SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February1Closed-loop reservoir management SPE 119098Jan-Dirk Jansen 1,2Sippe Douma 2Roald Brouwer 2Paul Van den Hof 1Okko Bosgra 1Arnold Heemink 11) Delft University of Technology2) Shell International Exploration & ProductionDataassimilationalgorithmsNoise Output InputNoiseSystem (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February2Closed-loop reservoir management Hypothesis: It will be possible to significantly increase life-cycle value by changing reservoir management from a batch-type to a near-continuous model-based controlled activity. Key elements:Optimization under physical constraints and geological uncertaintiesData assimilation aimed at continuous updating of system models Inspiration:Measurement and control theoryMeteorology and oceanographySPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February3Closed-loop reservoir managementDataassimilationalgorithmsNoise Output Input Noise System (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February4DataassimilationalgorithmsNoise Output Input Noise System (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.Step 1: Open-loop reservoir managementSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February5Example open-loop reservoir management3D reservoir8 injection wells4 production wellsPeriod of 10 years High-perm channelsMinimum rate of 0.1 stb/dMaximum rate of 400 stb/dNo discount factorro = 20 $/stb, rw = 3 $/stb, ri = 1 $/stbSPE 102913, van Essen, 2006SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February6Optimization techniquesGlobal versus localGradient-based versus gradient-freeConstrained versus non-constrainedClassical versus non-classical (genetic algorithms etc.)We use optimal control theoryHas been proposed for history matching and for flooding optimization in the 70s.Recently revived for use in smart wells/fields (Brouwer @ TU Delft, Sarma @ Stanford, Eclipse)SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February7Optimal control theory, summaryGradient based optimization technique local optimumObjective function: NPV or ultimate recoveryControls: injection/production rates, pressures or valve openings (102 to 103 control variables, 104 106 states )Gradients of objective function with respect to controls obtained from adjoint equation (implicit differentiation) Results in dynamic control strategy, i.e. controls change over timeComputational effort independent of number of controlsImplemented in oil-company reservoir simulator. Proprietary aspects: constraint-handling, EOR, location optimization SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February8SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February9Why this wouldnt workReal wells have pressure constraintsGravity and capillary forces cannot be controlledReal wells are sparse and far apartReal fields are optimized by engineersWe will never operate a reservoir just using a model We do not know the reservoir!SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February10Step 2: Robust open-loop reservoir managementDataassimilationalgorithmsNoise Output Input Noise System (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.See: van Essen et al., SPE 102913SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February11Step 3: Data assimilation (history matching)DataassimilationalgorithmsNoise Output Input NoiseSystem (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February12Data assimilation (computer-assisted history matching)Variational methods minimization of mismatchReynolds (Tulsa), Sarma (Stanford)Monte Carlo methodsMCMC: Por, Alpak (Shell), NA: Christie (Herriott Watt) Ensemble Kalman filtering meteorology, oceanographyEvensen (Norsk Hydro), Naevdal (IRIS), Oliver (U. of Oklahoma), McLaughlin (MIT)Reservoir-specific methodsStreamline-based Thiele (StreamSim), Datta-Gupta (A&M) Probability perturbation Caers (Stanford) Non-classical methods (Simulated annealing, GAs, )SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February13Step 4: Closed-loop reservoir managementDataassimilationalgorithmsNoise Output Input NoiseSystem (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February14TruthDataassimilationalgorithmsNoise Output Input NoiseSystem (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February151.Start from initial ensemble of reservoir model estimatesClosed-loop exerciseNoise Output InputNoiseSystem (reservoir, wells & facilities)Sensors Measured outputDataassimilationalgorithmsOptimizationalgorithmsControllableinput2.Determine optimal controllable input (over lifetime)4.Simulate ensemble (over measurement interval) & generate predicted output3.Simulate true reservoir (over measurement interval) & generate noisy measured output5.Update all ensemble members i.e. estimate states and parametersPredicted outputSystem modelsSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February16Earlier closed-loop exercisesBrouwer et al. (SPE 2004), Overbeek et al. (ECMOR 2004), J ansen et al. (First Break, 2005), Naevdal et al. (CG 2006): EnKF & OCT (adjoint)Aitokhuehi and Durlofsky (J PSE 2005): Probab. perturb. meth. & OCT (num. grads.)Sarma et al. (SPE 2005, CG 2006, PST 2008): OCT 2x (adj.) Wang, Li and Reynolds (SPE 2007): OCT (num. grads), SPSA, EnKF & EnKFChen, Oliver