Advertisement

Computational Geosciences

, Volume 20, Issue 6, pp 1287–1300 | Cite as

A stochastic inversion workflow for monitoring the distribution of CO2 injected into deep saline aquifers

  • Lorenzo PerozziEmail author
  • Erwan Gloaguen
  • Bernard Giroux
  • Klaus Holliger
Original Paper
  • 182 Downloads

Abstract

We present a two-step stochastic inversion approach for monitoring the distribution of CO2 injected into deep saline aquifers for the typical scenario of one single injection well and a database comprising a common suite of well logs as well as time-lapse vertical seismic profiling (VSP) data. In the first step, we compute several sets of stochastic models of the elastic properties using conventional sequential Gaussian co-simulations (SGCS) representing the considered reservoir before CO2 injection. All realizations within a set of models are then iteratively combined using a modified gradual deformation algorithm aiming at reducing the mismatch between the observed and simulated VSP data. In the second step, these optimal static models then serve as input for a history matching approach using the same modified gradual deformation algorithm for minimizing the mismatch between the observed and simulated VSP data following the injection of CO2. At each gradual deformation step, the injection and migration of CO2 is simulated and the corresponding seismic traces are computed and compared with the observed ones. The proposed stochastic inversion approach has been tested for a realistic, and arguably particularly challenging, synthetic case study mimicking the geological environment of a potential CO2 injection site in the Cambrian-Ordivician sedimentary sequence of the St. Lawrence platform in Southern Québec. The results demonstrate that the proposed two-step reservoir characterization approach is capable of adequately resolving and monitoring the distribution of the injected CO2. This finds its expression in optimized models of P- and S-wave velocities, density, and porosity, which, compared to conventional stochastic reservoir models, exhibit a significantly improved structural similarity with regard to the corresponding reference models. The proposed approach is therefore expected to allow for an optimal injection forecast by using a quantitative assimilation of all available data from the appraisal stage of a CO2 injection site.

