Hex-dominant mesh generation for subterranean formation modeling

Bulletin of Engineering Geology and the Environment, 2013

This paper presents a graphics system called the prism network and its boundary (PNB) aimed at representing the stratified solids that are formed in the subsurface terrain. It allows full 3D modelling of these types of spaces formed by superimposed layers bounded by stratification surfaces. A set of boreholes in the ground is used to generate a network of prisms that models the solid space and serves as the basis for creating two secondary networks, one of triangles and another of quadrilaterals, which define the model boundaries. This graphics system has been implemented in C??, using the standard OpenGL graphics API. The paper first defines and implements a model in the PNB data structure, the process by means of which it is generated is then described, and, finally, a range of applications to specific cases is presented and graphically illustrated.

Mathematical Geosciences

Mesh generation lies at the interface of geological modeling and reservoir simulation. Highly skewed or very small grid cells may be necessary to accurately capture the geometry of geological features, but the resulting poorly scaled or small grid cells can have a substantial negative impact on simulator accuracy and speed. One way to minimize numerical errors caused by gridding complex structures is to simulate on high-quality Voronoi meshes, which reduce grid orientation effects in fluid flow. This work presents a complete methodology to create Voronoi simulation grids, model fluid flow in complex geological systems, and visualize the results. A recently developed Voronoi meshing method that can automatically generate provably good unstructured meshes that conform to input surfaces creating closed volumes is used. Initially an analytical benchmark simulation is presented to validate the quality of the meshes and simulation results and demonstrate the superiority of simulation resu...

International journal for …, 2006

A great challenge for flow simulators of new generation is to gain more accuracy at well proximity within complex geological structures. For this purpose, a new approach based on hybrid mesh modeling was proposed in 2D in . In this hybrid mesh, the reservoir is described by a structured quadrilateral mesh and drainage areas around wells are represented by radial circular meshes. In order to generate a global conforming mesh, unstructured transition meshes constituted by convex polygonal elements satisfying finite volume properties are used to connect together these two structured meshes. Thus, the resulting mesh allows us to take full advantages of simplicity and practical aspects of structured meshes while complexity inherent to unstructured meshes is introduced only where strictly needed. This paper presents the 3D extension of the generation of such a hybrid mesh . The proposed method uses 3D power diagrams to generate the transition mesh. Due to the round off errors, this mesh is modified in order to ensure the conformity with the structured meshes. In addition, some criteria are introduced to measure the mesh quality, as well as an optimization procedure to remove and to expand small edges of the transition mesh under finite volume properties constraints. Numerical results are given to show the efficiency of the approach.

Geochemistry, 2010

Modelling of coupled physical processes in fractured and faulted media is a major challenge for the geoscience community. Due to the complexity related to the geometry of real fracture networks and fault systems, modelling studies have been mainly restricted either to two dimensional cases or to simplified orthogonal fracture systems consisting of vertical and horizontal fractures. An approach to generate three dimensional meshes for realistic fault geometries is presented. The method enables representation of faults in an arbitrary incline as two dimensional planes within a three dimensional, stratified porous matrix of a generic geometry. Based on a structural geological model, the method creates three dimensional unstructured tetrahedral meshes. These meshes can be used for finite element and finite volume numerical simulations. A simulation of a coupled fluid flow and heat transport problem for a two layered porous medium cut by two crossing faults is presented to test the reliability of the method.

