共查询到20条相似文献,搜索用时 13 毫秒
1.
We formulate conservation laws governing steam and nitrogen injection in a one-dimensional porous medium containing water.
Compressibility, heat conductivity and capillarity are neglected. We study the condensation front and shock waves arising
in the flow. We find that there are four possible types of solutions for the initial and boundary conditions of interest.
We describe a simple construction in the temperature saturation plane that determines the complete solution for the given
conditions. Applications of the theory developed here are in clean up of soil contaminated with nonaqueous phase liquids.
We show that a substantial cold gaseous zone develops in all solutions of practical interest, thus counteracting downward
migration of the pollutant. 相似文献
2.
The plane one-dimensional and radially symmetric problems of injection of superheated steam into a porous medium saturated with gas are considered. Self-similar solutions are constructed on the assumption that in this case four zones are formed in the porous medium, namely, a gas flow zone, superheated and wet steam zones, and a water slug zone formed due to steam condensation. On the basis of the solution obtained, both the effects of the boundary pressure, mass flow rate, and temperature of the injected superheated steam and the effect of the initial state of the porous medium on the propagation of the hydrodynamic and thermal fields in the porous medium are studied. 相似文献
3.
In this paper we study one-dimensional three-phase flow through porous media of immiscible, incompressible fluids. The model uses the common multiphase flow extension of Darcys equation, and does not include gravity and capillarity effects. Under these conditions, the mathematical problem reduces to a 2 × 2 system of conservation laws whose essential features are: (1) the system is strictly hyperbolic; (2) both characteristic fields are nongenuinely nonlinear, with single, connected inflection loci. These properties, which are natural extensions of the two-phase flow model, ensure that the solution is physically sensible. We present the complete analytical solution to the Riemann problem (constant initial and injected states) in detail, and describe the characteristic waves that may arise, concluding that only nine combinations of rarefactions, shocks and rarefaction-shocks are possible. We demonstrate that assuming the saturation paths of the solution are straight lines may result in inaccurate predictions for some realistic systems. Efficient algorithms for computing the exact solution are also given, making the analytical developments presented here readily applicable to interpretation of lab displacement experiments, and implementation of streamline simulators. 相似文献
4.
Transport in Porous Media - Fluid displacement in porous media can usually be formulated as a Riemann problem. Finding the solution to such a problem helps shed light on the dynamics of flow and... 相似文献
5.
C. Y. Wang 《Transport in Porous Media》2008,73(3):369-378
Fully developed laminar forced convection inside a semi-circular channel filled with a Brinkman-Darcy porous medium is studied.
Analytical solutions for flow and constant flux heat transfer are found using a mixture of Cartesian and cylindrical coordinates.
The problem depends on a parameter s, which is proportional to the inverse square of the Darcy number. Velocity boundary layers exist when s is large. Both friction factor-Reynolds number product and Nusselt number are determined. Closed form expressions for the
clear fluid () limit are found. Rare analytical solutions not only describe fundamental channel flows, but also serve as a check for more
complicated numerical solutions. 相似文献
6.
Xabier Garaizar 《Journal of Elasticity》1991,26(1):43-63
This paper describes a numerical algorithm for the Riemann solution for nonlinear elasticity. We assume that the material is hyperelastic, which means that the stress-strain relations are given by the specific internal energy. Our results become more explicit under further assumptions: that the material is isotropic and that the Riemann problem is uniaxial. We assume that any umbilical points lie outside the region of physical relevance. Our main conclusion is that the Riemann solution can be obtained by the iterative solution of functional equations (Godunov iterations) each defined in one- or two-dimensional spaces.Supported in part by AFOSR-88-0025. 相似文献
7.
