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Use of Streamline Flow Diagnostics for
Injection and Production Rate Allocation
Optimization
Shusei Tanaka
November, 2014
Background
2/19
• Determining optimal injection/production rates to maximize NPV is challenging
Heterogeneous geological reservoir
Reallocate well rate to sweep bypassed oil
• Rate reallocation algorithm needs to be fast and robust
Requires a number of simulations
Handle waterflood, EOR…
Improve NPV under multiple constraints
• Diagnose efficiency of the well
How much ‘Inj-1’ contributes to field NPV?
- Improve oil production rate
- Works only after breakthrough
SL-Based Flow Rate Allocation Optimization:
Previous Study
3/19
• Use of Well Allocation Factors (WAFs): [Thiele et. al, 2003]
Well Allocation Factor map [SPE84080]
[SPE113628]
- WAFs by offset oil production of well-pair
• Equalize arrival time of injection fluid: [Al-Hutali et. al, 2009]
Norm Wt. - 0
Aft
er
2 y
ears
Aft
er
5 y
ears
Aft
er
10 y
ears
Base
Base Improved
Norm Wt. - 0
Aft
er
2 y
ears
Aft
er
5 y
ears
Aft
er
10 y
ears
Base
- Control well rate to have equivalent
‘breakthrough’ time
- Increase well rate of high WAFs
Decrease
Increase
Decrease
Decrease
Decrease
Increase
- Improves sweep efficiency- Works only before breakthrough
- Improve oil production rate
- Works only after breakthrough
SL-Based Flow Rate Allocation Optimization:
Previous Study
4/19
• Use of Well Allocation Factors (WAFs): [Thiele et. al, 2003]
Well Allocation Factor map [SPE84080]
[SPE113628]
- WAFs by offset oil production of well-pair
• Equalize arrival time of injection fluid: [Al-Hutali et. al, 2009]
Norm Wt. - 0
Aft
er
2 y
ears
Aft
er
5 y
ears
Aft
er
10 y
ears
Base
Base Improved
Norm Wt. - 0
Aft
er
2 y
ears
Aft
er
5 y
ears
Aft
er
10 y
ears
Base
- Control well rate to have equivalent
‘breakthrough’ time
- Increase well rate of high WAFs
Decrease
Increase
Decrease
Decrease
Decrease
Increase
- Improves sweep efficiency- Works only before breakthrough
• Fast
• Not robust
• Does not optimize NPV
Motivation and Objective
5/19
• Previous study of SL-based waterflood optimization does not optimize NPV and limited applicability
• Study objective:
Propose a new NPV-based flow diagnostics
Develop a streamline-based rate allocation method to optimize NPV
Apply model to Brugge benchmark case
Brugge field: multiple well and constraints [SPE 119094]
Streamlines
Proposed Optimization Method:
Overall Workflow
6/19
2. Trace Streamlines and Find connection map
3. Calculate NPV diagnostic plot
4. Reallocate flow rate of unconstrained well
via ‘efficiency’
1. Run simulation model
‘Value’ and ‘NPV’ of a Streamline
7/19
Injector
Producer
𝐻𝐶𝐼𝑃𝑠𝑙 = 𝑞𝑠𝑙
𝑛𝑜𝑑𝑒
𝑆𝑜𝑏𝑜𝑅𝑜 ∆𝜏
𝑁𝑃𝑉𝑠𝑙 = 𝑞𝑠𝑙
𝑛𝑜𝑑𝑒
𝑆𝑜𝑏𝑜𝑅𝑜 + 𝑆𝑤𝑏𝑤𝑅𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉
𝑝𝑟𝑑
𝑛𝑜𝑑𝑒
∆𝜏 > 𝑡𝑟𝑠𝑚
Hydrocarbon value (Maximum possible revenue)
