JHomogenizer: a computational tool for upscaling permeability for flow in heterogeneous porous media

This paper presents an object-oriented programming approach for the design of numerical homogenization programs, called JHomogenizer. It currently includes five functional modules to compute effective permeability and simple codes for computing solutions for flow in porous media. Examples with graphical output are shown to illustrate some functionalities of the program. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. The software is freely available, and the open architecture of the program facilitates further development and can adapt to suit specific needs easily and quickly.     

Analysis of a mixed discontinuous Galerkin method for instationary Darcy flow

We present an a priori stability and convergence analysis of a new mixed discontinuous Galerkin scheme applied to the instationary Darcy problem. The analysis accounts for a spatially and temporally varying permeability tensor in all estimates. The proposed method is stabilized using penalty terms in the primary and the flux unknowns.     

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles, slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry, as long as it aligns with the grid. We prove optimal global first-order L ² convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface in transition to the Stokes elements.     

Application of health risk assessment method for geological environment at national and regional scales

Health risk, defined as possibility or probability of health damage, illness or death of humans due to exposure to risk factors in the environment, was derived for geological environment (soils) and estimated at national scale for the whole Europe and at more detailed regional scale for Slovak Republic. The assessment was based on data obtained from international geochemical mapping of Europe (Geochemical Atlas of the Europe—827 soil samples) and national geochemical mapping programme of the Slovak Republic (9,860 soil samples). The following chemical elements were evaluated: As, B, Ba, Be, Cd, Cu, F, Hg, Mn, Mo, Ni, Pb, Sb, Se and Zn. The health risk assessment method was based on calculations of average daily doses of individual elements analysed in every collected soil sample. Exposure levels were set by using exposure parameters and reference doses from integrated databases of US EPA. The results of calculations were transformed into various sorts of maps (dot, pixel) to delineate areas where increased contents of risk elements can pose risk to human health. The average levels of chronic and carcinogenic risk are presented in the form of tables for single European countries and administrative units of Slovak republic. The results of European mapping (Geochemical Atlas of Europe) indicate that increased levels of potentially toxic elements in soil (mainly As, Pb and Ni) occur primarily in the countries of southern and western Europe. Such elements are associated with increased health risk for resident population. For the countries of northern Europe health risk was estimated at significantly lower level. Relatively high sampling density in Slovak Republic made it possible to calculate health risk at more detailed scale for individual administrative units (municipalities, provinces). The increased health risk level was found in areas well known for high soil contamination (e.g. mining areas).     

松散砂粒孔隙结构、孔隙分形特征及渗透率研究

多孔介质孔隙结构特征是决定流体微观运移机制的重要方面。文章用环氧树脂固结松散石英砂磨制出二维多孔介质薄片,并用孔隙结构图像处理方法提取出孔隙结构参数信息;根据孔隙结构参数,建立描述孔隙结构的分形几何模型,分析松散地层孔隙结构的分形特征;进行多孔介质渗透率的实验测量和分形计算。结果表明:多孔介质的孔隙率和孔径与粒径之间存在线性相关性,拟合度分别达到-0.976 5和0.996 6;在方格边长ε和含有孔隙的格子总数N(ε)的双对数坐标系中,lnε-lnN(ε)数据点近似成直线,且不同样品的孔隙分布分维数值比较接近;而在孔径r与大于该孔径的孔隙总数N(r)的双对数坐标系中,lnr-lnN(r)的数据点必须进行分段回归分析,以便能更好地反映孔隙结构的实际情况;孔隙分布分维数和孔径分维数与粒径也存在较高的对应关系;中砂渗透率的实验测得值是5.19×10-5mm2,孔径分维数分段回归法计算的大孔隙多孔介质渗透率为5.75×10-5mm2,测量值与计算值较为接近,孔径分维数可以计算多孔介质的渗透率。     

Effect of faceting on pore geometry in texturally equilibrated rocks: implications for low permeability at low porosity

