Modeling the acidizing of carbonate formations with account for the occurrence of wormholes

he results of an investigation of hydrochloric acid treatment on micro and macroscales are presented. A petrophysical permeability-porosity dependence used in the averaged mathematical model and taking account of the wormhole formation effect on the level of individual pores is proposed. The values of the surface reaction rate on carbonate rock dissolving in hydrochloric acid are given from the results of laboratory studies. An optimum rate of hydrochloric acid plug injection is estimated and the constraints due to possible transition of the acidizing in the acid breaking of the formation are discussed.     

基于等几何分析的结构优化设计研究进展

结构等几何分析是计算固体力学领域一种新兴的数值方法,致力于将CAD（计算机辅助设计）和CAE（计算机辅助工程）纳入到统一的数学表达框架。等几何分析紧密联系几何信息,采用相同的数学表达将几何精确建模、结构分析和设计过程结合,为结构优化设计提供了新的选择和机会。相比基于有限元的结构优化方法,等几何优化设计方法可在一定程度上提高结构优化的精度、效率和便利性。本文针对具有代表性的结构等几何优化设计,包括形状优化、尺寸优化和拓扑优化等问题,系统梳理和综述了主要的等几何优化方法及其在结构优化设计中的应用。比较分析和评述了结构等几何优化设计方法的算法特点及计算优势与劣势,探讨了基于等几何分析的结构优化研究的前沿问题,并展望了未来的发展方向,包括：基于复杂剪裁CAD几何的高效等几何分析与优化设计、基于实体几何构造的结构等几何分析和优化设计、等几何分析与其他力学分析方法结合的结构优化、基于等几何分析的壳体优化设计、基于等几何分析的材料和结构一体化优化设计以及考虑不确定性的结构等几何优化设计等。     

Mathematical modeling of dynamic fracture processes in concrete

We solve the problem on the collision of steel cylindrical hammers in the velocity range up to 800 m/s with rectilinear concrete slabs. We consider the following two approaches to calculating concrete fracture under impact loading: the phenomenological approach in which the strength criteria are expressed in terms of invariant constraints imposed on the critical macrocharacteristics of the process, i.e., stresses and strains, and the approach in which the fracture is considered as the process of formation, growth, and confluence of microdefects under the action of applied stresses. We compare the results of mathematical modeling with the experimental data concerning the penetration depth and the exterior flushing value. In the framework of the proposed model of dynamic fracture in concrete, we calculate the strength of a concrete tetrahedral prism under the action of longitudinal loads. We obtain a satisfactory agreement of the results of mathematical modeling with experimental results.     

金华山软岩铁路隧道施工过程围岩屈服接近度分析

隧道施工过程中围岩处于复杂应力状态下,隧道围岩屈服区演化特征的确定对于围岩稳定性分析和开挖支护方案优化具有重要的意义。采用屈服接近度指标衡量围岩破坏接近程度可以合理地描述复杂应力状态下围岩的应力危险性,对Mohr-Coulomb类岩体材料的屈服接近度函数进行了相应的推导,并在非线性有限元用户子程序上编程予以实现。介绍了赣州-龙岩铁路DKl33+095～DKl38+237段软弱围岩单线隧道正台阶步施工方案以及湿喷纤维混凝土支护方案。为了对该隧道施工过程中隧道围岩屈服区的演化特征进行合理评价,采用非线性有限元法对软弱围岩条件下的铁路隧道施工过程进行了数值模拟,分析了施工过程中隧道围岩屈服接近度分布特征,判定了隧道台阶步施工过程中隧道围岩的稳定性。分析结果表明:该隧道施工过程中围岩破坏区主要发生在下台阶步施工过程中;屈服接近度指标比传统的塑性区分布提供的信息更加丰富,有利于工程技术人员定量地评价隧道开挖支护方案。     

