An Effective Reservoir Management by
Streamline-based Simulation, History
Matching and Optimization
Shusei Tanaka
May, 2014
โข Development of a general purpose streamline-based reservoir simulator: Inclusion of diffusive flux via Orthogonal Projection Illustration by black oil model Extension to a multicomponent system
โข Application to Brugge benchmark case: Streamline-based simulation Streamline-based BHP/WCT data integration Flow diagnostics for streamline-based NPV optimization
โข Conclusion
Outline
2/50
Streamline Technology: Overview
3/50
โข Key concept of Streamline: Fast IMPES-based reservoir simulation
History matching(HM) by calibration of travel time
Improves sweep efficiency by streamline information
Pressure field Streamlines Connection map
Problem Statement:
SL-based Reservoir Management
4/50
โข Challenges for mature field, multiple wellโฆ Quick forecasting
HM for individual well
Improve NPV by reallocating well rate
โข Streamline is efficient, but can we apply all the time? What if flow is not convective dominant?
How about prior to breakthrough for HM?
Can we improve NPV?
Mature field with multiple
wells
Development of a General Purpose Streamline-
based Simulator
Motivation
6/50
Solve 1D Convection EquationsCalculate Diffusive Flux on Grid
Compute Pressure & Velocity Field
โข Streamline simulation is difficult to apply ifโฆ
System of equation is highly nonlinear (ex. Gas injection)
Capillary and gravity effects are dominant
Error by Operator-Split
Error by IMPES
; 0
w
w ut
S
Why Split the Equation?
โข Water velocity does not follow total velocity with capillary (and gravity)
7/50
tuwu
Streamline
cowowtww pkFuFu
โข Split equation by physical mechanisms
Convective
Transport
Capillary
Diffusion 0
cowow
w pkFt
S
0
w
w ut
S 0
wt
w Fut
S
cowowtww pkFuFu
Saturation Transport
Equation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.2 0.4 0.6 0.8 1
Wa
ter
Sa
tura
tio
n
Normalized Distance
Correct Solution
Convection Flow
Too much diffusion
with large time step
(SPE 163640)
Operator Splitting
Capillary after
convection
8/50
0~
wtw
w Fuut
S
cowowtwwwtw pkFuFFFuu
~
~
โข Split equation by physical mechanisms
โข Anti-diffusive corrections
Computationally expensive:Function of (P, T, composition,
Initial state) for each grid, time step
0
w
w ut
S 0
wt
w Fut
S
Splitting with anti-
diffusive flux
Convection Eq.
Corrected Operator Splitting
Anti-diffusive concave envelope
9/50
0
w
w ut
S
wtww uufu
Parallel component,
calculate along
streamline
Anti-diffusive correction
not needed
Orthogonal Projection
โข Split equation into parallel and transverse flux terms
twf u
wu
tuwu
Streamline
10/50
twf u
wu
0
w
w ut
S 0
tw
w uft
S
0
w
w ut
S
tuwu
Orthogonal Projection
Parallel to Ut
(Solve along streamline)
Transverse to Ut
(Solve on grids)
Streamline
โข Split equation into parallel and transverse flux terms
wtww uufu
Parallel component,
calculate along streamline
Anti-diffusive correction not
needed
11/50
1.Compute pressure & velocity field
Include capillary effects
2.Trace streamlines
Solve 1D convection equations
Include capillarity and gravity
3.Map back saturation to grid
Calculate corrector term
Predictor-Corrector Workflow
Iterative IMPES
Orthogonal Projection
12/50
โข Pressure equation(IMPES)
โข Transport equation (along SL)
Orthogonal Projection:
Application to Multicomponent System
0
owgj
j
owgj
j
owgj
jj
owgj
jjr Qupuct
pScc
i
sl
ii fmt
cfgDpFyu
kyFfSym
sl
ii
owgj owgj jogwmm
m
jmjmcmjjij
t
jijj
sl
ij
ogwj
jiji
1
,2 , ,
ฮ
โข Transport equation (on Grid, corrector)
ogwj jmogwm
m
jmcjmmjjijtti DgpFykuuI
t
m
,
หห
Pc,Gravity along streamline
Transverse Pc,Gravity on grid
0
owgj
ijijjjijjjij qyuySyt
โข Governing equation
13/50