The pore geometry of texturally equilibrated rocks is controlled by the interfacial energy ratio between grain boundaries and solid–liquid boundaries. Faceting at pore walls, which is a common feature of pore networks in rocks, strongly affects the liquid distribution. We investigated the effects of faceting on the equilibrium pore geometries based on image analysis of several systems with various degrees of faceting and dihedral angles. The degree of faceting was assessed by the F value, which is the ratio of the flat interface length at the pore wall to the length of total interfacial boundary between solid and liquid. The F values tend to increase with increasing liquid volume fraction. Little-faceted systems show relatively homogeneous liquid distribution. Moderately-faceted systems with a higher dihedral angle (∼55°) are characterized by development of large pores surrounded by faceted walls and complementary shrinkage of triple junction tubes, whereas strongly faceted systems with a low dihedral angle show no evidence of shrinking triple junction tubes, although most pores are surrounded by faceted pore walls. The faceted systems tend to produce more facet boundaries at the pore walls due to the difference of interfacial energies between the flat and curved surfaces. In the systems with the same degree of faceting, heterogeneity of liquid distribution tends to decrease with dihedral angle. For faceting systems, the permeability of texturally equilibrated rocks with low liquid fraction would be significantly decreased by the relative reduction of triple junction volumes or by closure of channels along grain edge due to the truncation of facet walls.     

一种预测不同温度下非饱和土相对渗透系数的间接方法

高放核废料地下处置、城市供热管道及埋地高压电缆等工程建设的进行,使得考虑温度影响的非饱和土渗透性能越来越受到人们的重视。在考虑温度效应的非饱和土土-水特征曲线研究基础上,结合利用土-水特征曲线预测非饱和土相对渗透系数的方法,建立了一种预测不同温度下非饱和土相对渗透系数的间接方法。所建立的表达式是针对土-水特征曲线的整个吸力范围,从而使得其在应用上更具一般意义。利用MX-80班脱土和黄土土样的试验结果,对不同温度下相对渗透系数随吸力的变化进行了预测,得到了令人满意的结果     

Influence of damage on pore size distribution and permeability of rocks

The model proposed in this article relates permeability to porosity measurements that can easily be performed in the laboratory. The pore size distribution (PSD) curve is updated with strains and damage. The updated volumetric fractions of natural pores and cracks are introduced in the expression of permeability. Contrary to classical permeability models based on PSD integrations, the model proposed in this article accounts for possible changes in the porosity modes: one mode for undamaged samples and two modes for cracked samples. The proposed approach also accounts for varying states of damage, as opposed to classical fracture network models, in which the cracks pattern is fixed. The only material parameters that are required to describe the microstructure are the lower and upper bounds of the pores size for both natural pores and cracks. All the other PSD parameters involved in the model are related to macroscopic parameters that can easily be determined in the laboratory, such as the initial void ratio. The framework proposed in this article can be used in any damage constitutive model to determine the permeability of a brittle porous medium. Drained triaxial compression tests have been simulated. Before cracks initiation, permeability decreases while the larger natural pores are getting squeezed. After the occurrence of damage, permeability grows due to the increase of cracks density. The model performs well to represent the influence of the confining pressure on damage evolution and permeability variations. Copyright © 2012 John Wiley & Sons, Ltd.     

An upscaling method and a numerical analysis of swelling/shrinking processes in a compacted bentonite/sand mixture

This paper presents an upscaling concept of swelling/shrinking processes of a compacted bentonite/sand mixture, which also applies to swelling of porous media in general. A constitutive approach for highly compacted bentonite/sand mixture is developed accordingly. The concept is based on the diffuse double layer theory and connects microstructural properties of the bentonite as well as chemical properties of the pore fluid with swelling potential. Main factors influencing the swelling potential of bentonite, i.e. variation of water content, dry density, chemical composition of pore fluid, as well as the microstructures and the amount of swelling minerals are taken into account. According to the proposed model, porosity is divided into interparticle and interlayer porosity. Swelling is the potential of interlayer porosity increase, which reveals itself as volume change in the case of free expansion, or turns to be swelling pressure in the case of constrained swelling. The constitutive equations for swelling/shrinking are implemented in the software GeoSys/RockFlow as a new chemo‐hydro‐mechanical model, which is able to simulate isothermal multiphase flow in bentonite. Details of the mathematical and numerical multiphase flow formulations, as well as the code implementation are described. The proposed model is verified using experimental data of tests on a highly compacted bentonite/sand mixture. Comparison of the 1D modelling results with the experimental data evidences the capability of the proposed model to satisfactorily predict free swelling of the material under investigation. Copyright © 2004 John Wiley & Sons, Ltd.     

