A Generative Model of Discrete Fracture Networks Based on Latent Diffusion Model

ABSTRACT: Discrete fractures are prevalent in shallow crust and play a crucial role in the transport of fluids, mass, and heat underground. Therefore, accurately characterizing subsurface discrete fracture networks (DFNs) is essential for a wide range of scientific and engineering applications. Such characterization often relies on the inversion of indirect observational data. However, the inherent complexity of DFNs, together with the generally limited and sparse geological/geophysical data, present significant challenges to DFN characterization. In this study, we introduce a low-dimensional generative model for DFNs based on latent diffusion models (LDMs). The LDM is trained on DFN samples that incorporate well-acknowledged fracture statistical properties. Our results demonstrate that this method is able to generate high-quality DFNs from a low-dimensional latent space, and can properly reproduce the key fracture statistical distributions in terms of fracture location, length and orientation. This low-dimensional generative model provides an effective parameterization tool for subsurface DFN characterization. 1. INTRODUCTION Discrete fractures play a crucial role in governing mass and heat transport processes in the context of subsurface reservoir exploitation (Anderson and Fairley, 2008). The effective development of these reservoirs demands a comprehensive characterization of the underlying discrete fracture network (DFN) (Galloway et al., 2018; Lepillier et al., 2020). Given the high costs and technical challenges of directly observing subsurface fractures, the characterization process frequently relies on the inversion of indirect hydraulic or geophysical data (Afshari Moein et al., 2018; Hawkins et al., 2018; Jiang et al., 2023). However, such inversions often face ill-posedness problems, arising from the complex geometries of typically densely distributed fractures and the generally sparse nature of geological and geophysical data (Zhan et al., 2022; Jiang et al., 2023). Consequently, there is a pressing need for an effective low-dimensional parameterization method for DFNs to bridge the gap between their complexity and the limitations imposed by data scarcity. Traditional approaches treat each fracture as an independent entity, describing them through parameters related to their location, length and orientation. This leads to a high-dimensional and uncertain parameter space, which hinders the applicability of most inversion techniques.