Illustrative Example
100 mD
5 mD
โข Water injection 0.2PVI, then CO2 0.2PVI
โข Single time step for each injection period
โข Observe capillarity by parallel/transverse to Ut
tw uf
wu
14/50
Water Saturation and Capillary Flux
Distributions
โข Capillarity traps water at center by J-Function
โข Capillarity flows back water towards injector during gas injection period
Sw after water injection
Arrow: water capillary flux
Sw after gas injection
Arrow: water capillary flux
1)(
kSwJpcow
15/50
Water Capillary Flux:
Parallel and Transverse to Total Velocity
Total capillary fluxCapillary flux transverse
to total velocity
Capillary flux along
total velocity
โข Most of the capillary effects can be included along the streamlines
cow
t
tt
t
ow
t
w pu
uuI
u
ku
2
Along streamline On grids
16/50
cow
t
t
t
ow pu
uk
2
Water Saturation Distribution
Commercial, FD Operator Splitting
(no correction)Orthogonal Projection
โข OP can take large time step without anti-diffusive correction
17/50
Injection :: CO2
10 rb/D โ 1000 [Days]
Production :: BHP
(1900 psi)
2D Cross-Section CO2 Flooding Model
Pc, Convection
Pc, Gravity
Simulation model:โข 7 HC component + Waterโข Rel-Perm by Coreyโข Water-wet Capillarity
Initial & Boundary Conditionโข 2000+ psi , 212Fหโข Constant production BHP, constant CO2 injection at 10 rb/Dโข 1000 days
18/50
CO2 Mole Fraction Distribution:
Along Streamline
Including Pc & GravityConvection only
19/50
Production Mole Fraction of CO2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 200 400 600 800 1000
Pro
du
ctio
n M
ole
Fra
ctio
n(C
O2
)
Time [Days]
Streamline
Commercial Simulator
Number of time step:
Commercial FD = 56
Streamline = 21
20/50
CO2 Mole Fraction Distribution:
Final Distribution
Orthogonal Projection
(After corrector term)Commercial FD
(E300)
21/50
0
50
100
150
200
250
300
350
400
450
500
2D Areal 2D Cross-Section 2D Cross-SectionHetero
Goldsmith Field
E300 FIM
Streamline
Previous case
Comparisons of Number of
Time Step
Nu
mb
er
of
Tim
e S
tep
Tested simulation cases
in the paper
10ร
2ร4ร
3ร
22/50
0
50
100
150
200
250
300
350
400
450
500
2D Areal 2D Cross-Section 2D Cross-SectionHetero
Goldsmith Field
E300 FIM
Streamline
Previous case
Comparisons of Number of
Time Step
Nu
mb
er
of
Tim
e S
tep
Tested simulation cases
in the paper
10ร
2ร4ร
3ร
23/50
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 180 360 540 720 900 1080
Pro
du
ctio
n M
ole
Fra
ctio
n (
CO
2)
Time [Days]
Streamline
Commercial Simulator0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0E+00 2.5E+04 5.0E+04 7.5E+04 1.0E+05
Pro
du
ctio
n M
ole
Fra
ctio
n (
CO
2)
Time [Days]
Streamline
Commercial Simulator
Conclusions
24/50
โข Developed a new SL-based simulation method to incorporate capillarity and gravity and applied to CO2 injection cases
โข Computational advantages:โข Minimizes the saturation correction term
โข Can take large time steps without anti-diffusive corrections
โข Demonstrated by synthetic and field case:โข Iterative IMPES approach handles nonlinearity
โข Larger time stepping obtained compared with commercial FD simulator
Application to Brugge Benchmark:
- Streamline-Simulation
- History Matching
- NPV Optimization
Brugge Benchmark Example
26/50
โข Benchmark model for HM, optimization problemโข 20 producers, 10 injectors in complex geometryโข Conduct 40 years of waterflood, 1000 stb/d per wel
Oil saturation and well location
Initial So Net gross ratio
PorosityRock table ID
ECLIPSE vs. Streamline Simulation:
Water-Cut (4 producers)
27/50
Circle : ECLIPSE
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 7500 15000
Pro
du
ctio
n W
ate
r C
ut
Time [Days]
BR-P-18 ECL
BR-P-8
BR-P-12
BR-P-1
BR-P-18 SL
BR-P-8
BR-P-12
BR-P-1
Line: Streamline
