3D latent diffusion models for parameterizing and history matching multiscenario facies systems

TL;DR

This work develops a 3D latent diffusion framework (3D-LDM) to parameterize large, three-facies geomodels with uncertain geological scenarios, enabling efficient history matching in latent space while preserving geological realism. By coupling a 3D VAE with a DDIM-based diffusion process and adding a perceptual loss, the method generates diverse, geologically consistent realizations that respect hard data and flow statistics. Across three synthetic cases, latent-space history matching with ESMDA achieves substantial uncertainty reduction in both forecasts and scenario parameters, while offering dramatic gains in model-generation speed. The approach provides a unified, scalable pathway for integrating geology and data assimilation, with clear avenues for extension to MCMC, larger metaparameter ranges, and real-field applications.

Abstract

Geological parameterization procedures entail the mapping of a high-dimensional geomodel to a low-dimensional latent variable. These parameterizations can be very useful for history matching because the number of variables to be calibrated is greatly reduced, and the mapping can be constructed such that geological realism is automatically preserved. In this work, a parameterization method based on generative latent diffusion models (LDMs) is developed for 3D channel-levee-mud systems. Geomodels with variable scenario parameters, specifically mud fraction, channel orientation, and channel width, are considered. A perceptual loss term is included during training to improve geological realism. For any set of scenario parameters, an (essentially) infinite number of realizations can be generated, so our LDM parameterizes over a very wide model space. New realizations constructed using the LDM procedure are shown to closely resemble reference geomodels, both visually and in terms of one- and two-point spatial statistics. Flow response distributions, for a specified set of injection and production wells, are also shown to be in close agreement between the two sets of models. The parameterization method is applied for ensemble-based history matching, with model updates performed in the LDM latent space, for cases involving geological scenario uncertainty. For three synthetic true models corresponding to different geological scenarios, we observe clear uncertainty reduction in both production forecasts and geological scenario parameters. The overall method is additionally shown to provide posterior geomodels consistent with the synthetic true model in each case.

Figures (17)

• Figure 1: (a) Conditioning locations for all geomodels and well labels for (later) flow simulations. (b–f) Representative realizations corresponding to different geological scenarios from the Petrel-generated training set (scenario parameters are given for each geomodel, channel width in units of grid cells).
• Figure 2: Schematic of the training procedure for the 3D-LDM method and the computation of loss terms. The VAE component is shown in (a) and the U-net component in (b).
• Figure 3: Illustration of the geomodel generation process with the 3D-LDM method. In (a) the discrete-step denoising performed by the U-net in the latent space is shown, while in (b) the denoised latent variables and corresponding decoded geomodels with different numbers of total denoising steps are depicted.
• Figure 4: Randomly selected 3D-LDM generated realizations that span different geological scenarios. Scenario parameters are reported for each geomodel.
• Figure 5: Comparison of vertical cross sections ($y-z$ plane, $x=64$) for (a) randomly selected Petrel realizations and (b) 3D-LDM realizations.