Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach

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.

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

“…Availability of a surrogate model typically enables efficient computation of Sobol' indices [11][12][13][14][15]. This has enabled performing global sensitivity analysis on a wide range of applications including in ocean modeling [16,17], geosciences [18][19][20], and chemical kinetics [21][22][23] to name a few.…”

Bayesian experimental design for CO2 sequestration with leakage risk assessment

“…As in Saad et al (2018), we formulate the leakage Q leak as the CO 2 mass flux rate at the midway between the top and bottom aquifers divided by the injection rate. Q leak is a function of time, that is Q leak ( t k ) is a random variable for any t k ∈ [0, T ].…”