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 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.