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.     

Analysis of the Grain Size Properties and Flow Body Classes of the Mud Sand Flow: An Example of Liantanggang Collapsing Hill and Gully in Wuhua County of Guangdong

Mud sand flow is a kind of solid-liquid two-phase flow formed in collapsing hill and gully basin during rainfall. It is the main way to export erosion product. The discrimination of its fluid type is one of the collapsing hill and gully control theoretical basis. This paper analyzed the basic characteristics of mud sand flow like grain size and so on through fieldwork and sampling. The results show that the density of mud sand flow is between 1.16~1.60 t/m³ and the solids content is between 257.03~960.55 kg/m³, both of which decrease from the upper to the lower channel. The slurry of mud sand flow is composed mainly of silt and clay. As the density increases, the particle size distribution curve transforms from a single peak to the bimodal distribution similar to the weathering crust with no sorting, and the grain size of mud sand flow becomes coarser which shows a well positive linear correlation between the sediment median particle diameter and density of mud sand flow. The comparison during mud sand flow, hyperconcentrated flow and debris flow shows that collapsing hill and gully mud sand flow, which belongs to an intermediate class between hyperconcentrated flow and debris flow, has a closer link with debris flow. Therefore, mud sand flow can be considered as a sub-class of generalized debris flow that may be called as collapsing hill and gully type debris flow.     

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。     

基于结构两相阻力分析的泥石流堆积形态研究

针对泥石流的结构两相阻力特征,采用结构两相阻力对泥石流的堆积形态进行了静力学分析,推导出在一般条件下泥石流堆积形态的公式,并讨论了在不同条件下泥石流堆积形态的特点。分析表明采用结构两相阻力对泥石流堆积形态分析可以较合理的模化阻力项,能够表现泥石流体复杂的成分结构组成,较真实的反映实际泥石流的堆积形态特征。在特定材料条件下,结构两相阻力项转化为单一材料阻力项,所得到的相应结论与已有对单一材料的分析结论一致。     

非饱和带水-气二相流数值模拟研究进展

通过对近年来水-气二相流数值模拟情况的分析,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,以及近年来求解水-气二相流方程和污染物运移方程的各种方法,论述了各种方法的优点和不足.并提出了需进一步研究解决的问题.     

An experimental study of single and two-phase fluid flow through fractured granite specimens

Triaxial tests on the two-phase flow of air and water through fractured granite specimens were performed to discover whether the two-phase fluid flow within rock fractures was laminar or turbulent. The two-phase flow characterization was carried out based on the macroscopic two-phase steady state flow model and the homogeneous steady state flow model. Rock specimens with a single natural fracture (joint roughness coefficient, JRC < 10) were tested using two-phase, high pressure triaxial rig. Experimental results show that the estimated Reynolds numbers for various inlet fluid pressures are well below 1000. The findings of this study reveal that both single and two-phase flow through rock fractures (JRC < 10) can be characterized as laminar flows at moderate inlet fluid pressures. However, for single-phase air flow, an increase in inlet air pressures may result in the formation of turbulent flow.     

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。     

A dual-porosity model considering the displacement effect for incompressible two-phase flow

The dual-porosity model is usually employed to simulate the flow in fractured reservoirs. However, its original form for the multiphase flow does not consider the displacement effect under macropressure gradient. Especially for the incompressible multiphase flow, it predicts zero transfer term between fracture and matrix, which is unreasonable. To improve this, a modified double-porosity model is proposed for incompressible two-phase flow, in which the displacement effect is considered and the corresponding shape factor is derived. For the anisotropic case, the shape factor of displacement depends upon the velocity direction. The accuracy and the efficiency of the proposed dual-porosity model are indicated through numerical tests.     

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.     

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.     

CO2地质封存中储层流体压力演化规律的解析模型

为使解析模型可以更加科学准确地描述储层中多相流体的迁移机制与压力演化规律,提高解析计算与分析的精度。首先将储层中的流场划分为3个区域,然后根据渗流体积守恒方程反演储层中两相流体混合渗流区的各相流体饱和度,进而将总流度直接引入到达西公式中得到了一个适用于两相流的广义达西公式,据此推导出了一个更为精确的表征储层流体压力演化规律的解析模型。最后,通过案例分析,将该解析模型的计算结果与既有文献的显式积分解及TOUGH2/ECO2N的数值解进行对比,验证了该模型的可靠性及相比于既有文献的显式积分解在计算精度方面的优越性。此外,计算结果也表明,该解析模型虽然是在稳态流的假定条件下得到的,但对于实际储层流体压力演化的全过程均具有很强的表征能力,这主要归因于该模型可科学准确地确定饱和度,因此,可以在工程中推广应用。     

