An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring

TL;DR

The paper tackles uncertainty quantification in subsurface CO2 storage monitoring by introducing an uncertainty-aware Digital Shadow that blends Simulation-Based Inference with Ensemble Bayesian Filtering. It uses amortized Conditional Normalizing Flows to learn a nonlinear posterior transport for the plume state conditioned on multimodal time-lapse data, while treating permeability as a stochastic nuisance that is marginalized through training on simulated ensembles. The methodology combines physics-informed summary statistics and a neural sequential inference loop (Forecast–Training–Analysis) to update the plume state in a recursive, scalable fashion. Validation is performed in-silico on an offshore-style Compass model, showing that multimodal data, especially seismic information, yields substantial improvements in reconstruction quality and uncertainty calibration over using wells alone. The work establishes a first proof-of-concept for an uncertainty-aware Digital Shadow and lays groundwork toward a future Digital Twin for secure, optimized underground CO2 storage operations.

Abstract

Geological Carbon Storage GCS is arguably the only scalable net-negative CO2 emission technology available While promising subsurface complexities and heterogeneity of reservoir properties demand a systematic approach to quantify uncertainty when optimizing production and mitigating storage risks which include assurances of Containment and Conformance of injected supercritical CO2 As a first step towards the design and implementation of a Digital Twin for monitoring underground storage operations a machine learning based data-assimilation framework is introduced and validated on carefully designed realistic numerical simulations As our implementation is based on Bayesian inference but does not yet support control and decision-making we coin our approach an uncertainty-aware Digital Shadow To characterize the posterior distribution for the state of CO2 plumes conditioned on multi-modal time-lapse data the envisioned Shadow combines techniques from Simulation-Based Inference SBI and Ensemble Bayesian Filtering to establish probabilistic baselines and assimilate multi-modal data for GCS problems that are challenged by large degrees of freedom nonlinear multi-physics non-Gaussianity and computationally expensive to evaluate fluid flow and seismic simulations To enable SBI for dynamic systems a recursive scheme is proposed where the Digital Shadows neural networks are trained on simulated ensembles for their state and observed data well and/or seismic Once training is completed the systems state is inferred when time-lapse field data becomes available In this computational study we observe that a lack of knowledge on the permeability field can be factored into the Digital Shadows uncertainty quantification To our knowledge this work represents the first proof of concept of an uncertainty-aware in-principle scalable Digital Shadow.

Figures (28)

• Figure 1: Example of a setup of Geological Carbon Storage in a marine setting. Top: Schematic diagram showing the velocity model, the seismic acquisition setup with sources (denoted by red $X$ symbol), and receivers (denoted by the yellow $\nabla$ symbol). The setup also includes injection (left) and monitoring (right) wells. Bottom: the juxtaposition of multi-phase flow simulations for two different realizations of a permeability field drawn from a stochastic baseline established from active-source surface seismic data (Yin, Orozco, et al. 2024). Both realizations for the permeability are consistent with this baseline seismic survey but yield vastly different outcomes. Bottom-left CO2 plume remains well within the storage complex (denoted by the white dashed box). Bottom-right: plume obviously breaches Containment, due to the presence of an "unknown" high-permeability streak.
• Figure 2: The life cycle of the recurrent Digital Shadow at timestep $k=1$. Starting from the initial randomly chosen CO2 saturation, $\widehat{\mathbf{x}}_0\sim p(\mathbf{x}_0)$, samples from the joint distribution,$\mathbf{y}_{k}\sim p(\mathbf{x}_{k}, \mathbf{y}_{k})$, are simulated during the $\textsc{Forecast}$ step, consisting of fluid-flow and observation simulations. Samples from the joint distribution form a simulated training ensemble, $\{\mathbf{x}_k^{(m)},\mathbf{y}_k^{(m)} \}_{m=1}^{M}$, consisting of $M$ training pairs that are used to train the CNF, $p_{\widehat{\boldsymbol{\phi}}_k}(\mathbf{x}_{k} |\mathbf{y}_{k})$, which approximates the posterior. After training, the predicted plume is, during the $\textsc{Analysis}$ step, conditioned on the observed field data, $\mathbf{y}^{\mathrm{obs}}_k$, and samples from the CO2 plume posterior distribution, $p_{\widehat{\boldsymbol{\phi}}_k}(\widehat{\mathbf{x}}_{k} \mid\mathbf{y}_{k}^{\mathrm{obs}})$, are produced. These samples for the state are used as "priors" for the next time step. The symbol $\widehat{\quad}$ is used to distinguish between predicted "digital states" and analyzed states, conditioned on observed field data, $\mathbf{y}^{\mathrm{obs}}_k$. During the $\textsc{Analysis}$ step, the predicted states are corrected by the mapping $\mathbf{x}_k\mapsto \widehat{\mathbf{x}}_k$.
• Figure 3: a.
• Figure 4: b.
• Figure 6: Schematic diagram showing ground-truth data generation using a fixed realization for the permeability field (CO2 saturation shown in bright overlay on top of plots for permeability field).