Numerical modeling of fluid‐driven fractures in cohesive poroelastoplastic continuum

In this article, we investigate the main parameters that influence the propagation of a fluid‐driven fracture in a poroelastoplastic continuum. These parameters include the cohesive zone, the stress anisotropy, and the pore pressure field. The fracture is driven in a permeable porous domain that corresponds to weak formation by pumping of an incompressible viscous fluid at the fracture inlet under plane strain conditions. Rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fluid flow in the fracture is modeled by the lubrication theory. The movement of the pore fluid in the surrounding medium is assumed to obey the Darcy law and is of the same nature as the fracturing fluid. The cohesive zone approach is used as the fracture propagation criterion. The problem is modeled numerically with the finite element method to obtain the solution for the fracture length, the fracture opening, and the propagation pressure as a function of the time and distance from the pumping inlet. It is demonstrated that the plastic yielding that is associated with the rock dilation in an elastoplastic saturated porous continuum is significantly affected by the cohesive zone characteristics, the stress anisotropy, and the pore pressure field. These influences result in larger fracture profiles and propagation pressures due to the larger plastic zones that are developing during the fracture propagation. Furthermore, it is also found that the diffusion process that is a major mechanism in hydraulic fracture operations influences further the obtained results on the fracture dimensions, plastic yielding, and fluid pressures. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical modeling of fracking fluid migration through fault zones and fractures in the North German Basin

Gas production from shale formations by hydraulic fracturing has raised concerns about the effects on the quality of fresh groundwater. The migration of injected fracking fluids towards the surface was investigated in the North German Basin, based on the known standard lithology. This included cases with natural preferential pathways such as permeable fault zones and fracture networks. Conservative assumptions were applied in the simulation of flow and mass transport triggered by a high pressure boundary of up to 50 MPa excess pressure. The results show no significant fluid migration for a case with undisturbed cap rocks and a maximum of 41 m vertical transport within a permeable fault zone during the pressurization. Open fractures, if present, strongly control the flow field and migration; here vertical transport of fracking fluids reaches up to 200 m during hydraulic fracturing simulation. Long-term transport of the injected water was simulated for 300 years. The fracking fluid rises vertically within the fault zone up to 485 m due to buoyancy. Progressively, it is transported horizontally into sandstone layers, following the natural groundwater flow direction. In the long-term, the injected fluids are diluted to minor concentrations. Despite the presence of permeable pathways, the injected fracking fluids in the reported model did not reach near-surface aquifers, either during the hydraulic fracturing or in the long term. Therefore, the probability of impacts on shallow groundwater by the rise of fracking fluids from a deep shale-gas formation through the geological underground to the surface is small.     

岩爆破坏过程能量释放的数值模拟

岩爆是地下岩石开挖中的一种工程灾害现象,是岩体结构发生破坏时,由于内部储存的弹性能释放并转换为动能而造成动力形式的破坏。岩爆破坏过程中的能量释放与岩体在应力峰值前后的应力-应变特性紧密相关。另外,施工中开挖速度引起的加载速率的变化也会对岩爆的产生有明显影响。以岩体全过程应力-应变曲线试验为基础分析岩爆破坏过程。分析中采用的模型考虑了岩石峰值后应力-应变特性及加载速率的影响。运用数值方法对岩石洞室的开挖过程进行了模拟,在模拟中对岩体破坏的发生及弹性能释放过程进行了分析。数值分析结果显示,岩体洞室开挖过程中岩石破坏由岩体表面向岩体内部发展,岩石的弹性能释放率也随着破坏的发展而不断增加。分析结果还显示,岩体破坏时的弹性能释放速率会随着开挖速率的提高而明显增加。     

Numerical simulation of two-phase flow in conceptualized fractures

Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures.     

Numerical modeling of traffic-induced ground vibration

Ground vibrations due to road traffic constitute a major environmental problem. This paper presents a numerical model for the analysis and prediction of the ground vibrations due to the road traffic. A car model with four degrees of freedom is used for the determination of the load due to the road traffic. The load is then introduced in a 3D finite difference model for the determination of the traffic-induced ground vibrations. The numerical model is validated using field data. Numerical analyses show that both the amplitude and frequency of the traffic-induced vibrations are mainly affected by the vehicle speed, the road unevenness and the vehicle suspension system. Some recommendations are suggested for the reduction of these vibrations.     

Numerical modeling of intraoceanic arc growth

We investigate crustal growth processes on the basis of a 2D coupled geochemical—petrological-thermomechanical numerical model of retreating intraoceanic subduction. The model includes spontaneous slab retreat and bending, subducted crust dehydration, aqueous fluid transport, mantle wedge melting, and melt extraction resulting in crustal growth. Our numerical experiments show that (1) the rate of plate retreat influences both the rate of crust formation and composition of newly formed crust; (2) both the intensity of melt extraction and the age of subducted plate affect the volume of newly formed crust. In the present paper we describe possible scenarios of magmatic and geodynamic evolution of the arc system and then compare results with magmatic addition rates of Western Pacific arcs. Published in Russian in Vestnik Moskovskogo Universiteta. Geologiya, 2009, No. 4, pp. 30–43. The text was submitted by the authors in English.     

