Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media

Numerical models of groundwater flow require the assignment of hydraulic conductivities to large grid blocks discretizing the flow domain; however, conductivity data is usually available only at the much smaller scale of core samples. This paper describes a geostatistical model for hydraulic conductivity at both the core or point scale and that of grid blocks. Conductivity at the block scale is obtained empirically as a spatial power-average of point scale values. Assuming a multivariate Gaussian model for point log-conductivity, expressions are derived for the ensemble mean and variance of block conductivity. The expression for the ensemble mean of block scale conductivity is found to be similar to an expression for the ensemble effective conductivity of an infinite field derived analytically by earlier authors. Here, block conductivities obtained by power averaging are compared with effective conductivities obtained from a numerical flow model and are found to be in excellent agreement for a suitably chosen averaging exponent. This agreement deteriorates gradually as the log variance of conductivity increases beyond 2. For arbitrary flow field geometry and anisotropic conductivity covariances, the averaging exponent can be calibrated by recourse to numerical flow experiments. For cubic fields and an isotropic spatial covariance, the averaging exponent is found to be 1/3. In this particular case, it was found that flow field discretization at the block scale through local averaging of point conductivities gave similar results to those obtained directly using a point scale discretization of the flow field.     

Flow Characteristics of Large-Scale Liquefaction-Slip of the Loess Strata in Shibei Tableland, Guyuan City, Induced by the 1920 Haiyuan M8 1/2 Earthquake

Based on the dynamic triaxial liquefaction test of the loess samples which are taken from Shibei tableland, Guyuan City, Ningxia, China, the characteristics of dynamic strain, dynamic stress and pore water pressure are studied under cyclic loading. Triaxial shear test is conducted immediately after the sample reaches liquefaction point. During the test, the property of the liquefied soil is analyzed through fluid mechanics method, whereby the fluidity of the liquefied soil is represented by apparent viscosity.The results show that the fluidity of liquefied loess changes from "shear thickening" to "shear thinning" as the shear force continues, and the fluidity of liquefied loess is closely related to its structure. In addition, in the process of forming a new stable state, the apparent viscosity and deviant stress change with axial strain in a similar approach. When the sample reaches its stable state, it meanwhile shows a relatively stable apparent viscosity. According to the fluid mechanics and the law of conservation of energy, the slip distance of the liquefied soil is estimated, and the results are in good agreement with the field investigation results.     

Another look at the conceptual fundamentals of porous media upscaling

We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126).     

基于BISQ模型双相各向同性介质中地震波数值模拟

基于BISQ机制,推导了双相各向同性介质中弹性波数值模拟方程,并借助交错网格有限差分方法进行了波场模拟。证实了三种波(快纵波、慢纵波、横波SV)的存在和波场特征;在合成地震记录中,观测列三种波的反射,由于各种波相互之间的转换,转换波在地震记录中显示也很清楚,这使得波场变得更为复杂化。     

具有弱透水层的多层介质含水系统中污染质运移数值模拟研究——以大庆市纳污湖泡区为例

选取大庆市贴不贴泡区具有普遍意义的饱和-非饱和多层介质含水系统中石油类污染为研究对象.在分析水文地质条件的基础上, 利用实验研究获得含水系统中连接上下含水层的弱透水层的渗透规律, 然后运用数值模拟技术建立起此类含水系统中石油类污染质运移数值模拟模型.应用所建模型对污染质的污染趋势进行了预测, 并提出污染控制措施.      

A new scheme for numerical modelling of flow and transport processes in 3D fractured porous media

The objective of this work is to develop a new numerical approach for the three-dimensional modelling of flow and transient solute transport in fractured porous media which would provide an accurate and efficient treatment of 3D complex geometries and inhomogeneities. For this reason, and in order to eliminate as much as possible the number of degrees of freedom, the fracture network, fractures and their intersections, are solved with a coupled 2D–1D model while the porous matrix is solved independently with a 3D model. The interaction between both models is accounted for by a coupling iterative technique. In this way it is possible to improve efficiency and reduce CPU usage by avoiding 3D mesh refinements of the fractures. The approach is based on the discrete-fracture model in which the exact geometry and location of each fracture in the network must be provided as an input. The formulation is based on a multidimensional coupling of the boundary element method-multidomain (BEM-MD) scheme for the flow and boundary element dual reciprocity method-multidomain (BE-DRM-MD) scheme for the transport. Accurate results and high efficiency have been obtained and are reported in this paper.     

Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers

Deep saline aquifers are one of the most suitable geologic formations for carbon sequestration. The linear and global stability analysis of the time-dependent density-driven convection in deep saline aquifers is presented for long-term storage of carbon dioxide (CO₂). The convective mixing that can greatly accelerate the CO₂ dissolution into saline aquifers arises because the density of brine increases upon the dissolution of CO₂ and such a density difference may induce instability. The effects of anisotropic permeability on the stability criteria, such as the critical time for the appearance of convective phenomena and the critical wavelength of the most unstable perturbation, are investigated with linear and global stability analysis. The linear stability analysis provides a sufficient condition for instability while the global stability analysis yields a sufficient condition for stability. The results obtained from these two approaches are not exactly the same but show a consistent trend, both indicating that the anisotropic system becomes more unstable when either the vertical or horizontal permeability increases.     

Mantle process beneath Philippine Sea back-arc spreading ridges: A synthesis of peridotite petrology and tectonics

Abstract In order to obtain a general view of the mantle process beneath a back‐arc basin spreading ridge, the diversity of peridotite petrology and tectonic occurrences in two back‐arc basin spreading ridges from the Philippine Sea were examined: the Parece Vela Rift and the Mariana Trough. The Parece Vela Basin spreading ridge (Parece Vela Rift) was a physically fast/intermediate‐spreading ridge, although many tectono‐magmatic features resemble those of slow‐ to ultraslow‐spreading ridges. Two unusual features of the Parece Vela Rift further demonstrate the uniqueness of the ridge: full‐axial development of oceanic core complexes and exposure of mantle peridotite at segment midpoints. The Parece Vela Rift yields a lithological assemblage of residual but still fertile lherzolite/harzburgite, plagioclase‐bearing harzburgite and dunite; similar assemblages are reported from the equatorial Mid‐Atlantic Ridge at the Romanche Fracture Zone and the ultraslow‐spreading ridges from the Indian and Arctic Oceans. The tectono‐magmatic characteristics of the Parece Vela Rift suggest that diffuse porous melt flow and pervasive melt–mantle interaction were the important mantle processes there. Globally, this ‘porous melt flow‐type’ mantle process is likely to occur beneath a segment midpoint of the ridge having a thick lithosphere, typically an ultraslow‐spreading ridge. In contrast, the Mariana Trough is a typical slow‐spreading ridge, exposing mantle peridotite at segment ends. The Mariana Trough yields a lithological assemblage of residual harzburgite and veined harzburgite, a common assemblage among the global abyssal peridotite suite. The tectono‐magmatic characteristics of the Mariana Trough suggest that channeled melt/fluid flow and limited melt–mantle interaction are the important mantle processes there, because of the colder wall‐rock peridotite in the segment end. This ‘channeled melt flow‐type’ mantle process is likely to occur in the shallow lithospheric mantle at the segment ends of any spreading ridges.     

非均匀介质中交错网格高阶有限差分数值模拟

地震波场的数值模拟一直是地球物理学的一个重要的研究领域,而在数值正演模拟方法的研究中,计算精度和计算效率是评价该方法有效性及优越性的二个关键问题。这里从一阶速度—应力弹性波动方程出发,着重介绍如何构造离散化模型的网格,如何求解空间导数,如何选取边界条件等内容,从而更有效地提高数值计算的精度与计算效率。文中构造了不同类型的介质模型,并在交错网格中,利用高阶有限差分模拟非均匀介质的波场传播。模拟结果表明,该方法实现简单,具有很好地稳定性和较高的精度,能够直观、高效地反映出介质中波场的传播规律。