DYNAMIC RESPONSE OPTIMIZATION DESIGN FOR ENGINEERING STRUCTURES BASED ON RELIABILITY

IntroductionTheoptimumdesignofstructuraldynamicresponseisoneoftheimportantcontentsinthestructuraloptimizationdesign ,inwhichtherespondedphysicalquantityofstructuresunderdynamicexcitationaretakenasobjectorconstraintfunctions.Fortheproblemcomesdownsimultaneouslytothedynamiccharacteristicanalysisandthedynamicresponseanalysisaswellastheoptimumdesign ,itismoredifficultandcomplicatedthantheproblemofstructuralstaticoptimumdesign[1].However,therestillcomeoutsomeresearchproductionsinpastyears.Forexampl…     

数值流形方法及其在岩石力学中的应用

数值流形方法是目前岩石力学分析的主要方法之一.该方法起源于不连续变形分析,主要用于统一求解连续和非连续问题,其核心技术是在分析时采用了双重网格:数学网格提供的节点形成求解域的有限覆盖和权函数;而物理网格为求解的积分域.数学网格被用来建立数学覆盖,数学覆盖与物理网格的交集定义为物理覆盖,由物理覆盖的交集形成流形单元.流形方法的优点在于它使用了独立的数学和物理网格,具有和有限元明显不同的定义形式,且数学网格对于同一问题不同的求解精度的需求可以很方便地细化.由于该方法考虑了块体运动学,可以模拟节理岩体裂隙的开裂和闭合过程,因而在岩石力学中得到了广泛应用,近年来许多学者对该方法进行了研究.本文简要叙述了节理岩体的数值方法从连续到非连续的发展过程,详细地介绍了数值流形方法的组成和数值流形方法在岩石力学及其相关领域的研究和发展概况,最后就作者所关心的一些问题,如三维问题的数值流形方法、数值流形方法在物理非线性问题和裂纹扩展问题中的应用、相关的耦合方法等进行了探讨.      

工程爆破问题数值模拟研究

工程爆破方法在开矿、筑坝、修路和凿洞中得到了广泛使用,经验和分析表明,当炸药埋深超过40米时,重力对爆破抛掷现象有明显影响,但目前缺乏系境研究。本文提出了一个用于爆破作用下的岩体本构数学模型,并用二维轴对称数值计算方法对有重力影响的工程爆破问题初始阶段进行了详细研究,计算结果包括爆炸应力波的传播规律,岩体的加速与破坏过程,空腔与地表面的运动规律,抛掷区的形成与划定,能量分配关系等,结果表明:重力对爆炸波的传播基本无影响,重力仅影响抛掷区的大小和抛掷区动能占总爆炸能的比例。     

Thermodynamics, Kinetics, and Hydrodynamics of Mixed Salt Precipitation in Porous Media: Model Development and Parameter Estimation

Demands for hydrocarbon production have been increasing in recent years. Today many oilfields around the world are afflicted by the problem of scaling leading to severe formation damage and hampering of petroleum production from hydrocarbon reservoirs. In current study, a mathematical model for prediction of permeability reduction due to scale deposition is developed based on thermodynamics, kinetics, and hydrodynamics of mixed salt precipitation during flow through porous media. Model predictions are compared with sound experimental data for single deposition of barium sulfate and most importantly, for simultaneous precipitation of barium sulfate and strontium sulfate onto rock surface. Owing to high nonlinearity of the proposed model, kinetic parameters embedded in the mathematical model were tuned employing a new approach based on a hybrid algorithm consisting of particle swarm optimization (PSO) technique and pattern search (PS) algorithm. The average absolute deviations ranging from 1.03 to 9.3 % were observed between model forecasts and experimental data which corroborate the suitability and applicability of the model and also confirm the capability of PSO–PS hybrid algorithm as a highly efficient optimization tool. Estimated values for kinetic parameters are also in accordance with collision theory of chemical reactions.     

