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1.
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. 相似文献
2.
考虑气相影响的降雨入渗过程分析研究 总被引：4，自引：1，他引：3
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。 相似文献
3.
A three-dimensional, three-phase numerical model is presented for simulating the movement of immiscible fluids, including
nonaqueous-phase liquids (NAPLs), through porous media. The model is designed to simulate soil flume experiments and for practical
application to a wide variety of contamination scenarios involving light or dense NAPLs in heterogeneous subsurface systems.
The model is derived for the three-phase flow of water, NAPL, and air in porous media. The basic governing equations are based
upon the mass conservation of the constitutents within the phases. The descretization chosen to transform the governing equations
into the approximating equations, although logically regular, is very general. The approximating equations are a set of simultaneous
coupled nonlinear equations which are solved by the Newton-Raphson method. The linear system solutions needed for the Newton-Raphson
method are obtained using a matrix of preconditioner/accelerator iterative methods.
Because of the special way the governing equations are implemented, the model is capable of simulating many of the phenomena
considered necessary for the sucessful simulation of field problems including entry pressure phenomena, entrapment, and preferential
flow paths. The model is verified by comparing it with several exact analytic test solutions and three soil flume experiments
involving the introduction and movement of light nonaqueous-phase liquid (LNAPL) or dense nonaqueous-phase liquid (DNAPL)
in heterogeneous sand containing a watertable.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
In this paper, a fully coupled numerical model is presented for the finite element analysis of the deforming porous medium interacting with the flow of two immiscible compressible wetting and non-wetting pore fluids. The governing equations involving coupled fluid flow and deformation processes in unsaturated soils are derived within the framework of the generalized Biot theory. The displacements of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the present formulation. The other variables are incorporated into the model using the experimentally determined functions that define the relationship between the hydraulic properties of the porous medium, i.e. saturation, relative permeability and capillary pressure. It is worth mentioning that the imposition of various boundary conditions is feasible notwithstanding the choice of the primary variables. The modified Pastor–Zienkiewicz generalized constitutive model is introduced into the mathematical formulation to simulate the mechanical behavior of the unsaturated soil. The accuracy of the proposed mathematical model for analyzing coupled fluid flows in porous media is verified by the resolution of several numerical examples for which previous solutions are known. Finally, the performance of the computational algorithm in modeling of large-scale porous media problems including the large elasto-plastic deformations is demonstrated through the fully coupled analysis of the failure of two earth and rockfill dams. Furthermore, the three-phase model is compared to its simplified one which simulates the unsaturated porous medium as a two-phase one with static air phase. The paper illustrates the shortcomings of the commonly used simplified approach in the context of seismic analysis of two earth and rockfill dams. It is shown that accounting the pore air as an independent phase significantly influences the unsaturated soil behavior. 相似文献
5.
Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase 总被引：1，自引：0，他引：1
Carbon capture and storage is a recently discussed new technology, aimed at allowing an ongoing use of fossil fuels while preventing the produced CO2 to be released to the atmosphere. CCS can be modeled with two components (water and CO2) in two phases (liquid and CO2). To simulate the process, a multiphase flow equation with equilibrium phase exchange is used. One of the big problems arising in two-phase two-component flow simulations is the disappearance of the nonwetting phase, which leads to a degeneration of the equations satisfied by the saturation. A standard choice of primary variables, which is the pressure of one phase and the saturation of the other phase, cannot be applied here. We developed a new approach using the pressure of the nonwetting phase and the capillary pressure as primary variables. One important advantage of this approach is the fact that we have only one set of primary variables that can be used for the biphasic as well as the monophasic case. We implemented this new choice of primary variables in the DUNE simulation framework and present numerical results for some test cases. 相似文献
6.