Keywords

CO2 sequestration Stochastic inversion Gradual deformation VSP 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Avseth, P., Mukerji, T., Jørstad, A., Mavko, G., Veggeland, T.: Seismic reservoir mapping from 3-D AVO in a North Sea turbidite system. Geophysics 66, 1157–1176 (2001)CrossRefGoogle Scholar
  2. 2.
    Azevedo, L., Nunes, R., Correia, P., Soares, A., Guerreiro, L., Neto, G.S.: Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology. Geophysics 79, M1–M10 (2013)CrossRefGoogle Scholar
  3. 3.
    Biot, M.A., Willis, D.G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594–601 (1957)Google Scholar
  4. 4.
    Bohlen, T.: Parallel 3-D viscoelastic finite difference seismic modelling. Comput. Geosci. 28, 887–899 (2002)CrossRefGoogle Scholar
  5. 5.
    Bosch, M., Carvajal, C., Rodrigues, J., Torres, A., Aldana, M., Sierra, J.: Petrophysical seismic inversion conditioned to well-log data: methods and application to a gas reservoir. Geophysics 74, O1–O15 (2009)CrossRefGoogle Scholar
  6. 6.
    Brie, A., Pampuri, F., Marsala, A., Meazza, O.: Shear sonic interpretation in gas-bearing sands. SPE Annual Technical Conference and Exhibition (1995)Google Scholar
  7. 7.
    Buland, A., Omre, H.: Bayesian linearized AVO inversion. Geophysics 68, 185–198 (2003)CrossRefGoogle Scholar
  8. 8.
    Caers, J., Hoffman, T.: The probability perturbation method: a new look at Bayesian inverse modeling. Math. Geol. 38, 81–100 (2006)CrossRefGoogle Scholar
  9. 9.
    Carcione, J., Helle, H.: Numerical solution of the poroviscoelastic wave equation on a staggered mesh. J. Comput. Phys. 154, 520–527 (1999)CrossRefGoogle Scholar
  10. 10.
    Carcione, J.M.: Viscoelastic effective rheologies for modelling wave propagation in porous media. Geophys. Prospect. 46, 249–270 (1998)CrossRefGoogle Scholar
  11. 11.
    Carcione, J.M., Picotti, S., Gei, D., Rossi, G.: Physics and seismic modeling for monitoring CO2 storage. Pure Appl. Geophys. 163, 175–207 (2006)Google Scholar
  12. 12.
    Carman, P.: The determination of the specific surface of powders. J. Soc. Chem. Ind. 57, 225–234 (1938)Google Scholar
  13. 13.
    Celia, M., Bachu, S., Nordbotten, J., Kavetski, D., Gasda, S.: A risk assessment tool to quantify CO2 leakage potential through wells in mature sedimentary basins. In: Proceedings of the 8th Conference on Greenhouse Gas Technologies (2006)Google Scholar
  14. 14.
    Claprood, M., Gloaguen, E., Giroux, B., Konstantinovskaya, E., Malo, M., Duchesne, M.J.: Workflow using sparse vintage data for building a first geological and reservoir model for CO2 geological storage in deep saline aquifer. A case study in the St. Lawrence Platform, Canada. Greenh. Gases Sci. Technol. 2, 260–278 (2012)CrossRefGoogle Scholar
  15. 15.
    Coats, K., Nielsen, R., Terhune, M.H., Weber, A.: Simulation of three-dimensional, two-phase flow in oil and gas reservoirs. Soc. Petroleum Eng. J. 7, 377–388 (1967)CrossRefGoogle Scholar
  16. 16.
    Deutsch, C.V., Journel, A.G.: GSLIB: Geostatistical Software Library and User’s Guide (Applied Geostatistics). Oxford University Press (1997)Google Scholar
  17. 17.
    Doyen, P.: Seismic Reservoir Characterization: An Earth Modelling Perspective. EAGE (2007)Google Scholar
  18. 18.
    Eidsvik, J., Avseth, P., Omre, H., Mukerji, T., Mavko, G.: Stochastic reservoir characterization using prestack seismic data. Geophysics 69, 978–993 (2004)CrossRefGoogle Scholar
  19. 19.
    EU: Report from the commission to the European parliament and the council on the implementation of Directive 2009/31/EC on the geological storage of carbon dioxide. Technical Report. European Union (2014)Google Scholar
  20. 20.
    Fabien-Ouellet, G., Gloaguen, E., Giroux, B.: Viscoelastic forward and adjoint modeling with OpenCL on heterogeneous clusters. In: 78 th EAGE Conference & Exhibition. Vienna (2016)Google Scholar
  21. 21.
    Fornel, A., Estublier, A.: To a dynamic update of the Sleipner CO2 storage geological model using 4D seismic data. Energy Procedia 37, 4902–4909 (2013)CrossRefGoogle Scholar
  22. 22.
