Wall to liquid mass transport and diffusion controlled corrosion in fixed bed reactors

The diffusion controlled corrosion at the inner wall of a fixed bed reactor was studied in terms of the wall to liquid mass transfer coefficient. Variables studied are solution flow rate, physical properties, and packing size and geometry. The effect of drag reducing polymers on the rate of mass transfer and on the rate of corrosion was studied. The presence of the drag reducing polymer decreased the rate of both mass transfer and corrosion by a factor ranging from 8.92% to 39.47%. All variables were correlated by dimensionless equations. Possible applications of these data in heat transfer were highlighted.     

Modelling of mass transfer in combination with radical reactions

The diffusion-reaction equations for different model versions have been solved using a finite-differencing technique. In all models a reactant A is transferred from the gas to the liquid phase and reacts in the liquid with B to form P. The calculations comprised a simple stoichiometric model, a system with radical intermediates involved in the propagation steps and a version where also the termination reactions were included. The results show that the diffusion coefficients of radical intermediates can have significant influence on the profiles of concentrations and reaction rates near the G/L interface. Furthermore, it is shown that for very fast reactions differences in diffusion coefficients of the intermediates influence the by-product formation. For systems of two radical intermediates, the so-called mixed termination product is only formed in low quantities whereas the other two termination products dominate. The calculation of enhancement factors required in the design of a G/L reaction system can be performed with simplified models where the reactive intermediates do not occur in the expressions for the reaction rates. The optimum model for a specific design purpose can be found by tuning the functions that correlate the parameters of the complex model to the parameters of the simplified model. In principle it is possible to very easily evaluate a large number of alternatives.     

Transport of oxygen, sodium chloride, and sodium nitrate in biofilms

Diffusion coefficients of sodium chloride, sodium nitrate and oxygen were determined for heterotrophic biofilms. The biofilms were cultivated under different hydrodynamic and substrate loading conditions in tubular reactors resulting in biofilm densities between 3 and dry mass. Quantifying solute diffusion in the biofilm for these biofilms allowed to specifically evaluate the influence of biofilm density on diffusion while keeping other factors such as the type of substrate, the inoculum, and the reactor type constant. Two methods were used to measure diffusion coefficients. The two-chamber method was used to quantify the diffusion of sodium chloride and sodium nitrate. The diffusion coefficients for oxygen were measured based on oxygen concentration profiles in the biofilm measured using microelectrodes. The ratio between the diffusion coefficient in biofilm and water (f_D=D_F/D_W) was found to be lower than 1 in the majority of experiments. A clear correlation between f_D and biofilm density was found where f_D decreased with increasing biofilm density. For mean biofilm densities in the range of 10- can be approximated between 0.5 and 1. For larger densities of 20 or can be approximated as 0.8 or 0.4, respectively. For densities higher than is below 0.6. Advective transport mechanisms that would have resulted in f_D>1 can be neglected in the biofilms cultivated.     

Transport of hydrophobic pollutants through biofilms in biofilters

Treatment of air pollutants in a biofilter requires that the compound be effectively transported from the gas phase to the organisms that reside in a biofilm that forms upon a packing material. It has been suggested that biofilms have different transport properties than water making hydrophobic pollutants have higher removal rates than predicted based on water's transport properties. The objectives of this study were to experimentally determine partition and diffusion coefficients of a model hydrophobic compound (α-pinene) through natural and artificial biofilms and to relate these to biofilm characteristics such as solids content and the substrate (VOC) being consumed during biofilm generation. This was done by setting up bench-scale biofilters to generate biofilm to use in partitioning and transport experiments. Batch partitioning experiments were conducted that indicated that α-pinene has a higher degree of partitioning into biofilm than into water due to the presence of solids (two orders of magnitude). A diffusion cell has also been designed and built to study the partitioning from air and diffusion of α-pinene through various artificial biofilms. The average diffusion coefficient of α-pinene through agar, which has the same partitioning properties as water, was found to be (S.D.: ). Diffusion cell experiments performed with α-pinene using inactivated biofilm, previously grown on methanol and α-pinene, immobilized in agar indicate that initially sorption takes place within the film but after this initial lag phase, the transport rate is not significantly different from agar indicating the ratio of the diffusion and partition coefficient of the mobile phase is the same. Therefore, at steady state we expect the transport rates of hydrophobic pollutants through biofilms to be the same as through water.     

