No abstract

In Solid Modeling, a boundary representation (b-rep) defines solids by their bounding surfaces, providing an efficient volume description. Building on this representation, we present the notion of a Sealed Geological Model. In such a model, the geological surfaces define a partition of the domain of interest into regions; analytic functions can be defined in these regions to describe the spatial variations of the subsurface properties. Such descriptions can be used in Geophysics, 3D GIS, and for discretization purposes. In addition to the b-rep representational validity conditions, Sealed Geological Models must satisfy conditions of geological consistency. Bearing these conditions in mind, we describe a methodology to create and modify the shape of such sealed models interactively. We use the hierarchical relationship between geological surfaces to help reshape the contact between a fixed surface (a surface that other surfaces can slide along, such as a fault, erosion surface, or salt top) and a secondary deformable surface (e.g. horizon, older fault). Although designed to meet the demanding requirements of interactive model editing, our methodology could also make use of displacement vectors computed by an automatic process such as tomographic inversion or 3D balanced unfolding.

Effective workflows for translating Earth models into simulation models require grids that preserve geologic accuracy, offer flexible resolution control, integrate tightly with upscaling, and can be generated easily. Corner-point grids and pillar-based unstructured grids fail to satisfy these objectives; hence, a truly 3D unstructured approach is required. This paper describes unstructured cutcell gridding tools that address these needs and improve the integration of our overall reservoir-modeling workflows.The construction of simulation grids begins with the geologic model: a numerical representation of the reservoir structure, stratigraphy, and properties. Our gridding uses a geochronological (GeoChron) map from physical coordinates to an unfaulted and unfolded depositional coordinate system. The mapping is represented implicitly on a tetrahedral mesh that conforms to faults, and it facilitates accurate geostatistical modeling of static depositional properties. In the simplest use case, we create an explicit representation of the geologic model as an unstructured polyhedral grid. Away from faults and other discontinuities, the cells are hexahedral, highly orthogonal, and arranged in a structured manner. Geometric cutting operations create general polyhedra adjacent to faults and explicit contact polygons across faults. The conversion of implicit models to explicit grids is conceptually straightforward, but the implementation is nontrivial because of the limitations of finite precision arithmetic and the need to remove small cells formed in the cutting process.In practice, simulation grids are often constructed at coarser resolutions than Earth models. Our implementation of local grid coarsening and refinement exploits the flexibility of unstructured grids to minimize upscaling errors and to preserve critical geologic features. Because the simulation grid and the geologic model are constructed by use of the same mapping, fine cells can be nested exactly inside coarse cells. Therefore, flow-based upscaling can be applied efficiently without resampling onto temporary local grids. This paper describes algorithms and data structures for constructing, storing, and simulating cut-cell grids. Examples illustrate the accurate modeling of normal faults, y-faults, overturned layers, and complex stratigraphy. Flow results, including a fieldsector model, show the suitability of cut-cell grids for simulation.

No abstract

Non-manifold boundary representations (b-reps) are increasingly used in Geosciences for a variety of applications (3D geographical information systems, basin modeling, geophysical processing, etc.). Meanwhile, the uncertainties associated with subsurface data make it desirable to modify such models efficiently. We present a method to deform locally a surface in a triangulated b-rep while maintaining a constant number of spatial regions in the model. This method does not require completely rebuilding the model, and thus allows efficient and robust updates of the model definition. The method requires that the reshaped surface does not intersect the boundaries of its adjoining regions, which can be checked using existing collision detection algorithms. Also, the non-manifold contacts must be updated after the modification, and the triangles must be altered, to maintain sealed regions. For this, we propose to parameterize locally the surfaces that the modified surface moves along. This parametric space is used to 1) constrain the displacement of the deformed surface border and, 2) re-triangulate in the plane the neighboring surfaces around the modified contacts. The method, tested in the context of an interactive graphical manipulator, is very efficient and independent from the deformation mechanism.