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3D line-support grid flattening for more accurate geostatistical reservoir population with petrophysical properties

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Abstract

Reservoir models are essential if we need to clearly understand the fossil resources and, hence, to make better use of them. Feeding these models with physical properties on the basis of wells data is a key step in their construction. Line-support (LS) grid is the most popular grid in reservoir engineering, it is massively used for reservoir simulations. In the current methods used to populate with properties the LS grid of a reservoir unit, a Cartesian grid of equivalent size (in each direction), obtained by averaging the edge lengths, is first of all completed. The properties calculated in this way are then transferred as they are into the initial LS grid, because there is cell-for-cell correspondence. This leads to distortion of the Cartesian grid, making it fit the shape of the LS grid. This has the effect of altering calculations of correlation distances between well markers in geostatistical population simulations. Consequently, this primarily induces distortions on the simulated bodies. To resolve this problem, in this paper, we propose innovative methods for a “smooth” conversion from the LS grid of the structural space to the Cartesian grid of the geostatistical population space. The basic principle is to calculate the correlation distances between wells on the basis of “quasi-isometric” flattening of the stratigraphic unit LS grid in the population space. This same flattening technique is then used for inverse transfer of the properties from the population space to the structural space.

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References

  1. Gibbs A (1983) Balanced cross section from seismic sections in area of extensional tectonics. J Struct Geol 5(2):153–160

    Article  Google Scholar 

  2. Galera C, Bennis C, Moretti I, Mallet J-L (2003) Construction of coherent 3D geological blocks. Comput Geosci 29:971–984

    Article  Google Scholar 

  3. Matheron G, Beucher H, de Fouquet C, Galli A, Ravenne C (1987) Conditional simulation of the geometry of fluvio-deltatic reservoirs. Proceeding of the SPE ATCE Conference, Dallas, p 591–599

  4. Deutsh CV, Journel AG, GSLIB (1992) Geostatistical software library and user’s guide. Oxford University Press, New York

    Google Scholar 

  5. Chilès JP, Delfiner P (2012) Geostatistics: modeling spatial uncertainty. Wiley, New York

    Book  Google Scholar 

  6. Galli A, Beucher H, Le Loch G, Doligez B (1994) The Pros and Cons of the Truncated Gaussian method. In: Armstrong M, Down PA (eds) Geostatistical simulations. Kluwer Academic, Norwell, pp 217–233

    Chapter  Google Scholar 

  7. Schmitt M, Beucher H (1996) On the inference of the Boolean model. In: Baafi EY, Schofield NA (eds) Geostatistics Wollongong ′96, vol 1. Kluwer Academic, Norwell, pp 200–210

    Google Scholar 

  8. Le Ravalec M, NoeTinger B, Hu LY (2000) The FTT moving average (FTT-MA) generator: an efficient numerical method for generation and conditioning Gaussian simulations. Math Geol 32(6):701–703

    Article  Google Scholar 

  9. Zigelman G, Kimmel R, Kiryati N (2002) Texture mapping using surface flattening via multidimensional scaling. IEEE Trans Vis Comput Graph 8(2):198–207

    Article  Google Scholar 

  10. Shih-Wen H, Rong-Qi C (2007) A surface flattening method based on numerical simulation. In: Proceedings of the 16th IASTED international conference on applied simulation and modelling, Palma de Mallorca, p 267–270

  11. Zhong Y, Xu B (2006) A physically based method for triangulated surface flattening. Comput Aided Des 38:1062–1073

    Article  Google Scholar 

  12. Borrel P, Rappoport A (1994) Simple constrained deformations for geometric modelling and design. ACM Trans Graph 13(2):137–155

    Article  MATH  Google Scholar 

  13. Bennis C, Sassi W, Faure JL, Chehade FH (1996) One more step in gocad stratigraphic grid generation, taking into account faults and pinchouts. Proceeding of the European 3D reservoir modelling conference (SPE 35526). Stavanger, p 307–316

  14. Caumon G, Mallet JL (2004) 3D stratigraphic models: representation and stochastic modelling. International association for mathematical geology, 11th International Congress, Université de Liège, Belgium

  15. Caumon G, Lepage F, Sword C, Mallet J-L (2004) Building and editing a sealed geological model. Math Geol 36(4):405–424

    Article  MATH  Google Scholar 

  16. Chambers KT, DeBaun DR, Durlofsky LJ, Taggart IJ, Bernath A, Shen AY, Legarre HA, Goggin DJ (1999) Geologic modelling, upscaling and simulation of faulted reservoirs using faulted stratigraphic grids. In: Proceeding of the SPE fifteenth reservoir simulation symposium (SPE 51889), Houston, p 119–130

