Embedded Discrete Fracture Model Research Articles

A new analytically modified embedded discrete fracture model for pressure transient analysis in fluid flow

In the past few decades, multi-stage hydraulic fracturing has emerged as a crucial technology for the commercial development of unconventional oil and gas (UOG) resources. It is crucial to accurately and efficiently characterize transient fluid flow near fractures, which is a critical concern for many researchers. Discrete fracture models (DFMs) are primarily used to analyze the pressure transient behaviors of fluid flow in naturally fractured porous media. DFMs can accurately capture transient fluid flow near fractures, but they require a substantial number of grids to ensure computational accuracy, leading to higher computational costs. On the other hand, standard embedded discrete fracture models (EDFMs) based on pseudo-steady-state assumptions are computationally efficient, but they struggle to model the early transient fluid flow near fractures accurately. To address this limitation, we propose a new analytically modified EDFM (AEDFM) with structured Cartesian grids for analyzing the pressure transient behaviors of fluid flow in naturally fractured porous media.The transmissibility between the matrix and fractures is adjusted by multiplying it with a transient factor. In addition, we have validated the accuracy and efficiency of our proposed model through comparisons with results from analytical models and a standard well-testing software package. The results demonstrate the significance of our proposed model in accurately capturing transient fluid flow around fractures and reducing computational costs. In this work, we analyze the pressure transient behaviors of fluid flow using various parameter values and further evaluated the significance of the proposed modifications. The results indicate that AEDFM can effectively match the early nonlinear pressure drop near fractures compared to the standard EDFM. This work presents a powerful tool for the fast and accurate analysis of pressure transient behaviors of fluid flow in naturally fractured porous media.

From Streamline to Pathline: Visualizing Particle Trajectories Under Changing Velocity Fields

Summary Monitoring of subsurface fluid motion is critical for optimizing hydrocarbon production and CO2 sequestration. Streamlines are frequently used to visualize fluid flow; however, they provide only an instantaneous snapshot of the velocity field and do not offer an exact representation of fluid movement under varying field conditions. In contrast, pathlines are constructed by tracking individual particles within the fluid, enabling us to trace the movement of these particles as they traverse through changing velocity fields. Pathline is the trajectory that an individual fluid particle follows in the reservoir. It can be thought of as “recording” the path of a fluid element in the flow field for a given time interval. Pathlines are distinct from streamlines which represent a snapshot of the velocity field at a given instant. The direction the path takes is determined by the streamlines at a specific instant. To start with, streamlines are traced based on the grid face fluxes of finite-difference simulation. Streamline tracing continues till the time of flight equals the current time. The endpoints of the current streamlines become the starting points for the next tracing period. Thus, our formulation incorporates changing flow fields, and the process is repeated for each time interval until the end. The proposed injection monitoring method is tested using a 3D field-scale model with complex geologic features to demonstrate its power and utility. The pathlines were compared with streamlines, as well as the water saturation distribution. Three scenarios are tested: a constant well schedule, a changing well schedule with partial shut-in, and a changing well schedule with a whole field cessation. Results indicate that the pathline provides a more accurate swept volume, consistent with saturation distribution. The robustness of our algorithm and implementation is demonstrated with a complex embedded discrete fracture model (EDFM) to visualize flow patterns in discrete facture network. Pathlines display the fluid flow across fractures and are subsequently used to explore the sweep efficiency and the well connectivity.

