Machine learning enhanced data assimilation framework for multi-scale carbonate rock characterization

Carbonate reservoirs offer significant capacity for subsurface carbon storage, oil production, underground hydrogen storage, geothermal energy, and groundwater flow. Accurate characterization of fluid flow behavior in these rocks is therefore critical for both resource recovery and emissions mitigation, yet it remains challenging due to their inherent heterogeneity. The wide range of carbonate pore-throat size distribution, spanning from nm to cm, hinders a comprehensive pore structure characterization with conventional single-scale X-ray computed tomography (micro-CT) images. Multi-scale imaging, which refers to acquiring CT images at both macro and micro resolutions, has emerged as a practical strategy to bridge this gap. In practice, nm-scale CT imaging requires the physical extraction of mini-plugs from the macro core sample, while the selection of drilling locations remains largely subjective, lacking a quantitative framework for rigorous decision-making. Digital rock modeling can assist this decision-making process by predicting flow properties from macro-scale sample images. However, its computational cost remains prohibitive for routine use. To facilitate an efficient, digitalized sub-sampling decision-making workflow, we propose a machine learning-enhanced data assimilation framework that leverages experimental drainage relative permeability measurements to achieve efficient characterization of micro-scale structures. We train a dense neural network (DNN) as a proxy to a multi-scale pore network simulator and couple it with an ensemble smoother with multiple data assimilation (ESMDA) algorithm. The DNN-ESMDA framework simultaneously infers the CO₂-brine drainage relative permeability of microporosity phases with associated uncertainty estimation, revealing the relative importance of each rock phase and guiding future characterization. Our DNN-ESMDA framework achieves a significant computational speedup, reducing inference time from thousands of hours to seconds compared to conventional multi-scale numerical simulation. The machine learning-enhanced ESMDA framework therefore provides a practical approach for improving the multi-scale imaging workflow of carbonates.