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1.
We consider a model describing compressible nuclear waste disposal contamination in porous media. The transport of brine,
radionuclides and heat is described by a nonlinear coupled parabolic system. The viscosity of the fluid is unbounded and concentrations
and temperature dependent. Using a fixed point approach, we prove existence of physically relevant weak solutions. 相似文献
2.
Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior. 相似文献
3.
IntroductionIn the computation of petroleum reservoir engineering design,the nonlinear quadraticgradient term is neglected by assuming small pressure gradient or small compressibility.Theassumption of small pressure gradient may cause significant errors i… 相似文献
4.
Antonin Chambolle Benoît Desjardins Maria J. Esteban Céline Grandmont 《Journal of Mathematical Fluid Mechanics》2005,7(3):368-404
The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane. 相似文献
5.
Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed.Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model(DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density.The pressure propagation is slower in the direction of larger fracture density. 相似文献
6.
Gilles Carbou 《Journal of Mathematical Fluid Mechanics》2008,10(1):126-158
In this paper we study a penalization method used to compute the flow of a viscous fluid around a thin layer of porous material.
Using a BKW method, we perform an asymptotic expansion of the solution when a little parameter, measuring the thickness of
the thin layer and the inverse of the penalization coefficient, tends to zero. We compare then this numerical method with
a Brinkman model for the flow around a porous thin layer.
相似文献
7.
Timofey Shilkin 《Journal of Mathematical Fluid Mechanics》2005,7(1):72-84
We consider the coupled system of two nonlinear scalar parabolic equations modelling a simple uni-directional Poiseuille-type flow of a homogeneous incompressible Newtonian fluid whose viscosity is a temperature-dependent function. The energy balance equation of this system takes into account the phenomena of the viscous energy dissipation. We prove existence of a classical solution to this system on an arbitrary interval of time. The smooth solution turns out to be unique in a wider class of weak solutions. 相似文献
8.
In the present study, an algorithm is presented for the dual-porosity model formulated in Part I of this series. The resultant
flow equation with the dual-porosity formulation is of an integro-(partial) differential equation involving differential terms
for the Darcy flow in large fractures and integrals in time for diffusion within matrix blocks. The algorithm developed here
to solve this equation involves a step-by-step finite difference procedure combined with a quadrature scheme. The quadrature
scheme, used for the integral terms, is based on the trapezoidal method which is of second-order precision. This order of
accuracy is consistent with the first- and second-order finite difference approximations used here to solve the differential
terms in the derived flow equation. In an approach consistent with many petroleum reservoir and groundwater numerical flow
models, the example formulation presented uses a first-order implicit algorithm. A two-dimensional example is also demonstrated,
with the proposed model and numerical scheme being directly incorporated into the commercial gas reservoir simulator SIMED
II that is based on a fully implicit finite difference approach. The solution procedure is applied to several problems to
demonstrate its performance. Results from the derived dual-porosity formulation are also compared to the classic Warren–Root
model. Whilst some of this work confirmed previous findings regarding Warren–Root inaccuracies at early times, it was also
found that inaccuracy can re-enter the Warren–Root results whenever there are changes in boundary conditions leading to transient
variation within the domain. 相似文献
9.
Matrix–fracture transfer functions are the backbone of any dual-porosity or dual-permeability formulation. The chief feature
within them is the accurate definition of shape factors. To date, there is no completely accepted formulation of a matrix–fracture
transfer function. Many formulations of shape factors for instantly-filled fractures with uniform pressure distribution have
been presented and used; however, they differ by up to five times in magnitude. Based on a recently presented transfer function,
time-dependent shape factors for water imbibing from fracture to matrix under pressure driven flow are proposed. Also new
matrix–fracture transfer pressure-based shape factors for instantly-filled fractures with non-uniform pressure distribution
are presented in this article. These are the boundary conditions for a case for porous media with clusters of parallel and
disconnected fractures, for instance. These new pressure-based shape factors were obtained by solving the pressure diffusivity
equation for a single phase using non-uniform boundary conditions. This leads to time-dependent shape factors because of the
transient part of the solution for pressure. However, approximating the solution with an exponential function, one obtains
constant shape factors that can be easily implemented in current dual-porosity reservoir simulators. The approximate shape
factors provide good results for systems where the transient behavior of pressure is short (a case commonly encountered in
fractured reservoirs). 相似文献
10.
考虑页岩气藏开发中渗流的多尺度效应,提出了一个基于裂缝-孔隙双重介质的离散裂缝模型.在该模型中,基质、天然裂缝和人工压裂裂缝采用各自控制方程独立计算,不同介质之间通过流量交换相互关联.为分析模型可靠性,分别和基于渗透率粗化及压裂裂缝导流能力无穷大的模型对比.数值算例显示,伴随着网格细分,该模型与精确渗透率粗化模型具有相同计算精度,两者收敛速度均较快,但该模型易推广到多相流动问题,而等压模型对产量将有所高估.研究了地质参数和工艺参数对气井产量的影响规律.计算结果表明天然裂缝渗透率及基质孔隙扩散系数对产气速率有着重要影响,产气速率伴随着人工压裂裂缝导流能力、长度以及数目的增加而增加,但是增加幅度会逐步趋缓. 相似文献
11.
