PowerPoint Presentation

Ensemble based History MatchingOutlineReservoir modelling and simulationHistory matching problem and uncertainty predictionEnsemble Kalman filter (EnKF)Field case example

Reservoir Simulation and ModellingEngineering targetTo update sequentially geological model to match the model from field production dataBusiness targetTo reduce uncertainty in reserves and production targetsProject goalProvide continuously updated and integrated models with reduced and quantified uncertaintyChallenges impede history matching performanceUnknown parametersMeasurements (too much data)Uncertainty quantification.

Geological data

Geophysical data

Reservoir Engineering data

History Matching and Uncertainty PredictionHistoryPredictionInitial uncertaintyPredicted uncertaintyReduced predicted uncertaintyReduced initial uncertaintyBayesian formulationBayes theoremGaussian priorsMonte Carlo modelQuadratic cost-functionSequential processing of measurementsSequence of inverse problemsMinimization/SamplingIgnore model errorsSolve only for parameters?Ensemble methodsEnsemble Kalman Filtering vs Traditional History Matching Updates both static and dynamic quantities (such as pressure and saturations) Suitable for updating non-linear reservoir simulation models One flow simulation for each ensemble member No need of sensitivity coefficients Fully automated Ensemble members updated sequentially in time and reflecting latestassimilated data Uncertainty of prediction always up-to-date and straightforward from theensemble members Updates only static quantities (such as porosity andpermeability) Repeated flow simulations of the entire production history Sensitivity coefficient calculations Not fully automated History matching repeated with all data when new data are available Not suitable for real-time reservoir model updating Difficult for uncertainty assessment

Illustration of the EnKF from the point view of Bayesian conceptEnsemble Kalman Filtering vs Traditional History MatchingInitial modelSimulate 1st available measurementSimulation responseReservoir measurementAssimilationUpdate reservoir modelContinue simulationTimeInitial modelTune reservoir model by using entire historyMatch?Update reservoir modelFinal best matched modelYesNoOUTLINE OF THE ENKF ALGORITHMEnsemble matrixRelationship between the observed data and the true state vectorMethods to solve the assimilation step:Direct Inverse CalculationStandard EnKF Assimilation CalculationSquare Root Algorithm with Measurement PerturbationsSquare Root Algorithm without Measurement PerturbationsWhich one is better?

Direct Inverse Calculation Method

Enkf with Standard Assimilation Method

Square Root Algorithm with Measurement Perturbations

Square Root Algorithm without Measurement Perturbations