Methane Hydrate and Two-Dimensional Fluid Transport Model: Comparison with Blake Ridge Chlorinity Measurements

The potential benefits and risks of natural methane hydrate occurrences have raised the need to understand the processes governing hydrate formation and dissociation over the last decades, and models of increasing complexity have been developed for this purpose. We propose a formulation of a multi-dimensional methane hydrate model that couples the established chemistry of hydrate formation to the fluid flow in marine sediments undergoing compaction. The numerical model applies the Finite Volume Method to construct a segregated solver for the coupled system. The solution of the sequence of individual processes is stabilised with an adaptive Picard iteration in each time step. We implement the model based on the OpenFOAM library and extend the functionality by generalising the diffusion term to take into account variable porosity of the sediment matrix. The advantage of this robust and efficient scheme is that the formulation is conservative by construction, allowing an accurate solution of mass transport when strong concentration gradients develop in the vicinity of phase boundaries. We validate the model using data from the Blake Ridge hydrate province. Good agreement is found for the pore water chlorinity, a proxy for hydrate formation, except for regions where heterogeneous hydrate formation results in highly variable measurements.     

Local Well-Posedness for Fluid Interface Problems

In this paper, we prove the local well-posedness of the fluid interface problem with surface tension where the velocity fields are not assumed to be irrotational and the fluid domains are not assumed to be simply connected. Viewed as a Lagrangian system with the configuration space being an infinite dimensional manifold possessing many symmetries, this problem is reduced to the evolution of the interface, determined by its mean curvature, and the evolution of the rotational part of the velocity fields, determined by the symmetries. This framework also applies to several other fluid surface problems which are outlined in the paper.     

Jump Conditions and Surface-Excess Quantities at a Fluid/Porous Interface: A Multi-scale Approach

We present a two-step up-scaling approach that allows to derive the jump conditions that must be imposed at the interface to account for transport phenomena in a fluid/porous domain. This general approach is first applied to a heat conduction problem to illustrate the main steps of the analysis. The heat flux and temperature jump conditions are related to surface-excess quantities, whose values depend on the interface location. Good agreement between the mesoscopic and macroscopic results are obtained, whatever the position of the interface inside the transition region. The approach is then applied to the problem of a laminar flow over a porous medium. The Beavers and Joseph relation is recovered, but only for a particular position of the interface.     

Analysis of a Stochastic Implicit Interface Model for an Immersed Elastic Surface in a Fluctuating Fluid

We present some mathematical analyses of a recently proposed stochastic implicit interface model for an elastic surface immersed in an incompressible viscous fluid subject to fluctuation forces. We derive suitable a priori estimates and establish the well-posedness of pathwise solutions and provide uniform control on the solutions in probability.     

Interface Stability of Compressible Fluid Displacements in Porous Media

Transport in Porous Media - We use linear stability theory to investigate the effect of fluid compressibility on interface stability during a dissipative displacement (Darcy flow). We find that...     

Capillary Pressures by Fluid Saturation Profile Measurements During Centrifuge Rotation

A novel centrifuge technique to obtain the capillary pressure curve by measuring the local fluid distribution in a spinning core is presented. The Nuclear Tracer Imaging Centrifuge (NTIC) method measures the fluid saturation profile along the length of the core to directly obtain the capillary pressure curve. The proposed method is superior to conventional centrifuge techniques because (1) the capillary pressure curve is obtained at one rotational speed, (2) core plugs are not removed from the spinning centrifuge for imaging, and (3) no mathematical solution is needed to calculate the capillary pressure curve. The literature states that the various mathematical solutions used in conventional centrifuge tests are the greatest source of error, not the uncertainty in the experimental data. By eliminating the dependence of such solutions, the NTIC represents an alternative to conventional centrifuge tests, and may be used to validate the various mathematical procedures applied in conventional centrifuge capillary pressure tests. NTIC may also confirm the applicability of other imaging techniques that rely on core plug removal for saturation imaging, by verifying if there is no fluid re-distribution at static conditions.     

