Skip to main content

Advertisement

SpringerLink
Log in

Efficient parameter estimation for a methane hydrate model with active subspaces

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

Methane gas hydrates have increasingly become a topic of interest because of their potential as a future energy resource. There are significant economical and environmental risks associated with extraction from hydrate reservoirs, so a variety of multiphysics models have been developed to analyze prospective risks and benefits. These models generally have a large number of empirical parameters which are not known a priori. Traditional optimization-based parameter estimation frameworks may be ill-posed or computationally prohibitive. Bayesian inference methods have increasingly been found effective for estimating parameters in complex geophysical systems. These methods often are not viable in cases of computationally expensive models and high-dimensional parameter spaces. Recently, methods have been developed to effectively reduce the dimension of Bayesian inverse problems by identifying low-dimensional structures that are most informed by data. Active subspaces is one of the most generally applicable methods of performing this dimension reduction. In this paper, Bayesian inference of the parameters of a state-of-the-art mathematical model for methane hydrates based on experimental data from a triaxial compression test with gas hydrate-bearing sand is performed in an efficient way by utilizing active subspaces. Active subspaces are used to identify low-dimensional structure in the parameter space which is exploited by generating a cheap regression-based surrogate model and implementing a modified Markov chain Monte Carlo algorithm. Posterior densities having means that match the experimental data are approximated in a computationally efficient way.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andrade, J.E., Chen, Q., Le, P.H., Avila, C.F., Evans, T.M.: On the rheology of dilative granular media: bridging solid- and fluid-like behavior. Journal of the Mechanics and Physics of Solids 60(6), 1122–1136 (2012)

    Article  Google Scholar 

  2. Bastian, P., Heimann, F., Marnach, Ś.: Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE). Kybernetika 46(2), 294–315 (2010)

    Google Scholar 

  3. Beven, K., Freer, J.: Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology. J. Hydrol. 249(1–4), 11–29 (2001)

    Article  Google Scholar 

  4. Brooks, S., Gelman, A., Jones, G., Meng, X.L.: Handbook of Markov Chain Monte Carlo. CRC press, Boca Raton (2011)

  5. Bui-Thanh, T., Burstedde, C., Ghattas, O., Martin, J., Stadler, G., Wilcox, L.C.: Extreme-scale UQ for Bayesian inverse problems governed by pdes. In: Proceedings of the international conference on high performance computing, networking, storage and analysis, p. 3. IEEE Computer Society Press (2012)

  6. Bui-Thanh, T., Girolami, M.: Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo. Inverse Problems 30(11), 114,014,23 (2014)

    Article  Google Scholar 

  7. Butler, T., Jakeman, J., Wildey, T.: Combining push-forward measures and Bayes’ rule to construct consistent solutions to stochastic inverse problems. SIAM J. Sci. Comput. 40(2), A984–A1011 (2018)

    Article  Google Scholar 

  8. Choi, J., Dai, S., Cha, J., Seol, Y.: Laboratory formation of noncementing hydrates in sandy sediments. Geochem. Geophys. Geosyst. 15(4), 1648–1656 (2014)

    Article  Google Scholar 

  9. Constantine, P., Gleich, D.: Computing active subspaces with Monte Carlo. arXiv:1408.0545 (2014)

  10. Constantine, P.G.: Active subspaces, SIAM spotlights, vol. 2. Society for industrial and applied mathematics (SIAM), Philadelphia, PA. Emerging ideas for dimension reduction in parameter studies (2015)

  11. Constantine, P.G., Diaz, P.: Global sensitivity metrics from active subspaces. Reliability Engineering & System Safety 162, 1–13 (2017)

    Article  Google Scholar 

  12. Constantine, P.G., Dow, E., Wang, Q.: Active subspace methods in theory and practice: applications to kriging surfaces. SIAM J. Sci. Comput. 36(4), A1500–A1524 (2014)

