Estimation Of Effective Diffusion Coefficient Research Articles

Mesoscopic exploration on mass transfer in porous thermochemical heat storage materials

Mass transfer is the key characteristic that affects the charging and discharging performance of the porous materials used in thermochemical heat storage systems. Therefore, an algorithm is required to simulate the transport process within heat storage materials and to accurately evaluate the effective diffusion coefficient. This study is about porous calcium oxide, which is widely used in CaO-Ca(OH)2 or CaO-CaCO3 heat storage systems. In this paper, the fractal porous media that resemble real heat storage materials are reconstructed by a random walk method. Furthermore, the gas diffusion process through complicated porous microstructures within fractal porous media is simulated by an efficient lattice Boltzmann method. Results indicate that thermochemical heat storage materials have great fractal characteristic and materials with larger fractal dimension have more diffusion resistance. The effective gas diffusion coefficients of CaO and Ca(OH)2 are obtained from the ratios of effective gas diffusion coefficient and bulk gas diffusion coefficient that are 0.228 and 0.188 for CaO and Ca(OH)2, respectively. Additionally, it is found that calcium oxide samples prepared at higher temperatures have the poorer exothermic performance because of the poorer gas diffusion. Moreover, the correlation between the effective diffusion coefficients and the porosity of porous materials is numerically predicted and evaluated. The fractal model-LBM method developed in this paper may serve as a great tool for easy estimation of effective diffusion coefficients and mass transfer.

Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small‐Angle Neutron Scattering Measurements

AbstractThe determination of effective diffusion coefficients of gases or solutes in the water‐saturated pore space of mudrocks is time consuming and technically challenging. Yet reliable values of effective diffusion coefficients are important to predict migration of hydrocarbon gases in unconventional reservoirs, dissipation of (explosive) gases through clay barriers in radioactive waste repositories, mineral alteration of seals to geological CO2 storage reservoirs, and contaminant migration through aquitards. In this study, small‐angle and very small angle neutron scattering techniques have been utilized to determine a range of transport properties in mudrocks, including porosity, pore size distributions, and surface and volume fractal dimensions of pores and grains, from which diffusive transport parameters can be estimated. Using a fractal model derived from Archie's law, we calculate effective diffusion coefficients from these parameters and compare them to laboratory‐derived effective diffusion coefficients for CO2, H2, CH4, and HTO on either the same or related mudrock samples. The samples include Opalinus Shale from the underground laboratory in Mont Terri, Switzerland, Boom Clay from a core drilled in Mol, Belgium, and a marine claystone cored in Utah, USA. The predicted values were compared to laboratory diffusion measurements. The measured and modeled diffusion coefficients show good agreement, differing generally by less than factor 5. Neutron or X‐ray scattering analysis is therefore proposed as a novel method for fast, accurate estimation of effective diffusion coefficients in mudrocks, together with simultaneous measurement of multiple transport parameters including porosity, pore size distributions, and surface areas, important for (reactive) transport modeling.

Estimation of effective diffusion coefficients of drug delivery devices in a flow-through system

We present a numerical approach to estimating the effective diffusion coefficients of drug diffusion from a device into a container with a source and sink condition due to a fluid flowing through the system at a constant rate. In this approach we first formulate this estimation problem as a continuous, nonlinear, least-squares problem subject to a set of constraints containing a partial differential equation system. The nonlinear optimization problem is then discretized by applying a finite volume scheme in space and an implicit time-stepping scheme to the equation system, yielding a finite-dimensional, nonlinear, least-squares problem. An algorithm is proposed for the resulting finite-dimensional, constrained, nonlinear optimization problem. Numerical results using experimental data are presented to demonstrate the usefulness and accuracy of the method.

Estimation of effective diffusion coefficient and its effect on effectiveness factor for HDS catalytic process: A multi-scale approach

Effectiveness factors have great relevance in multiphase reactors modeling since they are the conventional way of incorporating the effects of intra-particle resistance reaction rate. This work determines the description level effect of catalytic pellet microstructure on mass and energy effective transport coefficients prediction, isothermal and no isothermal. For such a purpose some results about on evaluation of the effective diffusivity and conductivity with the methodology of volume averaging were applied. The obtained results along with a Langmuir–Hinshelwood/Hougen–Watson kinetic expression were applied to establish the concentration and temperature fields in a catalytic particle. The evaluation of concentration field and effectiveness factors were developed using two different models: pseudo- homogeneous mass and energy transport model for a catalytic particle with reaction in all domain, and heterogeneous mass and energy transport model with fluid-catalytic surface interphase reaction for a realistic porous structure model. The results show the differences in concentration and temperature profiles between both models and consequently in effectiveness factors. This could be ascribed to the form of evaluation of effective transport coefficients used in the pseudo-homogeneous model, and presumably to the simple shape of the unit cells used for the solution of the closure problem for the average transport equations with homogeneous reaction.

