3‐D mesoscale simulation of crack‐permeability coupling in the Brazilian splitting test

In this paper, mesoscale hydromechanical simulations are performed to study (1) fracture features and (2) crack‐gas permeability coupling evolution in the context of the tensile splitting test. The mesostructure is based on a 2‐phase 3‐D representation of heterogeneous materials, such as concrete, where stiff aggregates are embedded into a mortar matrix. To take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account microcracking. This mechanical model is cast into the framework of the enhanced finite element method. Concerning the coupling with gas permeability, a double‐porosity method is used to simulate the flow through the cracks and the porosity. The apparent gas permeability is afterwards evaluated by a homogenization method. On the basis of finite element simulations, influence of aggregate size on ultimate crack opening, macroscopic ultimate tensile stress, total dissipated energy, and gas permeability evolution is numerically investigated. Furthermore, gas permeability evolution is also compared with experimental results from the literature. In addition, in the spirit of a sequential multiscale approach, macroscale gas permeability equations are identified from the hydromechanical results coming from the mesoscale computations. These equations lead to a relation between macroscale gas permeability evolution and crack opening. Besides, we show how the aggregate size influences the percolation threshold and that after this threshold, a cubic relation between macroscale gas permeability and crack opening is obtained.     

A shear‐dilation‐based model for evaluation of hydraulically stimulated naturally fractured reservoirs

The role of shear dilation as a mechanism of enhancing fluid flow permeability in naturally fractured reservoirs was mainly recognized in the context of hot dry rock (HDR) geothermal reservoir stimulation. Simplified models based on shear slippage only were developed and their applications to evaluate HDR geothermal reservoir stimulation were reported. Research attention is recently focused to adjust this stimulation mechanism for naturally fractured oil and gas reservoirs which reserve vast resources worldwide. This paper develops the overall framework and basic formulations of this stimulation model for oil and gas reservoirs. Major computational modules include: natural fracture simulation, response analysis of stimulated fractures, average permeability estimation for the stimulated reservoir and prediction of an average flow direction. Natural fractures are simulated stochastically by implementing ‘fractal dimension’ concept. Natural fracture propagation and shear displacements are formulated by following computationally efficient approximate approaches interrelating in situ stresses, natural fracture parameters and stimulation pressure developed by fluid injection inside fractures. The average permeability of the stimulated reservoir is formulated as a function of discretized gridblock permeabilities by applying cubic law of fluid flow. The average reservoir elongation, or the flow direction, is expressed as a function of reservoir aspect ratio induced by directional permeability contributions. The natural fracture simulation module is verified by comparing its results with observed microseismic clouds in actual naturally fractured reservoirs. Permeability enhancement and reservoir growth are characterized with respect to stimulation pressure, in situ stresses and natural fracture density applying the model to two example reservoirs. Copyright © 2002 John Wiley & Sons, Ltd.     

Transient solution for a plane‐strain fracture driven by a shear‐thinning,power‐law fluid

This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical Modeling of Pore Pressure Influence on Fracture Evolution in Brittle Heterogeneous Rocks

Rock is a heterogeneous geological material. When rock is subjected to internal hydraulic pressure and external mechanical loading, the fluid flow properties will be altered by closing, opening, or other interaction of pre-existing weaknesses or by induced new fractures. Meanwhile, the pore pressure can influence the fracture behavior on both a local and global scale. A finite element model that can consider the coupled effects of seepage, damage and stress field in heterogeneous rock is described. First, two series of numerical tests in relatively homogeneous and heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. Second, to examine the initiation of hydraulic fractures and their subsequent propagation, a series of numerical simulations of the behavior of two injection holes inside a saturated rock mass are carried out. The rock is subjected to different initial in situ stress ratios and to an internal injection (pore) pressure at the two injection holes. Numerically, simulated results indicate that tensile fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. In addition, the heterogeneity of rock, the initial in situ stress ratio (K), the distance between two injection holes, and the difference of the pore pressure in the two injection holes all play important roles in the initiation and propagation of hydraulic fractures. At relatively close spacing and when the two principal stresses are of similar magnitude, the proximity of adjacent injection holes can cause fracturing to occur in a direction perpendicular to the maximum principal stress.     

