A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part I: theory and formulation

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction.     

数值流形法在处理强奇异性问题时的网格无关性

数值流形方法（NMM）的最大优势在于可以统一地处理岩土力学中的连续和非连续变形问题。它在求解断裂力学问题时无需强制裂纹与数学网格保持一致,非常适合应用于岩土工程中由连续到非连续的破坏过程模拟。在裂纹扩展过程中,裂纹与数学网格的相对位置将会是任意的,如裂纹尖端可能落在网格内部、网格节点上或网格边上等。因此,对同一条裂纹,通过旋转和移动数学网格构造了它们之间的这种相对位置关系以及一些可能对计算结果产生影响的极端情况,并以应力强度因子作为衡量标准,研究了NMM在处理线弹性断裂力学问题时的网格依赖性。研究表明,NMM即使在处理强奇异性问题时依然有着很好的网格无关性,进一步证实了它在模拟裂纹扩展问题时的鲁棒性。     

An Integrated Numerical Modelling–Discrete Fracture Network Approach Applied to the Characterisation of Rock Mass Strength of Naturally Fractured Pillars

Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength. Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite element/discrete element–discrete fracture network approach it is possible to study the failure of rock masses in tension and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link between rock mass strength and rock mass classification systems.     

Correlation of numerical and physical models - an approach to the estimation of rock mass behaviour

Critical deformations in rock masses are frequently controlled by pre-existing discontinuities. In other cases, for example, Study of discontinuum models provides valuable physical spacing. Study of discontinuum models provides valuable physical insights into rock mass deformation behaviour that are not as apparent from continuum studies. Examples from both continuum analysis and discontinuum modelling by the distinct element methods are discussed. These examples include: in-situ deformation tests on columnar basalt. Development of kink bands in laminated rock. Deformation of jointed rock during fluid injection for energy production. Fracture generation in brittle rock under compression.     

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.     

乌东德水电站地下厂房层状岩体稳定性及变形机制

乌东德水电站右岸地下厂房洞室群密集、开挖规模大、地质条件复杂,开挖期间变形破坏问题突出。在地应力实测资料、工程地质特性、开挖过程分析的基础上,利用离散元程序对右岸地下厂房开挖过程进行数值模拟,再现不同模型的应力场、位移场演化过程,分析陡倾角层面对于主厂房变形的影响作用。同时,构建高精度微震监测系统,对开挖诱发的微震活动实时在线监测;分析微震事件聚集规律、S波及P波能量比值Es /Ep分布特征,识别和圈定潜在风险区域,揭示围岩变形机制。微震监测与数值模拟结果表明：在开挖卸荷作用下,陡倾角层面附近岩石破裂,微震事件聚集,能量释放,引起围岩变形破坏。围岩以结构面控制的应力驱动型张拉破坏为主,并伴随少量重力驱动型变形。该研究结果为乌东德水电站地下厂房的开挖和支护设计方案提供重要依据。     

矿山层状反倾边坡岩体移动规律的试验研究

本文基于现代工程地质力学理论与相似模拟原理, 采用地质力学模拟试验方法, 以某矿顶帮边坡为工程实例, 结合大量滑坡实例综合分析, 研究了层状反倾边坡岩体随采矿工程发展的移动规律和潜在滑坡模式。     

An efficient method for packing polygonal domains with disks for 2D discrete element simulation

The discrete element method (DEM) is frequently used in numerical simulation of the behaviour of discontinuum often encountered in granular flow, soil or rock mechanics or powder compaction. The DEM requires an assemblage of elements that need to fill the domain geometry. Generation of such arrangement of elements, such as disks in 2D DEM simulation is not a trivial task. The available methods to create the arrangements of disks can either take considerable time, have limited control over the final outcome of the disk generation or exhibit difficulty in generating a tight arrangement of disk with varying radii. This paper presents an algorithm employing principles of computational geometry to efficiently generate a tight packing of disks while addressing the common problems of disk generation. The algorithm’s performance is linear with respect to time and scales well. As a demonstration of the algorithm’s capabilities, a DEM model of an ore pass is presented.     