Simulation of two-phase flow in 3D fractured reservoirs using a projection-based Embedded Discrete Fracture Model on Unstructured tetrahedral grids (pEDFM-U)

The modeling of fluid flow in heterogeneous, anisotropic and fractured porous media is relevant in many applications, including hydrocarbon and groundwater extraction, dispersion of contaminants, hydrogen or carbon dioxide (CO2) storage. Thus, accurate and scalable simulation of fluid flow through these formations continues to be a great challenge. The presence of fractures that are explicitly modeled, ranging from flow barriers to highly conductive channels, significantly increases the complexity of the numerical simulation. The Embedded Discrete Fracture Model (EDFM) produces results that can be as accurate as those obtained using equidimensional Discrete Fracture Models (DFM) at a much lower computational cost for highly conductive fractures, but it is not adequate for impermeable barriers. In contrast, the pEDFM (projection-based Embedded Discrete Fracture Model) produces accurate results for both, channels and barriers by using additional matrix-fracture connectivities. In its current versions, it is restricted to cartesian and corner-point grid geometries and to the classical Two Point Flux Approximation (TPFA) scheme. In this work, for the first time, the pEDFM is extended to handle unstructured tetrahedral meshes (pEDFM-U). In addition, interface fluxes are approximated by using the Multipoint Flux Approximation method with a Diamond stencil (MPFA-D). This allows for simulation of highly heterogeneous and anisotropic geo-models. The developed method is robust and can deal with full permeability tensors on arbitrary tetrahedral meshes. The advective terms are discretized considering an implicit First Order Upwind (FOU) method. Our method is implemented within the DARSim (Delft Advanced Reservoir Simulation) open-source simulator framework. Through several test cases, the proposed method showed to be robust and capable to accurately capture the effects of both high and low permeability fractures for general tetrahedral meshes, under arbitrary heterogeneous and anisotropic permeability tensors for the rock matrix.

A computationally efficient approach to model reactive transport during CO2 storage in naturally fractured saline aquifers

Energy storage is critical to any decarbonization, energy sustainability, and energy security strategy. Natural gas, CO2, and hydrogen will compete for sizeable geological storage sites in the future, and society needs to consider all possible storage sites. Saline aquifers and depleted hydrocarbon reservoirs have emerged as key sites for storage. While carbonate rocks possess significant storage potential, as evidenced by successful CO2-enhanced oil recovery (CO2-EOR) projects, most operational and planned Carbon Capture and Storage (CCS) initiatives primarily focus on sandstones. Consequently, extensive fundamental and applied research is necessary to advance technologies for carbonate rock utilization and capitalize on the storage capacities of vast saline aquifers and infrastructure available in near-abandoned depleted carbonate reservoirs. However, the challenges posed by the fracture systems and the substantial heterogeneity inherent to such reservoirs necessitate a comprehensive understanding of rock integrity and the role of fracture networks in the overall storage process. Moreover, modeling CCS in carbonates introduces additional complexities due to reactive minerals, such as calcite and dolomite, which can undergo reactions with injected CO2. Consequently, a numerical formulation capable of producing accurate results within a reasonable computational time is required, considering computationally intensive processes like fracture flow and geochemical reactions. In this work, three approaches to modeling naturally fractured media were assessed, such as the explicit representation of fractures through local grid refinement (LGR), the traditional dual permeability/dual porosity model (DPDK), and the embedded discrete fracture model (EDFM). The combination of EDFM with dynamic gridding in the matrix gridblocks demonstrated superior computational efficiency compared to LGR and DPDK simulations. This novel approach was 75 times faster than LGR and 37 times faster than DPDK while yielding comparable results in terms of different CO2 retention forms (free supercritical fluid, dissolved in water, and residual trapped gas) in one of the geological models investigated. Therefore, it was proposed a novel combination of EDFM and dynamic gridding as a suitable and accurate numerical approach to simulate reactive CO2 transport in fractured saline aquifers. This approach offers a practical means of efficiently evaluating carbonate reservoir targets for CCS projects, enabling effective decision-making in energy storage endeavors.

