Stanford Center for Reservoir Forecasting Direct updating of geostatistical reservoir models using iterative resampling with DISPAT Xiaojin Tan & Jef Caers SCRF 2012 SCRF 2012
Motivation Question addressed: How to update a single legacy reservoir model with new production data? Example Single legacy model matches history but there is No geostat input (variograms, TI) No parameterization No software for model updating
Basic idea Use the current existing reservoir model as a training image in a non-stationary geostatistical algorithm termed dispat. Using iterative spatial resampling (ISR) to update the current legacy model with the additional production data
DisPat Why Dispat? Every single real legacy model has non-stationary elements Conditioned to wells Conditioned to seismic Imposed layering and trends (vertical/horizontal) CPU-efficient for large models
Mariethoz et al., 2010 m1 m2 m3 Sampling Sampling r1 r2 1.only one parameter required 2.keep the same spatial continuity Mariethoz et al., 2010
Metropolis Sampling Current model mi proposal model m* Perturb using ISR proposal model current model flow simulation flow simulation Water Rate Water Rate target Accept with p=L(m*)/ L(mi) target days days
Updating with Dispat and ISR Summary Current reservoir = TI, Current reservoir = mi Start Sampler ISR proposes m* Run the flow simulator to obtain L(m*). Accept/rejection according to the Metropolis criterion The training image remains the same
Results Study properties of resampling with dispat apply ISR to realizations generated by dispat Updating with regions freeze a part of domain Flow modeling the influence of the amount of perturbation on a flow response
Properties of resampling with dispat Training image Single realization Data extracted dispat The only input required with dispat a base case to create perturbation with different amount of data extracted regular grids coarse grid locations avoid discontinuity near data locations
Conditioning with resampled points
Effect on ensemble average # resampled points =121 # resampled points =361 more perturbation blurry less perturbation crispy
Updating with regions # resampled points =18 # resampled points =128 fix the bottom part and perturb the top part
Updating with regions # resampled points =18 # resampled points =128
Effect on Ensemble Average # resampled points =18 # resampled points =128 no discontinuity at the region boundary more perturbation less perturbation
Flow modeling Investigate the influence of the amount of perturbation on a flow response Water Rate Water rate Time, days Producer well Injector well
Flow modeling Investigate the influence of the amount of perturbation on a flow response Large perturbation (small # resampled points) Large perturbation (small # resampled points) Large perturbation (small # resampled points) Water Rate Water Rate Water Rate Water Rate Black = base case Black = base case Black = base case Black = base case Small perturbation (large # resampled points) days
Reservoir updating: proof of concept A simple illustrative example: Legacy model new data Water rate Forecast with current model History data Producer well days Injector well
Reservoir updating proof of concept Updated with Metropolis a single legacy reservoir model updated model Water Rate target data days
Conclusions What is the appeal of the idea ? Practical No model parameterization No need for ensemble construction Applications envisioned Mature fields 4D seismic