Methods and systems for reservoir and wellbore simulation
Methods of exploiting a formation containing a reservoir of hydrocarbons utilize a gas-liquid drift-flux (DF) model for a multi-segmented wellbore (MSW). The DF model is provided for use in conjunction with a reservoir simulator. The DF model is configured to account for pipe inclinations of the MSW between −90° and +90° including horizontal or near-horizontal wellbores in addition to vertical and slanted wellbores. The DF model is based on mixture velocity as opposed to superficial velocities, thereby permitting the DF model to be integrated with reservoir models that utilize mixture velocity. The DF model can also be continuous and differentiable over all primary variables.
1. A method of optimizing hydrocarbon production of a subterranean reservoir of hydrocarbons traversed by at least one multi-segmented wellbore (MSW), comprising:
gathering information regarding the subterranean reservoir, wherein gathering the information comprises receiving logging information from at least one flow control device disposed between the subterranean reservoir and the at least one MSW;
providing the information to a reservoir simulator incorporating a gas-liquid drift-flux (DF) model that is based on mixture velocity within the pipe, wherein the DF model accounts for pipe inclinations between −90° and +90° of the at least one MSW; wherein the DF model is defined according to
u dr θ =( m 1 {u dr V }sin θ+ M 2 {u dr H }cos θ)× M 3 ,
where u dr θ is the drift velocity for a given pipe inclination angle θ between −90° and +90°,
u dr V and u dr H are respectively the vertical and horizontal drift velocities,
m 1 is a multiplier for the vertical drift velocity,
2 is a multiplier that corrects for transition at horizontal (θ=0°), and
3 is a multiplier that compensates for divergence when mixture velocity u m is below a selected threshold value; and
running the reservoir simulator to generate a solution to optimize hydrocarbon production of the subterranean reservoir, wherein the solution comprises one or more optimized settings for the at least one flow device.
2. The method of claim 1 , wherein the at least one MSW includes a segment inclined within two degrees of horizontal.
3. The method of claim 1 , wherein the DF model allows a user to specify segments of the at least one MSW that experience a number of different flow types through adjacent segments of the at least MSW, wherein the number of different flow types include upward flow, downward flow, upward-to-downward flow, downward-to-upward flow, and pure horizontal flow.
4. The method of claim 1 , wherein the solution specifies at least one of location and operational parameters for downhole equipment along a completion of the at least one MSW for production.
5. The method of claim 4 , further comprising using the solution to build the completion or control the downhole equipment, and producing hydrocarbons from the completion.
6. The method of claim 1 , wherein the selected threshold value is 1 m/s.
7. The method of claim 1 , wherein m 1 =1.
8. The method of claim 1 , wherein
u
dr
V
=
(
1
-
α
g
C
0
)
C
0
N
Ku
(
α
g
)
u
ch
α
g
C
0
ρ
g
/
ρ
L
+
1
-
(
α
g
C
0
)
where α g is the void fraction of the gas phase obtained from a determination of the reservoir simulator,
N Ku is the critical Kutateladze number,
u ch is a characteristic velocity,
ρ g is the density of the gas phase,
ρ L is the density of the liquid phase, and
C 0 is a profile parameter.
9. The method of claim 8 , wherein C 0 =1.
10. The method of claim 1 , wherein:
u
dr
H
=
gD
(
ξ
1
-
ξ
2
[
(
N
μ
)
ξ
3
(
N
E
o
¨
)
ξ
4
]
)
α
g
(
1
-
α
g
)
,
where g is the gravity constant,
D is the diameter the conduit,
ξ 1 ,ξ 2 , ξ 3 , and ξ 4 are horizontal flow fitting parameters,
N μ is a viscosity number, and
N Eö is an Eotos number.
11. The method of claim 1 , wherein 2 is a function of a mixture velocity, and 3 is a function of a mixture Reynold's number.
12. The method of claim 11 , wherein
2
=
[
1
-
2
1
+
exp
[
50
sin
(
θ
+
m
2
u
m
)
]
]
where m 2 is a fitted parameter and u m is the mixture velocity.
13. The method of claim 11 , wherein
3
=
[
1
+
1000
(
N
Re
)
m
+
1000
]
m
3
where m 3 is a fitted parameter and (N Re ) m is the mixture Reynold's number.
14. A processor-based system that stores program instructions that, when executed on the system, cause the system to perform the method of claim 1 .
15. A computer-readable medium storing program instructions that, when executed by a processor, cause the processor to perform the method of claim 1 .
16. The method of claim 1 , further comprising automatically modifying operation of the at least one flow control device based on the one or more optimized settings of the at least one flow device of the solution.
17. The method of claim 1 , wherein the solution comprises an optimized production pressure of the at least one MSW, and wherein the method further comprises automatically modifying a production pressure of the at least one MSW based on the optimized production pressure of the solution.
18. The method of claim 1 , wherein the at least one flow control device comprises a choke, a valve, a labyrinth device, a downhole separator, or a combination thereof.
19. The method of claim 1 , wherein the DF model accounts for pipe inclinations between −90° and +2° of the at least one MSW.