Sparse Geologic Dictionaries for Flexible and Low-Rank Subsurface Flow Model Calibration: Field Applications

Abstract:

Inference of spatially distributed reservoir and aquifer properties from scattered and spatially limited data poses a poorly constrained nonlinear inverse problem that can have many solutions. In particular, the uncertainty in the geologic continuity model can remarkably degrade the quality of fluid displacement predictions, hence, the efficiency of resource development plans. For model calibration, instead of estimating aquifer properties for each grid cell in the model, the sparse representation of the aquifer properties is estimated from nonlinear production data. The resulting calibration problem can be solved using recent developments in sparse signal processing, widely known as compressed sensing. This novel formulation leads to a sparse data inversion technique that effectively searches for relevant geologic patterns that can explain the available spatiotemporal data.

We recently introduced a new model calibration framework by using sparse geologic dictionaries that are constructed from uncertain prior geologic models. Here, we first demonstrate the effectiveness of the proposed sparse geologic dictionaries for flexible and robust model calibration under prior geologic uncertainty. We illustrate the effectiveness of the proposed approach in using limited nonlinear production data to identify a consistent geologic scenario from a number of candidate scenarios, which is usually a challenging problem in geostatistical reservoir characterization. We then evaluate the feasibility of adopting this framework for field application. In particular, we present subsurface field model calibration applications in which sparse geologic dictionaries are learned from uncertain prior information on large-scale reservoir property descriptions. We consider two large-scale field case studies, the Brugges and the Norne field examples. We discuss the construction of geologic dictionaries for large-scale problems and present reduced-order methods to speed up the computational aspect of the algorithm for field applications. Our results show that sparse geologic dictionaries offer a promising approach for field-scale data integration applications where the trade-offs between model dimensionality, computation speed, and geologic model plausibility should be reconciled effectively.