Film Mass Transfer Resistance Research Articles

Investigation into the Dissolution Kinetics of Different MgO Desulfurizers in Flue Gas Desulfurization.

The paper introduced hydrophilic functional groups on the surface of the MgO desulfurizer to improve its dispersion and hydrophilicity on the basis of reducing the particle size of the MgO desulfurizer to the nanometer level. Mechanical grinding technology was used to improve the traditional two-step method to lay the foundation for its large-scale production. The stability test showed that the ζ potential of the 5 wt % modified MgO desulfurizer was greater than 50 mV with 30 days of storage, and the sedimentation rate was not more than 7%. The dissolution reactivity and kinetics experiments showed that the decrease of particle size and the increase of hydrophilicity and dispersion were conducive to accelerating the dissolution rate of the MgO desulfurizer and reducing the apparent activation energy. Meanwhile, the good dissolution rate of the modified MgO nanofluids prepared by the improved method could reduce the liquid film mass transfer resistance and prolonged the penetration time.

Determination of Pore and Surface Diffusivities from Single Decay Curve in CSBR Based on Parallel Diffusion Model

A novel, simple numerical method to determine the pore and surface diffusivities in adsorbents from a single experimental concentration decay curve obtained using the batch adsorption technique was investigated in this study. The pore and surface diffusion coefficients were determined based on the conventional parallel diffusion model in its dimensionless form using a theoretical model correlation. The model assumed that the film mass transfer resistance was negligible, i.e., the condition with a large Biot number, from the single concentration decay curve. The procedure for determining the kinetic parameters was investigated, and the effectiveness of the proposed simple method was validated by comparing the parameters with those reported previously. The single decay curve of p-nitrophenol, obtained by the batch adsorption system using granular activated carbon as an adsorbent, was used for validation. The diffusivities determined by the simple method corresponded fairly well with the diffusivities reported previously.

Role of 1-methylimidazole in regulating the CO2 capture performance of triethylenetetramine-based biphasic solvents

Biphasic solvents are promising candidates for CO2 capture for low regeneration energy consumption. In this study, a novel phase splitter 1-methylimidazole (1-MI) was proposed for triethylenetetramine (TETA) aqueous solvent. 1-MI was proved to act as a phase splitter to induce the phase separation and as an absorption promoter to enhance the absorption rate. By tuning the concentrations of TETA and 1-MI, good phase separation performance was obtained in TETA-1-MI biphasic solvent, achieving a CO2-rich phase loading of 5.41 mol/L. 13C NMR revealed that the upper layer was the CO2-lean phase, containing 1-MI and a small amount of water, while the lower layer was the CO2-rich phase and mainly comprised of TETAH+ and TETA-carbamate. The kinetics results based on the double-film theory indicated that the CO2 absorption rate was mainly controlled by the gas film mass transfer resistance at lower CO2 loading and then by liquid film mass transfer resistance when CO2 loading was higher than 1 mol/L. Owing to the good phase separation behavior triggered by 1-MI, the regeneration heat of TETA-1-MI was 2.26 GJ/t CO2, which was comparable to that of the second-generation solvents, and 43.5 % lower than that of 5 M monoethanolamine (MEA). The present findings indicated that TETA-1-MI had a large loading capacity, high absorption rate, and low energy consumption, which can serve as a novel candidate for CO2 capture.

Mass transfer between microbubbles

HypothesisThe role of interfacial coatings in gas transport dynamics in foam coarsening is often difficult to quantify. The complexity of foam coarsening measurements or gas transport measurements between bubbles requires assumptions about the liquid thin film thickness profile in order to explore the effects of interfacial coatings on gas transport. It should be possible to independently quantify the effects from changes in film thickness and interfacial permeability by using both atomic force microscopy and optical microscopy to obtain time snapshots of this dynamic process. Further, it is expected that the surfactant and polymer interfacial coatings will affect the mass transfer differently. ExperimentsWe measure the mass transfer between the same nitrogen microbubbles pairs in an aqueous solution using two methods simultaneously. First, we quantify the bubble volume changes with time via microscopy and second, we use Atomic Force Microscopy to measure the film thickness and mass transfer resistances using a model for the gas transport. FindingsModelling of the interface deformation, surface forces and mass transfer across the thin film agrees with independent measurements of changes in bubble size. We demonstrate that an anionic surfactant does not provide a barrier to mass transfer, but does enhance mass transfer above the critical micelle concentration. In contrast, a polymer monolayer at the interface does restrict mass transfer.