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.     

Use of backpropagation neural network for landslide monitoring: a case study in the higher Himalaya

Static and dynamic rock slope stability analyses were performed using a numerical discontinuum modelling technique for a 700-m high rock slope in western Norway. The rock slope has been investigated by the Geological Survey of Norway (NGU), which has been carrying out rock slide studies for the county Møre and Romsdal in western Norway. The purpose of numerical modelling was to estimate the volume of the rock mass that could potentially slide under static and dynamic forces. This estimation was required to assess the run-up heights (tsunami) in a fjord that could potentially be caused by the rockslide. Three cases have been simulated for predicting the behaviour of the rock slope. First, an initial static loading is applied in the numerical model to simulate the prevailing rock mass conditions at the site. Second, saturated and weathered joint conditions are modelled by reducing the residual friction angle along the discontinuities of the rock mass. In doing so, the model simulates the effect of degradation of discontinuities in the rock slope. Third, a dynamic loading, based on peak ground accelerations expected in the area, is applied to simulate dynamic earthquake conditions.

These numerical studies have provided some useful insights into the deformation mechanisms in the rock slope. Both sliding and rotation of blocks start to occur once the residual friction angle along the discontinuities is reduced and when the region is shaken by a strong earthquake. The results indicate that, due to variations in the inclination of discontinuities, the entire slope does not become unstable and that down-slope sliding and rotation of blocks occur mainly on the top layers of the slope. Within the range of parameter values considered for this study, it is unlikely that the whole rock slope can be destabilised. The study provides an illustration of how the geo-mechanical properties of a rock mass can be integrated in a discontinuum rock slope model, which is used for predicting the behaviour of the slope under existing environmental and earthquake conditions. This model has helped not only to better understand the dynamics of the rockslide but also to estimate the potential rock volume that can become unstable when subjected to static and dynamic loads.     

两个值得关注的工程地质力学问题

岩体工程地质力学的问世 ,不仅推动了工程地质学科的发展 ,而且提高了解决实际工程问题的能力。在其发展过程中 ,新的研究课题不断地被提了出来。随着这些问题的解决 ,一些重要的理论、方法和技术将形成和逐步走向完善。作者认为以下两个工程地质力学问题值得我们关注 ,即边坡滚石机理和防治和工程地质力学综合集成理论和方法。     

Fracture toughness of geomaterials

An understanding of the fracture mechanics of geomaterials is important for the solution of many problems in geomechanics. One of the most important material properties involved in fracture mechanics is the fracture toughness, K_Ic. The short-rod test configuration proposed by Barker¹ has significant potential for becoming a standard test for fracture toughness determination in geomechanics. The purpose of this brief is to examine the application potential of the short-rod test for geomechanics problems.     

单轴压缩下横观各向同性岩石破裂过程的数值模拟

采用基于细观损伤力学基础上开发的RFPA2D数值模拟软件,用2种不同的岩石材料来组成7个不同岩层倾角的横观各向同性的岩石试件,通过单轴加载数值模拟试验,模拟横观各向同性岩石渐进破裂的整个过程,分析了岩层与最大主应力之间的倾角和强度之间的关系,讨论了不同岩层倾角的横观各向同性岩体的不同破裂模式及其破坏准则。     

基于连续—非连续方法的地质体材料变形—拉裂过程模拟——以岩样紧凑拉伸试验为例

地质体材料易发生拉裂,为了有效模拟地质体材料的变形-拉裂过程,自主研发了一种连续-非连续方法。该方法实质是拉格朗日元法与虚拟裂缝模型的耦合,既能较准确模拟应力应变场,又能较准确模拟连续介质向非连续介质转化的复杂过程。以岩样紧凑拉伸试验为例开展变形-拉裂过程研究,得到以下结果。紧凑拉伸岩样的变形-拉裂过程:在岩样的Ⅴ形缺口尖端附近出现最大主应力集中现象;节点发生分离,虚拟或真实裂缝扩展,最大主应力始终集中于虚拟裂缝的尖端位置;岩样被拉裂成两部分。最大不平衡力发生1次突增对应着1个节点的分离。在峰值之前,岩样的载荷-位移曲线表现出了硬化现象;随着岩样尺寸的增加,应力-应变曲线的峰值有所下降,这与Bazǎnt的尺度律相一致,且峰后应力-应变曲线的陡峭程度增大。目前针对紧凑拉伸试验的模拟结果是合理的,由此在一定程度上说明了提出的连续-非连续方法在连续介质向非连续介质转化模拟方面的突出能力。      

