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.     

A coupled model for solid deformation and gas leak flow

From the viewpoint of interaction mechanics of solid and gas, a coupled mathematical model is presented for solid coal/rock‐mass deformation and gas leak flow in parallel deformable coal seams. Numerical solutions using the strong implicit procedure (SIP) method to the coupled mathematical model for double parallel coal seams are also developed in detail. Numerical simulations for the prediction of safety range using protection layer mining are performed with experimental data from a mine with potential danger of coal/gas outbursts. Analyses show that the numerical simulation results are consistent with the measured data on the spot. The coupled model shows a positive future for applications in a wide range of gas‐leak‐flow‐related problems in mining engineering, gas drainage engineering and mining safety engineering. Copyright © 2004 John Wiley & Sons, Ltd.     

基于离散裂隙网络模型的裂隙水渗流计算

离散裂隙网络模型(Discrete Fracture Network（DFN）)是研究裂隙水渗流最为有效的手段之一。文章根据裂隙几何参数和水力参数的统计分布,利用Monte Carlo随机模拟技术生成二维裂隙网络,基于图论无向图的邻接矩阵判断裂隙网络的连通,利用递归算法提取出裂隙网络的主干网或优势流路径。基于立方定律和渗流连续性方程,利用数值解析法建立了二维裂隙网络渗流模型,分析不同边界条件下裂隙网络中的流体流动。结果表明,该方法可以模拟区域宏观水力梯度和边界条件下,裂隙网络水力梯度方向总的流量,以及节点的水位、节点间的流量和流动方向的变化特征,为区域岩溶裂隙水渗流计算提供了一种实用、可行的方法。      

A theoretical model for gas adsorption-induced coal swelling

Swelling and shrinkage (volumetric change) of coal during adsorption and desorption of gas is a well-known phenomenon. For coalbed methane recovery and carbon sequestration in deep, unminable coal beds, adsorption-induced coal volumetric change may cause significant reservoir permeability change. In this work, a theoretical model is derived to describe adsorption-induced coal swelling at adsorption and strain equilibrium. This model applies an energy balance approach, which assumes that the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid. The elastic modulus of the coal, gas adsorption isotherm, and other measurable parameters, including coal density and porosity, are required in this model. Results from the model agree well with experimental observations of swelling. It is shown that the model is able to describe the differences in swelling behaviour with respect to gas species and at very high gas pressures, where the coal swelling ratio reaches a maximum then decreases. Furthermore, this model can be used to describe mixed-gas adsorption induced-coal swelling, and can thus be applied to CO₂-enhanced coalbed methane recovery.     

煤型气碳同位素演化二阶段分馏模式及机理

天然气中甲烷Ｃ同位素组成是判识其母质类型和演化程度最有效的方法之一。国内外学者对煤型气δ＾１３Ｃ１与演化程度（Ｒ＾０）之间的关系做过大量的工作,取得了重要成果,但由于其研究对象的局限性,对其完整的同位素汪化分馏特征洞需进一步完善。由于我国含煤盆地广布,源岩的成烃演化完整而系统,使得系统研究其演化成为可能。本文通过我国不同盆地、不同时代和不同成烃演化的煤型气甲烷Ｃ同位素组成和源岩演化程度（Ｒ＾０）的     

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.     

多相流传输THM全耦合数值模型及程序验证

我国首个GCS示范工程神华多储层场地出现了单储层吸气量剧增的现象,在其原设计方案下,压缩后变冷的CO₂被注入至深部高温含水层中,引起首层含水层中流体压力和温度应力急剧变化,从而导致大量裂隙产生,增加了单储层的可注入性的同时,降低了系统总体封存能力,并带来了泄露风险。本文基于TOUGH-FLAC三维多相多组分THM耦合数值模拟程序,开发了场地尺度岩体开裂模块来研究CO₂注入方案对目标含水层耦合特性和开裂特性的综合影响,并设计了定速率、先增速后定速、间歇定速、间歇变速、二次变速等多类型注入方案,分别计算分析了储层岩体的热力学特性、多相流特性与开裂情况。结果表明：设计方案下含水层产生了较多的开裂现象,是导致其可注入性增大的根本原因,持续注入CO₂引起含水层岩体中有效应力大幅度降低,渗透率增加,定速率方案产生的温度应力最小,在设计各类注入方案中,定速率注入方案下储层的裂缝发育最少。     

河北平原土壤有机碳储量及固碳机制研究

利用2005年多目标区域土壤地球化学调查及20世纪70年代末全省第二次土壤普查土壤有机碳数据,对河北平原土壤有机碳密度及碳储量的时空变化规律、固碳机制及固碳潜力等问题进行了研究。结果表明,全省第二次土壤普查时土壤有机碳储量124．86Mt,2005年为176．08Mt,26年中增加了41．02％,表现出“碳汇”效应。据...     

