Transcript Optimization of Advanced Well Type and Performance
Optimization of Advanced Well Type and Performance
Louis J. Durlofsky
(from www.halliburton.com) Department of Petroleum Engineering, Stanford University ChevronTexaco ETC, San Ramon, CA
1
Acknowledgments
•
B. Yeten, I. Aitokhuehi, V. Artus
•
K. Aziz, P. Sarma
2
Multilateral Well Types TAML, 1999
3
Optimization of NCW Type and Placement
• Applying a Genetic Algorithm that optimizes via analogy to Darwinian natural selection • GA approach combines “survival of the fittest” with stochastic information exchange • Algorithm includes populations with generations that reproduce with crossover and mutation • General level of fitness as well as most fit individual tend to increase as algorithm proceeds 4
Encoding of Unknowns for GA 10101 10110 1011 010111 1101 1000 101 100110 1001 1010 ...
I1 J1 K1 l xy
q
h z Jn l xy
q
h z heel toe heel toe main trunk lateral multilateral well
• Representation allows well type to evolve (
Jn
0 generates a lateral) 5
Nonconventional Well Optimization p
l h x h y t h z
q
xy z
Unknowns
l J
q
t
1
xy
1
z
1 1
t l J
q
k z k k xy k
q d well
Objective Function
f
n Y
1
1
n
Q
Q Q w o g
T n
C
C C w o g
C well
• Objective function can be any simulation output (NPV, cumulative oil) 6
Flowchart for Single Geological Model 1 compose population 0101011101010111 1101001001111100 0010110111100010 1101011100111101 2 evaluate fitness y1 y2
Objective function
f
(or fitness): NPV, cumulative oil
reservoir simulator x1 x2 x3 x4 x5 x6 ANN skin transformer 3 perform a local search hill climber 4 rank based selection 5 reproduction 6 form children
7
Single Well Optimization Example
• Objective: optimum well and production rate that maximizes NPV, subject to GOR, WOR constraints
Optimum well (quad-lateral) 200.0
180.0
160.0
140.0
120.0
100.0
80.0
60.0
0 Best 10 20 Generation # 30 Average 40
8 (from Yeten et al., 2003)
Evolution of Well Types 100% 80% 60% 40% 20% 0% 1 3 5 7 9 11 invalid 13 15 monobore 17 19 1 lateral 21 23 2 laterals 25 27 29 3 laterals 31 33 4 laterals 35 37 39
9 (from Yeten et al., 2003)
Nonconventional Well Optimization with Geological Uncertainty ?
10
Optimization over Multiple Realizations
• Find well that maximizes
F
= <
f
> +
r
s
< f >
is average fitness of well over
N
risk attitude, s 2 is variance in
f
realizations, over realizations)
r
is • Evaluate each individual (well) for each realization (well
i
, realization
j
)
E in iz (G
F f
i
s
i
11
Risk Neutral (r =0) Optimization (Primary Production, Maximize NPV)
Realization # 12
Risk Averse (r = -0.5) Optimization (Primary Production, Maximize NPV)
Realization # 13
Comparison of Optimization Results Risk neutral attitude (r = 0)
well cost = $ 759,158 expected NPV = $ 3,506,390 std = $ 935,720
Risk averse attitude (r = -0.5)
well cost = $ 1,058,704 expected NPV = $ 3,401,210 std = $ 404,920 Realization # 14
Proxy - Unsupervised Cluster Analysis
• Attributes can be combined into principal components
cluster #
15
Proxy Estimate for a Single Realization (Primary Production, Monobore Wells) r = 0.93
actual fitness
16
Estimated Mean for All Realization (Primary Production, Monobore Wells) r = 0.97
actual mean fitness
17
www.halliburton.com
18
Smart Well Control: “Reactive” versus “Defensive”
• Reactive control: adjust downhole settings to react to problems (e.g., water or gas production) as they occur • Defensive control: optimize downhole settings to avoid or minimize problems. This requires: – Accurate reservoir description (HM models) – Optimization procedure • Optimize using gradients computed numerically or via adjoint procedure 19
Numerical Gradients
• Define cost function
J
(NPV, cumulative oil)
J
1
N n
0
L n
x n
1 ,
u n
x
- dynamical states,
u
- controls • Numerically compute
J
/
u
J
u
u
)
u
• Apply conjugate gradient technique to drive
J
/
u
to 0 20
Adjoint Procedure
• Define
augmented
cost function
J A
J A
1
N n
0
L n
x n
1 ,
u n
1)
g n
x n
1 ,
x n
,
u n
u
- Lagrange multipliers, - controls,
g x
- dynamical states, - reservoir simulation equations • Optimality requires first variation of
J A
= 0 ( d
J A
= 0):
L n
1
x n
1)
g n
x n
Tn
g n
1
x n
adjoint equations
0
J
u A n
L n
u n
1)
g n
u n
0
optimality criteria
21
Adjoint versus Numerical Gradient Approaches for Optimization
Numerical Gradients
Advantages
• Easily implemented • No simulator source code required Adjoint Gradients
Advantages
• Much faster for large number of wells & updates • Can also be used for HM
Main Drawback
• CPU requirements
Main Drawback
• Adjoint simulator required • Adjoint and numerical gradient procedures developed; implementation of smart well model into
