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1.
A new interpretation of the concept of relative phase permeability is given. Relative phase permeabilities are represented
in the form of fourth-rank tensors. It is shown that in the case of anisotropic porous media functions depending not only
on the saturation but also on the anisotropy parameters represented in the form of ratios of the principal values of the absolute
permeability coefficient tensor correspond to the classical representation of the relative phase permeabilities. For a two-phase
flow in anisotropic porous media with orthotropic and transversely-isotropic symmetry a generalized two-term Darcy’s law is
analyzed.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 87–94, March–April, 1998.
The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-00623). 相似文献
2.
M. N. Dmitriev 《Fluid Dynamics》2011,46(2):291-298
The Rapoport-Leas mathematical model of two-phase flow is generalized to include the case of anisotropic porous media. The
formula for the capillary pressure, which specifies the relationship between the phase pressures, contains a scalar function
of a vector argument. In order to determine the scalar function, the capillary pressure tensor and the tensor inverse to the
tensor of characteristic linear dimensions are introduced. The capillary pressure is determined by the contraction of the
second-rank tensors with a unit vector collinear to the phase pressure gradients, also assumed to be collinear. It is shown
that the saturation function introduced for isotropic porous media (Leverett function) can be generalized to include anisotropic
media and is now determined by a fourth-rank tensor. Generalized expressions for the Leverett and relative phase permeability
functions are given for orthotropic and transversely isotropic media with account for the hysteresis of the phase permeabilities
and capillary pressure. 相似文献
3.
4.
This article describes a semi-analytical model for two-phase immiscible flow in porous media. The model incorporates the effect
of capillary pressure gradient on fluid displacement. It also includes a correction to the capillarity-free Buckley–Leverett
saturation profile for the stabilized-zone around the displacement front and the end-effects near the core outlet. The model
is valid for both drainage and imbibition oil–water displacements in porous media with different wettability conditions. A
stepwise procedure is presented to derive relative permeabilities from coreflood displacements using the proposed semi-analytical
model. The procedure can be utilized for both before and after breakthrough data and hence is capable to generate a continuous
relative permeability curve unlike other analytical/semi-analytical approaches. The model predictions are compared with numerical
simulations and laboratory experiments. The comparison shows that the model predictions for drainage process agree well with
the numerical simulations for different capillary numbers, whereas there is mismatch between the relative permeability derived
using the Johnson–Bossler–Naumann (JBN) method and the simulations. The coreflood experiments carried out on a Berea sandstone
core suggest that the proposed model works better than the JBN method for a drainage process in strongly wet rocks. Both methods
give similar results for imbibition processes. 相似文献
5.
A method of calculating the conductivity of capillary networks which combines percolation concepts of conductivity in the
neighborhood of the flow threshold with the results obtained using the effective medium model is proposed. The conductivity
calculated theoretically is compared with experimental data. Water and oil phase permeabilities for combined flow through
a capillary network are determined as an example of the use of the relations obtained.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 79–83, January–February,
2000. 相似文献
6.
The interacting capillary bundle model proposed by Dong et al. [Dong, M., Dullien, F.A.L., Zhou, J.: Trans. Porous Media 31, 213–237 (1998); Dong, M., Dullien, F.A.L., Dai, L., Li, D.: Trans. Porous Media 59, 1–18 (2005); Dong, M., Dullien, F.A.L., Dai, L., Li, D.: Trans. Porous Media 63, 289–304 (2006)] has simulated correctly various aspects of immiscible displacement in porous media, such as oil production
histories at different viscosity ratios, the effects of water injection rate and of the oil–water viscosity ratio on the shape
of the displacement front and the independence of relative permeabilities of the viscosity ratio. In the interacting capillary
bundle model pressure equilibrium was assumed at any distance x measured along the bundle. Interaction between the capillaries also results in transfer of fluids across the capillaries.