Terrestrial carbon sequestration in southeast and south-central United States

Analyses of regional carbon sources and sinks are essential technologies in mitigating the accumulation of CO2 in the for assessing the economical feasibility of various carbon sequestration atmosphere and in preventing global warming. Such an inventory is a prerequisite for the regional trading of CO2 emission. As a U.S. Department of Energy Southeast Regional Carbon Sequestration Partner, we have estimated the state-level terrestrial carbon pools in the southeast and south-central US, and have projected the potential for terrestrial carbon sequestration in the region. This region includes： Alabama, Arkansas, Florida, Georgia, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, Texas, and Virginia. The total terrestrial carbon storage in southeast and south-central US （11 states） was estimated to be 21.1 Pg C. Total annual terrestrial carbon sink in the region was calculated to be 189.1 Tg C/a. Of the various carbon sinks, the annual forest carbon sink （estimated as 76 Tg C g/a） could compensate for 13% of the total annual greenhouse gas emission in the region in the early 1990s. Through proper policies and the use of best management practices, a further 9.3% of the total greenhouse gas emission could be offset by terrestrial sequestration （53.9 Tg C/a）.     

Discrete fracture model for simulating waterflooding processes under fracturing conditions

In our study, we develop a model for simulating fracturing processes in a poroelastic medium. The proposed approach combines the discrete fracture model enriched with contact plane mechanics. The model captures mechanical interactions of fractures and a deformable medium, fluid, and heat transfer in fractures and in a porous medium. Both effects of poroelasticity and thermoelasticity are accounted in our model. Mass and heat conservation equations are approximated by the finite volume method, and mechanical equilibrium equations are discretized by means of the Galerkin finite element approach. Two‐dimensional grid facets between 3‐dimensional finite elements are considered as possible fracture surfaces. Most of these facets are inactive from the beginning and are activated throughout the simulation. A fracture propagation criterion, based on Irwin's approach, is verified on each nonlinear iteration. When the criterion is satisfied, additional contact elements are added into finite element and discrete fracture model formulations respectively. The proposed approach allows modeling of existing natural and artificially created fractures within one framework. The model is tested on single‐ and multiple‐phase fluid flow examples for both isothermal and thermal conditions and verified against existing semianalytical solutions. The applicability of the approach is demonstrated on an example of practical interests where a sector model of an oil reservoir is simulated with different injection and production regimes.     

A generalized rigid particle contact model for fracture analysis

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material meso‐structure have recently been developed for fracture studies of quasi‐brittle material such as concrete. The formulation of a generalized contact model for rigid particle simulations is presented in which the contact discretization is a model parameter. The contact model performance for different discretizations is evaluated for uniaxial tensile tests, for uniaxial compression tests and for a notched beam in mode I. Copyright © 2005 John Wiley & Sons, Ltd.     

Parameters controlling pressure and fracture behaviors in field injectivity tests: A numerical investigation using coupled flow and geomechanics model

Field injectivity tests are widely used in the oil and gas industry to obtain key formation characteristics. The prevailing approaches for injectivity test interpretation rely on traditional analytical models. A number of parameters may affect the test results and lead to interpretation difficulties. Understanding their impacts on pressure response and fracture geometry of the test is essential for accurate test interpretation. In this work, a coupled flow and geomechanics model is developed for numerical simulation of field injectivity tests. The coupled model combines a cohesive zone model for simulating fluid-driven fracture and a poro-elastic/plastic model for simulating formation behavior. The model can capture fracture propagation, fluid flow within the fracture and formation, deformation of the formation, and evolution of pore pressure and stress around the wellbore and fracture during the tests. Numerical simulations are carried out to investigate the impacts of a multitude of parameters on test behaviors. The parameters include rock permeability, the leak-off coefficient of the fracture, rock stiffness, rock toughness, rock strength, plasticity deformation, and injection rate. The sensitivity of pressure response and fracture geometry on each parameter is reported and discussed. The coupled flow and geomechanics model provides additional advantages in the understanding of the fundamental mechanisms of field injectivity tests.     

Numerical simulations for coupled rock deformation and gas leak flow in parallel coal seams

Based on the new viewpoint of interaction mechanics for solid and gas, gas leakage in parallel deformable coal seams can be understood. That is, under the action of varied geophysical fields, the methane gas flow in a double deformable coal seam can be essentially considered to be compressible with time-dependent and mixed permeation and diffusion through a pore-cleat deformable, heterogeneous and anisotropic medium. From this new viewpoint, coupled mathematical models for coal seam deformation and gas leak flow in parallel coal seams were formulated and the numerical simulations for slow gas emission from the parallel coal seams are presented. It is found that coupled models might be close to reality. Meanwhile, a coupled model for solid deformation and gas leak flow can be applied to the problems of gas leak flow including mining engineering, gas drainage engineering and mining safety engineering in particular the prediction of the safe range using protective layer mining where coal and gas outbursts can efficiently be prevented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model

We introduce a discrete fracture network model of stationary Darcy flow in fractured rocks. We approximate the fractures by a network of planar circle disks, which is generated on the basis of statistical data obtained from field measurements. We then discretize this network into a mesh consisting of triangular elements placed in three-dimensional space. We use geometrical approximations in fracture planes, which allow for a significant simplification of the final triangular meshes. We consider two-dimensional Darcy flow in each fracture. In order to accurately simulate the channeling effect, we assign to each triangle an aperture defining its hydraulic permeability. For the discretization we use the lowest order Raviart-Thomas mixed finite element method. This method gives quite an accurate velocity field, which is computed directly and which satisfies the mass balance on each triangular element. We demonstrate the use of this method on a model problem with a known analytical solution and describe the generation and triangulation of the fracture network and the computation of fracture flow for a particular real situation.     