Modeling of mass transfer and thermal cracking during the coking of Athabasca residues

The kinetics of thermal cracking of films of vacuum residue from Athabasca bitumen in the temperature range of was modelled with liquid-phase mass transfer, reaction-dependent fluid properties, and coke formation by reaction of cracked products in the liquid phase. Previous investigations on the thermal cracking of vacuum residue in thin films showed that at low film thickness the coke yield was insensitive to the temperature and heating rate for thin films of bitumen. The coke yield increased with the thickness of the initial film, in the range from 20 to . At the same time, the viscosity of the reacting liquid increased rapidly with time, which would slow down the diffusion of products inside the film. This coupling of transport and reaction would enhance the formation of coke by increasing the rate of recombination reactions. The concept of intrinsic coke is used in a new kinetic model to account for the minimum observed coke formation in thin films. With increasing film thickness, the increasing yield of extrinsic coke is modelled through the change in fluid properties as a function of extent of reaction, which reduces the rate of diffusion in the reacting liquid phase. The model was able to properly account for the insensitivity of coke yield in thin films to reaction temperature and the dependence of coke yield on the thickness of the liquid film.     

Well-developed mass transfer in axial flows through randomly packed fiber bundles with constant wall flux

An analysis of the effects of fiber packing on mass transfer coefficients for axial fluid flow through fiber bundles with uniform wall flux in the well-developed limit is presented. The finite element method is used to solve the governing momentum and conservation of mass equations. The effective mass transfer coefficient depends strongly on fiber packing. Randomly packed fiber bundles have much lower mass transfer coefficients than regularly packed fiber bundles. Mass transfer rates are controlled by the lowest fiber packing regions through which most of the flow occurs.     

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.     

A theoretical and experimental study of simultaneous heat and mass transport resistances in a shallow fluidized bed dryer of mate leaves

A theoretical and a semi-theoretical modeling approach were applied in order to predict drying kinetics of mate leaves in a shallow fluidized bed dryer. The first procedure involves an internal diffusive mechanism of mass transport (Fick's second law), while the second one assumes that the resistance for water transport is represented by an apparent convective term analogous to the Newton's law of cooling (Lewis model). Since heat and mass transfer occurs at the same time, an energy equation assuming negligible internal conduction was written to the solid phase and it was coupled to the mass balance representing the mechanism of mass transfer. Model parameters were simultaneously tuned on experimental transient moisture content and on temperature profiles of mate leaves, which were obtained by varying the equivalent particle diameter approximately from 5.2 × 10⁻³ to 1.1 × 10⁻² m at the drying temperatures of 52 and 101 °C. A regression analysis based on the uncertainties in the calculated parameters as well as on the identification of possible tendencies in residuals corroborates the assumption of negligible internal heat transfer conduction and evidences that the semi-theoretical model of Lewis describes better than the purely diffusive model the transport of water over the whole period of drying. The estimated Biot number (0 < Bi < 100) reveals that both internal and external mass transport resistances play an important role for mate leaves drying and demonstrates that the single parameter of the Lewis model represents an effective coefficient that takes into accounts both diffusion and convection. A significant effect of the equivalent particle diameter and temperature on the drying constant and on the external heat transfer coefficient is also evidenced.     

Modeling and analysis of hydrogen permeation in mixed proton-electronic conductors

