Gas Transport In Porous Media Research Articles

Numerical investigation of conductance of porous media in high vacuum systems

In high vacuum systems or materials that have fine capillaries, the molecular transport can be characterized as being free-molecular flow regime. In this flow regime intermolecular interactions can be ignored and flow is determined entirely by molecule–surface collisions. The transport of gases and volatile compounds through porous media and filters with variety of geometries is of great interest in various industrial applications. Although the effect of porosity on gas flow in the most of the flow regimes has been explored, but there are a few investigations on gas transport in porous media and filers at free-molecular regime. In this investigation gas transport in porous media with various porosities and geometries is explored. Test Particle Monte-Carlo (TPMC) method is employed. The walls are assumed to be diffusive. The skeletal portion of the porous media (frame) is modelled by solid spheres. The developed numerical scheme is validated with non porous cases. The effect of porosity, sphere sizes of frame, porous geometry, gas type and temperature on the conductance is examined. The simulations are performed for a porous pipe and porous nozzle. Results demonstrate that porosity and filtration highly affects the conductance of pipe and nozzle and causes great pressure drop in high vacuum systems. The increase of sphere sizes at constant porosity causes conductance to grow. The gas type and temperature of gas affects the conductance of pipe and nozzle too.

Modeling of coupled deformation, water flow and gas transport in soil slopes subjected to rain infiltration

Rain infiltration into a soil slope leads to propagation of the wetting front, transport of air in pores and deformation of the soils, in which coupled processes among the solid, liquid and gas phases are typically involved. Most previous studies on the unsaturated flow and its influence on slope stability were based on the single-phase water flow model (i.e., the Richards Equation) or the water-air two-phase flow model. The effects of gas transport and soil deformation on the movement of groundwater and the evolution of slope stability were less examined with a coupled solid-water-air model. In this paper, a numerical model was established based on the principles of the continuum mechanics and the averaging approach of the mixture theory and implemented in an FEM code for analysis of the coupled deformation, water flow and gas transport in porous media. The proposed model and the computer code were validated by the Liakopoulos drainage test over a sand column, and the significant effect of the lateral air boundary condition on the draining process of water was discussed. On this basis, the coupled processes of groundwater flow, gas transport and soil deformation in a homogeneous soil slope under a long heavy rainfall were simulated with the proposed three-phase model, and the numerical results revealed the remarkable delaying effects of gas transport and soil deformation on the propagation of the wetting front and the evolution of the slope stability. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.

Gas Dispersion and Immobile Gas Content in Granular Porous Media

Gas dispersion is an important process often controlling gas transport in porous media. At present, however, relatively little is known about the relationship between gas dispersion and porous media physical properties. In this study, gas dispersion and mobile gas content in porous media were measured as a function of medium average particle diameter, particle size range, and pore gas velocity. A set of natural granular media consisting of sand and gravel with uniform particle size distributions covering average particle diameters from 0.5 to 14 mm was used. Clean sand and gravel were used to obtain media with specific particle size distributions via mechanical sieving. Gas dispersion and mobile gas content were measured by column tracer experiments using atmospheric air and nitrogen as tracer gases. Gas dispersion coefficients, gas dispersivities, and mobile gas contents were determined by fitting the advection-dispersion equation to the measured gas breakthrough curves. The results showed that gas dispersivity decreased with increasing mean particle diameter and increased with increasing particle size range (width of particle size distribution). Thus, the largest dispersivities were observed for media with a small mean particle diameter and a wide particle size distribution. A model concept for predicting gas dispersivity from mean particle diameter and particle size range was proposed. The mobile gas content increased with increasing pore gas velocity but was independent of either particle size range or mean particle diameter.

Modelling mass transport in solid oxide fuel cell anodes: a case for a multidimensional dusty gas-based model