基于图像识别的煤层井下宏观裂隙观测

煤层裂隙影响煤的力学性能和渗透性,且对于一个煤矿的安全生产具有重要意义。针对现有裂隙测量方法较低效且易受自然环境条件影响的问题,通过对煤壁裂隙拍照,结合数字图像处理技术,批量处理拍摄的照片,提取图片中的裂隙参数,得到煤壁上裂隙的倾角;然后根据采面、运输巷和回风巷之间的空间关系建立几何模型,可以求出裂隙的产状,为煤层裂隙系统的快速统计提供了一种新方法。经过实例验证,该方法高效准确且具有一定的实用性。     

A coupled discrete element model for the simulation of soil and water flow through an orifice

Soil erosion around defective underground pipes can cause ground collapses and sinkholes in urban areas. Most of these soil erosion events are caused by fluidization of the surrounding soil with subsequent washing into defective sewer pipes. In this study, this soil erosion process is simplified as the gradual washout of sand particles mixed with water through an orifice. The discrete element method is used to simulate the large deformation behavior of the sand particles, and the Darcy fluid model is coupled with this approach to simulate fluid flow through porous sand media. A coupled 3D discrete element model is developed and implemented based on this scheme. To simulate previous experiments using this coupled model considering the current computing capacity, we incorporated a ‘supply layer’ to study the continuous erosion process. The coupled model can predict the erosion flow rates of sand and water and the shape of erosion void. Thus, the model can be used as an effective and efficient tool to investigate the soil erosion process around defective pipes. Copyright © 2017 John Wiley & Sons, Ltd.     

和顺地区煤储层裂隙系统评价与渗透率预测研究

通过对沁水盆地和顺登记区周边矿井实际资料的研究,综合分析了煤储层裂隙的发育特征,15号煤储层渗透率非均质性的变化因素,并结合有效地应力的变化,对该区储层渗透率进行了预测,按其渗透率的大小分为4个类型,同时综合煤层气选区评价的其他参数认为,Ⅰ类区是下步勘探的首选目标。     

A supercoarsening multigrid method for poroelasticity in 3D coupled flow and geomechanics modeling

The Galerkin finite-element discretization of the force balance equation typically leads to large linear systems for geomechanical problems with realistic dimensions. In iteratively coupled flow and geomechanics modeling, a large linear system is solved at every timestep often multiple times during coupling iterations. The iterative solution of the linear system stemming from the poroelasticity equations constitutes the most time-consuming and memory-intensive component of coupled modeling. Block Jacobi, LSOR, and Incomplete LU factorization are popular preconditioning techniques used for accelerating the iterative solution of the poroelasticity linear systems. However, the need for more effective, efficient, and robust iterative solution techniques still remains especially for large coupled modeling problems requiring the solution of the poroelasticity system for a large number of timesteps. We developed a supercoarsening multigrid method (SCMG) which can be multiplicatively combined with commonly used preconditioning techniques. SCMG has been tested on a variety of coupled flow and geomechanics problems involving single-phase depletion and multiphase displacement of in-situ hydrocarbons, CO₂ injection, and extreme material property contrasts. Our analysis indicates that the SCMG consistently improves the convergence properties of the linear systems arising from the poroelasticity equations, and thus, accelerates the coupled simulations for all cases subject to investigation. The joint utilization of the two-level SCMG with the ILU1 preconditioner emerges as the most optimal preconditioning/iterative solution strategy in a great majority of the problems evaluated in this work. The BiCGSTAB iterative solver converges more rapidly compared to PCG in a number of test cases, in which various SCMG-accelerated preconditioning strategies are applied to both iterators.     

CO2吸附对煤岩热弹性模型影响的理论解释

引入煤岩对气体的吸附势函数，并假定吸附势函数是引起多孔介质变形和应力的一个因素，给出了考虑CO2吸附的煤岩热弹性模型的一般形式，分析了CO2吸附对煤岩热弹性模型的影响。结果表明，在弹性范围内，吸附势函数是通过改变热传导方程和热传导的热力学限制条件来间接影响介质的应力和变形的。而对应力一应变之间的关系表达式的形式没有影响。一旦给出自由能函数和吸附势函数的形式，就可以确定考虑气体吸附条件下介质的热弹性本构模型。