An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation

A numerical modeling framework is described that is able to calculate the coupled processes of fluid flow, geomechanics, and rock failure for application to general engineering problems related to reservoir stimulation, including hydraulic fracturing and shear stimulation. The numerical formulation employs the use of an embedded fracture modeling approach, which provides several advantages over more traditional methods in terms of computational complexity and efficiency. Specifically, the embedded fracture modeling strategy avoids the usual requirement that the discretization of the fracture domain conforms to the discretization of the rock volume surrounding the fractures. As fluid is exchanged between the two domains, conservation of mass is guaranteed through a coupling term that appears as a simple source term in the governing mass balance equations. In this manner, as new tensile fractures nucleate and propagate subject to mechanical effects, numerical complexities associated with the introduction of new fracture control volumes are largely negated. In addition, the ability to discretize the fractures and surrounding rock volume independently provides the freedom to choose an acceptable level of discretization for each domain separately. Three numerical examples were performed to demonstrate the utility of the embedded fracture model for application to problems involving fluid flow, mechanical deformation, and rock failure. The results of the numerical examples confirm that the embedded fracture model was able to capture accurately the complex and nonlinear evolution of reservoir permeability as new fractures propagate through the reservoir and as fractures fail in shear.     

A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.     

基于DDA方法一种流-固耦合模型的建立及裂隙体渗流场分析和应用

以非连续变形分析方法（DDA）为基础并采用稳态流体计算方法将二者结合进行裂隙岩体流-固耦合分析。利用DDA方法生成裂隙岩体模型,在此基础上采用矩阵搜索等方法形成新的裂隙水通网络模型。采用稳态迭代算法和立方定律求得裂隙水压力,并把裂隙水压力作为线载荷施加到块体边界,在DDA算法中每个迭代步完成后更新裂隙开度和水压值,与DDA算法结合研究裂隙水与块体之间相互作用关系。利用以上裂隙岩体流-固耦合计算方法研究了某水封油库开挖和运行过程洞室围岩流量和密封性,为该工程预测水封效果提供了有益的主要依据,也是国内首次采用DDA方法做大型工程的流-固耦合模型分析。     

Discrete fracture model for coupled flow and geomechanics

We present a fully implicit formulation of coupled flow and geomechanics for fractured three-dimensional subsurface formations. The Reservoir Characterization Model (RCM) consists of a computational grid, in which the fractures are represented explicitly. The Discrete Fracture Model (DFM) has been widely used to model the flow and transport in natural geological porous formations. Here, we extend the DFM approach to model deformation. The flow equations are discretized using a finite-volume method, and the poroelasticity equations are discretized using a Galerkin finite-element approximation. The two discretizations—flow and mechanics—share the same three-dimensional unstructured grid. The mechanical behavior of the fractures is modeled as a contact problem between two computational planes. The set of fully coupled nonlinear equations is solved implicitly. The implementation is validated for two problems with analytical solutions. The methodology is then applied to a shale-gas production scenario where a synthetic reservoir with 100 natural fractures is produced using a hydraulically fractured horizontal well.     

Fracture Permeability Alteration due to Chemical and Mechanical Processes: A Coupled High-Resolution Model

Reactive fluid-flow experiments in fractures subjected to normal stress suggest the potential for either increased or decreased permeability resulting from fracture-surface dissolution. We present a computational model that couples mechanical deformation and chemical alteration of fractures subjected to constant normal stress and reactive fluid flow. The model explicitly represents micro-scale roughness of the fracture surfaces and calculates elastic deformation of the rough surfaces using a semi-analytical approach that ensures the surfaces remain in static equilibrium. A depth-averaged reactive transport model calculates chemical alteration of the surfaces, which leads to alteration of the contacting fracture surfaces. The mechanical deformation and chemical alteration calculations are explicitly coupled, which is justified by the disparate timescales required for equilibration of mechanical stresses and reactive transport processes. An idealized analytical representation of dissolution from a single contacting asperity shows that under reaction-limited conditions, contacting asperities can dissolve faster than the open regions of the fracture. Computational simulations in fractures with hundreds of contacting asperities show that the transition from transport-limited conditions (low flow rates) to reaction-rate-limited conditions (high flow rates) causes a shift from monotonically increasing permeability to a more complicated process in which permeability initially decreases and then increases as contacting asperities begin to dissolve. These results are qualitatively consistent with a number of experimental observations reported in the literature and suggest the potential importance of the relative magnitude of mass transport and reaction kinetics on the evolution of fracture permeability in fractures subjected to combined normal stress and reactive fluid flow.     