Three-phase numerical model of water migration in partially frozen geological media: model formulation,validation, and applications 总被引：3，自引：0，他引：3
Scott L. Painter 《Computational Geosciences》2011,15(1):69-85
Water in the subsurface of the Earth’s cold regions—and possibly the subsurface of Mars—resides in the liquid, vapor, and
ice phases. However, relatively few simulations addressing full three-phase, nonisothermal water dynamics in below-freezing
porous media have been undertaken. This paper presents a nonisothermal, three-phase approach to modeling water migration in
partially frozen porous media. Conservation equations for water (as ice, liquid, and vapor) and a single gas species (in the
gas phase and dissolved in water) are coupled to a heat transport equation and solved by a finite-volume method with fully
implicit time stepping. Particular attention is given to the method of spatial differencing when the pore space is partially
filled with ice. The numerical model is able to reproduce freezing-induced water redistribution observed in laboratory experiments.
Simulations of Earth permafrost dynamics and of the formation and evolution of a planetary-scale cryosphere on Mars demonstrate
the new capabilities. 相似文献
7.
The theoretical and computational aspects of large strain static and dynamic partially saturated soil analysis are presented. The soil is assumed to be a three-phase material with a solid phase which may yield according to a generalized plasticity theory, whose liquid phase flows according to Darcy's law and where gaseous phase remains equal to the external ambient pressure. Permeability varies not only as a function of the degree of water saturation, but also as a function of the void ratio. These aspects are shown on several examples. 相似文献
8.
将二氧化碳注入到深部咸水层中,形成复杂的多组分、多相流系统。二氧化碳在压力梯度、浓度差作用下不断扩散,逐步带走盐溶液中的水分,导致各组分的相态变化,盐结晶析出,阻塞了咸水层孔隙通道,从而降低了二氧化碳的注入效率,研究该干化效应的影响因素并为工程选址提供依据具有重要意义。采用二维径向模型建立多相流体的流动方程,并结合相对渗透率和毛细压力方程探讨二氧化碳注入速率、咸水层含盐量、毛细压力的特征参数对干化效应的影响,干化效应可用固体饱和度值进行定量描述。结果表明：二氧化碳运移分3个区域：干涸区、气液相混合区及液相咸水区,干化效应主要发生在井周的干涸区。在毛细作用下固体饱和度随注入速率的减小而增大,随咸水层含盐量增大而增大,随毛细作用增大而增大。因此,提高二氧化碳的注入速率,向咸水层中注水稀释含盐量或选择粒径较大的均质咸水层减小毛细作用,均可降低盐结晶对孔隙通道的阻塞,提高注入效率。 相似文献
9.
A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here. 相似文献
10.
Raphaël di Chiara Roupert Gerhard Schäfer Philippe Ackerer Michel Quintard Guy Chavent 《Comptes Rendus Geoscience》2010,342(11):855-863
Multiphase flow modelling is a major issue in the assessment of groundwater pollution. Three-phase flows are commonly governed by mathematical models that associate a pressure equation with two saturation equations. These equations involve a number of secondary variables that reflect the fluid behaviour in a porous medium. To improve the computational efficiency of multiphase flow simulators, several simplified reformulations of three-phase flow equations have been proposed. However, they require the construction of new secondary variables adapted to the reformulated flow equations. In this article, two different approaches are compared to quantify these variables. A numerical example is given for a typical fine sand. 相似文献
11.
Hydrogen penetration in water through porous medium: application to a radioactive waste storage site
Hydrogen penetration in water through porous medium was analyzed in the paper. A two-phase compositional model approach was
considered. The first part of the work deals with the thermodynamic analysis of the hydrogen–water system. The thermodynamic
model was calibrated using the experimental data of hydrogen solubility in water. The phase densities, viscosities and phase
concentrations were presented in an analytical form. Moreover, the domain of validity of analytical laws—such as Henry’s,
Raoult’s and Kelvin’s laws—for the estimation of phase properties was presented for the analyzed system. The second part deals
with two-phase hydrodynamic behaviors. An analytical solution for the non-compressible flow was constructed. In general case,
the influence of relative permeabilities on the flow regimes was analyzed numerically. The notion pseudo-saturation was introduced
to define phase appearance. Actually, mobile gas created a time displaced front relatively slower than mobile gas flow. Diffusion
becomes really important for low mobile gas case as the penetration accelerates for the large range of saturation. In contrast,
the mass exchange phenomena have a small influence on the flow type. Thus, the regimes of hydrogen penetration in liquid were
shown really sensitive to the relative permeability form. 相似文献
12.
