双重介质中的一类核素迁移数学模型及其反演

探讨了孔隙与单裂隙双重介质中的一类核素迁移数学模型及其反演问题。该核素迁移模型是一个耦合的抛物型方程组定解问题。若已知排污点的核素浓度变化规律,利用Laplace变换及其逆变换方法,求得了核素迁移模型正问题的解析解;反之,由下游裂隙中某个点的实测核素浓度,利用偏微分方程的叠加原理和反问题的拟解法,反求出核素迁移模型反问题的解,即排污点的核素状态。最后,给出核素迁移模型的正问题和反问题的数值模拟。数值结果表明,正问题的解析解能够刻画核素的迁移规律,也显示出所提反问题方法能有效地反演核素污染源。     

某核废物处置预选区中核素迁移模拟研究

核素在裂隙介质中的迁移问题是核废物深地质处置中极为关注的问题。为了解裂隙介质中核素的迁移规律,建立了基于双重介质理论的描述核素在裂隙域和基质域中迁移的基本微分方程,利用拉普拉斯变换推导出其解析解;在对西北某核废物处置场预选区地水文地质条件分析的基础上,获取相关参数,利用一维多途径核素迁移模型,选取国内在花岗岩中研究较多的核素Cs-134、Co-57、Tc-99,模拟这几种核素的相对浓度随模拟时间、迁移距离的变化规律。模拟结果表明：在其他条件都相同的情况下,Cs-134的迁移是最快的,而Tc-99迁移是最慢的。     

双重介质中核素迁移模型的近似解析解及实验室使用条件

本文将双重介质中核过移模型的解析解进行了简化，得到了便于应用的近似解析解及其相关结论经推导给出了实验室利用近似解析解的条件以及求阻滞系数、固有扩散系数的公式。     

北方岩溶含水层双重介质水流模型及其应用探讨

本文将北方岩溶介质划分为两种基本类型:溶隙网络—溶孔型和溶隙网络—微裂隙型。概化出裂隙岩溶介质的双重介质水流模型。解决了下面几个问题:（1）认识北方岩溶介质所具有的双重介质性;（2）分别对孔隙和微裂隙所构成的岩块域和溶隙网络域建立数学模型,并用岩块和裂隙的水量交换项将两者耦合起来。模型中岩块并未被概化成某一特殊几何形态如球体或平行板,而是按其实际产出形态处理;（3）在岩块中也应用了二维水流模型。以往作者多用一维流方程,目的在于求其解析解,这有许多不足之处;（4）在裂隙和岩块域均采用有限单元法,将两个域的模型联立求数值解,克服了解析法或解析—数值法联合的局限性。 在给定参数情况下,本文进行了典型水文地质条件下的计算,证明了模型是能够较好地刻画溶隙网络—溶孔或微裂隙型介质的特征和水流特点的。同时,本文成功地应用了济南西南郊岩溶含水层的实际资料进行了模拟计算,对双重介质方法的实用进行了听的尝试。     

放射性核素在裂隙介质中迁移模型研究综述

指出了研究核素迁移问题的意义,归纳了裂隙介质的几种简化形式,概括总结了国内外对放射性核素在裂隙介质中迁移模式研究中的进展.提出了迁移数学模式的分类方法,并指出了目前迁移问题研究中存在的不足.     

含喉部裂隙介质CO_2反应迁移的格子Boltzmann模拟研究

CO_2地质封存是目前最经济、最可靠的CO_2减排技术之一,对CO_2反应迁移规律的研究具有重要的理论价值。采用Dardis多孔介质模型与已有的CO_2反应迁移模型耦合,对含喉部裂隙的复杂介质中反应迁移规律进行模拟研究。速度场的模拟结果表明,裂隙内的速度明显高于基质速度,在喉部中心线位置处速度达到最大值。溶解反应主要集中于入口段及裂隙的上、下边缘附近;受喉部的影响,喉部下游的裂隙边缘几乎不发生溶解反应。反应物H~+在裂隙及喉部中的浓度明显高于在基质中的浓度;而生成物Ca~(2+)的高浓度区则出现在下游基质区中。针对不同喉部位置的情况进行对比,分析其对反应率及组分浓度的影响规律。最后对含突扩孔的裂隙介质进行了模拟,发现其提高了裂隙内的速度及组分迁移,这与喉部裂隙介质内的规律正好相反。上述结果较好地说明了本模型具有模拟研究复杂裂隙介质内的CO_2反应迁移规律的能力。     