Engineering with Computers, 2014

This paper introduces a methodology for creating geometrically consistent subsurface simulation models, and subsequently tetrahedral finite element (FE) meshes, from geometric entities generated in gOcad software. Subsurface simulation models have an intrinsic heterogeneous characteristic due to the different geomechanics properties of each geological layer. This type of modeling should represent geometry of natural objects, such as geological horizons and faults, which have faceted representations. In addition, in subsurface simulation modeling, lower-dimension degenerated parts, such as dangling surfaces, should be represented. These requirements pose complex modeling problems, which, in general, are not treated by a generic geometric modeler. Therefore, this paper describes four important modeling capabilities that are implemented in a subsurface simulation modeler: surface re-triangulation, surface intersection, automatic volume recognition, and tetrahedral mesh generation. Surface re-triangulation is used for regenerating the underlying geometric support of surfaces imported from gOcad and of surface patches resulting from intersection. The same re-triangulation algorithm is used for generating FE surface meshes. The proposed modeling methodology combines, with some adaptation, meshing algorithms previously published by the authors. Two novel techniques are presented, the first for surface intersection and the second for automatic volume recognition. The main contribution of the present work is the integration of such techniques through a methodology for the solution of mesh generation problems in subsurface simulation modeling. An example illustrates the capabilities of the proposed methodology. Shape quality of generated triangular surface and tetrahedral meshes, as well as the efficiency of the 3D mesh generator, is demonstrated by means of this example.

2011

Recently, randomly close-packed Voronoi meshes have been proposed for simulating pervasive fracture processes in materials and structures by allowing fractures to grow only at the interelement faces of the polyhedral cells. The polyhedral cells are formulated as finite elements. A new meshing tool is presented here for creating randomly close-packed Voronoi meshes in nonconvex domains with internal surfaces. Applications using these meshes include blast and impact response of engineered structures as well as hydraulic fracturing in geostructures and the design of CO 2 sequestration processes to maintain the integrity of a reservoir caprock that contains preexisting fractures and joints.

SPE Reservoir Simulation Symposium, 2013

We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multi-scale geological heterogeneity and the prediction of flow through that heterogeneity. The research builds on 20+ years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation.

Modeling Earth Systems and Environment, 2015

The aim of this research is ideal solid meshing of a 3D geological body including topography for studies of finite element analysis. In many numerical analyses, solid meshing is abstruse and consumes much time and high CPU usage. This complexity increases with variety of shapes geometry and height heterogeneity of a surface. In geology, this issue is important and usually results to the removing topography. For this order, we try to mesh the topographic surface and create a shell block diagram in which top side is topographic surface. By having mesh spacing from topography, we defined shape functions of linear quadrilateral meshes for shell block. The sweep mesh applying in analytical software makes the block diagram ready for defining solid meshes. Since topographic loading and static analysis closely relate to each other, linear tetrahedron meshes are suitable for static analysis. In this way, with a minimum number of nodes, solid meshing is possible and for sensitive areas, there is enough space to regenerate finer meshes. Therefore, following the procedure of shape function definitions from linear plane to solid elements, we can idealize solid meshing for numerical analysis.

Computers & Geosciences, 2015

The internal structure and petrophysical property distribution of fault zones are commonly exceedingly complex compared to the surrounding host rock from which they are derived. This in turn produces highly complex fluid flow patterns which affect petroleum migration and trapping as well as reservoir behavior during production and injection. Detailed rendering and forecasting of fluid flow inside fault zones require high-resolution, explicit models of fault zone structure and properties. A fundamental requirement for achieving this is the ability to create volumetric grids in which modeling of fault zone structures and properties can be performed. Answering this need, a method for generating volumetric fault zone grids which can be seamlessly integrated into existing standard reservoir modeling tools is presented. The algorithm has been tested on a wide range of fault configurations of varying complexity, providing flexible modeling grids which in turn can be populated with fault zone structures and properties.

In the past decade, advancements in automatic mesh generation and topological data structures have made possible the use of a more general and abstract geometric model for the description of an analysis problem. Using a geometric model for describing a reservoir results in a conceptual model of the geothermal system, rather than a simple numerical simulation. The analyst builds the geometric model using true features of a reservoir, such as well bores and known fracture locations. Material properties and boundary conditions are then assigned to these features, not to the underlying finite element mesh or finite difference grid. This independent storage of the problem description makes it simple to run multiple analyses, potentially using different solution schemes. Definition of both 2-d and 3-d models can be greatly simplified through this more interactive, intuitive model creation process. State-of-the-art visualization and manipulation methods assist in conveying the conceptual model of the reservoir and the assumptions made for performing a simulation.