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Selecting Geostatistical Realizations Using Fast Flow Models for Reservoir Model Updating with the Ensemble Kalman Filters

Li, Xin 1; Kalla, Subhash 2; White, Christopher D.3; Shook, Michael 4
1 Subsurface Asset Consulting, Knowledge Reservoir, Houston, TX.
2 Upstream Research Center, ExxonMobil, Houston, TX.
3 Petroleum Engineering, Louisiana State University, Baton Rouge, LA.
4 Energy Technology Company, Chevron, Houston, TX.

Stochastic inversion methods such as the ensemble Kalman filter (EnKF) provide multiple reservoir models and forecasts, and integrate production and geologic data. The geologic knowledge encapsulated in the prior ensemble of reservoir models determines the diversity of the posterior ensemble. Selecting small sets of realizations that are nonetheless diverse and representative makes the inversion more efficient and robust.

To make prior ensembles manageably small, a subsample may be drawn using a univariate ranking of an easy-to-estimate secondary flow model response like effective permeability. However, ranking depends on the chosen response as well as engineering factors such as well spacing. Such samples may cause “filter divergence” which increases errors in reservoir property estimates. We address these complications by embracing the joint, multivariate distribution of many secondary responses and choosing realizations that are diverse in many responses.

We use single-phase tracer simulations for screening; the secondary responses include injectivity, Lorenz coefficients, and residence time statistics. Although the screening simulation simplifies the physics and operational constraints, tracer simulations include the heterogeneity and geometry of the full geomodels. Various injector-producer pairs are used to sample geomodel heterogeneity and anisotropy. This provides hundreds of secondary responses to describe the geomodels. Principal component analysis reduces secondary response dimensionality while preserving the desired model variability. Then, quasi-Monte Carlo Hammersley sequences sample the secondary response principal component space.

The multivariate secondary response (M2R) method, a naive random sample and two different univariate random samples are used to select 100 realizations from a suite of 1000 geomodels separately. These 4 100-member ensembles are used as prior ensembles for EnKF inversions of a waterflood, and convergence of each ensemble to the reference model is evaluated.

The comparison shows that multivariate response sampling mitigates filter divergence and improves inversion. The production forecasts from M2R-sampled geomodels match the reference model better than other samples.

The proposed flow-based screening method efficiently preserves geomodel variability and helps assess uncertainty within a stochastic modeling workflow.

 

AAPG Search and Discovery Article #90090©2009 AAPG Annual Convention and Exhibition, Denver, Colorado, June 7-10, 2009