A rigorous model for hydrogen permeation through dense mixed conductors was derived using the formalism of non-equilibrium thermodynamics for various operating modes and process conditions. The concentrations of charge carriers were rigorously included in this model through defect equilibria with the chemical environment at each membrane surface and through balance equations and a virtual pressure formalism within the membrane. Hydrogen permeation rates through proton-electron-hole mixed conductors were simulated using this framework under open-circuit, short-circuited, and applied potential operating modes. The sensitivity of H₂ permeation rates to the reduction-oxidation potentials at each side of the membrane and to the membrane properties (e.g. electron/hole diffusivity, oxygen binding energy) was examined in terms of the mobility and concentration of each charge carrier in order to identify rate-limiting steps for H₂ transport. These simulations showed that electronic transport controls H₂ permeation rates in proton-electron-hole mixed conductors typically used for H₂ permeation, especially when hydrogen chemical potentials are significantly different in the two sides of the membrane. These electronic conduction limitations arise from a region of very low electronic conductivity within the membrane, caused by a shift in the predominant charge carriers from electron to holes with decreasing hydrogen chemical potential. Under these asymmetrical conditions, H₂ permeation rates increase more markedly when an external electron-conducting path is introduced than at lower chemical potential gradients. Such interplay between rate-controlling variables leads to complex effects of H₂ chemical potential gradients on permeation rates. The effects of intrinsic membrane properties on H₂ permeation were examined by systematic changes in the defect equilibrium constants. A decrease in oxygen binding energy, manifested in a stronger tendency for reduction of the oxide membrane material, leads to higher electron concentrations and to higher rates for open-circuit operation, during which electron conduction limits H₂ transport rates.     

分形几何在研究层状岩体断裂滑落中的应用

应用分形几何研究了层状岩体断裂滑落的分形几何特征，并建立了层状岩体断裂滑落的分形模型。研究结果表明，分形维数值的大小与岩体层理面、节理面的分布及其力学特性密切相关，且最低的分形维数通常出现在层状岩体即将发生滑落之处，故可用分形维数的变化预报层状岩体的滑落。此外，还结合块体理论解析法实例，分析了巷道周围层状岩体的断裂滑落，其结果与分维理论分析结果一致，为进一步研究地下开采引起的采场围岩移动，乃至地表沉陷等问题开辟了一条新的途径。     

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.     

CFD modeling of pervaporative mass transfer in the boundary layer

Modeling mass transfer in the liquid boundary layer accounting for concentration polarization in pervaporation (PV) is particularly challenging since there is no practical way of experimentally determining solute concentration at the membrane surface. We have developed a computational fluid dynamics (CFD) approach to describe not only velocity distribution but also concentration profile in the liquid boundary layer of a slit membrane channel. The satisfactoriness of the numerical methodology used in CFD for obtaining concentration profiles were verified using a classic diffusion problem with its known analytical solution. The overall mass transfer coefficients from the numerical study were also compared with those from the experiment.     

Effect of the distribution of sorption sites on transport diffusivities: A contribution to the transport of medium-weight-molecules in polymeric materials

The detailed transports of both small and large molecules in heterogeneous media including either random disorder or periodic obstacles are known to decrease the value of macroscopic diffusion coefficients. This work proposes to analyze the successive displacements of medium-sized molecules in polymer materials according to the dispersion and topology of sorption sites from a modified application of the transition state theory. In absence of available information on the dispersion of rate constants between sorption macrosites for such molecules, their transport mechanisms at molecular scale is related to their sorption properties, which are more likely to be available. Simulations by kinetic Monte Carlo (KMC) techniques are presented for different distributions of occupancy values randomly allocated in space or distributed in self-similar clusters. Network structures are generated from the equilibrium occupancy on the basis of transition-state theory formulation on 2D lattice approximations. Different reconstruction strategies on 2D hexagonal lattices are examined regarding maximum likelihood principles including maximization of obstruction effects and minimization of either local or global variance of conductances between sorption sites. Effects of short time scales are assessed by comparing results obtained with networks verifying reversible and non-reversible random walks.     

A dispersion model of enhanced mass diffusion in nanofluids

An explanation for the enhancement of mass diffusion in nanofluids is presented using arguments based on dispersion in diluted fixed beds. Starting from the generalized Langevin equation, it is shown that the velocity field established around a Brownian nanoparticle is similar to the velocity field predicted by Brinkman equations leading to the analogy between dispersion in diluted fixed beds and dispersion in nanofluids. The proposed model predicts the order of magnitude of mass diffusion enhancement we observed recently (10-fold enhancement of rhodamine 6G mass diffusivity under the optimum conditions for a suspension of 10-nm alumina nanoparticles in deionized water). Contrarily to other Brownian motion-based models of diffusion in nanofluids, the proposed model samples the whole Maxwell–Boltzmann distribution of particle velocities rather than taking the non-representative root mean square velocity. The model also shows a strong dependence on the mass transfer Péclet number and, consequently, justifies the order of magnitude differences between the mass diffusivity and thermal conductivity enhancements reported in the literature.     