    Article  Google Scholar 

  13. Constantine, P.G., Kent, C., Bui-Thanh, T.: Accelerating Markov chain Monte Carlo with active subspaces. SIAM J. Sci. Comput. 38(5), A2779–A2805 (2016)

    Article  Google Scholar 

  14. Cortesi, A., Constantine, P., Magin, T.E., Congedo, P.M.: Forward and backward uncertainty quantification with active subspaces: application to hypersonic flows around a cylinder. Research report RR-9097, INRIA Bordeaux, équipe CARDAMOM. https://hal.inria.fr/hal-01592591 (2017)

  15. Cui, T., Law, K.J.H., Marzouk, Y.M.: Dimension-independent likelihood-informed MCMC. J. Comput. Phys. 304, 109–137 (2016)

    Article  Google Scholar 

  16. Dawe, R.A., Thomas, S.: A large potential methane source—natural gas hydrates. Energy sources. Part A: recovery utilization, and environmental effects 29(3), 217–229 (2007)

    Google Scholar 

  17. Dedner, A., Flemisch, B., Klöfkorn, R.: Advances in DUNE: proceedings of the DUNE: user meeting, held in October 6Th–8Th 2010 in Stuttgart, Germany. SpringerLink: Bücher. Springer, Berlin (2012)

    Google Scholar 

  18. Deusner, C., Bigalke, N., Kossel, E., Haeckel, M.: Methane production from gas hydrate deposits through injection of supercritical CO2. Energies 5(7), 2112 (2012)

    Article  Google Scholar 

  19. Freer, J., Beven, K.: Bayesian estimation of uncertainty in runoff prediction and the value of data: an applicaiton of the GLUE approach. Water Resour. Res. 32(7), 2161–2173 (1996)

    Article  Google Scholar 

  20. Grey, Z.J., Constantine, P.G.: Active subspaces of airfoil shape parameterizations. arXiv:1702.02909 (2017)

  21. Gupta, S., Deusner, C., Haeckel, M., Helmig, R., Wohlmuth, B.: Testing a thermo-chemo-hydro-geomechanical model for gas hydrate bearing sediments using triaxial compression lab experiments. Geochem. Geophys. Geosyst. 18(9), 3419–3437 (2017)

    Article  Google Scholar 

  22. Gupta, S., Helmig, R., Wohlmuth, B.: Non-isothermal, multi-phase, multi-component flows through deformable methane hydrate reservoirs. Comput. Geosci. 19(5), 1063–1088 (2015)

    Article  Google Scholar 

  23. Haario, H., Laine, M., Mira, A., Saksman, E.: DRAM: efficient adaptive MCMC. Stat. Comput. 16 (4), 339–354 (2006)

    Article  Google Scholar 

  24. Hager, C., Wohlmuth, B.: Nonlinear complementarity functions for plasticity problems with frictional contact. Comput. Methods Appl. Mech. Eng. 198(41), 3411–3427 (2009). https://doi.org/10.1016/j.cma.2009.06.021

    Article  Google Scholar 

  25. Hager, C., Wohlmuth, B.: Semismooth newton methods for variational problems with inequality constraints. GAMM Mitteilungen 33, 8–24 (2010)

    Article  Google Scholar 

  26. Hairer, M., Stuart, A.M., Vollmer, S.J.: Spectral gaps for a metropolis–hastings algorithm in infinite dimensions. Ann. Appl. Probab. 24(6), 2455–2490 (2014). https://doi.org/10.1214/13-AAP982

    Article  Google Scholar 

  27. Holodnak, J.T., Ipsen, I.C.F., Smith, R.C.: A probabilistic subspace bound with application to active subspaces ArXiv e-prints (2018)

  28. Huang, J., Griffiths, D.V.: Return mapping algorithms and stress predictors for failure analysis in geomechanics. J. Eng. Mech. 135(4), 276–284 (2009). https://doi.org/10.1061/(ASCE)0733-9399(2009)135:4(276)