Unified thermo-compositional-mechanical framework for reservoir simulation

We present a reservoir simulation framework for coupled thermal-compositional-mechanics processes. We use finite-volume methods to discretize the mass and energy conservation equations and finite-element methods for the mechanics problem. We use the first-order backward Euler for time. We solve the resulting set of nonlinear algebraic equations using fully implicit (FI) and sequential-implicit (SI) solution schemes. The FI approach is attractive for general-purpose simulation due to its unconditional stability. However, the FI method requires the development of a complex thermo-compositional-mechanics framework for the nonlinear problems of interest, and that includes the construction of the full Jacobian matrix for the coupled multi-physics discrete system of equations. On the other hand, SI-based solution schemes allow for relatively fast development because different simulation modules can be coupled more easily. The challenge with SI schemes is that the nonlinear convergence rate depends strongly on the coupling strength across the physical mechanisms and on the details of the sequential updating strategy across the different physics modules. The flexible automatic differentiation-based framework described here allows for detailed assessment of the robustness and computational efficiency of different coupling schemes for a wide range of multi-physics subsurface problems.     

Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework

Rock mass failure is a particularly complex process that involves the opening and sliding of existing discontinuities and the fracturing of the intact rock. This paper adopts an advanced discretisation approach to simulate rock failure problems within the discontinuous deformation analysis (DDA) framework. The accuracy of this approach in continuum analysis is verified first. Then, the advanced discretisation approach for fracturing modelling is presented, and the discretisation strategy is discussed. Sample rock static failures are simulated and the results are compared with experimental results. Thereafter, with a generalised definition of the artificial joints, this approach is further extended and applied in the simulation of blast-induced rock mass failures in which the instant explosion gas pressure obtained by the detonation pressure equation of state is loaded on the main blast chamber walls and the induced surrounding connected fracture surfaces. In the simulation instance of rock mass cast blasting, the whole process, including the blast chamber expansion, explosion gas penetration, rock mass failure and cast, and the formation of the final blasting pile, is wholly reproduced.     

Numerical modeling of stress-permeability coupling in rough fractures

A numerical model is described for coupled flow and mechanical deformation in fractured rock. The mechanical response of rock joints to changes in hydraulic pressure is strongly influenced by the geometric characteristics of the joint surfaces. The concept of this work is to combine straightforward finite element solutions with complex and realistic fracture surface geometry in order to reproduce the non-linear stress-deformation-permeability coupling that is commonly observed in fractures. Building on the numerous studies that have expanded the understanding of the key parameters needed to describe natural rough-walled fractures, new methods have been developed to generate a finite element mesh representing discrete fractures with realistic rough surface geometries embedded in a rock matrix. The finite element code GeoSys/Rockflow was then used to simulate the coupled effects of hydraulic stress, mechanical stress, and surface geometry on the evolving permeability of a single discrete fracture. The modeling concept was experimentally verified against examples from the literature. Modeling results were also compared to a simple interpenetration model.     

基于改进颗粒流声发射片的地下厂房洞室围岩局部损伤细观机制研究

通过改进的PFC-FLAC离散−连续耦合计算方法,提出了一种基于FLAC连续模型耦合区域节点速率双线性插值的PFC颗粒流声发射片模拟方法以及基于声发射强度的围岩破坏区深度细观角度判别方法,并将其应用于地下厂房洞室开挖面、岩锚吊车梁与岩壁接触面等局部围岩损伤细观机制与破化特性研究。研究结果表明：浅层围岩接触力链逐渐稀疏,大量微裂纹发育并汇集成宏观裂隙,最终出现浅层破裂区,呈拉裂破坏;随着距离开挖面的增大,围岩从开挖前期受力较大产生破坏、到开挖后期只有少量微裂纹产生,对应了围岩回弹卸荷区深度。在岩壁围岩劣化和吊车梁超载的情况下,吊车梁与岩壁竖直接触面和倾斜接触面分别发育大量拉裂纹和剪裂纹,宏观表现为拉裂破坏与滑移破坏。上述分析结果与三维有限元方法相一致,并弥补了后者围岩破坏显示方法单一、难以描述围岩损伤程度变化的缺点,为研究地下厂房洞室大变形与应力集中部位的宏细观特性与损伤机制提供参考。     

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal design of hydraulic fracturing in porous media using the phase field fracture model coupled with genetic algorithm

We present a framework for the coupling of fluid-filled fracture propagation and a genetic inverse algorithm for optimizing hydraulic fracturing scenarios in porous media. Fracture propagations are described by employing a phase field approach, which treats fracture surfaces as diffusive zones rather than of interfaces. Performance of the coupled approach is provided with applications to numerical experiments related to maximizing production or reservoir history matching for emphasizing the capability of the framework.     

