含液体非弹性多孔介质中波传播过程的失稳与逸散性

在基于Biot理论的饱和－非饱和多孔介质的动力－渗流模型中计及流固惯性耦合效应。对单轴应变的一维情况讨论了饱和和非饱和多孔介质中波传播传播过程的驻值失稳和逸散性,分解了流固粘弹耦合,流固惯性耦合,流固混合体的压缩性,孔隙水饱和度,及固体骨架在高应变速率下材料粘弹性本构行为等因素的影响。该工作将对克服饱和与非饱和多孔介质在强动荷载下波传播过程的数值求解困难提供理论上的依据和启示。     

页岩中页岩气渗流系数计算模型

依据页岩气在页岩孔隙中的渗流行为,建立了页岩气释放、扩散耦合模型,利用Laplace变换方法,将耦合模型转化为Laplace空间上常微分方程初边值问题,并找到了压力解析解,求得了渗透系数.实例计算验证了渗流模型及解的可靠性,丰富了页岩气不定常渗流理论.     

非饱和土一维固结的半解析解

首先对Fredlund的非饱和土一维固结理论进行简化,由得到的液相及气相的控制方程、Darcy定律及Fick定律,经Laplace变换及Cayley-Hamilton定理构造了顶面状态向量与任意深度处状态向量间的传递关系;通过引入边界条件,得到了大面积瞬时加荷情况多种边界条件下Laplace变换域内的超孔隙水压力、超孔隙气压力及土层沉降的解;采用Crump方法编制程序实现Laplace逆转换,得到了时间域内的超孔隙水压力、超孔隙气压力、土层沉降的半解析解;引用典型算例,对单面排水排气情况,与已有的解析解进行对比,验证其正确性;对单面排气不排水情况,与差分法结果进行对比进一步证明半解析解的正确性,并进行固结特性分析.该研究对非饱和土一维固结的研究具有重要的意义.     

土壤水流与溶质耦合运移问题的混合元-迎风广义差分法研究

本文研究了一维非饱和土壤水流与溶质耦合运移问题的数学模型, 建立了求其数值解的守恒混合元-迎风广义差分格式. 对非线性土壤水分入渗方程, 采用守恒混合元法进行离散模拟, 同时得到了土壤含水量和水分通量; 而对对流-扩散形式的溶质运移方程, 利用迎风的广义差分法离散求解. 且分析了解的存在唯一性, 并讨论了误差估计. 最后给出数值算例, 模拟结果表明利用本文格式来求解非饱和土壤水流与溶质耦合运移问题是可靠的, 且该格式具有稳定性和可实用性.     

非饱和土层一维固结问题的解析解

对一有限厚度,处于一维受荷状态,表面为透水透气面,底面为不透水不透气面的非饱和土层,依据Fredlund的非饱和土一维固结理论,由液相及气相的控制方程、Darcy定律及Fick定律,经Laplace变换及Cayley-Hamilton数学方法构造了顶面状态向量与任意深度处状态向量间的传递关系;通过引入初始及边界条件,得到了Laplace变换域内的超孔隙水压力、超孔隙气压力以及土层沉降的解;实现Laplace逆变换,得到了时间域内的解析解;用一典型算例,与差分法结果进行对比,验证了其正确性.     

多翼裂缝压裂偏心井半解析模型及其渗流特征

考虑压裂多翼裂缝偏心井的实际情况,建立了多翼裂缝偏心井的数学模型.采用Laplace变换和压降叠加原理得到Laplace空间多翼裂缝压裂偏心井井底压力的半解析解.采用非均匀流量法,对井底压力的半解析解进行离散.结合Stehfest数值反演获得实空间井底压力的数值解和产量分布.借助SAPHIR试井分析软件建立了储层的数值试井模型并进行了数值离散计算.将计算结果与该文的半解析模型计算结果进行了对比,验证了该文模型的正确性.结果表明,多翼裂缝压裂偏心井井底压力变化可划分为8个主要流动阶段.最后讨论了裂缝的无因次导流能力、裂缝的不对称因子和井的偏心距对井底压力变化和产量分布特征的影响.     