Estimation of Effective Diffusion Coefficient of Gaseous Species in MgO^|^ndash;C Refractories by Shrinking Core Model

Estimation of Effective Diffusion Coefficient of Gaseous Species in MgO^|^ndash;C Refractories by Shrinking Core Model

Determination of effective diffusion coefficients of drug delivery devices by a state observer approach

In this paper we present a state observer approach for the estimation of effective diffusion coefficients of a drug delivery device.In this approach, we construct estimators for the unknown effective diffusion coefficients characterizing thediffusion process of a drug release device using a combination of state observers from the area of adaptive control andthe drug diffusion models developed recently by us. We show that the constructed systems are asymptoticallystable and the estimators converge to the exact diffusion coefficients. An algorithm is proposedto recursively compute the estimatorsusing a given time series of a release profile of a device. To demonstrate the efficiency and usefulness of thisapproach, numerical experiments have been performed using experimentally observed drug release profiles of polymeric spherical devices.The numerical results show that the present approach is about 9 times faster than the conventional least squares method when applied to the test problems.

Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses

In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 [2–4]). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations.

Numerical methods for the estimation of effective diffusion coefficients of 2D controlled drug delivery systems

We present a numerical approach to the estimation of effective diffusion coefficients and other unknown parameters determining the diffusion process of a drug delivery device, based on experimental data. This approach is to formulate the estimation problem as a nonlinear least-squares problem subject to some constraints including a partial differential equation (PDE) system. Numerical algorithms are developed for both of the solution of the optimization problem and the discretization of the PDE system. To show the usefulness of the methods, numerical experiments are performed using some laboratory observed data. The numerical results show that the methods are accurate and reliable.

Mass transfer through meat. Part I. Determination of diffusion coefficient of nitrite by time lag method

A diffusion chamber technique based on time lag analysis for the estimation of effective diffusion coefficient of nitrite through calf meat is reported. For the solute studied, a reduction in effective diffusion coefficient was observed with a retardation of solute flux in both aqueous and calf meat layers. Here, we report the diffusion coefficient obtained by lag-time analysis for nitrite through a calf meat layer in an attempt to examine the precise effect of meat structure. The diffusion coefficient of nitrite in meat layer was found as, D = 1.1 × 10 −10 m 2/s.

Volatile Organic Compounds Volatilization from Multicomponent Organic Liquids and Diffusion in Unsaturated Porous Media

Vapor phase diffusion is an important transport process in the unsaturated zone affecting evaporation of volatile organic compounds (VOCs) from pure and multicomponent organic liquids. To evaluate some widely used empirical relationships for the estimation of effective diffusion coefficients in the unsaturated zone and to assess the validity of Raoult9s Law during aging of organic mixtures, two series of laboratory-scale column experiments were performed using pure toluene, pure methyl tert-butyl ether (MTBE), and two multicomponent “kerosene-type” liquids containing four to seven compounds. The analytical one-dimensional solution of Fick9s Second Law described the diffusion process of pure compounds very well in two sands with different water contents. The effective diffusion coefficients obtained correspond well to a recently published empirical relationship (Moldrup et al., 2000); the capacity factors fitted indicate equilibrium partitioning of the solute between gas phase and water. A one-dimensional numerical model based on the combination of Fick9s Second Law and Raoult9s Law was used to predict the volatilization and the diffusion process from multicomponent organic liquids. Both the vapor phase diffusion process of the VOCs and the aging of the organic mixtures were predicted very well solely on the basis of effective diffusion coefficients estimated from the empirical relationship and assuming an ideal mixture (e.g., an activity coefficient of 1 in Raoult9s Law).