Field Application of a Novel Multiresolution Multiwell Unconventional Reservoir Simulation: History Matching and Parameter Identification

Summary This study focuses on developing an efficient workflow by integrating a multiresolution simulation model and a multiobjective evolutionary algorithm (MOEA) for application to multiwell unconventional reservoirs. In this approach, hydraulic fractures are represented using a dual porosity, dual permeability system facilitated by an embedded discrete fracture model (EDFM). A novel fast-marching simulation method is used to cut down on computational expenses by an order of magnitude, greatly accelerating the history-matching process. A variety of integrated monitoring technologies were implemented to map out the hydraulic fracture network. Insights into hydraulic fracture locations were gleaned from warm-back analysis of distributed temperature sensing data, and these locations were then assimilated into the simulation model as embedded discrete fractures. For the simulation, a fast-marching-based multiresolution model was used to partition the reservoir into local and shared domains guided by the diffusive-time-of-flight (DTOF) principle. The local domain maintained the original 3D grids near the wells while transforming the remaining area into 1D grids to accelerate the simulation process. Before history matching, a thorough sensitivity analysis was conducted to pinpoint the most impactful parameters. Subsequently, the model was fine-tuned using production data through an MOEA. The most sensitive parameters in history matching were identified as fracture geometry and conductivity, fluid saturations, and rock compressibility in the stimulated reservoir volume (SRV) areas. After history matching, there was a noteworthy reduction in the uncertainty of these tuning parameters. The calibrated parameters are valuable to evaluate the effectiveness of the well completion design. Overall, this work emphasizes the innovative combination of techniques applied, the efficiency gains in the history-matching process, and the scalability of the approach to other oilfield applications.

A multi-mechanism numerical simulation model for CO2-EOR and storage in fractured shale oil reservoirs

Under the policy background and advocacy of carbon capture, utilization, and storage (CCUS), CO2-EOR has become a promising direction in the shale oil reservoir industry. The multi-scale pore structure distribution and fracture structure lead to complex multiphase flow, comprehensively considering multiple mechanisms is crucial for development and CO2 storage in fractured shale reservoirs. In this paper, a multi-mechanism coupled model is developed by MATLAB. Compared to the traditional Eclipse 300 and MATLAB Reservoir Simulation Toolbox (MRST), this model considers the impact of pore structure on fluid phase behavior by the modified Peng–Robinson equation of state (PR-EOS), and the effect simultaneously radiate to Maxwell–Stefan (M–S) diffusion, stress sensitivity, the nano-confinement (N-C) effect. Moreover, a modified embedded discrete fracture model (EDFM) is used to model the complex fractures, which optimizes connection types and half-transmissibility calculation approaches between non-neighboring connections (NNCs). The full implicit equation adopts the finite volume method (FVM) and Newton–Raphson iteration for discretization and solution. The model verification with the Eclipse 300 and MRST is satisfactory. The results show that the interaction between the mechanisms significantly affects the production performance and storage characteristics. The effect of molecular diffusion may be overestimated in oil-dominated (liquid-dominated) shale reservoirs. The well spacing and injection gas rate are the most crucial factors affecting the production by sensitivity analysis. Moreover, the potential gas invasion risk is mentioned. This model provides a reliable theoretical basis for CO2-EOR and sequestration in shale oil reservoirs.

A Dynamic Permeability Model in Shale Matrix after Hydraulic Fracturing: Considering Mineral and Pore Size Distribution, Dynamic Gas Entrapment and Variation in Poromechanics