A new method of characterizing mass transfer controlling mechanism in pollutant adsorption from aqueous solutions

Pollutant adsorption from aqueous solutions is usually controlled by diffusion or mass transfer which can be external film diffusion or intraparticle diffusion or both, depending on the relative magnitude of the film and intraparticle mass transfer resistances. Traditionally the Biot number is used to characterize mass transfer controlling mechanism in adsorption. In this work a new quantitative characterization method is proposed. Specifically the average fractional film mass transfer resistance is defined and used as an indicator of the relative importance of film and intraparticle mass transfer resistances. The average fractional film mass transfer resistance varies from 0 to 1, corresponding respectively to complete intraparticle diffusion control and complete film diffusion control. Numerical simulations of batch adsorption processes are performed and the corresponding average fractional film mass transfer resistance calculated for a wide range of process parameters. Based on the simulation results a correlation is obtained between the average fractional film mass transfer resistance and the Biot number, the adsorbate partition ratio and the separation factor. It is shown that the Biot number alone is not sufficient to characterize mass transfer controlling mechanism in adsorption.

Kinetic Study of Selective Chlorination of Iron in Ilmenite Ore

The selective chlorination of ilmenite with coke and chlorine gas was conducted in the fixed bed reactor and effects of coke content and reaction temperature on reaction rate were investigated. In particular, the chlorination rate of iron in ilmenite was simulated by the unreacted shrinking core model. The reaction rate was simulated by calculating the chlorine gas consumption rate as the unreacted core shrinks. In addition, each of reaction resistances that chemical reaction at the reaction interface, diffusion through the product layer, and boundary film mass transfer resistances were calculated. The simulated reaction rates were in good agreement with the experimental results and the rate controlling step changed as the chlorination reaction progressed. Furthermore, the diffusion resistance through the product layer was dominant at lower reaction temperature, whereas the chemical reaction was dominant as the reaction temperature increased. It is because the diffusion of chlorine gas through the product layer could be hindered at lower reaction temperatures. Key words: Ilmenite, Selective chlorination, Synthetic rutile, Shrinking core model

Silver-Exchanged Mordenite for Capture of Water Vapor in Off-Gas Streams: A Study of Adsorption Kinetics

Reduced silver-exchanged mordenite (Ag0Z) has been recognized as the benchmark adsorbent for radioactive iodine removal from the nuclear fuel reprocessing off-gases. It has also been shown to have a considerable adsorption capacity for water vapor, which is a major component (tritiated water) in the off-gases of spent nuclear fuel reprocessing facilities. Therefore, understanding the kinetics of water vapor adsorption on Ag0Z is necessary for a better design of off-gas treatment systems. The adsorption kinetics were studied through adsorption experiments of water vapor on Ag0Z pellets and analyses of the kinetic data with adsorption models that describe processes of mass transfer and inter/intracrystalline diffusion. Uptake curves of water vapor on Ag0Z pellets were obtained with a continuous-flow adsorption system at temperatures of 25, 40, 60, 100, 150, and 200 °C and dew points from −53.6 °C to 12.1 °C. The diffusion-controlling factors were determined experimentally and analytically. It was found that the diffusion process of water vapor in Ag0Z pellets was controlled by macropore diffusion. Gas film mass-transfer resistance also contributed to the adsorption process of the 0.9 mm Ag0Z pellets, but it could be minimized with a high gas velocity and small pellet radius. Kinetic models including macropore diffusion (MD), linear driving force (LDF) and shrinking core (SC) were used to fit the uptake curves. The macropore diffusivity for water vapor adsorption on Ag0Z pellets was determined using the three models. It was found that the LDF and SC models could well describe the kinetic process, while the fitting with the MD model was not quite as good due to the existence of external mass-transfer resistance for the 0.9 mm Ag0Z pellets.