Pore‐scale modeling of fluid‐particles interaction and emerging poromechanical effects

A micro‐hydromechanical model for granular materials is presented. It combines the discrete element method for the modeling of the solid phase and a pore‐scale finite volume formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the discrete element method pore‐scale finite volume coupling and Biot's theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions. Copyright © 2013 John Wiley & Sons, Ltd.     

Flow–stress coupled permeability tensor for fractured rock masses

In this paper a new analytical model is proposed to determine the permeability tensor for fractured rock masses based on the superposition principle of liquid dissipation energy. This model relies on the geometrical characteristics of rock fractures and the corresponding fracture network, and demonstrates the coupling effect between fluid flow and stress/deformation. This model empirically considers the effect of pre‐peak shear dilation and shear contraction on the hydraulic behavior of rock fractures and can be used to determine the applicability of the continuum approach to hydro‐mechanical coupling analysis. Results of numerical analysis presented in this paper show that the new model can effectively describe the permeability of fractured rock masses, and can be applied to the coupling analysis of seepage and stress fields. Copyright © 2008 John Wiley & Sons, Ltd.     

充水节理岩体中大断面隧洞开挖的数值模型研究

采用非饱和的渗流应力耦合模型分析了糯扎渡水电站2#导流洞的开挖过程,导流洞部分洞身穿过节理带,洞顶水头较高。详细地讨论了高水头和节理带对施工过程的影响。节理带采用描述高密度平行节理组的各向异性节理本构来逼近;考虑开挖引起的介质变形对渗透系数的影响;考虑排水引起的饱和度变化对渗透系数的影响。所用的非饱和瞬态耦合模型可以模拟出开挖引起的EDZ区域孔隙水压力急剧升高、有效应力减小、渗透系数动态的变化以及排水对洞室稳定性的提高。数值模拟的计算结果与国外类似试验的一般性观测结论相吻合,因此,可以用来评价水位以下隧洞施工方法和施工速度的合理性和经济性。     

Comparison of Permeability and Groutability of Ostur Dam Site Rock Mass for Grout Curtain Design

The focus of this study is the empirical hydromechanical behaviour of the Ostur dam site rock mass. The area surrounding the dam mostly consists of diorite and andesite, with primary fractures and hydrothermal veins. The hydromechanical behaviour of the rocks was determined using 500 water pressure tests at 5-m intervals. The hydrothermal veins and 2,739 discontinuities were studied and mapped along the dam axis. As a result, it was possible to design an optimum grout curtain for the dam axis. The empirical hydromechanical behaviour of the rock was studied to determine water flow and grout pressurised flow during the field tests that were conducted on two representative A-series grouting operation boreholes (one borehole for each abutment). The secondary permeability index (SPI), Lugeon value (LU), rock quality designation (RQD) and cement take (CT) values are presented and compared in this article. It is concluded that permeability and groutability are mostly controlled by the specifications and characteristics of the veins, especially in shallow areas and lower depths. A procedure is proposed based on a comparison of the trends in the RQD–SPI and LU–CT, and it is suggested that the areas with diverging trends require no treatment and that those with converging trends require heavy treatment. Additional complementary studies that were conducted during the construction stage have validated these results.     

Thermo‐hydro‐mechanical modeling with Langmuir's adsorption isotherm of the CO2 injection in coal

In this paper, we used a theoretical model for the variation of Eulerian porosity, which takes into account the adsorption process known to be the main mechanism of production or sequestration of gas in many reservoir of coal. This process is classically modeled using Langmuir's isotherm. After implementation in Code_Aster, a fully coupled thermo‐hydro‐mechanical analysis code for structures calculations, we used numerical simulations to investigate the influence of coal's hydro‐mechanical properties (Biot's coefficient, bulk modulus), Langmuir's adsorption parameters, and the initial liquid pressure in rock mass during CO₂ injection in coal. These simulations showed that the increase in the values of Langmuir's parameters and Biot's coefficient promotes a reduction in porosity because of the adsorption process when the gas pressure increases. Low values of bulk modulus increase the positive effect (i.e., increase) of hydro‐mechanical coupling on the porosity evolution. The presence of high initial liquid pressure in the rock mass prevents the progression of injected gas pressure when CO₂ dissolution in water is taken into account. Copyright © 2014 John Wiley & Sons, Ltd.     