In this work the mass transport phenomena taking place in the fuel channel and the porous electrode of the anode of planar solid oxide fuel cells (SOFCs) are discussed. A comprehensive review of SOFC mass transport models in the literature is given and a new multidimensional, multicomponent, isothermal, dynamic model of the mass transport phenomena taking place in the fuel channel and the porous electrode of the anode of planar SOFCs is presented. The model can be used to predict species composition profiles and is based on the dusty-gas model (DGM) [Mason, E.A., Malinauskas, A.P., 1983. Gas Transport in Porous Media: The Dusty-Gas Model: Elsevier; Jackson, R., 1977. Transport in Porous Catalysts: Elsevier], which is considered to be the most accurate of the existing mass transfer models in porous media [Suwanwarangkul, R., Croiset, E., Fowler, M.W., Douglas, P.L., Entchev, E., Douglas, M.A., 2003. Performance comparison of Fick's, dusty-gas and Stefan–Maxwell models to predict the concentration overpotential of a SOFC anode. Journal of Power Sources 122, 9-18]. Our two-dimensional DGM is validated using experimental data [Yakabe, H., Hishinuma, M., Uratani, M., Matsuzaki, Y., Yasuda, I., 2000. Evaluation and modeling of performance of anode-supported solid oxide fuel cell. Journal of Power Sources 86, 423-431] and it is tested against a two-dimensional Stefan–Maxwell model (SMM) and against one-dimensional models (Fick's model, SMM and DGM) reported in the literature. It is shown that a detailed model is essential for the accurate prediction of concentration overpotentials especially at high fuel utilisation conditions, which are typical operating conditions for fuel cells [Hernández-Pacheco, E., Singh, D., Hutton, P.N., Patel, N., Mann, M.D., 2004. A macro-level model for determining the performance characteristics of solid oxide fuel cells. Journal of Power Sources 138, 174-186].

Effect of transition from slip to free molecular flow on gas transport in porous media

Traditional models, such as the advection-diffusion and the dusty gas models, overlook the contribution of the transition flow regime between the slip and the free molecular flow, on the gas transport in porous media. In this work we demonstrate that, due to the existence of this intermediate regime, the Klinkenberg [Drill. & Prod. Prac. 1941, 200 (1941)] parameter b depends on the pressure. Reported experiments were used to corroborate such an effect and a formulation that extends the Klinkenberg equation—to include the effect of a region at pore scale where both molecule-molecule and molecule-wall interactions are important—was developed. The mathematical form of the extended Klinkenberg equation remains the same, but the slippage Klinkenberg’s parameter b is now a generalized parameter that is a function of Knudsen’s number. It was demonstrated that the widely accepted relation between the parameter b and the Knudsen diffusion coefficient is a good approximation just for Knudsen numbers corresponding to the free molecular flow regime. The model proposed in this paper reproduces the experimental data and predicts practical situations where important errors on total flow rate can be expected if the transition flow regime is neglected in the formalism.

Three dimensional model of oxygen transport in a porous diffuser of a PEM fuel cell

AbstractBinary molecular diffusion and pressure‐driven fluxes of gas in porous media are studied. A 2‐dimensional model of gas transport in porous media is developed in the field of nonzero gradients of pressure and concentration. Spatial distributions of oxygen concentration and fluxes in a porous diffuser are analyzed for geometric and physical parameters of the electrode. A three‐dimensional generalization of the model is performed. Application to oxygen‐flow modeling in electrodes of polymer electrolyte fuel cells (PEFC) is discussed for two simple configurations of gas supply channels: serpentine and interdigitated. Comparison of the results obtained for the two configurations is carried out. Oxygen flux through the catalytic membrane plane is investigated for physical characteristics of gases and the diffuser, geometry of the gas supply channels, and gas pressure in them. Recommendations for an optimal pressure regime for the specific geometry of the system and its physical characteristics are given.

New equations for binary gas transport in porous media,: Part 1: equation development

A rigorous understanding of the mass and momentum conservation equations for gas transport in porous media is vital for many environmental and industrial applications. We utilize the method of volume averaging to derive Darcy-scale, closure-level coupled equations for mass and momentum conservation. The up-scaled expressions for both the gas-phase advective velocity and the mass transport contain novel terms which may be significant under flow regimes of environmental significance. New terms in the velocity expression arise from the inclusion of a slip boundary condition and closure-level coupling to the mass transport equation. A new term in the mass conservation equation, due to the closure-level coupling, may significantly affect advective transport. Order of magnitude estimates based on the closure equations indicate that one or more of these new terms will be significant in many cases of gas flow in porous media.

New equations for binary gas transport in porous media, Part 2: experimental validation

A previous study [Water Resour Res 39 (3) (2003) doi:10.1029/2002WR001338] questioned the validity of the traditional advection–dispersion equation for describing gas flow in porous media. In an original mathematical derivation presented in Part 1 [Adv Water Resour, this issue] we have demonstrated the theoretical existence of two novel physical phenomena which govern the macroscopic transport of gases in porous media. In this work we utilize laboratory experiments and numerical modeling in order to ascertain the importance of these novel theoretical terms. Numerical modeling results indicate that the newly derived sorptive velocity, arising from closure level coupling effects, does not contribute noticeably to the overall flux, under the conditions explored in this work. We demonstrate that the newly discovered “slip coupling” phenomenon in the mass conservation equation plays an important role in describing the physics of gas flow through porous solids for flow regimes of both environmental and industrial interest.