Experimental and numerical study of a falling film absorber in an ammonia-water absorption chiller

In this paper, experimental and numerical studies of heat and mass transfer in a falling film absorber are presented. The investigated absorber is a plate heat exchanger used in a falling film configuration. The ammonia-water solution flows in a falling film mode along the plates. The vapour flows co-current with the falling film and the coolant fluid is in a counter-current flow with the falling film. A prototype of ammonia-water absorption chiller is used to experimentally study the absorber behaviour in real operating conditions. A macro study of the absorber and a local analysis deduced from local temperatures measurements along the falling film are presented. A numerical model and a simulation tool are developed in order to complete the experimental investigations. The associated numerical parametric study aims to separate the coolant mass flow rate impact. The model is validated with experimental data and a maximal relative error of 15% is observed between experimental and numerical results. The results of this study suggest that during the absorption process, mass transfers are controlled by the falling film mass transfer resistance and that the liquid-side heat transfer resistance is negligible.

Adsorption of copper on glass beads coated with chitosan: Stirred batch and fixed bed analysis

Chitosan is a natural polymer largely studied for heavy metal adsorption applications, since the amino and hydroxyl groups present in its structure can act as chelation sites. However, this material presents some drawbacks as an adsorbent due to its low mechanical strength. Studies have shown that the use of immobilized chitosan on glass beads can improve the mechanical strength of adsorbent and enhance mass transfer properties. For this reason, stirred batch experiments of copper adsorption on chitosan immobilized onto glass beads were performed to estimate the surface diffusion coefficient and the chitosan film thickness, considering an inert solid glass core. The kinetic data were modelled by a surface diffusion model incorporating the external film mass transfer resistance. Column experiments were also performed for copper solution at different flow rates and a film‐surface diffusion model was used to describe the breakthrough adsorption experiments, using the chitosan film thickness estimated from the batch experiment (φ = 2.5 µm). The input parameters for this model were determined by batch experiments or estimated from correlations available in the open literature. The surface diffusion coefficients (0.98–1.72 × 10−10 cm2 · min−1) of copper in the chitosan film for different flow rates were estimated. The experimental data and the model agreed, indicating that the film thickness and the mass transfer parameters were well predicted.

Analysis of general rate model of linear chromatography considering finite rates of the adsorption and desorption steps

This article presents semi-analytical solutions and temporal moments of the general rate model of chromatography with a focus on evaluating the effect of finite rates for the adsorption and desorption steps, typically considered to be in equilibrium. The model equations are analytically solved in the Laplace domain and numerical Laplace inversion is applied to get back solutions in the actual time domain. The expression of first four temporal moments are derived from the analytical solutions in the Laplace domain. The derived analytical solutions and moments are helpful tools to predict dynamic behaviors inside the column and to evaluate the influence of model parameters on the elution profiles, in particular the effect of finite rates of the intrinsic adsorption and desorption steps. The correctness of analytical solutions are verified through the numerical solutions of a high resolution finite volume scheme. Several case studies are considered to quantify effects of the rate constants for adsorption and desorption, axial dispersion, film mass transfer resistance, intraparticle diffusion resistance, and inlet boundary conditions on the elution profiles.