    Article  Google Scholar 

  29. Hyodo, M., Li, Y., Yoneda, J., Nakata, Y., Yoshimoto, N., Nishimura, A.: Effects of dissociation on the shear strength and deformation behavior of methane hydrate-bearing sediments. Mar. Pet. Geol. 51, 52–62 (2014)

    Article  Google Scholar 

  30. Hyodo, M., Nakata, Y., Yoshimoto, N., Ebinuma, T.: Basic research on the mechanical behaviour of methane hydrate sediments mixture. Soils. Found. 45(1), 75–85 (2005)

    Google Scholar 

  31. Jefferson, J.L., Gilbert, J.M., Constantine, P.G., Maxwell, R.M.: Reprint of: Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model. Computers & Geosciences 90, 78–89 (2016)

    Article  Google Scholar 

  32. Jirasek, M., Bazant, Z.: Inelastic analysis of structures. Wiley, London (2002)

    Google Scholar 

  33. Kaipio, J., Somersalo, E.: Statistical and computational inverse Problems, vol. 160. Springer Science & Business Media, Berlin (2006)

    Google Scholar 

  34. Kimoto, S., Oka, F., Fushita, T.: A chemo-thermo-mechanically coupled analysis of ground deformation induced by gas hydrate dissociation. Int. J. Mech. Sci. 52(2), 365–376 (2010)

    Article  Google Scholar 

  35. Klar, A., Soga, K., NG, Y.A.: Coupled deformation-flow analysis for methane hydrate extraction. Geotechnique 60(10), 765–776 (2010)

    Article  Google Scholar 

  36. Klar, A., Uchida, S., Soga, K., Yamamoto, K.: Explicitly coupled thermal flow mechanical formulation for gas-hydrate sediments. SPE J. 18, 196–206 (2013)

    Article  Google Scholar 

  37. Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp 481–492. University of California Press, Berkeley (1951)

  38. Lee, J.Y., Francisca, F.M., Santamarina, J.C., Ruppel, C.: Parametric study of the physical properties of hydrate-bearing sand, silt, and clay sediments: 2. Small-strain mechanical properties. J. Geophys. Res. 115(B11), 11p (2010)

    Google Scholar 

  39. Lee, J.Y., Yun, T.S., Santamarina, J.C., Ruppel, C.: Observations related to tetrahydrofuran and methane hydrates for laboratory studies of hydrate bearing sediments. Geochem. Geophys. Geosyst. 8(6), Q06003 (2007)

    Article  Google Scholar 

  40. Leube, P.C., Geiges, A., Nowak, W.: Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design. Water Resources Research 48(2), W02501 (2012)

    Article  Google Scholar 

  41. Lukaczyk, T., Palacios, F., Alonso, J.J., Constantine, P.: Active subspaces for shape optimization. In: Proceedings of the 10th AIAA multidisciplinary design optimization conference, pp. 1–18 (2014)

  42. Martin, J., Wilcox, L.C., Burstedde, C., Ghattas, O.: A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM J. Sci. Comput. 34(3), A1460–A1487 (2012)

    Article  Google Scholar 

  43. Masui, A., Haneda, H., Ogata, Y., Aoki, K.: Effects of methane hydrate formation on shear strength of synthetic methane hydrate sediments. The Fifteenth International Offshore and Polar Engineering Conference 8, 364–369 (2005)

    Google Scholar 

  44. Miyazaki, K., Masui, A., Sakamoto, Y., Aoki, K., Tenma, N., Yamaguchi, T.: Triaxial compressive properties of artificial methane-hydrate-bearing sediment. Journal of Geophysical Research: Solid Earth 116(B06102), (2011)

  45. Miyazaki, K., Masui, A., Tenma, N., Ogata, Y., Aoki, K., Yamaguchi, T., Sakamoto, Y.: Study on mechanical behavior for methane hydrate sediment based on constant strain-rate test and unloading-reloading test under triaxial compression. International Journal of Offshore and Polar Engineering 20(1), 61–67 (2010)