  17. Johnson C, Jones T (1988) Putting geology into reservoir simulations: a three-dimensional modeling approach. In: Proceedings of the SPE ATCE (SPE 18321), Houston, p 585–594

  18. Mallet J-L (2004) Space-time mathematical framework for sedimentary geology. Math Geol 36(1):1–32

    Article  MATH  MathSciNet  Google Scholar 

  19. Swanson D (1988) A new geological volume computer modeling system for reservoir description. In: Proceedings of the SPE ATCE (SPE 17579), New Orleans, p 293–302

  20. Adachi J, Hartman T, Lomas L, Plumb R, Gil I, Sanchez M, Taghavi R (2008) “Automatic grid generation, property rezoning and geomechanical analysis of petrel-ECLIPSE petroleum reservoir data with FLAC3D”, in continuum and distinct element numerical modeling in geo-engineering. In: R. Hart et al. (eds) Proceeding of the 1st International FLAC/DEM Symposium. Itasca Consulting Group, Minneapolis, August 2008 (Paper No. 02-01)

  21. Blacker T (1996) The cooper tool. In: Proceedings of the 5th international meshing roundtable, Pittsburgh, p 13–30

  22. Owen SJ (1998) A survey of unstructured mesh generation technology. In: Proceedings of the 7th international meshing roundtable, Dearborn, p 239–267

  23. Frey PJ, George PL (2010) Mesh generation: application to finite elements second edition. Wiley Online Library, Hoboken

    Google Scholar 

  24. Horna S, Bennis C, Borouchaki H, Delage C, Rainaud JF (2010) Isometric unfolding of stratigraphic grid units for accurate property populating—mathematical concepts. In: Proceedings 12th European Conference on the Mathematics of Oil Recovery (ECMOR), Oxford, p 1–12

  25. Horna S, Bennis C, Crabie T, Peltier S, Rainaud JF (2010) Extracting and unfolding a stratigraphic unit to update property population. In: 72nd EAGE Conference and Exhibition, Barcelona, p 1–6

  26. Borouchaki H (2008) APLAT3D surface flattening toolkit. University of Technology of Troyes, Troyes

    Google Scholar 

  27. Villard J, Borouchaki H (2005) Adaptive meshing for cloth animation. Eng Comput 20:333–341

    Article  Google Scholar 

  28. Cherouat A, Borouchaki H, Giraud-Moreau L (2010) Mechanical and geometrical approaches applied to composite fabric forming. Int J Mater Form 3(2):1189–1204

    Article  Google Scholar 

  29. McCartney J, Hinds BK, Seow BL (1999) The flattening of triangulated surfaces incorporating darts and gussets. Comput Aided Des 4(31):249–260

    Article  Google Scholar 

  30. Bennis C, Vézien JM, Iglésias G (1991) Piecewise surface flattening for non-distorted texture mapping. ACM SIGGRAPH ′91, Computer Graphics, Las Vegas, pp 237–246

  31. Levy B, Petitjean S, Ray N, Maillot J (2002) Least squares conformal maps for automatic texture atlas generation. SIGGRAPH 2002. ACM Trans Graph 21(3):362–371

    Article  Google Scholar 

  32. Lévy B, Mallet JL (1998) Non-distorted texture mapping for sheared triangulated meshes. In: ACM SIGGRAPH, Proceedings of the 25th annual conference on computer graphics and interactive techniques, Orlando, p 343–352

  33. Maillot J, Yahia H, Verroust A (1993) Interactive texture mapping. In: ACM SIGGRAPH, Proceedings of the 20th annual conference on computer graphics and interactive techniques, Anaheim, p 27–34

  34. Saroul L, Figueiredo O, Hersch RD (2006) Distance preserving flattening of surface sections. IEEE Trans Vis Comput Graph 12(1):26–35

    Article  Google Scholar 

  35. Sheffer A, Hart JC (2002) Seamster: inconspicuous low-distortion texture seam layout. Proceedings of the conference on visualization ′02. Boston, 27 October–01 November 2002, p 291–298

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Acknowledgments

The authors are very grateful to Thomas Crabié, Christophe Delage and Emmanuel Klein for their help to implement the presented algorithms and for their valuable remarks.

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Correspondence to Chakib Bennis.

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Bennis, C., Borouchaki, H., Dumont, C. et al. 3D line-support grid flattening for more accurate geostatistical reservoir population with petrophysical properties. Engineering with Computers 30, 403–421 (2014). https://doi.org/10.1007/s00366-012-0311-9

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  • DOI: https://doi.org/10.1007/s00366-012-0311-9

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