CFD Simulation and Modeling of Membrane‐Assisted Separation of Organic Compounds from Wastewater

The extraction of volatile organic compounds (VOC) from water in porous hollow fibers was simulated with toluene, a hazardous material. The system to be simulated included a VOC stream and air as stripping gas, which were contacted using a porous hollow‐fiber membrane contactor. To model the process, the contactor was considered as three compartments, including shell side, porous membrane, and tube side. The model equations were derived and solved using computational fluid dynamics of momentum and mass transfer in all zones of the contactor. The profiles of concentration and pressure were obtained for the VOC in the hollow fibers.     

Modeling the controlled release of microencapsulated drugs: theory and experimental validation

The release of active principles from microencapsulated drugs has been studied and treated extensively in the literature. However, only empirical or semiempirical models have been proposed. Often, such models are not able to describe correctly the articulated behavior of the release phenomenon. This paper, based on a first principles approach, defines a fully theoretical model of the release process within the human body.The key point of this work is the penetration theory that describes the experimental evidence of release dependency from square root of time.In addition, the paper deals with the observed lead-lag time characterizing the release dynamics of active principle that diffuses towards the external solution. A detailed analysis of the transport phenomena involved, focuses the attention on the diffusive mechanism, which is strictly related to the existing affinity between active principle and polymer coating. Finally, the good agreement between experimental release data, for different active principles, and corresponding simulated curves allows the proposed model to be considered of real value for predictive design purposes.     

Simulations of mass transfer limited reaction in a moving droplet to study transport limited characteristics

Transport limited heterogeneous reactions with asymmetric transport rates in the non-reacting phase can exhibit an interesting switch in the concentrations of the reactants in the reacting phase from one limiting reactant to the other. This switch, called “cross-over” [Mchedlov-Petrossyan P.O., Khomenko G., Zimmerman W.B., 2003a. Nearly irreversible, fast heterogeneous reactions in premixed flow. Chemical Engineering Science 58, 3005-3023; Mchedlov-Petrossyan P.O., Zimmerman W.B., Khomenko G.A., 2003b. Fast binary reactions in a heterogeneous catalytic batch reactor. Chemical Engineering Science 58, 2691-2703], relates to the optimum design of the tubular reactor as all the reactants in the reacting phase are completely consumed at cross-over. The cross-over phenomenon, which has been studied by a number of researchers using phenomenological modelling, is investigated here by developing a distributed model using level-set simulations, in order to explore the possibility of the existence of cross-over in the frame of reference of a moving droplet. Cross-over occurs for a droplet moving due to buoyancy with asymmetric transfer rates of the reactants in the non-reacting phase and an instantaneous reaction occurring inside the droplet (reacting phase). The cross-over length obtained using the level-set simulation is found to be within 0.7-8% of that obtained using the phenomenological model. Computational experiments are performed by varying the ratios of the initial concentrations of the reactants and the transfer rates of the reactants, in order to obtain the parametric region for the existence of cross-over which is also compared with the theoretical prediction.     

Hollow fiber membrane contactor transient experiments for the characterization of gas/liquid thermodynamics and mass transfer properties

We present results from experiments and numerical simulations of contact between a non-reactive gas (N₂O and CO₂) and a physical solvent (H₂O) occurring in a polypropylene (PP) hollow fiber membrane contactor. The closed-loop liquid flow within the experimental setup provides transient curves representing the progressive saturation of the solvent by the gas. We develop an in-house numerical model to fully characterize the gas/liquid mass transfer both in the non-wetted and in the wetted modes, i.e., when the liquid starts partially wetting the pores of the membrane. Using experiments and numerical simulations, we show that the Henry constant (H) and the molecular diffusion coefficient of a non-reactive gas absorbing into a liquid solvent can be extracted by parameter estimation. Both parameters are obtained within a single experiment at a constant temperature and the comparison with temperature-dependant correlations yields excellent agreement over the whole range of temperature studied in this work. Simulations show a partial wetting of the membrane pore by the liquid meniscus during a contact between CO₂ and H₂O, possibly due to the plasticizer effect of CO₂ inside the membrane contactor fibers.     

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.