Surface-Based Geological Reservoir Modelling Using Grid-Free NURBS Curves and Surfaces

Building geometrically realistic representations of geological heterogeneity in reservoir models is a challenging task that is limited by the inflexibility of pre-defined pillar or cornerpoint grids. The surface-based modelling workflow uses grid-free surfaces that allows efficient creation of geological models without the limitations of pre-defined grids. Surface-based reservoir modelling uses a boundary representation approach in which all heterogeneity of interest (structural, stratigraphic, sedimentological, diagenetic) is modelled by its bounding surfaces, independent of any grid. Volumes bounded by these surfaces are internally homogeneous and, thus, no additional facies or petrophysical modelling is performed within these geological domains and no grid or mesh discretisation is needed during modelling. Any heterogeneity to be modelled within such volumes is incorporated by adding surfaces. Surfaces and curves are modelled using a parametric non-uniform rational B-splines (NURBS) description. These surfaces are efficient to generate and manipulate, and allow fast creation of multiple realisations of geometrically realistic reservoir models. Multiple levels of surface hierarchy are introduced to allow modelling of all features of interest at the required level of detail; surfaces at one hierarchical level are constructed so as to truncate or conform to surfaces of a higher hierarchical level. This procedure requires the joining, terminating and stacking of surfaces to ensure that models contain watertight surface-bounded volumes. NURBS curves are used to represent well trajectories accurately, including multi-laterals or side-tracks. Once all surfaces and wells have been generated, they are combined into a reservoir model that takes into account geological relationships between surfaces and preserves realistic geometries.