Estimation Of Mass Transfer Parameters Research Articles

New insights from modelling and estimation of mass transfer parameters in fixed-bed adsorption of Bisphenol A onto carbon materials

The removal of Bisphenol A, 2,2-bis (4-hydroxyphenyl) propane (BPA) in fixed-bed columns was investigated by breakthrough adsorption tests at different operation conditions and further prediction by a mathematical model to describe the adsorption-diffusion process onto two synthesized carbon porous materials. In this study, a xerogel (RFX) prepared by an optimized conventional sol-gel method and a lignin-based activated carbon (KLP) obtained via chemical activation were used in batch and fixed-bed adsorption experiments. The materials were fully characterized and their adsorptive properties were compared to those obtained with a commercial activated carbon (F400). RFX and KLP materials reached the equilibrium adsorption in only 24 h, whereas F400 activated carbon required 48 h. In addition, F400 and KLP adsorbents showed higher equilibrium adsorption capacity values (qe = 0.40 and 0.22 kg/kg, for F400 and KLP, respectively) than that obtained for the xerogel (qe = 0.08 kg/kg). Both synthesized carbon-adsorbents were studied in fixed-bed adsorption tests, exploring the effect of the operation conditions, e.g., initial BPA concentration (0.005–0.04 kg/m3), weight of adsorbent (0.01–0.05 g) and volumetric flow rate (0.2 to 1.0 mL/min), on the adsorption performance of the column. All the tested adsorption columns reached the equilibrium in a very short time, due to the efficient dimensionless of the bed. Additionally, the regeneration of the exhausted adsorbent was studied, achieving the total reuse of the solids after three consecutive cycles using methanol as regeneration agent. Finally, a mathematical model based on mass conservation equations was proposed, allowing to efficiently fit the experimental BPA breakthrough curves and estimate the external and adsorbed-phase mass transfer coefficients with a high accuracy.

Dynamics of fluid migration into porous solid matrix during high pressure treatment

A mathematical approach was used to describe the mechanism of pressure-driven flow during the holding period of high pressure processing (HPP). A lumped method was used for the estimation of mass transfer parameters using an analogy to Fick’s second law. In addition, a least squares optimization algorithm was introduced as inverse parameter estimators to obtain the associated mass diffusivity coefficients. The approach was verified using a model system involving liquid diffusion (1% w/w ascorbic acid solution) into a porous solid matrix (apple cubes) under HPP conditions (100–600MPa) with different holding times (0–30min). The associated fluid diffusivity values ranged 4.38×10−9–2.19×10−8m2s−1. Finally, a simple linear model was fitted to the experimental data at 100 and 600MPa which could be used to estimate the total porosity of the solid matrix. Thus, finite element numerical solutions combined with simple Fickian approach could be used to model the unsaturated liquid flow in to a porous solid matrix. The study also showed that the liquid in-flow decreased in blanched apples subjected to similar HPP confirming the need for a porous structure for the efficient liquid flow.

Cocoa Beans Microwave Pulse Drying: Characterization of the Moisture Transfer

The aim of this study was to characterize the moisture transfer during microwave pulse drying of cocoa beans. Experiments were carried out on fermented cocoa beans using a domestic microwave oven. Three microwave power levels (450 W, 600 W and 700 W) were used. The moisture transfer characterization was made using the estimation of mass transfer parameters and a modeling. The estimated mass transfer parameters were the Biot number (Bi), the diffusivity (D) and the mass transfer coefficient (km). They were given by the analytical method of Dincer. The 2nd Fick’s law was used for the moisture transfer modelling. The results obtained showed that for the whole microwave powers, the Bi values were included between 0.57 and 0.62. The D values, for the various microwaves powers (450 W, 600 W and 700 W), were respectively 6.01×10-9 m².s-1, 10.27 ×10-9 m².s-1and 11.94×10-9 m².s-1. The km values varied between 9.87×10-7 m.s-1and 21.33×10-7 m.s-1. The Fick’s model application showed a good adequacy between the experimental values and those simulated. R² of the Fick’s model for the whole microwave power levels, was higher than 0.998.

Equilibrium or Nonequilibrium Models: A Critical Issue in Determination of Gas Diffusivity in Oil

The various effects of a diffusion process on estimation of a gas-diffusion coefficient were studied in the complete paper. Considering both classical and recently attempted boundary conditions, the effects of taking into account the nonequilibrium nature of a diffusion process on estimation of mass-transfer parameters using pressure-decay data of carbon dioxide (CO2), methanw(CHH), and nitrogen (N2) dissolution in Athabasca bitumen at two different temperatures were found to be negligible, considering the gas/oil-interface resistance on calculated values of diffusivities.

Estimation of mass transfer parameters during dehydroxylation in a large ceramic body by inverse methods

An inverse problem of the parameter estimation for the water transport during dehydroxylation in a large cylindrical ceramic body is solved. The transport is described by a standard type of non-stationary diffusion equation with a volumetric generation. The inverse problem is solved by the Levenberg–Marquardt method, with the estimated parameters being the water transfer diffusivity and water generation per unit volume. Their temperature dependencies are obtained within the dehydroxylation regime for 450 °C, 500 °C, 550 °C, and 600 °C, using experimental data from isothermal heating measurements. The activation energy of the diffusion process is estimated from the temperature dependence of the diffusivity, yielding 72.9 kJ mol −1.