A Continuum Model for Fluid Foams

A continuum theory of fluid foams regarded as a continuum of hexagonal micro cells with fluid walls is derived and some qualitative aspects of the equilibrium problem are discussed.     

钙质砂与结构接触面的本构模型研究

基于接触面的宏、细观物理特征,建立了单调加载条件下钙质砂与结构接触面的弹塑性增量本构关系。从接触面的宏观条件上考虑,该模型将弹性模量取为法向压力的指数函数,采用非关联流动法则和Mohr-columb屈服函数,以及切向塑性功为硬化参量,适用于多数接触摩擦问题。在细观上将滑动面抽象为锯齿面,同时将摩擦系数取为塑性功的双曲线函数,以考虑钙质砂颗粒破碎对接触面力学特性的影响。模型概念简单、参数较少,通过理论计算与钙质砂拉拔试验结果比较,显示了模型的合理性。     

On the Equivalence of the Discontinuous One- and Two-Domain Approaches for the Modeling of Transport Phenomena at a Fluid/Porous Interface

In the quest (i) to determine the form of the boundary conditions that must be applied at a fluid/porous interface and (ii) to determine the value of the jump parameters that appear in the expression for these boundary conditions, two different approaches are commonly considered: the so-called one-domain and two-domain approaches. These approaches are commonly thought to be different, and they are thus sometimes compared to each other to determine the value of jump parameters. In this article, we show that the two-domain and discontinuous one-domain approaches are actually strictly equivalent, provided that the latter is mathematically interpreted in the sense of distributions. This equivalence is shown in details for a heat conduction problem and for the more classical Darcy-Brinkman problem. We show in particular that interfacial jumps are introduced in the discontinuous one-domain approach through Dirac delta functions. Numerical issues are then discussed that show that subtle discretization truncation errors give rise to large variations that can be mis-interpreted as the sign of the existence of jump parameters.     

A Model of Buoyancy-Driven Two-Phase Countercurrent Fluid Flow

We seek simple analytical solutions in a model of gas flow driven by a combination of buoyancy, viscous, and capillary forces. Traveling-wave solutions describe propagation of the top and bottom of the gas plume. The top of the plume has low gas saturation, but propagates much faster than the bottom. The theoretical maximum of the velocity of propagation of the top of the plume provides a simple conservative estimate of the time until plume evolution will dramatically slow down. A sequence of rarefaction and traveling-wave solutions characterizes the transition zones between the top and bottom stable regions. The analytical results are applied to studying carbon dioxide flow caused by leaks from deep geological formations used for CO₂ storage. The results are also applicable for modeling flow of natural gas leaking from seasonal gas storage, or for modeling of secondary hydrocarbon migration.     

硅微机械陀螺仪的机电接口模型分析

建立了某种硅微机械陀螺仪的电路模型,分析了寄生电容对接口电路的影响.结果表明,合理的接口电路不仅消除了大部分的寄生电容的影响,而且减小了信号的衰减幅度,抑制了大部分的耦合信号和噪声信号.最后对接口电路进行了改进,除了保留以上的一些优点外,还减小了载波信号的变化和电源变化对电容分辨率的影响,提高了整个电路的分辨率.     

Homogenized Interface Model Describing Inhomogeneities Located on a Surface

We study the influence of heterogeneities located near a planar surface on the elastic response of a three-dimensional elastic medium. These heterogeneities can be either reinforcements, like steel reinforcements in concrete, or defects, like micro-cracks periodically distributed. We prove that their influence is of the second order from an energetic viewpoint. Then, we propose an ??up to second order effective model?? in which the influence of the heterogeneities is given by a surface energy contribution involving both the jump of displacement across the surface and the tangential strain components on the surface. The effective coefficients entering in the definition of the surface energy are obtained by solving ??elementary?? elastic problems formulated on an infinite representative cell containing the defects. We analyze this model, in particular the properties of the effective surface coefficients, and establish its coherence with limit models previously described in the literature for stiff or soft interfaces. This approach is finally applied to several kinds of heterogeneities.     

