Contamination of a porous bed by a moving front with a finite porosity jump

The contamination of an initially porous bed by a moving low-concentrated suspension is studied. In the framework of a hyperbolic model taking into account large variations of porosity, several exact solutions are given to the problem with a finite porosity jump at the leading contamination front in the case of flows with plane and cylindrical waves. The fact that the particle front lags behind the carrier liquid front is explained. It is shown that the finiteness of the porosity jump at the contamination wave front causes the deceleration in the jump motion, which can be used to determine experimentally the governing parameters of the model. It is also shown that some solutions with several jumps may exist.     

Jump Condition for Diffusive and Convective Mass Transfer Between a Porous Medium and a Fluid Involving Adsorption and Chemical Reaction

In this paper, mass transfer at the fluid–porous medium boundaries is studied. The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., ), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.     

Exact Solution for Coupled Reactive Flow and Dissolution with Porosity Changes

We derive exact solution for mineral-dissolution reactive flows in porous media with porosity variations. These conditions are relevant to injection of incompatible liquids into aquifers for disposal or waste storage, rock alteration during well stimulation by acidising or invasion of corrosive, far-from-equilibrium fluids related to ore deposit formation and heap or in situ leaching in mineral processing. Despite the porosity change making the one-dimensional flow equations nonlinear, the problem allows for exact integration, and a novel analytical model is developed. It allows presenting typical curves for breakthrough concentrations and porosity evolution. The exact solution provides a tool for predictive testing of reactive models that account for porosity creation. The analytical model derived exhibits high agreement with laboratory data, which validate the model.     

Porosity variations in saline media caused by temperature gradients coupled to multiphase flow and dissolution/precipitation

We present a theoretical-numerical investigation of porosity variations induced by temperature gradients in unsaturated saline media. It is known that temperature variations cause humidity variations which lead to liquid flow towards and vapour flow away from the hot source. When this phenomenon occurs in saline media, the liquid is salt saturated brine, so that evaporation causes salt precipitation and an ensuing porosity reduction. Condensation of water causes salt dissolution and porosity increase. This process may be important in the case of heat generating waste because it suggests that selfsealing may take place near the waste. On the other hand, salt mass balance will lead to porosity increases in other zones.     

Measurement of Sediment Retention in a Sandy Tidal Flat Based on Pressure Drop Model

Sediment can either play an important role in subsurface environments as a food source for bacteria or deteriorate the subsurface environments by its retention. Thus, understanding sediment retention is useful for designing the management of subsurface environments. The pressure drop model derived from the Kozeny–Carman model is experimentally verified by the seepage flow in sand beds. It was found that the water head in the sand bed under steady-state flow and variations of the water head corresponding to changes in the boundary water head could be reproduced by the pressure drop model. As the porosity of the sand bed is taken into account in the pressure drop model, the sediment retention can be predicted from variations of the porosity. Experimental results showed that the water head in the sand bed varied due to sediment retention. This ensured that variances in the porosity of the sand bed could be predicted, leading to the investigation onto sediment retention. A method based on the pressure drop model is proposed to measure temporal variations of the water head in a sandy tidal flat and river water head. From field experiments, the temporal variations of the water head in the tidal flat could be predicted when the porosity of the tidal flat was used. Conversely, it is expected that sediment retention in the tidal flat can be predicted based on the variations of the porosity, if the water head in the tidal flat is observed temporally.     

环境模拟实验室中近地层风速廓线的形成研究

在环境模拟实验室中利用阻尼网对实验区形成的近地层风速廓线进行了数值模拟和实验研究.阻尼网的布置方案以变孔隙率阻尼网作为指导,选用30目和16目定孔隙率阻尼网4种不同高度的混合式布置方式.数值模拟采用Fluent软件,将结构复杂的阻尼网简化为具有一定厚度的多孔介质模型,湍流模型为标准k-\varepsilon模型.结果表明可将阻尼网作为多孔介质处理,定孔隙率阻尼网的组合可在短实验段内形成所需近地层的风速廓线,模拟值与实验值吻合良好.     

Fast X-ray Micro-Tomography of Multiphase Flow in Berea Sandstone: A Sensitivity Study on Image Processing

