Subsurface fracture networks skip fracture-by-fracture sampling: a latent diffusion model generates native 3D voxel fields and honors 84.2% of sparse well voxels
Synopsis
Subsurface fracture networks were previously sampled fracture by fracture from prescribed statistics, which made sparse well observations hard to enforce. Here 2D and 3D networks are represented as binary occupancy fields, compressed by a variational autoencoder into a compact latent space, and learned by a diffusion model, with well observations injected through a learned conditioning encoder, classifier-free guidance, and diffusion posterior sampling. The 2D conditional model satisfies 99.6% of prescribed well observations, while the native 3D volumetric field satisfies 84.2% of observed well voxels while keeping fracture volume fraction close to the reference ensemble.
Interpretation
Fracture-network generation moves from sampling individual fractures to learning the distribution of whole binary occupancy fields in a compact latent space, shared by the 2D and 3D cases. Conventional stochastic discrete fracture network generators sample individual fractures from prescribed marginal distributions of location, length, and orientation; those marginals suit unconditional generation but do not by themselves determine the higher-order spatial organization and connectivity of a network. Generated ensembles match held-out validation ensembles in fracture area or volume fraction, two-point correlation functions, and chord-length distributions, and the reconstructed 3D fracture-plane count stays close to the reference ensemble.
Sparse well observations enter the sampling process through three complementary mechanisms rather than being filtered after generation. A learned conditioning encoder maps observed values and their location mask to a latent-resolution context, classifier-free guidance tunes that context's influence during sampling, and diffusion posterior sampling corrects the latent trajectory along the gradient of the mismatch between decoded fields and observations. The 2D conditional realizations satisfy 99.6% of prescribed well observations; in 3D, where each vertical borehole constrains a full fine-resolution column, conditional realizations satisfy 84.2% of well voxels, well above the unconditional rate.
Three-dimensional fractures are modeled directly as a native volumetric occupancy field instead of being reassembled from separate 2D projections. An earlier 3D generative parameterization described fracture occurrence and geometric attributes through separately generated 2D maps and focused on unconditional reproduction of fracture statistics, without incorporating sparse field observations into generation. The mean fracture volume fraction of the 3D conditional realizations stays near the training-ensemble mean, indicating that improved observation consistency does not come at the cost of a large change in overall fracture density.
Perspective
The demonstrated scope is 2D and 3D synthetic fracture networks: the 2D domain spans meters and is discretized into a pixel grid, while the 3D domain is a 10 m cube discretized into voxels, with training and validation ensembles generated from prescribed distributions and dfnWorks. Conditional evaluation uses wells sampled from held-out validation realizations, with a 2D well as a single pixel and a 3D well as a full voxel column. Flow-response comparisons for generated ensembles use multi-phase simulations across three 2D fracture configurations.
The lower 3D satisfaction rate relative to 2D is attributed possibly to the stronger constraint that each 3D borehole specifies a complete fine-resolution column while fracture surfaces remain only two to three voxels thick. The training-time consistency loss markedly raises generated fracture volume fraction and produces thicker fracture sheets in 3D, so the featured 3D model omits it and relies on learned conditioning, classifier-free guidance, and diffusion posterior sampling alone.