A Methodology for Estimation of Mass Transfer Parameters in a Detailed Chromatography Model Based on Frontal Experiments

A methodology for estimation of the unknown physical parameters in a detailed model for chromatographic processes is proposed. The model describes the concentration of the solute in the mobile phase and considers external/internal mass transfer resistance. The external volume and its mixing effect are also considered. The unknown model parameters estimated are the bed void, the axial dispersion coefficient, the liquid film mass transfer coefficient, the effective diffusion coefficient and the apparent bead porosity. All the parameters in the model were subsequently determined in three classes of experiments, the external mixing behaviour, the mobile phase behaviour and the stationary phase behaviour. The estimates are based on the sum of the least squares of the residuals between the experimental breakthrough curves and the model response. The methodology is exemplified by frontal experiments with lysozyme, bovine serum albumin and immuno globulin γ on a well-defined column set-up. When the mixing properties in the external volume had to be accounted for, to avoid adding broadening behaviour to the dispersion coefficient, the film mass transfer coefficient and the diffusion coefficient were also investigated. The results show that it is possible to estimate the unknown parameters using the proposed methodology.

Kinetic and mass transfer parameters of maltotriose hydrolysis catalyzed by glucoamylase immobilized on macroporous silica and wrapped in pectin gel.

Kinetic and mass transport parameters were estimated for maltotriose hydrolysis using glucoamylase immobilized on macroporous silica and wrapped in pectin gel at 30 degrees C. Free enzyme assays were used to obtain the intrinsic kinetic parameters of a Michaelis-Menten equation, with product inhibition by glucose. The uptake method, based on transient experimental data, was employed in the estimation of mass transfer parameters. Effective diffusivities of maltotriose in pectin gel were estimated by fitting a classical diffusion model to experimental data of maltotriose diffusion into particles of pectin gel in the absence of silica. The effective diffusivities of maltotriose in silica were obtained after fitting a bidisperse model to experimental data of maltotriose hydrolysis using glucoamylase immobilized in silica and wrapped in pectin gel.

Identification of mass transfer parameters in three-phase biofilm reactors

This work presents the analysis of dynamic models describing oxygen transfer and reaction in three-phase biofilm reactors. The modelling is mainly aimed at designing experiments for the estimation of mass transfer parameters in these systems. Systems with and without reaction are investigated separately and distinct approaches are used to simplify the model equations in the two cases. In order to show their limitations, simplified models are compared to a mechanistic model describing oxygen gas–liquid transfer, liquid–solid transfer, and diffusion and reaction within the biofilm. Model reliability in the estimation of the parameters is established through a sensitivity analysis. In the case of plain oxygen absorption in the liquid phase and adsorption without reaction in the biofilm layer two limiting cases are considered for slow and fast diffusion within the biofilm. When assuming fast diffusion, the simplified model has an error of less than 4% (relative to the mechanistic model) in the estimation of volumetric gas–liquid mass transfer coefficient ( k L a) in the case of low solid hold-up or low value of k L a. In the case of a reacting system, half-order and zero-order expressions for the biochemical reaction are used to calculate explicitly the oxygen flux at the biofilm surface without remarkable deviation from the values calculated through the mechanistic model. On the basis of this analysis, criteria are given to design experiments for the estimation of mass transfer parameters in three-phase biofilm reactors.

Predicting the performance of fixed-bed granular activated carbon adsorbers

Granular Activated Carbon (GAC) adsorption is an effective treatment technology for the removal of Synthetic Organic Chemicals (SOCs) from drinking water supplies. This treatment process can be expensive if not properly designed. Application of mathematical models is an attractive method to evaluate the impact of process variables on process design and performance. In this study, a mathematical modeling methodology incorporating the pore and surface diffusion model (PSDM) is proposed for known mixtures in fixed-bed adsorbers. Thermodynamic correlations for estimation of equilibrium parameters and empirical correlations for estimation of mass transfer parameters are presented. The PSDM was successfully compared to a 6-component mixture for empty bed contact times (EBCTs) of 2.4, 4.9, and 9.56 minutes.

Predicting the performance of fixed-bed granular activated carbon adsorbers

Granular Activated Carbon (GAC) adsorption is an effective treatment technology for the removal of Synthetic Organic Chemicals (SOCs) from drinking water supplies. This treatment process can be expensive if not properly designed. Application of mathematical models is an attractive method to evaluate the impact of process variables on process design and performance. In this study, a mathematical modeling methodology incorporating the pore and surface diffusion model (PSDM) is proposed for known mixtures in fixed-bed adsorbers. Thermodynamic correlations for estimation of equilibrium parameters and empirical correlations for estimation of mass transfer parameters are presented. The PSDM was successfully compared to a 6-component mixture for empty bed contact times (EBCTs) of 2.4, 4.9, and 9.56 minutes.