Microscopic-based fluid flow simulation of invasion on a two-dimensional lattice. II. Mobilization and cohesion

An algorithm for modeling secondary invasion processes in porous media is presented. Mobilization of trapped defender fluid is accomplished through interfacial interaction rules. Cohesive forces are also included within the defender phase. A series of simulation runs are performed using two-dimensional lattices and examined to determine optimal conditions for secondary invasions that sweep the trapped defender phase from the porous medium.     

Direct measurement of porous media local hydrodynamical permeability using gas MRI.

The concept of hydraulic permeability is at the core of modeling single phase or multi-phase flow in heterogeneous porous media, as it is the spatial distribution of the permeability that primarily governs the behavior of fluid flow in the medium. To date, the modeling of fluid flow in porous media has been hampered by poor estimates of local permeability. Magnetic Resonance Imaging is well known for its ability to measure non-invasively the local density and flow rate of different fluids saturating porous media [1,2]. In this paper we demonstrate the first non-invasive method for the direct measurement of a single projection of the local permeability tensor of a porous medium using gas-phase MRI. The potential for three-dimensional imaging of the medium permeability is also discussed. The limitations of the method are listed and results are presented in a model porous medium as well as in a real oil reservoir rock.     

Thermal-physical and thermoelectric properties of solids near the polymorphic and superconducting transitions

The relationships are presented for the effective thermal conductivity and thermoelectric power coefficients near the superconducting and polymorphic phase transitions. The relationships are verified using the experimental data obtained for porous media saturated with a fluid. The experimental data obtained for the high-temperature superconductor YBa₂Cu₃O _x (x = 6.8, 6.9) and n-InAs are analyzed.     

Two-phase filtration of multicomponent mixtures with a retrograde region of the phase diagram

The results of mathematical and physical modeling of an isothermal filtration of multicomponent mixtures with a retrograde region of the phase diagram are presented. By the example of mixtures of hydrocarbons of the methane line, the conditions at which the hydrocarbon-two-phase fluid?porous space system is a self-oscillation system are determined. The data obtained make it possible to explain certain regularities of the filtration of gas-condensate mixtures and can be used to increase the extraction of gas-condensate deposits.     

考虑相重新分布的双重介质分形油藏不稳定渗流压力动态特征

基于分形油藏渗流力学,针对存在井筒储集、表皮效应和井筒相重新分布影响下的不稳定渗流问题,建立双重介质分形油藏有效井径数学模型,并采用Douglas-Jones预估校正法求得无限大地层定产量生产条件下的非线性数值解.由数值解可知,该系统完整的压降曲线由四个流动区组成.最后分析各个分形参数、相重新分布参数和双重介质参数变化时压力的变化规律,做出典型压力曲线图版,为研究复杂渗流系统中相重新分布影响下的不稳定渗流规律提供参考.     

Conditional methods for continuum reacting flows in porous media

A special version of conditional moment closure—PCMC—is suggested for modeling reacting flows in porous media. The model involves conditioning on a special tracer scalar, which is introduced to characterize scalar transport in the gaseous phase. (i.e., for the flow in the interparticle space or in the pores). The model accounts for interparticle variations of species concentrations and emulates diffusion in the interparticle space. Special boundary conditions that are consistent with conventional conditions at the phase interface are obtained for the PCMC model. The model is tested against complete direct simulation of a reacting flow in porous media with favourable results.     

Inhomogeneity-induced second-order phase transitions in the Potts model on hierarchical lattices

Thermodynamics of the Potts model with an arbitrary number of states is analyzed for a class of hierarchical lattices of fractal dimension d > 1. In contrast to the case of crystal lattice, it is shown that all phase transitions on lattices of this type are of the second order. Critical exponents are determined, their dependence on structural parameters is examined, and scaling relations between them are established. A structural criterion for change in transition order is discussed for inhomogeneous systems. Application of the results to critical phenomena in phase transitions in dilute crystals and porous media is discussed.     

Modeling the Process of Extracting Valuable Metals from Metal-Containing Materials by the Method of Filtration Combustion

Doklady Physics - An original mathematical model and a numerical method are proposed for describing the filtration combustion of porous metal-containing media taking into account the phase...     

Phase transition in the isotropic <Emphasis Type="Italic">m</Emphasis>-vector model on a random graph

The thermodynamics of a phase transition is investigated within an isotropic m-vector model on a graph with sparse random connections. This model adequately describes superconductivity and superfluidity (m=2), Heisenberg magnets (m=3), and some structural transitions in different systems with macroscopic disorder (gels, composites, and porous media). It is demonstrated that the phase transition is characterized by classical effective-field anomalies. The thermodynamics of the phase transition is also analyzed in terms the proposed model at low temperatures. The dependences of the thermodynamic parameters on the external field, the mean coordination number, and the dimension of the order parameters are determined.     

Etude des transformations liquide ⇄ solide ⇄ solide du chlorure de cesium divise

A study of the phase size effect upon the transition temperatures of cesium chloride has been carried out by thermal analysis and X-ray diffraction of samples obtained by condensation of the compound into porous materials of which the pore radii lie between 3.5 nm and 65 nm. The results show a decrease of the liquid ? solid transformation point with the pore radius for both rising and falling temperatures, while the polymorphic transition temperatures are decreased for cooling and increased for heating. The polymorphic transformation vanishes for CsCl in which the pore radii are smaller than 7.7 nm. The transition temperature variations are explained by homogeneous nucleation theory.     

Anomalous fluid transport in porous media induced by biofilm growth

Magnetic resonance measurements of the transition from normal to anomalous hydrodynamic dispersion in porous media due to biological activity are presented. Fractional advection-diffusion equations are shown to provide models for the measured impact of biofilm growth on porous media transport dynamics.     

