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In the last years, hydraulic fracturing (HF) has reached maturity, becoming a fundamental aspect of hydrocarbon productivity enhancement and an important component of well costs. Interest on HF has also increased following unconventional resources exploitation, where commercial hydrocarbons rates cannot be otherwise achieved. This work reviews and...
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... sector model ( Figure 6) was extracted from the full field geological model (see Figure 7) to evaluate the performance of the HF well. The sector dimensions are ~ 1300 4000 150 meters. ...
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... equivalent fractured well model was also built for the Mars well using the EDFM-coarse grid as input, replacing fracture DOFs with the needed number of auxiliary well completions (see Figure 16). As proof of validity for the methodology, the results of the simulation incorporating the equivalent fractured well are reported in Figure 17 against the ones achieved with EDFM-coarse model, in terms of gas production, simulation run-time and pressure distribution inside the field. It can be noticed as the gas production forecast and pressure distribution in the field is aligned and the computational time is reduced with respect to the EDFM-coarse. ...
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... Compared with DFMs that use unstructured gridding (Karimi-Fard et al. 2004;Hoteit and Firoozabadi 2005;Matthäi et al. 2005;Hui et al. 2013), EDFM offers the practical advantage of integrating discrete fracture networks (DFNs) with a structured background grid that limits the overall grid cell count for field applications. Many enhancements of the original embedding technique have been proposed for applications to naturally and hydraulically fractured reservoirs (Hajibeygi et al. 2011;Moinfar et al. 2014;Panfili et al. 2015;Fumagalli et al. 2016;Tene et al. 2017;Jiang and Younis 2017;Chai et al. 2018;Xu and Sepehrnoori 2019). EDFM and DPDK have been compared in Moinfar et al. (2011) and Vo et al. (2020). ...
Natural fracture systems comprise numerous small features and relatively few large ones. At field scale, it is impractical to treat all fractures explicitly. We represent the largest fractures using an embedded discrete fracture model (EDFM) and account for smaller ones using a dual-porosity, dual-permeability (DPDK) idealized representation of the fracture network. The hybrid EDFM + DPDK approach uses consistent discretization schemes and efficiently simulates realistic field cases. Further speedup can be obtained using aggregation-based upscaling. Capabilities to visualize and post-process simulation results facilitate understanding for effective management of fractured reservoirs. The proposed approach embeds large discrete fractures as EDFM within a DPDK grid (which contains both matrix and idealized fracture continua for smaller fractures) and captures all connections among the triple media. In contrast with existing EDFM formulations, we account for discrete fracture spacing within each matrix cell via a new matrix-fracture transfer term and use consistent assumptions for classical EDFM and DPDK calculations. In addition, the workflow enables coarse EDFM representations using flow-based cell-aggregation upscaling for computational efficiency. Using a synthetic case, we show that the proposed EDFM + DPDK approach provides a close match of simulation results from a reference model that represents all fractures explicitly, while providing runtime speedup. It is also more accurate than previous standard EDFM and DPDK models. We demonstrate that the matrix-fracture transfer function agrees with flow-based upscaling of high-resolution fracture models. Next, the automated workflow is applied to a waterflooding study for a giant carbonate reservoir, with an ensemble of stochastic fracture realizations. The overall workflow provides the computational efficiency needed for performance forecasts in practical field studies, and the 3D visualization allows for the derivation of insights into recovery mechanisms. Finally, we apply a finite-volume tracer-based flux post-processing scheme on simulation results to analyze production allocation and sweep for understanding expected waterflood performance.
... As a powerful approach to simulating arbitrary fracture geometries in reservoir simulators using structured grids, the EDFM has received much attention in recent years (Li and Lee, 2008;Moinfar et al., 2014;Panfili et al., 2015;Sepehrnoori et al., 2020). In this method, without building a conforming grid, the fractures are inserted into the grid as a separate domain. ...
... This method was later extended to three-dimensional models (Moinfar et al., 2014;Cavalcante Filho et al., 2015). Since the introduction of the EDFM, research has shown the high accuracy and flexibility of the EDFM in the simulation of complex fractures (Panfili et al., 2015;Du et al., 2017;Flemisch et al., 2018). Studies were also conducted to extend its capability and improve its accuracy and performance for different types of problems. ...
