Machine learning enhanced data assimilation framework for multiscale carbonate rock characterization

TL;DR

This work tackles the challenge of characterizing multiscale carbonate rocks where high-resolution imaging and comprehensive multi-scale simulations are computationally prohibitive. It introduces a DNN surrogate for a multi-scale pore network model (XPM) and couples it with the ensemble smoother with multiple data assimilation (ESMDA) to perform fast, uncertainty-quantified inference of microporosity relative permeability from limited measurements. In a cm-scale Malaysian carbonate core case, the approach reduces inference time from thousands of hours to seconds while providing calibrated posterior estimates and uncertainty bounds for microporosity phases. The framework offers a generalizable, efficient toolkit for digital-twin–driven characterization of multiscale porous materials across geoenergy applications.

Abstract

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.

Figures (10)

• Figure 1: Raw micro-CT images of carbonate rock sample at $26.4 \; \mu m$ voxel size; (a) Circular cross section; (b) Internal structure along the core sample length; (c) Experimental measurement of steady-state $CO_2$-brine drainage relative permeability curves.
• Figure 2: Schematic illustration of segmentation workflow for a dry-scan cm-scale carbonate rock sample from Malaysia at $26.4 \mu m$ voxel size; (a) Filtered dry-scan images, dark red represents the highest density, light red to green represent the microporosity regions, and the blue represent the resolved pore spaces; (b) Dry scan images with resolved pore spaces segmented as black color; (c) Two-end connectivity analysis showing the flow path provided by one of the grayscale value microporosity region; (d) Segmented images with three microporosity phases, presented as light blue, light green, and orange; (e) Grayscale value histogram of dry-scan images with resolved pore spaces segmented (volume fraction of resolved pore is 3.8%) ; (f) Grayscale value histogram of dry-scan images.
• Figure 3: Workflow to define the permeability and Lomeland-Ebeltoft-Thomas (LET) relative permeability model parameter ranges; (a) high-resolution images at $165\; nm$ from a analogous sample in the same formation; (b) the nano-scale images are cropped and segmented into 120 cube binary images; Run PNM simulation on these cubes and define: (c) permeability ($k=4.07e^4\varphi^{3.43}$) and (d) LET parameter ranges accordingly.
• Figure 4: Schematic illustration of eXtensive Pore Modeling (XPM): (a) Multi-scale micro-CT images with resolved pores, microporosity phases, and solid phase segmented; (b) Extracted pore network from resolved pore regions with pnextract; (c) Link microporosity voxels to their surrounding resolved pores, creating connection between microporosity phases and resolved pore regions, while different colors indicate which resolved pore each microporosity voxel is connected to; (d) Predict relative permeability from the multi-scale images by solving Stoke equation in resolved pore networks and Darcy equation in the Darcy cells (microporoisty voxels).
• Figure 5: Schematic illustration of DNN-ESMDA workflow for fast inference of microporosity phase relative permeability of a cm-scale Malaysian carbonate sample: (a) Dry scan micro-CT images ; (b) Segmented images based on two-end connectivity, phase 0 as the resolved pore; (c) Subset the image into a subvolume for computational efficiency, phase 0 as the resolved pore; (d) Validate the subvolume simulation results with the whole core; (e) Use the subvolume as input image for 300 XPM simulation with Latin Hypercube sampling across the LET parameter space; (f) Train a three layer dense neural network (DNN) with XPM simulation results; (g) The training results of DNN; (h) Coupling DNN with ESMDA to establish a DNN-ESMDA framework for fast inference of microporosity phase relative permeability.