Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

Water Resources Research

Volumn 50, Issue 12, 2014, Pages 9414-9431

  Porta, G ^a   Tamellini, L ^a,b   Lever, V ^a   Riva, M ^a,c  

^a POLITECNICO DI MILANO   (Italy)

^b EPFL   (Switzerland)

^c UNIVERSITY OF ARIZONA   (United States)

Author keywords

basin compaction; compaction driven flow; inverse modeling; Polynomial Chaos Expansion

Indexed keywords

COMPACTION; GEOCHEMISTRY; INVERSE PROBLEMS; MAXIMUM LIKELIHOOD; MAXIMUM LIKELIHOOD ESTIMATION; POLYNOMIAL APPROXIMATION; POLYNOMIALS; QUARTZ; SANDSTONE; SEDIMENTOLOGY; SETTLING TANKS; UNCERTAINTY ANALYSIS;

GENERALIZED POLYNOMIAL CHAOS; GEOCHEMICAL SYSTEMS; INPUT-OUTPUT MAPPING; INVERSE MODELING; MECHANICAL COMPACTION; POLYNOMIAL CHAOS EXPANSION; PRESSURE AND TEMPERATURE; SOBOL SENSITIVITY INDICES;

PARAMETER ESTIMATION;

ANISOTROPY; BOUNDARY CONDITION; COMPACTION; ESTIMATION METHOD; GEOCHEMICAL SURVEY; INVERSE ANALYSIS; MECHANICAL PROPERTY; NONLINEARITY; SANDSTONE; SEDIMENTARY BASIN; UNCERTAINTY ANALYSIS;

CHAOHE BASIN; CHINA;

EID: 85027919651     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2014WR015838     Document Type: Article

References (55)