各向异性软岩的变形与渗流耦合特性试验研究

根据泥质粉砂岩和泥岩在垂直和平行于层理面的条件下进行的三轴压缩和渗流试验,得到了不同围压及岩石成层条件下泥质粉砂岩和泥岩的弹性模量,建立了基于层理面夹角和围压的软岩弹性模量控制方程。渗透张量与应力的耦合关系是各向异性渗流耦合分析的关键问题,通过引入应力主轴与渗透主轴非一致时渗透张量与应力的响应关系,建立了各向异性渗透张量与应力耦合的控制方程,并对比了试验数据与计算结果,为各向异性软岩渗流应力耦合分析模型的建立奠定了理论基础。     

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.     

Study of pore pressure change during mining and its application on water inrush prevention: a numerical simulation case in Zhaogezhuang coalmine,China

Most of water inrush incidents in coalmines are originally derived from a seepage flow through rock mass fractures, particularly in fault zones. Water inrush is typically caused by hydromechanical coupling interactions induced by human activities. Taking the Zhaogezhuang coalmine in northern China as an example, the progress of a lagging water inrush, which occurred at a depth of about ?1,100 m, was simulated and analyzed based on the hydromechanical coupling mechanism. A 3D model incorporating the main structures of the study area was constructed based on the geological data and field investigation. The equivalent continuum medium was employed to describe fault zones. Processes of determining the mechanical, rheological and hydraulic parameters are discussed in details. Three hydromechanical coupling models are applied: (1) the elastoplastic strain-fluid coupling mechanism in rock mass within the fault zone, (2) the inelastic creep-fluid coupling mechanism in rock materials within the fault gouge, and (3) the stress-permeability coupling mechanism in the fractured porous rocks. The evolution of water-recharge zones along the fault zone was presented in different mining phases. By comparing the simulated pore pressures with the in situ monitored ones, the following conclusions can be drawn: (1) the actual hydraulic behaviors are a combination of the long-term trends and short-term effects; (2) the creep-fluid coupling model reflects the rock hydraulic behaviors of long-term trends, while the elastoplastic strain-fluid coupling model demonstrates the short-term effects; (3) a prediction method called ‘time window’ for the risk of the lagging water inrush is proposed. Its feasibility is discussed.     

岩石损伤过程中的热-流-力耦合模型及其应用初探

岩石损伤过程热-流-力（THM）耦合问题的研究对于深部采矿等许多工程领域都具有重要的理论意义。以岩石的损伤为主线,在多场耦合分析方程中引入损伤变量,基于质量守恒和能量守恒原理,提出岩体损伤过程中的THM耦合模型。通过把均匀弹性介质THM耦合响应的模拟结果与理论分析结果进行对比,验证了程序及有限元实施的正确性。然后,用该耦合模型进行了不同地应力条件下流固耦合过程的数值模拟,探讨了水压力对于岩石损伤过程的作用机制。数值模拟表明,水压力导致了拉伸损伤范围的扩大和损伤程度的加剧,同时亦对剪切损伤具有抑制作用。     

The influence of pumping parameters in fluid‐driven fractures in weak porous formations

