Nonlinear, multicomponent, mass transport in porous media

In this paper we consider multicomponent mass transport in porous media for non-dilute solutions. This process is described by coupled, nonlinear transport equations that must be spatially smoothed in order to be useful. This spatial smoothing, or upscaling, is achieved by the method of volume averaging for the case of negligible adsorption, desorption, and heterogeneous reaction. For pure diffusion, the results demonstrate that a single tortuosity tensor applies to the transport of all species. When convective transport is important, the process becomes much more complex and it is difficult to generalize about the behavior of the various dispersion tensors.     

A synchronous cellular automaton model of mass transport in porous media

In this work we present a fully synchronous coarse grained cellular automaton model for large-scale simulations at molecular level. The model is based on Margolus partitioning scheme, which was generalized as to describe quantitatively diffusion, adsorption and directed flow in porous media. Our aim is to create conceptually simple and computationally efficient framework to model the mass transport in porous materials with large representative volume. This work focuses on the fundamental aspects of the generalized Margolus cellular automaton. We exemplify the model by solving several diffusion problems, studying the monolayer adsorption, chromatography on disordered porous structures and chemical transformation in a system with phase separation. The results indicate that the model reflects the essential features of these phenomena. Absence of round-off errors, fully synchronous way of implementation, autonomous physically meaningful time scale and ease-to-handle boundary conditions make this model a promising framework for study various transport phenomena in porous structures.     

Multiphase mass transport with partitioning and inter-phase transport in porous media

We derive the effective mass-transfer coefficient between two fluid phases in a porous medium, one of which is flowing and the other is immobile. A passive tracer is advected by the flowing phase, becomes partitioned at the fluid-fluid interface and diffuses in the immobile phase. We use traditional volume-averaging methods to obtain a unit-cell boundary-value problem for the calculation of the effective mass-transfer coefficient. The problem is controlled by the Peclet number of the flowing phase, by a second dimensionless parameter that captures diffusion and partition in the two phases and by the geometrical properties of the porous medium.We derive asymptotic results for the scaling of the mass-transfer coefficient under various limiting conditions. Then, we use numerical methods that solve for the flow velocity field under Stokes flow conditions, and for the transport problem. The numerical results verify the asymptotic scaling expressions and provide estimates of the coefficient for a number of special cases. In particular, we find that when the immobile phase is wetting the solid (in the form of films), the mass transfer coefficient is larger than in the non-wetting case (where the phase is distributed in the form of blobs). Shape factors for practical applications are also obtained.     

Non-Newtonian flow in porous media

In this article we present a review of the single-phase flow of non-Newtonian fluids in porous media. The four main approaches for describing the flow through porous media in general are examined and assessed in this context. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.     

Experimental study and mathematical model of nanoparticle transport in porous media

Two types of polysilicon nanoparticles (PN) were used in oil fields to improve oil recovery and enhance water injection respectively in this work. The physical properties of the nanoparticles were studied experimentally, and pore characteristics of sandstone were investigated by mercury injection experiments. The adsorption experiments of lipophobic and hydrophilic polysilicon nanoparticles (LHPN) were conducted to testify wettability change (from oil wetting to water wetting) of sandstone surface, and the nanoparticles attached to pore walls were observed by a transmission electron microscope (TEM). A mathematical model to describe the nanoparticles transport carried by two-phase flow in random porous media was presented and a numerical simulator was developed to simulate two application examples of the nanoparticles in oilfields. An important discovery is that water-phase permeabilities of these sandstones increase from 1.6 to 2.1 times of their original values. However, there are decreases in their absolute permeabilities because of nanoparticle adsorption on pore surfaces and nanoparticle capture at pore throats. The important parameters such as the distributions of porosities and permeabilities, the changes in water injection capability and oil recovery are obtained successfully by numerical simulation approach. Furthermore, the permeabilities obtained from numerical simulation have a good match with experimental data. The conclusion that polysilicon nanoparticles are effective agents for enhancing water injection capability or improving oil recovery can be safely drawn.     

近冰点多孔介质中甲烷水合物生成的温度敏感性

水合物技术是实现天然气储存、气体分离、海水淡化和二氧化碳捕集等的潜在可行途径之一,水合物技术为了降低生产成本同时又保持系统流动性,通常选择冰粉或冰浆等形式使生成反应在冰点附近进行;自然界的天然气水合物多数赋存于天然的多孔介质内,随着全球气温升高,甲烷水合物在临界条件附近的敏感性会导致储层的稳定性下降及潜在的甲烷大量释放,尤其是受气候变化影响较大的冻土带天然气水合物,其储层温度一般也处于冰点附近。本工作研究了硅砂(0.1~0.5 mm)中甲烷水合物在近冰点的形成过程与动力学特征,分别在273.75, 273.85和273.95 K小温差下研究了压力、温度、反应速率和甲烷吸收量变化,分析并计算了硅砂孔隙中水合物、水相和气相的最终体积饱和度。温度与反应速率的变化表明,水合物生成过程呈现出明显的三个阶段,在不同的阶段,温度和反应速率表现出独特的变化特征如峰值、持续时间等,同时对环境温度的敏感性非常强,温度升高后甲烷水合物生长速率及其在孔隙中的饱和度均有所降低,低温下水合物生长点晚及对应诱导期持续更长。     