We derive an approximate analytical solution, which describes the interface dynamics during the injection of supercritical
carbon dioxide into homogeneous geologic media that are fully saturated with a host fluid. The host fluid can be either heavier
(e.g., brine) or lighter (e.g., methane) than the injected carbon dioxide. Our solution relies on the Dupuit approximation
and explicitly accounts for the buoyancy effects. The general approach is applicable to a variety of phenomena involving variable-density
flows in porous media. In three dimensions under radial symmetry, the solution describes carbon dioxide injection; its two-dimensional
counterpart can be used to model seawater intrusion into coastal aquifers. We conclude by comparing our solutions with existing
analytical alternatives. 相似文献
8.
Clément Louriou Hanène Ouerfelli Marc Prat Mustapha Najjari Sassi Ben Nasrallah 《Transport in Porous Media》2012,91(1):153-171
We study numerically and experimentally the displacement of a liquid by a gas in a two-dimensional model porous medium. In
contrast with previous pore network studies on drainage in porous media, the gas pressurization is fully taken into account.
The influence of the gas injection rate on the displacement pattern, breakthrough time and the evolution of the pressure in
the gas phase due in part to gas compressibility are investigated. A good agreement is found between the simulations and the
experiments as regards the invasion patterns. The agreement is also good on the drainage kinetics when the dynamic liquid
films are taken into account. 相似文献
9.
I. K. Gimaltdinov M. V. Stolpovskii M. K. Khasanov 《Journal of Applied Mechanics and Technical Physics》2018,59(1):1-8
This paper presents a mathematical model for methane hydrate–carbon dioxide replacement by injection of carbon dioxide gas into a porous medium rich in methane and its gas hydrate. Numerical solutions describing the pressure and temperature variation in a reservoir of finite length are obtained. It is shown that the replacement process is accompanied by a decrease in pressure and an increase in temperature of the porous medium. It is established that during the time of complete replacement of methane from a reservoir decreases with increasing permeability of the porous medium and the pressure of the injected gas. 相似文献
10.
Brinkman Flow of a Viscous Fluid Through a Spherical Porous Medium Embedded in Another Porous Medium
An analytical investigation for a two-dimensional steady, viscous, and incompressible flow past a permeable sphere embedded in another porous medium is presented using the Brinkman model, assuming a uniform shear flow far away from the sphere. Semi-analytical solutions of the problem are derived and relevant quantities such as velocities and shearing stresses on the surface of the sphere are obtained. The streamlines inside and outside the sphere and the radial velocity are shown in several graphs for different values of the porous parameters \({\sigma _1 =(\mu /\tilde {\mu }) (a/\sqrt{K_1 })}\) and \({\sigma _2 =(\mu /\tilde {\mu }) (a/\sqrt{K_2 })}\) , where a is the radius of the sphere, μ is the dynamic viscosity of the fluid, \({\tilde {\mu }}\) is an effective or Brinkman viscosity, while K 1 and K 2 are the permeabilities of the two porous media. It is shown that the dimensionless shearing stress on the sphere is periodic in nature and its absolute value increases with an increase of both porous parameters σ 1 and σ 2. 相似文献
11.
A boundary layer analysis is presented for the natural convection past an isothermal sphere in a Darcy porous medium saturated
with a nanofluid. Numerical results for friction factor, surface heat transfer rate, and mass transfer rate have been presented
for parametric variations of the buoyancy ratio parameter N
r, Brownian motion parameter N
b, thermophoresis parameter N
t, and Lewis number L
e. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number)
on these parameters has been discussed. 相似文献
12.