Method and analysis for the upscaling of structural data

3D geological models are created to integrate a set of input measurements into a single geological model. There are many problems with this approach, as there is uncertainty in all stages of the modelling process, from initial data collection to the approach used in the modelling scheme itself to calculate the geological model. This study looks at the uncertainty inherent in geological models due to data density and introduces a novel method to upscale geological data that optimises the information in the initial dataset. This method also provides the ability for the dominant trend of a geological dataset to be determined at different scales. By using self-organizing maps (SOM's) to examine the different metrics used to quantify a geological model, we allow for a larger range of metrics to be used compared to traditional statistical methods, due to the SOM's ability to deal with incomplete datasets. The classification of the models into clusters based on the geological metrics using k-means clustering provides a useful insight into the models that are most similar and models that are statistical outliers. Our approach is guided and can be calculated on any input dataset of this type to determine the effect that data density will have on a resultant model. These models are all statistical derivations that represent simplifications and different scales of the initial dataset and can be used to interrogate the scale of observations.     

Testing helium equilibrium between quartz and pore water as a method to determine pore water helium concentrations

The effectiveness of carbon capture and geologic storage depends on many factors, including and especially the permeability of the reservoir’s caprock. While caprock integrity is generally assumed if petroleum has been preserved, it is poorly constrained in reservoirs containing only saline waters, and CO₂ leakage poses a potential risk to shallow aquifers. Naturally-occurring He accumulates in pore waters over time with the concentration being strongly dependent on the long term flux of fluid through the caprock. Furthermore, a small fraction of pore-water He diffuses into quartz and this may be used as a proxy for He concentrations in pore water, where dissolved gas samples are difficult to obtain, such as in deep sedimentary basins. In this paper He contained in quartz grains is measured and compared to previously measured pore water concentrations. Quartz was purified from core samples from the San Juan Basin, New Mexico and the Great Artesian Basin, South Australia. Quartz separates were heated at 290 °C to release He from the quartz. The quartz from the San Juan Basin and high purity quartz from the Spruce Pine Intrusion, North Carolina was repeatedly impregnated at varying pressures using pure He, heated and analyzed to build He sorption isotherms. The isotherms appear linear but vary between samples, possibly due to fluid inclusions within the quartz grains as high purity quartz samples partition only 1.5% of He that partitions into San Juan Basin samples. Concentrations of He in the pore water were calculated using the He-accessible volume of the quartz and the air–water He solubility. The mean San Juan Basin He pore water concentration was 2 × 10^–5 cc STP He/g water, ∼400 times greater than atmospheric solubility. Great Artesian Basin samples contain a mean He concentration of 3 × 10^–6 cc STP He/g water or 65 times greater than atmospheric solubility. However, pore water He concentrations in both the San Juan and Great Artesian Basins differ by up to an order of magnitude compared to samples collected with an alternate method. The reason for the offset is attributable to either partial saturation of the pore volume or a lack of He equilibrium between quartz and pore water. Coating of clay or other mineral phases on quartz grains, which tends to reduce the effective diffusion coefficient, may cause the latter. This technique of assessing permeability is promising due to the abundance of existing core samples from numerous basins where carbon sequestration may ultimately occur.     

用积分法求取岩石孔隙结构特征值

针对图解法求取孔隙结构特征值使用条件严格,同时误差较大,而矩法饱和度范围又受限于试验。采用积分法求取特征值,即对孔隙半径进行积分求取特征值。积分法必须先获取孔隙半径数学表达式,即毛管压力数学模型。对毛管压力数学模型进行了探究,在双对数坐标系下推导并建立了毛管压力幂函数模型,采用最小二乘法求取模型参数,并通过对比Sami论文数据验证了推导的模型。深入分析矩法与积分法的联系可知,代入孔隙半径数学表达式即可用积分法求取岩石孔隙结构特征值。最后,对3种方法求取结果进行分析讨论,得出积分法算法严谨,更加接近真实值。这一研究加深了对岩石微观孔隙结构认识。     

