A new surface-based geological modelling approach is developed to generate bounding surfaces based on NURBS (non-uniform rational B-splines) to represent geological heterogeneity of interest without imposing it on a predefined grid. The surfaces represent a broad range of heterogeneity types across a range of length-scales, including structural heterogeneity such as folds, faults or fractures, stratigraphic heterogeneity associated with sediment bodies of various scales and geometries (e.g. clinoforms, channelized features or build-ups) and boundaries between different facies or lithologies.

Reservoir modelling using parametric NURBS surfaces has many advantages over conventional grid-based reservoir modelling approaches. A surface-based modelling approach overcomes issues related to geometrical complexity (e.g. non-monotonic surfaces) and representing heterogeneity over a range of length scales. The NURBS representation of these surfaces provides a computationally efficient way to represent their complex geometry. With a limited number of control points, complex and geometrically realistic surfaces can be created, with high level of detail where needed. Because NURBS form smooth surfaces, no stairstepping effects are introduced. The strength of NURBS surfaces lies in representing geologically-realistic complex heterogeneity explicitly across multiple scales.


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  1. Belayneh, M., Geiger, S. and Matthäi,S.K.
    [2006] Numerical simulation of water injection into layered fractured carbonate reservoir analogs. AAPG Bulletin90(10), 1473–1493, 10.1306/05090605153.
    https://doi.org/10.1306/05090605153 [Google Scholar]
  2. Börner, J.H., Bär, M. and Spitzer, K.
    [2015] Electromagnetic methods for exploration and monitoring of enhanced geothermal systems - A virtual experiment. Geothermics55, 78–87, 10.1016/j.geothermics.2015.01.011.
    https://doi.org/10.1016/j.geothermics.2015.01.011 [Google Scholar]
  3. Caumon, G., Collon-Drouaillet, P., Le Carlier de Veslud, C., Viseur, S. and Sausse, J.
    [2009] Surface-Based 3D Modeling of Geological Structures. Mathematical Geosciences41(8), 927–945, 10.1007/s11004‑009‑9244‑2.
    https://doi.org/10.1007/s11004-009-9244-2 [Google Scholar]
  4. Geiger, S. and Matthäi, S.
    [2012] What can we learn from high-resolution numerical simulations of single- and multi-phase fluid flow in fractured outcrop analogues?Geological Society, London, Special Publications 374, 10.1144/sp374.8.
    https://doi.org/10.1144/sp374.8 [Google Scholar]
  5. Graham, G. H., Jackson, M. D. and Hampson, G. J.
    [2015] Three-dimensional modeling of clinoforms in shallow-marine reservoirs: Part 1. Concepts and application. AAPG Bulletin99(6), 1013–1047, 10.1306/01191513190.
    [Google Scholar]
  6. Jackson, M. D., Hampson, G. J., Saunders, J. H., El-Sheikh, A., Graham, G. H. and Massart, B. Y. G.
    [2013] Surface-based reservoir modelling for flow simulation. Geological Society, London, Special Publications387(1), 271–292, 10.1144/sp387.2.
    https://doi.org/10.1144/sp387.2 [Google Scholar]
  7. Jackson, M. D., Hampson, G. J. and Sech, R. P.
    [2009] Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 2. Geologic controls on fluid flow and hydrocarbon recovery. AAPG Bulletin93(9), 1183–1208, 10.1306/05110908145.
    https://doi.org/10.1306/05110908145 [Google Scholar]
  8. Jones, N. L., Budge, T. J., Lemon, A. M. and Zundel, A. K.
    [2002] Generating MODFLOW Grids from Boundary Representation Solid Models. Ground Water40(2), 194–200, 10.1111/j.1745‑6584.2002.tb02504.x.
    https://doi.org/10.1111/j.1745-6584.2002.tb02504.x [Google Scholar]
  9. Massart, B. Y. G., Jackson, M. D., Hampson, G. J., Johnson, H. D., Legler, B. and Jackson, C. A.-L.
    [2016] Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 1. Surface-based modeling. AAPG Bulletin100(5), 697–721, 10.1306/02011614221.
    https://doi.org/10.1306/02011614221 [Google Scholar]
  10. Piegl, L. A. and Tiller, W.
    [1997] The NURBS book. Springer, London.
    [Google Scholar]
  11. Pyrcz, M. J., Catuneanu, O. and Deutsch, C. V.
    [2005] Stochastic surface-based modeling of turbidite lobes. AAPG Bulletin89(2), 177–191, 10.1306/09220403112.
    https://doi.org/10.1306/09220403112 [Google Scholar]
  12. Ruiu, J., Caumon, G. and Viseur, S.
    [2015] Modeling Channel Forms and Related Sedimentary Objects Using a Boundary Representation Based on Non-uniform Rational B-Splines. Mathematical Geosciences, 1–26, 10.1007/s11004‑015‑9629‑3.
    https://doi.org/10.1007/s11004-015-9629-3 [Google Scholar]
  13. Salinas, P., Pavlidis, D., Adam, A. G., Xie, Z., Pain, C. C. and Jackson, M. D.
    [2016] Dynamic unstructured mesh adaptivity for improved simulation of near-wellbore flow in reservoir-scale models. 15th European Conference on the Mathematics of Oil Recovery. EAGE, Amsterdam, The Netherlands.
    [Google Scholar]
  14. Sech, R. P., Jackson, M. D. and Hampson, G. J.
    [2009] Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 1. Surface-based modeling to capture high-resolution facies architecture. AAPG Bulletin93(9), 1155–1181, 10.1306/05110908144.
    https://doi.org/10.1306/05110908144 [Google Scholar]
  15. Zehner, B., Börner, J. H., Görz, I. and Spitzer, K.
    [2015] Workflows for generating tetrahedral meshes for finite element simulations on complex geological structures. Computers & Geosciences79, 105–117, 10.1016/j.cageo.2015.02.009.
    [Google Scholar]

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