Non-Newtonian fluid flow through porous media is of considerable interest in several fields, ranging from environmental sciences
to chemical and petroleum engineering. In this article, we consider an infinite porous domain of uniform permeability k and porosity f{\phi} , saturated by a weakly compressible non-Newtonian fluid, and analyze the dynamics of the pressure variation generated within
the domain by an instantaneous mass injection in its origin. The pressure is taken initially to be constant in the porous
domain. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; n, < 1 describes shear-thinning behavior, n > 1 shear-thickening behavior; for n = 1, the Newtonian case is recovered. The law of motion for the fluid is a modified Darcy’s law based on the effective viscosity μ
ef
, in turn a function of f, H, n{\phi, H, n} . Coupling the flow law with the mass balance equation yields the nonlinear partial differential equation governing the pressure
field; an analytical solution is then derived as a function of a self-similar variable η = rt
β
(the exponent β being a suitable function of n), combining spatial coordinate r and time t. We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem
depending on a geometrical parameter d, valid for plane (d = 1), cylindrical (d = 2), and semi-spherical (d = 3) geometry. When a shear-thinning fluid is considered, the analytical solution exhibits traveling wave characteristics,
in variance with Newtonian fluids; the front velocity is proportional to t
(n-2)/2 in plane geometry, t
(2n-3)/(3−n) in cylindrical geometry, and t
(3n-4)/[2(2−n)] in semi-spherical geometry. To reflect the uncertainty inherent in the value of the problem parameters, we consider selected
properties of fluid and matrix as independent random variables with an associated probability distribution. The influence
of the uncertain parameters on the front position and the pressure field is investigated via a global sensitivity analysis
evaluating the associated Sobol’ indices. The analysis reveals that compressibility coefficient and flow behavior index are
the most influential variables affecting the front position; when the excess pressure is considered, compressibility and permeability
coefficients contribute most to the total response variance. For both output variables the influence of the uncertainty in
the porosity is decidedly lower. 相似文献
13.
Transport in Porous Media - We study the impact, on the drying rate, of the presence of suspended elements, such as calcium sulfate ions, in the interstitial fluid of a porous medium. In order to... 相似文献
14.
In the present investigation we have presented the peristaltic flow of a linear Maxwell model through porous boundaries in
a porous medium. The governing non-dimensional partial differential are solved in wave frame by using regular perturbation
method and assumed form of solution. We have discussed the problem only for free pumping case. The effects of various physical
parameters involved in the problem have been investigated and shown graphically. 相似文献
15.
Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium 总被引:1,自引:1,他引:0
In this paper, we solve the unsteady mixed convection flow near the stagnation point on a heated vertical flat plate embedded in a Darcian fluid-saturated porous medium by means of an analytic technique, namely the Homotopy Analysis Method. Different from previous perturbation results, our analytic series solutions are accurate and uniformly valid for all dimensionless times and for all possible values of mixed convection parameter, and besides agree well with numerical results. This provides us with a new analytic approach to investigate related unsteady problems. 相似文献
16.
Luigi La Ragione 《Meccanica》2006,41(4):413-423
We propose an example of an incremental elastic problem for a granular material. The mechanical behavior of this material
is sensitive to the confining pressure that typically is applied before any loading. Experiments, numerical simulations, and
theoretical models show that the effective elastic moduli of a granular medium are function of the confining pressure in non-linear
way. Therefore, if we consider a reference state where the pressure is not constant the material behaves differently in each
point and, for example, the stress associated to a subsequently loading should be obtained as solution of a non-homogeneous
material. We focus our attention on this kind of problem for a granular material that fills an hollow cylinder first isotropically
compressed and then sheared under a rotatory motion. Next a small perturbation is applied on the boundaries of the specimen
and we evaluate the corresponding stress distribution in the plane perpendicular to the axis of the cylinder. 相似文献
17.
18.
Donald A. Nield 《Transport in Porous Media》2008,73(3):379-380
The subject of the title is discussed. 相似文献
19.
The convective boundary-layer flow on an impermeable vertical surface in a fluid-saturated porous medium is considered where the flow results from the heat released by an exothermic catalytic reaction on the surface converting a reactive component within the convective fluid to an inert product. The reaction is modelled by first-order kinetics with an Arrhenius temperature dependence. Numerical solutions of the governing equations are obtained for a range of parameter values. These show, for large activation energies, that localized rapid changes in wall temperature and localized high reaction rates occur a little way from the leading edge. Asymptotic expansions, valid at large distances from the leading edge, are derived, the form that these expansions take is qualitatively different depending on whether or not reactant consumption is included in the model. 相似文献
20.
A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed. 相似文献