1. Babuska, I.; F. Nobile, and, R. Tempone, (2010), A stochastic collocation method for elliptic partial differential equations with random input data, SIAM Rev.; 52 (2), 317-355, doi: 10.1137/100786356.
2. Bäck, J.; F. Nobile, L. Tamellini, and, R. Tempone, (2011), Stochastic Spectral Galerkin and Collocation methods for PDEs with random coefficients: A numerical comparison, in Spectral and High Order Methods for Partial Differential Equations, Lect. Notes in Comput. Sci. and Eng.; vol. 76, edited by.; J. Hestaven, and, E. Ronquist, pp. 43-62, Springer, Heidelberg, doi: 10.1007/978-3-642-15337-2-3.
3. Balakrishnan, S.; A. Roy, M. G. Ierapetritou, G. P. Flach, and, P. G. Georgopoulos, (2003), Uncertainty reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method, Water Resour. Res.; 39 (12), 1350, doi: 10.1029/2002WR001810.
4. Beck, J.; F. Nobile, L. Tamellini, and, R. Tempone, (2014), A quasi-optimal sparse grids procedure for groundwater flows, in Spectral and High Order Methods for Partial Differential Equations, Lect. Notes in Comput. Sci. and Eng.; vol. 95, edited by, M. Azaiez, et al.; pp 1-16, Springer, Switzerland, doi: 10.1007/978-3-319-01601-6-1.
5. Beha, A.; R. O. Thomsen, and, R. Littke, (2008), A rapid method of quantifying the resolution limits of heat-flow estimates in basin models, J. Pet. Geol.; 31, 167-178, doi: 10.1111/j.1747-5457.2008.00414.x.
6. Bonnesen, E. P.; F. Larsen, T. O. Sonnenborg, K. Klitten, and, L. Stemmerik, (2009), Deep saltwater in Chalk of North-West Europe: Origin, interface characteristics and development over geological time, Hydrogeol. J.; 17, 1643-1663, doi: 10.1007/s10040-009-0456-9.
7. Carrera, J.; and, S. P. Neuman, (1986), Estimation of aquifer parameters under transient and steady state conditions. 1: Maximum likelihood method incorporating prior information, Water Resour. Res.; 22 (2), 199-210, doi: 10.1029/WR022i002p00199.
8. Chkifa, A.; A. Cohen, R. Devore, and, C. Schwab, (2013), Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs, ESAIM: Math. Model. Num.; 47 (1), 253-280, doi: 10.1051/m2an/2012027.
9. Ciriello, V.; A. Guadagnini, V. Di Federico, Y. Edery, and, B. Berkowitz, (2013), Comparative analysis of formulations for conservative transport in porous media through sensitivity-based parameter calibration, Water Resour. Res.; 49, 5206-5220, doi: 10.1002/wrcr.20395.
10. Ernst, O.; A. Mugler, H. J. Starkloff, and, E. Ullmann, (2012), On the convergence of generalized polynomial chaos expansions, ESAIM: Math. Model. Num. Anal.; 46, 317-339, doi: 10.1051/m2an/2011045.
11. Fajraoui, N.; F. Ramasomanana, A. Younes, T. Mara, P. Ackerer, and, A. Guadagnini, (2011), Use of global sensitivity analysis and polynomial chaos expansion for interpretation of non reactive transport experiments in laboratory scale porous media, Water Resour. Res.; 47, W02521, doi: 10.1029/2010WR009639.
12. Fajraoui, N.; T. A. Mara, A. Younes, and, R. Bouhlila, (2012), Reactive transport parameter estimation and global sensitivity analysis using sparse Polynomial Chaos Expansion, Water Air Soil Pollut.; 223 (7), 4183-4197, doi: 10.1007/s11270-012-1183-8.
13. Formaggia, L.; A. Guadagnini, I. Imperiali, V. Lever, G. M. Porta, M. Riva, A. Scotti, and, L. Tamellini, (2013), Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model, Comput. Geosci.; 17 (1), 25-42, doi: 10.1007/s10596-012-9311-5.
14. Gambolati, G.; G. Ricceri, W. Bertoni, G. Brighenti, and, E. Vuillermin, (1991), Mathematical simulations of the subsidence of Ravenna, Water Resour. Res.; 27 (11), 2899-2918, doi: 10.1029/91WR01567.
15. Gambolati, G.; P. Teatini, D. Bau, and, M. Ferronato, (2000), Importance of poroelastic coupling in dynamically active aquifers of the Po river basin, Italy, Water Resour. Res.; 36 (9), 2443-2459, doi: 10.1029/2000WR900127.
16. Gerritsma, M.; J. B. van der Steen, P. Vos, and, G. Karniakidis, (2010), Time-dependent generalized polynomial chaos, J. Comput. Phys.; 229 (22), 8333-8363, doi: 10.1016/j.jcp.2010.07.020.
17. Ghanem, R. G.; and, P. D. Spanos, (1991), Stochastic Finite Elements: A Spectral Approach, Springer, N. Y.
18. Hoffmann, J.; D. L. Galloway, and, H. A. Zebker, (2003), Inverse modeling of interbed storage parameters using land subsidence observations, Antelope Valley, California, Water Resour. Res.; 39 (2), 1031, doi: 10.1029/2001WR001252.
19. Hurwitz, S.; V. Lyakhovsky, and, H. Gvirtzman, (2000), Transient salt transport modelling of shallow brine beneath a freshwater lake, the sea of Galilee, Israel, Water Resour. Res.; 36 (1), 101-107, doi: 10.1029/1999WR900292.
20. Huvaz, O.; R. O. Thomsen, and, S. Noeth, (2005), A method for analyzing geothermal gradient histories using the statistical assessment of uncertainties in maturity models, J. Pet. Geol.; 38, 107-118, doi: 10.1111/j.1747-5457.2005.tb00075.x.
21. Jiao, J. J.; and, C. Zheng, (1998), Abnormal fluid pressures caused by deposition and erosion of sedimentary basins, J. Hydrol.; 204, 124-137, doi: 10.1016/S0022-1694(97)00115-7.
22. Kashyap, R. L.; (1982), Optimal choice of AR and MA parts in autoregressive moving average models, IEEE Trans. Pattern Anal.; 4 (2), 99-104.
23. Kreitler, C. H.; (1989), Hydrogeology of sedimentary basins, J. Hydrol.; 106, 29-53, doi: 10.1016/0022-1694(89)90165-0.
24. Lagarias, J. C.; J. A. Reeds, M. H. Wright, and, P. E. Wright, (1998), Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM J. Optim.; 9 (1), 112-147, doi: 10.1137/S1052623496303470.
25. Laloy, E.; B. Rogiers, J. A. Vrugt, D. Mallants, and, D. Jacques, (2013), Efficient posterior exploration of a high-dimensional groundwater model from two-stage MCMC simulation and polynomial chaos expansion, Water Resour. Res.; 49, 2664-2682, doi: 10.1002/wrcr.20226.
