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1.
Accurate models of multiphase flow in porous media and predictions of oil recovery require a thorough understanding of the
physics of fluid flow. Current simulators assume, generally, that local capillary equilibrium is reached instantaneously during
any flow mode. Consequently, capillary pressure and relative permeability curves are functions solely of water saturation.
In the case of imbibition, the assumption of instantaneous local capillary equilibrium allows the balance equations to be
cast in the form of a self-similar, diffusion-like problem. Li et al. [J. Petrol. Sci. Eng. 39(3) (2003), 309–326] analyzed oil production data from spontaneous countercurrent imbibition experiments and inferred that
they observed the self-similar behavior expected from the mathematical equations. Others (Barenblatt et al. [Soc. Petrol. Eng. J. 8(4) (2002), 409–416]; Silin and Patzek [Transport in Porous Media 54 (2004), 297–322]) assert that local equilibirum is not reached in porous media during spontaneous imbibition and nonequilibirium
effects should be taken into account. Simulations and definitive experiments are conducted at core scale in this work to reveal
unequivocally nonequilbirium effects. Experimental in-situ saturation data obtained with a computerized tomography scanner
illustrate significant deviation from the numerical local-equilibrium based results. The data indicates: (i) capillary imbibition
is an inherently nonequilibrium process and (ii) the traditional, multi-phase, reservoir simulation equations may not well
represent the true physics of the process. 相似文献
2.
We consider a constant coefficient coagulation equation with Becker–D?ring type interactions and power law input of monomers
J
1(t) = α t
ω, with α > 0 and . For this infinite dimensional system we prove solutions converge to similarity profiles as t and j converge to infinity in a similarity way, namely with either or constants, where is a function of t only. This work generalizes to the non-autonomous case a recent result of da Costa et al. (2004). Markov Processes Relat. Fields
12, 367–398. and provides a rigorous derivation of formal results obtained by Wattis J. Phys. A: Math. Gen. 37, 7823–7841. The main part of the approach is the analysis of a bidimensional non-autonomous system obtained through an appropriate
change of variables; this is achieved by the use of differential inequalities and qualitative theory methods. The results
about rate of convergence of solutions of the bidimensional system thus obtained are fed into an integral formula representation
for the solutions of the infinite dimensional system which is then estimated by an adaptation of methods used by da Costa
et al. (2004). Markov Processes Relat. Fields
12, 367–398.
相似文献
3.
We consider transport of a solute obeying linear kinetic sorption under unsteady flow conditions. The study relies on the
vertical unsaturated flow model developed by Indelman et al. [J. Contam. Hydrol. 32 (1998), 77–97] to account for a cycle of infiltration and redistribution. One of the main features of this type of transport,
as compared with the case of a continuous water infiltration, is the finite depth of solute penetration. In the infiltration
stage an analytical solution that generalizes the previous results of Lassey [Water Resour. Res. 24 (1988), 343–350] and Severino and Indelman [J. Contam. Hydrol. 70 (2004), 89–115] is derived. This solution accounts for quite general initial solute distributions in both the mobile and
immobile concentration. When the redistribution is also considered, two timescales become relevant, namely: (i) the desorption
rate k−1, and (ii) the water application time tap. In particular, we have assumed that the quantity ε =(k tap)−1 can be regarded as a small parameter so that a perturbation analytical solution is obtained. At field-scale the concentration
is calculated by means of the column model of Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979), 461–467], i.e. as ensemble average over an infinite series of randomly distributed and uncorrelated soil columns.
It is shown that the heterogeneity of hydraulic properties produces an additional spreading of the plume. An unusual phenomenon
of plume contraction is observed at long times of solute propagation during the drying period. The mean solute penetration
depth is studied with special emphasis on the impact of the variability of the saturated conductivity upon attaining the maximum
solute penetration depth. 相似文献
4.
Germán A. Enciso Morris W. Hirsch Hal L. Smith 《Journal of Dynamics and Differential Equations》2008,20(1):115-132
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward
an equilibrium or toward the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results
in terms of the measure-theoretic notion of prevalence, developed in Christensen (Israel J. Math., 13, 255–260, 1972) and Hunt et al. (Bull. Am. Math. Soc., 27, 217–238, 1992). For monotone reaction–diffusion systems with Neumann boundary conditions on convex domains, we show the
prevalence of the set of continuous initial conditions corresponding to solutions that converge to a spatially homogeneous
equilibrium. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is
given to the measurability of the various sets involved. 相似文献
5.
