Statistical behaviors for renormalization of correlated permeability field

In this article, the statistical properties for the renormalized permeability obtained from the renormalization of the correlated permeability field are investigated. In contrast to the uncorrelated porous media, the scaling of the variance of the renormalized permeability field exhibits a crossover behavior. When the correlation lengths are larger compared with the domain scale covered by the renormalization procedure, the variance of the renormalized permeability will decrease slowly and the scaling exponent will be close to zero. As the renormalization number increases, the covered domain scale will eventually become larger than the correlation lengths, and then the scaling property will transit to the uncorrelated case. The convergent values of the renormalized permeability for isotropic and anisotropic correlated media are also investigated. Both the theoretical analysis and the simulation results show that larger correlation length in one direction will lead to a larger convergent value in the corresponding direction. For the log-normal permeability field, numerical simulations show that the crossover scaling and also the convergent value for the renormalized permeability can be fitted very well by simple mathematical functions.     

A difference-fractal model for the permeability of fibrous porous media

In this Letter, a difference-fractal model for the permeability of viscous flow through fibrous porous media is proposed. Since fractal objects have well-defined geometric properties, and are discrete and discontinuous, we apply the difference approach to developing the fractal model. The model of non-dimensional permeability is expressed as a function of porosity and fractal dimension. To verify the validity of the proposed model, the predicted permeability values are compared with those of experimental measurements. A good agreement between the prediction of the fractal model and the existing experimental data from the literature is found.     

The origins of dragon-kings and their occurrence in society

A society is a medium with a complex structure of one-to-one relations between people. Those could be relations between friends, wife–husband relationships, relations between business partners, and so on. At a certain level of analysis, a society can be regarded as a gigantic maze constituted of one-to-one relationships between people. From a physical standpoint it can be considered as a highly porous medium. Such media are widely known for their outstanding properties and effects like self-organized criticality, percolation, power-law distribution of network cluster sizes, etc. In these media supercritical events, referred to as dragon-kings, may occur in two cases: when increasing stress is applied to a system (self-organized criticality scenario) or when increasing conductivity of a system is observed (percolation scenario). In social applications the first scenario is typical for negative effects: crises, wars, revolutions, financial breakdowns, state collapses, etc. The second scenario is more typical for positive effects like emergence of cities, growth of firms, population blow-ups, economic miracles, technology diffusion, social network formation, etc. If both conditions (increasing stress and increasing conductivity) are observed together, then absolutely miraculous dragon-king effects can occur that involve most human society. Historical examples of this effect are the emergence of the Mongol Empire, world religions, World War II, and the explosive proliferation of global internet services. This article describes these two scenarios in detail beginning with an overview of historical dragon-king events and phenomena starting from the early human history till the last decades and concluding with an analysis of their possible near future consequences on our global society. Thus we demonstrate that in social systems dragon-king is not a random outlier unexplainable by power-law statistics, but a natural effect. It is a very large cluster in a porous percolation medium. It occurs as a result of changes in external conditions, such as supercritical load, increase in system elements’ sensitivity, or system connectivity growth.     

Fluctuation kinetics of diffusion-controlled processes: Strong effects due to correlations and fluctuations

We summarize some recent results related to fluctuation-induced kinetics of diffusion-controlled processes. We show that kinetic behavior can be drastically changed due to fluctuation effects, spatial correlations between particles, and anomalous transport properties. In addition, we show that correlation-induced kinetics in some systems can govern the temporal evolution over the entire time domain.     

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.     

An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks

In this paper, an analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks is presented. A dual-domain model is applied to simulate the heterogeneous porous media embedded with a constructal tree network based on the fractal distribution of pore space and tortuosity nature of flow paths. The analytical expressions for seepage velocity, pressure drop, local and global permeability of the network and binary system are derived, and the transport properties for the optimal branching structure are discussed. Notable is that the global permeability (K_n) of the network and the volume fraction (f_n) occupied by the network exhibit linear scaling law with the fractal dimension (D_p) of channel diameter bylogK_n∼0.46D_p and logf_n∼1.03D_p, respectively. Our analytical results are in good agreement with the available numerical results for steady-state soil vapor extraction and indicate that the fractal dimension for pore space has significant effect on the permeable properties of the media. The proposed dual-domain model may capture the characteristics of heterogeneous porous media and help understanding the transport mechanisms of the radial flow in the media.     

