Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations

TL;DR

The study tackles the computational bottleneck of history matching in large-scale CO$_2$ storage by training deep learning surrogates primarily on inexpensive flow-only simulations and a small set of coupled runs, enabled by an effective rock compressibility. It introduces a novel surface-displacement surrogate built with a residual U-Net that leverages pressure and saturation surrogates, achieving median errors below 4% across variables. The surrogates are integrated into a hierarchical MCMC framework that explicitly accounts for surrogate-model error via a full covariance matrix, yielding substantial uncertainty reduction when using both subsurface and surface data. The results demonstrate significant training-time reductions (order-of-magnitude) while maintaining accurate predictions of saturation, pressure, and surface uplift, with practical implications for efficient monitoring and decision-making in CO$_2$ storage operations.

Abstract

Deep learning surrogate modeling shows great promise for subsurface flow applications, but the training demands can be substantial. Here we introduce a new surrogate modeling framework to predict CO2 saturation, pressure and surface displacement for use in the history matching of carbon storage operations. Rather than train using a large number of expensive coupled flow-geomechanics simulation runs, training here involves a large number of inexpensive flow-only simulations combined with a much smaller number of coupled runs. The flow-only runs use an effective rock compressibility, which is shown to provide accurate predictions for saturation and pressure for our system. A recurrent residual U-Net architecture is applied for the saturation and pressure surrogate models, while a new residual U-Net model is introduced to predict surface displacement. The surface displacement surrogate accepts, as inputs, geomodel quantities along with saturation and pressure surrogate predictions. Median relative error for a diverse test set is less than 4% for all variables. The surrogate models are incorporated into a hierarchical Markov chain Monte Carlo history matching workflow. Surrogate error is included using a new treatment involving the full model error covariance matrix. A high degree of prior uncertainty, with geomodels characterized by uncertain geological scenario parameters (metaparameters) and associated realizations, is considered. History matching results for a synthetic true model are generated using in-situ monitoring-well data only, surface displacement data only, and both data types. The enhanced uncertainty reduction achieved with both data types is quantified. Posterior saturation and surface displacement fields are shown to correspond well with the true solution.

Figures (24)

• Figure 1: Model domain used for both the flow-only and coupled flow-geomechanics simulations. The full domain includes the storage aquifer, surrounding region, overburden and underburden. A realization of the storage aquifer is shown on the right.
• Figure 2: Locations of injection wells (I1--I4) and observation wells (O1--O5) in the storage aquifer are shown in (a). Locations of the surface vertical displacement measurements (directly above the storage aquifer) shown in (b).
• Figure 3: CO$_2$-brine relative permeability and capillary pressure curves used in all simulations. Capillary pressure curve in (b) is for a cell with porosity of 0.2 and permeability of 20 md.
• Figure 4: Schematic of the extended recurrent R-U-Net architecture for pressure and saturation prediction in the storage aquifer over $n_t$ time steps. Figure modified from han2023surrogate.
• Figure 5: Schematic of the R-U-Net architecture for surface displacement prediction at a specific time.