Comparison of Numerical Formulations for Two-phase Flow in Porous Media

Numerical approximation based on different forms of the governing partial differential equation can lead to significantly different results for two-phase flow in porous media. Selecting the proper primary variables is a critical step in efficiently modeling the highly nonlinear problem of multiphase subsurface flow. A comparison of various forms of numerical approximations for two-phase flow equations is performed in this work. Three forms of equations including the pressure-based, mixed pressure–saturation and modified pressure–saturation are examined. Each of these three highly nonlinear formulations is approximated using finite difference method and is linearized using both Picard and Newton–Raphson linearization approaches. Model simulations for several test cases demonstrate that pressure based form provides better results compared to the pressure–saturation approach in terms of CPU_time and the number of iterations. The modification of pressure–saturation approach improves accuracy of the results. Also it is shown that the Newton–Raphson linearization approach performed better in comparison to the Picard iteration linearization approach with the exception for in the pressure–saturation form.     

Numerical Reliability for Mixed Methods Applied to Flow Problems in Porous Media

This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Element (MFE) and Mixed-Hybrid Finite Element (MHFE) methods. The behavior of these methods is investigated under the influence of two factors: the mesh discretization and the medium heterogeneity. We show that, unlike the MFE, the MHFE suffers with the presence of badly shaped discretized elements. Thereat, a numerical reliability analyzing software (Aquarels) is used to detect the instability of a matrix-inversion code generated automatically by a symbolic manipulator. We also show that the spectral condition number of the algebraic systems furnished by both methods in heterogeneous media grows up linearly according to the smoothness of the hydraulic conductivity. Furthermore, it is found that the MHFE could accumulate numerical errors if large jumps in the tensor of conductivity take place. Finally, we compare running-times for both algorithms by giving various numerical experiments.     

Numerical Homogenization of Two-Phase Flow in Porous Media

Homogenization has proved its effectiveness as a method of upscaling for linear problems, as they occur in single-phase porous media flow for arbitrary heterogeneous rocks. Here we extend the classical homogenization approach to nonlinear problems by considering incompressible, immiscible two-phase porous media flow. The extensions have been based on the principle of preservation of form, stating that the mathematical form of the fine-scale equations should be preserved as much as possible on the coarse scale. This principle leads to the required extensions, while making the physics underlying homogenization transparent. The method is process-independent in a way that coarse-scale results obtained for a particular reservoir can be used in any simulation, irrespective of the scenario that is simulated. Homogenization is based on steady-state flow equations with periodic boundary conditions for the capillary pressure. The resulting equations are solved numerically by two complementary finite element methods. This makes it possible to assess a posteriori error bounds.     

A Finite Volume Scheme for the Transport of Radionucleides in Porous Media

The COUPLEX1 Test case (Bourgeat et al., 2003) is devoted to the comparison of numerical schemes on a convection–diffusion–reaction problem. We first show that the results of the simulation can be mainly predicted by a simple analysis of the data. A finite volume scheme, with three different treatments of the convective term, is then shown to deliver accurate and stable results under a low computational cost.     

环境中高氯酸盐的来源、污染现状及其分析方法

高氯酸盐是一种持久性的无机污染物,它能够抑制碘的吸收并削弱甲状腺功能。随着高效灵敏的分离检测方法的发展,研究人员在多种环境介质中都检测到了高氯酸根,其环境污染问题引起了广泛的关注。最近的研究表明,环境中的高氯酸盐并非都来自于人为污染源及含有高氯酸盐的化肥,也有在大气中自然产生的,而且环境中存在大气来源的高氯酸根的背景值。在重点介绍了高氯酸盐的污染现状、分析方法以及自然条件下大气中产生高氯酸根的机理等方面的最新研究进展之后,提出今后应开展环境中高氯酸根背景值的调查研究。为此,应开发具有更低检出限的分析方法,并借助南极地区独特的地理优势开展南极雪冰中高氯酸盐的相关研究,从而获得不同历史时期环境中高氯酸根的背景值,并研究高氯酸根背景值的影响因素,为研究自然条件下大气中产生高氯酸根的机理提供基础数据。     