    Google Scholar 

  46. Moridis, G.J., Collett, T.S., Boswell, R., Kurihara, M., Reagan, M.T., Koh, C., Sloan, E.D.: Toward production from gas hydrates: current status, assessment of resources, and simulation-based evaluation of technology and potential. SPE Reserv. Eval. Eng. 12, 745–771 (2009)

    Article  Google Scholar 

  47. Moridis, G.J., Collett, T.S., Pooladi-Darvish, M., Hancock, S., Santamarina, C., Boswell, R., Kneafsey, T., Rutqvist, J., Kowalsky, M.B., et al., Reagan M.T.: Challenges, uncertainities and issues facing gas production from gas hydrate deposits. SPE Reserv. Eval. Eng. 14, 76–112 (2011)

  48. Nowak, W., de Barros, F.P.J., Rubin, Y.: Bayesian geostatistical design: task-driven optimal site investigation when the geostatistical model is uncertain. Water Resources Research 46(3), W03535 (2010)

    Article  Google Scholar 

  49. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: Machine learning in python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

  50. Piñero, E., Marquardt, M., Hensen, C., Haeckel, M., Wallmann, K.: Estimation of the global inventory of methane hydrates in marine sediments using transfer functions. Biogeosciences 10(2), 959–975 (2013)

    Article  Google Scholar 

  51. Pinkert, S.: The lack of true cohesion in hydrate-bearing sands. Granul. Matter 19(3), 57 (2017)

    Article  Google Scholar 

  52. Pinkert, S., Grozic, J.L.H.: Prediction of the mechanical response of hydrate-bearing sands. J. Geophys. Res. Solid Earth 119(6), 4695–4707 (2014)

    Article  Google Scholar 

  53. Pinkert, S., Grozic, J.L.H., Priest, J.A.: Strain-softening model for hydrate-bearing sands. International Journal of Geomechanics 15(6), 04015, 007 (2015)

    Article  Google Scholar 

  54. Priest, J.A., Rees, E.V.L., Clayton, C.R.I.: Influence of gas hydrate morphology on the seismic velocities of sands. J. Geophys. Res. Solid Earth 114(B11), B11205 (2009)

    Article  Google Scholar 

  55. Rutqvist, J.: Status of the TOUGH-FLAC simulator and recent applications related to coupled fluid flow and crustal deformations. Computers &, Geosciences 37, 739–750 (2011)

    Article  Google Scholar 

  56. Santamarina, J.C., Ruppel, C.: The impact of hydrate saturation on the mechanical, electrical, and thermal properties of hydrate-bearing sand, silts, and clay. Geophysical Characterization of Ga Hydrates. Geophys Dev. Ser 14, 373–384 (2010)

    Google Scholar 

  57. Simo, J., Hughes, T.: Computational inelasticity. Interdisciplinary applied mathematics. Springer, New york (2006)

    Google Scholar 

  58. Sloan, E.D.: Gas hydrates: review of physical/chemical properties. Energ. Fuel. 12, 191–196 (1998)

    Article  Google Scholar 

  59. de Souza Neto, E., Peric, D., Owen, D.: Computational methods for plasticity: theory and applications. Wiley, New York (2011)

  60. Stuart, A.M.: Inverse problems: a Bayesian perspective. Acta Numerica 19, 451–559 (2010)

    Article  Google Scholar 

  61. Sultan, N., Cochonat, P., Canals, M., Cattaneo, A., Dennielou, B., Haflidason, H., Laberg, J.S., Long, D., Mienert, J., Trincardi, F., Urgeles, R: Triggering mechanisms of slope instability processes and sediment failures on continental margins: a geotechnical approach. Mar. Geol. 213(1-4), 291–321 (2004)