Identification of radiative properties of reticulated ceramic porous inert media using ray tracing technique

The radiative properties of reticulated porous inert media are computationally identified using the real three-dimensional structural data of porous media. The computational grids data are reconstructed from three-dimensional computer tomography scans and magnetic resonance image scans of different reticulated porous media. A ray tracing algorithm is used to track the rays inside the grid structure. Statistically large numbers of rays are traced for their path length and incident angle, which are used to find the probability based equivalent extinction coefficient and scattering phase function. The equivalent extinction coefficients are found for porous media with different porosities and pore densities. The dependency of specular and diffuse scattering phase functions on the porous structure and surface reflectance are also studied.     

Investigation of the percolation transition in a nonwetting liquid-nanoporous medium system

The flows of liquid into and out of a nanoporous medium are studied as processes leading to the fluctuation formation and the growth of fractal clusters of filled and empty pores, respectively. The conditions for stable growth of such fluctuations are analyzed as a function of the interfacial energy between the liquid and the porous medium and the surface energy of the liquid. Expressions are obtained for the pressure at which the barrier for fluctuation filling and emptying of the pores vanishes. In general, it is shown for porous media with a pore-size distribution that these processes can be interpreted as a percolation phase transition. The volume and susceptibility of a liquid-porous medium system near the transition points with inflow and outflow of the liquid are calculated. The phenomenon of nonoutflow of a nonwetting liquid from a porous medium and hysteresis of the flow of liquid into and out of a porous medium are explained on the basis of the mechanism considered. The results of an experimental investigation of these processes in the system liquid Wood’s alloy-silochrome 80 and silochrome 120 are presented. The experimental data obtained can be described on the basis of the proposed mechanism.     

Modeling of heterogeneous combustion in porous media under free convection

A mathematical model and a numerical method, based on the combination of explicit and implicit finite difference schemes, have been developed for investigating the unsteady gas flows in porous objects with zones of heterogeneous combustion when gas pressure at object boundaries is known. Used approach enables to solve problems of filtration combustion for both forced filtration and free convection, so it can be efficiently applied for modeling the combustion zones in porous media, which may arise from natural or man-caused disasters. One-dimensional unsteady processes of heterogeneous combustion in porous object under free convection have been investigated using numerical experiment. Two regimes of combustion wave propagation have been revealed – wave movement up and down in the object – and it is shown that these regimes are significantly different in degree of burn of solid combustible material, the temperature in the combustion zone and propagation velocity of combustion wave.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Detecting anomalous phase synchronization from time series

Modeling approaches are presented for detecting an anomalous route to phase synchronization from time series of two interacting nonlinear oscillators. The anomalous transition is characterized by an enlargement of the mean frequency difference between the oscillators with an initial increase in the coupling strength. Although such a structure is common in a large class of coupled nonisochronous oscillators, prediction of the anomalous transition is nontrivial for experimental systems, whose dynamical properties are unknown. Two approaches are examined; one is a phase equational modeling of coupled limit cycle oscillators and the other is a nonlinear predictive modeling of coupled chaotic oscillators. Application to prototypical models such as two interacting predator-prey systems in both limit cycle and chaotic regimes demonstrates the capability of detecting the anomalous structure from only a few sets of time series. Experimental data from two coupled Chua circuits shows its applicability to real experimental system.     

Tortuosity for streamlines in porous media

An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assumed that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as: c = 0.32, D T c = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.     

Some illustrative examples of the use of a spectral-element method in ocean acoustics

Some numerical results in the time domain obtained with the spectral-element method are presented in order to illustrate the high potential of this technique for modeling the propagation of acoustic waves in the ocean in complex configurations. A validation for a simple configuration with a known solution is shown, followed by some simulations of the propagation of acoustic waves over different types of ocean bottoms (fluid, elastic, and porous) to emphasize the wide variety of media that can be considered within the framework of this method. Finally, a movie illustrating upslope propagation over a viscoelastic wedge is presented and discussed.     

Effects of quenched disorder in the two-dimensional Potts model: a Monte Carlo study

Motivated by recent experiments on phase behavior of systems confined in porous media, we have studied the effect of randomness on the nature of the phase transition in the two-dimensional Potts model. To model the effects of the porous matrix we introduce a random distribution of couplings P(J(ij))=pdelta(J(ij)-J1)+(1-p)delta(J(ij)-J2) in the q state Potts Hamiltonian. An extensive Monte Carlo study is made on this system for q=5. We studied two different cases of disorder (a) J(1)/J(2)-->infinity and p=0.8 and (b) J(1)/J(2)=10 and p=0.5. We observed, in both cases, that the weak first order transition that appears in the pure case, changes to a second-order transition. A finite size scaling analysis shows that the correlation length exponent nu is close to 1 and the best fit to the dependence of the specific heat on system size is logarithmic. This suggests that both cases belong to the universality class of the Ising model. In contrast, the magnetic exponents point to a different universality class.     

Surface precrystallization of normal C24 alkane in porous glass

The behavior of the enthalpy and specific heat of normal C24 alkane in the bulk and in porous glasses is investigated using an adiabatic scanning microcalorimeter. Enthalpy jumps, which precede a phase transition in the entire volume of the pores, are found in porous glass with characteristic pore size 1000 Å at a transition from the isotropic liquid into the rotator phase RII. The enthalpy jumps are interpreted as a layerwise growth of a crystal phase on the surface of porous glass. It is also found that porous glass substantially changes the phase behavior of alkanes.