水—气二相流及污染物运移数值模拟研究

本文通过对近些年来水－气二相流数值模拟进展情况的分析,总结了在水－气二相流模拟过程中,各个主要参数或物理过程的数学概化方法,以及近年来在求解水气二相流方程和污染运移方程的方法上的改进情况。并在此基础上提出了需进一步研究解决的问题。     

考虑气相影响的降雨入渗过程分析研究

降雨入渗过程是水在下渗的过程中驱替空气的水-气二相流过程,对这一过程的精确模拟一直是渗流计算的难点,目前的处理方法通常是忽略孔隙气压力变化的影响。根据多相流理论,结合质量守恒定律和达西定律,建立了水-气二相流模型,模型的求解采用积分有限差分法和Newton-Raphson迭代方法,通过变换主要变量来表达相态的变化,实现了水相、气相边界条件及降雨入渗边界的精确模拟。利用上述模型对一土柱试验进行模拟,从而验证了模型的正确性,研究了一均质土层的降雨入渗过程,得到了孔隙水压力、孔隙气压力和毛细压力及含水率的变化过程。根据入渗率与地表孔隙气压力的变化关系,验证了孔隙气压力的增大对入渗水流产生阻滞作用。在求解非稳定渗流问题中,考虑空气压力变化的影响是值得研究的。     

库水位下降时的岸坡非稳定渗流问题研究

水位下降时岸坡的渗流是涉及土体由饱和向非饱和状态过渡的水-气二相流过程,目前相关研究成果大都假设孔隙气压力为0,忽略孔隙气的影响。根据水、空气的质量守恒定律和达西定律,结合多相流理论建立水-气二相流模型,采用高效的积分有限差分法求解,通过变换主要变量,实现饱和（单相）与非饱和（二相）的相互转变,并给出各种边界条件下合理的数学处理方法。通过Muskat渗流问题,验证了上述模型的正确性;并对某土质岸坡水位下降时的非稳定渗流问题进行分析,结果表明,岸坡的基质吸力小于浸润线以上的负孔隙水压力,在浸润线以上的很大区域为毛细管水饱和带,其土体饱和且基质吸力为0,这对边坡稳定十分不利,精确分析水位下降的边坡稳定问题时,孔隙气压力变化的影响值得研究。     

煤层气产出过程中气—水两相流与煤岩变形耦合数学模型研究

气－水二相流和煤岩变形耦合作用是煤层气产出过程中一种复杂的物理现象，为准确描述这一现象，本文建立了气－水二相流和煤岩变形的微分方程，并用有限元分别将它们进行离散化，然后讨论了煤岩变形模型和气－水二相流模型进行耦合数值求解的方法。     

包气带水研究方向浅议

包气带水是地球水体的重要组成部分.研究包气带水的形成及运动规律不仅对阐明地下水的形成具有重要意义,而且是实现农业节水的关键.本文在阐述包气带水特征的基础上,指出了包气带水研究方向:一是包气带中土壤水的调控研究,二是水-气二相流数值模拟研究.     

塔里木盆地北部油气运移二维二相数值模拟分析

油气运移和聚集过程实际上是油（气）水饱和度知疏导层的变化过程，盆地中油（气）二相流动问题的研究就是对这一过程的定量描述，本项研究是在前人工作基础上，考察压实作用造成骨架变形来推导新的二维二相流动方程，它容描述异常压力演化与二相流动于一式，在模拟方法上采用有限分析的数值方法，这应用于新疆塔里木盆地北部地区，展示了该区异常压力、含水饱和度弥散状扩散效应以及流速场在地质历史时期动态模拟演化特征；指出了该     

水--煤层气两相流体在煤层中的渗流规律

采用煤体承受有效应力、水-气混合流动及固一流相互作用的基本原理，建立了煤层气开采过程中水-煤层气两相流渗的基本方程，通过自行设计的实验装置，测定了煤层中水-煤层气共同流动时的两相流体的流量，渗透率及随水的饱和度变化关系，并据此模拟出了反映水-煤层气渗透基本规律，从而为煤层气开采提供了理论基础。     

静止均匀环境中气泡射流特性的研究--形成区及形成后区特性的数值研究(Ⅱ)

采用气-液两相流两方程湍流模型,结合混合有限分析法,对静止环境中气泡射流进行数值模拟和分析.相对各种积分模型,这种模拟气泡射流的微分方程方法具有较强的预报性和普遍的适应性.数值计算结果与试验资料的较好吻合,从而验证了湍流模型和计算方法的有效性和正确性.     