In the first part of this paper the process of fluid transfer between two capillaries is analysed and an algebraic expression
for this flow is derived. Consistency with the assumption of pressure equilibration requires that all transfer must take place
at the positions of the oil/water menisci in the tubes without any pressure drop. It is shown that fluid transfer between
the tubes has no effect on the predictions obtained with the model. In the second part of the paper the interacting tube bundle
model is made more realistic by assuming fluid transfer between the tubes all along the single phase flow regions across a
uniform resistance, resulting in pressure differences throughout the single phase regions between the fluids present in the
different tubes. The results of numerical simulations obtained with this improved interacting capillary bundle model show
only small differences in the positions of the displacement front as compared with the predictions of the idealized model. 相似文献
7.
Calculating the Anisotropic Permeability of Porous Media Using the Lattice Boltzmann Method and X-ray Computed Tomography 总被引:1,自引:0,他引:1
Yuan Gao Xiaoxian Zhang Pratap Rama Ying Liu Rui Chen Hossein Ostadi Kyle Jiang 《Transport in Porous Media》2012,92(2):457-472
A lattice Boltzmann (LB) method is developed in this article in a combination with X-ray computed tomography to simulate fluid
flow at pore scale in order to calculate the anisotropic permeability of porous media. The binary 3D structures of porous
materials were acquired by X-ray computed tomography at a resolution of a few microns, and the reconstructed 3D porous structures
were then combined with the LB model to calculate their permeability tensor based on the simulated velocity field at pore
scale. The flow is driven by pressure gradients imposed in different directions. Two porous media, one gas diffusion porous
layer used in fuel cells industry and glass beads, were simulated. For both media, we investigated the relationship between
their anisotropic permeability and porosity. The results indicate that the LB model is efficient to simulate pore-scale flow
in porous media, and capable of giving a good estimate of the anisotropic permeability for both media. The calculated permeability
is in good agreement with the measured date; the relationship between the permeability and porosity for the two media is well
described by the Kozeny–Carman equation. For the gas diffusion layer, the simulated results showed that its permeability in
one direction could be one order of magnitude higher than those in other two directions. The simulation was based on the single-relaxation
time LB model, and we showed that by properly choosing the relaxation time, it could give similar results to those obtained
using the multiple-relaxation time (MRT) LB method, but with only one third of the computational costs of MRTLB model. 相似文献
8.
This article presents a mathematical model describing flow of two fluid phases in a heterogeneous porous medium. The medium
contains disconnected inclusions embedded in the background material. The background material is characterized by higher value
of the non-wetting-phase entry pressure than the inclusions, which causes non-standard behavior of the medium at the macroscopic
scale. During the displacement of the non-wetting fluid by the wetting one, some portions of the non-wetting fluid become
trapped in the inclusions. On the other hand, if the medium is initially saturated with the wetting phase, it starts to drain
only after the capillary pressure exceeds the entry pressure of the background material. These effects cannot be represented
by standard upscaling approaches based on the assumption of local equilibrium of the capillary pressure. We propose a relevant
modification of the upscaled model obtained by asymptotic homogenization. The modification concerns the form of flow equations
and the calculation of the effective hydraulic functions. This approach is illustrated with two numerical examples concerning
oil–water and CO2–brine flow, respectively. 相似文献
9.
The present work examines a method of solving three-dimensional problems of two-phase filtration based on averaging the equations and introducing functions reflecting the layering of the flow in collectors inhomogeneous over the thickness. These functions are constructed from the calculation of the two-dimensional flow in the plane of the vertical cross section of the bed. This approach is generalized to the case of the displacement of petroleum by aqueous solutions of chemical reagents. Inhomogeneous problems of multiphase filtration may only be solved numerically. However, in the case of three-dimensional flow, even the use of an effective difference scheme is beset with considerable difficulties, dueprimarily to the increased requirements for memory and speed of operation of the computer. In [1] a principle of approximate integration of the filtration equations in a thin inclined bed was proposed. Assuming a hydrostatic law of vertical pressure distribution, the equations were averaged, and successive solution of problems of ever smaller dimensionality was carried out, not with the initial curves of phase permeability, but with curves of averaged phase permeability. Subsequently, there was further development of this principle of capillary-gravitational equilibrium, and others, to deal with the case of flooding of an inhomogeneously laminar bed [2, 3]. A significantly different approach to the determination of the auxiliary functions, not involving assumptions to as the relations between the viscous drag and the capillary and gravitational forces, is to use the solution of the two-dimensional problem of the replacement of petroleum by water in the plane of the vertical cross section of the bed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 71–75, May–June, 1977. 相似文献
10.