Traditional research on apparent permeability in shale reservoirs has mainly focussed on effects such as poromechanics and porosity-assisted adsorption layers. However, for a more realistic representation of field conditions, a comprehensive multi-scale and multi-flowing mechanism model, considering the fracturing process, has not been thoroughly explored. To address this research gap, this study introduces an innovative workflow for dynamic permeability assessment. Initially, an accurate description of the pore size distribution (PSD) within three major mineral types in shale is developed using focussed ion beam-scanning electron microscopy (FIB-SEM) and nuclear magnetic resonance (NMR) data. Subsequently, an apparent permeability model is established by combining the PSD data, leading to the derivation of dynamic permeability. Finally, the PSD-related dynamic permeability model is refined by incorporating the effects of imbibition resulting from the fracturing process preceding shale gas production. The developed dynamic permeability model varies with pore and fracture pressures in the shale reservoir. The fracturing process induces water blockage, water-film formation, and water-bridging phenomena in shale, requiring additional pressure inputs to counteract capillary effects in hydrophilic minerals in shale, But also increases the overall permeability from increasing permeability at larger scale pores. Unlike traditional reservoirs, the production process commences when the fracture is depleted to 1–2 MPa exceeds the pore pressure, facilitated by the high concentration of hydrophobic organic matter pores in shale, this phenomenon explains the gas production at the intial production stage. The reduction in adsorption-layer thickness resulting from fracturing impacts permeability on a nano-scale by diminishing surface diffusion and the corresponding slip flow of gas. this phenomenon increases viscous-flow permeability from enlarged flow spacing, but the increased viscous flow does not fully offset the reduction caused by adsorbed-gas diffusion and slip flow. In addition to the phenomena arising from various field conditions, PSD in shale emerges as a crucial factor in determining dynamic permeability. Furthermore, considering the same PSD in shale, under identical pore spacing, the shape factor of slit-like clay minerals significantly influences overall permeability characteristics, much more slit-shaped pores(higher shape factor) reduce the overall permeability. The dynamic permeability-assisted embedded discrete fracture model (EDFM) showed higher accuracy in predicting shale gas production compared to the original model.

A novel streamline simulation method for fractured reservoirs with full-tensor permeability

In this work, we develop a novel streamline (SL) simulation method that integrates seamlessly within the embedded discrete fracture model (EDFM). The novel SL-based method is developed based on a hybrid of two-point flux approximation (TPFA) and mimetic finite difference (MFD) methods, which is applicable to a two-phase anisotropic flow in fractured reservoirs. We refer to this novel approach as EDFM-TPFA-MFD-SL. The approach is operated in an IMplicit Pressure Explicit Saturation (IMPES) manner. First, this work establishes a novel EDFM utilizing a hybrid TPFA-MFD scheme to solve the pressure equation for phase flux approximation. Subsequently, we introduce a practical streamline tracing workflow designed to derive the distribution of streamlines within the reservoir domain and the time-of-flight distribution along each individual streamline. This feature allows for the parallel computation of water saturation along the streamlines. Two numerical examples are presented to validate the superiority of the proposed EDFM-TPFA-MFD-SL method compared to the existing streamline-based EDFM on cases with full-tensor permeability. The results show that the proposed method could significantly mitigate the numerical dissipation and reduce the computation costs. Another numerical example demonstrates the effectiveness of the proposed method in dealing with complex fracture networks and providing rapid flow diagnostics, indicating its significant potential for real-world field applications.

Development of a Scalable Parallel Compositional Simulator for Thermo-Hydromechanical Coupling in Fractured Rocks Using an Embedded Discrete Fracture Model

Summary Numerical simulation of thermo-hydromechanical (THM) coupling in practical complex fractured rocks is an essential but challenging issue for the evaluation and optimization of underground energy production. In this study, we present our work on a scalable parallel compositional simulator for THM coupling, which is suitable for massive 3D polygonal fractures. In addition, we also present the improvements, parallel implementation, and optimization of an embedded discrete fracture model (EDFM). A unified cell-centered grid system based on the finite volume method (FVM) is used for all governing equations, and an extended stencil is adopted for mechanical equations to resolve the low-resolution defect of the traditional FVM. The deformation of both matrix rock and fractures is considered. A sequential fully implicit (SFI) method is adopted to solve THM coupling. This simulator is validated against three analytical solution models. Finally, we apply the simulator to two cases including a multilayered shale gas reservoir with massive natural fractures and a fractured geothermal model using CO2 as a working fluid. We also test the performance and parallel scalability on 1,024 CPU cores with up to 50 million matrix gridblocks and 5.5 million fracture gridblocks. The results show that this simulator can efficiently solve the THM coupling problem in practical massive fractures.