NPV along SL (Prospected revenue)
• Hydrocarbon value and NPV along Streamline from time T to reservoir life, trsm
𝑷𝑽 = න𝟎
𝒔
𝑨 𝝃 𝝓 𝝃 𝒅𝝃 = න𝟎
𝒔𝒒𝒔𝒍𝝓 𝒔
𝒖𝒕(𝒔)𝒅𝝃 = 𝒒𝒔𝒍න
𝟎
𝒔 𝝓 𝒔
𝒖𝒕(𝒔)𝒅𝝃
= 𝒒𝒔𝒍𝝉
𝜏 𝜉 0=𝑠 𝜙 𝑠
𝑢𝑡(𝑠)𝑑𝜉
Pore volume:
Time-of-Flight (TOF):
Pore volume × Saturation × FVF × Price
Discount rate Reservoir life
I1 I2 I3
I6
I5
I7 I8
NPV-based Efficiency of Streamline
P1 P2
P3 P4 P5
P6 P7
8/19
HCIP, integrate along SL
NPV, integrate along SL, only reservoir life time
𝐻𝐶𝐼𝑃𝑠𝑙 = 𝑞𝑠𝑙
𝑛𝑜𝑑𝑒
𝑆𝑜𝑏𝑜𝑅𝑜 ∆𝜏
𝑁𝑃𝑉𝑠𝑙 = 𝑞𝑠𝑙
𝑛𝑜𝑑𝑒
𝑆𝑜𝑏𝑜𝑅𝑜 + 𝑆𝑤𝑏𝑤𝑅𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉
𝑝𝑟𝑑
𝑛𝑜𝑑𝑒
∆𝜏 > 𝑡𝑟𝑠𝑚
𝑒𝑠𝑙 =𝑁𝑃𝑉𝑠𝑙𝐻𝐶𝐼𝑃𝑠𝑙
• Efficiency of a SL
• Streamline efficiency by hydrocarbon value and NPV using economic values
I4
I1 I2 I3
I6
I5
I7 I8
NPV-based Efficiency of Well Pair
P1 P2
P3 P4 P5
P6 P7
9/19
𝑁𝑃𝑉𝑝𝑎𝑖𝑟 =
𝑠𝑙
𝑁𝑃𝑉𝑠𝑙
𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟 =
𝑠𝑙
𝐻𝐶𝐼𝑃𝑠𝑙
• Well pair efficiency by hydrocarbon value and NPV
𝑒𝑝𝑎𝑖𝑟 =𝑁𝑃𝑉𝑝𝑎𝑖𝑟𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟 HCIP
NPVHCIP and NPV,
integrate by SL bundle
• Well pair efficiency
I4
NPV-Based Flow Diagnostics
10/19
I1 I2 I3
I6
I5
I7 I8
P1 P2
P3 P4 P5
P6 P7
𝑒𝑝𝑎𝑖𝑟
=𝑁𝑃𝑉𝑝𝑎𝑖𝑟
𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟
5-connection from Inj-4 pairv
pairr
HCIP (Normalized)
NP
V (N
orm
aliz
ed)
𝑰𝟒𝐆𝐨𝐨𝐝
𝑷𝟒
𝑰𝟒𝐏𝐨𝐨𝐫
𝑷𝟕
NPV-based diagnostic plot
I4
(𝑁𝑃𝑉,𝐻𝐶𝐼𝑃 are normalized by field maximum 𝐻𝐶𝐼𝑃)
MCERIN
PV
(Norm
aliz
ed)
Streamline-based Rate Allocation:
A New Approach
𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤 = 𝑞𝑝𝑎𝑖𝑟
𝑜𝑙𝑑𝑒𝑝𝑎𝑖𝑟ҧ𝑒𝑓𝑖𝑒𝑙𝑑
𝑞𝑤𝑒𝑙𝑙 = 𝑟
𝑝𝑎𝑖𝑟
𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤
ത𝐞𝐟𝐢𝐞𝐥𝐝
decrease rate
Increase rate
Before update After update
Total value (Normalized)
11/19
MCERIN
PV
(Norm
aliz
ed)
Total value (Normalized)
Streamline-based Rate Allocation:
A New Approach
decrease rate
Increase rate
Before update After update
• Advantages:• Dynamically visualize efficiency of the injector and producer
• Able to propose ‘better’ well rate by post processing
12/19
𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤 = 𝑞𝑝𝑎𝑖𝑟
𝑜𝑙𝑑𝑒𝑝𝑎𝑖𝑟ҧ𝑒𝑓𝑖𝑒𝑙𝑑
𝑞𝑤𝑒𝑙𝑙 = 𝑟
𝑝𝑎𝑖𝑟
𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤
ത𝐞𝐟𝐢𝐞𝐥𝐝
13/19
• 3 years of waterflood, 8 injectors and 7 producers• Constraint: Field water injection/production 2500 [rb/day], min/max BHP per well• Relative oil, water price = 1, -0.2 $/bbl, Discount rate = 10%• Compare developed model with 3 approaches:
• Uniform injection (Uniform), Well allocation factors (WAFs), Equalize Arrival Time (EqArrive), Developed model (SLNPV)
Permeability Field Initial Oil Saturation SLs by Uniform Injection
I1 I2 I3
I6
I5
I7 I8
P1 P2
P3 P4 P5
P6 P7
I4
Demonstration: 2D Multi-well Case
0.0E+00
5.0E+04
1.0E+05
1.5E+05
2.0E+05
2.5E+05
3.0E+05
0 180 360 540 720 900 1080
Net
Pre
sen
t V
alu
e [
$]
Time [Days]
SLNPVEqArriveWAFsUniform