GPRS
underway 22
Smart Well Model
• Numerical gradient approach (Yeten et al., 2002) allows use of existing (commercial) simulator • Applying
ECLIPSE
multi-segment wells option 23
Optimization Methodology - Fixed Geology
• Sequential restarts applied to determine optimal settings 24
Impact of Smart Well Control - Example
• Channelized reservoir, 4 controlled branches • Production at fixed liquid rate with GOR and WOR constraints (three-phase system) 25
Effect of Valve Control on Oil Production Oil rate - uncontrolled case Oil rate - controlled case
• Downhole control provides an increase in cumulative oil production of 47% (from Yeten et al., 2002) 26
Optimized Valve Settings
27
Optimization with History Matching
• Actual geology is unknown (one model selected randomly represents “actual” reservoir and provides “production” data) • Update reservoir models based on synthetic history • Optimize using current (history-matched) model Optimization Step Pass # Restart Points New history-matched reservoir model 28
History Matching Procedure
• Facies-based probability perturbation algorithms (Caers, 2003) • Multiple-point geostatistics (training images) • Performs two levels of nonlinear optimization (facies and
k
f ) • History matching based on well pressure, cumulative oil and water cut (for each branch) • Initial models from same training image as “actual” models 29
History Matching Objective Functions
• Two levels of optimization – Single parameter facies optimization minimize
r D
[ 0 , 1 ]
g
(
r D
)
j
(
D j
(
r D
)
D
model data,
D obs D obs
,
j
) 2 observed data – Multivariate permeability-porosity optimization 0
i
1
α
j
(
D j
D
) 2
α
f
k
30
Channelized Model I
• Unconditioned 2 facies model, 20 x 20 x 6 grid • Quad-lateral well with a valve on each branch – Constant total fluid rate (10 MSTB/D initial liquid rate) – Shut-in well if water cut > 80% • OWG flow, M < 1; 4 optimization and HM steps 31
Optimization on Known Geology 3000 2500 2000 1500 1000 500 0 0 500
days
without valves with valves
1000 0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 0 500
days
without valves with valves
1000
• Valves provide ~40% gain in cumulative oil over no-valve base case 32
Dimensionless Increase in N
p
• Dimensionless cumulative oil difference,
N
N
N p target model w/valves N p known geology, w/valves
N p k nown geology, no valves N p k nown geology, n o valves
N
N
= 0 (no valves result) = 1 (known geology result) 33
Illustration of Incremental Recovery 3000 2500 2000 1500 1000 500 0 0
N
=1
N
=0.5
N
=0
500
days
HM with valves without valves with valves
1000
34
Optimization with History Matching 3000 2500 2000 1500 1000 500 0 0
Known geol. w/o valves HM w/valves Known geol. w/valves
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 0 500
days
1000 500
days
• Optimization with history matching gives
N
=0.94
• Repeating for different initial models:
N
=0.90
0.18
1000
35
Channelized Model II
• Unconditioned 2 facies model, 20 x 20 x 6 grid • Different training image than Channelized Model I, same well and other system parameters 36
Optimization with History Matching - CM II
3000 2500 2000 1500 1000 500 0 0
N
=0.41
Known geol. w/o valves HM w/valves Known geol. w/valves 200 400
days
600 800 1000 • Repeating for different initial models:
N
=0.44
0.27
• Inaccuracy may be due to nonuniqueness of HM 37
Optimization over Multiple HM Models Number of HM Models
1 3 5
N (
s
)
0.44 0.27
0.85 0.16
0.84
• Use of multiple history-matched models provides significant gains 38
Effect of Conditioning (on Facies)
Model CM I CM II
Single HM Model
N
w/o HM, w/ cond
N
w/ HM, w/o cond 0.58 ± 0.17
0.54 ± 0.27
0.90 ± 0.18
0.44 ± 0.27
N
w/HM, w/cond 0.88 ± 0.06
0.64 ± 0.17
• Partial redundancy of conditioning and production data reduces impact of conditioning in some cases • For CM II, use of 3 conditioned and history matched models gives
N
= 0.83 0.10 (~same as w/o cond) 39
Summary
• Presented genetic algorithm for optimization of nonconventional well type and placement • Applied GA under geological uncertainty • Developed combined valve optimization – history matching procedure for real-time smart well control • Demonstrated that optimization over multiple history-matched models beneficial in some cases 40
Research Directions
• Developing efficient proxies for optimization of well type and placement under geological uncertainty • Implementing adjoint approach (optimal control theory) and multisegment well model into
GPRS
for determination of valve settings • Plan to incorporate additional data (4D seismic) and accelerate history matching procedure 41