Pauline Collon-Drouaillet

An algorithm for 3D simulation of branchwork karst networks using Horton parameters and ★ Application to a synthetic case

Abstract This paper presents a method to stochastically simulate 3D karstic networks and more specifically branchwork pattern cave systems. Considering that they can be compared with 3D fluvial networks, the topological classification of Strahler and the corresponding ratios of Horton are used to define three morphometric parameters. These parameters are integrated in an algorithm that computes branches hierarchically to obtain a final network organized around the main observed inlet and outlet with a branching complexity controlled by the user. Each branch corresponds to a low-cost path between two points calculated with the 𝒜★ graph search algorithm. Speleogenetic information on inception horizons, palaeo-water tables and fractures is accounted for by adapted definitions of the searching functions of 𝒜★. The method is demonstrated on a 3D synthetic case with discrete fractures networks, inception horizons and a palaeo-water table. The simulated karsts have a realistic geometry and are geologically consistent.

Voronoi grids conforming to 3D structural features

Flow simulation in a reservoir can be highly impacted by upscaling errors. These errors can be reduced by using simulation grids with cells as homogeneous as possible, hence conformable to horizons and faults. In this paper, the coordinates of 3D Voronoi seeds are optimized so that Voronoi cell facets honor the structural features. These features are modeled by piecewise linear complex (PLC). The optimization minimizes a function made of two parts: (1) a barycentric function, which ensures that the cells will be of good quality by maximizing their compactness; and (2) a conformity function, which allows to minimize the volume of cells that is isolated from the Voronoi seed w.r.t., a structural feature. To determine the isolated volume, a local approximation of the structural feature inside the Voronoi cells is used to cut the cells. It improves the algorithm efficiency and robustness compared to an exact cutting procedure. This method, used jointly with an adaptive gradient solver to minimize the function, allows dealing with complex 3D geological cases. It always produces a Voronoi simulation grid with the desired number of cells.

Building Centroidal Voronoi Tessellations For Flow Simulation In Reservoirs Using Flow Information

The generation of reservoir grids has to take into account numerous flow parameters, static and dynamic, from the fine-scale geological models to minimize discretization errors. These parameters are generally encoded separately as constraints on cell size, orientation and aspect ratio. In this paper, we propose to encode them all at a time in a Riemannian metric tensor field and to apply a global optimization method. This method is based on Centroidal Voronoi Tesselation algorithms under Lp norm and generates unstructured hex-dominant reservoir grids, optimum in terms of sampling. We appy these principles to generate flow-based reservoir grids. We use a fine-scale velocity field to compute the norm and the directions of the metric tensor: the generated grids are refined in regions of high flow, and the cell facets are oriented along the streamline directions. The grids are therefore suitable to a discretization with two-point flux approximation. The simulation results obtainedd with these grids are then compared with those computed on a standard Cartesian grid of the same size. These first results are encouraging and need further investigation. The method is general, and can account for other dynamic parameters, such as vorticity, that can be weighted and introduced in the metric tensor. Furthermore, CVT algorithms can be adapted to take into account fine-scale static features in the grid generation process. Because the gridding is fully automatic, a possible extension of this work is to update the grid between simulation time steps to reflect changes in boundary conditions.

Special Issue on Three-Dimensional Structural Modeling

Three-dimensional (3D) structural models are generalizations of geological maps and cross-sections used by geologists for the last 200 years. They describe the geometry and layout of rock units in 3D space by honoring available observations, measurements and geological concepts. They are used on a daily basis in industry and academia to improve one’s understanding of an area, to quantify geological processes and to address natural resource management problems (oil and gas, mining, geothermal energy, ground water). This area of research raises interesting questions concerning the ways to build these models and to appropriately describe, analyze and reduce the associated uncertainty. For these ends, new conceptual models relating to geological processes and geometric parameters are needed. This issue gathers contributions regarding all of these aspects. In preparing this special issue, we have received a total of 25 paper proposals and 13 full papers, of which 5 are published in the present issue and 2 are still in revision. We would like to thank all the authors for their contributions and the reviewers for both their help and remarks, which have been essential to the editorial process. 3D structural modeling emerged in the 1970s by generating computerized depth maps with contouring techniques. These methods are very effective and are still in use today for the processing and analysis of topographic surfaces and depth maps. However, they raise problems when it comes to fault management, or when dealing with complex surfaces having several Z-values for the same geographic coordinate (e.g., recumbent folds, salt tops). This limitation motivated the development of techniques