Projection-based low-dimensional parameterization method for three-dimensional discrete fracture networks through generative adversarial network

Fracture network characterization is an important yet intractable task in many subsurface applications related to energy recovery, storage, and waste disposal. A major challenge is the lack of advanced methods for parameterizing complex fracture networks within low-dimensional parameter spaces to address the ill-posedness caused by the inherent complexity of subsurface fractures and pervasive data scarcity. In this work, we propose a deep-learning-assisted, projection-based approach to generate high-fidelity three-dimensional (3D) discrete fracture networks (DFNs) from low-dimensional latent spaces. Since directly generating 3D DFNs is computationally prohibitive, we decompose the task into two more tractable ones: generating two-dimensional (2D) DFNs and establishing the projection relationship between 2D and 3D DFNs. We treat a 2D DFN as the projection of its 3D counterpart on a 2D plane, introducing two parameters, fracture dip angle and projection distance, to describe the projection relationship. We first develop three generative models to generate 2D DFNs, dip angle maps, and projection distance maps from low-dimensional latent spaces through Wasserstein generative adversarial networks with gradient penalty (WGAN-GP), and then construct 3D DFNs via reverse projection of these three 2D components. We demonstrate that the proposed approach faithfully generates 50-fracture 3D DFNs (300 parameters via conventional methods) from a 40-dimensional latent space, and 100-fracture 3D DFNs (600 conventional parameters) from a 72-dimensional space. Fracture connectivity and fluid flow characteristics in the generated 3D DFNs are also comprehensively analyzed to illustrate the approach’s effectiveness and robustness in generating high-fidelity 3D DFNs while maintaining substantial diversity to facilitate subsequent DFN inversion.