- ECLIPSE without NNC option
Comparisons of Oil Saturation
Distribution
28/50
Initial oil saturation
After 20 years
Streamline Commercial (ECL)
Presented at student paper contest 2013
Application to Brugge Benchmark:
- Streamline-Simulation
- History Matching
- NPV Optimization
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 500 1000 1500 2000
Wat
er
Cu
t
Time [Days]
Streamline-based Inverse Modeling
30/50
min ๐ฟ๐๐ค๐๐ก โ ๐๐ค๐๐ก๐ฟ๐ค
๐ฟ๐
1. Run reservoir simulation by given model
2. Trace Streamlines and calculate parameter sensitivity
3. Update parameters to satisfy:
Observation
Prediction
Motivation and Objective
31/50
Streamlines0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 500 1000 1500 2000
Wat
er C
ut
Time [Days]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000
CO
2M
ole
Fra
ctio
n
Time [Days]
WCT
โข What can we tell prior to breakthrough? Pressure data can be used while not considered previously
โข Study objective New approach to calculate pressure sensitivity along SL
Simultaneous inversion of pressure and water-cut data
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 50 100 150 200
Bo
tto
m H
ole
Pre
ssu
re
Time [Days]
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 50 100 150 200
Bo
tto
m H
ole
Pre
ssu
re
Time [Days]
BHP
Observation
Initial
ik
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 500 1000 1500 2000
Wat
er
Cu
t
Time [Days]
๐ฟ๐๐ค๐๐ก
Production WCT
Parameter Sensitivity Along Streamline
32/50
โข TOF( ): Travel time of neutral tracer along streamlines
, ,
, ,x y z
Inlet
dsx y z
u
๐๐ก
๐๐๐= โ
๐๐
๐๐
๐๐
๐๐๐โ๐๐
๐๐ก
โ1
=1
๐โฒ(๐)
โ๐๐๐๐
โข Water-cut travel time sensitivity:
injectorProducer
[He et. al,2003]
๐๐๐โ๐๐๐๐
=๐โ๐๐๐๐๐
โโ๐๐๐๐
โข Bottom hole pressure sensitivity: [new]
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 50 100 150 200
Bo
tto
m H
ole
Pre
ssu
re
Time [Days]Production BHP
๐ฟ๐๐โ๐
๐๐๐โ๐๐๐๐
โ๐๐๐
๐โ๐๐๐๐๐
โ๐๐๐
โ๐๐๐๐
Rate-Rate constraint
Rate-BHP constraint
Sensitivity Results: 1D CPG
(3phase Gas Injection)
-20.0
-15.0
-10.0
-5.0
0.0
0.0 0.5 1.0
Pre
ssu
re S
en
siti
vity
, wrt
k
Normalized Distance
Analytical (Stremaline)
Adjoint Method
0.0
5.0
10.0
15.0
20.0
0.0 0.5 1.0
Pre
ssu
re S
en
siti
vity
, wrt
k
Normalized Distance
Analytical (Stremaline)
Adjoint Method
33/50
Inj: Gas Rate
Prd: Rate
Producer BHP sensitivity to k
Injector BHP sensitivity to k
Sensitivity Results: 2D Areal
34/50
Inj
P1
P2P3
P4
Injector BHP sensitivity by k
P1 BHP sensitivity of by k
Permeability field(Wells by rate constraint)
Adjoint Proposed
Inversion of Permeability by LSQR
35/50
โข Run simulation and get following parameter
โข Solve LSQR Matrix :
โข Advantages:โข Find pressure/WCT sensitivity during SL simulationโข Localized (high resolution) changes in permeability
min ๐ฟ๐๐ค๐๐ก โ ๐๐ค๐๐ก๐ฟ๐ค + ๐ฟ๐๐โ๐ โ ๐๐โ๐๐ฟ๐ค + ๐ฝ1 ๐๐ฟ๐ค + ๐ฝ2 ๐๐ฟ๐ค
๐๐ค๐๐ก๐๐โ๐๐ฝ1๐๐ฝ2๐
โ๐ค =
๐ฟ๐๐ค๐๐ก๐ฟ๐๐โ๐00
Water-Cut Pressure - Smoothness- Consistency with
static model
Scaled by stdev
History Matching of Brugge Field
โข Use simulation result of Real.77 as observed dataโข Use Real.1 as initial modelโข Assume 3 years of data is available
Reference model Initial model
36/50
Available Observation Data
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
144.0 644.0 1144.0
Pro
du
ctio
n W
ate
r C
ut
[-]
Time [Days]
BR-P-11
BR-P-12
BR-P-15
BR-P-18
BR-P-11
BR-P-12
BR-P-15
BR-P-18
โข Only 4 producers have water breakthroughโข Pressure data is available for 30 wells
Water cut:
InitialObserved
37/50
Reference kx Initial kx
Change of kx, WCT Change of kx, WCT&BHP
High perm at middle layer
Change of Permeability
38/50
Reduction of Data Mismatch
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 20 40 60 80 100
No
rmal
ize
d A
bso
lute
Err
or.
