Discretizing two‐dimensional complex fractured fields for incompressible two‐phase flow

Abstract

SUMMARYA method is introduced to discretize irregular and complex two-dimensional fractured media. The geometry of the fractured media is first analysed by searching and treating the complex configurations. Based on that, the method generated a good mesh quality and allows for including finer grids. An incompressible two-phase flow problem is solved to compare the developed method and a public method based on the approximation of a 1D fracture by the edges of a 2D finite element grid of the porous media. The comparison showed that the developed method (i) represents better the fractured domain by maintaining the geometric integrity of input surfaces and geologic data, (ii) provides, for sample and complex fractured domains, excellent and more accurate results, and (iii) is much less sensitive to the grid sizes. Furthermore, the method has to be more efficient than the other methods for transport problems and has to provide better predictable results; this is mainly based on point (ii) and because the method produces optimal triangular grids.

An efficient method for discretizing 3D fractured media for subsurface flow and transport simulations

“…In this work, an elementary criterion has been adopted, which consists of an evaluation of the element quality with respect to the equilateral simplex. For a triangular element, the quality is expressed as [30] …”

“…Examples are poorly conditioned problems, and non-linear and/or transient analyses. Different techniques can be used to evaluate the mesh quality [10,30] to provide some indication about the suitability of the discretization type under consideration. In this work, an elementary criterion has been adopted, which consists of an evaluation of the element quality with respect to the equilateral simplex.…”

“…The optimality of the method arises from the mesh quality obtained using fine and coarse grid levels. Mustapha and Dimitrakopoulos [30] have simplified 2D complex fracture configurations to facilitate the generation of a mesh quality without a refinement procedure to improve the mesh quality of complex fractured configurations. In that work, the 2D geometry of the fracture network is adapted instead of the 2D mesh.…”

“…Step 2: The discrete points obtained in Step 1 are used to generate a 2D finite element mesh for F 1 , F 2 and the boundaries of the domain as shown in Figure 4(c); the algorithm used in this step is presented in [30].…”

“…In this work, we extend the 2D approach developed in [30] to 3D. The basic idea is to locally transform the complex and critical geometric configurations of fractured media.…”