Efficient Uncertainty Quantification of Reservoir Properties for Parameter Estimation and Production Forecasting
Three levels of uncertainty and their impact on reservoir estimation and forecasting are examined: (1) definition of reservoir facies geometry derived from uncertain geologic and geophysical information; (2) non-uniqueness of identifying the permeability distribution through inverse parameter estimation using injection and production data; and (3) unknown, fine-scale spatial variation in the heterogeneous rock properties. Inverse parameter estimation with pilot points and kriging is used to create accurate estimates of the permeability field. Efficient sampling of the uncertainty space surrounding these estimates through both probability-field (p-field) simulation and sequential Gaussian simulation (sGs) is demonstrated using a test case reservoir with permeability dominated by a sand-shale, facies distribution. A geologic conceptual model, measured permeabilities at the wells and 2100 days of injection and production data are used to estimate the permeability distribution and create empirical prediction intervals for future production. Diversity of the estimated and sampled fields across all three levels of uncertainty is examined through multi-dimensional scaling. Sampled permeability fields provide precise and accurate parameter estimation from injection and production data. The sGs fields create a wider prediction interval and underestimate the true production rates relative to the p-field samples. For a given estimated variogram model, the p-field samples result in shorter ranges and lower nugget values relative to the sGs fields. Conditional sampling through p-field and sGs simulation provides greater diversity in the solution space than the parameter estimation alone for a fraction of the computational expense.