基于分形维数的巷道围岩裂隙演化规律研究

为探究泥质巷道受水平应力及动力扰动影响下的围岩裂隙演化规律,以盘州市山脚树矿226轨道石门为工程背景,综合运用现场调研、数值模拟、分形理论分析等研究方法,对动力扰动下泥质巷道的变形破坏特征、围岩裂隙演化规律、围岩裂隙分形演化特征等问题展开研究。结果表明:动力扰动前,巷道裂隙区和塑性区扩展范围随侧压系数的增加而逐步增大,巷道发生较大变形;受扰动后,随侧压系数的增加,围岩裂隙密度逐步增大,浅部裂隙扩展贯通并逐步延展至深部,巷道裂隙区和塑性区呈现全面不规则扩展。在扰动影响下,巷道围岩裂隙的分形维数较扰动前表现出明显的升维现象,随着侧压系数的增加,裂隙网络更为复杂,浅部裂隙进一步向深部蔓延,使岩体破裂程度更大,导致巷道发生严重变形破坏。      

Fully coupled hydro-mechanical numerical manifold modeling of porous rock with dominant fractures

Coupled hydro-mechanical (HM) processes are significant in geological engineering such as oil and gas extraction, geothermal energy, nuclear waste disposal and for the safety assessment of dam foundations and rock slopes, where the geological media usually consist of fractured rock masses. In this study, we developed a model for the analysis of coupled hydro-mechanical processes in porous rock containing dominant fractures, by using the numerical manifold method (NMM). In the current model, the fractures are regarded as different material domains from surrounding rock, i.e., finite-thickness fracture zones as porous media. Compared with the rock matrix, these fractured porous media are characterized with nonlinear behavior of hydraulic and mechanical properties, involving not only direct (poroelastic) coupling but also indirect (property change) coupling. By combining the potential energy associated with mechanical responses, fluid flow and solid–fluid interactions, a new formulation for direct HM coupling in porous media is established. For indirect coupling associated with fracture opening/closure, we developed a new approach implicitly considering the nonlinear properties by directly assembling the corresponding strain energy. Compared with traditional methods with approximation of the nonlinear constitutive equations, this new formulation achieves a more accurate representation of the nonlinear behavior. We implemented the new model for coupled HM analysis in NMM, which has fixed mathematical grid and accurate integration, and developed a new computer code. We tested the code for direct coupling on two classical poroelastic problems with coarse mesh and compared the results with the analytical solutions, achieving excellent agreement, respectively. Finally, we tested for indirect coupling on models with a single dominant fracture and obtained reasonable results. The current poroelastic NNM model with a continuous finite-thickness fracture zone will be further developed considering thin fractures in a discontinuous approach for a comprehensive model for HM analysis in fractured porous rock masses.     

The application of remote sensing and structural analysis in groundwater exploration in basement terrains, Darfur region, Western Sudan

Darfur region is one of the most vulnerable areas in Sudan that suffer from shortage in water supply. The objective of the current study is to utilize remote sensing techniques combined with the structural analysis to recognize the most potential fracture zones for groundwater occurrences in the hard rock terrains of Darfur region. The old ductile deformation features in Darfur region delineated from Landsat imageries are used for the structural analysis to determine and classify the fractures in the hard rock terrains of the region. Based on the structural analysis conducted in this study, Darfur region was divided into two domains—the western domain of the pre-Pan-African age that is affected by the two deformational phases (D1 and D2), and the eastern domain represented by the basement related to the Pan-African orogeny. The most potential fractures in the western domain are in the NW–SE and NE–SW trends that classified as extensional and release open fractures for the deformations D1 and D2. In the eastern domain, the main potential fractures for groundwater occurrence are in E–W and N–S directions that are classified as extensional and release open fractures of the deformation D3. From the results of the structural analysis, the main potential fracture systems in Darfur region trend are NW–SE, NE–SW, and E–W directions. The intersections of these fracture systems are the most promising targets for drilling, with consideration of the topography, the rates of recharge, and the underlying geology. The geophysical data and boreholes information in Zalingei and north of El Geneina areas in West Darfur confirm the results obtained from remote sensing data and structural analysis, in which the NW–SE, NE–SW, and E–W fractures trends are the most potential fractures in Darfur region.     