砂砾岩水力压裂裂缝扩展规律的数值模拟分析

砂砾岩储层一般具有岩性和渗透性变化大、孔隙度低、连通性差、孔隙结构复杂和非均匀性严重等特点,因此,在水力压裂过程中,裂缝扩展形态难以控制,大规模改造难度大。针对国内某典型砂砾岩油藏特征,采用数值计算方法对砂砾岩压裂裂缝的扩展规律进行了研究,包括地应力场、砾石含量和粒径等对裂缝扩展形态及压裂压力的影响。研究表明,砾石的存在增加了压裂裂纹扩展的复杂性,裂纹主要有止裂、偏转、穿透和吸附4种表现模式,但主应力差严格控制着裂纹的走向,随着主应力差的增大,裂纹由总体绕砾扩展转变为总体穿砾扩展,失稳压力随着主应力差的增大而明显减小;砾石含量的多少体现了砂砾岩试样宏观的非均匀性,含量越高均匀性越差,随着砾石含量的提高,裂纹与砾石的相互作用占据主导地位,失稳压力随砾石含量的增加而增大;当砾石体积含量一定时,砾石粒径对压裂压力的影响主要取决于砾石排列的随机性,失稳压力随砾石粒径的增大而略有增大。     

接触摩擦问题的数值模拟

无网格伽辽金法(EFGM)可脱离单元的概念,特别适合岩体裂纹面的接触摩擦分析。基于EFGM,在裂纹面引入罚参数,通过迭代计算,得到裂纹面真实的应力状态,从而模拟闭合裂纹的粘接、滑移和张开行为,数值结果表明该方法是合理可行的。     

Numerical modeling of reservoirs or pipes in groundwater seepage

In groundwater studies, the numerical modeling of complex boundary conditions can be made easier by considering reservoirs and pipes as “reservoir” finite elements, which can store or release large volumes of water at almost constant hydraulic head. The numerical code to be used must solve the complete conservation equation with unlinked functions for the water retention curve and the unsaturated hydraulic conductivity, and the ability to describe these as step functions. Four examples illustrate the performance of the “reservoir” element: reservoir pumping, laboratory variable-head permeability test, vertical flow in an open borehole, and pumping test with well storage.     

Numerical modeling and experiments of coarsening foam

Numerical and experimental results of drying and wetting foam are presented. Foam can be wetted by wash water delivered on its top boundary, or drained by allowing the liquid to move downward in response to gravity. These processes are governed by nonlinear equations that in special cases accept exact solutions. Here we develop a numerical model that satisfies realistic boundary conditions. Numerical results are presented in conjunction with experiments conducted with coarsening foam. In addition, calculations were carried out modeling the wetting and draining of coarsened foam. From the simulations and experiments, coarsening bubbles were found responsible for accelerating drainage, or vice versa.     

Numerical modeling of the Rideau Valley Watershed

Using the Mike11 modeling system by the Danish Hydraulic Institute, a detailed model of the Rideau Valley Watershed was constructed. It includes 532 km of rivers and lakes, 106 basins, 122 bridges and culverts, and 20 water control structures. The model was calibrated using measured streamflow data for a time period of 5 years; additional 5 years of data was used for validation. Various methods, both qualitative and quantitative, were used to evaluate the model performance. It was found that the model can simulate the hydrological response with a reasonable to high degree of accuracy. This model is now being used for various watershed management purposes, including flood forecasting, dam safety assessment, quantification of wetland functions, and derivation of design flows.     

花岗岩粗糙单裂隙对流换热特性的数值模拟

在干热岩储层中开采地热能,往往需要对储层进行人工水力压裂以形成贯穿的换热通道。然而,热储中的对流换热对干热岩的采热率有重要影响,经过人工刺激的储层会形成几何形态各异的裂隙面,而裂隙粗糙程度的不同则会引起换热性能的显著差异。因此,选取4条Barton的经典岩石裂隙粗糙度曲线,在试验室条件下建立一个单裂隙对流换热模型。详细分析了花岗岩粗糙裂隙中热工质的换热特性。结果表明:局部对流换热系数沿着裂隙长度方向逐渐降低;节理粗糙系数JRC值越大,平均对流换热系数就越大,表明换热性能越好;局部对流换热系数的分布与JRC曲线的几何轮廓形态有很好的相关性,波峰波谷的变化趋势相一致;相对于温度而言,高流速对局部对流换热系数具有放大效应,流速越大,局部对流换热系数波动越大。     