Linear general rate model of chromatography for core–shell particles: Analytical solutions and moment analysis

Due to their proven performance and improved availability, core–shell particles are increasingly applied for chromatographic separations. This paper presents semi-analytical solutions and a moment analysis of a detailed mathematical model for fixed-beds packed with core–shell particles. The model considers axial dispersion, interfacial mass transfer, intraparticle diffusion, linear adsorption, and the injection of rectangular pulses. The Laplace transformation is used as a basic tool to derive semi-analytical solutions. In addition the first three statistical temporal moments are derived from solutions in the Laplace domain. The numerical Laplace inversion is applied for back transformation of the solution in the actual time domain. In order to demonstrate their potential, different scenarios are considered to quantify the effects of the relative core size, axial dispersion, film mass transfer resistance and intraparticle diffusion resistance in the porous layer on the elution profiles. An important new result is the derivation of a plate height equation for fully porous and core–shell particles respecting the Danckwerts boundary conditions.

Supercritical extraction of essential oil from Echium amoenum seed : Experimental, modeling and genetic algorithm parameter estimation

Mathematical modeling of supercritical CO2 extraction of essential oil from Echium amoenum seed was carried out. The effect of process variables such as pressure (15, 20, 25 and 30 MPa), temperature (313, 318, 323 and 328 K) and CO2 flow rate (0.6, 0.9, 1.2 and 1.5 ml/min) on the recovery of essential oil extraction was investigated in a series of experiments conducted in a laboratory scale apparatus. The chemical composition of recovered essential oil (fatty acids) was analyzed by GC-FID. The mathematical model was developed utilizing diffusion-controlled regime in the pore and film mass transfer resistances with axial dispersion of the mobile phase at dynamic conditions. Henry's law was used to describe the equilibrium state of solid and pore fluid phases. The obtained mass transfer equations for the mobile and stationary phases were solved using the numerical explicit method of line, and the modeling pre- dictions of oil extraction recovery were validated via comparison with experimental data. Genetic algorithm (GA) was applied to estimate the optimum value of the Henry constant. Finally, applying the validated model the extraction re- covery was investigated as a function of effective variables such as dynamic extraction time and supercritical fluid temperature, pressure and flow rate. A set of optimal operating conditions were determined via modeling parametric analysis to achieve the objective function of maximum recovery.

Transcolumn dispersion in a computational mimic of an analytical silica monolith reconstructed from sub-microtomographic scans using computational fluid dynamics

Analysis of transcolumn dispersion in an analytical silica monolith is presented via direct numerical simulations in a topological model reconstructed from 3D nanotomographic scans. This was the first instance to incorporate retention in the study of dispersion behavior in reconstructed models for monoliths. The low scanning resolution employed in this work allowed simulating retained behavior with no appreciable loss of prediction accuracy. Heterogeneities of the order of 1–2 domain lengths were observed from peak parking and transient dispersion simulations, indicating a relatively homogeneous core in silica monoliths. Analysis of the short-range interchannel dispersion revealed that equilibration at the domain-level occurred mainly through lateral diffusion. Phenomena not captured by the model, viz. transcolumn eddy dispersion and dispersion due to external film mass transfer resistance, were estimated from deviations of simulated data from experimental values. Three scenarios were explored to model the transcolumn and external film mass transfer resistance contributions to overall dispersion. In the first case, when transcolumn dispersion was controlled by a convection mechanism, the transcolumn velocity biases were within the experimentally observed ranges for silica monoliths. Deviations of estimated film mass transfer resistance from that predicted by penetration theory varied inversely with the zone-retention factor. In the second case, when film penetration theory was assumed to hold good and the transcolumn contribution was modeled to exhibit a coupled diffusive-convective behavior, the corresponding persistence-of-velocity lengths revealed that about 20–30% of the column length was utilized in relaxing the transcolumn concentration gradients. A phenomenological approach was proposed to estimate transcolumn dispersion from the simulated transverse dispersion coefficients and column residence times. The parameters estimated from the proposed approach were compared with the third scenario, wherein transcolumn dispersion was modeled according to Giddings’ couple equation, while external film mass transfer resistance was assumed to deviate from film penetration theory. In the absence of any method to predict a priori or directly measure transcolumn dispersion and external film mass transfer resistance in silica monoliths, this approach served as a first approximation to judge the magnitude of each contribution to overall dispersion.