... Cheng et al. (2021) combined a two-set nodes Green Element Method in a triangular grid with the EDFM to solve nonlinear problems. Some other researchers focused on improving the simulation accuracy by adjusting the local grid through LGR, and several studies have reported the improvement of EDFM accuracy when combining it with moderate LGR of the cells intersected by the fractures (Panfili et al., 2015;Yang et al., 2018;Wang et al., 2019). As an example, Panfili et al. (2015) used the EDFM with single-level LGR and compared this method with several other methods in terms of efficiency and accuracy. ...
Transient flow around hydraulic fractures is an important topic in the study of tight reservoirs. In this work, the Embedded Discrete Fracture Model (EDFM) is combined with nested local grid refinement (LGR) to improve its accuracy for simulating near-fracture transient flow. An automatic grid refinement procedure is developed to iteratively conduct LGR around complex fractures. In each iteration, the cells intersected by or close to fractures are selected and refined. The size of the refinement region and the level of refinement can be adjusted. Through this process, the cell size in the near-fracture region is reduced rapidly, while the total cell count remains at a relatively low level. An analysis of the optimal refinement ratio for regular Cartesian grids is also conducted. Furthermore, the EDFM is implemented in grids with nested LGR, and connections between the matrix and fractures are properly determined to compute the transmissibility factors as input for reservoir simulators.
The developed methodology is first verified against a logarithmic LGR model for different fracture orientations, and the results show that different flow regimes can be reliably simulated. Subsequently, the flow regimes for non-orthogonal, non-parallel, and nonplanar hydraulic fractures are studied with this approach to illustrate the unique patterns of transient flow around complex fractures. This work provides a general and convenient method to perform transient analysis for reservoirs with complex fracture geometries.
... However, the geometries of the fractures are lost in the assumption of dual-porosity models, and the real fracture network cannot be represented in dualcontinuum models [9]. Panfili et al. [10] showed that the homogenization used in dual-continuum models could introduce unphysical fracture flows between disconnected areas. Moinfar et al. [11] investigated the examples of reservoirs with complex fracture networks where dual-continuum models cannot provide precise solutions. ...
The embedded discrete fracture model (EDFM) has been popular for the modeling of fractured reservoirs due to its flexibility and efficiency while maintaining the complex geometry of fracture networks. Though the EDFM has been validated for single-phase flow simulations, some recent cases show that the EDFM might result in apparent errors in multiphase flow situations. The projection-based embedded discrete fracture model (pEDFM) and the integrally embedded discrete fracture model (IEDFM) are two recently developed methods, which intend to improve the accuracy of the EDFM. In this study, a projection-based integrally embedded discrete fracture model (pIEDFM) is proposed, which combines the advantages of the pEDFM and the IEDFM. Similar to the pEDFM, the pIEDFM uses a kind of additional connections between fracture and nonneighboring matrix cells to obtain more physically authentic velocity fields. As a significant improvement, a semi-analytical cone-shaped pressure distribution that follows the IEDFM is adopted in the pIEDFM to capture the sharp pressure change near the fracture surfaces. Comparisons with benchmark results and explicit-fracture fine grid simulation results show that the pIEDFM provides accurate solutions using a moderate amount of grids. The proposed pIEDFM is also applied to coupled flow and geomechanical simulation for fractured reservoirs. Comparison of our coupled simulation results with that of the EDFM shows that the pIEDFM is applicable for the coupled simulation, and the different methods for matrix-fracture transmissibility between the pIEDFM and the EDFM may lead to deviations in stress fields predicted by geomechanical modeling, which eventually affects the oil production, water cut, and oil saturation profiles.
... Jiang et al. (2014) carried out the numerical simulation of CO2 geological storage in shale reservoir. Panfili and Cominelli (Panfili et al., 2015) used the EDFM to simulate the injection process of miscible gas in fractured carbonate reservoir. Yu et al. (YuXu et al., 2018) used the EDFM to simulate the shale gas transportation and production process in multi-stage fractured horizontal wells. ...
