Prediction Of Mass Transfer Coefficients Research Articles

Mass transfer in the core-annular and fast fluidization flow regimes of a CFB

In gas–solid reactors, particularly circulating fluidized beds (CFB) it is becoming increasingly more important to be able to predict the conversion and yield of reactant species given the ever rising cost of the reactants and the ever decreasing acceptable level of effluent contaminants. As such, the development and use of predictive models for the reactors is necessary for most processes today. These models all take into account, in some manner, the interphase mass transfer. The model developer, unless equipped with specific experimentally based empirical correlations for the reactor system under consideration, is required to go to the open literature to obtain correlations for the mass transfer coefficient between the solid and gas phases. This is a difficult task at present, since these literature values differ by up to 7 orders of magnitude. The wide variation in the prediction of mass transfer coefficients in the existing literature is credited to flow regime differences that can be identified in the cited literature upon careful inspection. A new theory is developed herein that takes into account the local hydrodynamics. The resulting model is compared with data generated in the NETL cold flow test facility and with values from the literature. The new theory and the experimental data agree quite well, providing a fundamentally based mass transfer model for predictive reactor simulation codes.

Fixed-bed adsorption in drinking water treatment: a critical review on models and parameter estimation

A review is given on the state of modelling of fixed-bed adsorption processes in drinking water treatment with special consideration of parameter estimation. In particular, the Homogenous Surface Diffusion Model (HSDM) and the Linear Driving Force Model (LDF model) are compared and evaluated with respect to availability of the required model parameters. In this context, methods for predicting equilibrium and mass transfer parameters are critically discussed under particular consideration of the specific drinking water characteristics. Feasibilities and limits of different approaches for estimating equilibrium parameters are exemplarily shown. In particular, Polanyi's potential theory, a modified Freundlich equation, and the adsorption analysis for complex mixture solutions are considered. Furthermore, empirical correlations for predicting mass transfer coefficients for single-solute and multi-component adsorbate systems are presented and evaluated.

Comparison of Axisymmetric and Three-Dimensional Models for Gas Uptake in a Single Bifurcation During Steady Expiration

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.

Two-phase mass transfer coefficient prediction in stirred vessel with a CFD model

In the present paper, gas dispersion in a laboratory scale (5 L) stirred bioreactor is modelled using a commercial computational fluid dynamics (CFD) code FLUENT 6.2 (Fluent Inc., USA). A population balance model (PBE) is implemented in order to account for the combined effect of bubble breakup and coalescence in the tank. The impeller is explicitly described in three dimensions using the two-phase and Multiple Reference Frame (MRF) Model. Dispersed gas and bubbles dynamics in the turbulent flow are modelled using an Eulerian–Eulerian approach with dispersed k – ϵ turbulent model and modified standard drag coefficient for the momentum exchange. Parallel computing is used to make efficient use of the computational power in order to predict spatial distribution of gas hold-up, Sauter mean bubble diameter, gas–liquid mass transfer coefficient and flow structure. The numerical results from different distribution of classes are compared with experimental data and good agreement is achieved.

Determination of mass transfer coefficients for packing materials used in biofilters and biotrickling filters for air pollution control. 1. Experimental results

Gas film mass transfer coefficients ( k G a t , k G a w ) and liquid film mass transfer coefficients ( k L a w ) for packing materials used in biofilters and biotrickling filters for air pollution control were determined experimentally. Lava rock, polyurethane foam cube (PUF), Pall ring, porous ceramic beads, porous ceramic Raschig rings and compost–woodchips mixtures were investigated. The experiments were performed at gas velocities ranging from 100 to 8000 m h - 1 and liquid velocities of 0.1 – 12 m h - 1 , i.e., a wide range that covers most biofilters and biotrickling filters. k G a t in biofilter packings ranged from about 500 to 2500 h - 1 , while k G a w and k L a w in biotrickling filters ranged from 100 to 8000 h - 1 , and 1 to 300 h - 1 , respectively, depending on the packings and the conditions. This is markedly lower than mass transfer coefficients usually observed for conventional wet scrubbing. The gas film mass transfer coefficient ( k G a t ) of 50:50% vol compost–woodchips mixture, a common biofilter packing, was greater than this of a 20% vol compost and 80% woodchips mixture, though the mass transfer was not increased by increasing further the volume fraction of compost. All compost mixtures exhibited a greater gas film mass transfer coefficient than lava rock or other synthetic materials. The mass transfer coefficients of compost mixtures was also influenced by packing method and it was directly proportional to the surface area of the bulking agents added. The gas film mass transfer coefficient ( k G a w ) of five biotrickling filter packing materials increased linearly with gas velocity. The effect of liquid on the gas film mass transfer coefficient was not significant. Of all the biotrickling filter packings, the porous ceramic beads had the highest gas and liquid film mass transfer coefficients followed by lava rock, porous ceramic rings, 1 in Pall ring and PUF cubes. The liquid film mass transfer coefficient ( k L a w ) was directly proportional to liquid velocity and the effect of gas velocity was negligible. Several correlations allowing prediction of mass transfer coefficients are presented in Part 2 of this paper.