Adsorption dynamics of p-nitrophenol in structured fixed bed with microfibrous entrapped activated carbon

Adsorption dynamics of p-nitrophenol (PNP) in the structured fixed bed filled with granular activated carbon in the inlet and microfibrous entrapped activated carbon composites in the outlet at various flow rates and inlet concentrations were studied. A modified version of the homogeneous surface diffusion model (HSDM) involving surface diffusion, film mass transfer and axial dispersion was proposed to simulate the adsorption dynamics of PNP in the structured fixed bed. The breakthrough curve of PNP in the structured fixed bed is steeper than that in the individual activated carbon fixed bed with the same bed height. The length of unused bed (LUB) of the structured bed decreases almost 20% compared with that of the individual bed. The model simulations indicate that intraparticle diffusion resistances, film mass transfer resistances and the resistance due to axial dispersion decrease by adding the microfibrous entrapped activated carbon composites in the outlet of the bed. The experimental and modeled results indicate that the mass transfer and utilization of bed capacity are enhanced by adding the microfibrous entrapped activated carbon composites in the outlet of the structured bed.

A revisit of the concept of external film mass transfer resistance in the packed beds used in high-performance liquid chromatography

This work discusses the origins of the apparent contradiction between expected and predicted external film mass transfer resistance terms in chromatographic columns. The expected term was rigorously derived from the presumed thickness of the thin stagnant film of eluent surrounding the spherical particles contained in the column beds. The predicted terms were based on the commonly accepted models of Pfeffer, Wilson and Geankoplis, Kataoka, Sircar, and Lightfoot. The significant differences observed between the expected and predicted values of the Sherwood number are explained by the fact that the models of external mass transfer developed in chemical engineering account for mass transfer across the hydrodynamic boundary layer of eluent, the layer through which the eluent velocity continuously decreases from the constant fluid velocity in the center of the eluent stream, far away from the surface, to zero. In contrast, the expected term accounts for diffusion through the thin layer of eluent against the particles, in which the eluent velocity is actually zero. It is shown that the predicted mass transfer resistance term is accounted for by the trans-channel eddy diffusion term directly derived in the general theory of the dynamics of chromatography.

Perturbation chromatography with inert core adsorbent: Moment solution for two-component nonlinear isotherm adsorption

The moment analysis is applied to study two-component perturbation chromatography with linearized nonequilibrium adsorption. General expressions for the first and second chromatographic moments of components and waves are given by taking into account axial dispersion, film mass transfer resistance, and intraparticle diffusion resistance for chromatographic column packed with inert core adsorbents. The well-known results for moment solution of the single-component case and special two-component case are extended to the general two-component case.

New insights on mass transfer kinetics in chromatography

AbstractThe mass transfer kinetics of thiourea, phenol, ethylbenzene, propylbenzene, butylbenzene, and amylbenzene were studied on a Gemini‐C18 (5 μm, 110 A˚, 375 m2/g) column (150 mm × 4.6 mm) eluted with methanol/water solutions (100, 90, and 20% v/v). Each of the successive steps of the mass transfer of these solutes (axial diffusion, eddy dispersion, film mass transfer resistance, and transparticle mass transfer resistance) was unambiguously measured, using a combination of the peak parking method, the total pore blocking method, and moment analysis, in a wide range of reduced linear velocities. The results obtained offer new insights on the mass transfer kinetics in chromatographic columns. They show first that the eddy dispersion A‐term is strongly correlated with the particle porosity. The complex, anastomosed transcolumn flow pattern causes extra band broadening. This transcolumn effect was found to be markedly smaller with porous particles than with nonporous particles of the same size. Second, the film mass transfer coefficient of retained compounds is smaller for porous than for nonporous particles, a result consistent with concentration gradients being steeper at the wall of solid particles than across the entrance surface of pores. The external mass transfer coefficient decreases with increasing fraction of the surface area of the particles that is open to pores, e.g., with increasing particle porosity. © 2010 American Institute of Chemical Engineers AIChE J, 2011