孔隙气压对核废物地质处置热-流-固耦合影响的有限元分析

为考察孔隙气体压力对高放废物地质处置中的热-流-固耦合过程的影响,借用Leiws等建立的可变形孔隙介质中非等温空气流和水流模型,在其水连续性方程中加入了温度梯度引起的水分扩散项,研制出相应的热-水-气-应力耦合弹塑性二维有限元程序。针对一个假定的高放废物地质处置库模型,在相同的初始温度、孔隙水压力和岩体应力条件下,取3种缓冲层中的初始孔隙气体压力,通过数值模拟考察了处置库近场的主应力、饱和度、气和水的流速、温度和孔隙压力的分布与变化。结果显示,当缓冲层中的初始孔隙气压力较高时,其对围岩中应力影响较大。     

帷幕灌浆扩散半径及数值模拟的研究

从连续性方程出发,考虑浆液压力对土体孔隙率的影响,分析推导了浆液在多孔介质中的渗流规律,并给出了扩散半径的简单近似计算公式;然后将二相流理论应用到注浆研究中,假设孔隙由水和浆液完全充填,且二者不相混溶,建立了浆液驱水的非稳定渗流模型。根据某大坝的实际情况,用FLAC软件中的二相流模块对大坝灌浆过程进行了模拟分析,并与推导公式相比较。由于二相流理论考虑了毛细压力的作用,模拟得到的浆液扩散速率递减得更快。模拟结果表明,浆液和水之间存在着一个过渡带,浆液的饱和度在不同时间和位置上是变化的。随着时间的延长,浆液扩散得越远,但其速率逐渐减小。扩散半径不仅与渗透系数有关,还与孔隙度有关,而且孔隙度较渗透系数对扩散半径有着更大的影响。二相流理论可以更好地模拟帷幕灌浆的浆液扩散情况。     

Multiscale simulations of porous media flows in flow-based coordinate system

In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system. A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system.     

分形法估算分散性污染物的运移时间

污染物运移的分形模型导出一个新的适于任意浓度的污染物运移时间公式.对于一个高度非均质含水层中逐渐形成的污染羽,新公式预算出低浓度更早到达的测点.污染峰或羽的运移时间一般经常从达西定律中采用估算平均孔隙流速法得到,而此估算仅仅提供平均浓度(或污染脉冲的峰值浓度)的运移时间信息.近来,计算出任意浓度的运移时间是一个很直接的过程,并且对一个无反应污染物而言,其突破曲线部分的方程被发展.在文中,我们推导出这些方程去概括污染物运移的分形模型.     

A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition

Advances in pore-scale imaging (e.g., μ-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utilized for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.We implement a phase-field model for the direct pore-scale simulation of incompressible flow of two immiscible fluids. The model naturally lends itself to the transport of fluids with large density and viscosity ratios. In the phase-field approach, the fluid-phase interfaces are expressed in terms of thin transition regions, the so-called diffuse interfaces, for increased computational efficiency. The conservation law of mass for binary mixtures leads to the advective Cahn–Hilliard equation and the condition that the velocity field is divergence free. Momentum balance, on the other hand, leads to the Navier–Stokes equations for Newtonian fluids modified for two-phase flow and coupled to the advective Cahn–Hilliard equation. Unlike the volume of fluid (VoF) and level-set methods, which rely on regularization techniques to describe the phase interfaces, the phase-field method facilitates a thermodynamic treatment of the phase interfaces, rendering it more physically consistent for the direct simulations of two-phase pore-scale flow. A novel geometric wetting (wall) boundary condition is implemented as part of the phase-field method for the simulation of two-fluid flows with moving contact lines. The geometric boundary condition accurately replicates the prescribed equilibrium contact angle and is extended to account for dynamic (non-equilibrium) effects. The coupled advective Cahn–Hilliard and modified Navier–Stokes (phase-field) system is solved by using a robust and accurate semi-implicit finite volume method. An extension of the momentum balance equations is also implemented for Herschel–Bulkley (non-Newtonian) fluids. Non-equilibrium-induced two-phase flow problems and dynamic two-phase flows in simple two-dimensional (2-D) and three-dimensional (3-D) geometries are investigated to validate the model and its numerical implementation. Quantitative comparisons are made for cases with analytical solutions. Two-phase flow in an idealized 2-D pore-scale conduit is simulated to demonstrate the viability of the proposed direct numerical simulation approach.     

