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The distribution of fracture network is crucial to characterize the behaviorsof flow field and solute transport, especially for enhanced geothermal systems,as fractures provide preferential flow paths. However, estimating theparameters of the fracture networks and quantifying their uncertainties basedon observing data is a nontrivial task because inverse modeling of fracturedmodel is strongly nonlinear and non-Gaussian distributed. To address thisissue, a novel inverse modeling framework is proposed for the estimation of thefracture networks. The hierarchical parameterization method is adopted in thiswork. For a small number of large fractures, each fracture is characterized byfracture length, azimuth and coordination of the fracture center. For densesmall fractures, fracture density and fractal dimension are utilized tocharacterize the fracture networks. Moreover, we adopt variational auto-encoderand generative adversarial network (VAE-GAN) and fuse the GAN objective withprior constraint information to capture the distribution of the parameters ofcomplex fracture networks and to satisfy the prior knowledge of fracturefields, thereby mapping the high-dimensional complex parameter distributioninto low-dimensional continuous parameter field. Afterwards, relying on theBayesian framework, ensemble smoother is adopted based on the collected datafrom hydraulic tomography to reduce the uncertainty of the fracturedistribution. Two numerical cases with different complexity are used to testthe performance of the proposed framework. The results show that the proposedalgorithm can estimate effectively the distribution of the fracture fieldsafter providing sufficient prior constraint information and hydraulic headmeasurements.

Fracture network characterization with deep generative model based stochastic inversion