The mass transfer kinetics in columns packed with Halo-ES shell particles

AbstractThe average mesopore size of the new Halo-ES-Peptide shell particles is 160Å, markedly larger than that of the classical Halo shell particles (90Å). We found that this change causes a considerable decrease of the film mass transfer resistance measured for columns packed with these particles. We analyze data obtained by systematic measurements of the C term of the van Deemter equation for the peptide β-lipotropin (MW = 769Da), the protein insulin (MW = 5800Da), and a series of non-retained polystyrene standards (MW = 6400 and 13,200). The improvement in column performance is explained by an increase of the fraction of the external surface area of the shell that allows the entrance of the sample molecules inside the particle. The fraction of the shell surface accessible to a probe controls the rate of its external film mass transfer, i.e. its rate of transfer between the interstitial and the stagnant eluent. Although measurable, the increase in sample diffusivity through the porous shells does not account for the better performance of Halo-ES-peptide columns. Furthermore, the analysis of the HETPs data of small molecules (uracil, acetophenone, toluene, and naphthalene, MW< 150) reveals that the eddy diffusion (A) term of these new columns is 25% lower than that of the classical Halo columns. This result is consistent with the impact of intra-particle diffusivity on the eddy diffusion mechanism in packed columns. As shell diffusivity increases, so does the rate of transfer of sample molecules between the eluent stream-paths flowing through the packed particles and across the column diameter. Dispersion through short-range inter-channel and trans-column eddies is reduced.

Non-invasive measurement of eddy diffusion in very efficient liquid chromatography columns packed with sub-3 μm shell particles

Mass transfer kinetics in a particular column packed with 2.6 μ m Kinetex-C 18 particles was measured using a series of non-invasive methods. According to the manufacturer, this column was the most efficient one in a lot of 133 columns of the same dimensions, packed with particles of the same batch, with an efficiency about 6% larger than the lot average. The total eddy diffusion term of this column was determined by subtracting from the experimental HETP data (1) the longitudinal diffusion term (given by the peak parking method); (2) the trans-particle solid–liquid mass transfer resistance term (given by the peak parking method and an axial diffusion model); and (3) the external film mass transfer resistance term (derived from the Wilson and Geankoplis correlation). The results are analyzed based on the general coupling theory of eddy diffusion of Giddings and are compared to those previously obtained with a column packed with 2.7 μ m Halo-C 18 column, which also has a low eddy diffusion term. The particular column investigated shows no trans-column velocity bias and a smaller reduced short-range inter-channel eddy diffusion term than the Halo column. This result explains the unusual efficiency of this exceptionally well packed column.

Experimental determination of intraparticle diffusivity and fluid film mass transfer coefficient using batch contactors

The mass transfer properties of adsorbates are generally critical factors for design of a fixed bed adsorber. For single-component systems, the completely mixed batch reactor (CMBR) method is a convenient and frequently used experimental technique for determining mass transfer properties. However, the effect of fluid film mass transfer resistance is neglected in the conventional analytical technique of CMBR method when estimating the intraparticle diffusivity ( D S). This effect should be considered to determine the diffusivities more accurately. In this study, a new analytical technique was proposed for determination of D S and fluid film mass transfer coefficient ( k F) from one concentration decay curve and it was applied in practical experiments. This technique will be useful to estimate diffusivities when the fluid film mass transfer resistance cannot be regarded as being negligible. Under the experimental conditions of this study, the fluid film mass transfer resistance could be neglected at high stirring speeds (i.e., >200 rpm). Therefore, values of D S can be estimated by the conventional technique from kinetic experiments performed at relatively high stirring speeds. On the other hand, values of k F obtained by the proposed technique showed a similar tendency to values estimated from Hixson's empirical equation.