The embedded discrete fracture model (EDFM) combines the advantages of previous numerical models for fractured reservoirs, achieving a good balance between calculation cost and simulation accuracy. In this work, an integrally embedded discrete fracture model (iEDFM) is introduced to further improve the simulation accuracy and expand the application of the model. The iEDFM has a new gridding method that can arbitrarily grid the fractures according to the requirements rather than finely subdividing fracture elements. Then, with a more precise pressure distribution assumption inside the matrix blocks, we are able to obtain a semi-analytic calculation method of matrix-fracture transmissibility applied to iEDFM. Several case studies were conducted to demonstrate the advantage of iEDFM and its applicability for intersecting and nonplanar fractured reservoirs, and a 3D case with a modified dataset from a reported seismic survey could be used to demonstrate the potential application of the iEDFM in real field studies.

The embedded discrete fracture model (EDFM), among different flow simulation models, achieves a good balance between efficiency and accuracy. In the EDFM, micro-scale fractures that cannot be characterized individually need to be homogenized into the matrix, which may bring anisotropy into the matrix. However, the simplified matrix–fracture fluid exchange assumption makes it difficult for EDFM to address the anisotropic flow. In this paper, an integrally embedded discrete fracture model (iEDFM) suitable for anisotropic formations is proposed. Structured mesh is employed for the anisotropic matrix, and the fracture element, which consists of a group of connected fractures, is integrally embedded in the matrix grid. An analytic pressure distribution is derived for the point source in anisotropic formation expressed by permeability tensor, and applied to the matrix–fracture transmissibility calculation. Two case studies were conducted and compared with the analytic solution or fine grid result to demonstrate the advantage and applicability of iEDFM to address anisotropic formation. In addition, a two-phase flow example with a reported dataset was studied to analyze the effect of the matrix anisotropy on the simulation result, which also showed the feasibility of iEDFM to address anisotropic formation with complex fracture networks.