(481d) Uncertainty Quantification in CO2 Sequestration Using Surrogate Models From Polynomial Chaos Expansion

In this paper, surrogate models are iteratively built using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system.  Output variables from the numerical simulator are approximated as polynomial functions of uncertain parameters.  Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude.  However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion.

To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method [1], we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion.  Our approach makes it possible to keep the number of terms small in the expansion.  We compare the proposed MIP-based subset selection method against the classical stepwise regression algorithm for building sparse PCE models [2].  The PCE models from our proposed method are simpler than the ones using stepwise regression.  

Monte Carlo (MC) simulation is then performed by substituting the values of the uncertain parameters into the closed-form polynomial functions.  Based on the results of MC simulation, the uncertainties of injecting CO2 underground are quantified for a saline aquifer.  Moreover, based on the PCE model, we formulate an optimization problem to determine the optimal CO2 injection rate so as to maximize the gas saturation (residual trapping) during injection, and thereby minimize the chance of leakage.

References cited:

1. Oladyshkin, S.; Class, H.; Helmig, R.; Nowak, W. An integrative approach to robust design and probabilistic risk assessment for CO2 storage in geological formations. Computational Geosciences 2011, 15, 565–577.

2. Blatman, G.; Sudret, B. An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probabilistic Engineering Mechanics 2010, 25, 183-197.