堆浸工艺水动力学研究

利用无量纲的形式推导出堆浸工艺中通过非饱和堆我动区和滞留区的溶质运移模型,通过最小二乘法确定模型参数,并就两种不同供液情形下的解析解进行了讨论.该模型可用来研究堆浸中溶质浓度的变化规律.     

定荷载和双面排水条件下非饱和土一维固结的解析解

基于多孔介质弹性理论,结合粒间吸应力表示的有效应力原理,建立了非饱和土固结的耦合偏微分控制方程.考虑一维问题,采用Laplace积分变换,得到了定荷载和双面排水条件下非饱和土固结的解析解答.通过数值算例,分析了土体饱和度对超孔隙水压力、有效应力以及土层沉降的影响规律.结果表明,土体的初始饱和度越高,则孔隙水压力消散得越快,有效应力增加越快.     

非饱和土固结的混合物理论（Ⅰ）

非饱和土是由土粒、水、气组成的三相介质，本以混合物理论为基础研究了非饱和土的固结问题。中导出了各向异性多孔介质及非饱和土 的有效应力的理论公式，把有效应力原理和Curie对称原理作为非饱和土的两个重要的本构原理，建立了非饱和 土固结的数学模型：由25个方程求解25个未知量。在增量线性化的情况下，本模型简化为5个控制方程求解5个未知量：3个固相位移、孔隙水压力和孔隙气压力。模型中包含7个材料参数，都可由试验测定，便于工程应用，Biot理论是本模型的特例。     

双向流固耦合作用下狭窄左冠状动脉内两相血流分析

基于血流与血管壁间双向流固耦合作用,将血液设为两相流体,运用计算流体力学方法对左冠状动脉内血流进行瞬态数值模拟.研究了一个心动周期内典型时刻下左冠状动脉内血流分布特性,并与Newton(牛顿)血液和两相血液模型对比,分析了两相血液和流固耦合作用对血流特性的影响.结果表明,左冠状动脉左回旋支远段和钝缘支近心端外侧分布了低速涡流区,该区域内壁面切应力和红细胞体积分数均较小,为动脉粥样硬化的形成与发展提供了合适的生理环境.左冠状动脉分叉处管壁形变量较大,引起管壁内膜功能发生紊乱,促进了粥样硬化斑块的形成.3种血液模型对比可知,红细胞的流动特性对血流速度及壁面切应力等血流动力学特性影响较大,双向流固耦合模型更符合真实的血液流动情况.     

Excess pore water pressure due to ground surface erosion

The Laplace transform is applied to solve the groundwater flow equation with a boundary that is initially fixed but that starts to move at a constant rate after some fixed time. This problem arises in the study of pore water pressures due to erosional unloading where the aquifer lies underneath an unsaturated zone. We derive an analytic solution and examine the predicted pressure profiles and boundary fluxes. We calculate the negative pore water pressure in the aquifer induced by the initial erosion of the unsaturated zone and subsequent erosion of the aquifer.     

垃圾填埋气体渗流过程中压力分布的滑脱解

考虑气体滑脱效应条件下，建立了垃圾填埋场气体渗流的数学模型．采用摄动法及积分变换法对模型进行解析求解，定量研究填埋气体的压力分布特征，并结合监测数据对模型参数与模型可靠性进行灵敏度分析和验证．结果表明：滑脱效应对气体渗流有较大影响，考虑滑脱效应条件的气体压力小于未考虑滑脱效应条件的气体压力，且得到的滑脱解与实测数值吻合较好．因此，研究填埋气体渗流时不能忽略滑脱效应．这不仅对于填埋场释放气体控制系统的设计和管理提供理论依据，而且可为低渗透油气藏工程开发过程中试井数据的确定提供科学的技术支持．     

Partitioned penalty methods for the transport equation in the evolutionary Stokes–Darcy‐transport problem