Melting experiments carried out at 1-atm and at 2 kbar on mid-ocean ridge basalts dredged from the mid-Atlantic ridge near the Kane Fracture Zone (KFZ, 22° to 25° N. latitude) provide a basis for evaluating the role of crystal fractionation in generating compositional variability observed in normal mid-ocean ridge basalt. The 1-atm olivine-plagioclase-clinopyroxene saturation boundary for KFZ lavas defines a path in mineral projection schemes and in oxide-oxide diagrams that is displaced from the same experimentally determined boundaries in FAMOUS (Grove and Bryan 1983) and Oceanographer Fracture Zone (Walker et al. 1979) basalts. The glass margins of sparsely phyric KFZ lavas record small amounts of near surface, low pressure fractional crystallization, and their glass and bulk rock compositions are similar. An important signature of low pressure differentiation is recorded in the quenched glass margins of moderately phyric KFZ lavas compared to their bulk rock compositions, and the glass has evolved along low-pressure fractionation paths that are similar to those produced in the 1-atm experiments. Many of the lavas have retained phenocrysts in equilibrium proportions, so that their bulk rock compositions represent liquid compositions. When the effects of near-surface differentiation and crystal accumulation are removed from the Kane data set, and only liquid compositions are considered, a suite of basalt magmas can be identified that forms a trend in mineral component projection schemes parallel to the 1-atm oliv-plag-cpx multiple saturation boundary, but displaced from it toward olivine. These basalts have only olivine and plagioclase as phenocrysts, and are well removed from clinopyroxene saturation at low pressure. The compositional variation can not be generated by mixing any primary liquid composition with a low pressure liquid that has evolved along the oliv-plag-cpx multiple saturation boundary. Major and trace element models of this trend using olivine, plagioclase and clinopyroxene as fractionating phases match the compositional variability. This compositional trend is generated by fractionation at pressures greater than 2 kbar, but within the plagioclase stability field. A review of the data for other normal MORB suites from this part of the mid-Atlantic ridge reveals a similar elevated pressure fractionation signature which persists when the effects of low pressure magma mixing are removed from the data set. 相似文献
13.
Magnus Wangen 《国际地质力学数值与分析法杂志》1997,21(2):91-120
The upstream-weighted finite element method with lumped mass matrix is applied to the modelling of oil migration in compacting sedimentary basins. An implicit formulation is made in Lagrangian co-ordinates of a pressure, saturation and a temperature equation, which is based on immiscible two-phase flow of oil and water. The formulation accounts for the compaction of the sediments, the generation of oil from solid organic material (kerogen), the eventual pore space generated by kerogen breakdown, and the density variations of the fluids which may set up thermal convection. The model is validated by comparison with results from a one-dimensional (1D) fractional flow-based migration model. A 2D case example showing oil expulsion from source rocks, and the filling of a trap is presented. The mass balance of the model is easily checked because all oil in the basin originates from breakdown of kerogen. Compared with other alternatives, the simple upstream-weighted finite element method is suggested as a possible first choice for a numerical method for the modelling of oil migration in compacting sedimentary basins. It easily deals with the complex geometry of a basin, it yields reasonably good results, is simple to implement, and the same implementation applies to all spatial dimensions. © 1997 by John Wiley & Sons, Ltd. 相似文献
14.
We present a network flow model to compute transport, through a pore network, of a compositional fluid consisting of water with a dissolved hydrocarbon gas. The model captures single-phase flow (below local bubble point conditions) as well as the genesis and migration of the gas phase when bubble point conditions are achieved locally. Constant temperature computational tests were run on simulated 2D and 3D micro-networks near bubble point pressure conditions. In the 2D simulations which employed a homogeneous network, negligible capillary pressure, and linear relative permeability relations, the observed concentration of CO2 dissolved in the liquid phase throughout the medium was linearly related to the liquid pressure. In the case of no gravity, the saturation of the gas phase throughout the medium was also linearly related to the liquid pressure; under gravity, the relationship became nonlinear in regions where buoyancy forces were significant. The 3D heterogeneous network model had nonnegligible capillary pressure and nonlinear relative permeability functions. While 100 % of the CO2 entered the 3D network dissolved in the liquid phase, 25 % of the void space was occupied by gas phase and 47 % of the CO2 exiting the outlet face did so via the gaseous phase after 500 s of simulation time. 相似文献
15.