Synchrotron-based fast micro-tomography is the method of choice to observe in situ multiphase flow and displacement dynamics on the pore scale. However, the image processing workflow is sensitive to a suite of manually selected parameters which can lead to ambiguous results. In this work, the relationship between porosity and permeability in response to systematically varied gray-scale threshold values was studied for different segmentation approaches on a dataset of Berea sandstone at a voxel length of 3  \(\upmu \) m. For validation of the image processing workflow, porosity, permeability, and capillary pressure were compared to laboratory measurements on a larger-sized core plug of the same material. It was found that for global thresholding, minor variations in the visually permissive range lead to large variations in porosity and even larger variations in permeability. The latter is caused by changes in the pore-scale flow paths. Pore throats were found to be open for flow at large thresholds but closed for smaller thresholds. Watershed-based segmentation was found to be significantly more robust to manually chosen input parameters. Permeability and capillary pressure closely match experimental values; for capillary pressure measurements, the plateau of calculated capillary pressure curves was similar to experimental curves. Modeling on structures segmented with hysteresis thresholding was found to overpredict experimental capillary pressure values, while calculated permeability showed reasonable agreement to experimental data. This demonstrates that a good representation of permeability or capillary pressure alone is not a sufficient quality criterion for appropriate segmentation, but the data should be validated with both parameters. However, porosity is the least reliable quality criterion. In the segmented images, always a lower porosity was found compared to experimental values due to micro-porosity below the imaging resolution. As a result, it is recommended to base the validation of image processing workflows on permeability and capillary pressure and not on porosity. Decane-brine distributions from a multiphase flow experiment were modeled in a thus validated \(\upmu \) -CT pore space using a morphological approach which captures only capillary forces. A good overall correspondence was found when comparing (capillary-controlled) equilibrium fluid distributions before and after pore-scale displacement events.     

Porosity Variations in Saline Media Induced by Temperature Gradients: Experimental Evidences and Modelling

Porosity variations in saline media containing humidity are induced by temperature gradients. A temperature imposed on a porous salt sample prepared with some brine and closed to mass transfer leads to significant variations of porosity in few weeks. Modelling of the experiments permits to understand the processes involved.     

Impact of Non-uniform Properties on Governing Equations for Fluid Flows in Porous Media

The macroscopic governing equations of a compressible multicomponents flow with non-uniform viscosity and with mass withdrawal (due to heterogeneous reactions) in a porous medium are developed. The method of volume averaging was used to transform local (or microscopic) governing equations into averaged (or macroscopic) governing equations. The impacts of compressibility, non-uniform viscosity, and mass withdrawal on the form of the averaged equations and on the value of the macroscopic transport coefficients were investigated. The results showed that the averaged mass conservation equation is significantly affected by mass withdrawal when a specific criterion on the size of the domain is respected. The results also showed that the form of the averaged momentum equations is not affected by mass withdrawal, by compressibility effects or by non-uniform viscosity, provided that the Reynolds number at the pore level is small. Nonetheless, the velocity field is affected by the heterogeneous reaction via the averaged mass conservation equation, and also by viscosity variations due to the presence of the volume-averaged viscosity (which value changes with position) in the averaged momentum equations. A new closure variable definition was proposed to formulate the closure problem, which avoided the need to solve an integro-differential equation in the closure problem. This formulation was used to show that the permeability tensor only depends on the geometry of the porous medium. In other words, that tensor is independent on whether the fluid is compressible/incompressible, has uniform/non-uniform viscosities, and whether mass withdrawal due to heterogeneous reactions is present/absent.     

A numerical study of heat transfer of a porous block with the random porosity model in a channel flow

 In this paper, heat transfer of a hot plate with a porous block in a channel flow is numerically investigated. A porous block is simulated as a fin type heat sink. The random/artificial porosity models are used to generate the distribution of porosity. In fact, the distribution of porosity in porous medium is irregular, thus the random porosity model is more realistic than the constant or variable porosity model to describe the phenomena happening in porous medium. Therefore, the distribution of porosity of porous block obeys the random porosity model, and the factors of mean porosity and standard deviation are taken into consideration. The variations of the porosity and the velocity in porous block are no longer smooth. For obtaining more heat transfer rate, the artificial porosity model is proposed. The heat transfer rates of the several cases derived by the artificial porosity model are better than those of the random porosity model. The thermal performance of porous block is larger than that of solid block as the mean porosity is larger than 0.5. Received on 5 March 2001 / Published online: 29 November 2001     

Comparison between oxide-reduced and water-atomized copper powders used in making sintered wicks of heat pipe

Oxide-reduced copper powder can be produced efficiently at low cost. The volume shrinkage, porosity, maximum pore size, permeability and thermal conductivity of wicks sintered from two oxide-reduced （OR） powders were compared with one from water-atomized （WA） powder. The green specimens were sintered at temperatures from 800 to 1000 ℃ in a tube furnace under a reduction stream of 10% hydrogen and 90% argon. The results show that the property variations of OR - 100 and WA wicks due to porosity changes have a similar tendency and range. Nine hundred degree celsius is a recommended sintering temperature for producing ideal wicks for use in heat pipes. A smaller maximum pore size can be obtained by increasing the green density.2007 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.     

