Fractures play important roles in fluid and heat flow during heat extraction from an enhanced geothermal system (EGS). Quantifying the associated uncertainties in fractures is critical for predicting long-term thermal performance of EGSs. Considerable advancements have been made regarding the inversion of fracture characteristics such as aperture distribution. However, most previous studies assumed a constant fracture aperture to simplify the inversion, while both experimental and numerical results indicated significant variations in fracture aperture due to complex thermo-hydro-mechanical (THM) coupled processes during heat extraction. This study introduces a multi-stage inversion framework that integrates the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) with a THM coupled model to capture the dynamic evolution of fracture aperture. The framework executes multiple aperture inversions at different times during EGS operation. In each inversion stage, we use ES-MDA to invert for fracture aperture by assimilating tracer data, and then perform THM modeling to analyze fracture aperture evolution under coupled THM processes and predict thermal performance. We propose a principle to assure a smooth transition between two consecutive inversion stages, that the posterior aperture fields obtained in an inversion stage are used as the prior aperture fields for the following stage, and the temperature field simulated in the previous inversion stage serves as the initial temperature field for the following stage. Application of the framework to a synthetic field-scale EGS model demonstrates its efficacy in capturing the dynamic evolution of fracture aperture, resulting in more accurate thermal predictions compared with previous inversion methods assuming constant fracture aperture.

A major challenge in the inversion of subsurface parameters is the ill-posedness issue caused by the inherent subsurface complexities and the generally spatially sparse data. Appropriate simplifications of inversion models are thus necessary to make the inversion process tractable and meanwhile preserve the predictive ability of the inversion results. In the present study, we investigate the effect of model complexity on the inversion of fracture aperture distribution as well as the prediction of long-term thermal performance in a field-scale single-fracture EGS model. Principal component analysis (PCA) was used to map the original cell-based aperture field to a low-dimensional latent space. The complexity of the inversion model was quantitatively represented by the percentage of total variance in the original aperture fields preserved by the latent space. Tracer, pressure and flow rate data were used to invert for fracture aperture through an ensemble-based inversion method, and the inferred aperture field was then used to predict thermal performance. We found that an over-simplified aperture model could not reproduce the inversion data and the predicted thermal response was biased. A complex aperture model could reproduce the data but the thermal prediction showed significant uncertainty. A model with moderate complexity, although not resolving many fine features in the “true” aperture field, successfully matched the data and predicted the long-term thermal behavior. The results provide important insights into the selection of model complexity for effective subsurface reservoir inversion and prediction.