0.0E+00
5.0E+04
1.0E+05
1.5E+05
2.0E+05
2.5E+05
3.0E+05
0 180 360 540 720 900 1080
Net
Pre
sen
t V
alu
e [
$]
Time [Days]
SLNPVEqArriveWAFsUniform
14/19
Recovery Factor Net Present Value
2D Multi-well: Recovery and NPV
SLNPV:
Maximum NPV at 2 years
2.5 times of uniform injection
0.0
0.1
0.2
0.3
0.4
0 180 360 540 720 900 1080
Re
cove
ry F
acto
r [-
]
Time [Days]
SLNPVEqArriveWAFsUniform
15/19
Result of Saturation Distribution:
Uniform Injection and SLNPV
SLNPVUniform injection
: at 0.5 yrs
Reduced injection
Increased injection
High water saturation
High oil saturation
NPV-Based Flow Diagnostics
2D Multiwell Example
16/19
𝑁𝑃𝑉𝑝𝑎𝑖𝑟 =
𝑠𝑙
𝑞𝑠𝑙
𝑛𝑜𝑑𝑒
𝑆𝑜𝑏𝑜𝑅𝑜 + 𝑆𝑤𝑏𝑤𝑅𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉
𝑝𝑟𝑑
𝑛𝑜𝑑𝑒
∆𝜏 > 𝑡𝑟𝑠𝑚
InjectorP/I 1 2 3 4 5 6 7 8
1 96879 45170 0 38964 0 0 0 0
2 0 26458 25571 0 0 0 0 0
3 77264 0 0 49230 0 40210 0 0
4 0 54433 0 53080 0 0 0 0
5 0 66903 80531 0 78445 0 0 18356
6 0 0 0 19642 0 -4292 5050 0
7 0 0 0 4419 18840 0 -6175 -21328
Pro
du
cer
Predicted NPV, until end of the simulation
I1 I2 I3
I6
I5
I7 I8
P1 P2
P3 P4 P5
P6 P7
I4
17/19
Oil Saturation and Well Location
• Constraints:- Field water injection qt <= 20,000 bbl/d- Well flow rate qti <= 6000 bbl/d- Producer BHP > 100 psi, Injector BHP < 6000 psi
• Simulation Model:- Synthetic water flooding - 20 producers, 10 injectors- 20 years of simulation- Relative oil, water price = 1, -0.2 $/bbl
Brugge Benchmark Model
Streamlines by Sw
SLN
PV
Un
ifo
rm In
ject
ion
Streamlines by Injector
Example of SLs: After 10 Years
Not sweep aquifer region
Sweep aquifer region
Increased Inj-Prd
connection
18/19
0.00
0.04
0.08
0.12
0.16
0.20
0 1200 2400 3600 4800 6000 7200
Re
cove
ry F
acto
r [-
]
Time [Days]
SLNPVEqArriveWAFsUniform
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
3.E+07
3.E+07
4.E+07
0 1200 2400 3600 4800 6000 7200
Net
Pre
sen
t V
alu
e [
$]
Time [Days]
NPVEqArriveWAFsUniform
Recovery Factor Net Present Value
Recovery Factor and NPV
Injection Rate Production Rate
Updated Well Rate by SLNPV
0
1000
2000
3000
4000
5000
6000
7000
0 1200 2400 3600 4800 6000 7200
Pro
du
ctio
n R
ate
[b
bl/
day
]
Time [Days]
BR-P-1 BR-P-2BR-P-3 BR-P-4BR-P-5 BR-P-6BR-P-7 BR-P-8BR-P-9 BR-P-10BR-P-11 BR-P-12BR-P-13 BR-P-14BR-P-15 BR-P-16BR-P-17 BR-P-18BR-P-19 BR-P-20
0
1000
2000
3000
4000
5000
6000
7000
0 1200 2400 3600 4800 6000 7200
Inje
ctio
n R
ate
[b
bl/
day
]
Time [Days]
BR-I-1 BR-I-2BR-I-3 BR-I-4BR-I-5 BR-I-6BR-I-7 BR-I-8BR-I-9 BR-I-10
19/19
• Have developed a new SL-based rate allocation method to improve recovery considering NPV
• Proposed a new diagnostic plot to visualize the relative value and efficiency of a well in the asset
• Results in greater NPV compared to prior streamline-based rate allocation methods
• Can be applied to IOR/EOR simulation study with any commercial simulator by post processing
Conclusions
20/19