Efficient and accurate quantification of uncertainty for multiphase flow with the probabilistic collocation method

SPE Journal

Volumn 14, Issue 4, 2009, Pages 665-679

  Li, Heng ^a   Zhang, Dongxiao ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HYDROCARBONS; PETROLEUM ANALYSIS; PETROLEUM RESERVOIR ENGINEERING; PETROLEUM RESERVOIRS; PROBABILITY DENSITY FUNCTION; UNCERTAINTY ANALYSIS;

ACCURATE QUANTIFICATIONS; HETEROGENEOUS RESERVOIRS; KARHUNEN-LOEVE EXPANSION; PERMEABILITY AND POROSITIES; PETROLEUM RESERVOIR SIMULATION; POLYNOMIAL CHAOS EXPANSION; PROBABILISTIC COLLOCATION METHOD; UNCERTAINTY QUANTIFICATIONS;

MONTE CARLO METHODS;

EID: 76349104633     PISSN: 1086055X     EISSN: None     Source Type: Journal    
DOI: 10.2118/114802-PA     Document Type: Article

References (23)

1. Chen, Z., Huan, G., and Ma, Y. 2006. Computational Methods for Multiphase Flows in Porous Media. Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics (SIAM).
2. Cushman, J.H. 1997. The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles. Norwell, Massachusetts: Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers.
3. Dagan, G. 1989. Flow and Transport in Porous Formations. New York: Springer.
4. Gelhar, L.W. 1993. Stochastic Subsurface Hydrology. Englewood Cliffs, New Jersey: Prentice-Hall.
5. Ghanem, R. 1998. Scales of Fluctuation and the Propagation of Uncertainty in Random Porous Media. Water Resources Research 34 (9): 2123-2136. DOI: 10.1029/98WR01573. (Pubitemid 28407884)
6. Ghanem, R. and Dham, S. 1998. Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media. Transport in Porous Media 32 (3): 239-262. DOI: 10.1023/A:1006514109327. (Pubitemid 128789844)
7. Ghanem, R.G. and Spanos, P.D. 1991. Stochastic Finite Elements: A Spectral Approach. New York: Springer.
8. Killough, J.E. 1995. Ninth SPE Comparative Solution Project: A Reexamination of Black-Oil Simulation. Paper SPE 29110 presented at the SPE Reservoir Simulation Symposium, San Antonio, Texas, USA, 12-15 February. DOI: 10.2118/29110-MS.
9. Li, H. and Zhang, D. 2007. Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods. Water Resources Research 43: W09409. DOI: 10.1029/2006WR005673. (Pubitemid 350064084)
10. Lu, Z. and Zhang, D. 2007. Stochastic Simulations for Flow in Nonstationary Randomly Heterogeneous Porous Media Using a KL-Based Moment-Equation Approach. Multiscale Model, and Simul. 6 (1): 228-245. DOI: 10.1137/060665282.
11. Mathelin, L., Hussaini, M.Y, and Zang, T.A. 2005. Stochastic approaches to uncertainty quantification in CFD simulations. Numerical Algorithms 38 (1-3): 209-236. DOI: 10.1007/BF02810624. (Pubitemid 41195956)
12. Neuman, S.P. 1997. Stochastic approach to subsurface flow and transport: a view to the future. In Subsurface Flow and Transport: A Stochastic Approach, ed. G. Dagan and S.P. Neuman, Chap. VI, 231-241. Cambridge, UK: International Hydrology Series, Cambridge University Press.
13. Rubin, Y. 2003. Applied Stochastic Hydrogeology. New York: Oxford University Press.
14. Sarma, P., Durlofsky L., and Aziz, K. 2005b. Efficient Closed-Loop Production Optimization Under Uncertainty. Paper SPE 94241 presented at the SPE Europec/EAGE Annual Conference, Madrid, Spain, 13-16 June. DOI: 10.2118/94241-MS.
15. Sarma, P., Durlofsky, L.J., and Aziz, K. 2008. Kernel principal component analysis for efficient, differentiable parameterization of multipoint geostatistics. Mathematical Geosciences 40: 3-32.
16. Tatang, M.A., Pan, W, Prinn, R.G., and McRae, G.J. 1997. An efficient method for parametric uncertainty analysis of numerical geophysical models. J. Geophys. Res. 102 (D18): 21925-21932. DOI: 10.1029/97JD01654. (Pubitemid 127560927)
17. Villadsen, J. and Michelsen, M.L. 1978. Solution of Differential Equation Models by Polynomial Approximation. Upper Saddle River, New Jersey: Physical and Chemical Engineering Science, Prentice-Hall.
18. Wiener, N. 1938. The Homogeneous Chaos. American Journal of Mathematics 60 (4): 897-936. DOI: 10.2307/2371268.
19. Xiu, D. and Kamiadakis, G.E. 2002. Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput. Methods Appl. Mech. Eng. 191 (43): 4927-4948. DOI: 10.10167S00457825(02)00421-8. (Pubitemid 35212677)
20. Zhang, D. 2002. Stochastic Methods for Flow in Porous Media: Coping With Uncertainties. San Diego, California: Academic Press.
21. Zhang, D. and Lu, Z. 2004. An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions. Journal of Computational Physics 194 (2): 773-794. DOI: 10.1016/j.jcp.2003.09.015. (Pubitemid 38284244)
22. Zhang, D. and Tchelepi, H. 1999. Stochastic Analysis of Immiscible Two-Phase Flow in Heterogeneous Media. SPE J. 4 (4): 380-388. SPE-59250-PA. DOI: 10.2118/59250-PA. (Pubitemid 32271208)
23. Zhang, D., Li, L., and Tchelepi, H.A. 2000. Stochastic Formulation for Uncertainty Analysis of Two-Phase Flow in Heterogeneous Reservoirs. SPEJ. 5 (1): 60-70. SPE-59802-PA. DOI: 10.2118/59802-PA. (Pubitemid 32272572)