On the nonlinear dynamics of a saline boundary layer formed by throughflow near the surface of a porous medium

We consider gravitational instability of saline boundary layers, observed at the subsurface of salt lakes. This boundary layer is the result of the convective transport induced by the evaporation at the horizontal surface of a confined porous medium. When this upward transport is balanced by salt dispersion, a steady state boundary layer is formed. However, this boundary layer can be unstable when perturbed. This results in complex groundwater motion and density fields. The aim of this paper is to investigate the existence of finite amplitude solutions describing these resulting patterns (both the number of solutions and their structure), their stability, and their dependency on the system Rayleigh and Péclet numbers. For this purpose we construct a low-dimensional dynamical system (a reduced model) by projecting the nonlinear model equations onto a relatively small set of eigenfunctions of the problem linearized at criticality. The Galerkin projection approach is complicated by the fact that the problem under consideration is non-self-adjoint due to the existing evaporation. This implies that the eigenfunctions do not form an orthogonal set and therefore the adjoint eigenfunctions are used for the projection. The reduced model is constructed in such a way that it is capable of providing solutions in the strongly nonlinear regime as well. Convergence of these solutions towards the fully nonlinear model results is shown by means of direct numerical simulations. Further, the reduced model seems to partly capture the complex nonlinear behavior as seen in Hele-Shaw experiments by Wooding et al. [R.A. Wooding, S.W. Tyler, I. White, P.A. Anderson, Convection in groundwater below an evaporating salt lake: 2. evolution of fingers or plumes, Water Resour. Res. 33 (6) (1997) 1219-1228]. The physical transition mechanism that explains the occurrence of some observed bifurcation types is presented as well.     

The effect of spatial correlations on steady-state nucleation kinetics in dense fluid systems

A widely used expression for the steady-state nucleation rate is determined, in part, by the concentration of critical nuclei in a constrained equilibrium state of the system under consideration. We show that when a dense solvent is present, the values of the constrained equilibrium concentrations reflect the spatial correlations that arise from reactant-solvent molecule collisions. We evaluate the effect of such correlations for a simple, model fluid in terms of measurable reaction rate constants; our analysis shows that correlations influence each step in the multistep process of cluster formation and that the overall impact on the nucleation rate is cumulative. We argue that the very low, homogeneous nucleation rates observed in certain miscibility gap experiments are easily understood in the context of our analysis.Supported in part by a grant from the Research Corporation of the Cottrell Foundation.John Simon Guggenheim Memorial Fellow.     

Probing interfacial dynamics of water in confined nanoporous systems by NMRD

The confined dynamics of water molecules inside a pore involves an intermittence between adsorption steps near the interface and surface diffusion and excursions in the pore network. Depending on the strength of the interaction in the layer(s) close to the surface and the dynamical confinement of the distal bulk liquid, exchange dynamics can vary significantly. The average time spent in the surface proximal region (also called the adsorption layer) between a first entry and a consecutive exit allows estimating the level of ‘nanowettablity’ of water. As shown in several seminal works, NMRD is an efficient experimental method to follow such intermittent dynamics close to an interface. In this paper, the intermittent dynamics of a confined fluid inside nanoporous materials is discussed. Special attention is devoted to the interplay between bulk diffusion, adsorption and surface diffusion on curved pore interfaces. Considering the nano or meso length scale confinement of the pore network, an analytical model for calculating the inter-dipolar spin–lattice relaxation dispersion curves is proposed. In the low-frequency regime (50?KHz–100?MHz), this model is successfully compared with numerical simulations performed using a 3D-off lattice reconstruction of Vycor glass. Comparison with experimental data available in the literature is finally discussed.     

Development of a new correlation to calculate permeability for flows with high Knudsen number

Flows with high Knudsen number play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow with high Knudsen number using modified lattice Boltzmann method(LBM) through a porous medium in a channel. The effect of collision between molecules and solid walls, which is required to accurately simulate transition flow regime, is taken into account using a modified relaxation time. Slip velocity on the wall, which is another significant difficulty in simulating transition flow regime, is captured using the slip reflection boundary condition(SRBC). The geometry of porous medium is considered as in-line and staggered. The results are in good agreement with previous works. A new correlation is obtained between permeability, Knudsen number and porosity for flows in transition flow regimes.     

Molecular dynamics simulation of decomposition and thermal conductivity of methane hydrate in porous media

The hydrate has characteristics of low thermal conductivity and temperature sensitivity. To further analysis the mechanism of thermal conductivity and provide method for the exploitation, transportation and utilization of hydrate, the effect of decomposition and thermal conductivity of methane hydrate in porous media has been studied by using the molecular dynamics simulation. In this study, the simulation is carried out under the condition of temperature 253.15 K-273.15 K and pressure 1 MPa. The results show that the thermal conductivity of methane hydrate increases with the increase of temperature and has a faster growth near freezing. With the addition of porous media, the thermal conductivity of the methane hydrate improves significantly. The methane hydrate-porous media system also has the characteristics of vitreous body.With the decrease of the pore size of the porous media, thermal conductivity of the system increases gradually at the same temperature. It can be ascertained that the porous media of different pore sizes have strengthened the role of the thermal conductivity of hydrates.     

Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

We study the influence of nonlinearity on wave localization in one-dimensional random media. Using a discrete nonlinear Schrödinger equation with a random on-site energy term, we calculate the localization length in a numerically exact manner. Unlike in many previous works, we fix the intensity of the incident wave and calculate quantities as a function of other parameters. We find that localization is enhanced due to nonlinearity for the focusing and defocusing nonlinearities. For small nonlinearity, the localization length is a decreasing function of nonlinearity. For sufficiently large nonlinearity, however, the localization length is found to approach a saturation value.     