Tight oil and gas reservoirs with huge development potential are widely distributed all over the world and horizontal well technique is a popular development technology for such kinds of reservoirs. However, the efficiency of conventional horizontal well technology is usually unsatisfying due to the unfavorable flow conditions caused by the nature of tight reservoirs, such as low matrix permeability and narrow pore throat. Multi-stage fractured horizontal well technology is an emerging attractive technology that can greatly improve oil production by generating highly conductive fracture networks in tight reservoirs. and numerical simulation method is generally used to predict the production dynamics of the multi-stage fractured horizontal wells. Nevertheless, the complex geological conditions of reservoirs would greatly increase the difficulties and time required to implement a complete simulation (including model building and calculation). Therefore, in this paper, deep convolution generative adversarial networks (DCGAN) based on U-Net framework was applied to establish the dynamic mapping relationship between fracture pattern and reservoir pressure during the production process, that is, the dynamic reservoir pressure distribution can be obtained by image mapping the fracture distribution details. The results showed that the efficiency of U-Net framework based deep convolution in extracting, dividing and splicing the geometric features of fracture network is significant, and the generative adversarial networks model can effectively predict the reservoir pressure distribution according to the fracture network geometry after being trained with 6000 sets of data. Herein, the training accuracy of the proxy model towards sample data was compared, and the confrontation between the generator and the discriminator in the iterative training process was clarified according to the error function. Furthermore, the prediction accuracy towards pressure distribution at different fracture network geometry scales by the proxy model was compared. Results indicated that the pressure diffusion range predicted by the proxy model is basically consistent with the range obtained from the numerical simulation, with a mean square error (MSE) generally smaller than 0.2. In addition, the relationship between the prediction accuracy of the proxy model and the number of sample data and iterative training times was also studied, which showed that the mean square error of the proxy model kept decreasing with the increasing iteration cycles and sample size, which met the basic law of statistical learning. Moreover, it is worth mentioning that the proposed method may also shed light on the applications of DCGAN in other reservoir-related problems.
... Therefore, detailed near-well/near-fracture models are necessary to provide sufficient resolution for the matrix-fracture interactions (Mayerhofer et al. 2010;Cipolla et al. 2010a;Cipolla et al. 2010b). However, a fine grid simulation requires too much CPU time and it is impractical to perform for the entire domain in field cases with multiple hydraulic-fracture stages Weng et al. 2014;Panfili et al. 2015). ...
... Several modeling approaches for fractured-well have been proposed in the literature, attempting to improve the solution efficiency while maintaining the accuracy. One simple approach is applying local grid refinement (LGR) on a coarse background grid (Mallison et al. 2010;Cipolla et al. 2010b;Artus and Fructus 2012;Panfili et al. 2015;Jiang and Younis 2015b;Jiang and Younis 2016;Xue et al. 2019). A number of meshing algorithms are available to generate adaptive and optimized mesh with good quality around discrete fractures. ...
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed near-well/near-fracture models are necessary to provide sufficient resolution, but they are computationally impractical for field cases with multiple fracture stages. Previous works in the literature of unconventional simulations mainly focus on gridding level that adapts to wells and fractures. Limited research has been conducted on nonlinear strategies that exploit locality across timesteps and nonlinear iterations. To perform localized computations, an a-priori strategy is essential to first determine the active subset of simulation cells for the subsequent iteration. The active set flags the cells that will be updated, and then the corresponding localized linear system is solved. This work develops localization methods that are readily applicable to complex fracture networks and flow physics in unconventional reservoirs. By utilizing the diffusive nature of pressure updates, an adaptive algorithm is proposed to make adequate estimates for the active domains. In addition, we develop a localized solver based on nonlinear domain decomposition (DD). Compared to a standard DD method, domain partitions are dynamically constructed. The new solver provides effective partitioning that adapts to flow dynamics and Newton updates. We evaluate the developed methods using several complex problems with discrete fracture networks. The results show that large degrees of solution locality present across timesteps and iterations. Compared to a standard Newton solver, the new solvers enable superior computational performance. Moreover, Newton convergence behavior is preserved, without any impact on solution accuracy.
... Therefore, detailed near-well/near-fracture models are necessary to provide sufficient resolution for the matrix-fracture interactions [3,4,6]. However, a fine grid simulation requires too much CPU time and it is impractical to perform for the entire domain in field cases with multiple hydraulic-fracture stages [5,7,8]. ...
... Several modeling approaches for fractured-well have been proposed in the literature, attempting to improve the solution efficiency while maintaining the accuracy. One simple approach is applying local grid refinement (LGR) on a coarse background grid [4,[8][9][10][11][12][13][14]. A number of meshing algorithms are available to generate adaptive and optimized mesh with good quality around discrete fractures. ...