The enriched-embedded discrete fracture model (nEDFM) for fluid flow in fractured porous media

The embedded discrete fracture model (EDFM) is widely adopted for simulating fluid flow in fractured porous media, but it faces limitations when dealing with blocking fractures due to its assumption of symmetric and linear pressure distribution around fractures. To improve this, our work presents a novel numerical framework named the enriched-embedded discrete fracture model (nEDFM). This framework, based on a non-conforming grid and discretized using the mass-conservative finite volume method, offers significant advancements. An attractive feature of the nEDFM is its applicability to both conductive and blocking fractures, as well as isotropic and anisotropic matrix permeability, all while maintaining a low computational cost. The local shape function, which introduces two enriched degrees of freedom for every fracture cell, is developed to model the discontinuities of pressure and its gradient on two sides of the fracture. Additionally, two equations for coupling the matrix and reduced fracture are supplemented to close the system and improve the accuracy of mass exchange between the matrix and fracture. Comparative assessments between the nEDFM, classical EDFM, and projection-based EDFM (pEDFM) demonstrate the superior performance of nEDFM. Specifically, the nEDFM outperforms the EDFM for conductive fractures and can obtain better pressure distribution inside blocking fractures than the pEDFM. In scenarios involving anisotropic matrix permeability with either conductive or blocking fractures, the nEDFM can get solutions comparable to those obtained by the reference solution. Hence, the nEDFM emerges as an accurate and flexible method for simulating fluid flow in fractured porous media.

Blasingame production decline curve analysis for fractured tight sand gas wells based on embedded discrete fracture model

Blasingame production decline curve analysis (PDCA) is crucial for extracting natural gas from fractured tight sandstone reservoirs (FTSRs). The natural gas flow in FTSRs is complex due to high-velocity non-Darcy (hvnD) flow, threshold pressure gradient (TPG), and stress sensitivity of reservoirs. These factors pose a challenge in solving nonlinear equations. In this paper, we establish a mathematical model for the flow of natural gas in FTSRs. The fracture is characterized by a hvnD flow coupled using an embedded discrete fracture model (EDFM). The gas flow in the matrix is coupled with the TPG. Stress sensitivity has been considered in both fractures and matrix. The finite volume method (FVM) was employed to discretize and solve the nonlinear equations in the model. The pressure-normalized rate algorithm and gas flow model were used to present a Blasingame production decline curve for fractured horizontal wells in FTSRs. The Blasingame production decline curve can be used to identify natural gas flow regimes, matrix petrophysical properties, and fracture parameters. The effect of the hvnD flow in fractures, the lvnD flow in the matrix (TPG), stress sensitivity, fracture parameters, and production schedule on the Blasingame production decline curve and pressure profile are discussed in detail. This study provides scientific and theoretical support for predicting gas wells performance and the gas production decline law in FTSRs.

Prediction Model for Tight Gas Wells with Time-Dependent Mechanism and Stress Sensitivity Effect.

In the production process of tight gas wells, reservoir fluid distribution and gas-water relative permeability vary with time. However, traditional models fail to handle the time-dependent mechanism and stress sensitivity effect in the reservoir, leading to significant errors in the dynamic analysis results. To address this issue, this article presents a prediction model for fractured well production in tight gas reservoirs. It is based on a three-dimensional embedded discrete fracture model (EDFM), which considers the influences of the time-dependent mechanism and stress-dependent reservoir permeability. Transient flow equations are treated by using the finite volume method to obtain the solution of the model. The accuracy and reliability of the model are verified by comparison with the results of the commercial simulator Eclipse and the field application. Based on the model's solution, this study emphasizes the analysis of the impact of the time-dependent mechanism and reservoir stress sensitivity on gas well productivity. Simulation results show that the time-dependent relative permeability curve can decrease the level of irreducible water saturation and promote the migration of irreducible water, resulting in an increase in water permeability and a decrease in gas permeability. This effect will reduce the period of stable gas production and increase the level of water production. Besides, reservoir stress sensitivity will reduce daily water production and accelerate gas well decline. It is necessary to control the production pressure difference reasonably during the production process to effectively reduce the negative impact of stress sensitivity effects. The results indicate that when the relative permeability curve and the reservoir permeability are constant, the real gas production capacity of the reservoir will be strengthened. The application of field case studies shows that the theoretical model exhibits stronger adaptability, achieves better fitting results, and can guide the compilation and adjustment of development plans for water-bearing tight gas reservoirs. These findings provide insights into understanding the effects of the time-dependent mechanism on gas production rates in tight gas reservoirs. Furthermore, this study offers useful guidance for the prediction of field-scale gas production.