In this work, we investigate the main pumping parameters that influence a fluid‐driven fracture in cohesive poroelastic and poroelastoplastic weak formations. These parameters include the fluid viscosity and the injection rate. The first parameter dominates in the mapping of the propagation regimes from toughness to viscosity, whereas the second parameter controls the storage to leak‐off dominated regime through diffusion. The fracture is driven in weak permeable porous formation by injecting an incompressible viscous fluid at the fracture inlet assuming that the fracture propagates under plane strain conditions. Fluid flow in the fracture is modeled by lubrication theory. Pore fluid movement in the porous formation is based on the Darcy law. The coupling follows the Biot theory, whereas the irreversible rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fracture propagation criterion is based on the cohesive zone approach. Leak‐off is also considered. The investigation is performed numerically with the FEM to obtain the fracture opening, length, and propagation pressure versus time. We demonstrate that pumping parameters influence the fracture geometry and fluid pressures in weak formations through the viscous fluid flow and the diffusion process that create back stresses and large plastic zones as the fracture propagates. It is also shown that the product of the propagation velocity and fluid viscosity, µv that appears in the scaling controls the magnitude of the plastic zones and influences the net pressure and fracture geometry. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions for the case of weak porous formation. Copyright © 2014 John Wiley & Sons, Ltd.     

岩石裂隙的非饱和渗透特性及其演化规律研究

岩石裂隙的非饱和渗透特性是岩土、能源和环境等领域科学研究中的热点问题。采用三维激光扫描获取花岗岩裂隙的表面形貌特征,分析裂隙微观形貌特征对非饱和渗透特性的影响。研究在张拉、压缩、剪切等复杂荷载作用下裂隙开度分布的演化规律,建立复杂荷载作用下岩石裂隙非饱和毛细压力曲线演化模型。基于裂隙的微观形貌特征推导了岩石裂隙非饱和相对渗透系数模型,通过与试验数据对比,验证了模型的准确性和有效性,并在此基础上建立了复杂荷载作用下岩石裂隙非饱和相对渗透系数演化模型。研究成果对非饱和条件下裂隙岩体的水-力耦合机制研究具有一定指导意义。     

Poro‐elasto‐plastic response of an unconsolidated formation confined with stiff seal rocks under radial injection

In this article, we evaluate geomechanics of fluid injection from a fully penetrating vertical well into an unconsolidated formation confined with stiff seal rocks. The coupled behavior of an isotropic, homogeneous sand layer is studied under injection pressures that are high enough to induce plasticity yet not fracturing. Propagation of the significant influence zone surrounding the injection borehole, quantified by the extent of the plastic domain in the elasto‐plastic model, is examined for the first time. First, a new fully coupled axisymmetric numerical model is developed. A comprehensive assessment is performed on pore pressures, stresses/strains, and failure planes during the entire transient period of an injection cycle. Results anticipate existence of five distinctive zones in terms of plasticity state: liquefaction at wellbore; two inner plastic domains surrounding the wellbore, where failure occurs along two planes and major principal stress is in vertical direction; remaining of the plastic domain, where formation fails along one plane and major principal stress is in radial direction; and a non‐plastic region. Failure mechanism at the wellbore is found to be shear followed by liquefaction. Next, a novel methodology is proposed based on which new weakly coupled poro‐elasto‐plastic analytical solutions are derived for all three stress/strain components. Unlike previous studies, extension of the plastic zone is obtained as a function of injection pressure, incorporating plasticity effects on the subsequent elastic domain. Solutions, proven to be a good approximation of numerical simulations, offer a huge advantage as the run time of coupled numerical simulations is considerably long. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled finite‐element simulation of injection well testing in unconsolidated oil sands reservoir

This paper presents a finite‐element (FE) model for simulating injection well testing in unconsolidated oil sands reservoir. In injection well testing, the bottom‐hole pressure (BHP) is monitored during the injection and shut‐in period. The flow characteristics of a reservoir can be determined from transient BHP data using conventional reservoir or well‐testing analysis. However, conventional reservoir or well‐testing analysis does not consider geomechanics coupling effects. This simplified assumption has limitations when applied to unconsolidated (uncemented) oil sands reservoirs because oil sands deform and dilate subjected to pressure variation. In addition, hydraulic fracturing may occur in unconsolidated oil sands when high water injection rate is used. This research is motivated in numerical modeling of injection well testing in unconsolidated oil sands reservoir considering the geomechanics coupling effects including hydraulic fracturing. To simulate the strong anisotropy in mechanical and hydraulic behaviour of unconsolidated oil sands induced by fluid injection in injection well testing, a nonlinear stress‐dependent poro‐elasto‐plastic constitutive model together with a strain‐induced anisotropic permeability model are formulated and implemented into a 3D FE simulator. The 3D FE model is used to history match the BHP response measured from an injection well in an oil sands reservoir. Copyright © 2013 John Wiley & Sons, Ltd.     

