Using embedded discrete fracture models (EDFMs) to simulate realistic fluid flow problems

A large amount of world's hydrocarbon reserves lies in reservoirs where one of the key features is the presence of a system of fractures spanning different length scales. Fractures may provide ways to drain the matrix, but they also drive gas and water towards wells. Fractures intensity, geometry and conductivity are characterised in conjunction with matrix properties using all possible data, such as production logging, mud-losses, image log, well test, geophysics and outcrops. This may lead to a geometrical characterisation in terms of a discrete fracture network (DFN), with the definition of a set of geometrical 2D objects embedded in the matrix domain. A DFN is a computational challenge for conventional dual-porosity simulators, where a dual medium formulation is cast in a corner point geometry grid (CPG). In this context small, with respect to CPG grid spacing, fractures can be easily incorporated using some practical recipes, see Dershowitz et al. (2000), in single porosity or in dual-porosity models. On the other hand, long range, interconnected fractures cannot be integrated in the simulation model unless some crude approximation is implemented in order to fit the fracture network geometry into the Warren and Root (1963) dual media framework, at least as it is available in conventional commercial simulators, see e.g, Eclipse (2011) . A more accurate solution is the implementation of unstructured gridding where the matrix is discretized by tetrahedral or more general polyhedra and the fractures are discretized using 2D polygons. These grids can be used with finite volume, connectivity based reservoir simulators (see Karimi-fard et al. (2004)), but the approach is computationally inefficient for most of the commercial simulators, and this motivated the development of the EDFM by Li and Lee (2008). In this approach the intersections between fractures and matrix blocks define the degrees of freedom (DOFs) for the high connectivity medium. Then, 2D flow between fracture DOFs and 1D flow between fractures and matrix can be integrated with 3D flow in the CPG grid representing the matrix. In a nut-shell, an unstructured grid for the fracture network is comined with a structured grid for the matrix. Differently from Li and Lee (2008), our implementation is not based on the customisation of the reservoir simulator. Rather, we exploit the capability of most commercial simulators to define non neighbouring connections across grid cells to implement EDFM in a non-invasive manner. Our results confirm that EDFM can be as effective as fully unstructured gridding but much more computationally efficient