Geologic Modelling Using Parametric NURBS Surfaces
C. Jacquemyn, Y. Melnikova, M.D. Jackson, G.J. Hampson and C.M. John
Event name: ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery
Session: Geological Modelling
Publication date: 29 August 2016
Info: Extended abstract, PDF ( 1.49Mb )
Price: € 20
Most reservoir modelling/simulation workflows represent geological heterogeneity on a pillar-grid defined early in the modelling process. However, it is challenging to represent many common geological features using pillar grids: examples include intersecting faults, recumbent folds, slumps, and non-monotonic injection structures such as salt diapirs. It is also challenging to represent multi-scale features, because the same number of pillars must be present in all layers so there is little flexibility to adjust the areal grid resolution. We present a surface-based geological modelling (SBGM) workflow that uses NURBS (Non-Uniform Rational B-Splines) surfaces to represent geological heterogeneities without reference to a pre-defined grid. The NURBS surfaces represent a broad range of heterogeneity types, including faults, fractures, stratigraphic surfaces across a range of length-scales, and boundaries between different facies or lithologies. The geological model is constructed using the NURBS surfaces and a mesh created only when required for flow simulation or other calculations. The mesh preserves the geometry of the modelled surfaces. NURBS surfaces are an efficient and flexible tool to model complex geometries and are common in many modelling and engineering disciplines; however, they are rarely used in reservoir modelling. Complex surfaces can be created using a small number of control points; modelling with NURBS surfaces is therefore computationally efficient. We report here a variety of new stochastic approaches to create geological NURBS surfaces, including (1) extrusion of spatially variable cross-sections, (2) parametric 3D geometry templates, and (3) perturbation of control points to yield similar results to some pixel-based geostatistical methods. Surface interactions, such as erosion, stacking or conforming, are enforced to ensure geological relationships are preserved and the boundary representation is watertight. We illustrate our NURBS SBGM approach via a number of examples, including channelized sandbodies, clinoforms, sedimentary cycles, fractures, crosscutting faults, recumbent folds and combinations thereof.