Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

Accurate modeling of hydrocarbon production is a necessary, yet challenging step for economic exploitation of unconventional resources. One of the main challenges is to model flow to a horizontal well from a complex network of hydraulic and natural fractures. Many unconventional reservoirs comprise well-developed natural fracture networks with multiple orientations and complex hydraulic fracture patterns based on microseismic data. Conventional dual porosity and dual permeability models are not adequate for modeling these complex networks of natural and hydraulic fractures. Also, it is neither practical nor advantageous to model a large number of pre-existing fractures with a discrete fracture model. Therefore, an appropriate approach to model production from low-permeability reservoirs is to perform discrete fracture modeling for hydraulic fractures and employ a dual continuum approach for numerous natural fractures. We have developed a coupled dual continuum and discrete fracture method to simulate production from unconventional oil and gas reservoirs. Large-scale hydraulic fractures (macro-fractures) are modeled explicitly using a discrete fracture model, called EDFM, and numerous small-scale natural fractures (micro-fractures) are modeled using a dual continuum approach. The hybrid model includes three domains: matrix, discrete-fracture, and continuum-fracture domains. A systematic approach is devised to calculate transport parameters between all three domains. Moreover, EDFM allows for not only transverse and longitudinal hydraulic fractures but also macro-fractures of any orientation. Thus, the coupled model provides an effective and reliable environment to improve stimulation designs and completion strategies. We present several examples in this study to show the applicability, robustness, and performance of the hybrid method for the simulation of unconventional oil and gas reservoirs. We examine multi-stage hydraulic fractures with multiple configurations in the presence of numerous pre-existing fractures. Simulations show a noticeable contribution from natural fracture networks on total production. Furthermore, for the tight oil reservoir examined in this study, the stimulation scheme with longer hydraulic fractures improves cumulative oil production compared to the scheme with larger number of shorter hydraulic fractures. We also examine production from a tight gas reservoir wherein hydraulic fractures partially penetrate the formation height. Simulations indicate that inefficient fracture treatment can result in significant loss of production.

Two discrete-fracture models (DFMs) based on different, independent numerical techniques have been developed for studying the behavior of naturally fractured reservoirs. One model is based on unstructured gridding with local refinement near fractures, while in the second model fractures are embedded in a structured matrix grid. Both models capture the complexity of a typical fractured reservoir better than conventional dual-permeability models, leading to a more accurate representation of fractured reservoirs. The accuracy of the DFM approaches is confirmed by their match with a structured, grid-aligned, explicit-fracture model in tests involving capillary imbibition during water flooding and gravity drainage in oil-gas systems. The DFMs are insensitive to grid orientation. Simulations also show consistency and agreement of results of the DFM methods in synthetic models with complex fracture patterns. Our simulations indicate that conventional dual-permeability approaches are appropriate when the fracture system is very sparse relative to the grid spacing. In these situations a DFM can be used as the basis for defining dual-permeability model parameters. However, conventional dual-permeability approaches are inadequate in the presence of high localized anisotropy and preferential channeling. When used with general purpose reservoir simulators, both DFMs show computational performance that is comparable to that of dual-permeability models.

Many naturally fractured reservoirs around the world have depleted significantly and improved oil recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs is still challenging owing to permeability anisotropies and contrasts. Non-physical abstractions inherent in conventional dual porosity and dual permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies of discrete fracture modeling suffer from large simulation run times and the industry has not found applications for them yet, even though they give more accurate representations of fractured reservoirs than dual continuum models. We developed a novel discrete fracture model for an in-house compositional reservoir simulator that borrows the dualmedium concept from conventional dual continuum models and also incorporates the effect of each fracture explicitly. In contrast to dual continuum models, fractures have arbitrary orientations and can be angled or vertical, honoring the complexity of a typical fractured reservoir. Likewise, the new discrete fracture model does not need mesh refinement around fractures and offers computationally-efficient simulations compared to other discrete fracture models. Examples of water-flooding and gas injection are presented in this paper to demonstrate the accuracy, robustness, and applicability of the developed model for studying IOR processes in naturally fractured reservoirs. Simulations show that favorable rock wettability along with capillary pressure contrasts between matrix and fractures causes noticeable incremental oil recovery in water floods. Likewise, simulations of gas injection demonstrate that high-permeability fractures not only expedite gas breakthrough, but also increase segregation of gas towards the top of the reservoir, leading to very low sweep efficiency. Furthermore, oil recovery from naturally fractured reservoirs is found to be sensitive to the fracture inclination angle.

The effect of geomechanics on fluid flow is more crucial in fractured reservoirs due to presence of fissures, which might be more stress-sensitive than the rock matrix. The flow characteristics of fractures are significantly affected by effective normal stress exerting on them. In spite of extensive experimental and field studies that have demonstrated the dynamic behavior of fractures, fracture properties have been often treated as static parameters in the simulations of naturally fractured reservoirs. Realistic modeling of production in fractured systems requires including the dynamic behavior of fractures into a discrete fracture model.We have incorporated the dynamic behavior of fractures into an embedded discrete fracture model, called EDFM. The coupled model allows inclusion of the impact of stress regime on fluid flow in a 3D discrete fracture network. We use empirical joint models to represent normal deformation of pre-existing natural fractures and couple them with the EDFM approach. Using these models, the aperture and permeability of an arbitrary-oriented fracture become functions of the effective normal stress acting on the fracture plane. In addition, we allow for fracture-conductivity tables to model dynamic behavior of propped hydraulic fractures in stimulated reservoirs.We present several examples in this study to show the applicability and performance of the coupled geomechanics-EDFM approach for the simulation of naturally fractured reservoirs. We examine the effect of pressure-dependent fracture properties on production leading to the conclusion that fracture deformation, caused by effective stress changes, substantially affects hydrocarbon recovery. Our simulations show that the significance of such effects on production strongly depends on parameters controlling the deformation behavior of fractures. Simulations also show that creating sufficiently highconductivity fractures during stimulation treatment of unconventional reservoirs can mitigate the adverse effect of hydraulic fracture closure on production to a good extent. Furthermore, the coupled geomechanics-EDFM approach does not degrade the computational performance of EDFM, which is a promising new approach for modeling discrete fractures in a robust and efficient manner.