Comparison Between Analytical and Numerical Methods in Evaluating the Pollution Transport in Porous Media

Contaminant transport modelling in environmental engineering is generally conducted to evaluate the potential impact of contaminant migration on the subsurface environment or for interpreting tracer tests or groundwater quality data. In the past few decades a number of mathematical models have been established for evaluating the migration of pollution as indicated in the literature. This paper presents a comparison between a number of analytical and numerical models in evaluating pollution transport in soils. Three analytical models and a finite element model developed in this research are used for comparing four numerical examples under different conditions. Four cases of advection dominated problem with line source boundary, advection dominated problem with semi-line source boundary, advection–dispersion–sorption problem with line source boundary and advection–dispersion–sorption problem with semi-line source are considered. Based on the results the best analytical model that has a higher accuracy is recommended for practical applications.     

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 Calculation of Equivalent Cell Permeability Tensors for General Quadrilateral Control Volumes

A new method for upscaling fine scale permeability fields to general quadrilateral-shaped coarse cells is presented. The procedure, referred to as the conforming scale up method, applies a triangle-based finite element technique, capable of accurately resolving both the coarse cell geometry and the subgrid heterogeneity, to the solution of the local fine scale problem. An appropriate averaging of this solution provides the equivalent permeability tensor for the coarse scale quadrilateral cell. The general level of accuracy of the technique is demonstrated through application to a number of flow problems. The real strength of the conforming scale up method is demonstrated when the method is applied in conjunction with a flow-based gridding technique. In this case, the approach is shown to provide results that are significantly more accurate than those obtained using standard techniques.     

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.     

多孔介质中水气交替注入微观渗流模拟

针对水气交替注入(water-alternating-gas,WAG)过程中,油气水三相渗流的微观机理认识不足和油气水三相流体在多孔介质中分布规律认识不准确等问题,基于三维孔隙网络模型,应用孔隙级模拟方法,从微观角度模拟了不同润湿性多孔介质中的WAG驱替过程.结果表明:连通性较好的多孔介质中,原油主要在前两轮的WAG循环中被驱替出来;在前两轮WAG驱替之后,流体饱和度和分布规律达到比较稳定的状态,但在完全水湿模型中油相仍然在多孔介质中流动.得出的WAG驱替过程中各相流体饱和度的变化规律、各相流体分布规律和驱替类型,较好地阐述和解释了多孔介质中的微观驱替机理.     

反硝化增强去除乙醇对多孔介质渗透性的影响

随着乙醇混合汽油的不断推广应用,乙醇将成为地下水中与苯、甲苯、乙苯及二甲苯的同分异构体（BTEX）共存的一种新型污染物。通过4 个含水砂柱实验,研究了乙醇存在及其强化去除对含水介质渗透性能的影响。结果表明：在有限溶解氧与反硝化增强修复条件下,乙醇去除率达92% 以上;生物过程对介质渗透能力影响程度随乙醇初始浓度、消耗速率与补充频率而变化：乙醇初始浓度接近1 000 mg/L 和3 000 mg/L 时,乙醇消耗快,补充频率高,渗透系数下降总体上有连续性,最大下降幅度达一个数量级（×10-1 cm/s）;乙醇初始浓度达到5 000 mg/L 时,渗透性下降显著,可下降两个数量级,但乙酸的积累可影响生物活性,并使得渗透性变化出现反复;当不含乙醇时,汽油溶解组分对介质渗透性能的影响相对不明显。     

Equivalent Permeability and Simulation of Two-Phase Flow in Heterogeneous Porous Media

The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs.     

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.     

Equivalent Permeability and Simulation of Two-Phase Flow in Heterogeneous Porous Media

The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs.     

低渗储层多孔介质渗吸系数的分形分析

水自发渗吸驱油是低渗裂缝性油藏的重要采油机理,分析渗吸影响因素,研究油藏渗吸潜力,有效地利用渗吸效应,对提高石油采收率具有重要意义.系统分析了油藏渗吸及渗吸系数的研究现状,进而基于储层岩石孔隙结构的分形特征,推导了平均实际流速与平均直线流速的关系,考虑原始水饱和度的影响,建立了低渗油藏多孔介质渗吸系数的分形模型.结果表...     