Gas transport in porous media under dynamic conditions

The dynamic version of the Wicke-Kallenbach diffusion cell with one compartment closed and equipped with a sensitive pressure gauge was used for determination of sets of Mean Transport Pore Model and Dusty Gas Model parameters for an industrial catalyst (ICI 52-1 in reduced form). The dynamic pressure responses due to gas composition step changes of inert gases (H 2, He, N 2, Ar) were measured and fitted to the system of partial differential equations which describe the transport (mass balances with Maxwell-Stefan constitutive equations). The optimum textural parameters were obtained by simultaneous matching of all experiments. The model parameters are material constants of the porous solid and, thus, do not depend on temperature, pressure and kind of the transported gases. Both diffusion models gave a good agreement between experiments and calculations. The parameter reliability is discussed.

Retardation of Dissolved Oxygen Due to a Trapped Gas Phase in Porous Media

AbstractInformation on the transport of dissolved gases in ground water is needed to design ways to increase dissolved gas concentrations in ground water for use in in situ bioremediation (e.g., O2 and CH4) and to determine if dissolved gases are conservative tracers of ground‐water flow (e.g., He). A theoretical model was developed to describe the effect of small quantities of trapped gas bubbles on the transport of dissolved gases in otherwise saturated porous media. Dissolved gas transport in porous media can be retarded by gas partitioning between the mobile aqueous phase and a stationary trapped gas phase. The model assumes equilibrium partitioning where the retardation factor is defined as R = 1 + H′(Vg/Vw) where H' is the dimensionless Henry's Law constant for the dissolved gas, and Vg and Vw are the volumes of the trapped gas and water phases, respectively. At 15°C and with Vg/ Vw= 0.05, the predicted retardation factors for He, O2, and CH4 are 5.8, 2.4, and 2.3, respectively. The validity of the model was tested for dissolved oxygen in small‐scale column experiments over a range of trapped gas volumes. Retardation factors of dissolved oxygen increased from 1 to 6.6 as Vg/Vw increased from 0 to 0.123 and are in general agreement with model predictions except for the larger values of Vg/Vw. The theoretical and experimental results suggest that gas partitioning between the aqueous phase and a trapped gas phase can greatly influence rates of dissolved gas transport in ground water.

Gas transport in unsaturated zones: Multicomponent systems and the adequacy of Fick's laws

A complete understanding of multicomponent gas transport in porous media (unsaturated zones) requires a knowledge of Knudsen transport, the molecular and nonequimolar components of diffusive flux, and viscous (pressure‐driven) flux. The constitutive equations relating these flux components are available from the “dusty gas” model of Mason et al. (1967). This paper presents a brief discussion of the principles underlying each of the above flux mechanisms, illustrated with binary systems, and then casts the constitutive equations in forms thought to be most useful for the study of natural unsaturated zones. A derivation is presented showing that the constitutive equations maintain the same form when expressed in terms of the potentiometric head of a gas column in a gravitational field, a conclusion of considerable practical importance for the study of natural systems. Very small pressure gradients (1 Pa/m or less) can produce viscous fluxes greater than or equal to diffusive fluxes; conversely, pressure gradients of this magnitude can be generated by diffusive processes. The viscous and diffusive fluxes are coupled in the constitutive equations through the Knudsen diffusivities; a knowledge of Knudsen diffusivities is necessary to calculate the viscous component of flux and pressure gradients. Equations are derived allowing calculation of Knudsen diffusivities from measurements of the Klinkenberg effect. The accuracy of Fick's first law (and by inference, Fick's second law) is shown to depend primarily on the relative magnitudes of the viscous and diffusive flux components. Methods are presented for approximating these flux components, in order to determine whether the multicomponent equations are needed for a given problem. These estimates depend on a knowledge of concentration profiles of stagnant (zero flux) gases. To a first approximation, Ar and N2 are considered to be stagnant gases in subsoil environments. Fick's law(s) are, essentially by definition, inadequate to deal with stagnant gases. In the examples presented, the error associated with estimating total fluxes of nonstagnant gases by Fick's law ranges from a few percent to orders of magnitude. Other conclusions are as follows: (1) major gas concentration gradients can be produced solely by transport phenomena; (2) any study of natural systems that requires a knowledge of N2 (or Ar) fluxes, as opposed to assuming them to be stagnant, must be based on a multicomponent analysis; (3) any study of systems in which a nonatmospheric gas constitutes a significant fraction of the gases present must be based on multicomponent analysis; (4) concentration profiles of stagnant gases can be used to determine the direction, and semiquantitatively the magnitude, of the net gas flux into or out of unsaturated zones; (5) with permeability equal to 10−12 m2, for pressure gradients greater than 10 N m−3 viscous fluxes predominate, the Stefan‐Maxwell equations become inapplicable, and the general equations must be used; (6) the net gas flux may be dominated by viscous effects even when individual gas fluxes are primarily diffusive; and (7) the measurement of pressure differentials necessary for a definitive check on the validity of these models in most natural systems is at (or beyond) the limits of present technology.