平面单裂隙介质中核素的迁移模型

本文提出核素在平面单裂隙中的迁移模型 ,用于模拟放射性核素在裂隙介质中的迁移问题 ,并以实例说明该模型的可靠性     

基于等效连续介质模型的单裂隙渗流数值模拟研究

基岩裂隙介质的空间变异性导致裂隙渗流情况十分复杂。在等效连续介质模型的基础上,建立数值分析模型研究了裂隙宽度和渗透系数对单裂隙渗流的影响。利用单裂隙立方定律对裂隙流量进行解析计算,并在单一变量研究原则下,利用MODFLOW创建了光滑平行板单裂隙介质的数值模型。据等效理论,将单裂隙宽度放大10倍的条件下,解析解计算结果比模拟结果高出6个数量级;不同裂隙宽度条件下,数值模拟结果与解析计算结果都表现出通过单个裂隙的水流量随着裂隙的宽度的增加而增加;不同渗透系数条件下,稳定流与非稳定流条件下得到的流量都随渗透系数的减小而变小。     

硝基苯在含水层中迁移转化影响因素的定量研究

通过室内模拟实验,确定了影响硝基苯在含水层中迁移转化的主要因素,并采用解析解方法计算出各因素的影响水平。研究表明,硝基苯在淤泥介质中的吸附能力大于砂砾介质,其在淤泥介质中的阻滞系数为2.22,在砂砾介质中的阻滞系数为1.74。根据一级动力学方程计算得出,硝基苯在淤泥介质中的自然衰减总速率常数为0.063 5/h,在砂砾介质中的自然衰减总速率常数为0.0059/h。而且,不论是在淤泥介质还是在砂砾介质中,生物降解作用均是硝基苯迁移转化过程的主要影响因素,其影响水平占硝基苯自然衰减能力的50%左右。     

裂隙岩石介质中核素迁移的模型及其算子分裂、迎风、均衡格式

建立了放射性核素在裂隙岩石介质中迁移的双重介质模型,对模型的求解提出了一种新的数值方法—Galerkin有限元法与算子分裂、迎风、均衡格式相结合的新方法,给出了水质模型算子分裂、迎风、均衡格式的稳定性条件,且所得到的计算格式是非负的。最后通过对核素90Sr 100年、99Tc 1000年的预测计算,验证了本文所提方法的有效性和稳定性,并得出了一些有重要意义的结论。     

考虑固结效应的溶质传输研究

传统的孔隙介质水动力学采用对流-扩散方程,研究溶质在流体中的迁移。在这个过程中,孔隙介质被认为是不变形的,因而是一个稳态问题。针对二维情况下孔隙介质变形对溶质传输的影响,给出了考虑孔隙介质固结效应的溶质传输方程,并且探讨了该类问题的求解方法。     

Errors in the upstream mobility scheme for countercurrent two-phase flow in heterogeneous porous media

In reservoir simulation, the upstream mobility scheme is widely used for calculating fluid flow in porous media and has been shown feasible for flow when the porous medium is homogeneous. In the case of flow in heterogeneous porous media, the scheme has earlier been shown to give erroneous solutions in approximating pure gravity segregation. Here, we show that the scheme may exhibit larger errors when approximating flow in heterogeneous media for flux functions involving both advection and gravity segregation components. Errors have only been found in the case of countercurrent flow. The physically correct solution is approximated by an extension of the Godunov and Engquist–Osher flux. We also present a new finite volume scheme based on the local Lax–Friedrichs flux and test the performance of this scheme in the numerical experiments.     

