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Stanford Center for Reservoir Forecasting

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1 Stanford Center for Reservoir Forecasting
Direct updating of geostatistical reservoir models using iterative resampling with DISPAT Xiaojin Tan & Jef Caers SCRF 2012 SCRF 2012

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 Conditioning with resampled points

11 Effect on ensemble average
# resampled points =121 # resampled points =361 more perturbation blurry less perturbation crispy

12 Updating with regions # resampled points =18 # resampled points =128
fix the bottom part and perturb the top part

13 Updating with regions # resampled points =18 # resampled points =128

14 Effect on Ensemble Average
# resampled points =18 # resampled points =128 no discontinuity at the region boundary more perturbation less perturbation

15 Flow modeling Investigate the influence of the amount of perturbation on a flow response Water Rate Water rate Time, days Producer well Injector well

16 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

17 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

18 Reservoir updating proof of concept
Updated with Metropolis a single legacy reservoir model updated model Water Rate target data days

19 Conclusions What is the appeal of the idea ? Practical No model parameterization No need for ensemble construction Applications envisioned Mature fields 4D seismic

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