利用时间分裂的错格伪谱法模拟地震波在基于改进BISQ模型的双相介质中的传播

改进的BISQ(Biot-Squirt)模型中各参数具有明确的物理意义和可实现性,在不引入特征喷流长度的情况下可将Biot流动和喷射流动两种力学机制有机地结合起来;而高精度的地震波场数值模拟技术是研究双相介质地震波传播规律的重要手段。本文从本构方程、动力学方程和动力学达西定律出发,推导了基于改进BISQ模型的双相各向同性介质的一阶速度--应力方程组;采用时间分裂错格伪谱法求该方程组的数值解,模拟半空间及层状双相介质中的地震波场。数值模拟结果表明:①与传统方法相比,时间分裂错格伪谱法波场数值模拟的精度更高,压制网格频散效果更好;②在非黏滞相界情况下,慢纵波呈传播性,而在黏滞相界情况下,慢纵波呈扩散性,以静态模式出现在震源位置;③双相介质分界面处,各类波型复杂的反射透射规律可由数值模拟结果清晰展现。     

磨料两相圆形射流紊流方程的建立及其求解

根据一定合理假设从单相圆形层流边界方程的建立和求解入手，分别建立了两相圆形层流射流边界层方程，单相圆形紊流边界层方程和两相圆形紊流边界层方程并给出了各种情况下的流速分布等参数的解答，为研究磨料两相射流对材料的打击和切割作用奠定了理论基础。     

多孔介质中毛细压力、饱和度和相对渗透率的确定方法

目前石油溢出或者地下储油罐泄漏等原因引起的土壤和地下水非水相流体（NAPLs）污染问题越来越引起人们的关注，由NAPLs、水和气所组成的两相或三相系统中的多相流问题亦是当前的研究热点。其中毛细压力（h），饱和度（S）和相对渗透率（k）是多孔介质多相流研究中的三个重要参数，在多相流室内试验研究中是主要的物理监测量，而且三者之间基本关系式的确定是多相流模拟时进行流动控制方程求解的前提条件。本文从室内试验和模型关系两个方面综述了土壤中NAPLs、水和气所组成的多相流系统中毛细压力、饱和度和相对渗透率以及它们之间相关关系的确定方法。     

Modelling Two-Phase Incompressible Flow in Porous Media Using Mixed Hybrid and Discontinuous Finite Elements

In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors.     

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.     

Adjoint analysis of Buckley-Leverett and two-phase flow equations

This paper analyzes the adjoint equations and boundary conditions for porous media flow models, specifically the Buckley-Leverett equation, and the compressible two-phase flow equations in mass conservation form. An adjoint analysis of a general scalar hyperbolic conservation law whose primal solutions include a shock jump is initially presented, and the results are later specialized to the Buckley-Leverett equation. The non-convexity of the Buckley-Leverett flux function results in adjoint characteristics that are parallel to the shock front upstream of the shock and emerge from the shock front downstream of the shock. Thus, in contrast to the behavior of Burgers’ equation where the adjoint is continuous at a shock, the Buckley-Leverett adjoint, in general, contains a discontinuous jump across the shock. Discrete adjoint solutions from space-time discontinuous Galerkin finite element approximations of the Buckley-Leverett equation are shown to be consistent with the derived closed-form analytical solutions. Furthermore, a general result relating the adjoint equations for different (though equivalent) primal equations is used to relate the two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solutions from space-time discontinuous Galerkin finite element approximations of the two-phase flow equations are observed to obey this relationship.