Probabilistic modeling and global sensitivity analysis for $CO_2$ storage in geological formations: a spectral approach

TL;DR

This paper presents a spectral approach using polynomial chaos expansions to efficiently simulate and analyze the uncertainty in $CO_2$ storage in geological formations, focusing on leakage risks and optimal injection rates.

Contribution

It introduces a non-intrusive spectral method for uncertainty quantification in $CO_2$ storage, enabling efficient sensitivity analysis and risk assessment.

Findings

Polynomial chaos accurately models stochastic responses.

Computed probabilities of excess $CO_2$ leakage.

Identified optimal injection rates to minimize leakage risk.

Abstract

This work focuses on the simulation of $CO_2$ storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on $CO_2$ leakage. To simulate the process, a non-isothermal two-phase two-component flow system with equilibrium phase exchange is used. Since model evaluations are computationally intensive, instead of traditional Monte Carlo methods, we rely on polynomial chaos (PC) expansions for representation of the stochastic model response. A non-intrusive approach is used to determine the PC coefficients. We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies. In addition to characterizing the distributions of model observables, we compute probabilities of excess $CO_2$ leakage. Moreover, we consider the injection rate as a design parameter and compute an optimum injection rate that ensures that the risk of excess pressure buildup at the leaky well remains below acceptable levels. We also provide a comprehensive analysis of sensitivities of $CO_2$ leakage, where we compute the contributions of the random parameters, and their interactions, to the variance by computing first, second, and total order Sobol' indices.