Skip to main content

Spline-based reservoir’s geometry reconstruction and mesh generation for coupled flow and mechanics simulation


In this paper, the geometry of oil reservoirs is reconstructed by using B-splines surfaces. The technique exploits the reservoir’s static model’s simplicity to build a robust piecewise continuous geometrical representation by means of Bèzier bicubic patches. Interpolation surfaces can manage the reservoir’s topology while translational surfaces allow extrapolating it towards its sideburdens. After that, transfinite interpolation (TFI) can be applied to generate decent hexahedral meshes. In order to test the procedure, several open-to-the-public oil reservoir datasets are reconstructed and hexahedral meshes around them are generated. This reconstruction workflow also allows having different meshes for flow and mechanics by computing a projection operator in order to map pressures from the original flow mesh to the generated reference mechanics mesh. As an update respect to a previous version of this research, we already incorporate blending functions to the TFI procedure in order to attract the mesh towards the reservoir, which allows grading the hexahedral meshes in the appropriate manner. Finally, field scale reservoir compaction and subsidence computations are carried out by using continuous Galerkin FEM for both flow and mechanics in order to demonstrate the applicability of the proposed algorithm.

This is a preview of subscription content, access via your institution.


  1. Angus, D., Verdon, J., Fisher1, Q., Kendall, J., Segura, J., Kristiansen, T., Crook, A., Yu, J.S.S., Dutko, M.: Integrated fluid-flow, geomechanic and seismic modelling for reservoir characterisation. Focus Article coordinated by Kurt Wickel, UK, pp. 27–35 (2011)

  2. Atkinson, K.: An introduction to numerical analysis. Wiley, New York (1978)

    Google Scholar 

  3. Becker, E., Carey, G., Oden, J.: Finite elements: an introduction, The Texas Finite Element Series, vol. I. Prentice-Hall Inc., Englewood Cliffs, New Jersey (1981)

    Google Scholar 

  4. Bell, J.: Practical methods for estimating in situ stresses for borehole stability applications in sedimentary basins. J. Pet. Sci. Eng. 38, 111–119 (2003)

    Article  Google Scholar 

  5. Berg, M.D., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational geometry algorithms and applications. Springer, Berlin (2000)

    Google Scholar 

  6. Coussy, O.: Poromechanics. Wiley, New York (2004)

    Google Scholar 

  7. Curtis, F.G., Wheatley, P.O.: Applied numerical analysis. Pearson, USA (2004)

    Google Scholar 

  8. Dean, R., Gai, X., Stone, C., Minkoff, S.: A comparison of techniques for coupling porous flow and geomechanics. No. 79709 in SPE Reservoir Simulation Symposium. SPE, Houston (2003)

  9. Farin, G.: Curves and surfaces for computer-aided geometric design a practical guide, 4th edn. Academic Press, San Diego (1993)

    Google Scholar 

  10. Farin, G.: NURBS from projective geometry to practical use, 2nd edn. A K Peters, Massachusetts (1999)

    Google Scholar 

  11. Florez, H.: A new method for building B-spline curves and its application to geometry design and structured grid generation. No. CIE-21268 in 21st Computers and Information in Engineering Conference. Pittsburgh Pennsylvania (2001)

  12. Florez, H.: Domain decomposition methods for geomechanics. Ph.D. thesis, The University of Texas at Austin (2012)

  13. Florez, H., Wheeler, M., Rodriguez, A.: A mortar method based on nurbs for curve interfaces. No. 313 in 46th US Rock Mechanics/Geomechanics Symposium. Chicago (2012)

  14. Florez, H., Wheeler, M., Rodriguez, A.: A mortar method based on nurbs for curve interfaces. Proceedings of the 13th European Conference on the Mathematics of Oil Recovery (ECMOR XIII). Biarritz, France (2012)

  15. Florez, H., Wheeler, M., Rodriguez, A., Monteagudo, J.: Domain decomposition methods applied to coupled flow-geomechanics reservoir simulation. No. 141596 in SPE Reservoir Simulation Symposium. The Woodlands, Texas (2011)

  16. Gai, X.: A coupled geomechanics and reservoir flow model on parallel computers. Ph.D. thesis, The University of Texas at Austin (2004)

  17. Geel, K.: Description of the brugge field and property realisations. TNO. Bruges, Belgium (2009)

  18. Hearn, D.: Computer Graphics, C Version, 2nd edn. Prentice Hall (1997)

  19. Hovorka, S.: Frio brine pilot: lessons learned and questions restated. Fourth Annual Conference on Carbon Capture and Sequestration. Alexandria Virginia (2005)

  20. Thompson, J.F., Soni, B.K., Weatherill, N.: Handbook of grid generation. CRC Press, Boca Raton (1999)

    Google Scholar 

  21. Juntunen, M., Wheeler, M.F.: Two-phase flow in complicated geometries. Comput. Geosci. 17, 239–247 (2013)

    Article  Google Scholar 

  22. Kim, J., Tchelepi, H., Juanes, R.: Stability; accuracy and efficiency of sequential methods for coupled flow and geomechanics. No. 119084 in 2009 SPE Reservoir Simulation Symposium. SPE, The Woodlands, Texas, USA (2009)

  23. Kincaid, D., Cheney, W.: Numerical Analysis. Brooks/Cole Publishing Company, USA (1991)

    Google Scholar 

  24. Lewis, R., Schrefler, B.: The finite element method in the static and dynamic deformation and consolidation of porous media, 2nd edn. Wiley, New York (1998)

    Google Scholar 

  25. Lie, K., Krogstad, S., Ligaarden, I.S., Natvig, J.R., Nilsen, H.M., Skaflestad, B.: Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci. 16, 297–322 (2012)

    Article  Google Scholar 

  26. Mustapha, H.: G23fm: a tool for meshing complex geological media. Comput. Geosci. 15, 385–397 (2011)

    Article  Google Scholar 

  27. Oden, J.T., Carey, G.F.: Finite elements: special problems in solid mechanics, The Texas Finite Element Series, vol. V. Prentice-Hall Inc., Englewood Cliffs, New Jersey (1984)

    Google Scholar 

  28. Piegl, L., Tiller, W.: The NURBS book, 2nd edn. Springer, Berlin (1997)

    Book  Google Scholar 

  29. Schlumberger: ECLIPSE file formats 2007.1 Reference Manual. Copyright Ⓒ1991–2007 Schlumberger (2007)

  30. Sun, S., Wheeler, M.F.: Projections of velocity data for the compatibility with transport. Comput. Methods Appl. Mech. Eng. 195(1), 653–673 (2006)

    Article  Google Scholar 

  31. Zoback, M.: Determination of stress orientation and magnitude in deep wells. Int. J. Rock Mech. Min. Sci. 40, 1049–1076 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Horacio Florez.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Florez, H., Manzanilla-Morillo, R., Florez, J. et al. Spline-based reservoir’s geometry reconstruction and mesh generation for coupled flow and mechanics simulation. Comput Geosci 18, 949–967 (2014).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • B-splines
  • Geometry reconstruction
  • Geomechanics
  • Finite elements
  • Mesh generation