There has been a surge of work on models for coupling surface‐water with groundwater flows which is at its core the Stokes–Darcy problem, as well as methods for uncoupling the problem into subdomain, subphysics solves. The resulting (Stokes–Darcy) fluid velocity is important because the flow transports contaminants. The numerical analysis and algorithm development for the evolutionary transport problem has, however, focused on a quasi‐static Stokes–Darcy model and a single domain (fully coupled) formulation of the transport equation. This report presents a numerical analysis of a partitioned method for contaminant transport for the fully evolutionary system. The algorithm studied is unconditionally stable with one subdomain solve per step. Numerical experiments are given using the proposed algorithm that investigates the effects of the penalty parameters on the convergence of the approximations.     

Mathematical Modeling to Simulate the Movement of Contaminants in Groundwater

The objectives of this paper are twofold. Firstly, we formulate a system of partial differential equations that models the contamination of groundwater due to migration of dissolved contaminants through unsaturated to saturated zone. A closed form solution using the singular perturbation techniques for the flow and solute transport equations in the unsaturated zone is obtained. Indeed, the solution can be used as a tool to verify the accuracy of numerical models of water flow and solute transport. The second part of this paper, deals with how the water level in a water reserve drops due to pumping water out of a well that is some distance away.     

Stability of nonlinear microbial bioconversion system concerning glycerol’s active transport and 1,3-PD’s passive transport

In this study, a new nonlinear mathematical model is developed to describe the conversion of glycerol to 1,3- propanediol by Klebsiella pneumoniae and the changes of concentrations of intracellular substances are taken into consideration. We consider the cases that glycerol passes the membrane by active transport and 1,3-propanediol passes the membrane by passive transport. We firstly study the solution’s existence and uniqueness and prove that the solution is bounded in a positive quadrant. Secondly, we discuss the existence of equilibrium solutions and calculate them, dependent on some given steady accuracy by Newton’s Method. Lastly, we analyze the asymptotical behavior and the global stability of the mathematical model.     

A mathematical model to characterise effects of liquid hold-up on bosh silicon transport in the dripping zone of a blast furnace

A first principle based mathematical model has been developed to characterise the effect of total liquid hold-up on the bosh silicon distribution behaviour in the dripping zone of a blast furnace. Two specific cases of hold-up behaviour have been investigated, namely, hold-up in the absence and in the presence of counter current gas flow conditions. The model exemplifies coupled phenomenon of chemical kinetics, transport processes and liquid hold-up to characterise the silicon behaviour in the dripping zone. The present modelling investigation shows that the bosh silicon level diminishes with the enhanced liquid hold-up in the dripping zone. Further, the influence of counter current gas flow on the hold-up is not significant. However, it has been observed that the liquid phase temperature reduces with increased liquid hold-up in dripping zone under steady state operating conditions. The model predictions of bosh silicon distribution have been validated with the published literatures (bulk values) and found to be in good agreement.     

A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations

We present a rigorous mathematical treatment of a model describing rain water infiltration through the vadose zone in case of runoff of the excess water. The main feature of the mathematical problem emerging from the model lies on the boundary condition on the ground surface which is in the form of a unilateral constraint. Existence and uniqueness of a weak solution is proved under general assumptions. We present also the results of a numerical study comparing the proposed model with other models which approach in a different way the rain water infiltration problem. Copyright © 2006 John Wiley & Sons, Ltd.     

存在过渡区的复合气藏中凝析气的渗流模型及其应用

根据凝析气在多孔介质中渗流的相态变化特征,建立了凝析油-气不稳定渗流的基本微分方程,同时引入了凝析油-气两相拟压力函数对渗流方程进行了线性化处理;针对形成不同流体区域的凝折气藏、有边水的凝析气藏、岩性尖灭凝析气藏及井底存在污染和改善等多种情况,针对存在过渡区的复合凝析气藏建立了凝折油-气渗流新模型,模型更适合凝析气藏实际情况,并求出了凝析气藏油-气拟压力分布的拉氏空间解析解,确立了对凝析气井进行压力恢复试井的具体解释方法,从而为指导气田的合理开发提供可靠的依据.