Computational Geosciences

, Volume 21, Issue 5–6, pp 835–848 | Cite as

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

  • Sean McGovern
  • Stefan Kollet
  • Claudius M. Bürger
  • Ronnie L. Schwede
  • Olaf G. Podlaha
Open Access
Original Paper

Abstract

As sedimentation progresses in the formation and evolution of a depositional geologic basin, the rock strata are subject to various stresses. With increasing lithostatic pressure, compressional forces act to compact the porous rock matrix, leading to overpressure buildup, changes in the fluid pore pressure and fluid flow. In the context of petroleum systems modelling, the present study concerns the geometry changes that a compacting basin experiences subject to deposition. The purpose is to track the positions of the rock layer interfaces as compaction occurs. To handle the challenge of potentially large geometry deformations, a new modelling concept is proposed that couples the pore pressure equation with a level set method to determine the movement of lithostratigraphic interfaces. The level set method propagates an interface according to a prescribed speed. The coupling term for the pore pressure and level-set equations consists of this speed function, which is dependent on the compaction law. The two primary features of this approach are the simplicity of the grid and the flexibility of the speed function. A first evaluation of the model concept is presented based on an implementation for one spatial dimension accounting for vertical effective stress. Isothermal conditions with a constant fluid density and viscosity were assumed. The accuracy of the implemented numerical solution for the case of a single stratigraphic unit with a linear compaction law was compared to the available analytical solution [38]. The multi-layer setup and the nonlinear case were tested for plausibility.