An Index for Estimating the Stability of Brittle Surrounding Rock Mass: FAI and its Engineering Application

Based on the geometric analysis of the relationship between the stress state at a point and the yield surface defined in the principal stress space, a coefficient ω is set up as an estimation index to describe the stress-induced yield risk. After yield, the equivalent plastic shear strains is usually used to characterize the failure degree (FD) of the material and adopted here as an index of the damage degree for the surrounding rock masses. Then, a unified variable combining ω and FD, named failure approaching index (FAI), is constructed to estimate the stability of rock mass which may be at different deformation stages. The formulas of FAI are derived for some popular yield criteria in geomechanics. Details for such development are addressed in the paper. Its rationality is verified by numerical simulation and comparative analysis of the conventional triaxial compression tests and typical tunnel projects. In addition, the method for applying FAI to the stability estimation of surrounding rock mass is proposed. As examples, the stability of the underground powerhouse, access tunnels and headrace tunnels at the Jinping II hydropower station are estimated by making use of the method we presented. The results indicate that not only is the index rational in mechanics, but the theory also has good expansibility, and the estimation methods are simple and practical as well. It is easier for field engineers to analyze and understand the numerical results.     

塔中Ⅰ号断裂构造特征地质力学模拟

在前人研究基础上，对塔中I号断裂带地层进行岩石力学试验，并用相似材料地质力学模拟试验研究塔中I号断裂带在后期应力场作用下演化过程。结果表明，塔中I号断裂对塔中地区的地质构造起控制性作用。张裂和剪裂为该区地层的主要破裂机制，所产生的裂缝集中发育于中部的奥陶纪和寒武纪地层。     

A Review of Some Rock Mechanics Issues in Geothermal Reservoir Development

Rock mechanics and geomechanical studies can provide crucial information for economic geothermal reservoir development. Although significant progress has been made in reservoir geomechanics, technical challenges specific to the geothermal area (high temps, data collection, experimentation issues) have prevented widespread use of geomechanics in geothermal reservoir development. However, as the geothermal industry moves to develop more challenging resources using the concept of enhanced geothermal systems (EGS), and to maximize productivity from conventional resources, the need for improved understanding of geomechanical issues and developing specific technologies for geothermal reservoirs has become critical. Rock mechanics research and improved technologies can impact areas related to in-situ stress characterization, initiation and propagation of artificial and natural fractures, and the effects of coupled hydro-thermo-chemo-mechanical processes on fracture permeability and induced seismicity. Rock mechanics/geomechanics research, including experimental and theoretical investigations as well as numerical and analytical solutions, has an important role in optimizing reservoir design and heat extraction strategies for sustainable geothermal energy development. A number of major areas where rock mechanics research can facilitate geothermal systems development are reviewed in this paper with particular emphasis on EGS design and management.     

Particle manifold method (PMM): A new continuum‐discontinuum numerical model for geomechanics

Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle‐based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum‐discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd.     

The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks

We present a discussion of the state-of-the-art on the use of discrete fracture networks (DFNs) for modelling geometrical characteristics, geomechanical evolution and hydromechanical (HM) behaviour of natural fracture networks in rock. The DFN models considered include those based on geological mapping, stochastic generation and geomechanical simulation. Different types of continuum, discontinuum and hybrid geomechanical models that integrate DFN information are summarised. Numerical studies aiming at investigating geomechanical effects on fluid flow in DFNs are reviewed. The paper finally provides recommendations for advancing the modelling of coupled HM processes in fractured rocks through more physically-based DFN generation and geomechanical simulation.