... Lee et al. [39], Li and Lee [40], Hajibeygi et al. [41] and Moinfar et al. [42] introduced and extended EDFM, which does not require simulation grid to conform to fracture geometry. Recent works on the implementations of EDFM for various types of problems include [8,[12][13][14][43][44][45][46][47][48]. ...
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed near-well/near-fracture models are necessary to provide sufficient resolution, but they are computationally impractical for field cases with multiple hydraulic-fracture stages.
Previous works in the literature of unconventional simulations mainly focus on the gridding level that adapts to wells and fractures. Limited research has been conducted on nonlinear strategies that exploit locality across timesteps and nonlinear iterations. It was reported that an individual Newton update is typically sparse and nonlinear convergence is constrained by a small portion of the model. To perform localized computations, an a-priori strategy is essential to first determine the active subset of simulation cells for the subsequent iteration. The active set flags the cells that will be updated, and then the corresponding localized linear system is solved.
The objective of this work is to develop localization methods that are readily applicable to complex fracture networks and flow physics in unconventional reservoirs. By utilizing the diffusive nature of pressure updates, an adaptive algorithm is proposed to make adequate estimates for the active domains. In addition, we further develop a localized solver based on nonlinear domain decomposition (DD). Compared to a standard DD method, domain partitions are dynamically constructed. The new solver provides effective partitioning that adapts to flow dynamics and Newton updates.
We evaluate the developed methods using several complex problems with discrete fracture networks. The problems consider multi-phase and compositional fluid systems with phase changes. The results show that large degrees of solution locality present across timesteps and iterations. Compared to a standard Newton solver, the new solvers enable superior computational performance. Moreover, Newton convergence behavior is preserved, without any impact on solution accuracy.
... The basic idea and formulations of the EDFM have been proposed and extended by several researchers (Hearn et al., 1997;Lee et al., 2001;Philip et al., 2005;Li and Lee, 2008;Moinfar et al., 2014). Extensive previous studies have also shown the high reliability and computational efficiency of the model (Moinfar et al., 2014;Panfili et al., 2015;Xu et al., 2017;Du et al., 2017;Flemisch et al., 2018). For example, Panfili et al. (2015) compared the EDFM with the local grid refinement method and the equivalent fractured well method, and in their study, the EDFM obtained a higher computational efficiency compared with the local grid refinement method. ...
... Extensive previous studies have also shown the high reliability and computational efficiency of the model (Moinfar et al., 2014;Panfili et al., 2015;Xu et al., 2017;Du et al., 2017;Flemisch et al., 2018). For example, Panfili et al. (2015) compared the EDFM with the local grid refinement method and the equivalent fractured well method, and in their study, the EDFM obtained a higher computational efficiency compared with the local grid refinement method. Du et al. (2017) compared the EDFM with an unstructured gridding fracture model for full-field well interference studies, and the EDFM was found to have a significant advantage regarding computational efficiency while maintaining high accuracy. ...
... Panfili and Cominelli (2014), Fumagalli et al. (2016), and Xu and Sepehrnoori (2019) implemented the EDFM in corner-point grids. Panfili et al. (2015) and Yang et al. (2018) demonstrated the use of EDFM with moderate local grid refinement to improve the simulation accuracy of this model. ...
Recently, the unstructured gridding technique has been extensively used in reservoir simulation because of the high flexibility it provides to represent geologically realistic reservoirs. The embedded discrete fracture model (EDFM) has also attracted attention in recent years for the simulation of complex fractures in various types of matrix gridding. In this work, we develop a methodology to apply the EDFM in 2D and 3D unstructured grids using an element-based finite volume method (EbFVM). In this method, triangular and quadrilateral elements are used in 2D grids, and tetrahedron, prism, hexahedron, and pyramid elements are used in 3D grids. New approaches to addressing matrix-fracture connectivity and reducing the number of fracture unknowns in this type of grid are presented. The methodology is implemented in an EDFM preprocessing code.
A series of case studies are presented to demonstrate the methodology in 2D and 3D simulations using an in-house compositional reservoir simulator. Different types of elements are used in the simulations to represent the reservoir geometries. Both primary and secondary recovery processes are simulated. The results show that when the number of control volumes is similar, the proposed method can obtain similar results on different grids with various types of elements, which confirms the effectiveness of the approach. Case studies with complex reservoir geometries are also presented to demonstrate the applicability of the model.
