SpringerLink
Log in

MeshIt—a software for three dimensional volumetric meshing of complex faulted reservoirs

  • Original Article
  • Published:
Environmental Earth Sciences Aims and scope Submit manuscript

Abstract

Flow, mass and energy transport processes in natural reservoirs are controlled to a large degree by the presence of geological heterogeneities including structures such as fractures and fault zones embedded in a spatially varying three-dimensional (3D) porous matrix of the reservoir. Despite recent advances, currently, state-of-the-art models rely on a number of simplifications partly related to our inability to represent heterogeneities as observed in the field into dynamic model realizations. In this respect, an adequate geometric representation of the discrete system is a basic requirement. In this study, we show how fundamental concept from computational geometry can be assembled and used to bridge the gap between geological and dynamic forward models. The result is an automated, open source software solution (MeshIt) to generate quality 3D meshes suitable for the study of flow and transport processes in faulted and fractured reservoirs. The software enables us to integrate into a 3D volumetric representation dip** structures, comprising fault zones and fractures as well as inclined well paths. This permits us to correctly simulate interactions between discrete flow paths along these interacting components and the 3D flow within the reservoir matrix. The crucial factor that makes the approach applicable to real case reservoirs is that all algorithms are local and scalable parallel and have computing times increasing approximately linearly with data volumes. We test the performance and the robustness of the software against three different scenarios of increasing complexity and further discuss current limitations and range of applicability of the software. Although all examples describe geothermal applications, it is worth mentioning that the approach is equally valid for other applications in geoscience from oil and gas industry to carbon capture and sequestration issues.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. http://www.dgi.com/earthvision/evmain.html.

  2. http://www.pdgm.com/products/gocad.aspx.

  3. http://www.software.slb.com/products/platform/Pages/petrel.aspx.

  4. http://www.microsoft.com/visualstudio.

  5. http://ww.qt-project.org.

  6. http://www.vtk.org.

  7. http://www.pdgm.com/products/gocad.aspx.

  8. http://www.dgi.com/earthvision/evmain.html.

  9. http://www.software.slb.com/products/platform/Pages/petrel.aspx.

  10. http://www.comsol.com.

References

  • Ahmed T, Meehan N (eds) (2011) Advanced reservoir management and engineering, 2nd edn. Gulf Professional Publishing, Houston

    Google Scholar 

  • Amenta N, Bern M, Kamvysselis M (1998) A new Voronoi-based surface reconstruction algorithm. In: Proceedings of the 25th annual conference on computer graphics and interactive techniques, SIGGRAPH’98, pp 415–421

  • Baca RG, Arnett RC, Langford DW (1984) Modelling fluid flow in fractured porous rock masses by finite-element techniques. Int J Numer Meth Fluids 4(4):337–348

    Article  Google Scholar 

  • Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25:861–884

    Article  Google Scholar 

  • Blessent D, Therrien R, MacQuarrie K (2009) Coupling geological and numerical models to simulate groundwater flow and contaminant transport in fractured media. Comput Geosci 35:1897–1906

    Article  Google Scholar 

  • Blöcher G, Cacace M, Lewerenz B, Zimmermann G (2010a) Three dimensional modelling of fractured and faulted reservoirs: framework and implementation. Chemie der Erde Geochem 70(3):145–153

    Article  Google Scholar 

  • Blöcher G, Zimmermann G, Moeck I, Brandt W, Hassanzadegan A, Magri F (2010b) 3D numerical modelling of hydrothermal processes during the lifetime of a deep geothermal reservoir. Geofluids 10:406–421

    Article  Google Scholar 

  • Boissonnat JD, Cazals F (2002) Smooth surface reconstruction via natural neighbor interpolation of distance functions. Computational Geometry 22:185–203

    Article  Google Scholar 

  • Braun J, Sambridge M (1995) A numerical method for solving partial differential equations on highly irregular grids. Nature 376:655–660

    Article  Google Scholar 

  • Cacace M, Blöcher G, Watanabe N, Moeck I, Börsing N, Scheck-Wenderoth M, Kolditz O, Huenges E (2013) Modelling of fractured carbonate reservoirs: outline of a novel technique via a case study from the Molasse Basin, southern Bavaria, Germany. Env Earth Sci 70(8):3585–3602

    Article  Google Scholar 

  • Caumon G, Lepage F, Sword CH, Mallet J-L (2004) Building and editing a sealed geological model. Math Geol 26:405–424

    Article  Google Scholar 

  • Caumon G, Collon-Douaillet P, Carlier Le, de Veslud C, Viseaur S, Sausse J (2009) Surface-based 3D modelling of geological structures. Math Geosci 41:927–945

    Article  Google Scholar 

  • Chen M, Buscheck T, Wagoner J, Sun Y, White J, Chiaramonte L, Aines R (2013) Analysis of fault leakage from Leroy underground natural gas storage facility, Wyoming, USA. Hydrogeol J 21:1429–1445

