Bed Of Porous Particles Research Articles

A quantitative study of water proton relaxation in packed beds of porous particles with varying water content

A quantitative analysis of the dependence of water proton relaxation on water content in randomly packed beds of Sephadex is undertaken. A combination of Osmotic and Capillary theory is used to describe the morphological changes occurring in the packed beds as the water content is lowered. At each water content the water proton relaxation is calculated using a “proton exchange-diffusion” model which takes into account fast chemical exchange between water and dextran hydroxyl protons and the diffusion of water molecules between the water compartments inside and outside the Sephadex beads. The relaxation time distributions are shown to provide a sensitive probe of the air-water distribution in the bed and of the shrinkage of the Sephadex beads at lower water contents. The theoretical models provide an accurate, quantitative description of the relaxation behavior except for the largest beads at high water contents when there is slow diffusion between the water compartments. In this case, a more realistic three-dimensional description of the air-water distribution in a randomly packed bed is required.

Flow through beds of porous particles

Intraparticle convection is receiving increased attention in studies of beds of porous particles, especially in biotechnology applications involving cell immobilization and perfursion chromatography. This work presents two approximate models for describing the flow field within a porous particle contained in a fixed or fluidized bed. The first is a swarm model where a spherical porous particle of a specified permeability is contained in a matrix of a different permeability that is equated to the overall bed permeability. Brinkman's equations are solved in both the particle and matrix domains. The second is a cell model in which the spherical porous particle is placed in a spherical envelope of fluid whose diameter is chosen so that the overall bed porosity is conserved. The Stokes equations are solved for the envelope fluid, and Brinkman's or Darcy's equations are solved for the porous particle. For both models, a vector invariant solution is employed which yields the pressure and velocity fields directly in terms of the fundamental solutions to Laplace's equation and the modified Helmholtz equation. Results are presented for the drag force per particle, the overall bed permeability, and the velocity and pressure profiles within the particle. The results of the two different models are similar. An important observation is that the intraparticle velocity is approximately two orders of magnitude larger for particle in a typical packed bed than for an isolated particle under similar conditions, owing to the increased resistance to flow outside the particle caused by the other bed particles. As a result, intraparticle convection plays a key role in reactant transport within the porous particle phase.

Ceramic membrane microfilter as an immobilized enzyme reactor

This study investigated the use of a ceramic microfilter as an immobilized enzyme reactor. In this type of reactor, the substrate solution permeates the ceramic membrane and reacts with an enzyme that has been immobilized within its porous interior. The objective of this study was to examine the effect of permeation rate on the observed kinetic parameters for the immobilized enzyme in order to assess possible mass transfer influences or shear effects. Kinetic parameters were found to be independent of flow rate for immobilized penicillinase and lactate dehydrogenase. Therefore, neither mass transfer nor shear effects were observed for enzymes immobilized within the ceramic membrane. Both the residence time and the conversion in the microfilter reactor could be controlled simply by regulating the transmembrane pressure drop. This study suggests that a ceramic microfilter reactor can be a desirable alternative to a packed bed of porous particles, especially when an immobilized enzyme has high activity and a low Michaelis constant.

Evaporation from a packed bed of porous particles into superheated vapor

An experimental and computational study of evaporation into superheated steam from porous particles, which form a packed bed, is performed. The goal of the study is to develop a predictive model of the drying process in packed beds with steam as the drying medium. The direct experimental measurement using load cells of the weight of alumina particles of various diameters in a packed bed during the drying process produced a complete continuous drying curve. A range of experimental conditions are examined, and a correlating equation for the overall heat transfer coefficient developed. Evaporation from a single spherical porous particle is modeled as occurring at a receding liquid/vapor interface within the particle. The drying process in a single particle is assumed to be thermally controlled. The single particle model is incorporated into an overall model for drying in a packed bed. The model predicted overall and local drying rates, as well as transient temperature distributions in the packing. The results of this study indicate that drying in a packed bed of significant depth occurs in three phases. The three phases of drying correspond to periods where the entire bed is in the constant drying rate regime, portions of the bed have entered the falling rate regime, and the entire bed is in the falling rate regime, respectively. The existence of these phases of drying are confirmed by both measured temperature distributions and measured drying rates. Predictions of the overall drying rate from the model show favorable agreement with measured drying curves.