We investigate traveling wave solutions in a family of reaction-diffusion equations which includes the Fisher–Kolmogorov–Petrowskii–Piscounov (FKPP) equation with quadratic nonlinearity and a bistable equation with degenerate cubic nonlinearity. It is known that, for each equation in this family, there is a critical wave speed which separates waves of exponential decay from those of algebraic decay at one of the end states. We derive rigorous asymptotic expansions for these critical speeds by perturbing off the classical FKPP and bistable cases. Our approach uses geometric singular perturbation theory and the blow-up technique, as well as a variant of the Melnikov method, and confirms the results previously obtained through asymptotic analysis in [J.H. Merkin and D.J. Needham, (1993). J. Appl. Math. Phys. (ZAMP) A, vol. 44, No. 4, 707–721] and [T.P. Witelski, K. Ono, and T.J. Kaper, (2001). Appl. Math. Lett., vol. 14, No. 1, 65–73]. 相似文献
6.
The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg.
49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg.
58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg.
13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering
32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech.
53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech.
53, 1986, 855–863]. 相似文献
7.
The dynamics and stability of the high-speed fiber spinning process with spinline flow-induced crystallization and neck-like deformation have been studied using a simulation model equipped with governing equations of continuity, motion, energy, and crystallinity, along with the Phan-Thien–Tanner constitutive equation. Despite the fact that a simple one-phase model was incorporated into the governing equations to describe the spinline crystallinity, as opposed to the best-known two-phase model [Doufas et al. J Non-Newton Fluid Mech, 92:27–66, 2000a]; [Kohler et al. J Macromol Sci Phys, 44:185–202, 2005] that treats amorphous and crystalline phases separately in computing the spinline stress, the simulation has successfully portrayed the typical nonlinear characteristic of the high-speed spinning process called neck-like spinline deformation. It has been found that the criterion for the neck-like deformation to occur on the spinline is for the extensional viscosity to decrease on the spinline, so that the spinning is stabilized by the formation of the spinline neck-like deformation. The accompanying linear stability analysis explains this stabilizing effect of the spinline neck-like deformation, corroborating a recent experimental finding [Takarada et al. Int Polym Process, 19:380–387, 2004].This paper was presented at the 2nd Annual European Rheology Conference 2005 on April 21–23, 2005, in Grenoble, France. 相似文献
8.
The complexity measure from Shiner et al. [Physical Review E 59, 1999, 1459–1464] (henceforth abbreviated as SDL-measure) has recently been the subject of a fierce debate. We discuss the
properties and shortcomings of this measure, from the point of view of our recently constructed fundamental, statistical mechanics-based
measures of complexity Cs(γ,β) [Stoop et al., J. Stat. Phys. 114, 2004, 1127–1137]. We show explicitly, what the shortcomings of the SDL-measure are: It is over-universal, and the implemented
temperature dependence is trivial. We also show how the original SDL-approach can be modified to rule out these points of
critique. Results of this modification are shown for the logistic parabola. 相似文献
9.
In this work, we show that for linear upper triangular systems of differential equations, we can use the diagonal entries
to obtain the Sacker and Sell, or Exponential Dichotomy, and also –under some restrictions– the Lyapunov spectral intervals. Since any bounded and continuous coefficient matrix function can be smoothly transformed to an upper
triangular matrix function, our results imply that these spectral intervals may be found from scalar homogeneous problems.
In line with our previous work [Dieci and Van Vleck (2003), SIAM J. Numer. Anal. 40, 516–542], we emphasize the role of integral separation. Relationships between different spectra are shown, and examples
are used to illustrate the results and define types of coefficient matrix functions that lead to continuous Sacker–Sell spectrum
and/or continuous Lyapunov spectrum.
相似文献
10.
The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected. 相似文献
11.