Modeling Effective Interface Laws for Transport Phenomena Between an Unconfined Fluid and a Porous Medium Using Homogenization

In this chapter of the special issue of the journal “Transport in Porous Media,” on the topic “Flow and transport above permeable domains,” we present modeling of flow and transport above permeable domains using the homogenization method. Our goal is to develop a heuristic approach which can be used by the engineering community for treating this type of problems and which has a solid mathematical background. The rigorous mathematical justification of the presented results is given in the corresponding articles of the authors. The plan is as follows: We start with the section “Introduction” where we give an overview and comparison with interface conditions obtained using other approaches. In Sect. 2, we give a very short derivation of the Darcy law by homogenization, using the two-scale expansion in the typical pore size parameter ε. It gives us the definition of various auxiliary functions and typical effective properties as permeability. In Sect. 3, we introduce our approach to the effective interface laws on a simple 1D example. The approximation is obtained heuristically using the two steps strategy. For the 1D problem we calculate the approximation and the effective interface law explicitly and show that it is valid at order O(ε ²). Next, in Sect. 4 we give a derivation of the Beavers–Joseph–Saffman interface condition and of the pressure jump condition, using homogenization. We construct the corresponding boundary layer and present a heuristic calculation, leading to the interface law and being based on the rigorous mathematical result. In addition, we show the invariance of the law with respect to the small variations in the choice of the interface position. Finally, there is a short concluding section. The research of A.M. was partially supported by the GDR MOMAS (Modélisation Mathématique et Simulations numériques liées aux problèmes de gestion des déchets nucléaires) (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN).     

吸流管道动力学模型的研究现状与展望

围绕吸流管道的稳定性与振动问题,对近年来的主要研究工作加以综述并提出预测,其中包括运动方程的归纳与讨论、管道自由端口处的流固耦合理论、定常流速下吸流管道的稳定性机理以及今后值得进一步研究的某些问题.     

An Analytical Model for Fluid Imbibition in Organic Nanopores

Transport in Porous Media - Estimating the fluid imbibition flow in natural system composed of nanopores is challenging due to the strong fluid/rock molecular scale interaction and the invalidation...     

Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence

We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.     

Nonlinear Dynamics of Two-Degrees-of-Freedom Fluid Conveying Elasto-Visco-Plastic Model System

The local and global nonlinear dynamics of a two-degrees-of-freedom model system conveying fluid is studied. The undeflected model consistsof an inverted T formed by three rigid rods, with the tips of the twohorizontal rods resting on the viscous foundation. The foundationexhibits a visco-elasto-plastic response, including the Bauschingereffect. The vertical rigid rod of an annular cross-section is subjectedto a conservative (dead) force. Also, it conveys fluid having bothstatic and pulsation components. First, the method of multiple scales isused for the analysis of the local dynamics of the system withvisco-elastic response. Attention is focused on modal interactionphenomena in weak excitation at primary resonance and on hardsub-harmonic excitation. Two different asymptotic expansions areutilised to get a structural response for typical ranges of excitationparameters. Numerical integration of the governing equations is thenperformed to validate the results of asymptotic analysis in each case. Afull global nonlinear dynamics analysis of the visco-elasto-plasticsystem is performed. The role of plastic deformations in thedestabilisation of the system is discussed. Large-amplitude nonlinearoscillations of the visco-elasto-plastic system are studied, includingthe influence of material hardening and of static and periodiccomponents of pulsating fluid. Chaotic regimes of motion with andwithout plastic effects are considered. The results of the analysis maybe used in devices composed of a rather short tube connected to a notcompletely fixed foundation resting on the soil exhibitingelasto-plastic behaviour.