Probabilistic modeling and global sensitivity analysis for CO 2 storage in geological formations: a spectral approach
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AbstractThis work focuses on the simulation of CO2 storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on CO2 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 CO2 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 CO2 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.
CitationSaad BM, Alexanderian A, Prudhomme S, Knio OM (2017) Probabilistic modeling and global sensitivity analysis for CO 2 storage in geological formations: a spectral approach. Applied Mathematical Modelling. Available: http://dx.doi.org/10.1016/j.apm.2017.09.016.
SponsorsResearch reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST) under the Academic Excellency Alliance (AEA) UT Austin-KAUST project ”Uncertainty quantification for predictive modeling of the dissolution of porous and fractured media”. Computational resources for the simulations presented in this publication have been made available by KAUST Research Computing and KAUST SuperComputing Lab. Bilal Saad is grateful for the support by the Saudi Arabia Basic Industries Corporation (SABIC). Bilal Saad, Serge Prudhomme, and Omar Knio are also participants of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
JournalApplied Mathematical Modelling