Quasi-static imbibition was simulated using random and correlated stochastic network models. Using the snap-off pore-scale
displacement observed by Lernormand et al. (1983) the effects of many parameters on relative permeabilities and residual saturation reported in the literature were
reproduced and explained. Increased relative permeabilities and decreased residual non-wetting phase saturation were the results
of an increased contact angle (Li and Wardlaw, 1986b; Gauglitz and Radke, 1990; Blunt et al., 1992; Mogensen and Stenby, 1998) a decreased pore–throat aspect ratio, the presence of long-range pore-pore size correlations
(Iaonnidis and Chatzis, 1993; Blunt, 1997a), or local pore–throat correlations (Jerauld and Salter, 1990; Iaonnidis and Chatzis,
1993). By modifying the level of snap-off, or its spatial distribution, these parameters varied the efficiency of the displacement
patterns and ultimately affect relative permeabilities and residual saturations. Mani and Mohanty (1999) performed simulations
on networks with infinite-ranged fractional Brownian motion (fBm) correlations and reported trends of relative permeabilities
and residual saturations that were opposite to others’ results (Ioannidis and Chatzis, 1993; Blunt, 1997a). Applying a cut-off
length to the fBm correlations reversed Mani and Mohanty’s trends to conform with the common observations. 相似文献
12.
Mohamed Abd El-Aziz 《Meccanica》2007,42(4):375-386
An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting
fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into
account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The
resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then
solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting
method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic
parameter M, the viscosity/temperature parameter θ
r
, the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number,
and the local Sherwood number are presented graphically and in tabulated form. 相似文献
13.
The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular
cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in ε, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds
number of Re
d
≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of ε by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re
d
≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry
of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared
velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless,
the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales. 相似文献
14.
A systematic application of the group analysis method for modeling fluids with internal inertia is presented. The equations
studied include models such as the nonlinear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small
volume concentration of gas bubbles (Iordanski Zhurnal Prikladnoj Mekhaniki i Tekhnitheskoj Fiziki 3, 102–111, 1960; Kogarko Dokl. AS USSR 137, 1331–1333, 1961; Wijngaarden J. Fluid Mech. 33, 465–474, 1968), and the dispersive shallow water model (Green and Naghdi J. Fluid Mech. 78, 237–246, 1976; Salmon 1988). These models are obtained for special types of the potential function W(r,[(r)\dot],S){W(\rho,\dot \rho,S)} (Gavrilyuk and Teshukov Continuum Mech. Thermodyn. 13, 365–382, 2001). The main feature of the present paper is the study of the potential functions with W
S
≠ 0. The group classification separates these models into 73 different classes. 相似文献
15.
Nozaki and Taya (ASME J. Appl. Mech. 64 (1997) 495–502) analyzed the elastic field in a convex polygonal inclusion in an infinite body. By numerical analysis, they
found that, when the shape of the inclusion is a regular polygon, “the strain at the center of inclusion” and “the strain
energy per unit volume of inclusion” have strange and remarkable properties: these values are the same as those of a circular
inclusion and are invariant for inclusion's orientation if the shape of the inclusion is not a square. In this paper, we first derive a simple, exact expression of the Eshelby tensor for an arbitrary polygonal inclusion. Using
the expression, we then show a mathematical explanation why these special properties appear.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
Stephen Schecter 《Journal of Dynamics and Differential Equations》2006,18(1):53-101
The Dafermos regularization of a system of n conservation laws in one space dimension admits smooth self-similar solutions of the form u=u(X/T). In particular, there are such solutions near a Riemann solution consisting of n possibly large Lax shocks. In Lin and Schecter (2004, SIAM. J. Math. Anal. 35, 884–921), eigenvalues and eigenfunctions of the linearized Dafermos operator at such a solution were studied using asymptotic expansions. Here we show that the asymptotic expansions correspond to true eigenvalue–eigenfunction pairs. The proofs use geometric singular perturbation theory, in particular an extension of the Exchange Lemma. 相似文献
17.
In the present work, the effect of MHD flow and heat transfer within a boundary layer flow on an upper-convected Maxwell (UCM)
fluid over a stretching sheet is examined. The governing boundary layer equations of motion and heat transfer are non-dimensionalized
using suitable similarity variables and the resulting transformed, ordinary differential equations are then solved numerically
by shooting technique with fourth order Runge–Kutta method. For a UCM fluid, a thinning of the boundary layer and a drop in
wall skin friction coefficient is predicted to occur for higher the elastic number. The objective of the present work is to
investigate the effect of Maxwell parameter β, magnetic parameter Mn and Prandtl number Pr on the temperature field above the sheet. 相似文献
18.
