆ
(
Δ
p
a
)
ⅆ
(
ln
t
a
)
=
Δ
p
a
t
a
.
8. The method of claim 2 wherein the reservoir fluid is slightly compressible and the transforming of the variable-rate pressure falloff data is based on the properties of the slightly compressible reservoir fluid contained in the reservoir wherein the transforming step comprises:
determining a shut-in time relative to the end of the injection period; and
determining a pressure difference.
9. The method of claim 8 the transforming step comprises:
determining a shut-in time relative to the end of the injection period: Δt=t−t ne ; and
determining a pressure difference: Δp(t)=p w (t)−p i ;
wherein:
t ne is the time at the end of injection period;
p w (t) is the pressure at time t; and
p i is the initial pressure at time t=t ne .
10. The method of claim 9 further comprising the step of preparing a log-log graph of a pressure function versus time: I(Δp)=f(Δt).
11. The method of claim 10 where
I
(
Δ
p
)
=
∫
0
Δ
t
Δ
p
ⅆ
Δ
t
or
∫
0
t
Δ
p
ⅆ
t
.
12. The method of claim 9 further comprising the step of preparing a log-log graph of a pressure derivatives function versus time: Δp′=f(Δt).
13. The method of claim 12 where
Δ
p
′
=
ⅆ
(
Δ
p
)
ⅆ
(
ln
Δ
t
)
=
Δ
p
Δ
t
or
ⅆ
(
Δ
p
)
ⅆ
(
ln
t
)
=
Δ
p
t
.
14. The method of claim 9 wherein the reservoir transmissibility is determined quantitatively in field units from a before-closure match point as:
k
h
μ
=
141.2
(
24
)
p
wsD
(
0
)
C
bc
(
p
0
-
p
i
)
[
p
bcD
(
t
D
)
∫
0
Δ
t
[
p
w
(
τ
)
-
p
i
]
ⅆ
τ
]
M
.
15. The method of claim 9 wherein the reservoir transmissibility is determined quantitatively in field units from an after-closure match point as:
kh
μ
=
141.2
(
24
)
p
awsD
(
0
)
C
bc
(
p
a
0
-
p
ai
)
[
p
bcD
(
t
D
)
∫
0
Δ
t
a
[
p
aw
(
τ
)
-
p
ai
]
ⅆ
τ
]
M
.
16. The method of claim 5 wherein the reservoir transmissibility is determined quantitatively in field units from a before-closure match point as:
kh
μ
=
141.2
(
24
)
p
wsD
(
0
)
C
bc
(
p
0
-
p
i
)
[
p
bcD
(
t
D
)
∫
0
Δ
t
[
p
w
(
τ
)
-
p
i
]
ⅆ
τ
]
M
.
17. The method of claim 5 wherein the reservoir transmissibility is determined quantitatively in field units from an after-closure match point as:
kh
μ
=
141.2
(
24
)
p
awsD
(
0
)
C
bc
(
p
a
0
-
p
ai
)
[
p
bcD
(
t
D
)
∫
0
Δ
t
a
[
p
aw
(
τ
)
-
p
ai
]
ⅆ
τ
]
M
.
18. A system for determining a reservoir transmissibility of at least one layer of a subterranean formation by using variable-rate pressure falloff data from the at least one layer of the subterranean formation measured during an injection period and during a subsequent shut-in period, the system comprising:
a plurality of pressure sensors for measuring pressure falloff data; and
a processor operable to transform the pressure falloff data to obtain equivalent constant-rate pressures and to determine quantitatively the reservoir transmissibility of the at least one layer of the subterranean formation by analyzing the variable-rate pressure falloff data using type-curve analysis according to a fracture-injection/falloff test model.
19. A computer program, stored on a tangible storage medium, for analyzing at least one downhole property, the program comprising executable instructions that cause a computer to:
determine quantitatively a reservoir transmissibility of the at least one layer of the subterranean formation by analyzing the variable-rate pressure falloff data with a fracture-injection/falloff test model.
20. The computer program of claim 19 wherein the determining step is accomplished by transforming the variable-rate pressure falloff data to equivalent constant-rate pressures and using type curve analysis to match the equivalent constant-rate rate pressures to a type curve to determine the reservoir transmissibility.
21. The computer program of claim 19 wherein the determining step is accomplished by transforming the variable-rate pressure falloff data to equivalent constant-rate pressures and using after closure analysis to determine the reservoir transmissibility.