Volatile Organic Compounds Volatilization from Multicomponent Organic Liquids and Diffusion in Unsaturated Porous Media

Vapor phase diffusion is an important transport process in the unsaturated zone affecting evaporation of volatile organic compounds (VOCs) from pure and multicomponent organic liquids. To evaluate some widely used empirical relationships for the estimation of effective diffusion coefficients in the unsaturated zone and to assess the validity of Raoult's Law during aging of organic mixtures, two series of laboratory‐scale column experiments were performed using pure toluene, pure methyl tert‐butyl ether (MTBE), and two multicomponent “kerosene‐type” liquids containing four to seven compounds. The analytical one‐dimensional solution of Fick's Second Law described the diffusion process of pure compounds very well in two sands with different water contents. The effective diffusion coefficients obtained correspond well to a recently published empirical relationship (Moldrup et al., 2000); the capacity factors fitted indicate equilibrium partitioning of the solute between gas phase and water. A one‐dimensional numerical model based on the combination of Fick's Second Law and Raoult's Law was used to predict the volatilization and the diffusion process from multicomponent organic liquids. Both the vapor phase diffusion process of the VOCs and the aging of the organic mixtures were predicted very well solely on the basis of effective diffusion coefficients estimated from the empirical relationship and assuming an ideal mixture (e.g., an activity coefficient of 1 in Raoult's Law).

Volatile Organic Compounds Volatilization from Multicomponent Organic Liquids and Diffusion in Unsaturated Porous Media

Vapor phase diffusion is an important transport process in the unsaturated zone affecting evaporation of volatile organic compounds (VOCs) from pure and multicomponent organic liquids. To evaluate some widely used empirical relationships for the estimation of effective diffusion coefficients in the unsaturated zone and to assess the validity of Raoult's Law during aging of organic mixtures, two series of laboratory-scale column experiments were performed using pure toluene, pure methyl tert-butyl ether (MTBE), and two multicomponent “kerosene-type” liquids containing four to seven compounds. The analytical one-dimensional solution of Fick's Second Law described the diffusion process of pure compounds very well in two sands with different water contents. The effective diffusion coefficients obtained correspond well to a recently published empirical relationship (Moldrup et al., 2000); the capacity factors fitted indicate equilibrium partitioning of the solute between gas phase and water. A one-dimensional numerical model based on the combination of Fick's Second Law and Raoult's Law was used to predict the volatilization and the diffusion process from multicomponent organic liquids. Both the vapor phase diffusion process of the VOCs and the aging of the organic mixtures were predicted very well solely on the basis of effective diffusion coefficients estimated from the empirical relationship and assuming an ideal mixture (e.g., an activity coefficient of 1 in Raoult's Law).

A laboratory technique for investigation of diffusion and transformation of volatile organic compounds in low permeability media

A laboratory diffusion cell technique that permits spatial and temporal estimates of porewater concentrations over short intervals suitable for estimation of effective diffusion coefficients ( D e) and degradation rate constants ( k) of volatile organic compounds (VOCs) in saturated low permeability media is presented. The diffusion cell is a sealed cylinder containing vapour reservoirs for sampling, including a vapour reservoir source and an array of vapour-filled “mini-boreholes”, which are maintained water- and sediment-free by slightly negative porewater pressures. The vapour reservoirs were sampled by Solid Phase Micro-Extraction (SPME), resulting in minimal disturbance to the experimental system. Porewater concentrations are estimated from the measured vapour concentrations. Experiments were conducted using a non-reactive medium and five VOCs with a range in partitioning properties. Calibration experiments showed that equilibrium partition coefficients could be used for calculating concentrations in the vapour reservoir source from concentrations in the SPME coating after a 1-min microextraction and that the reservoir concentration was insignificantly affected by sampling. However, equilibrium was not reached during the one-min extraction of the boreholes; the microextraction reduced the borehole vapour concentrations, leading to diffusion of VOCs from porewater into the vapour-filled borehole. Thus, empirical partitioning coefficients were required for the determination of porewater VOC concentrations. The experimental data and numerical modelling indicate masses extracted by SPME extraction are relatively small, with minimal perturbation on processes studied in diffusion experiments. This technique shows promise for laboratory investigation of diffusion and transformation processes in low permeability media.

Entrapment of Urease in glycol-containing polymeric matrices and estimation of effective diffusion coefficient of urea

Urease enzyme was immobilized in copolymer matrices containing poly(ethylene glycol) (PEG; MW 14000 and 1000) or polypropylene glycol (PPG; MW 2000), prepared with 2-hydroxyethyl methacrylate (HEMA) and/or N-vinyl-2-pyrrolidone (VP). Urease-immobilized copolymer matrices were stored in phosphate buffer solutions of pH 7.0 at 4°C, and the activity of the enzyme was determined periodically for up to 90 days. The highest activity was observed for HEMA and VP containing PEG (MW 14000) matrix. The matrices comprising VP and PEG (MW 14 000) did not have mechanical stability and degraded in 3 weeks, while all the others were stable and demonstrated enzyme activities for up to 3 months. The effective diffusion coefficients of urea in these polymer matrices were calculated with a ‘diffusion and reaction model’ and the highest effective diffusion coefficient was found in the HEMA and VP containing PEG matrix, possibly due to its highly porous structure.