岩质高边坡卸荷带形成及其工程性状研究

首先针对边坡开挖或河谷下切的卸荷过程, 讨论了边坡应力场的分布, 提出了边坡二次应力的“驼峰应力分布”规律。在此基础上, 分析了伴随边坡二次应力场的形成, 岩质高边坡卸荷带的形成机理。进-步, 结合三峡船闸高边坡的开挖和监测实践, 讨论了卸荷带的工程地质意义及其力学性状表现。最后, 利用本文的基本观点, 对三峡船闸高边坡卸荷带进行了合理的数值模拟研究。     

Modeling and simulation of an acoustic well stimulation method

This paper presents a mathematical model and a numerical procedure to simulate an acoustic well stimulation (AWS) method for enhancing the permeability of the rock formation surrounding oil and gas wells. The AWS method considered herein aims to exploit the well-known permeability-enhancing effect of mechanical vibrations in acoustically porous materials, by transmitting time-harmonic sound waves from a sound source device—placed inside the well—to the well perforations made into the formation. The efficiency of the AWS is assessed by quantifying the amount of acoustic energy transmitted from the source device to the rock formation in terms of the emission frequency and the well configuration. A simple methodology to find optimal emission frequencies for a given well configuration is presented. The proposed model is based on the Helmholtz equation, a sound-hard boundary condition at the casing, and an impedance boundary condition that effectively accounts for the porous solid–fluid interaction at the interface between the rock formation and the well perforations. Exact non-reflecting boundary conditions derived from Dirichlet-to-Neumann maps are utilized to truncate the circular cylindrical waveguides considered in the model. The resulting boundary value problem is then numerically solved by means of the finite element method. A variety of numerical examples are presented in order to demonstrate the effectiveness of the proposed procedure for finding optimal emission frequencies.     

深埋地下洞室断裂型岩爆机理的数值模拟

针对深部岩体中由断层、节理等不连续性结构面引发的岩爆地质灾害, 根据深埋地下隧洞中潜在发震断裂的分布特征和几何形态建立数值分析模型, 采用离散元单元法模拟存在刚性平直断裂的深部围岩的开挖响应, 并分别考察开挖接近并通过断裂附近时围岩应力状态的变化特征。通过探讨断裂的存在对围岩应力状态改变的作用机理, 揭示出断裂型岩爆是开挖面附近一定范围内存在的断裂构造在高应力作用下发生错动, 导致能量突然释放, 对围岩造成强烈冲击作用的结果, 基本与地震的断层“粘滑”机制相类似。     

A dynamic damage constitutive model for a rock mass with non-persistent joints under uniaxial compression

Most problems faced by the practicing rock mass engineering involve the evaluation of rock mass dynamic strength and deformability. As part of a rock mass, the mesoscopic flaws such as the microcracks and the macroscopic ones such as the joints both inherently affect the rock mass dynamic strength and deformational behavior. Nearly none of the existing models can handle the co-effect of these two kinds of flaws on the rock mass dynamic mechanical behavior. This study focusses on the rock mass with multi-sets of non-persistent joints and establishes a mathematical model accounting for the anisotropy in dynamic strength and deformability induced by the joints. Accordingly, an approach incorporating the existing models or methods to enable perfect simulation of the dynamic stress-strain relationship of a rock mass is proposed, in which the joint geometrical parameters such as the joint length and dip angle, the strength ones such as the joint internal friction and the deformational ones such as the joint normal and shear stiffness can all be taken into account. In order to investigate the validity of the proposed model, a series of calculation examples have been made and the results fits very well with the theoretical ones.     

A Dual Approach to Optimum Truss Design

Abstract

This paper considers the problem of finding member sizes which minimize the weight of a pin-jointed truss of fixed geometry while satisfying constraints upon joint displacements, member stresses, and minimum sizes. Aspects of both mathematical programming methods and optimality criteria methods for designing large trusses are discussed. The optimality criteria approach is further extended and the whole truss design problem is recast into a new dual formulation in which constraint activity levels are used as variables in a mathematical programming solution method. This new dual formulation unifies both the optimality criteria and mathematical programming approaches to the problem of truss design. The paper is theoretical in nature, being largely devoted to a proof of the dual method. A discussion of the likely implications and usefulness of the dual approach to truss design is given with comments upon its possible modes of practical use.     