Keywords

Basin modelling Geological modelling Level set methods 

References

  1. 1.
    Adalsteinsson, D., Sethian, J.A.: The fast construction of extension velocities in level set methods. J. Comput. Phys. 148(1), 2–22 (1999)CrossRefGoogle Scholar
  2. 2.
    Athy, L.F.: Density, porosity, and compaction of sedimentary rocks. AAPG Bull. 14(1), 1–24 (1930)Google Scholar
  3. 3.
    Audet, D.M., Fowler, A.C.: A mathematical model for compaction in sedimentary basins. Geophys. J. Int. 110(3), 577–590 (1992). doi:10.1111/j.1365-246X.1992.tb02093.x CrossRefGoogle Scholar
  4. 4.
    Bahr, D.B., Hutton, E.W., Syvitski, J.P., Pratson, L.F.: Exponential approximations to compacted sediment porosity profiles. Comput. Geosci. 27, 691–700 (2001)CrossRefGoogle Scholar
  5. 5.
    Benson, D.J.: Computational methods in Lagrangian and Eulerian hydrocodes. Comput. Methods Appl. Mech. Eng. 99(2), 235–394 (1992)CrossRefGoogle Scholar
  6. 6.
    Bethke, C.M.: A numerical model of compaction-driven groundwater flow and heat transfer and its application to the paleohydrology of intracratonic sedimentary basins. J. Geophys. Res. Solid Earth 90(B8), 6817–6828 (1985). doi:10.1029/JB090iB08p06817 CrossRefGoogle Scholar
  7. 7.
    Bethke, C.M.: Modeling subsurface flow in sedimentary basins. Geogr. Rundsch. 78(1), 129–154 (1989)CrossRefGoogle Scholar
  8. 8.
    de Boer, R.: Theory of porous media: past and present. ZAMM - J. Appl. Math. Mech./Zeitschrift für Angewandte Mathematik und Mechanik 78(7), 441–466 (1998)CrossRefGoogle Scholar
  9. 9.
    Chen, Z., Ewing, R.E., Lu, H., Lyons, S.L., Maliassov, S., Ray, M.B., Sun, T.: Integrated two-dimensional modeling of fluid flow and compaction in a sedimentary basin. Comput. Geosci. 6(3–4), 545–564 (2002). doi:10.1023/A:1021211803088 CrossRefGoogle Scholar
  10. 10.
    Christopher, L.M.: Forward Modeling of Compaction and Fluid Flow in the Ursa Region, Mississippi Canyon Region, Gulf of Mexico. Ph.D. thesis, Pennsylvania State University (2006)Google Scholar
  11. 11.
    Donea, J., Huerta, A., Ponthot, J.P., Rodriguez-Ferran, A.: Arbitrary Lagrangian—Eulerian methods. In: Encyclopedia of Computational Mechanics. Wiley (2004)Google Scholar
  12. 12.
    Frolkovic, P.: Application of level set method for groundwater flow with moving boundary. Adv. Water Resour. 47, 56–66 (2012). doi:10.1016/j.advwatres.2012.06.013 CrossRefGoogle Scholar
  13. 13.
    Fullsack, P.: An arbitrary Lagrangian-Eulerian formulation for creeping flows and its application in tectonic models. Geophys. J. Int. 120(1), 1–23 (1995). doi:10.1111/j.1365-246X.1995.tb05908.x CrossRefGoogle Scholar
  14. 14.
    Gibson, R.E.: The progress of consolidation in a clay layer increasing in thickness with time. Geotechnique 8 (4), 171–182 (1958)CrossRefGoogle Scholar
  15. 15.
    Hantschel, T., Kauerauf, A.: Fundamentals of Basin and Petroleum Systems Modeling. Springer, Berlin (2009)Google Scholar
  16. 16.
    Hartmann, D., Meinke, M., Schröder, W.: Differential equation based constrained reinitialization for level set methods. J. Comput. Phys. 227(14), 6821–6845 (2008)CrossRefGoogle Scholar
  17. 17.
    Kikinzon, E., Kuznetsov, Y., Maliassov, S., Sumant, P.: Modeling fluid flow and compaction in sedimentary basins using mixed finite elements. Comput. Geosci. 1–14 (2015). doi:10.1007/s10596-015-9470-2
  18. 18.
    Longoni, M., Malossi, A.C.I., Quarteroni, A., Villa, A., Ruffo, P.: An ALE-based numerical technique for modeling sedimentary basin evolution featuring layer deformations and faults. J. Comput. Phys. 230 (8), 3230–3248 (2011)CrossRefGoogle Scholar
  19. 19.
    Longoni, M., Malossi, A.C.I., Villa, A.: A robust and efficient conservative technique for simulating three-dimensional sedimentary basins dynamics. Comput. Fluids 39(10), 1964–1976 (2010)CrossRefGoogle Scholar
  20. 20.
    Malladi, R., Sethian, J.A.: Image processing via level set curvature flow. Proc. Natl. Acad. Sci. 92(15), 7046–7050 (1995)CrossRefGoogle Scholar
  21. 21.
    Min, C.: On reinitializing level set functions. J. Comput. Phys. 229(8), 2764–2772 (2010). doi:10.1016/j.jcp.2009.12.032 CrossRefGoogle Scholar
  22. 22.
    Minkoff, S.E., Stone, C.M., Bryant, S., Peszynska, M., Wheeler, M.F.: Coupled fluid flow and geomechanical deformation modeling. J. Pet. Sci. Eng. 38(1), 37–56 (2003)CrossRefGoogle Scholar
  23. 23.
    Nazem, M., Sheng, D., Carter, J.P., Sloan, S.W.: Arbitrary Lagrangian Eulerian method for large-strain consolidation problems. Int. J. Numer. Anal. Methods Geomech. 32(9), 1023–1050 (2008). doi:10.1002/nag.657 CrossRefGoogle Scholar
  24. 24.
    Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces, vol. 153. Springer Science & Business Media (2003)Google Scholar
  25. 25.
    Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)CrossRefGoogle Scholar
  26. 26.
    Poelchau, H.S., Baker, D.R., Hantschel, T., Horsfield, B., Wygrala, B.: Basin simulation and the design of the conceptual basin model. In: D.H. Welte, B. Horsfield, D.R. Baker (eds.) Petroleum and Basin Evolution, pp 3–70. Springer, Berlin (1997), doi:10.1007/978-3-642-60423-2_2 CrossRefGoogle Scholar
  27. 27.
    Schrefler, B.A., Scotta, R.: A fully coupled dynamic model for two-phase fluid flow in deformable porous media. Comput. Methods Appl. Mech. Eng. 190(24), 3223–3246 (2001)CrossRefGoogle Scholar
  28. 28.
    Sethian, J.A.: A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed. J. Differ. Geom. 31, 131–161 (1989)CrossRefGoogle Scholar
  29. 29.
    Sethian, J.A.: Theory, algorithms, and applications of level set methods for propagating interfaces. Acta Numer. 5, 309–395 (1996)CrossRefGoogle Scholar
  30. 30.
    Sethian, J.A., Straint, J.: Crystal growth and dendritic solidification. J. Comput. Phys. 98(2), 231–253 (1992). doi:10.1016/0021-9991(92)90140-T CrossRefGoogle Scholar
  31. 31.
    Sussman, M., Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H., Welcome, M.L.: An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148(1), 81–124 (1999)CrossRefGoogle Scholar
  32. 32.
    Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114(1), 146–159 (1994)CrossRefGoogle Scholar
  33. 33.
    Terzaghi, K.: Erdbaumechanik auf bodenphysikalischer Grundlage. Franz Deuticke, Vienna (1925)Google Scholar
  34. 34.
    Tuncay, K., Ortoleva, P.: Quantitative basin modeling: present state and future developments towards predictability. Geofluids 4(1), 23–39 (2004). doi:10.1111/j.1468-8123.2004.00064.x CrossRefGoogle Scholar
  35. 35.
    Ungerer, P.H., Pelet, R.: Extrapolation of the kinetics of oil and gas formation from laboratory experiments to sedimentary basins. Nature (1987)Google Scholar
  36. 36.
    Vila, J., Gonzalez, C., LLorca, J.: A level set approach for the analysis of flow and compaction during resin infusion in composite materials. Compos. A: Appl. Sci. Manuf. 67, 299–307 (2014). doi:10.1016/j.compositesa.2014.09.002 CrossRefGoogle Scholar
  37. 37.
    Villa, A., Formaggia, L.: Implicit tracking for multi-fluid simulations. J. Comput. Phys. 229(16), 5788–5802 (2010). doi:10.1016/j.jcp.2010.04.020 CrossRefGoogle Scholar
  38. 38.
    Wangen, M.: Physical Principles of Sedimentary Basin Analysis. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  39. 39.
    Yu, J.D.: Two-Phase Viscoelastic Jetting. Lawrence Berkeley National Laboratory (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Forschungszentrum JülichJülichGermany
  2. 2.Shell Global Solutions International B.V.AmsterdamThe Netherlands

Personalised recommendations