In this paper, we consider a two-dimensional fluid-rigid body problem.
The motion of the fluid is modelled by the Navier-Stokes equations, whereas
the dynamics of the rigid body is governed by the conservation
laws of linear and angular momentum. The rigid body is supposed
to be an infinite cylinder of circular cross-section.
Our main result is the existence and uniqueness of global strong solutions. 相似文献
12.
13.
Olivier Steiger 《Journal of Mathematical Fluid Mechanics》2006,8(4):456-481
On the basis of semigroup and interpolation-extrapolation techniques we derive existence and uniqueness results for the Navier–Stokes
equations. In contrast to many other papers devoted to this topic, we do not complement these equations with the classical
Dirichlet (no-slip) condition, but instead consider stress-free or slip boundary conditions. We also study various regularity
properties of the solutions obtained and provide conditions for global existence. 相似文献
14.
We consider a planar stationary flow of an incompressible viscous fluid in a semiinfinite strip governed by the Stokes system
with a body forces field. We show how this fluid can be stopped at a finite distance of the entrance of the semi-infinite
strip by means of a feedback field depending in a sub-linear way on the velocity field. This localization effect is proved
reducing the problem to a non-linear bi-harmonic type one for which the localization of solutions is obtained by means of
the application of a suitable energy method. Since the presence of the non-linear terms defined through the body forces field
is not standard in the fluid mechanics literature, we establish also some results about the existence and uniqueness of weak
solutions for this problem. 相似文献
15.
If a drop of fluid of density 1 rests on the surface of a fluid of density 2 below a fluid of density 0, 0 < 1 < 2, the surface of the drop is made up of a sessile drop and an inverted sessile drop which match an external capillary surface. Solutions of this problem are constructed by matching solutions of the axisymmetric capillary surface equation. For general values of the surface tensions at the common boundaries of the three fluids the surfaces need not be graphs and the profiles of these axisymmetric surfaces are parametrized by their tangent angles. The solutions are obtained by finding the value of the tangent angle for which the three surfaces match. In addition the asymptotic form of the solution is found for small drops. 相似文献
16.
The linear stability of a thin vertical fluid layer heated from below is considered. Here the gravitational field consists of two parts: a constant part and a time-dependent part varying periodically. The time-dependent part has been expressed in Fourier series. The effect of gravity modulation on the fluid layer is examined. Using an asymptotic analysis the convective threshold has been determined. Some comparisons are made with the known results. 相似文献
17.
Takaaki Nishida Yoshiaki Teramoto Hideaki Yoshihara 《Journal of Mathematical Fluid Mechanics》2005,7(1):29-71
We provide the Hopf bifurcation theorem, which guarantees the existence of time periodic solution bifurcating from the stationary flow down an inclined plane under certain assumptions on the eigenvalues of the problem obtained by linearization around the stationary flow. Since we reduce the problem to the fixed domain, the inhomogeneous terms of reduced equations and reduced boundary conditions contain the highest derivatives. To deal with these we apply the Lyapunov–Schmidt decomposition directly. 相似文献
18.
Christiaan Le Roux 《International Journal of Non》2009,44(1):31-41
We prove the existence and uniqueness of steady flows of incompressible fluids of grade three subject to slip and no-slip boundary conditions in bounded domains. The slip boundary condition is a non-linear generalization of the Navier slip boundary condition and permits situations in which the solid boundary undergoes non-rigid tangential motion. The existence proof is based on a fixed point method in which the boundary-value problem is decomposed into four linear problems. 相似文献
19.
The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. In this paper, non-linear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed are studied. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov-Schmidt Reduction method. By using the reduced bifurcation equations, the periodic solutions are determined to analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions near the new stability boundary. 相似文献
20.
In this paper, we study the existence and uniqueness of a degenerate parabolic equation, with nonhomogeneous boundary conditions,
coming from the linearization of the Crocco equation [12]. The Crocco equation is a nonlinear degenerate parabolic equation
obtained from the Prandtl equations with the so-called Crocco transformation. The linearized Crocco equation plays a major
role in stabilization problems of fluid flows described by the Prandtl equations [5]. To study the infinitesimal generator
associated with the adjoint linearized Crocco equation – with homogeneous boundary conditions – we first study degenerate
parabolic equations in which the x-variable plays the role of a time variable. This equation is doubly degenerate: the coefficient in front of ∂x vanishes on a part of the boundary, and the coefficient of the elliptic operator vanishes in another part of the boundary.
This makes very delicate the proof of uniqueness of solution. To overcome this difficulty, a uniqueness result is first obtained
for an equation in which the elliptic operator is symmetric, and it is next extended to the original equation by combining
an iterative process and a fixed point argument (see Th. 4.9). This kind of argument is also used to prove estimates, which
cannot be obtained in a classical way. 相似文献