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Production optimization [email protected]
Robust production optimization
1. Have an ensemble of history matched models
2. Robust production optimization: Optimize for all ensemble members.
Define a monetary value F, e.g.,F = (money of oil – cost of water produced/injected –cost of chemicals –cost of cleaning produced water)
Robust production optimization
UiS: • Find optimal production
strategies given uncertainty in reservoir description
• Apply methodologies to relevant EOR processes
IRIS:• Further development of methodology• Collaboration between IRIS, UiS, TU
Delft, TNO• IRIS-PhD student, Yiteng Zhang
Aojie Hong, PhD student at UiS (Prof. Reidar Brattvold)
Andreas S. Stordal, Sen. Research Scientist IRIS
Short literature review
• Ensemble based optimization– Lorentzen et al., 2006, SPE 99690
• Used ensemble of forecasts to optimize a single model
– Chen et al., 2008, SPE 112873• Ensemble of forecasts to optimize an
ensemble of models
– Raniolo et al., 2013, IOR 2013• Ensemble based optimization of a polymer
development strategy
Findings of Raniolo et al., 2013
• Difficult to calculate gradient valid for 100 different models
• Selected 5 realizations which was combined with 100 engineering controls (due to large variability in models)
• Use 20 controls per realizations• 30 iterations• Both water injection (10 %) and
polymer injection (16 %) better than do nothing case
Improved theoretical understanding of the ensemble
based algorithms• Do & Reynolds, Comp. Geosci., 2013,
points out the connection between simultaneous perturbation stochastic approximation (SPSA) and EnOpt
• Stordal et al., Math Geosci, 2015 shows connection between EnOpt and a well-defined natural evolution strategy, Gaussian Mutation Optimization (GMO)
Findings of Stordal et al., 2015
• Robust formulation of EnOpt can be extended to GMO
• Geological uncertainty makes algorithms more prone to Monte Carlo sampling errors
• Developes a variance reduction scheme that modifies the gradient computation in EnOpt
Production optimization results
Mathematical Geosciences , June 2015,
Stordal et al. A Theoretical look at Ensemble-Based Optimization in Reservoir Management
• Stordal is currently working with PhD student Yiteng Zhang and co-workers from TU Delft on improving the EnOpt
• A large number of simulations might be required. Can we use proxy models to speed up the optimization?
Capacitance-Resistance model (CRM) as a proxy model
• A. Hong, R. Bratvold & G. Nævdal: “Robust Production Optimization with Capacitance-Resistance Model as Precursor”, ECMOR XV, 2016
Motivation
Robust optimization (RO) requires a very large number of reservoir simulations, and it can be very computationally expensive to use grid-based reservoir models for RO. Thus, a proxy model could be useful to reduce the computational cost for RO.
Basic Requirements of a Proxy Model
1. Be able to capture the most important physics and mechanisms affecting production prediction (useful/relevant)
2. Be very computationally attractive (tractable)
• Albertoni & Lake (2003) introduced CRM to investigate connection and response time between producer and injector in waterfloodedreservoir using only production and injection rate data
Capacitance-Resistance Model (CRM)
• a material balance based model and derivedfrom total fluid continuity equation (andsaturation equation).
• few model parameters. Two main ones are– Connectivities: describes the fraction of water
injected by an injector that contributes to thetotal production of a producer;
– Time Constants: a characteristic time for thepressure wave to travel from an injector to aproducer.
• reduces a grid-based model to a two-point (injector-to-producer) model.
New workflow
1) screen and choose a proxy model relevant forproduction prediction of the reservoir system inquestion;
2) generate pseudo production data by running the grid-based model with a set of random controls;
3) determine the parameters of the proxy model bymatching the pseudo production data;
4) validate the proxy model by comparing its prediction tothe grid-based model’s with a new set of randomcontrols;
5) perform robust optimization using the validated proxymodel to find the optimal controls;
6) run grid-based simulations again with this optimalcontrol to get the optimized objective value.
Traditional Workflow: uses grid-based models all the way.
Implementation on a test case
• Grid-Based Model: 2D model with 4 injectors and 1 producer, oil and water phases.
• CRM-Based Model: Coupled CRMP.• Control: Water injection rate.• Objective: To maximize the
expected Net Present Value (eNPV).
• RO Method: EnOpt.• Ensemble Size: 100 realizations.
Match CRM model (right) to reservoir model (left)
Validate the CRM model
Results of optimization with new and traditional workflow
Workflow Base Traditional New eNPV
[million $] 23.624
(before RO) 32.031
(after RO) 31.837
(after RO) Total Computational Time
[seconds] - 31,980 2,800
Conclusion of study
• Found a different optimal solution with new approach
• Comparable NPV• Huge saving in computational time
• Plan to do further work on model reduction approaches– Aojie Hong will visit Larry Lake in 2017– Will also look into other approaches