Thermal‒hydraulic‒mechanical‒chemical coupling analysis of enhanced geothermal systems based on an embedded discrete fracture model

Enhanced geothermal system (EGS) is subject to the comprehensive effects of multiple physical fields during the long-term heat extraction process, including hydraulic (H), thermal (T), mechanical (M) and chemical (C) fields. The embedded discrete fracture model (EDFM) can effectively simulate the variations of flow, temperature, mechanical and concentration fields in fractured reservoirs. At present, however, the thermo-hydro-mechanical-chemical (THMC) coupling model based on EDFM is less researched. In this paper, the THMC coupling model of fractured reservoir is established based on EDFM by considering the changes in reservoir heterogeneity and physical properties as well as water–rock reactions. Then, the spatiotemporal evolution of flow, temperature, displacement and concentration fields in the operation process of EGS is simulated and analyzed. And the following research results are obtained. First, when the permeability of the basement rock is low, the production temperature decrease during exploitation is gradual, allowing EGS to maintain a high exploitation temperature for an extended period. However, lower permeability may result in a decrease in the quality flow rate from production wells, thereby affecting net heat extraction power. Second, when fracture permeability or fracture opening changes, EGS can output higher temperature stably for a certain period and then the temperature decreases at different amplitudes. When the fracture permeability increases to a certain value or the fracture opening decreases to a certain value, the influence of the change in fracture parameters on production temperature gets weak. Third, After 40 years of EGS operation, considering variable property fluids results in a 22 °C lower exploitation temperature compared to using constant property fluids, and considering water–rock reactions results in a 15 °C lower exploitation temperature, with a 12.5 % increase in reservoir average porosity. In conclusion, when researching a long-term operating EGS, it is necessary to comprehensively consider the influences of reservoir rock parameters, physical properties of injected fluid, water–rock reaction and other factors. And in the future, attention shall be paid to the two-way coupling of chemical reaction and mechanical deformation of other mineral compositions in the reservoir to the hydro-thermo-chemical field influence, so as to provide more accurate and reliable prediction for the engineering development and utilization of EGS reservoirs.

Coupled hydro-mechanical-chemical simulation of CCUS-EOR with static and dynamic microscale effects in tight reservoirs

Tight reservoir can be potentially stimulated via CO2 injection and serves as potential sites for CO2 storage. However, simplifying flow mechanisms in hydro-mechanical-chemical coupling simulations can cause significant deviations in forecasting productivity and storage performance. In this study, a coupled hydro-mechanical-chemical model with both static and dynamic microscale effects was established for the first time. We characterized the impact of micro- and nanopores on the multicomponent thermodynamics and multiphase flow of CO2 and in-situ oil by considering the critical property shift, capillary pressure, and boundary slip. The matrix and hydraulic fracture system were constructed based on the embedded discrete fracture model (EDFM). The effect of mineral reaction in the matrix and time-varying width and permeability of propped fractures were also involved in the model to address practical field-scale problems. An iteratively coupled scheme was used in a more comprehensive model to compute the flow and mechanical parameters at each time step, with the impact of different degrees of microscale effects studied by changing the proportions of micropores and nanopores. Two fluid models with different minimum miscible pressures (MMPs) were used to simulate the miscible and immiscible production processes. The stress sensitivity was analyzed based on the Biot poroelasticity theory and time-varying fracture conductivity, with the results suggesting that stress sensitivity can reduce overall production by slower outward pressure movement but can inhibit gas channeling and breakthrough to a certain extent. The detailed analysis of microscale effects, miscibility, and stress sensitivity in this work is of practical significance for tight reservoir development and CO2 geological storage.