    Gassmann, F.: Elastic waves through a packing of spheres. Geophysics 16, 673–685 (1951)CrossRefGoogle Scholar
  23. 23.
    Giroux, B.: Performance of convolutional perfectly matched layers for pseudospectral time domain poroviscoelastic schemes. Comput. Geosci. 45, 149–160 (2012)CrossRefGoogle Scholar
  24. 24.
    Glover, P.: What is the cementation exponent? A new interpretation. Lead. Edge 28, 82–85 (2009)CrossRefGoogle Scholar
  25. 25.
    González, E.F., Mukerji, T., Mavko, G.: Seismic inversion combining rock physics and multiple-point geostatistics. Geophysics 73, R11–R21 (2008)CrossRefGoogle Scholar
  26. 26.
    Grana, D., Mukerji, T., Dvorkin, J., Mavko, G.: Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method. Geophysics 77, M53—M72 (2012)Google Scholar
  27. 27.
    Greenberg, M.L., Castagna, J.P.: Shear-wave velocity estimation in porous rocks: theoretical formulation, preliminary verification and applications. Geophys. Prospect 40, 195–209 (1992)CrossRefGoogle Scholar
  28. 28.
    Gunning, J., Glinsky, M.E.: Detection of reservoir quality using Bayesian seismic inversion. Geophysics 72, R37–R49 (2007)CrossRefGoogle Scholar
  29. 29.
    Han, D.h., Batzle, M.L.: Gassmann’s equation and fluid-saturation effects on seismic velocities. Geophysics 69, 398–405 (2004)CrossRefGoogle Scholar
  30. 30.
    Hansen, T.M., Cordua, K.S., Mosegaard, K.: Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling. Comput. Geosci. 16, 593–611 (2012)CrossRefGoogle Scholar
  31. 31.
    Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127–140 (1963)CrossRefGoogle Scholar
  32. 32.
    Hu, L.Y.: Gradual deformation and iterative calibration of Gaussian-related stochastic models. Math. Geol. 32, 87–108 (2000)CrossRefGoogle Scholar
  33. 33.
    Hu, L.Y.: Combination of dependent realizations within the gradual deformation method. Math. Geol. 34, 953–963 (2002)CrossRefGoogle Scholar
  34. 34.
    Hu, L.Y., Blanc, G., Noetinger, B.: Gradual deformation and iterative calibration of sequential stochastic simulations. Math. Geol. 33, 475–489 (2001)CrossRefGoogle Scholar
  35. 35.
    Kozeny, J.: Über kapillare Leitung des Wassers im Boden. Akad. Wiss. Wien 136, 271–306 (1927)Google Scholar
  36. 36.
    Larsen, A.L., Ulvmoen, M., Omre, H., Buland, A.: Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model. Geophysics 71, R69–R78 (2006)CrossRefGoogle Scholar
  37. 37.
    Le Ravalec, M.: Inverse Stochastic Modeling of Flow in Porous Media: Applications to Reservoir Characterization. Editions OPHRYS (2005)Google Scholar
  38. 38.
    Le Ravalec, M., Mouche, E.: Calibrating transmissivities from piezometric heads with the gradual deformation method: an application to the Culebra Dolomite unit at the Waste Isolation Pilot Plant (WIPP), New Mexico, USA. J. Hydrol. 472-473, 1–13 (2012)CrossRefGoogle Scholar
  39. 39.
    Le Ravalec, M., Noetinger, B., Hu, L.Y.: The FFT moving average (FFT-MA) generator: an efficient numerical method for generating and conditioning Gaussian simulations. Math. Geol. 32, 701–723 (2000)CrossRefGoogle Scholar
  40. 40.
    Lie, K.A.: An Introduction to reservoir simulation using Matlab: User guide for the Matlab Reservoir Simulation Toolbox (MRST). Technical Report. SINTEF ICT. Oslo, Norway (2015)Google Scholar
  41. 41.
    Lumley, D., Sherlock, D., Daley, T., Huang, L., Lawton, D., Masters, R., Verliac, M., White, D.: Highlights of the 2009 SEG Summer Research Workshop on CO2 Sequestration. Lead. Edge 29, 138–145 (2010)CrossRefGoogle Scholar
  42. 42.
    Malo, M., Bédard, K.: Basin-scale assessment for CO2 storage prospectivity in the province of Québec, Canada. Energy Procedia 23, 487–494 (2012)CrossRefGoogle Scholar
  43. 43.
    Martin, J.C.: Some mathematical aspects of two phase flow with application to flooding and gravity segregation. Prod. Month. 22(6), 22–35 (1958)Google Scholar
  44. 44.
    Martin, J.C.: Partial integration of equations of multiphase flow. Soc. Petroleum Eng. J. 8, 370–380 (1968)CrossRefGoogle Scholar
  45. 45.