COMPUTER SIMULATION OF MASS TRANSFER IN AGGREGATIVE FLUIDIZED BEDS

A mathematical model for simulation of unsteady-state mass transfer in an aggregative fluidized bed of porous particles is proposed. A quasi-steady state approach is being used to solve the model. A computer program is written for solving the model and the rate of drying of air in a fluidized bed of silica-gel particles is calculated as an example. To evaluate the accuracy of the proposed model, a pilot-scale fluidized bed is erected and the experimental results are compared to the calculated values. A good agreement is observed between them.

Dynamic behavior of supercritical extraction of kerogen from shale

AbstractA model is presented for the supercritical reaction‐extraction of a solid component from a bed of porous particles through which the solvent flows. Accounted for are reaction at an intraparticle position, pore diffusion, interphase mass and heat transfer, and flow in a differential reactor. The behavior of the bed is dynamic since both temperature and concentration of extractable solid vary with time.The model is compared with experimental data for the extraction with toluene of kerogen from a bed of Colorado shale particles. Curves of effluent bitumen concentration vs. time were measured and fitted with predicted curves to evaluate three parameters: preexponential factor and activation energy for the conversion of insoluble kerogen to soluble bitumen, and the diffusivity of toluene at the critical point. The predicted curves agreed well with the experimental results and gave reasonable values for the parameters. Rates of reaction‐extraction as well as extraction curves exhibited a sharp dip as the reactor was heated through the critical temperature.

Diffusion in packed beds of porous particles

AIChE JournalVolume 34, Issue 4 p. 679-683 R & D Note Diffusion in packed beds of porous particles Stephen Whitaker, Stephen Whitaker Laboratoire Energétique et Phénomènes, de Transfert, Université de Bordeaux I, 33405 Talence Cedex, France Department of Chemical Engineering, University of California, Davis, CA 95616Search for more papers by this author Stephen Whitaker, Stephen Whitaker Laboratoire Energétique et Phénomènes, de Transfert, Université de Bordeaux I, 33405 Talence Cedex, France Department of Chemical Engineering, University of California, Davis, CA 95616Search for more papers by this author First published: April 1988 https://doi.org/10.1002/aic.690340419Citations: 11 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume34, Issue4April 1988Pages 679-683 RelatedInformation

Intraparticle diffusion coefficients in packed columns: Measurement by arrested‐flow gas chromatography

AbstractArrested‐flow chromatography was used to determine intraparticle diffusivities of large‐pore particles packed in columns. Particle and column tortuosity factors were determined for helium tracer in nitrogen carrier gas at 40°C and atmospheric pressure. Semiempirical modifications of Maxwell's, Burger's, Jeffrey's, and Rayleigh's relations for the composite diffusivity of spherical particles in a stationary medium are proposed for the effective composite diffusion coefficient for a packed bed of porous particles. The equations, modified to represent accurately the extraparticle void diffusion based on measurements for beds of nonporous particles, are used to evaluate intraparticle diffusivities from experimental data obtained by arrested‐flow chromatography.

Coefficients of mass transfer between a fluidized bed and the surface of a capillary-porous body

Results are presented from a theoretical determination of coefficients of mass transfer between a fluidized bed of porous particles and a capillary-porous body.

Kinetics of the elimination of a liquid from a porous body by porous particles. II

An analytic description is given for the removal of bound liquid from a porous body immersed in a fluidized bed of porous particles, particularly during the period of decreasing drying rate.

The characterization of fixed beds of porous solids from pulse response

AbstractThe response of a fixed bed of porous particles through which fluid flows to a pulse of tracer gas has been analyzed by a number of methods. It is found that analysis of the Fourier transformed and the Laplace transformed response curves for small values of the parameters of the integrals provides accurate estimates of intraparticle diffusivity and Peclet group for axial dispersion when additional information provided by the experiments is used to resolve interaction between the process coefficients in the dynamic response.

Dispersion and diffusion in beds of porous particles

The frequency response of a number of beds packed witth porous catalyst spheres has been measured. The experiments were carried out within the range of Reynolds number from 1 to 200. By analysis of the responses, coefficients of intra-particle diffusivity and the coefficients of axial dispersion were obtained with good accuracy. The accuracy of the diffusivity coefficients appeared to be about 10 per cent. The dependence of the axial dispersion coefficient upon Reynolds number agreed with the form of a recently published theory, and a significant difference in the packing characteristics of different grades of catalyst particles was found. A statistical analysis showed that the experimental frequency response of the bed agreed with the differential equation and the solutions used in the theoretical analysis. Radial dispersion characteristics were measured by injection of tracer into fluid flowing through the packed bed. The measurements were found to be in good agreement with a recent theory.

A physical model for mixed phase flow through beds of porous particles

A physical model for mixed phase flow through beds of porous particles