In the last 30 years, some authors have been studying several classes of boundary value problems (BVP) for partial differential
equations (PDE) using the method of reduction to obtain a difference equation with continuous argument which behavior is determined
by the iteration of a one-dimensional (1D) map (see, for example, Romanenko, E. Yu. and Sharkovsky, A. N., International Journal of Bifurcation and Chaos 9(7), 1999, 1285–1306; Sharkovsky, A. N., International Journal of Bifurcation and Chaos 5(5), 1995, 1419–1425; Sharkovsky, A. N., Analysis Mathematica Sil 13, 1999, 243–255; Sharkovsky, A. N., in “New Progress in Difference Equations”, Proceedings of the ICDEA'2001, Taylor and Francis, 2003, pp. 3–22; Sharkovsky, A. N., Deregel, Ph., and Chua, L. O., International Journal of Bifurcation and Chaos 5(5), 1995, 1283–1302; Sharkovsky, A. N., Maistrenko, Yu. L., and Romanenko, E. Yu., Difference Equations and Their Applications, Kluwer, Dordrecht, 1993.). In this paper we consider the time-delayed Chua's circuit introduced in (Sharkovsky, A. N., International Journal of Bifurcation and Chaos 4(5), 1994, 303–309; Sharkovsky, A. N., Maistrenko, Yu. L., Deregel, Ph., and Chua, L. O., Journal of Circuits, Systems and Computers 3(2), 1993, 645–668.) which behavior is determined by properties of one-dimensional map, see Sharkovsky, A. N., Deregel, Ph.,
and Chua, L. O., International Journal of Bifurcation and Chaos 5(5), 1995, 1283–1302; Maistrenko, Yu. L., Maistrenko, V. L., Vikul, S. I., and Chua, L. O., International Journal of Bifurcation and Chaos 5(3), 1995, 653–671; Sharkovsky, A. N., International Journal of Bifurcation and Chaos 4(5), 1994, 303–309; Sharkovsky, A. N., Maistrenko, Yu. L., Deregel, Ph., and Chua, L. O., Journal of Circuits, Systems and Computers 3(2), 1993, 645–668. To characterize the time-evolution of these circuits we can compute the topological entropy and to distinguish
systems with equal topological entropy we introduce a second topological invariant. 相似文献
19.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2007,9(4):506-516
In reference [7] it is proved that the solution of the evolution Navier–Stokes equations in the whole of R
3 must be smooth if the direction of the vorticity is Lipschitz continuous with respect to the space variables. In reference
[5] the authors improve the above result by showing that Lipschitz continuity may be replaced by 1/2-H?lder continuity. A
central point in the proofs is to estimate the integral of the term (ω · ∇)u · ω, where u is the velocity and ω = ∇ × u is the vorticity. In reference [4] we extend the main estimates on the above integral term to solutions under the slip boundary
condition in the half-space R
+3. This allows an immediate extension to this problem of the 1/2-H?lder sufficient condition.
The aim of these notes is to show that under the non-slip boundary condition the above integral term may be estimated as well
in a similar, even simpler, way. Nevertheless, without further hypotheses, we are not able now to extend to the non slip (or
adherence) boundary condition the 1/2-H?lder sufficient condition. This is not due to the “nonlinear" term (ω · ∇)u · ω but to a boundary integral which is due to the combination of viscosity and adherence to the boundary. On the other hand,
by appealing to the properties of Green functions, we are able to consider here a regular, arbitrary open set Ω.
相似文献
20.
Adrian Postelnicu 《Heat and Mass Transfer》2007,43(6):595-602
The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium
subjected to a chemical reaction is numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion
(Soret) effects. The transformed governing equations are solved by a very efficient numerical method, namely, a modified version
of the Keller-box method for ordinary differential equations. The parameters of the problem are Lewis, Dufour and Soret numbers,
sustentation parameter, the order of the chemical reaction n and the chemical reaction parameter γ. Local Nusselt number and local Sherwood number variations and dimensionless concentration
profiles in the boundary layer are presented graphically and in tables for various values of problem parameters and it is
concluded that γ and n play a crucial role in the solution. 相似文献