V. Sh. Shagapov I. G. Khusainov R. M. Khafizov 《Journal of Applied Mechanics and Technical Physics》2006,47(1):91-98
The pressure testing of a hole in porous and permeable rock by gas injection is considered. An integral equation for the hole
pressure relaxation is obtained whose numerical and analytical solutions describe the dependence of the relaxation time of
hole pressure on the reservoir properties of the surrounding porous rock as well as on the initial gas content and the initial
pressure gradient in the hole.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 109–118, January–February, 2006. 相似文献
11.
Unsteady-state (USS) core flood experiments provide data for deriving two-phase relative permeability and capillary pressure
functions. The experimental data is uncertain due to measurement errors, and the accuracy of the derived flow functions is
limited by both data and modeling errors.
History matching provides a reasonable means of deriving in-phase flow functions from uncertain unsteady-state experimental
data. This approach is preferred to other analytical procedures, which involve data smoothing and differentiation. Data smoothing
leads to loss of information while data differentiation is a mathematically unstable procedure, which could be error magnifying.
The problem is non-linear, inverse and ill posed. Hence the history-matching procedure gives a non-unique solution.
This paper presents a procedure for quantifying the uncertainty in two-phase flow functions, using unsteady-state experimental
data. We validate the methodology using synthetic data.
We investigate the impact of uncertain flow functions on a homogeneous reservoir model using the Buckley–Leverett theory.
Using a synthetic, heterogeneous reservoir model, we estimate the uncertainty in oil recovery efficiency due to uncertainty
in the flow functions. 相似文献
12.
C.G. Speziale 《Theoretical and Computational Fluid Dynamics》1999,13(3):161-166
A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated
to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent
flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow
– the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear
K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero
when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it
too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics
in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are
also discussed.
Received 19 February 1998 and accepted 23 October 1998 相似文献
13.
14.
在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程.采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间.对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效.分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度.当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑.压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显. 相似文献
15.
Darcy's flow of a weakly compressible fluid through double porosity media is studied in the framework of the homogenization theory. In previous papers, various classes of single-phase flow have been detected with various determination of the effective permeability tensor for each class. In this paper, the full model including transient phenomena is developed, where the macroscale momentum balance equation represents a modification of Darcy's law with a nonequilibrium term. The effective permeability tensor appears to be nonstationary and is changing during the system evolution in time. Three relaxation times characterize the transient transformations of each component of the macroscale flow velocity.This effect is superposed with the second relaxation phenomenon caused by the exchange flow between dense blocks and the highly conductive matrix. The relaxation times for the effective permeability and for the exchange flow are shown to have different orders.All relaxation parameters are explicitly determined through solutions of cell problems. 相似文献
16.
A new model of the flow of two miscible, mutually-insoluble fluids in a porous medium with the formation of an emulsion and
adsorption of the fluid components on the skeleton is proposed. The model takes into account the effect of interphase mass
transfer on the emulsion dynamics and the active porosity. A continuous general solution of the one-dimensional model and
the problem of breakdown of a discontinuity is constructed. The flow regimes generated in displacement problems which depend
on the shape of the adsorption isotherms and the densities of the fluid components are considered. The time dependence of
the production rate is constructed for frontal displacement regimes and for displacement regimes with the formation of a zone
of mixing (Riemann wave) of the initial reservoir and injected fluids. These functions coincide, at least qualitatively, with
the experimental data [1] indicating an initial increase in production rate even against a background of falling reservoir
pressure, transition through a maximum, and subsequent decline.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 77–88, January–February,
1997.