Prediction of effective diffusivity and using of it in designing pulsed sieve plate extraction columns

Pulsed columns are one of the most important liquid–liquid extraction equipments which have an extensive application in different industries. Determination of the mass transfer coefficients as one of the fundamental parameters is of great importance in pulsed columns design. In this paper, previous works which have been done on this subject is reviewed and a set of previous models presented in the past literature are examined. Comparison between these models and the experimental results shows that although some of these equations may have satisfactory results, they do not have enough accuracy for design. This research is based on the substitution of effective diffusivity for molecular diffusivity and attempt to access it experimentally. Using effective diffusivity in equations which have been derived from solving of continuity equation in spherical coordinates will result in more accurate prediction of mass transfer coefficients. Experimental results will lead to prediction of effective diffusivity as a function of Reynolds number. Making use of the presented model in prediction of mass transfer coefficients and calculation of column's height is in great compatibility with experimental results and is suggested for better design.

PREDICTION OF MASS TRANSFER COEFFICIENT IN BUBBLE COLUMN USING ARTIFICIAL NEURAL NETWORK

The volumetric mass transfer coefficient kL.a was calculated using two gases (air and CO2) in water and NaOH solution. The experiments were carried out using 0.1 m column diameter. Empirical and Artificial Neural Network (ANN) correlation were developed to predicted mass transfer coefficient in form of dimensionless groups (Sh, Re,Bo and We). The use of Back Propagation Neural Network (BPNN) gave better results than other correlations found in literature and than the empirical one found in this study.

Model Assessment for the Prediction of Mass Transfer Coefficients in Liquid‐Liquid Extraction Columns

AbstractA large number of theories are reported in the literature for the calculation of individual mass transfer coefficients and each has a well defined application range, which depends on the nature of the continuous and the dispersed phases. Each theory is also based on a different transfer mode, e.g., the dispersed phase depends essentially on the drop behavior, which is directly related to the drop size. However, an accurate determination of the overall mass transfer coefficient depends upon the choice of the combination of theories to be used for the calculation of the individual mass transfer coefficients, i.e., for the continuous and dispersed phases. In the present work, different combinations for the calculation of the overall mass transfer coefficient have been tested for the commonly recommended Acetone/Toluene/Water system, which is characterized by relatively large drop sizes.

Prediction of mass transfer coefficients in non‐Newtonian fermentation media using first‐principles methods

Bubble flows in non-Newtonian fluids were analyzed using first-principles methods with the aim to compute and predict mass transfer coefficients in such fermentation media. The method we used is a Direct Numerical Simulation (DNS) of the reactive multiphase flow with deformable boundaries and interfaces. With this method, we are able for the first time to calculate mass transfer coefficients in non-Newtonian liquids of different rheologies without any experimental data. In the current article, shear-thinning fluids are considered. However, the results provide the basis for further investigations, such as the study of viscoelastic fluids.

A New Correction Factor for Theoretical Prediction of Mass Transfer Coefficients in Bubble Columns

The volumetric liquid-side mass transfer coefficients kLa in 1-butanol, toluene, ethanol and tap water were used in order to show that, when the classical penetration theory is applied to ellipsoidal bubbles, it needs to be corrected. The kLa data were obtained in a 0.102 m diameter bubble column operated in the homogeneous flow regime at pressures varied from 0.1 to 1.0 MPa. The new correction factor (lower than unity) was correlated with the dimensionless Eötvös number, Eo (gravitational force to surface tension force ratio). The kLa data (32 points) are fitted with a mean error of 8.2%.

Prediction of Mass Transfer Coefficients in a Packed Bed using Tamarind Nut Shell Activated Carbon to Remove Phenol

Phenol is a refractive pollutant that is generated from almost all the types of industries. Removal of phenol can be achieved economically by using a cost effective technique like adsorption on to activated carbon. The present paper reports on the preparation and characterization of activated carbon from tamarind nutshell, an agricultural waste byproduct, and its use in a packed bed for the removal of phenol. The breakthrough curves for column sorption of phenol from aqueous solutions to TNSAC have been measured at various flow rates and different particle sizes at 28 °C. The results obtained showed that the sorption of phenol is dependent on both the flow rate and the particle size of the adsorbent, and that the breakpoint time and phenol removal yield decrease with increasing flow rate and particle size. The overall mass transfer coefficient is calculated from the experimental data and compared with the values obtained from the correlation. Experimental values are in excellent agreement with the predicted values from the correlation.