and Zhang (SPE 2008): EnkF & EnOptPeters et al. (SPE 2008): Bruges field many combinationsSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February17Closed-loop example Initial ensembleSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February18Closed-loop example Ensemble updates at different timesSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February19Closed-loop example Cumulative production for different control strategies 0 500 1000 1500 2000 2500 30000123456x 105Time, dField rates, m3/d ideal case, cumwaterideal case, cumoil30 days, cumwater30 days, cumoil1 year, cumwater1 year, cumoil2 years, cumwater2 years, cumoil4 years cum, water4 years cum, oilreactive, cumwaterreactive, cumoilSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February20Closed-loop example NPV and contributions from water & oil productionHypothesis: It will be possible to significantly increase life-cycle value by changing reservoir management from a batch-type to a near-continuous model-based controlled activity.1 2 3 4 5 68.599.51010.5x 107NPV, $1 2 3 4 5 6-2-1.5-1.0-0.50 Discounted water costs, $1 2 3 4 5 68.599.51010.5x 107Discounted oil revenues, $reactiveopen-loop1 month 1 year2 years4 yearsSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February21Why do such crude models sometimes work so well?System-theoretical aspects SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February22Observability, controllability, identifiabilityControllability of a dynamic system is the ability to influence the states through manipulation of the inputs.Observability of a dynamic system is the ability to determine the states through observation of the outputs.Identifiablity of a dynamic system is the ability to determine the parameters from the input-output behavior.See Zandvliet et al., Computational Geosciences, 2008, 12 (4) 808-822.System modelstate (p,S)parameters (k,,)output (pwf ,qw ,qo )input (pwf ,qt )SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February23Does this mean that we dont need geology?System-theoretical aspectsFor our system the (few) identifiable parameter patterns correspond just to the (few) controllable state patternsReservoir dynamics lives in a state space of a much smaller dimension than the number of gridblocks in our modelsSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February24NO!System-theoretical aspectsI mean yes, we do need geology!Interpreting the history match results requires geological insightWell location-optimization requires a geological modelHowever, we need to focus on the relevant geology: Which geological features are identifiable? Which geological features influence controllability?SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February25Well rates ideal, reactive cases 0 1000 2000 30000100200300400Producer 1time, drate, m3/d0 1000 2000 30000200400600800Producer 2time, drate, m3/d0 1000 2000 30000100200300400Producer 3time, drate, m3/d0 1000 2000 3000050100150200250Producer 4time, drate, m3/d0 1000 2000 30000204060Injector 1time, drate, m3/d0 1000 2000 30000204060Injector 2time, drate, m3/d0 1000 2000 30000204060Injector 3time, drate, m3/d0 1000 2000 30000204060Injector 4time, drate, m3/d0 1000 2000 30000204060Injector 5time, drate, m3/d0 1000 2000 30000204060Injector 6time, drate, m3/d0 1000 2000 30000204060Injector 7time, drate, m3/d0 1000 2000 30000204060Injector 8time, drate, m3/dSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February26Well rate injector 5, 1/month case 0 500 1000 1500 2000 2500 300005101520253035404550time, drate, m3/dInitial optimized rateSmoothed optimal rateSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February27Closed-loop reservoir management learnings so farSize of the prize still unknown (open-loop and closed-loop) Specific optimization and data assimilation techniques not of major importance Increased update frequency leads to increased NPV Simple reservoir models sometimes work well for control (for fixed well positions) Reservoir dynamics lives in low-order space. How do we determine the relevant geology? Input also contains redundancy: different controls may lead to nearly same NPV Combination with short-term production optimization?SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February28Questions?DataassimilationalgorithmsNoise Output Input NoiseSystem (reservoir, wells & facilities)OptimizationalgorithmsSensors System modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February29Back-up slidesSPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February30Example robust open-loopSame truth100 different reservoir models (6 shown)Optimize expectation of objective functionVan Essen et al., SPE 102913SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February31Robust optimization results3 control strategies applied to set of 100 realizations:reactive control, nominal optimization, robust optimizationVan Essen et al., SPE 102913SPE119098 - 2009 Reservoir Simulation Symposium, Woodlands, USA, 2-4 February32Reduced-order modellingDataassimilationalgorithmsNoise Output Input Noise System (reservoir, wells & facilities)OptimizationalgorithmsSensors Low-order modelsPredicted output Measured outputControllableinputGeology, seismics,well logs, well tests,fluid properties, etc.up/downscalingHigh-order models