砂西油田低渗透储层成岩储集相及储集空间演化模式

综合应用取心井的岩石铸体薄片、图像分析、扫描电镜、电子探针能谱、阴极发光、粘土矿物X衍射分析和镜质体反射率等实验测试资料,研究了E₃¹储层的成岩作用、成岩演化序列和成岩阶段划分。通过分析低渗透储层成岩作用对储集物性的影响,认为造成本区储层砂岩较低渗透率的主要成因机理是成岩期各种自生矿物的充填和胶结作用。根据成岩作用及其特有的储集空间组合,将E₃¹储层划分为4种成岩储集相类型:A相——不稳定组分中强溶解次生孔隙成岩储集相、B相——中等胶结中强压实残余粒间孔成岩储集相、C相——碳酸盐强胶结成岩储集相、D相——早期硬石膏强胶结成岩储集相。详细阐述了低渗透储层中各类成岩储集相的特征及其形成机制,并探讨了其储集空间类型及演化模式。     

二阶段聚类法在地质遗迹分类与开发中的应用

地质遗迹的科学分类是指导地质遗迹保护、利用与开发的重要依据.文章运用二阶段聚类法,选用地质遗迹的价值类型、开发成本、所在地经济与财政状况等因素为变量,以浙江省国家级地质遗迹为例研究地质遗迹的分类与开发,并对各类地质遗迹的保护、利用与开发提出具体建议.     

Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow

We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique.     

Absorption characteristics of a Stoneley wave in multilayered media and the logging method for estimating permeability

The aim of the study is to increase the reliability of estimation of the acoustic parameters of a layered permeable formation using new software, based on two-velocity continuum equations for 2D numerical simulation of acoustic waves propagating in a borehole. The key method is the method of finite differences as applied to solving equations of the continuum filtration theory. The dissipative characteristics of Stoneley waves have been identified for the case of their propagation in a layered formation. These aspects should be taken into account when using Stoneley waves to estimate the permeability of geologic media.     

Mesoscale experimental study on chemical composition,pore size distribution,and permeability of tailings

To study the seepage characteristics of tailing sand, an indoor sand column test was performed with three kinds of tailing sand obtained from Henan and Shaanxi provinces, China. River sand, quartz sand, and glass beads were also employed for comparison. Using the nuclear magnetic resonance, the researchers studied pore size distribution and permeability under different hydraulic gradients. The chemical composition and particle morphology were analyzed by energy-dispersive spectrometry and X-ray diffraction. The results were as follows. (1) The three kinds of tailings sand are small in diameter, mainly in the range from 0.15 to 0.5 mm. Their diameter distribution is more concentrated than river sand. The surface of tailing sand is rough. As for chemical composition, tailing sand contains many kinds of metal elements. (2) With hydraulic gradient increasing, the micropores in the tailings samples become fewer, the larger pores grow in number, and the peak of the pore size distribution changes to the left; blocking is more obvious. (3) The small pores gradually decrease during the test. Under the influence of groundwater pressure, the smaller gravel could migrate and block tiny pores. The structure of particle arrangement becomes denser. Therefore, it would prevent the seepage liquid from passing through the medium. The permeability coefficient K decreases.     

确定含水层渗透系数的冲击试验方法

运用Hvorslevr冲击试验方法测定CIRP试验场地下研究设施(URF)试验含水层的渗透系数。由于含水层厚度小、富水性差,正在进行核素迁移试验,以及操作空间有限,因此不能进行抽水或注水试验,同时考虑到试验范围较小,故采取冲击试验求含水层的渗透系数。含水层介质为亚粘土,隔水底板距URF底板面约6m。试验的冲击量小,可以忽略URF内南部含水层对试验结果的影响。试验钻孔的孔径和井管内径相近,减小了钻孔结构对试验结果的影响。试验结果(472×10-4、658×10-4cm/s)与采用自URF内试验含水层的未扰动土柱所作的室内渗透试验结果(41×10-4～82×10-4cm/s)在同一数量级。