Machine learning enhanced data assimilation framework for multiscale carbonate rock characterization

Carbonate reservoirs offer significant capacity for subsurface carbon storage, oil production, and underground hydrogen storage. X-ray computed tomography (X-ray CT) coupled with numerical simulations is commonly used to investigate the multiphase flow behaviors in carbonate rocks. Carbonates exhibit pore size distribution across scales, hindering the comprehensive investigation with conventional X-ray CT images. Imaging samples at both macro and micro-scales (multi-scale imaging) proved to be a viable option in this context. However, multi-scale imaging faces two key limitations: the trade-off between field of view and voxel size necessitates resource-intensive imaging, while multi-scale multi-physics numerical simulations on resulting digital models incur prohibitive computational costs. To address these challenges, we propose a machine learning-enhanced data assimilation framework that leverages experimental drainage relative permeability measurements to achieve efficient characterization of micro-scale structures, delivering a data-driven solution toward a high-fidelity multiscale digital rock modeling. 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. 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 computational speedup, reducing inference time from thousands of hours to seconds compared with the usage of conventional multiscale numerical simulation. Given this computational efficiency and applicability, the machine learning-enhanced ESMDA framework presents a generalizable approach for characterizing multiscale carbonate rocks.

💡 Research Summary

Carbonate reservoirs are pivotal for carbon capture and storage, hydrocarbon production, and underground hydrogen storage, yet their pore structures span several orders of magnitude—from nanometres to centimetres—making comprehensive characterization extremely challenging. Conventional approaches rely on X‑ray computed tomography (CT) at a single resolution, which forces a trade‑off between field of view and voxel size. Consequently, high‑resolution micro‑CT can only image a tiny fraction of a core, while multiscale, multiphysics simulations that combine macro‑ and micro‑scale data demand prohibitive computational resources (thousands of CPU hours).

The authors address these bottlenecks by integrating machine learning with data assimilation. First, they acquire a centimetre‑scale carbonate core (38 mm × 69 mm) from the Central Luconia formation, obtaining low‑resolution macro‑CT (26.4 µm voxels) and drainage CO₂‑brine relative permeability curves. To supplement the sparse data, high‑resolution micro‑CT images (165 nm voxels) from an analogous sample are segmented into 120 sub‑volumes. A non‑local mean filter and two‑end connectivity analysis are used to partition the low‑resolution image into three microporosity phases (low, medium, high entry capillary pressure) based on grayscale thresholds, preserving a physical link between intensity and entry pressure.

Physical parameters for each phase—porosity, capillary pressure (Brooks‑Corey), and permeability—are calibrated using gradient‑based regression against experimental measurements, achieving a whole‑core porosity of 0.346 (experimental 0.347) and matching mercury intrusion data.

The core innovation lies in replacing the computationally intensive pore‑network model (xpm) with a dense neural network (DNN) surrogate. The DNN is trained on the 120 high‑resolution sub‑images, each processed through the xpm simulator to generate input‑output pairs linking phase properties (porosity, entry pressure, λ) to relative permeability. Once trained, the DNN predicts relative permeability in milliseconds on a GPU, providing a fast forward model.

Ensemble Smoother with Multiple Data Assimilation (ESMDA) is then employed. An ensemble of candidate parameter sets is generated; for each member the DNN predicts the relative permeability curves, which are compared to the measured drainage data. The ESMDA algorithm updates the ensemble iteratively, yielding posterior distributions for the three microporosity phases and quantifying uncertainties. This simultaneous inversion and uncertainty quantification reveals the relative importance of each phase to overall flow, guiding future sampling strategies.

Performance gains are dramatic: traditional multiscale simulations would require thousands of CPU hours per ensemble, whereas the DNN‑ESMDA workflow completes the entire inversion in seconds—a speed‑up of six orders of magnitude. The framework also provides sensitivity analysis, indicating which microporosity phase dominates flow at different capillary pressures.

Beyond the case study, the authors argue that the DNN‑ESMDA approach is generic. It can be applied to other porous media (sandstones, shales) and extended to incorporate additional physics such as chemical reactions or thermal effects. By coupling fast machine‑learning surrogates with rigorous Bayesian data assimilation, the method makes high‑fidelity multiscale digital rock modeling tractable for routine use, enabling more informed decisions in carbon storage, oil recovery, and emerging hydrogen storage projects.