Immobilization of urease and estimation of effective diffusion coefficients of urea in HEMA and VP copolymer matrices

AbstractEnzyme urease was immobilized in copolymer matrices of 2‐hydroxyethyl methacrylate (HEMA) and N‐vinyl pyrrolidone (VP). The activities of immobilized urease stored in phosphate buffer solution of pH 7.0 at 4°C were examined periodically for up to 90 days. For the matrices of higher VP/HEMA mole ratio in the structure, a higher volume increase and enhanced apparent activity were observed, while HEMA polymer alone proved to have the most stable matrix for prolonged activity. No appreciable amount of enzyme leakage was experienced for any of the matrices prepared. The effective diffusion coefficients of urea through these polymer matrices were calculated with a ‘diffusion and reaction’ model and the highest effective diffusion coefficient was found with pure HEMA matrix, possibly due to its laminated structure.

A study of macromolecular diffusion through native porcine mucus

A diffusion chamber technique based on time-lag analysis for the estimation of effective diffusion coefficients of radiolabelled macromolecules of varying molecular weights through native mucus gel is reported. For all solutes studied, a reduction in effective diffusion coefficients was observed with a retardation of solute flux in both aqueous and mucus layers. Over the molecular weight range of solutes investigated (126-186,000 Daltons), a consistent effect of molecular weight was evident with regard to the retarding effect of mucus. No apparent or absolute molecular weight cut-off for macromolecular transfer was exhibited. However, at high molecular weights (greater than 30,000 Daltons) the retardation was greatly enhanced. The results confirm that mucus can be regarded as a gel with finite pores, but that it does not constitute an absolute barrier to even high molecular weight solutes.

Estimation of effective diffusion coefficients of model solutes through gastric mucus: assessment of a diffusion chamber technique based on spectrophotometric analysis

A diffusion chamber technique based on spectrophotometric analysis to determine effective diffusion coefficients for solutes with various relative molecular mass (Mr) values and properties, passing through native mucus gel, is reported. For all solutes studied, a reduction in effective diffusion coefficients is observed with a retardation of solute flux by a factor of at least two. For the solutes investigated (with Mr values ranging from 126-14,400 u), no consistent effect of solutes of low Mr was evident with regard to the retarding effect of mucus; however, at high Mr values (greater than 4000 u) the retardation was greatly enhanced. A possible relationship between charged solutes of low Mr and the degree of retardation was observed, which possibly suggests the presence of ionic interactions of the solutes with the largely negatively charged mucus gel. The results provide further evidence for the suggestion that mucus is acting more than simply as a gel support for an unstirred water layer and is perhaps a more potent diffusion barrier to specific solutes.

Diffusion Flow Laws in Metamorphic Rocks

Rocks which deform by pressure solution obey a diffusion flow law with a linear viscous or Newtonian stress to strain-rate relation. Undeformed relics of original grains preserved within newly grown crystals at grain boundaries under tension and presolved surfaces, together with accumulation of inert particles at grain boundaries under compression, are diagnostic evidence of a diffusion flow law. At a given stress, strain-rate is inversely proportional to the grain size to a power of two or three. A geologically useful plot has inverse temperature versus the logarithm of grain size as coordinates. Such a graph is separated into fields by three boundaries which meet at a triple point; within each field, either lattice diffusion, grain-boundary diffusion, or a dislocation flow law is predominant. It may be possible to calibrate this graph from naturally deformed rocks. Photomicrographs of isoclinally folded greenschist-grade quartzites and rhyolitic flows from the South Mountain–Blue Ridge area in Maryland demonstrate a diffusive mass transfer deformation mechanism, but estimates of effective diffusion coefficient compared to currently available laboratory diffusion data are insufficient to identify the diffusion path with certainty. However, the comparatively low ratio of metamorphic temperature to melting temperature and the physical nature of grain boundaries in metamorphic rocks, particularly concentrations of low-density impurities at grain boundaries, suggest the grain-boundary diffusion flow law.