Conditional model for sorption in porous media with fractal properties

In this study, the conditional moment closure approach, which is proven to be very useful for modelling of reactions in turbulent flows, is extended to characterise adsorbing, desorbing or reacting flows in porous media. A complete specification of the porous distance conditioned moment closure model, which is formulated in terms of single-conditioned expectations, is presented. The closure of the model equations is obtained assuming the diffusion approximation for fluxes of the reactive species. The model simulates complex multi-cascade processes of convective and diffusive transport of species between pores in a continuous and consistent manner and is a generalisation of dual (or triple) porosity concept. The model addresses the major difficulty of describing transport, entrapment and sorption processes in porous media with fractal properties, where distant transport occurs in the largest pores or fractures, while the adsorbing or desorbing surface is mainly allocated in small pores. The model is able to simulate various regimes of methane replacement by CO₂ in a coal sample, which makes it useful for optimising the design and parameters of enhanced coal bed methane recovery operations. It is demonstrated that the power-low decrease in downstream methane concentration, which has been observed experimentally, can be accurately reproduced by the model.     

On the closure problem of turbulence model theory

ＯＮＴＨＥＣＬＯＳＵＲＥＰＲＯＢＬＥＭＯＦＴＵＲＢＵＬＥＮＣＥＭＯＤＥＬＴＨＥＯＲＹＴｓａｉＳｈｕ－ｔａｎｇ（蔡树棠）ＬｉｕＹｕ－ｌｕ（刘宇陆）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ;ＳｈａｎｑｈａｉＩｎｓｔｏｆＡｐｐｌ．Ｍａｔｈ．ａｎｄＭｅｃｈ．,...     

A k–$${\varepsilon}$$ turbulence closure model of an isothermal dry granular dense matter

The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k–\({\varepsilon}\) turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model.     

On the theory of elastic shells made from a material with voids

In this paper we present a theory for porous elastic shells using the model of Cosserat surfaces. We employ the Nunziato–Cowin theory of elastic materials with voids and introduce two scalar fields to describe the porosity of the shell: one field characterizes the volume fraction variations along the middle surface, while the other accounts for the changes in volume fraction along the shell thickness. Starting from the basic principles, we first deduce the equations of the nonlinear theory of Cosserat shells with voids. Then, in the context of the linear theory, we prove the uniqueness of solution for the boundary initial value problem. In the case of an isotropic and homogeneous material, we determine the constitutive coefficients for Cosserat shells, by comparison with the results derived from the three-dimensional theory of elastic media with voids. To this aim, we solve two elastostatic problems concerning rectangular plates with voids: the pure bending problem and the extensional deformation under hydrostatic pressure.     

Two-phase flow in heterogeneous porous media: The method of large-scale averaging

The analysis of two-phase flow in porous media begins with the Stokes equations and an appropriate set of boundary conditions. Local volume averaging can then be used to produce the well known extension of Darcy's law for two-phase flow. In addition, a method of closure exists that can be used to predict the individual permeability tensors for each phase. For a heterogeneous porous medium, the local volume average closure problem becomes exceedingly complex and an alternate theoretical resolution of the problem is necessary. This is provided by the method of large-scale averaging which is used to average the Darcy-scale equations over a region that is large compared to the length scale of the heterogeneities. In this paper we present the derivation of the large-scale averaged continuity and momentum equations, and we develop a method of closure that can be used to predict the large-scale permeability tensors and the large-scale capillary pressure. The closure problem is limited by the principle of local mechanical equilibrium. This means that the local fluid distribution is determined by capillary pressure-saturation relations and is not constrained by the solution of an evolutionary transport equation. Special attention is given to the fact that both fluids can be trapped in regions where the saturation is equal to the irreducible saturation, in addition to being trapped in regions where the saturation is greater than the irreducible saturation. Theoretical results are given for stratified porous media and a two-dimensional model for a heterogeneous porous medium.     

Effect of variable porosity on laminar convection in a uniformly heated vertical porous channel

The present investigation is devoted to the study of fully developed mixed convective flow through a vertical porous channel. The lateral variations of porosity and thermal diffusivity in the bed near the wall, are approximated by exponential functions. The correlation between permeability and porosity is brought through Kozney-Carman approximation. The volume averaged one dimensional low speed momentum equation proposed by Vafai is employed for the analysis of the problem. Results are obtained for steady heating of ascending cold fluid and steady cooling of ascending hot fluid. For the above physical situations it is observed that the heat transfer rate, and ratio of friction factor increases with increase in porous parameter, whereas the ratio of mass flow rate decreases with increase in porous parameter. The velocity profiles exhibit hydrodynamic channelling and peak velocity shifts towards the wall for higher values of the porous parameter. For steady heating of ascending could fluid increase in Rayleigh number enhances the heat transfer rate, and mass flow rate, while it reduces the ratio of friction factor. An opposite trend is observed for the case of steady cooling of ascending hot fluid.     

Homogeneous turbulence subjected to rotation-dominated plane distortion

A new configuration of distorted homogeneous turbulence is investigated in the domain of rotation-dominated elliptical flows. The experimental results are compared with exact numerical solutions obtained in Fourier space for the linear part of the problem. The inherently periodic character of the flow results in typical oscillatory variations of the anisotropy and the pressure-strain correlations. A new two-point closure approach of the EDQNM type is proposed for the nonlinear problem; it is based on a representation of the spectral tensor by scalar functions expanded in terms of spherical harmonics.