某铀尾矿库区地下水238^U迁移模拟

将铀尾矿库核素迁移问题概括为均质多孔介质中稳定的二维水流条件下的三维溶质迁移问题,利用Visual Modflow软件（MT3D）采用全隐式差分法对某铀尾矿库放射性核素迁移进行了模拟研究,模拟值结果与浓度实测值较吻合,揭示了尾矿库放射性核素时空迁移规律。     

Laboratory simulation of geogas microbubble flow

Preliminary laboratory tests provided first data on the behavior of gas microbubbles through porous media in the framework of the geogas theory. Under experimented conditions with laboratory equipment arranged for pressure controlled gas-tracer injection and sampling, gas microbubbles moved up to ten times faster than singlephase flow in dry media under the same injection pressure. Microbubbles were determined to be very sensitive to changes in injection pressure and their terminal velocity seems to be described with good approximation by the Stokes formula. The capability of microbubbles to pick up and transport upward for short distances solid ultra-small particles (metallic and radionuclide compounds) has been proved. Results are consistent with a time-dependent process linked to the transport properties of microbubbles (e.g., flotation), such as that reported by some authors.     

A mixed solution for two-dimensional unsteady flow in fractured porous media

A mixed finite element–boundary element solution for the analysis of two-dimensional flow in porous media composed of rock blocks and discrete fractures is described. The rock blocks are modelled implicitly by using boundary elements whereas finite elements are adopted to model the discrete fractures. The computational procedure has been implemented in a hybrid code which has been validated first by comparing the numerical results with the closed-form solution for flow in a porous aquifer intercepted by a vertical fracture only. Then, a more complex problem has been solved where a pervious, homogeneous and isotropic matrix containing a net of fractures is considered. The results obtained are shown to describe satisfactorily the main features of the flow problem under study. © 1997 by John Wiley & Sons, Ltd.     

An analytical solution for the transient response of saturated linear elastic porous media

The motions of fluid and solid phases in saturated porous media are coupled by inertial, viscous and mechanical interactions as described by Biot's equations. A one-dimensional exact analytical solution of the Biot's equations for the completely general solution of the transient problem in saturated, linear, elastic, porous media is presented. The problem is solved by using the Fourier series. The transient response of porous media is shown for typical material properties of a natural granular deposit and for different degrees of viscous coupling. The analytical results show the mechanics of dispersive wave propagation in saturated porous media and they should provide a useful comparison term for the existing numerical solution methods.     

Autorun analysis of sedimentary porous materials

Fundamentals of autorun analysis have been given to describe porous media geometry, including sedimantary rocks. The mathematical abstraction of porous media has been presented on the basis of random fields. Classical parameters of porous media, such as porosity and specific surface, have been expressed in terms of autorun function. Finally, a stochastic model has been proposed for the underlying generating mechanism of the porous medium. This model is capable of producing synthetic porous medium and, on the average, porosity as well as the specific surface. The first autorun coefficient is asymptotically equal to the porosity of the medium concerned. It also has been observed that the porosity together with the autorun function are sufficient to produce the specific surface value of the medium.On leave from the Technical University of Istanbul, Taksim, Turkey.     

Modelling of steady‐state fluid flow in 3D fractured isotropic porous media: application to effective permeability calculation

In this paper, 3D steady‐state fluid flow in a porous medium with a large number of intersecting fractures is derived numerically by using collocation method. Fluid flow in the matrix and fractures is described by Darcy's law and Poiseuille's law, respectively. The recent theoretical development presented a general potential solution to model the steady‐state flow in fractured porous media under a far‐field condition. This solution is a hypersingular integral equation with pressure field in the fracture surfaces as the main unknown. The numerical procedure can resolve the problem for any form of fractures and also takes into account the interactions and the intersection between fractures. Once the pressure field and then the flux field in fractures have been determined, the pressure field in the porous matrix is computed completely. The basic problem of a single fracture is investigated, and a semi‐analytical solution is presented. Using the solution obtained for a single fracture, Mori‐Tanaka and self‐consistent schemes are employed for upscaling the effective permeability of 3D fractured porous media. Copyright © 2012 John Wiley & Sons, Ltd.