Treatment of model error in subsurface flow history matching using a data-space method

Subsurface flow models are inherently imperfect, and the associated model error can lead to unreliable flow predictions. In this work, we introduce treatments for model error in a data-space inversion (DSI) framework. DSI is a history matching procedure that constructs posterior flow predictions (for quantities of interest) directly, within a Bayesian setting, using a large set of prior-model flow simulation results and observed data. The model error considered in this work derives from the use of upscaled/coarsened surrogate models for the prior-model flow simulations required by DSI. Our error treatment entails the simulation of a set of corresponding pairs of fine and upscaled models. These results are used to construct a principal component analysis (PCA) representation of error. A linear regression approach is introduced to capture the coupled nature of the coarse-scale simulation output and model error. To construct posterior DSI predictions, a joint inversion on coarse-scale simulation data and model error is performed using an ensemble smoother with multiple data assimilation. Both the prior simulation data and error terms are parameterized using PCA-based procedures. Results are presented for two-phase flow in 3D channelized geomodels. The corrected prior and DSI posterior results are compared to reference results generated from fine-scale simulations. Comparisons are presented for flow statistics, Mahalanobis distance, and relative error for multiple (synthetic) true models. The coupled model error treatment is shown to provide highly accurate prior results and posterior predictions that agree closely with reference results. Significant improvement relative to uncorrected coarse models is observed. The treatments developed here can be used to represent error from many different sources in a variety of subsurface flow settings.

Automated summary

Subsurface flow models are imperfect and model error can lead to unreliable predictions. This study introduces a method to handle model error in a data-space inversion framework, showing that the coupled model error treatment provides highly accurate results.