A Continuous Projection-Based EDFM Model for Flow in Fractured Reservoirs

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.

An improved dual-porosity dual-permeability modeling workflow for representing nonplanar hydraulic fractures

The Dual-Porosity Dual-Permeability (DPDK) model is commonly used for upscaling and simulating fractured reservoirs. However, many common upscaling approaches lead to disconnected fracture, particularly when simulating Discrete Fracture Networks (DFN) and nonplanar hydraulic fractures that are not aligned with the axes of corner-point grids supported by most reservoir simulation packages using the Two-Point Flux Approximation (TPFA) technique for flow and mass transfer calculations. This misalignment could result in inaccurate computed fluxes when fractures are disconnected in the upscaling process. Our previous works attempted to address this problem in DFNs by detecting misalignments and adjusting DPDK fracture parameters locally. However, such methods required explicit knowledge of the fracture coordinates. This paper introduces a novel approach based on area interpolation, which identifies disconnected fractures from fracture images without extracting fracture coordinates, significantly improving detection efficiency. This study primarily focuses on nonplanar fractures, aiming to simulate them using the DPDK model accurately. The simulations are compared with those obtained using the Embedded Discrete Fracture Model (EDFM). This work illustrates how nonplanar hydraulic fractures can be effectively simulated in a DPDK model. Our results demonstrate that the adjusted/corrected DPDK model can offer superior or comparable performance to an EDFM for simulating nonplanar fractures. The proposed method is flexible and readily applied in commercial simulation software.

Enhanced gas production from low-permeability hydrate reservoirs based on embedded discrete fracture models: Influence of branch parameters

The low permeability of marine hydrate reservoirs makes it difficult for trail results to meet the demand for exploitation. Hydraulic fracturing and multi-branch wells are the primary methods for enhancing productivity. This study proposed a new production enhancement method of multi-branch wells combined with multi-stage fracturing (MWMF) based on the embedded discrete fracture model (EDFM). By simulation of the Shenhu area, the multi-physical field evolution of the MWMF production process was first revealed, followed by the systematic analysis of the MWMF production enhancement effect with branch parameters. Results indicated that the cumulative gas production of MWMF increased by 327% compared with only horizontal wells. The production of four-branch wells exhibited a 7% reduction compared to horizontal wells using the MWMF method, suggesting increased branch numbers inhibit production. Increasing branch length was positively correlated with enhanced production. Notably, the influence of branch length on gas production became more pronounced as the number of branches increased. The interface of the three-phase layer (TPL) and hydrate-bearing layer (HBL) was the most suitable location for branch well placement. This novel study provides valuable insights into new applications of the MWMF method in developing low-permeability hydrate reservoirs.

General Optimization Framework of Water Huff-n-Puff Based on Embedded Discrete Fracture Model Technology in Fractured Tight Oil Reservoir: A Case Study of Mazhong Reservoir in the Santanghu Basin in China

Summary Water injection huff-n-puff (WHnP) is currently an important technology to improve the recovery of tight reservoirs. On the one hand, this technology can replenish the formation energy, and on the other hand, it can effectively replace the oil in a tight reservoir. In this paper, the effect of WHnP on cumulative oil production and oil increase rate is simulated and analyzed by comparing depleted development and WHnP scenarios, using numerical simulation methods. A field-scale numerical simulation was modeled based on typical fluid, reservoir, and fracture characteristics of Mazhong tight oil, coupled with geomechanical effects, stress sensitivity, and embedded discrete fractures. The result of different WHnP cycles is studied, and the limiting WHnP cycle is determined to be four cycles. The WHnP efficiency is compared for different permeability scales from 0.005 to 1 md, and it is determined that WHnP at a permeability of 0.01 md resulted in the largest production enhancement. Subsequently, sensitivity studies are conducted using an orthogonal experimental design for six uncertain parameters, including the WHnP cycle, production pressure difference, permeability, natural fracture density, hydraulic fracture half-length, and conductivity. The results show that throughput period and permeability are important parameters affecting cumulative oil production, and permeability and natural fracture density are important parameters affecting oil increase rate. In addition, contour plots of permeability and WHnP cycle, hydraulic fracture half-length, and conductivity are generated. Based on these plots, the optimal conditions with better enhanced recovery results in different WHnP scenarios can be easily determined. This study can better solve the problems encountered in WHnP of tight reservoirs and provide a theoretical basis for stable and efficient development.