A restructured framework for modeling oxygen transfer in two‐phase partitioning bioreactors

This communication proposes a mechanistic modification to a recently published method for analyzing oxygen mass transfer in two-phase partitioning bioreactors (Nielsen et al., 2003), and corrects an oversight in that paper. The newly proposed modification replaces the earlier empirical approach, which treated the two liquid phases as a single, homogeneous liquid phase, with a two-phase mass transfer model of greater fundamental rigor. Additionally, newly developed empirical models are presented that predict the mass transfer coefficient of oxygen absorption in both aqueous medium and an organic phase (n-hexadecane) as a function of bioreactor operating conditions. Experimental values and theoretical predictions of mass transfer coefficients in two-phase dispersions, k(L)a(TP), are compared. The revised approach more clearly demonstrates the potential for oxygen mass transfer enhancement by organic phase addition, one of the motivations for employing a distinct second phase in a partitioning bioreactor.

Dense gas extraction using a hollow fiber membrane contactor: experimental results versus model predictions

Hollow fiber membrane contactors offer a number of advantages over dispersed phase contactors for mass transfer operations such as extraction of aqueous feeds. In addition, dense gases provide benefits that traditional extraction solvents do not. A mathematical model of a membrane contactor was developed that predicts the steady state fluid velocities and solute concentrations by solving the applicable conservation equations. The gravitational force term was included because the low kinematic viscosity of dense gases can render buoyancy-induced flow significant. A method of calculating the individual and overall mass transfer coefficients from the model results is also presented. The model was validated by comparing predicted Sherwood versus Graetz numbers for tube flow to those obtained from the classical equations that have been repeatedly confirmed by experiment. The three boundary conditions examined were constant wall concentration, constant flux, and linear variation of wall concentration with length. For all three cases the model predictions were in close agreement with those of the classical equations over a wide range of Graetz numbers, except for the constant flux condition at Graetz numbers greater than about 1000. This exception reflects a limit on the mass transfer rate imposed by the constant flux boundary condition. Graetz numbers greater than 1000 (found with short tubes or very high velocities) are not usually encountered in practical applications. Model results are compared to experimental data for the extraction of isopropanol or acetone from water into dense CO 2, obtained over a range of flow rates using modules of different packing densities. Overall the model predicted the data reasonably well, proving the model to be a useful tool for evaluating potential new applications of the technology. For the isopropanol extractions the average absolute errors in the predicted mass transfer coefficients and yields were 29% and 31%, respectively, while for the acetone work the average absolute errors were 39% and 11%. In both cases the predicted mass transfer coefficients were lower than the observed values at the highest aqueous flow rates studied; usually the error became less negative (then increasingly positive in some instances) with decreasing flow rate. This trend is partly attributable to flow maldistribution (leading to reduced efficiency) caused by unavoidable non-uniform fiber spacing and variation in fiber diameter. Other possible sources of modeling error are discussed as well. With acetone, most of the resistance to mass transfer was in the aqueous phase boundary layer, as expected for a solute with a relatively high partition coefficient ( m A). On the other hand, for isopropanol (a lower m A compound) a greater portion of the resistance was attributable to the solvent-filled pore and the solvent phase boundary layer, although the aqueous resistance was still significant. Mass transfer coefficients and yields were higher for acetone than for isopropanol, and aqueous boundary layer penetration was more rapid; both results were a consequence of the higher m A of acetone. For both solutes, usually the mass transfer coefficient increased with increasing aqueous phase Graetz number, as expected when the aqueous phase mass transfer resistance is important. Moreover, yield generally increased with increasing solvent/feed ratio as anticipated.

Experimental results versus model predictions for dense gas extraction using a hollow fiber membrane contactor

Hollow fiber membrane contactors offer a number of advantages over dispersed phase contactors for extraction of aqueous feeds. In addition, dense gases provide benefits that traditional extraction solvents do not. In a previous paper we described the development of a mathematical model of a membrane contactor, and showed that model predictions were reasonably close to experimental data obtained in our laboratory for the extraction of isopropanol or acetone from water into dense CO 2. In this paper, results obtained by others upon extraction of various solutes from aqueous solution into dense CO 2 or propane were also compared to model predictions. Solutes studied ranged from low m A (i.e., partition coefficient) compounds like caffeine, ethanol, and dimethylformamide, to high m A ones such as 1,2-dichloroethane and ethyl acetate. Again the predicted mass transfer coefficients and yields were reasonably close to the actual ones, except for the data obtained using a membrane module that was particularly susceptible to flow maldistribution. With higher m A solutes, most of the mass transfer resistance was in the aqueous phase boundary layer. On the other hand, some of the resistance encountered with lower m A compounds shifted to the solvent-filled pore and the solvent phase boundary layer, although the aqueous resistance was still significant in most cases. In general, mass transfer coefficients and yields were higher for solutes with higher partition coefficients, and aqueous boundary layer penetration was more rapid. The results presented in this and in our previous paper validate the ability of the model to predict hollow fiber membrane contactor performance in dense gas extraction. This validation confirms the utility of the model for screening potential applications of the technology, with considerable reduction in the required amount of expensive laboratory experimentation.