    Article  Google Scholar 

  • Cherubini Y, Cacace M, Blöcher G, Scheck-Wenderoth M (2013) Impact of single inclined faults on the fluid flow and heat transport: results from 3D finite element simulations. Env Earth Sci 70(8):3603–3618

    Article  Google Scholar 

  • Chew L-P (1989) Constrained Delaunay triangulations. Algorithmica 4:97–108

    Article  Google Scholar 

  • Committee on Fracture Characterization and Fluid Flow, National Research Council (2006) Rock fractures and fluid flow: contemporary understanding and applications. The National Academic Press, Washington

  • Davatzes N, Aydin A (2005) Distribution and nature of fault architecture in a layered sandstone and shale sequence: an example from the Moab fault, Utah. AAPG Memoir 8:153–180

    Google Scholar 

  • De Rooij R (2008) Towards improved numerical modelling of karst aquifers: coupling turbulent conduit flow and laminar matrix flow under variably saturated conditions. Ph.D. thesis, University of Neuchâtel, 130 pages

  • Dietrich P, Helmig R, Sauter M, Hötzl H, Köngeter J, Teutsch G (eds.) (2005) Flow and transport in fractured porous media, Springer, Berlin

  • Edelsbrunner H, Mücke EP (1994) Three-dimensional alpha shapes. ACM Trans Graph 13:43–72

    Article  Google Scholar 

  • Euler N, Sword CH, Dulac JC (1998) A new tool to seal a 3D earth model: a cut with constraints. In: Proceedings of the 68th SEG annual meeting, Society of Exploration Geophyiscists, pp 710-713

  • Evazi M, Mahani H (2010) Unstructured-coarse-grid generation using background-grid approach. SPE J 15(2):326–340

    Article  Google Scholar 

  • Farmer C (2005) Geological modelling and reservoir simulation. In: Iske A, Randen T (eds) Mathematical methods and modelling in hydrocarbon exploration and production, vol 7. Springer, Berlin, pp 119–212

    Chapter  Google Scholar 

  • Graf T, Therrien R (2008) A method to discretize non-planar fractures for 3D subsurface flow and transport simulations. Int J Numer Meth Fluids 56:2069–2090

    Article  Google Scholar 

  • Graham RL (1972) An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set. Inf Process Lett 1:132–133

    Article  Google Scholar 

  • Hofmann H, Blöcher G, Börsing N, Maronde N, Pastrik N, Zimmermann G (2014) Potential for enhanced geothermal systems in low permeability limestones – stimulation strategies for the Western Malm karst (Bavaria). Geothermics 51:351–367

    Article  Google Scholar 

  • Holm R, Kaufmann R, Heismund BO, Ian E, Espedal MS (2006) Meshing of domains with complex internal geometries. Numer Linear Algeb Appl 13:717–731

    Article  Google Scholar 

  • Kaiser BO, Cacace M, Scheck-Wenderoth M (2013) 3D coupled fluid and heat transport simulations of the Northeast German Basin and their sensitivity to the spatial discretization: different sensitivities for different mechanisms of heat transport. Environ Earth Sci 70(8):3643–3659

    Article  Google Scholar 

  • Kolditz O, Görke UJ, Shao H, Wang W (eds) (2012) Thermo-hydro-mechanical-chemical processes in porous media, 1st edn. Springer, Berlin

    Google Scholar 

  • Matthäi SK, Geiger S, Roberts SG, Paluszny A, Belayneh M, Burri A, Mezentsev A, Lu H, Coumou D, Driesner T (2007) Numerical simulation of multi-phase fluid flow in structurally complex reservoirs. Geol Soc Lond Spec Publ 292(1):405–429

    Article  Google Scholar 

  • Merland R, Caumon G, Lévy B, Collon-Drouaillet P (2014) Voronoi grids conforming to 3D structural features. Comput Geosci 18(3–4):373–383

    Article  Google Scholar 

  • Miller GL, Talmor D, Teng S-H, Walkington NJ, Wang H (1996) Control volume meshes using sphere packing: generation, refinement and coarsening. In: Proceedings of the 5th international meshing roundtable, Pittsburgh, pp 47–61

  • Möller T (1997) A fast triangle-triangle intersection test. J Graph Tools 2:25–30

    Article  Google Scholar 

  • Mustapha H, Dimitrakopoulos R (2011) Discretizing two-dimensional complex fractured fields for incompressible two-phase flow. Int J Numer Meth Fluids 65:764–780

    Article  Google Scholar 

  • Mustapha H, Mustapha K (2007) A new approach to simulating flow in discrete fracture networks with an optimized mesh. SIAM J Sci Comput 29(4):1439–1459