A deformation rig for synchrotron microtomography studies of geomaterials under conditions down to 10 km depth in the Earth

A hard X‐ray transparent triaxial deformation apparatus, called HADES, has been developed by Sanchez Technologies and installed on the microtomography beamline ID19 at the European Radiation Synchrotron Facility (ESRF). This rig can be used for time‐lapse microtomography studies of the deformation of porous solids (rocks, ceramics, metallic foams) at conditions of confining pressure to 100 MPa, axial stress to 200 MPa, temperature to 250°C, and controlled aqueous fluid flow. It is transparent to high‐energy X‐rays above 60 keV and can be used for in situ studies of coupled processes that involve deformation and chemical reactions. The rig can be installed at synchrotron radiation sources able to deliver a high‐flux polychromatic beam in the hard X‐ray range to acquire tomographic data sets with a voxel size in the range 0.7–6.5 µm in less than two minutes.     

A new method for simulation and analysis of displacement of fluids in porous media

Using the principle of diffusion-limited aggregation(DLA),a new model is introduced to simulate the displacement of one fluid by another in porous media.The results agree with experiments.apparently they do not leave out film-flow phenomena.Simultaneously,we also present a new numerical method to treat our results by the lattice Boltzmann method(LBM),All these will be helpful for analysing similar subjects.     

一维随机介质中准态模式的局域化程度对其阈值的影响

基于将Maxweil方程与四能级原子系统速率方程相结合而建立起的随机激光时域理论,并利用有限时域差分法,研究了一维随机激活介质中激光模式的输出强度与抽运速率之间的关系.结果表明,与传统激光模式相似,随机激光模式的强度随抽运速率的变化不仅具有阈值特性,而且具有饱和特性.用模式的空间区域来表征模式的局域化程度,发现局域化程度越强的模式,阈值越低.不过,这种关系不是一一对应的.这表明模式的局域化程度是决定阈值大小的重要因素,但不是唯一的因素.     

Enhancement of microstructure and initial permeability due to Cu substitution in Ni0.50−xCuxZn0.50Fe2O4 ferrites

Structural and magnetic properties of Cu substituted Ni_0.50−xCu_xZn_0.50Fe₂O₄ ferrites (where x=0.0-0.25) prepared by an auto combustion method have been investigated. The X-ray diffraction patterns of these compositions confirmed the formation of the single phase spinel structure. The lattice parameter increases with the increase in Cu²⁺ content obeying Vegard's law. The particle size of the starting powder compositions varied from 22 to 72 nm. The theoretical density increases with increase in copper content whereas the Néel temperature decreases. The bulk density, grain size and permeability increases up to a certain level of Cu²⁺ substitution, beyond that all these properties decrease with increase in Cu²⁺ content. The bulk density increases with increase in sintering temperatures up to 1250 °C for the parent composition, while for substituted compositions it increases up to 1200 °C. Due to substitution of Cu²⁺, the real part of the initial permeability increases from 97 to ∼390 for the sample sintered at 1100 °C and from 450 to 920 for the sample sintered at 1300 °C. The ferrites with higher initial permeability have a relatively lower resonance frequency, which obey Snoek's law. The initial permeability strongly depends on average grain size and intragranular porosity. The saturation magnetization, M_s, and the number of Bohr magneton, n(μ_B)_, decreases up to x=0.15 due to the reduction of the A-B interaction in the AB₂O₄ spinel type ferrites. Beyond that value of x, the M_s and the n(μ_B) values are enhanced. The substitution of Cu²⁺ influences the magnetic parameters due to modification of the cation distribution.     

The numerical simulation and analysis of three-dimensional seawater intrusion and protection projects in porous media

For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the numerical simulation of the practical situation in the Laizhou Bay Area of Shandong Province, predictive numerical simulation and analysis of the consequence of protection projects, underground dams, tidal barrage projects and the applied modular form of project adjustment have been finished. By using the theory and techniques of differential equation prior estimates, the convergence results have been got. Supported by the Major State Basic Research Program of China (Grant No. 19990328), the National Tackling Key Problem (Grant No. 2005020069), the National Natural Sciences Foundation of China (Grant Nos. 10771124 and 10372052), and the Doctorate Foundation of the Ministry of Education of China (Grant No. 20030422047)     

Oscillatory dynamics induced in polyelectrolyte gels by a non-oscillatory reaction: A model

We develop a general model and the associated numerical algorithm to compute the swelling dynamics of chemo-responsive polyelectrolyte gels immersed in a reactive ionic solution kept at a non-equilibrium stationary state by a permanent feed of fresh reactants. Using an autocatalytic bistable but nonoscillatory reaction, namely, the bromate-sulfite reaction, we predict that a piece of hydrogel that swells/shrinks as a function of p H can exhibit spontaneous mechanical and chemical oscillations. This constitutes the extension to realistic and experimentally feasible conditions of results previously obtained on a toy model with artificial swelling conditions.