This work demonstrates the extensiveness of the EDFM to unstructured matrix grids. It also shows the compatibility of the EDFM with various numerical approximation schemes. The use of unstructured gridding with mixed types of elements facilitates the representation of complex reservoir geometries, and through the combination with the EDFM, complicated gridding around fractures is avoided. Therefore, the approach in this work has high flexibility for simulating densely fractured media with complex geometries.
... However, as corner-point grids being the industry standard, it is very beneficial to apply the EDFM to corner-point grids for the study of realistic reservoirs. However, existing studies mentioning corner-point grids with EDFM (Panfili et al., 2015;Fumagalli et al., 2016;de Sousa Junior et al., 2016) have not comprehensively considered the complexities pertaining to the numerical formulations and geometrical calculations. ...
Corner-point is an industry-standard type grid for application in reservoir simulation. The flexible gridding in corner-point grids provides several advantages over Cartesian grids for the representation of complex geological features. In this work, an embedded discrete fracture model (EDFM) is extended to corner-point grids with a full-permeability-tensor formulation to simulate complex fractures in this type of grids. The developed model is implemented in an IMPEC, compositional reservoir simulator. We first describe the formulations of the full-permeability-tensor implementation together with the modified governing equations for EDFM simulations. Then, we present methodologies for computing matrix-fracture intersections and fracture-fracture connections in the EDFM considering the various block geometries in corner-point grids. Subsequently, case studies are presented to verify the developed model, where the impacts of grid distortion and cross derivatives on simulation results are discussed. Three-dimensional case studies are also shown to illustrate the influence of natural fractures on secondary recovery. The results of this study demonstrate the reliability of the developed model, and they also show the compatibility of the EDFM with different types of numerical solution schemes in existing simulators.
... Also the applications typically assume that the properties and geometry of the fracture network remain relatively constant (Norbeck et al. 2016). DP/DK models tend to homogenize the fractures contributing to flow in each simulation 20 block by ignoring their connectivity; thus unphysical fracture flows could be established between disconnected areas of the reservoir (Panfili et al. 2015).Moinfar et al. (2011)demonstrated examples where the DK model fails to provide satisfactory solutions in the presence of fracture system with high heterogeneity. Another shortcoming is that DP/DK models treat matrix and fracture as two parallel continuous systems coupled 25 by transfer functions. ...
... EDFM borrows the concept of transport index to tie the additional computational control-volumes for fractures to matrix. Recent works on the implementations of EDFM for various types 55 of problems includePanfili et al. (2015), Jiang and Younis (2016),Tene et al. (2016), Norbeck et al. (2016) and Fumagalli et al. (2016). Note that EDFM is not suitable in the cases where fracture permeability lies below that of matrix, as recently revealed byTene et al. (2017). ...
The discrete fracture-matrix (DFM) approaches based on conforming grids become popular for modeling fractured reservoirs in the last decade. However, the application of conforming DFMs at field scale is limited due to its prohibitive computational cost. In recent years, embedded discrete fracture model (EDFM) has received considerable attention as a promising alternative. EDFM incorporates the effect of each fracture explicitly without requiring the simulation grid to conform to the fracture geometry. A compromise between accuracy and efficiency could be achieved in EDFM by enabling the use of standard corner-point grids for the background matrix domain.
Although many works confirm the high accuracy of EDFM for the solutions of pressure and velocity field, very few results have been presented to examine its accuracy for the saturation solutions from multiphase flow problems. This paper shows that EDFM can induce large errors for multiphase displacement processes, due to its incapability to capture the proper flux split through a fracture. For the first time in the literature we present a systematic evaluation on the performances of EDFM for multiphase flow and provide a detailed analysis to illuminate when and why the method fails. The analysis motivates us to exploit the projection-based extension of EDFM (pEDFM) as an effective method to resolve the limitations associated with EDFM. pEDFM is recently developed by Tene et al. (2017) to address the issue of flow barriers, and is based on the introduction of extended fracture-matrix fluxes. Moreover, we make several improvements upon the original pEDFM method. A physical constraint on the preprocessing stage is proposed to overcome the limitation in a ‘naive implementation’ of pEDFM.
A number of test cases with different fracture geometries are presented to benchmark the performances of the improved pEDFM method for multiphase flow. Grid convergence studies are conducted for different numerical schemes. The results show that improved pEDFM significantly outperforms the original EDFM method.