    Article  Google Scholar 

  • Noorishad J, Tsang C, Witherspoon P (1992) Theoretical and field studies of coupled hydromechanical behaviour of fractured rocks—1. Development and verification of a numerical simulator. Int J Rock Mech Min Sci Geomech Abstr 29(4):401–409

  • Normani SD, Sykes JF (2010) Paleoclimate analyses of density-dependent groundwater flow with pseudo-permafrost in discretely fractured crystalline rock setting. In: Carrera J (ed) XVII international conference on water resources—CMWR 2010, Barcelona, Spain, 21–14 June

  • O’Rourke J (1998) Computational geometry in C, 2nd edn. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge

  • Paluszny A, Matthäi SK, Hohmeyer M (2007) Hybrid finite element-finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks. Geofluids 7(2):186–208

    Article  Google Scholar 

  • Pellerin J, Lévy B, Caumon G, Botelli A (2014) Automatic surface meshing of 3D structural models at specific resolution: a method based on Voronoi diagrams. Comput Geosci 62:103–116

    Article  Google Scholar 

  • Prévost M, Lepage F, Durlofsky LJ, Mallet L-L (2005) Unstructured 3D gridding and upscaling for coarse modelling of geometrically complex reservoirs. Pet Geosci 11:339–345

    Article  Google Scholar 

  • Schomaker V, Waser J, Marsh RE, Bergman G (1959) To fit a plane or a line to a set of points by least squares. Acta Crystallogr A 12:600–604

    Article  Google Scholar 

  • Segura JM, Carol I (2004) On zero-thickness interface elements for diffusion problems. Int J Numer Anal Meth Geomech 28(9):947–962

    Article  Google Scholar 

  • Shewchuck JR (2002) Delaunay refinement algorithms for triangular mesh generation. Comput Geom Theory Appl 22(1–3):21–74

    Article  Google Scholar 

  • Shizake SG, Sudicky E, Schwartz F (1998) Density-dependent solute transport in discretely-fractured geologic media: is prediction possible? J Contam Hydrol 434:273–291

    Google Scholar 

  • Shreiner D, Sellers G, Kessenich J, Licea-Kane B (2013) The OpenGL programming guide, 8th edn. Addison-Wesley Professional, Essex

  • Si H (2015) TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans Math Softw 41(2):1–36

    Article  Google Scholar 

  • Souche L, Lepage F, Iskenova G (2013) Volume based modelling—automated construction of complex structural models. In: 75th EAGE conference and exhibition incorporating SPE EUROPEC 2013 London, UK, 10–13 June

  • Squillacote A (2008) The Paraview Guide, 3rd edn. Kitware, Inc

  • Tearpock DJ, Bischke RE (2002) Applied subsurface Geological Map** with structural methods, 2nd edn, Prentice Hall, New Jersey

  • Therrien R, Sudicky E (1996) Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media. J Contam Hydrol 23:1–44

    Article  Google Scholar 

  • Verbree E (2006) Piecewise linear complex representation through conforming Delaunay tetrahedralization. In: Raubal M, Miller H, Frank A, Goodchild M (eds) GIScience 2006. Springer, Heidelberg, vol 4197, pp 385–388

  • Zimmermann G, Tischner T, Legarth B, Huenges E (2009) Pressure-dependent production efficiency of an Enhanced Geothermal System (EGS): stimulation results and implications for hydraulic fracture treatments. Pure appl Geophys 166:1089–1106

    Article  Google Scholar 

  • Zimmermann G, Moeck I, Blöcher G (2010) Cyclic waterfrac stimulation to develop an Enhanced Geothermal System (EGS)—conceptual design and experimental results. Geothermics 39:59–69

    Article  Google Scholar 

Download references

Acknowledgments

This work has been performed in the framework of the GeoEn-phase 2 project and funded by the Federal Ministry of Education and research [BMBF, Grant 03G0767A]. A special thank goes to Dr. Si Hang from the WIAS Institute in Berlin for sharing his expertise in the field of mesh generation. The authors would like to acknowledge Prof. Guillaume Caumon whose comments as a reviewer provide valuable to improve not only the quality and scientific merit of the manuscript, but also help finding novel solutions to some aspects of the meshing software.

Author information

Authors and Affiliations

  1. Helmholtz Centre Potsdam (GFZ) German Research Centre for Geosciences, Telegrafenberg, 14473, Potsdam, Germany

    Mauro Cacace & Guido Blöcher

Authors
  1. Mauro Cacace
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guido Blöcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauro Cacace.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cacace, M., Blöcher, G. MeshIt—a software for three dimensional volumetric meshing of complex faulted reservoirs. Environ Earth Sci 74, 5191–5209 (2015). https://doi.org/10.1007/s12665-015-4537-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12665-015-4537-x

Keywords

Search

Navigation