Transport and retention of polymer-stabilized zero-valent iron nanoparticles in saturated porous media: Effects of initial particle concentration and ionic strength

This study investigated the transport and retention of polyacrylic acid and polyvinylpyrrolidone stabilized zero-valent iron nanoparticles (PAA-ZVIN and PVP-ZVIN) in saturated porous media. The transport experiments were conducted in sand packed columns. The breakthrough curves (BTCs) and retention curves of ZVIN were analyzed. Results of transport experiments showed that increasing initial particle concentration and ionic strength led to a decrease in ZVIN transport. The zeta potentials and hydrodynamic diameters of PAA-ZVIN were apparently more negative compared to PVP-ZVIN. Results indicated that some mechanisms such as aggregation, ripening, and surface roughness had considerable impact on ZVIN retention in porous media.     

A two-scale modeling of motion-induced fluid release from thin fibrous porous media

In this work, a two-scale two-phase modeling methodology is presented for studying fluid release from saturated/unsaturated thin fibrous media when brought in contact with a moving solid surface. Our macroscale model is based on the Richards’ equation for two-phase fluid transport in porous media. The required constitutive relationships, capillary pressure and relative permeability as functions of medium's saturation, are obtained through microscale modeling. At microscales, a 3-D model based on fiber diameter, fiber orientation, and medium's solid volume fraction (SVF), is generated to resemble the internal structure of the fibrous sheets and be used in full-morphology analysis as well as microscale permeability simulation. A mass convection boundary condition is considered here to model the fluid transport at the boundary in contact with the target surface. It was shown that the mass convection coefficient, k_f, plays a significant role in determining the release rate and is expected to be in the range of 10^-6<k_f<10^-9, depending on the properties of the fluid, fibrous sheet, the target surface as well as the speed of the relative motion, and remains to be determined experimentally.     

A research into thermal field in fluid-saturated porous media

Until now, the theory, methodology of investigations, and interpretation of thermometry data have been most completely developed for single-phase (oil, water, or gas) flows in formations. However, multiphase (oil+gas, oil+water, and oil+water+gas) flows in formations are more common in practice. This is primarily typical for fields featuring a high value of gas factor and saturation pressure, as well as for cases of formation tests at low values of bottom-hole pressure. Analysis of actual thermograms under these conditions has shown that the earlier-developed techniques for the cases of single-phase flows in the formation and the well cannot be applied here.This paper presents research data on the influence of the adiabatic and Joule-Thomson effects and the heat of fluid degassing on temperature field in porous medium.     

Simulating oil flow in porous media under asphaltene deposition

A simulator for one-phase flow in porous media near a wellbore is coupled with a thermodynamic model and a network model in order to predict the change in petroleum flow under asphaltene deposition. The thermodynamic model is capable of predicting the quantity of precipitated asphaltene. The network model is used to predict formation damage due to in situ asphaltene deposition. The model is qualitatively evaluated using data from literature. Results are in concordance with expected physical behavior.     

The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures

Tracer diffusion simulations within random porous structures show that tortuosity factors are independent of diffusion mechanism for all practical void fractions when an equivalent Knudsen diffusivity is correctly defined. Previous studies concluded that tortuosity factors, a geometric property of the void space as defined, increase with increasing Knudsen number, K_n, a measure of the relative number of molecule-surface and intermolecular collisions. The model porous structures in this study consist of random-loose packings of spheres overlapped to achieve a given void fraction and to accurately reflect the void space in practical porous solids. Effective diffusivities were estimated using tracer or flux-based Monte Carlo methods for Knudsen numbers of 10⁻³-10¹⁰; the two methods lead to similar diffusivities for void fractions of 0.06-0.42. Tortuosity factors estimated using the number-averaged distance between collisions, 〈l_p〉, for the characteristic void length scale increased with increasing Knudsen number, even though simulations in infinite cylinders confirmed the accuracy of the Bosanquet equation for all values of K_n. These unexpected changes in a geometric property of the void space become most apparent near the percolation void fraction (∼0.04). For example, the Knudsen tortuosity factor defined in this manner is 1.8 times larger than in the bulk regime for a solid with 0.10 void fraction. Even at high void fractions (∼0.42), the two extreme values of tortuosity factor differ by a factor of ∼1.4. These apparent effects of diffusion mechanism on tortuosities reflect the inaccurate use of number-averaged chord lengths when tracer reflections from random obstacles obey the Knudsen cosine law for diffuse reflection. A corrected length scale, first proposed by Derjaguin, leads to tortuosity factors independent of K_n for void fractions above 0.20; tortuosities differ by only 18% and 4% between Knudsen and bulk regimes even for void fractions of 0.10 and 0.15, respectively. The residual differences at void fractions below 0.10 arise from the increasingly serial nature of the remaining voids. Thus, a long-standing inconsistency between the defined geometric nature of tortuosity factors and their inexplicable dependence on diffusion mechanism is essentially resolved. In practice, these simulations allow the consistent and accurate use of tortuosity factors determined at any value of K_n for all diffusion regimes; they also prescribe, rigorously for void fractions above 0.15 and empirically for lower void fractions, the length scale relevant to diffusion in the Knudsen and transition diffusion regimes.     