Pre
ssu
re
Number of Iteration
0.0
0.3
0.6
0.9
1.2
1.5
0 20 40 60 80 100
No
rmal
ize
d A
bso
lute
Err
or,
Wat
er
Cu
t
Number of Iteration
Pressure RMSE error WCT RMSE error
Individual well
Mean
39/50
โข Have developed a new SL-based method to integrate pressure data into prior geologic models
โข Same advantages as prior streamline work:โข Analytic calculation of streamline sensitivitiesโข Requires only a single flow simulation per iteration
โข Can be applied to field pressure/rate data prior to water breakthrough
โข Can be integrate pressure with water-cut or GOR simultaneously, for black-oil and compositional simulation
Conclusion
40/50
Presented at student paper contest 2014
Application to Brugge Benchmark:
- Streamline-Simulation
- History Matching
- NPV Optimization
Overview
42/50
โข Problem: Determining optimal injection/production rates to
maximize NPVโข Solution:
Developed a new streamline and NPV-based rate allocation method
โข Advantages: Visualize efficiency of injector and producer Extensible to any secondary recovery process with
commercial simulator
- Improve oil production rate
- Works only after breakthrough
SL-based Flow Rate Allocation
Optimization: Previous Study
43/50
โข Use of Well Allocation Factors (WAFs): [Thiele et. al, 2003]
Well Allocation Factor map [SPE84080]
[SPE113628]
- WAFs: offset oil production of well-pair
โข 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
โbreakthroughโ time
- Increase well rate of high WAFs
Decrease
Increase
Decrease
Decrease
Decrease
Increase
- Improves sweep efficiency- Works only before breakthrough
โข Fast
โข Not robust
โข Does not optimize NPV
Proposed Optimization Method:
Overall Workflow
44/50
2. Trace Streamlines and Find connection map
3. Calculate NPV diagnostic plot
4. Reallocate well rate
via efficiency
1. Run simulation model
I1 I2 I3
I6
I5
I7 I8
NPV-based Efficiency of Streamline
P1 P2
P3 P4 P5
P6 P7
Hydrocarbon value, along SL
NPV along SL, integrate over reservoir life time
๐ฃ๐ ๐
= ๐๐ ๐
๐๐๐๐
๐๐๐๐๐ ๐ โ๐
๐๐ ๐ = ๐๐ ๐
๐๐๐๐
๐๐๐๐๐ ๐ + ๐๐ค๐๐ค๐ ๐ค โ๐ โ 1 + ๐ โโ๐/365โ
๐๐๐
๐๐๐๐
โ๐ > ๐ก๐๐ ๐
โข Hydrocarbon value and NPV along streamline
Pore volume ร Saturation ร FVF ร Price
Discount rate Reservoir life
I4
45/50
NPV-based Flow Diagnostics
I1 I2 I3
I6
I5
I7 I8
P1 P2
P3 P4 P5
P6 P7
๐๐๐๐๐ =ฯ๐ ๐ ๐๐ ๐ฯ๐ ๐ ๐ฃ๐ ๐ Total value
NPV
5-connection from Inj-4
Total value (Normalized)
NP
V (N
orm
aliz
ed)
๐ฐ๐๐๐จ๐จ๐
๐ท๐
๐ฐ๐๐๐จ๐จ๐ซ
๐ท๐
NPV-based diagnostic plot
I4
46/50
NP
V (N
orm
aliz
ed)
Streamline-based Rate Allocation:
A New Approach
47/50
๐๐๐๐ค = ๐๐๐๐๐๐๐๐๐าง๐๐๐๐๐๐
เดค๐๐๐ข๐๐ฅ๐
decrease rate
Increase rate
Before update After update
Total value (Normalized)
NP
V (N
orm
aliz
ed)
Total value (Normalized)
Streamline-based Rate Allocation:
A New Approach
48/50
๐๐๐๐ค = ๐๐๐๐๐๐๐๐๐าง๐๐๐๐๐๐
เดค๐๐๐ข๐๐ฅ๐
decrease rate
Increase rate
Before update After update
โข Advantages:โข Dynamically visualize efficiency of the injector and producer
โข Able to propose โbetterโ well rate during SL-simulation
Oil Saturation and Well Location
โข Constraints:- Field water injection qt <= 20,000 bbl/d- Well flow rate qti <= 6000 bbl/d- Producer BHP > 100 psi, Injector BHP < 6000 psi
โข Simulation Model:- Synthetic water flooding - 20 producers, 10 injectors- 20 years of simulation- Relative oil, water price = 1, -0.2 $/bbl
Brugge Benchmark Application
โข Compare developed model with 3 approaches: โข Uniform injection (Uniform), Well allocation factors
(WAFs), Equalize Arrival Time (EqArrive), Developed model (SLNPV)
49/50
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
50/50
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
51/50
MCERI
โข Have developed a new SL-based rate allocation method to improve recovery considering NPV
โข Proposed a new diagnostic plot to visualize the relative value and efficiency of a well in the asset
โข Results in greater NPV compared to prior streamline-based rate allocation methods
โข Can be applied to IOR/EOR simulation study with any commercial simulator, with low computational cost
Conclusions
54