The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00991). 相似文献
17.
In this article, we describe some aspects of the diffuse interface modelling of incompressible flows, composed of three immiscible
components, without phase change. In the diffuse interface methods, system evolution is driven by the minimisation of a free
energy. The originality of our approach, derived from the Cahn–Hilliard model, comes from the particular form of energy we
proposed in Boyer and Lapuerta (M2AN Math Model Numer Anal, 40:653–987,2006), which, among other interesting properties, ensures
consistency with the two-phase model. The modelling of three-phase flows is further completed by coupling the Cahn–Hilliard
system and the Navier–Stokes equations where surface tensions are taken into account through volume capillary forces. These
equations are discretized in time and space paying attention to the fact that most of the main properties of the original
model (volume conservation and energy estimate) have to be maintained at the discrete level. An adaptive refinement method
is finally used to obtain an accurate resolution of very thin moving internal layers, while limiting the total number of cells
in the grids all along the simulation. Different numerical results are given, from the validation case of the lens spreading
between two phases (contact angles and pressure jumps), to the study of mass transfer through a liquid/liquid interface crossed
by a single rising gas bubble. The numerical applications are performed with large ratio between densities and viscosities
and three different surface tensions. 相似文献
18.
Finite Element-Based Characterization of Pore-Scale Geometry and Its Impact on Fluid Flow 总被引:1,自引:0,他引:1
We present a finite element (FEM) simulation method for pore geometry fluid flow. Within the pore space, we solve the single-phase
Reynold’s lubrication equation—a simplified form of the incompressible Navier–Stokes equation yielding the velocity field
in a two-step solution approach. (1) Laplace’s equation is solved with homogeneous boundary conditions and a right-hand source
term, (2) pore pressure is computed, and the velocity field obtained for no slip conditions at the grain boundaries. From
the computed velocity field, we estimate the effective permeability of porous media samples characterized by section micrographs
or micro-CT scans. This two-step process is much simpler than solving the full Navier–Stokes equation and, therefore, provides
the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner
than solving the full Navier–Stokes’ equation. Given the realistic laminar flow field, dispersion in the medium can also be
estimated. Our numerical model is verified with an analytical solution and validated on two 2D micro-CT scans from samples,
the permeabilities, and porosities of which were pre-determined in laboratory experiments. Comparisons were also made with
published experimental, approximate, and exact permeability data. With the future aim to simulate multiphase flow within the
pore space, we also compute the radii and derive capillary pressure from the Young–Laplace’s equation. This permits the determination
of model parameters for the classical Brooks–Corey and van-Genuchten models, so that relative permeabilities can be estimated. 相似文献
19.
The results of calculating the flow and heat transfer in annular porous interlayers are presented as functions of the Rayleigh
number, the geometry of the interlayer, and the anisotropy of the permeability. The existence of single-vortex and multivortex
convection regimes depending on the permeability anisotropy coefficient is established and their importance for the effectiveness
of the heat-insulating properties of cylindrical interlayers is shown.
Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–128, July–August,
1998.
The work was carried out with support from the Russian Foundation for Basic Research (project No. 96-01-000584). 相似文献
20.
An equation of state for a volumetrically stretched cavitating liquid medium that holds in the entire span of volume concentrations
of bubbles ranging from cavitation nuclei to the stage of formation of a cellular foam structure is obtained based on a proposed
macrorheological model. The dependence of the modulus of volume elasticity of a liquid on the volume concentration of bubbles
is plotted, and a method for estimating the relaxation time for tensile stresses in cavitating liquid media is proposed.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 35–46, January–February, 1998. 相似文献