PhD Final Defense – Christian Munoz

Surrogate Modeling Applications in Geological CO2 Storage

Advisor: Professor Alexandre Tartakovsky

Abstract

Geological carbon storage is one of the few scalable pathways for reducing atmospheric CO2 on the timescale of mid-century climate targets, and its safe deployment rests on predictions of plume migration and pressure buildup from high-fidelity reservoir simulation. Three tasks stand between such a simulator and an operating storage project: forecasting the reservoir state, parameter estimation to estimate uncertain geological properties from monitoring data, and design optimization to select injection rates and well locations. Each demands far more than a single forward run, so direct Monte Carlo over the full simulator is prohibitive. The deeper obstacle is statistical: at the Illinois Basin-Decatur Project (IBDP) studied throughout this work, the unknown reservoir-property values on a million-cell grid outnumber the available high-fidelity simulations by orders of magnitude, so the training budget, not the cost of any single run, is the fundamental bottleneck. This dissertation shows that all three tasks become tractable, at full grid resolution and with quantified uncertainty, within the low-dimensional Karhunen-Loeve (KL) latent spaces of the parameter and state fields.

The central instrument is a trainable-by-parts KL-DNN surrogate, in which a nested KL expansion and a low-rank singular value decomposition make basis discovery feasible without the spatial coarsening or subsampling that comparable operator-learning models require. Shown to be a special case of DeepONet whose components can be trained separately, it attains lower pressure error than DeepONet on the identical IBDP ensemble while reducing training time by orders of magnitude.

Because a surrogate used for inference must report its own error, deep ensembling is combined with a randomized maximum-a-posteriori (MAP) loss whose noise hyperparameter is selected by maximizing the log predictive probability rather than pointwise accuracy, yielding a calibrated stochastic surrogate suitable as a data likelihood. A central finding follows: when data are limited, it is calibration rather than pointwise accuracy that governs the quality of the history match. A single joint KL expansion of the three correlated geological fields reduces the parameter vector to a handful of coefficients

with an explicit prior the geostatistical workflow does not otherwise provide; randomized MAP over these coefficients reproduces the IBDP pressure response at every instrumented location in seconds.

Finally, admitting the injection rate and injector coordinates as surrogate inputs turns the forward model into a design tool. Embedded in the NSGA-II genetic algorithm, it yields the Pareto front trading maximized injected CO2 mass against a minimized pressure Area of Review and extends to geological uncertainty by optimizing a single robust decision across the ensemble and testing it on held-out realizations. Together the four contributions constitute one latent-space workflow for prediction, inference, and design from a small simulation budget.