    Mavko, G., Mukerji, T., Dvorkin, J.: The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media. Cambridge University Press (2009)Google Scholar
  46. 46.
    Menke, W.: Geophysical data analysis: Discrete inverse theory, vol. 45. Academic Press (2012)Google Scholar
  47. 47.
    Møll Nilsen, H., Herrera, P.A., Ashraf, M., Ligaarden, I., Iding, M., Hermanrud, C., Lie, K.A., Nordbotten, J.M., Dahle, H.K., Keilegavlen, E.: Field-case simulation of CO2-plume migration using vertical-equilibrium models. Energy Procedia 4, 3801–3808 (2011)CrossRefGoogle Scholar
  48. 48.
    Mukerji, T., Jørstad, A., Avseth, P., Mavko, G., Granli, J.R.: Mapping lithofacies and pore-fluid probabilities in a North Sea reservoir: seismic inversions and statistical rock physics. Geophysics 66, 988–1001 (2001)CrossRefGoogle Scholar
  49. 49.
    Nilsen, H.M., Lie, K.A., Andersen, O.: Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Comput. Geosci. 20, 49–67 (2016)CrossRefGoogle Scholar
  50. 50.
    Njiekak, G., Schmitt, D.R., Yam, H., Kofman, R.S.: CO2 rock physics as part of the Weyburn-Midale geological storage project. Int. J. Greenhouse Gas Control 16, S118–S133 (2013)Google Scholar
  51. 51.
    Nordbotten, J., Celia, M.: Analysis of plume extent using analytical solutions for CO2 storage. In: Proceedings of the 16th conference on Computational Methods in Water Resources (2006)Google Scholar
  52. 52.
    Nordbotten, J.M., Celia, M.A., Bachu, S.: Injection and storage of CO2 in deep saline aquifers: analytical solution for CO2 plume evolution during injection. Transport Porous Media 58, 339–360 (2005)CrossRefGoogle Scholar
  53. 53.
    Nordbotten, J.M., Kavetski, D., Celia, M.A., Bachu, S.: Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environ. Sci. Technol. 43, 743–749 (2009)CrossRefGoogle Scholar
  54. 54.
    Perozzi, L., Giroux, B., Kofman, R., Schmitt, D.: Preparatory work for the seismic monitoring of CO2 storage at a prospective site in the St. Lawrence Lowlands, Canada. In: 76th European Association of Geoscientists and Engineers Conference and Exhibition - Amsterdam (2014)Google Scholar
  55. 55.
    Ramirez, A., White, D., Hao, Y., Dyer, K., Johnson, J.: Estimating reservoir permeabilities using the seismic response to CO2 injection and stochastic inversion. Int. J. Greenhouse Gas Control 16, S146–S159 (2013)CrossRefGoogle Scholar
  56. 56.
    Rimstad, K., Omre, H.: Impact of rock-physics depth trends and Markov random fields on hierarchical Bayesian lithology/fluid prediction. Geophysics 75, R93–R108 (2010)CrossRefGoogle Scholar
  57. 57.
    Roggero, F., Hu, L.: Gradual deformation of continuous geostatistical models for history matching. SPE Annual Technical Conference and Exhibition (1998)Google Scholar
  58. 58.
    Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM: Society for Industrial and Applied Mathematics (2004)Google Scholar
  59. 59.
    Tillier, E., Le Ravalec, M., Da Veiga, S.: Simultaneous inversion of production data and seismic attributes: application to a synthetic SAGD produced field case. Oil Gas Sci. Technol. Rev. IFP Energies nouvelles 67, 289–301 (2012)Google Scholar
  60. 60.
    Ulvmoen, M., Omre, H.: Improved resolution in Bayesian lithology/fluid inversion from prestack seismic data and well observations: Part 1 - Methodology. Geophysics 75, R21–R35 (2010)CrossRefGoogle Scholar
  61. 61.
    Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004)CrossRefGoogle Scholar
  62. 62.
    Wood, A.: A Textbook of Sound: Being an Account of the Physics of Vibrations with Special Reference to Recent Theoretical and Technical Developments. G. Bell and Sons Limited (1955)Google Scholar
  63. 63.
    Ying, Z., Gomez-Hernandez, J.: An improved deformation algorithm for automatic history matching. Report 13, Stanford Center for Reservoir Forecasting (SCRF) Annual Report. Stanford (2000)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut National de la Recherche ScientifiqueCentre Eau Terre EnvironnementQuébecCanada
  2. 2.Applied and Environmental Geophysics Group, Institute of Earth SciencesUniversity of LausanneLausanneSwitzerland

Personalised recommendations