An integrative approach to robust design and probabilistic risk assessment for CO2 storage in geological formations
- First Online:
- 361 Downloads
CO2 storage in geological formations is currently being discussed intensively as a technology with a high potential for mitigating CO2 emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis or stochastic approaches based on a brute-force approach of repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a higher-order orthogonal basis of polynomials to approximate dependence on uncertain parameters (porosity, permeability, etc.) and design parameters (injection rate, depth, etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation, and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs with a minimum failure probability. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al., Comput Geosci 13:451–467, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speed-up by a factor of 100 compared with the Monte Carlo evaluation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO2 injection, including uncertainty in the analysis leads to a systematic and significant shift of the predicted leakage rates toward higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios.
KeywordsPolynomial chaos CO2 storage Multiphase flow Porous media Risk assessment Uncertainty Integrative response surfaces
Unable to display preview. Download preview PDF.
- 2.Askey, R., Wilson, J.: Some basic hypergeometric polynomials that generalize Jacobi polynomials. Memoirs of the American Mathematical Society, p. 319. AMS, Providence (1985)Google Scholar
- 5.Class, H., Ebigbo, A., Helmig, R., Dahle, H., Nordbotten, J.N., Celia, M.A., Audigane, P., Darcis., M., Ennis-King, J., Fan, Y., Flemisch, B., Gasda, S., Jin, M., Krug, S., Labregere, D., Naderi, A., Pawar, R.J., Sbai, A., Sunil, G.T., Trenty, L., Wei, L.: A benchmark-study on problems related to CO2 storage in geologic formations. Comput. Geosci. 13, 451–467 (2009)CrossRefGoogle Scholar
- 8.Flemisch, B., Fritz, J., Helmig, R., Niessner, J., Wohlmuth, B.: DUMUX: a multi-scale multi-physics toolbox for flow and transport processes in porous media. In: Ibrahimbegovic, A., Dias, F. (eds.) ECCO3MAS Thematic Conference on Multi-scale Computational Methods for Solids and Fluids, Cachan, France, 28–30 November 2007Google Scholar
- 9.Ghomain, Y., Pope, G.A., Sepehrnoori, K.: Development of a response surface based model for minimum miscibility pressure (MMP) correlation of CO2 flooding, paper SPE 116719. In: 2008 SPE Annual Technical Conference and Exhibition, Denver, CO, 21–24 September 2008. doi:10.2118/116719-MS
- 12.IPCC: Special report on carbon dioxide capture and storage. Technical Report, Intergovernmental Panel on Climate Change (IPCC), prepared by Working Group III. Cambridge University Press, Cambridge (2005)Google Scholar
- 19.Li, H., Zhan, D.: Probabilistic collocation method for flow in porous media: comparisons with other stochastic methods. Water Resour. Res. 43, 44–48 (2009)Google Scholar
- 20.Lin, G., Tartakovsky, A.M.: An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media. Water Resour. Res. 32, 712–722 (2009)Google Scholar
- 24.Oladyshkin, S., Class, H., Helmig, R., Nowak, W.: Datadriven robust design and probabilistic risk assessment: application to underground carbon dioxide storage. Abstract #H41L-03 presented at 2010 Fall Meeting, AGU, San Francisco, California, 13–17 Dec (2010)Google Scholar
- 27.Webster, M., Tatang, M.A., Mcrae, G.J.: Application of the probabilistic collocation method for an uncertainty analysis of a simple ocean model. MIT Joint Program on the Science and Policy of Global Change Report Series No. 4. Massachusetts Institute of Technology, Cambridge (1996)Google Scholar
- 29.Wildenborg, A.F.B., Leijnse, A.L., Kreft, E., Nepveu, M.N., Obdam, A.N.M., Orlic, B., Wipfler, E.L., van der Grift, B., van Kesteren, W., Gaus, I., Czernichowski-Lauriol, I., Torfs, P., Wójcik., R.: Risk assessment methodology for CO2 storage—the scenario approach. In: Benson, S.M. (ed.) The CO2 Capture and Storage Project for Carbon Dioxide Storage in Deep Geological Formations for Climate Change Mitigation, Ch. 33., pp. 1293–1316. Elsevier, Amsterdam (2005)CrossRefGoogle Scholar