Reservoir History Matching with Latent Diffusion Model Parameterization and ES-MDA

Abstract

Abstract Reservoir history matching is fundamentally ill-posed, because the dimensionality of the spatial property fields far exceeds the information contained in production data. In this study, we address this problem with a latent diffusion model that combines a variational autoencoder for compact geological representation with a diffusion process that defines the geological fields over its latent space. This model is integrated with a reservoir simulator and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) workflow, in which only porosity is represented in latent space; permeability is derived through a deterministic Kozeny–Carman transform, which reduces the parameter dimensionality by half while maintains petrophysical consistency. History matching is performed in the latent space of the diffusion model. This preserves the assumptions underlying the ensemble update, while the reverse diffusion process and decoder recover the detailed geological structure at each history matching step. Applied in a carbonate reservoir case with hundreds of wells, the method reduces the history-matching misfit by an order of magnitude. It is also generalized well to forecast periods for two selected testing realizations, using the same configuration without further tuning. The reduction of uncertainty correlates with proximity to wells, indicating that the uncertainty reduction is driven by the spatial information represented by the observational data. The approach delivers calibrated and generalizable history matching with substantially efficient parameterization.