Improving Mass Transfer Coefficient Prediction in Bubbling Columns via Sphericity Measurements

The prediction of the oxygen transfer coefficients (kL) in bubbling columns is studied. Bubbling columns have important applications as bioreactors. It is found that the coefficient is strongly inf...

CO 2 release in multiple-effect distillers controlled by mass transfer with chemical reaction

For predicting the CO 2 release rates in multiple-effect distillers, the theory of desorption with chemical reaction was applied. The mass transfer processes and the reaction kinetics controlling the CO 2 release were described. In the pH and temperature range found in the evaporator stages of multiple-effect distillers, the alkaline reaction mechanism with the steps CO 2 + OH − ↔ HCO 3 − and HCO 3 − + OH − ↔ CO 3 2− + H 2O predominates. The reaction CO 2 + OH − ↔ HCO 3 − is relatively slow, and therefore it is the rate-determining step in the reaction mechanism. Information for predicting mass transfer coefficients in water films flowing over horizontal tubes is still limited. Different approaches were shown. The phase interface area for CO 2 release was described as the sum of the surface area of the liquid film on the tubes plus the surface area of the liquid between the tubes, assuming that liquid columns can be expected to occur between the tubes. Depending on the magnitude ofthe mass transfer coefficient, it was found that CO 2 desorption from the evaporating brine either takes place in the transition regime from a slow to a fast reaction or in the fast reaction regime. Mass transfer and chemical reactions simultaneously take place in the boundary layer at the phase interface. Mass transfer is slightly enhanced by the reaction. The chemical rate constant becomes more important and the mass transfer coefficient less important in the correlation for the CO 2 release rate.

Variation in iron, aluminum and dissolved organic carbon mass transfer coefficients in lakes

Steady-state mass balance models have been successfully used to predict annual loads and concentrations of numerous substances in lakes. A major limitation of the model is that the value of the mass transfer coefficient, ν X , for some substance, X, is assumed constant and is taken as a mean value of a set of calibration lakes. The range in mean values between lakes for ν X is typically two- to three-fold. Thus, there is some potential for error in model predictions if the true but unknown value for a given lake differs from the mean, calibration value. Moreover, the use of a region-specific value for ν X for all lakes in a region means that when environmental conditions change, the model will have to be re-calibrated requiring many more years of monitoring. In this study, mass balances for two substances, total iron and aluminum, are presented along with simple empirical relationships that predict mass transfer coefficients for iron as a function of dissolved organic carbon (DOC) concentration and aluminum as a function of DOC and pH. The relationships, which are consistent with current understanding of iron and aluminum behavior, account for >90% of the variation in ν X . Improvements in mass balance model predictions are expected when these coefficients are used in place of constant values.

Correction of the Penetration Theory Applied for Prediction of Mass Transfer Coefficients in a High-Pressure Bubble Column Operated with Gasoline and Toluene.

The volumetric liquid-phase mass transfer coefficients kLa were measured by an optical probe in a 0.102-m (inner diameter) bubble column operated under both ambient (0.1 MPa) and high pressures (0.2, 0.5, 1.0, 2.0 and 4.0 MPa). The measurement was performed during desorption of oxygen from gasoline and toluene by nitrogen. The superficial gas velocity was varied in the range 0.01–0.2 m·s–1.The classical penetration theory was used for the sake of prediction of the experimental data. The theory was corrected, however, due to the ellipsoidal shape of the bubbles formed in the bed. By applying the new correction factor which is a function only of bubble size, the deviation between experimental kLa coefficients and calculated ones for both liquids was 8.8%.

A semi-analytical model for dissolved oxygen mass transfer coefficient at the sediment–water interface

Relying on the fundamental principles of mass transport in a turbulent flow, we have developed a semi-analytical model for a mass transfer coefficient in a sediment water interface over a smooth bed. The governing equations with boundary conditions reflect a mechanism of shear dispersion in a turbulent flow. The model is formulated in terms of the Sherwood-Reynolds-Schmidt functional dependence. Unlike previous regression-type models, the mass transfer coefficient at the sediment-water interface is parameterized by the friction coefficient. Flow conditions over a smooth bed ranging in Reynolds number from 1800 to 7000 were used to verify the model. The predicted mass transfer coefficients are in very good agreement with the experimental data.

Erratum to “Prediction of mass-transfer coefficient for solute transport in porous media” [J. Contam. Hydrol. 50 (2001) 1–19

Erratum to “Prediction of mass-transfer coefficient for solute transport in porous media” [J. Contam. Hydrol. 50 (2001) 1–19