Numerical study on S-wave transmission across a rough,filled discontinuity

This paper presents a numerical simulation of S-wave propagation across a rough, filled discontinuity using the universal distinct element code (UDEC). The ability of UDEC to simulate a stress wave across a smooth and planar discontinuity filled with an elastic material is validated through comparisons with analytical solutions. Next, the effect of the plastic deformation of the fill on the wave propagation is investigated. The model is extended to further study S-wave propagation across a filled discontinuity with rough interfaces, which is described using a sawtooth. The transmission coefficient defined by the energy is used to measure the wave attenuation. Finally, a parametric study is conducted to investigate the influences of the filled thickness, asperity angle, and incident amplitude on the transmission waves and transmission coefficients. The asperity angle and filled thickness together determine the transmitted waveform and transmission coefficient. The transmitted wave may be cut off when the incident wave amplitude exceeds a threshold value. The transmission coefficient decreases with a different trend with the incident wave amplitude increasing when the asperity angle varies. Compared with planar discontinuity, a filled discontinuity with rough interfaces is more sensitive to the amplitude of the incident wave. The causes of these phenomena are analyzed in detail. In addition, the deformation of the fill material is strongly related to the wave attenuation.     

考虑流-固耦合的隧道开挖数值模拟

根据隧道工程施工实际情况和地下水渗流的基本规律,以及弹塑性力学理论,建立了在应力场和渗流场耦合作用下隧道开挖数学模型,借助Comsol模拟了隧道开挖过程中围岩应力场及渗流场的变化规律。研究结果表明：在原岩开挖时,隧道围岩变形及地面沉降大,不利于周围建筑的安全,隧道内积水,施工无法进行;进行灌浆处理后,围岩变形小,地面沉降得到控制,有利于施工及周围建筑的安全。     

数值流形方法及其与耦合方法的比较

介绍了数值流形方法的基本原理,讨论了数学覆盖、物理覆盖、权函数和位移函数的概念,比较了该方法与DDA和FEM的耦合方法在对一维特性函数逼近的精确度,并用这两种方法模拟了地下放顶煤开挖的过程,最后的结果显示数值流形方法具有较好的相容性和精确度.     

古气候数值模拟:进展评述

数值模拟是古气候研究的一个重要内容。过去30年来,古气候数值模拟研究在相当程度上深化了我们对古气候变化机制的理解。在轨道尺度上,数值模拟证明了冰后期气候系统变化主要是对地球轨道参数变化的响应,同时揭示了温室气体、植被、海洋、冰盖等反馈因子的重要性。针对短尺度气候变化,数值模拟揭示出大洋传送带对北大西洋淡水注入的敏感性。在构造尺度上,数值模拟揭示了气候系统对于高原抬升、海道开合、大陆漂移导致的古地理变化、大气CO2浓度变化和太阳常数变化等的响应,揭示了气候系统突变对驱动因子阈值的敏感性。目前,古气候模拟研究中还存在分辨率不高、模拟结果与记录不完全吻合、模拟的边界条件不清楚等诸多问题。今后古气候模拟研究的改进有赖于模式的改进和计算机运算速度的提高,也有赖于对变化机制的更深理解和对边界条件更精确的重建。     

Numerical modeling of the Sakuma Dam reservoir sedimentation

The present study attempts to predict the reservoir sedimentation in 32 km region of the Tenryu River between the Hiraoka and Sakuma Dams in Japan. For numerical simulations of the reservoir sedimentation, the one-dimensional model of the Hydrologic Engineering Centre-River Analysis System (HEC-RAS) is used together with the inclusion of channel geometry, bed gradation curve, Exner-5 bed sorting mechanisms, fall velocity of the particle, and flow and sediment boundary conditions pertaining to modeling region. The modeling region of the Tenryu River is divided into 48 river stations with 47 reaches in the numerical simulations. The numerical model is calibrated using the available data for 48 years from 1957 to 2004. The formulae of sediment transport function, Manning’s roughness coefficient, computational increment and fall velocity have been identified for getting the best estimation of the Sakuma Dam reservoir sedimentation. Combination of obtained sensitive parameters and erodible limits of 2 m gave the best comparison with the measured bed profile. The computed results follow the trend of measured data with a small underestimation. Although Manning’s roughness coefficient has an effect on the sedimentation, no direct relation is found between the Manning’s roughness coefficient and reservoir sedimentation. It is found that the temperature of water has no effect on the reservoir sedimentation.     

Numerical modeling of dredging effect on berthing structure

Piles and diaphragm wall-supported berthing structure on marine soils are loaded laterally from horizontal soil movements generated by dredging. The literature on the adequacy of the finite element method modeling of berthing structure to analyze their behavior during dredging is limited. This paper describes a finite element approach for analyzing the lateral response of pile and diaphragm wall during dredging. Piles are represented by equivalent sheet-pile walls and a plane strain analysis using the finite element method is performed. Results from the finite element method are compared with full-scale field test data. Full-scale field test was conducted on a bearing structure to measure the lateral deflection on pile and diaphragm wall for their full length using inclinometer during dredging in sequence. The finite element method results are in good agreement with full-scale field results. Conclusions are drawn regarding application of the analytical method to study the effect of dredging on piles and diaphragm wall-supported berthing structures.