The West Farrington pluton in the North Carolina Piedmont isconcentrically zoned from gabbro-diorite near the chilled marginsto leucogranodiorite in the center. A crystallization modelfor the West Farrington pluton has been derived utilizing chemical,petrographic, field, and experimental data. The model involvessimple in situ fractional crystallization from the margins inward,with minimal contamination, crystal settling and floating, ormetasomatism. Rocks of the pluton can be considered as mixturesof early crystallizing minerals (liquidus or near-liquidus phases)and crystallized interstitial liquids. Relative percentage ofentrapped pore liquid increased with increasing degree of crystallization. The original tonalite magma began crystallizing Fe-Ti spinels,plagioclase, and hornblende within a short temperature interval.Crystallization of these minerals controlled fractionation trends.The initial water content in the magma was probably 2–3per cent; under such conditions water saturation would havebeen reached after about 60 per cent of the magma crystallized,assuming crystallization in the lower epizone at about 2000bars total pressure. 相似文献
16.
多孔介质中毛细压力、饱和度和相对渗透率的确定方法 总被引：3，自引：0，他引：3
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。 相似文献
17.
In this paper we study a one-dimensional model for oil recovery by steamdrive. This model consists of two parts: a (global)
interface model and a (local) steam condensation/capillary diffusion model. In the interface model a steam condensation front
(SCF) is present as an internal boundary between the hot steam zone (containing water, oil and steam) and the cold liquid
zone (containing only water and oil). Disregarding capillary pressure away from the SCF, a 2× 2 hyperbolic system arises for
the water and steam saturation. This system cannot be solved uniquely without additional conditions at the SCF. To find such
conditions we blow up the SCF and consider a parabolic transition model, including capillary diffusion. We study in detail
the existence conditions for traveling wave solutions. These conditions provide the missing matching conditions at the SCF
in the hyperbolic limit. We show that different transition models yield different matching conditions, and thus different
solutions of the interface model. We also give a relatively straightforward approximation and investigate its validity for
certain ranges of model parameters.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
E.F. Kaasschieter 《Computational Geosciences》1999,3(1):23-48
Immiscible two‐phase flow in porous media can be described by the fractional flow model. If capillary forces are neglected,
then the saturation equation is a non‐linear hyperbolic conservation law, known as the Buckley–Leverett equation. This equation
can be numerically solved by the method of Godunov, in which the saturation is computed from the solution of Riemann problems
at cell interfaces. At a discontinuity of permeability this solution has to be constructed from two flux functions. In order
to determine a unique solution an entropy inequality is needed. In this article an entropy inequality is derived from a regularisation
procedure, where the physical capillary pressure term is added to the Buckley‐Leverett equation. This entropy inequality determines
unique solutions of Riemann problems for all initial conditions. It leads to a simple recipe for the computation of interface
fluxes for the method of Godunov.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
20.
非饱和带水气二相渗流动力学模型 总被引：3，自引：0，他引：3
非饱和带地下水运动实质上是一个水气二相渗流过程。本文以多相渗流理论为基础,从水气二相渗流的连续性方程和达西定律出发,推导了非饱和带水气二相渗流的耦合动力学模型,讨论了模型的IMPES和全隐式联立求解方法的原理和步骤,认为IMPES求解方法由于达西系数项的处理,饱和度的计算均采用显式,因此该解法具有稳定性差、精度低且要求计算时间步长小的局限性;而全隐式联立求解方法是联立求解气相、水相方程,同时求出压力和饱和度值,因此压力和饱和度值都是隐式求出,具有较高精度,且无条件稳定,应是今后模型求解的重点研究内容 相似文献