  The distribution of fracture network is crucial to characterize the behaviors
of flow field and solute transport, especially for enhanced geothermal systems,
as fractures provide preferential flow paths. However, estimating the
parameters of the fracture networks and quantifying their uncertainties based
on observing data is a nontrivial task because inverse modeling of fractured
model is strongly nonlinear and non-Gaussian distributed. To address this
issue, a novel inverse modeling framework is proposed for the estimation of the
fracture networks. The hierarchical parameterization method is adopted in this
work. For a small number of large fractures, each fracture is characterized by
fracture length, azimuth and coordination of the fracture center. For dense
small fractures, fracture density and fractal dimension are utilized to
characterize the fracture networks. Moreover, we adopt variational auto-encoder
and generative adversarial network (VAE-GAN) and fuse the GAN objective with
prior constraint information to capture the distribution of the parameters of
complex fracture networks and to satisfy the prior knowledge of fracture
fields, thereby mapping the high-dimensional complex parameter distribution
into low-dimensional continuous parameter field. Afterwards, relying on the
Bayesian framework, ensemble smoother is adopted based on the collected data
from hydraulic tomography to reduce the uncertainty of the fracture
distribution. Two numerical cases with different complexity are used to test
the performance of the proposed framework. The results show that the proposed
algorithm can estimate effectively the distribution of the fracture fields
after providing sufficient prior constraint information and hydraulic head
measurements.