Modeling rock failure using the numerical manifold method followed by the discontinuous deformation analysis

A complete rock failure process usually involvesopening/sliding of preexisting discontinuities as well as fracturing in intact rock bridges to form persistent failure surfaces and subsequent motions of the generated rock blocksThe recently developed numerical manifold method(NMM)has potential for modelling such a complete failure processHowever,the NMM suffers one limitation,i.e.,unexpectedmaterial domain area change occurs in rotation modellingThis problem can not be easily solved because the rigidbody rotation is not represented explicitly in the NMM.Thediscontinuous deformation analysis(DDA) is specially developed for modelling discrete block systems.The rotationinduced material area change in the DDA modelling canbe avoided conveniently because the rigid body rotation isrepresented in an explicit form.In this paper,a transitiontechnique is proposed and implemented to convert a NMMmodelling to a DDA modelling so as to simulate a completerock failure process entirely by means of the two methods,in which the NMM is adopted to model the early fracturingas well as the transition from continua to discontinua,whilethe DDA is adopted to model the subsequent motion of thegenerated rock blocks.Such a numerical approach also improves the simulation efficiency greatly as compared with acomplete NMM modelling approach.The fracturing of arock slab with pre-existing non-persistent joints located ona slope crest and the induced rockfall process are simulated.The validity of the modelling transition from the NMM tothe DDA is verified and the applicability of the proposed numerical approach is investigated.     

岩石双孔爆破过程的流形元法模拟

在流形元基本理论基础上,引入断裂力学的裂纹产生及扩展判据,应用二阶流形元对岩石双孔爆破过程进行了研究,模拟了双孔同时起爆和毫秒延时起爆两种条件下裂纹的产生和扩展、块体的形成以及漏斗形成过程,分析了爆炸载荷作用下岩石的破坏规律以及起爆条件对该过程的影响,验证了流形元法在研究冲击载荷作用下岩石从连续体到不连续体破坏过程的准确性和有效性,为研究类似问题提供一个新的思路和方法。     

Epsilon-continuation approach for truss topology optimization

In the present paper, a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems. This approach is an improved version of the epsilon-relaxed approach developed by the authors previously. In the proposed approach, we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach. Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution found from the previous optimization process as the initial design for the next optimization. This continuation process is continued until a small termination value of the relaxation parameter is reached. Convergence analysis of the proposed approach is also presented. Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs. The project supported by the National Natural Science Foundation of China (10102003, 10032010 and 10032030)     

Nonlinear Coupled Mathematical Model for Solid Deformation and Gas Seepage in Fractured Media

Based on detailed investigation into the interactional physical mechanism of solid deformations and gas seepage in rock matrix and fracture, a nonlinear coupled mathematical model of solid deformation and gas seepage is put forward and the FEM model is built up to carry out numerical analysis. The coupled interaction laws between solid deformations and gas seepage in rock matrix and fractures has been emphasized in the model, which is a vital progress for coupled mathematical model of solid deformation and gas seepage of rock mass media. As an example, the methane extraction in fractured coal seam has been numerically simulated. By analyzing the simulation results, the law of methane migration and exchange in rock matrix and fractures is interpreted.     

砂岩方梁断裂过程区范围的实验确定方法

裂纹前端的断裂过程区是引起岩石非线性断裂及尺寸效应的主要原因。利用数字图像相关技术对砂岩开展了三点弯曲梁实验,获得观测区域高精度的全场位移和应变数据,根据断裂韧带区域水平位移和水平应变的分布特征,结合裂尖岩石颗粒变化的微观分析,提出采用裂纹尖端水平位移波动性和水平应变突变性所得到的波动系数和水平应变突变值,确定断裂过程区形状和临界尺寸的方法。结果表明:砂岩断裂过程区的形状为不规则的狭长带状区域,断裂过程区的临界长度为11~13mm,临界宽度为1.58~2.36mm。断裂过程区区域内形变在趋向裂尖时呈指数增加,但其单位区域内的形变增量呈波动状态。该方法能够更加准确判断岩石断裂过程区的范围,有助于分析岩石的非线性断裂特性。     

On Optimal Shell Prestressing

Abstract

The problem of optimum selection and distribution of prestressing forces in a shell structure subjected to different loads is solved within membrane theory. The range of admissible prestressing tensors at a shell point is deter mined and the selection of optimum prestressing is described. The problem is discretized, linearized, and reduced to that of linear mathematical programming. A method of tracing cable trajectories is given. Graph theory approach is applied to form design combinations of elementary loads when these are related by logical conditions. An outline is given of the computation of a prestressed secondary containment of a nuclear reactor.