Prior Aperture Realizations From Far-Field Stress Approximation for Ensemble-Based Data Assimilation in Naturally Fractured Reservoirs

Fractures are ubiquitous in reservoirs used for geothermal heat extraction, CO₂ storage, and other subsurface applications. Their significant impact on flow and transport requires accurate characterization for performance estimation and risk assessment. However, fracture geometry and aperture are usually associated with large uncertainties. Data assimilation (or history matching) is a well-established tool for reducing the uncertainty of model parameters and states to improve simulation results. In recent years, ensemble-based methods like the ensemble smoother with multiple data assimilation (ESMDA) have gained popularity. A key aspect of those methods is a well-constructed prior ensemble that accurately reflects available knowledge. Here, we consider a geological scenario where fracture geometry is known, and opening is created by shearing. Generating prior realizations of aperture with geomechanical simulators might become computationally prohibitive, while purely stochastic approaches neglect important geological information. We therefore introduce the far-field stress approximation (FFSA), a proxy model in which this stress is projected onto the fracture planes and shear displacement is approximated with linear elastic theory. We compensate for modeling errors by introducing additional uncertainty in the underlying model parameters. The FFSA efficiently generates reasonable prior realizations at low computational costs. The resulting posterior ensemble obtained from our ESMDA framework matches the flow and transport behavior of the synthetic reference at measurement locations and improves the estimation of fracture aperture. These results markedly outperform those obtained from prior ensembles based on two naïve stochastic approaches, thus underlining the importance of accurate prior modeling.