    Article  Google Scholar 

  62. Sultan, N., Cochonat, P., Foucher, J.P., Mienert, J.: Effect of gas hydrates melting on sea floor slope instability. Mar. Geol. 213(1), 379–401 (2004)

    Article  Google Scholar 

  63. Troldborg, M., Nowak, W., Tuxen, N., Bjerg, P.L., Helmig, R., Binning, P.J.: Uncertainty evaluation of mass discharge estimates from a contaminated site using a fully Bayesian framework. Water Resources Research 46(12), W12552 (2010)

    Article  Google Scholar 

  64. Uchida, S., Soga, K., Yamamoto, K.: Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research: Solid Earth 117, B03209 (2012)

    Article  Google Scholar 

  65. Vollmer, S.J.: Dimension-independent mcmc sampling for inverse problems with non-gaussian priors. SIAM/ASA Journal on Uncertainty Quantification 3(1), 535–561 (2015)

    Article  Google Scholar 

  66. Vrugt, J., ter Braak, C., Gupta, H., Robinson, B.: Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? Stoch. Env. Res. Risk A. 23(7), 1011–1026 (2008)

    Article  Google Scholar 

  67. Vrugt, J.A., Ter Braak, C., Diks, C., Robinson, B.A., Hyman, J.M., Higdon, D.: Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling. International Journal of Nonlinear Sciences and Numerical Simulation 10(3), 273–290 (2009)

    Article  Google Scholar 

  68. Waite, W.F., Santamarina, J.C., Cortes, D.D., Dugan, B., Espinoza, D.N., Germaine, J., Jang, J., Jung, J.W., Kneafsey, T.J., Shin, H., Soga, K., Winters, W.J., Yun, T.S.: Physical properties of hydrate-bearing sediments. Reviews of Geophysics 47(4), RG4003 (2009)

    Article  Google Scholar 

  69. Wood, D.: Soil behaviour and critical state soil mechanics. Cambridge University Press, Cambridge (1991)

    Book  Google Scholar 

  70. Xuerui, G., Marcelo, S.: A geomechanical model for gas hydrate-bearing sediments. Environmental Geotechnics 4(2), 143–156 (2017)

    Article  Google Scholar 

  71. Yun, T.S., Santamarina, J.C., Ruppel, C.: Mechanical properties of sand, silt, and clay containing tetrahydrofuran hydrate. J. Geophys. Res. 112(B04), 106 (2007)

    Google Scholar 

  72. Zienkiewicz, O., Taylor, R.: The finite element method for solid and structural mechanics. The finite element method elsevier science (2013)

Download references

Funding

Financial support for BW, SM, and MTP was provided by the German Research Foundation (DFG, Project WO 671/11-1). The work of SG and CD was further funded by the German Federal Ministries of Economy (BMWi) and Education and Research (BMBF) through the SUGAR project (grant nos. 03SX250, 03SX320A, and 03G0856A), and the EU-FP7 project MIDAS (grant agreement no. 603418).

Author information

Authors and Affiliations

  1. Chair for Numerical Mathematics, Technical University Munich, Boltzmannstr. 3, 85748, Garching bei München, Germany

    Mario Teixeira Parente, Steven Mattis & Barbara Wohlmuth

  2. Department of Mathematics, University of Bergen, Bergen, Norway

    Barbara Wohlmuth

  3. GEOMAR Helmholtz Centre for Ocean Research Kiel, Wischhofstr. 1-3, 24148, Kiel, Germany

    Shubhangi Gupta & Christian Deusner

Authors
  1. Mario Teixeira Parente
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven Mattis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shubhangi Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christian Deusner
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Barbara Wohlmuth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Teixeira Parente.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teixeira Parente, M., Mattis, S., Gupta, S. et al. Efficient parameter estimation for a methane hydrate model with active subspaces. Comput Geosci 23, 355–372 (2019). https://doi.org/10.1007/s10596-018-9769-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-018-9769-x

Keywords

Mathematics Subject Classification (2010)

Search

Navigation