多尺度多孔介质有效气体输运参数的分形特征

非常规油气资源的孔隙结构及其连通性非常复杂,其孔隙尺度从毫米到纳米跨越多个量级.多孔介质中气体的输运过程不仅依赖于介质的多尺度微观结构特征,还依赖于气体的相关属性.气体在多尺度多孔介质中的输运过程包括无滑流、滑脱流和过渡流,涉及分子扩散和努森扩散等多种机制,因此很难用唯一的连续介质理论来描述气体的输运特征.大量的数据表明真实多孔介质中的内部孔隙具有分形标度特征,因此采用分形几何表征多尺度多孔介质的孔隙结构,引入孔隙分形维数和迂曲度分形维数定量表征多孔介质的微结构和弯曲流道,建立多尺度多孔介质气体输运过程的细观模型;推导了多尺度多孔介质中气体的有效渗透率和有效扩散系数,并讨论了多尺度多孔介质微结构参数和气体属性对于气体等效输运特性的定量影响.该研究不仅可以丰富渗流理论,且有利于深入理解非常规油气藏的产出机制.      

Forward and Inverse Problems in Modeling of Multiphase Flow and Transport Through Porous Media

The paper deals with numerical simulation techniques for forward and inverse modelling in multiphase (multicomponent) flow through porous media. The forward simulation software system MUFTE-UG uses recent discretization techniques and fast solvers. The efficient integration of optimization strategies for the solution of the inverse problems is demonstrated in detail and also applied to practical numerical examples.     

基于孔隙网络模型的非水溶相液体运移实验研究进展

进行多孔介质中非水溶相液体（Non Aqueous Phase Liquids，NAPLs）运移的微观机理研究，微观孔隙网络模型实验是目前应用比较广泛且行之有效的方法。通过网络模型实验，获得对NAPLs在多孔介质中运移更深入的认识。从多孔介质孔隙结构测量、孔隙网络模型制作、NAPLs运移网络模型实验和数值模拟4个方面评述了该方向的研究进展，结果显示测量孔隙结构方法、图像刻蚀技术、可视化测量实验数据方法等有力地促进了本实验研究的发展。分析了孔隙网络模型实验存在的问题以及未来的发展趋势，对开展孔隙网络模型实验研究有一定的启发作用。     

Application of Numerical and Analytical Methods to Geotechnical Engineering

This is a summing-up report of the topic on application of numerical and analytical methods to geotechnical engineering, presented in the Third National Symposium on Numerical and Analytical Methods in Geomechanics. The application to rock mass and engineering is emphasized in this paper, based on the papers submitted to this symposium.     

数值解及解析解在岩体工程中的应用

本文是在第三届全国岩土力学数值分析和解析方法讨论会上所作的专题综述报告,是据提交给会议的部分论文,着重从数值方法在岩体工程的应用方面进行概括。它包括以下若干方面的课题,如岩体本构方程的模拟、锚喷支护的分析、岩体工程的反分析计算、洞室及竖井的围岩稳定与支护以及高边坡的稳定分析。从所提交的会议论文来看,在研究上述课题时,所采用的方法种类繁多,并具有独特的见解,它们在工程上的应用也已经取得了可喜的成效。     

Comparison of Numerical and Analytical Liquefaction Analyses of Tailings

The seismic performance of a tailings impoundment can be adversely affected by the behavior of the retained tailings. However, there remains considerable uncertainty in tailings liquefaction analysis. Twenty cyclic simple shear tests conducted on tailings from a gold mine in Quebec, Canada, were simulated numerically. The simulations indicated that the dynamic behavior of tailings could be modelled reasonably well, except that the weighted cyclic resistance curve of the tailings differed from that of clean sand which was used to develop the constitutive model (UBCSAND). An (N₁)_60-CS value of 10 blows/30 cm was estimated for the tailings based on calibration at a CSR of 0.10 for 15 cycles of loading. Numerical simulation of the behavior of a 20-m-high deposit of tailings during an earthquake (M_w = 5.9) indicated liquefaction of the upper 8 m of tailings. Liquefaction analysis using the Simplified method with published magnitude scaling factors (MSF) did not predict the occurrence of liquefaction. The use of MSF values calculated from the laboratory testing predicted liquefaction in the upper 8 m of tailings, corresponding quite well with the numerical simulation. The results indicate that both analytical and numerical methods can be used to evaluate the potential for tailings liquefaction under seismic loads.     

