Summary: Most unconventional oil and gas reservoirs are known to have several natural fractures in different orientations, which are consistent with the prevailing stresses when they were created. The accurate and efficient modeling of natural and hydraulic fractures presents a significant computational challenge. In this work, we show the limitations of the embedded discrete-fracture model (EDFM) and present the first 3D projection-based EDFM (pEDFM) algorithm and compositional simulation studies with realistic fracture networks in a fully 3D space. The simulation results from this work indicate that the pEDFM presented can model realistic fractured unconventional reservoirs accurately and efficiently. To validate the model, we present some simplistic fracture cases that can be meshed and modeled easily using explicit-fracture modeling in commercial-reservoir simulators. From the cases studied, we observe that using progressively finer grids near the hydraulic-fracture surfaces helps to improve model accuracy because this allows us to capture the sharp pressure drops expected near these fracture surfaces. The simulation results show that, unlike EDFM, the robust pEDFM algorithm presented here is accurate even at the low fracture-conductivity values expected in many of these ubiquitous natural fractures. In this paper, we present the first full 3D compositional modeling with pEDFM. We demonstrate that our model can accurately and efficiently model multiply fractured horizontal wells in unconventional reservoirs, which have complex networks of thousands of fractures at various orientations.

The commercial development of unconventional resources with multiply fractured horizontal wells has been in the spotlight over the last ten years because of the significant contribution of unconventional oil and gas (UOG) reservoirs to the total US oil and gas production. UOG reservoirs contain multiscale fractures with heterogeneous properties, so the focus has been on efficient and accurate models that can account for these fractures individually. One of such models is the embedded discrete fracture model (EDFM), which has been applied to various types of fractured reservoirs. This work shows that the application of EDFM in fractured tight rocks yields significant errors because it cannot account for the expected transient flow between the matrix and fractures. To address the limitation when EDFM is used in tight rocks with structured Cartesian grids, we modified the matrix/fracture non-neighboring connection (NNC) flux in EDFM by multiplying it with a transient factor. We obtained this factor as in the transient matrix/fracture transfer term for dual-continuum models and implemented it in in our open-source shale simulator. We simulated a single vertical fracture in the middle of a tight reservoir with and without this EDFM modification and show the importance of the proposed modification. We also simulated cyclic gas enhanced oil recovery (CGEOR) in a fractured Bakken shale oil well and analyzed the model results using standard rate-transient analysis plots to evaluate the significance of the proposed modification. The results show that the standard EDFM underestimates oil and gas production by up to 73% at early times. This work presents the first analytical modification of EDFM to account for the nonlinear pressure drop expected near fracture surfaces. Comparing the modified and standard EDFM model results to a reference solution shows that the modified EDFM matches it. In contrast, the standard EDFM cannot match the reference solution when we use structured Cartesian grids with linear spacing. Additionally, by timing the simulation of a representative Bakken shale oil reservoir with 256 fractures, we show that the analytical modification proposed is only 1.5% slower than the standard EDFM.

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.

Various models featuring horizontal wells with multiple fractures have been proposed to characterize flow behavior over time in tight and shale gas systems. Currently, only very little is known about the effects of nonideal fracture patterns and coupled primary-secondary fracture interactions on reservoir performance in unconventional gas reservoirs. We developed a 3D Voronoi mesh-maker that provides the flexibility to accurately represent various complex and irregular fracture patterns. A numerical model was developed based on such fracture concepts to assess the potential performance of unconventional gas reservoirs. We conducted simulations using up to a half-million cells and considered production periods that are orders of magnitude longer than the expected life of wells and reservoirs. Our aim is to account for a wide range of flow regimes that can be observed in irregular fracture patterns, and to fully assess even slight nuances in flow behavior. We investigated coupled primary-secondary fractures, with multiple vertical hydraulic fractures intersecting horizontal secondary "stress-release" fractures. We studied irregular fracture patterns to show the effect of fracture angularity and nonplanar fracture configurations on production. The results indicate that the presence of high-conductivity secondary fractures results in the highest increase in production, while, contrary to expectations, strictly planar and orthogonal fractures yield better production performance than nonplanar and nonorthogonal fractures with equivalent propped fracture lengths.