A two‐dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing

Within the framework of our discontinuous deformation analysis for rock failure algorithm, this paper presents a two‐dimensional coupled hydromechanical discontinuum model for simulating the rock hydraulic fracturing process. In the proposed approach, based on the generated joint network, the calculation of fluid mechanics is performed first to obtain the seepage pressure near the tips of existing cracks, and then the fluid pressure is treated as linearly distributed loads on corresponding block boundaries. The contribution of the hydraulic pressure to the initiation/propagation of the cracks is considered by adding the components of these blocks into the force matrix of the global equilibrium equation. Finally, failure criteria are applied at the crack tips to determine the occurrence of cracking events. Several verification examples are simulated, and the results show that this newly proposed numerical model can simulate the hydraulic fracturing process correctly and effectively. Although the numerical and experimental verifications focus on one unique preexisting crack, because of the capability of discontinuous deformation analysis in simulating block‐like structures, the proposed approach is capable of modeling rock hydraulic fracturing processes. Copyright © 2014 John Wiley & Sons, Ltd.     

Fully coupled simulation of a hydraulic fracture interacting with natural fractures with a hybrid discrete‐continuum method

A hybrid discrete‐continuum numerical scheme is developed to study the behavior of a hydraulic fracture crossing natural fractures. The fully coupled hybrid scheme utilizes a discrete element model for an inner domain, within which the hydraulic fracture propagates and interacts with natural fractures. The inner domain is embedded in an outer continuum domain that is implemented to extend the length of the hydraulic fracture and to better approximate the boundary effects. The fracture is identified to propagate initially in the viscosity‐dominated regime, and the numerical scheme is calibrated by using the theoretical plane strain hydraulic fracture solution. The simulation results for orthogonal crossing indicate three fundamental crossing scenarios, which occur for various stress ratios and friction coefficients of the natural fracture: (i) no crossing, that is, the hydraulic fracture is arrested by the natural fracture and makes a T‐shape intersection; (ii) offset crossing, that is, the hydraulic fracture crosses the natural fracture with an offset; and (iii) direct crossing, that is, the hydraulic fracture directly crosses the natural fracture without diversion. Each crossing scenario is associated with a distinct net pressure history. Additionally, the effects of strength contrast and stiffness contrast of rock materials and intersection angle between the hydraulic fracture and the natural fracture are also investigated. The simulations also illustrate that the level of fracturing complexity increases as the number and extent of the natural fractures increase. As a result, we can conclude that complex hydraulic fracture propagation patterns occur because of complicated crossing behavior during the stimulation of naturally fractured reservoirs. Copyright © 2017 John Wiley & Sons, Ltd.     

An explicitly coupled hydro‐geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks

Modeling hydraulic fracturing in the presence of a natural fracture network is a challenging task, owing to the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and existing natural interfaces. Understanding these complex interactions through numerical modeling is critical to the design of optimum stimulation strategies. In this paper, we present an explicitly integrated, fully coupled discrete‐finite element approach for the simulation of hydraulic fracturing in arbitrary fracture networks. The individual physical processes involved in hydraulic fracturing are identified and addressed as separate modules: a finite element approach for geomechanics in the rock matrix, a finite volume approach for resolving hydrodynamics, a geomechanical joint model for interfacial resolution, and an adaptive remeshing module. The model is verified against the Khristianovich–Geertsma–DeKlerk closed‐form solution for the propagation of a single hydraulic fracture and validated against laboratory testing results on the interaction between a propagating hydraulic fracture and an existing fracture. Preliminary results of simulating hydraulic fracturing in a natural fracture system consisting of multiple fractures are also presented. Copyright © 2012 John Wiley & Sons, Ltd.