层次分析法在甘肃省地质灾害易发性评价中的应用

在研究分析甘肃省内地质灾害类型和发育特点基础上,总结出甘肃省的主要致灾类型为滑坡(含崩塌)和泥石流.确立了主要灾害本身的活动规律和影响因素,厘定滑坡分布密度等历史危害性和暴雨分布等10项指标为影响地质灾害发育程度的主要凶素.采用层次分析方法建立了递阶层次结构体系,并构造出判断矩阵和特征向量,应用模糊数学方法进行了地质灾害易发区和防治区划分,取得了良好的应用效果.     

基于转移概率随机模拟的DNAPL运移二维和三维数值模拟对比研究

非均质介质的空间维度变化对重非水相流体（DNAPL） 的运移具有重要的影响。在充分考虑地质体的空间连续 性、不对称性以及各向异性等特征的基础上,采用基于马尔可夫链的转移概率（transition probability） 模型来构建非均质 随机场。该文通过TMVOC-MP软件来模拟DNAPL在非均质介质中的运移规律,探讨非均质随机场的水平空间连续性、 空间维度变化以及侧向运移过程对DNAPL运移的影响。结果表明,介质的水平空间连续性越好,DNAPL在水平方向的 迁移范围越大,在垂向的迁移范围越小;相比于三维模型,二维模型中DNAPL在水平方向的展布更大、在透镜体上的蓄 积量更多,在实际应用中以二维模型代替三维模型会加大模拟结果与实际污染情况之间的误差;侧向运移过程削弱了单 个平面的非均质性对DNAPL运移的控制,当存在侧向运移时,DNAPL绕过透镜体所运移的距离以及在透镜体上的蓄积 量会相应减小。     

孔隙介质润湿性的核磁共振刻度特征的测量

核磁共振测量技术已能够快速而无损地获得孔隙介质的物性信息, 但对于颗粒表面润湿性的测量还处于定性到半定量的水平.采用毛细管法和玻璃板法对经不同浓度二甲基二氯硅烷溶液处理的玻璃表面润湿性测量, 然后对核磁共振方法测量的孔隙介质润湿性结果进行标定, 进而得到孔隙介质润湿性系列的刻度特征.实验表明, 对于玻璃颗粒孔隙介质, 核磁共振测量的结果在作为表面处理剂的二甲基二氯硅烷溶液浓度0 %~ 0.7%变化范围内才与孔隙介质润湿性的变化有着明确的对应关系.在此范围之外, 对应的驰豫时间的变化虽然较大, 但其对于润湿性的刻度已没有明确的作用.      

Effect of Clay Minerals on Transport of Surfactants Dispersed Multi-walled Carbon Nanotubes in Porous Media

Clay minerals can hinder the transport of various contaminants in soil and aquifer, but how clay minerals affect the transport of nanoparticles in aquifers has not been investigated in depth. In this paper, the transport of surfactants dispersed multi-walled carbon nanotubes (MWCNTs) in well-defined quartz sand and mixtures of quartz sand and clay minerals (kaolinite and montmorillonite) with varying ionic strengths was studied. Sodium dodecyl benzenesulfonate (SDBS) and octyl-phenol-ethoxylate (TX100) MWCNT suspensions can migrate through quartz sand easily, but the presence of less than 2% w/w clay minerals in quartz sand can significantly hinder the transport of MWCNT suspensions, especially at high ion strength (0.6 mM CaCl2). The inhibition mechanism of clay minerals for surfactant-dispersed MWCNTs in porous media is the interception of MWCNTs. Kaolinite has stronger inhibition effect for MWCNTs transport than montmorillonite because more kaolinite can be retained in the quartz sand. Adsorption of surfactants by clay minerals does not affect the transport of MWCNTs significantly. This finding is important for the environmental assessment of MWCNT transport risks in soils and aquifers.