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.     

Modeling competing hydraulic fracture propagation with the extended finite element method

We present an extended finite element framework to numerically study competing hydraulic fracture propagation. The framework is capable of modeling fully coupled hydraulic fracturing processes including fracture propagation, elastoplastic bulk deformation and fluid flow inside both fractures and the wellbore. In particular, the framework incorporates the classical orifice equation to capture fluid pressure loss across perforation clusters linking the wellbore with fractures. Dynamic fluid partitioning among fractures during propagation is solved together with other coupled factors, such as wellbore pressure loss (\(\Delta p_w\)), perforation pressure loss (\(\Delta p\)), interaction stress (\(\sigma _\mathrm{int}\)) and fracture propagation. By numerical examples, we study the effects of perforation pressure loss and wellbore pressure loss on competing fracture propagation under plane-strain conditions. Two dimensionless parameters \(\Gamma = \sigma _\mathrm{int}/\Delta p\) and \(\Lambda = \Delta p_w/\Delta p\) are used to describe the transition from uniform fracture propagation to preferential fracture propagation. The numerical examples demonstrate the dimensionless parameter \(\Gamma \) also works in the elastoplastic media.     

Finite element simulations of 3D planar hydraulic fracture propagation using a coupled hydro-mechanical interface element

Two-dimensional hydraulic fracturing simulations using the cohesive zone model (CZM) can be readily found in the literature; however, to our knowledge, verified 3D cohesive zone modeling is not available. We present the development of a 3D fully coupled hydro-mechanical finite element method (FEM) model (with parallel computation framework) and its application to hydraulic fracturing. A special zero-thickness interface element based on the CZM is developed for modeling fracture propagation and fluid flow. A local traction-separation law with strain softening is used to capture tensile cracking. The model is verified by considering penny-shaped hydraulic fracture and plain strain Kristianovich‑Geertsma‑de Klerk hydraulic fracture (in 3D) in the viscosity- and toughness-dominated regimes. Good agreement between numerical results and analytical solutions has been achieved. The model is used to investigate the influence of rock and fluid properties on hydraulic fracturing. Lower stiffness tip cohesive elements tend to yield a larger elastic deformation around the fracture tips before the tensile strength is reached, generating a larger fracture length and lower fracture pressure compared with higher stiffness elements. It is found that the energy release rate has almost no influence on hydraulic fracturing in the viscosity-dominated regime because the energy spent in creating new fractures is too small when compared with the total input energy. For the toughness-dominated regime, the released energy during fracturing should be accurately captured; relatively large tensile strength should be used in order to match numerical results to the asymptotic analytical solutions. It requires smaller elements when compared with those used in the viscosity-dominated regime.     

长江中下游河湖洪水演进的数值模拟

以长江中下游(宜昌-大通)防洪系统为对象,在水文、河道及湖盆地形现状条件下,建立了一个能适应各种复杂条件的一二维非恒定流模型,来进行长江干流、河网、湖泊、分蓄洪区垸及水库的洪水演进和调度仿真.所建模型的洞庭湖部分采用无结构网格二维非恒定有限体积格式,以适应湖区复杂的边界形状和保持水量平衡.河网区部分采用一维非恒定流显隐结合的分块三级算法,以准确实现河网汊点流量的自动分配和往复流动.为了提高模拟精度和扩展模拟功能,在水流数值模拟的范围内侧重讨论了内外动边界处理、分蓄洪运用及阻力项计算等环节,提出了合理可行的数值处理方法.采用20世纪80年代至90年代共6年汛期洪水资料对所建模型进行了严格的率定和检验,高精度的模拟结果证实了模型的合理性和有效性.     

Numerical Modeling of Hydraulic Fractures Interaction in Complex Naturally Fractured Formations

A recently developed unconventional fracture model (UFM) is able to simulate complex fracture network propagation in a formation with pre-existing natural fractures. A method for computing the stress shadow from fracture branches in a complex hydraulic fracture network (HFN) based on an enhanced 2D displacement discontinuity method with correction for finite fracture height is implemented in UFM and is presented in detail including approach validation and examples. The influence of stress shadow effect from the HFN generated at previous treatment stage on the HFN propagation and shape at new stage is also discussed.