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。     

Fast computation of arrival times in heterogeneous media

We continue the work that was initiated in (K. H. Karlsen, K.-A. Lie, and N. H. Risebro. A fast marching method for reservoir simulation. Comp. Geo., 4(2) (2000)185–206) on a marching method for simulating two-phase incompressible immiscible flow of water and oil in a porous medium. We first present an alternative derivation of the marching method that reveals a strong connection to modern streamline methods. Then, through the study of three numerical test cases we present two deficiencies: (i) the original marching algorithm does not always compute the correct solution of the underlying difference equations, and (ii) the method gives largely inaccurate arrival times in the presence of large jumps within the upwind difference stencil. As a remedy of the first problem, we present a new advancing-front method, which is faster than the original marching method and guarantees a correct solution of the underlying discrete linear system. To cure the second problem, we present two adaptive strategies that avoid the use of finite-difference stencils containing large jumps in the arrival times. The original marching method was introduced as a fast tool for simulating two-phase flow scenarios in heterogeneous formations. The new advancing-front method has limited applicability in this respect, but may rather be used as a fast and relatively accurate method for computing arrival times and derived quantities in heterogeneous media.     

Numerical approximation of water–air two-phase flow by the mixed finite element method

A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems.     

南海南部礼乐盆地构造热演化研究

礼乐盆地位于南海海域南部,是一个形成于中新生代的叠合盆地,长期以来缺乏构造热演化方面研究。本文在认识礼乐盆地构造演化的基础上,选用盆地内地震测线(L2剖面),应用二维横向不均匀拉张模型对礼乐盆地构造热演化史进行了模拟研究。模拟结果揭示了盆地在新生代的构造热演化特征:(1)盆地经历了两次连续的拉张过程,第一期拉张幅度较小,拉张系数在1.05左右,第二次拉张程度较第一次拉张强烈,深水地区拉张系数达到1.3;(2)礼乐盆地两次拉张使得盆地逐步升温,第二次拉张结束时达到历史最高温时期,之后热流持续下降;(3)盆地不同构造部位热流史具有差异性,其中深水区经历的古热流最高,达75mW/m2,礼乐滩最低,仅为63mW/m2。     

Numerical simulation of two-phase flow in conceptualized fractures

Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures.     

Fast 3D Reservoir Simulation and Scale Up Using Streamtubes

This paper presents an implementation of a semianalytical method for oil recovery calculation in heterogeneous reservoirs that is both fast and accurate. The method defines streamline paths based on a conventional single-phase incompressible flow calculation. By calculating the time-of-flight for a particle along a streamline and assigning a volumetric flux to each streamline, the cumulative pore volume of a streamtube containing the streamline can be calculated. Subsequently, the streamtube geometries are kept constant and the effects of the time varying mobility distribution in two-phase flow are accounted for by varying the flow rate in each streamtube, based on fluid resistance changes along the streamtube. Oil recovery calculations are then done based on the 1D analytical Buckley–Leverett solution. This concept makes the method extremely fast and easy to implement, making it ideal to simulate large reservoirs generated by geostatiscal methods. The simulation results of a 3D heterogeneous reservoir are presented and compared with those of other simulators. The results shows that the new simulator is much faster than a traditional finite difference simulator, while having the same accuracy. The method also naturally handles the upscaling of absolute and relative permeability. We make use of these upscaling abilities to generate a coarse curvilinear grid that can be used in conventional simulators with a great advantage over conventional upscaled Cartesian grids. This paper also shows an upscaling example using this technique.     

非饱和带水气二相流动参数确定实验研究

对非饱和带水气二相流动的关键参数确定,尤其是二相流动中气相参数确定的实验方法进行了探索,得出了相应的参数结果,建立了气压自动采集系统,为进一步的非饱和带水气二相流动的实验模拟与数值模拟提供了参数依据。     

包气带水气二相流国外研究综述

与传统的包气带中水流研究相比,水气二相流更准确地描述了包气带中的水与空气的流动情况,这对更好地了解固体废物处置场中污染物的运动规律具有重要的意义.与一相流明显不同的是,二相流考虑了空气的运动及其对水流的作用.根据国外近几十年来不同研究者的研究结果,总结了入渗过程中水的流动、空气对水流的影响及空气本身的压力变化情况,并分析了不同作者研究结果的差别.