Uncertainty Quantification in CO₂Sequestration Using Surrogate Models from Polynomial Chaos Expansion

Abstract

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 a 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, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the * To whom correspondence should be addressed † National Energy Technology Laboratory, Pittsburgh, PA, US ‡ Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, US 1 number of terms small in the expansion. 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 CO 2 underground are quantified for a saline aquifer. Moreover, based on the PCE model, we formulate an optimization problem to determine the optimal CO 2 injection rate so as to maximize the gas saturation (residual trapping) during injection, and thereby minimize the chance of leakage.

Engineering Aspects Related to the Use of Microalgae for Biofuel Production and CO2 Capture from Flue Gases

“…Driven by the increasing concerns related to the effects of CO 2 levels on global warming, several technologies for carbon mitigation are currently being developed around the world. Among those, carbon capture coupled with geological storage (CCS) is considered the most realistically feasible and economically viable method for reducing CO 2 concentration in the atmosphere (Zhang and Sahinidis 2012). However, CCS techniques are characterized by several limitations that might hinder their application at the real scale, whereby biological carbon capture through microalgae is today becoming a realistic alternative to CCS technologies.…”

“…The separated CO 2 is then compressed and transported (usually through pipelines) to the storage site. Finally, in the sequestration step, compressed CO 2 is injected into deep geological formations, such as saline aquifers, depleted oil/gas reservoirs, or deep un-mineable coal seams (Zhang and Sahinidis 2012).…”

Uncertainty analysis of carbon sequestration in an active CO2-EOR field

“…However, typical Monte Carlo methods are computationally expensive as they require a large number of model simulations. Recently, several studies applied polynomial chaos expansion (PCE) to quantify risks of geological CO 2 storage (GCS) (Zhang and Sahinidis, 2013;Oladyshkin et al, 2010Oladyshkin et al, , 2011Ashraf et al, 2013). The PCE approach was first introduced by Wiener (1938) to determine the evolution of uncertainty in dynamic systems based on homogenous chaos theory.…”

Global Sensitivity Analysis to Assess Salt Precipitation for CO2 Geological Storage in Deep Saline Aquifers

“…A surrogate model is an engineering method used when an outcome of interest cannot be directly measured; thus a model of the outcome is used as an alternative. Zhang and Sahinidis used the surrogate model from the polynomial chaos expansion (PCE) to conduct uncertainty analysis, but they mainly considered the uncertainty between the residual water saturation and the injection rate [22]. Wu et al proposed the use of Kriging surrogate models for uncertainty and sensitivity analysis in nuclear engineering [23].…”