鲁棒优化和概率预测量化地质模型不确定性 quantifying geologic …
TRANSCRIPT
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Quantifying Geologic Uncertainty through Brownfield Optimization and Probabilistic Forecasting
鲁棒优化和概率预测量化地质模型不确定性
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Agenda • New Approach to History Matching • Probabilistic Forecasting • Introduction to Robust Optimization
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Keynes’ Challenge Would I Rather Have One Precise History
Match Or A Range Of Plausible Solutions?
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Bayesian Formulation
1701-1761
P 𝑚𝑚𝑚𝑚𝑚|𝑚𝑑𝑑𝑑 = 𝑃(𝑚𝑚𝑚𝑚𝑚)P(𝑚𝑑𝑑𝑑|𝑚𝑚𝑚𝑚𝑚)
P(𝑚𝑑𝑑𝑑)
Posterior Probability Prior Probability Conditional Probability
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Metropolis-Hastings Markov Chain Monte Carlo (MCMC)
Markov Chain
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SPE 175122
Proxy-based Acceptance-Rejection (CMG PAR)
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Two Parameter Proof of Concept
HM Parameters:• Permeability• Skin
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Reference Result – 5000 Brute ForceSearch
5% HM Error
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Results from Current EnginesDE DECE
PSO Proxy
Each engineruns 100jobs
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Results from Current EnginesDE DECE
PSO Proxy
Each engineruns 100jobs
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Results from CMG PAR
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Brugge HM Case Study
Courtesy of TNO
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HM Workflow
Rank and Select Representative
Geologic Realizations
Apply Additional Uncertain
Parameters
Select History Match
Parameters
Run CMG PAR Engine
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Rank Geologic Realizations
0
2000000
4000000
6000000
8000000
10000000
12000000
0 20 40 60 80 100 120
Oil
Prod
uced
(m3)
ID
Cumulative Oil versus ID
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Probabilistic Forecasts C
umul
ativ
e O
il (b
bl)
Cum
ulat
ive
Oil
(bbl
)
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Probabilistic Forecast Proof of Concept
• 9th SPE comparative solution project • 24×25×15 grid • 1 water injection well, 12 producers
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History Matching Parameters • Permeability multipliers
• 15 multipliers, one for each layer • KV to KH ratio
• One for entire model
SWT and capillary pressure (end points and exponents)
10
SLT (end points and exponents)
6
Permeability multipliers 15 KV to KH ratio 1
Total 32
Summary of HM parameters
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History Matching
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Probabilistic Forecast
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Probabilistic Forecast Workflow using CMG PAR Sampling Method
Bayesian HM using CMG PAR
• Experimental design
• RBF proxy modelling
• Proxy-based Acceptance-Rejection (PAR) sampling
Filtering HM Result
• Review HM result
• Determine HM quality thresholds
• Identify models with acceptable HM quality
Probabilistic Forecast
• Set forecast well constraints
• Forecast simulations based on acceptable HM models
• Statistical analysis
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Traditional Nominal Optimization
Are we “precisely wrong?”
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What is Robust Optimization?
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Nominal vs. Robust Optimization Nominal Optimization Pros • Fast: one simulation per
scenario • Likely to improve results
Cons • No guarantee of success • May be suboptimal in
reality
Robust Optimization Pros • Higher probability of
success • Lower risk
Cons • Additional computation
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Base Case Realization 1 Realization 2 Realization 3 Realization 4 Realization 5 Results: Optimal Wells Locations
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Robust Optimization
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Base Case Histogram
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Base Case vs. Nominal
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Base Case vs. Nominal & Robust Optimizations
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Cumulative Probability: Base Case – Nominal – Robust Optimization
RF < 32% Probability Base case 96% Nominal
optimization 39%
Robust optimization 9%
RF < 32%
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Bayesian HM using CMG PAR
Filtering HM Result
Probabilistic Forecast
Select Best Case for
each Realization
Robust Optimization
Probabilistic Forecast
Robust Optimization for Brownfields
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Cumulative Probability: Base Case – Nominal – Robust Optimization
NPV
Pro
babi
lity
0
10
20
30
40
50
60
70
80
90
100
Base Case
Optimized Case
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Conclusions • In today’s market more than ever quantifying
uncertainty is crucial • CMG has tools to help carry geologic
uncertainty easily through your workflows • Carrying this uncertainty through the workflow
provides immense value in making better decisions
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CMG’s Vision To be the leading developer and supplier of dynamic reservoir technologies in the WORLD