Fractional model for simulating Long-Term fracture conductivity decay of shale gas and its influences on the well production

Due to the high-content of clay and kerogen, shale will always show viscoelastic mechanical behaviors during the development of shale gas, which will lead to the increase of proppant embedment and do harm to gas recovery from shale reservoirs. In the previous studies, viscoelastic mechanical behaviors of reservoir rock had not been coupled with productivity model of gas well and the long-term fracture conductivity was overestimated. In order to figure out the creep damage to long-term fracture conductivity and predict the estimated ultimate recovery of shale gas wells accurately, a novel time-varying fracture conductivity model based on fractional calculus was developed for simulating the long-term decay of fracture conductivity. Proppant deformation, proppant embedment, and shale creep described by fractional Kelvin model were taken into consideration in the time-varying fracture conductivity model and it was coupled with embedded discrete fracture model (EDFM) to simulate the well performance. Simulation results show that: Daily gas production curve simulated by the EDFM with creep damage under field conditions of a shale gas well in Sichuan Province, China was aligned with its production data. The damage rate of cumulative production considering shale creep is more than twice that only caused by proppant deformation and proppant embedment. And the formation viscous modulus determines the strength of the shale viscoelastic mechanical behaviors. According to formation viscous modulus, the shale reservoirs can be divided into three types: Type I with strong creep damage (E2v < 5GPa), Type Ⅱ with moderate creep damage (5GPa < E2v < 30GPa), and Type III with few creep damage (E2v > 30GPa).

Thermal-hydraulic-mechanical-chemical modeling and simulation of an enhanced geothermal system based on the framework of extended finite element methods - Embedded discrete fracture model

The thermo-hydro-mechanical-chemical (THMC) coupling process plays a crucial role in Enhanced Geothermal System (EGS), particularly during long-term heat extraction. However, most models for fractured reservoirs are computationally expensive, with very dense grids required, especially near fractures, limiting their practical use in EGS research. The embedded discrete fracture model (EDFM) can construct fracture and matrix grids independently, significantly reducing computational complexity while maintaining high accuracy. Although it is suitable for efficiently evaluating the long-term performance of heat extraction in fractured reservoirs, there are few THMC-coupled models based on EDFM, and THMC coupling effects have often been overlooked in evaluations of the environmental benefits of EGS. To address this, a fully THMC-coupled model based on EDFM and the extended finite element method (XFEM) is proposed and verified. The evolution of heat production and environmental benefits of an EGS over 30 years are presented. The results show that the production temperature and electric power remain highly efficient in the first 5 years and decrease by 7.8% and 15.4% respectively over 15 years. Moreover, the total amount of extracted heat during this period is 6.52 × 1012 kJ, which is equivalent to saving 22.26 × 108 kg of coal consumption and reducing CO2 emissions by 5.83 Mt, SO2 emissions by 189.22 × 105 kg, and NOx emissions by 166.96 × 105 kg. These findings highlight the significant potential of geothermal energy for energy supply and environmental benefits. Additionally, the study investigates the effects of critical operating and physical parameters on the production performance of EGS, including injection temperature, injection flow rate, initial reservoir temperature, and initial reservoir permeability. This work serves as a reference for both the theoretical THMC coupled model and practical EGS engineering.