Selecting appropriate model complexity: An example of tracer inversion for thermal prediction in enhanced geothermal systems

Abstract

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 longterm 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.

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

“…The multi-physics simulation platform used in this study, GEOS, is available in Settgast et al (2022). The synthetic flow, pressure, tracer, and thermal data, as well as the scripts used for aperture generation, principal component analysis and ES-MDA are available in Wu et al (2024).…”

“…The synthetic flow, pressure, tracer, and thermal data, as well as the scripts used for aperture generation, principal component analysis and ES‐MDA are available in Wu et al. (2024).…”