On the constancy of the free energy reduction caused by imbibition in porous media

The presents study brings to light that the free energy reduction per surface unit, Δg, which is considered as the driven force that leads the imbibition of liquids into porous media, does not show any dynamic behaviour during the rise of the liquids. Therefore, this quantity is a constant parameter that characterized the capillary rise processes. As a consequence, it has been also proved that, because of this fact, the liquid flow verifies the hypotheses that are needed in order to the results of the imbibition experiments can be analysed by Washburn's equation. This study has been carried out by means of a new methodology based on the analysis of the velocity profile associated to the increase in the weight of the porous medium caused by the rise of the liquid.     

Aerodynamic behavior of a gas mask canister containing two porous media

This paper discusses the aerodynamic behaviors of a gas mask canister with a complex inner structure and two porous materials in the filter layer and the activated carbon layer. The effects of the distribution and area of holes in the main sieve diaphragm and the thickness of the activated carbon layer on the pressure drop and the flow structure were determined using computational fluid dynamic (CFD) tools. The momentum loss of porous flow calculated by Forchheimer's equation was added to the source term in the momentum equation. Streakline flow visualization was employed to observe gas flow structures within the empty canister and to identify the shortcomings of the prototype canister. Simulation results for the estimated inertial and viscosity parameters in Forchheimer's equation agree closely with experimental values. The porosity of the canister for intake flows of 15-135 L/min causes the flow behavior to transition gradually from linear (viscous effect) to slight non-linear behavior (slight inertia effect). This study uses air age as an index of the time that air resides within the canister to displace the adsorption time of toxic gas. This approach conveniently elucidates overall filter capacity and the positions of dead zones in the activated carbon layer. The simulation results reveal that the channel design of the main sieve diaphragm dominates the aerodynamic behavior of the fluid within the activated carbon layer. Better hole distribution and a larger hole area correspond to a lower pressure drop, a smaller dead zone, and a higher adsorption time. The results in this study provide a valuable reference for designing channels in the main sieve diaphragm, and will be helpful in designing gas mask canisters.     

Novel NMR techniques for porous media research

Recent years have seen a significant progress in the study of porous media of natural and industrial sources. This paper provides a brief outline of the recent technical development of NMR in this area. These progresses are relevant for NMR applications in material characterization.     

Supercritical fluid flow in porous media: modeling and simulation

The present work aims the modeling and simulation of supercritical fluid flow through porous media. This type of flow appears in several situations of interest in applied science and engineering, as the supercritical flow in porous materials employed in chromatography, supercritical extraction and petroleum reservoirs. The fluid is constituted of one pure substance, the flow is monophasic, highly compressible and isothermal. The porous media is isotropic, possibly heterogeneous, with rectangular format and the flow is two-dimensional. The heterogeneities of porous media are modeled by a simple power law, which describes the relationship between permeability and porosity. The modeling of the hydrodynamic phenomena incorporates the Darcy's law and the equation of mass conservation. Appropriated correlations are used to model, in a realistic form, the density and the viscosity of the fluid. A conservative finite-difference scheme is used in the discretization of the differential equations. The nonlinearity is treated by Newton method, together with the conjugate gradient method. The results of the simulation for pressure and mobility of supercritical and liquid propane flowing through porous media are presented, analyzed and graphically depicted.     

Particulate clusters and permeability in porous media

The permeability of particulate colloidal titanium dioxide, P25, was investigated during sedimentation, permeation and filtration when suspended in water at a consistent ionic strength similar to tap water. Happel's cell model of permeability was used to determine the apparent particle size during these processes, and compared with the size of particle clusters measured using laser diffraction under identical ionic conditions and varying degree of shear. The primary particle size of the P25 was determined to be 28 nm, from consideration of the surface area and density of the particles, and the cluster size during permeation and filtration was close to 100 nm. During sedimentation the cluster size was determined to be close to 10 μm, which is the same size obtained by laser diffraction when measuring under conditions of low shear. Using the above two sizes (28 nm and 10 μm) as limits in Happel's permeability model it was possible to determine an ‘operating envelope’ of permeability that matched the experimentally measured values for the sedimentation, permeation and filtration processes.     

Comparison of Wicke-Kallenbach and Graham's diffusion cells for obtaining transport characteristics of porous solids

Counter-current gas diffusion measurements on a series of porous solids covering a broad range of pore sizes (mean pore radii between 78 nm and ) were performed in the Wicke-Kallenbach and Graham's diffusion cells. Mutual agreement of diffusion fluxes from both cells was found in the whole range of tested pore radii and inert gas systems. For pore materials with mean pore radii exceeding the experimentally unavoidable tiny total pressure gradient induces additional permeation flow which precludes the use of Graham's law for evaluation of transport parameters of the porous solids. Transport parameters together with 95% confidence regions were determined for porous materials with pore radii up to and the prevailing diffusion mechanism, intimately connected with the shape of confidence regions, was estimated.