Gas transport in unsaturated porous media: The adequacy of Fick's law

The increasing use of natural unsaturated zones as repositories for landfills and disposal sites for hazardous wastes (chemical and radioactive) requires a greater understanding of transport processes in the unsaturated zone. For volatile constituents an important potential transport mechanism is gaseous diffusion. Diffusion, however, cannot be treated as an independent isolated transport mechanism. A complete understanding of multicomponent gas transport in porous media (unsaturated zones) requires a knowledge of Knudsen transport, the molecular and nonequimolar components of diffusive flux, and viscous (pressure driven) flux. The constitutive equations relating these flux components are available from the “dusty gas” model of Mason et al. (1967). This review presents a brief discussion of the underlying principles and interrelationships among each of the above flux mechanisms. Some aspects of these transport mechanisms are, to our knowledge, generally unrecognized in the Earth science literature. The principles underlying the transport mechanisms are illustrated with binary systems; the constitutive equations are then cast in forms thought to be most useful for the study of natural unsaturated zones. The viscous and diffusive fluxes are coupled in the constitutive equations through the Knudsen diffusivities; a knowledge of Knudsen diffusivities is necessary to calculate the viscous component of flux and pressure gradients. The Knudsen diffusivities can be calculated from measurements of the Klinkenberg effect. Two examples are presented showing that in natural systems, very small pressure gradients (1 Pa/m or less) can produce viscous fluxes greater than or equal to diffusive fluxes and that, conversely, pressure gradients of this magnitude can be generated by diffusive processes. The example calculations show that major concentration gradients can be developed for stagnant (zero flux, nonreactive) gases. A method is presented for approximating the viscous and diffusive flux components of gases in a multicomponent system from a knowledge of the concentration profiles of stagnant gases. In subsoil environments, argon and nitrogen are considered to be stagnant gases. Fick's laws are essentially, by definition, inadequate to deal with stagnant gases. In the examples presented, the error associated with estimating the total fluxes of nonstagnant gases by Fick's law, relative to stationary coordinates, ranges from a few percent to orders of magnitude.

Gaseous diffusion equations for porous materials

Commonly used equations of gaseous transport by diffusion are examined and the two parameters required for each equation are tabulated from the literature. The advantages and limitations of the commonly used linear — D/ D o = a( S− b) — and curvilinear — D/ D o = KS m — equations are considered and a new diffusion equation is proposed to combine the advantages of the previous equations. This new equation, like the others, requires only two parameters. It takes the form D/ D o = [( S− u)/(1− u)] v and may serve as a basis for studying and more accurately modeling gas transport in porous media.

Anomalous transport phenomena in semihydrophobic fuel cell electrodes

The so-called bubbling and weeping effects observed with porous semihydrophobic fuel cell electrodes are discussed in terms of gas transport in porous media. It is shown that the bubbling of gas on the electrolyte side can be accounted for by transport equations valid in the intermediate region between ordinary and Knudsen diffusion. The anomalous transport of liquid toward the gas side is attributed to isothermal distillation proceeding in the electrode pores. A gradient of the partial pressure of water vapour in the pores is the principal cause for both effects.

Flow and Diffusion of Gases in Porous Media

A generalized treatment of gas transport in porous media is presented as developed on the basis of the ``dusty-gas'' model, a model in which a porous medium is described as consisting of uniformly distributed, giant molecules (dust) held stationary in space. The problem is broken down into a series of special cases which involve the various combinations of gradients in composition, pressure, and temperature. Equations are given for the description of several well-known phenomena. These include isobaric, isothermal diffusion; diffusion under the influence of a pressure gradient; Poiseuille's flow equation, including the Knudsen minimum; the Kramers—Kistemaker effect; thermal transpiration; and the effect of pressure on the thermal-diffusion factor. The results are likewise applicable to capillaries by a suitable substitution for geometric parameters.