A Damage Mechanics Model for Porous Media

When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. This paper introduces the concept of effective stress and the modified Mohr–Coulomb criterion as a means for examining the problem of consolidation response of a damage-susceptible poroelastic geomaterial, which is considered to be a novel development in the application of damage mechanics to the study of poroelastic phenomena. Then, a damage mechanics model for porous media is established and applied to analyze the Biot’s consolidation problem of damaged soils. The comparison between the numerical predictions and the classical solutions shows that the computational damage model developed in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media.     

控水结构面透水性的模糊综合评价方法

以溪洛渡水利枢纽为例，用模糊综合评价方法，对坝区控水的层间和层内错动面的透水性进行综合评价，评价结果可以作为设计和施工过程中的依据。     

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.      

渗透率空间变异性对重非水相流体运移的影响

中针对多孔介质中水、气和非水相流体的多相流运移特点,建立了由包气带至饱和带的 NAPLs- 水 - 气三相流模 型。用 Karhunen-Loeve 展开方法构建 4 个空间变异性不同的渗透率随机场。在此基础上,分别模拟 4 种情景重非水相流体 (DNAPLs)的泄漏运移过程。通过分析 DNAPLs 饱和度的空间分布以及其空间矩随时间的变化来探讨渗透率空间变异性对 DNAPLs 运移的影响。结果显示,随着渗透率空间变异性的增强,DNAPLs 饱和度的空间变异性增大。渗透率场中的优势通 道对 DNAPLs 运移有着显著影响,直接决定 DNAPLs 的运移路径和饱和度分布。渗透率场的各向异性降低了 DNAPLs 在垂向 上的运移速度,影响污染羽的形态。     

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.     

A Comparison of In Situ Analytical Methods for Trace Element Measurement in Gold Samples from Various South African Gold Deposits

Trace element concentrations in gold grains from various geological units in South Africa were measured in situ by field emission‐electron probe microanalysis (FE‐EPMA), laser ablation‐inductively coupled plasma‐mass spectrometry (LA‐ICP‐MS) and synchrotron micro X‐ray fluorescence spectroscopy (SR‐μ‐XRF). This study assesses the accuracy, precision and detection limits of these mostly non‐destructive analytical methods using certified reference materials and discusses their application in natural sample measurement. FE‐EPMA point analyses yielded reproducible and discernible concentrations for Au and trace concentrations of S, Cu, Ti, Hg, Fe and Ni, with detection limits well below the actual concentrations in the gold. LA‐ICP‐MS analyses required larger gold particles (> 60 μm) to avoid contamination during measurement. Elements that measured above detection limits included Ag, Cu, Ti, Fe, Pt, Pd, Mn, Cr, Ni, Sn, Hg, Pb, As and Te, which can be used for geochemical characterisation and gold fingerprinting. Although LA‐ICP‐MS measurements had lower detection limits, precision was lower than FE‐EPMA and SR‐μ‐XRF. The higher variability in absolute values measured by LA‐ICP‐MS, possibly due to micro‐inclusions, had to be critically assessed. Non‐destructive point analyses of gold alloys by SR‐μ‐XRF revealed Ag, Fe, Cu, Ni, Pb, Ti, Sb, U, Cr, Co, As, Y and Zr in the various gold samples. Detection limits were mostly lower than those for elements measured by FE‐EPMA, but higher than those for elements measured by LA‐ICP‐MS.     

PML Absorbing Boundary Condition for Seismic Numerical Modeling by Convolutional Differentiator in Fluid-Saturated Porous Media

The perfectly matched layer(PML) was first introduced by Berenger as an absorbing boundary condition for electromagnetic wave propagation.In this article,a method is developed to ex-tend the PML to simulating seismic wave propagation in fluid-saturated porous medium.This non-physical boundary is used at the computational edge of a Forsyte polynomial convolutional differenti-ator(FPCD) algorithm as an absorbing boundary condition to truncate unbounded media.The incor-poration of PML in Biot's equations is gi...