Summary Various researchers have evaluated different methods of modeling fractured reservoirs accurately and efficiently. Of these methods, the embedded discrete fracture model (EDFM) is one of the most popular because it does not require the mesh for the simulation domain to conform to the orientation of the natural fractures. However, it is limited because it cannot accurately model low-conductivity fractures. Although the projection-based EDFM (pEDFM) was developed to address this limitation of the EDFM, recent studies show that pEDFM still cannot accurately model low-conductivity fractures that are neither parallel to the simulation grid nor cutting through the matrix cell diagonals. In these cases, it has been observed that reservoir fluids can flow around low- or even zero-conductivity fractures. This paper presents a rigorous analysis, which reveals that the error when modeling inclined low-conductivity fractures with pEDFM is because the projections of the fracture on the gridblock faces are discontinuous. This discontinuity implies that the matrix cell interfaces along the path of the fractures only project a fraction of the fracture area on these interfaces in each direction. So, none of these faces captures the sealing potential of these interfaces, and the pore fluid can flow around even zero-conductivity fractures. We present a robust algorithm that ensures that the projections of inclined fractures on cell faces are continuous in 3D. We refer to the model based on this algorithm as the continuous projection-based EDFM (CPEDFM) and show that it directly solves the pEDFM limitation. We present the simulation of several cases and their selected projection faces to demonstrate why CPEDFM works. We also verify the CPEDFM method by comparing the CPEDFM and pEDFM model results to high-resolution simulation results. To demonstrate the feasibility of modeling complex, realistic systems using CPEDFM, we simulate a 3D compositional Eagle Ford shale reservoir with 75 low-conductivity and 75 high-conductivity fractures. The results show that pEDFM overestimates production because it does not fully account for the sealing effects of inclined low-conductivity fractures. In conclusion, this paper presents a novel numerical model for accurately and efficiently simulating reservoirs containing fractures of arbitrary conductivity, size, and orientation in 3D.