26. Lander, R. H.; and, O. Walderhaug, (1999), Predicting porosity through simulating sandstone compaction and quartz cementation, AAPG Bull.; 83 (3) 433-449.
27. Le Maitre, O.; and, O. Knio, (2010), Spectral Methods for Uncertainty Quantification, Sci. Comput.; Springer, Berlin.
28. Li, W.; Z. Lu, and, D. Zhang, (2013), Stochastic analysis of unsaturated flow with probabilistic collocation method, Water Resour. Res.; 49, W08425, doi: 10.1029/2008WR007530.
29. Liao, Q.; and, D. Zhang, (2013), Probabilistic collocation method for strongly nonlinear problems. 1: Transform by location, Water Resour. Res.; 49, 7911-7928, doi: 10.1002/2013WR014055.
30. Lin, G.; and, A. M. Tartakovsky, (2009), An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media, Adv. Water Resour.; 34, 1527-1538, doi: 10.1016/j.advwatres.2008.09.003.
31. McPherson, B. J. O. L.; and, J. D. Bredehoeft, (2001), Overpressures in the Uinta basin, Utah: Analysis using a three-dimensional basin evolution model, Water Resour. Res.; 37 (4), 857-871, doi: 10.1029/2000WR900260.
32. Milliken, K. L.; (2004), Late diagenesis and mass transfer in sandstone-shale sequences, Treat. Geochem.; 7, 115-158.
33. Müller, F.; P. Jenny, and, D. W. Meyer, (2011), Probabilistic collocation and Lagrangian sampling for advective tracer transport in randomly heterogeneous porous media, Adv. Water Resour.; 34, 1527-1538, doi: 10.1016/j.advwatres.2011.09.005.
34. Nelder, J. A.; and, R. Mead, (1965), A simplex method for function minimization, Comput. J.; 7 (4), 308-313, doi: 10.1093/comjnl/7.4.308.
35. Nobile, F.; R. Tempone, and, C. G. Webster, (2008), An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal.; 46, 2411-2442, doi: 10.1137/070680540.
36. Oelkers, E. H.; P. A. Bjorkum, and, W. M. Murphy, (1996), A petrographic and computational investigation of quartz cementation and porosity reduction in North Sea sandstones, Am. J. Sci.; 296, 420-452.
37. Oladyshkin, S.; H. Class, and, W. Nowak, (2013), Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: Methodology and application to history matching for carbon dioxide storage in geological formations, Comput. Geosci.; 17 (4), 671-687, doi: 10.1007/s10596-013-9350-6.
38. Osborne, M. J.; and, R. E. Swarbrick, (1999), Diagenesis in North Sea HPHT clastic reservoirs consequences for porosity and overpressure prediction, Mar. Pet. Geol.; 16, 337-353, doi: 10.1016/S0264-8172(98)00043-9.
39. Riva, M.; A. Guadagnini, S. P. Neuman, E. Bianchi Janetti, and, B. Malama, (2009), Inverse analysis of stochastic moment equations for transient flow in randomly heterogeneous media, Adv. Water Resour.; 10, 271-280, doi: 10.1016/j.advwatres.2009.07.003.
40. Riva, M.; M. Panzeri, A. Guadagnini, and, S. P. Neuman, (2011), Role of model selection criteria in geostatistical inverse estimation of statistical data and model parameters, Water Resour. Res.; 47, W07502, doi: 10.1029/2011WR010480.
41. Saad, G.; and, R. Ghanem, (2009), Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter, Water Resour. Res.; 45, W04417, doi: 10.1029/2008WR007148.
42. Schneider, F.; M. Bouteca, and, G. Vasseur, (1994), Validity of the porosity/effective stress concept in sedimentary basin modeling, First Break, 12, 321-326.
43. Sobol, I. M.; (2001), Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simulat.; 55 (1-3), 271-280, doi: 10.1016/S0378-4754(00)00270-6.
44. Sochala, P.; and, O. Le Maitre, (2013), Polynomial Chaos expansion for subsurface flows with uncertain soil parameters, Adv. Water Resour.; 62, 139-154, doi: 10.1016/j.advwatres.2013.10.003.
45. Sudret, B.; (2007), Global sensitivity analysis using polynomial chaos expansion, Reliab. Eng. Syst. Safety, 93 (7), 964-979, doi: 10.1016/i.ress.2007.04.002.
46. Taylor, T. R.; M. R. Giles, L. A. Hathon, T. N. Diggs, N. R. Braunsdorf, G. V. Birbiglia, M. G. Kittridge, C. I. Macaulay, and, I. S. Espejo, (2010), Sandstone diagenesis and reservoir quality prediction: Models, myths, and reality, AAPG Bull.; 94 (8), 1093-1132, doi: 10.1306/04211009123.
47. Tuncay, K.; and, P. Ortoleva, (2004), Quantitative basin modeling: Present state and future developments towards predictability, Geofluids, 4, 23-39, doi: 10.1111/j.1468-8123.2004.00064.x.
48. Walderhaug, O.; (1994), Precipitation rates for quartz cement in sandstones determined by fluid-inclusion microthermometry and temperature-history modeling, J. Sediment Res.; Sect. A, 64, 324-333.
49. Walderhaug, O.; (1996), Kinetic modeling of quartz cementation and porosity loss in deeply buried sandstone reservoirs, AAPG Bull.; 80, 731-745.
50. Wangen, M.; (2010), Physical Principles of Sedimentary Basin Analysis, Cambridge Univ. Press, Cambridge, U. K.
51. Wieck, J.; M. Pearson, and, L. Strayer, (1995), A finite element method for simulating fault block motion and hydrothermal fluid flow within rifting basins, Water Resour. Res.; 31 (12), 3241-3258, doi: 10.1029/95WR02114.
52. Xiu, D.; and, J. Hestaven, (2005), High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput.; 27, 1118-1139, doi: 10.1137/040615201.
53. Xiu, D.; and, G. E. Karniadakis, (2002), The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput.; 24 (2), 619-644, doi: 10.1137/S1064827501387826.
54. Zhang, G.; D. Lu, M. Ye, M. Gunzburger, and, C. Webster, (2013), An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling, Water Resour. Res.; 49, 6871-6892, doi: 10.1002/wrcr.20467.
55. Zhao, K.; and, I. Lerche, (1993), Inversion of dynamical indicators in quantitative basin analysis models. II: Synthetic tests and a case history using dynamical indicator tomography, Math. Geol.; 25, 107-123, doi: 10.1007/BF00893268.