Empirical Mass Transfer Research Articles

Magnetic resonance microscopy analysis of advective transport in a biofilm reactor

In this article we present magnetic resonance microscopy (MRM) characterization of the advective transport in a biofilm capillary reactor. The biofilm generates non-axial flows that are up to 20% of the maximum axial velocity. The presence of secondary velocities of this magnitude alters the mass transport in the bioreactor relative to non-biofilm fouled reactors and questions the applicability of empirical mass transfer coefficient approaches. The data are discussed in the context of simulations and models of biofilm transport and conceptual aspects of transport modeling in complex flows are also discussed. The variation in the residence time distribution due to biofilm growth is calculated from the measured propagator of the motion. Dynamical systems methods applied to model fluid mixing in complex flows are indicated as a template for extending mass transport theory to quantitatively incorporate microscale data on the advection field into macroscale mass transfer models.

Kinetics of a reactive dye adsorption onto dolomitic sorbents

A novel wastewater treatment technique has been investigated, for reactive dye removal, in batch kinetic systems. These experimental studies have indicated that charred dolomite has the potential to act as an adsorbent for the removal of Brilliant Red reactive dye from aqueous solution. The effect of initial dye concentration, adsorbent mass:liquid volume ratio, and agitation speed on dye removal have been determined with the experimental data mathematically described using empirical external mass transfer and intra-particle diffusion models. The experimental data show conformity with an adsorption process, with the removal rate heavily dependent on both external mass transfer and intra-particle diffusion.

A COMPARATIVE ANALYSIS OF THE MASS TRANSFER COEFFICIENTS OF THREE MODELS OF MEMBRANE BLOOD OXIGENATORS USING WATER AND A PERFLUOROCARBON EMULSION

A dynamic method with water and a perfluorocarbon emulsion was used to determine the total mass transfer coefficients of three models of membrane blood oxygenators. The experiments were performed with blood oxygenators with exchange areas of 0.25, 0.7, and 1.6 m2. Experimental conditions were varied by changing gas flow rates from 0.5 to 6 l/min. and the liquid from 0.5 to 2.5 l/min. The Liquid phases used were distilled water and an emulsion formulated with Oxypherol FC-43 diluted with distilled water up to 18,5 % v/v. The experiments were done in triplicate totalizing 650 runs. The simultaneous scanning of two variables resulted in data in response surface form, which were plotted as three-dimensional graphic maps for the volumetric mass transfer coefficient Kla(s−1), the total mass transfer coefficient K(ml(O2 STP).cm−2.s−1.mmHg−1), and the t-Student normalized errors. Empirical mass transfer correlations were adjusted for these mass transfer devices by the variations in the gas and liquid flow rates. The mass transfer coefficient maps are useful to seek for the optimum operating conditions, to provide knowledge about the responses to variations on the operational situation, to help to evaluate new devices under development, to enhance the production quality control, to choose an equipment for a given situation, and as a marketing appeal, since it provides an impressive amount of information about the equipment's performance to the perfusionists.

The generalized Lévêque equation and its practical use for the prediction of heat and mass transfer rates from pressure drop

Based on the generalized Lévêque equation (GLE) a new type of analogy between pressure drop and heat transfer has been discovered, that may be used in the cross corrugated channels of chevron type plate heat exchangers, in packed beds, in tube bundles, in crossed rod matrices or in many other spacewise periodic arrangements. Experimental data on heat transfer in tube bundles in crossflow, both inline, and staggered arrangements, had been recently tested in greater detail. Using an empirical correlation for pressure drop in these arrangements from the literature that has been successfully tested against a large number of experimental pressure drop data, heat transfer data collected earlier could be very well represented from the pressure drop correlation and the GLE. The data for staggered bundles have been shown to be in better agreement with this new method, than with the existing empirical heat and mass transfer correlations. Somewhat larger deviations for inline tube bundles had been found at lower Reynolds numbers. Here a simple and physically reasonable correction function of Re is presented, which leads to a better agreement for the inline bundles, too. Additionally, it can be shown for a number of literature data on tube bundles and on crossed rod matrices that the agreement with the GLE prediction is even better if original pressure drop data from the same sources are available in place of a pressure drop correlation. The method results in reasonable heat or mass transfer predictions from frictional pressure drop, which may be widely used in chemical engineering applications.

Equilibrium and mass transfer characteristics of 2-chlorophenol removal from aqueous solution by liquid membrane

Experiments were conducted to investigate the extraction of 2-chlorophenol (2-CP) from aqueous solution by liquid membrane. Main research efforts were focused on the identification of the optimal operating conditions for the liquid membrane system. An equilibrium equation of the Langmuir-type was proposed for describing the equilibrium 2-CP distribution between the external aqueous phase and the internal water-in-oil (W/O) emulsion phase. The proposed model predicts reasonably well the 2-CP phase equilibrium relation. Furthermore, a mass transfer model based on the linear driving force principle was also adopted in this work for representing 2-CP mass transfer from the external aqueous phase to the W/O emulsion. The simplified mass transfer model involved only a single parameter, i.e. the empirical mass transfer coefficient, which was easily established using observed data generated under various operating conditions. The mass transfer model considerably facilitates estimation of the 2-CP mass transfer rate in the liquid membrane system.

A DYNAMIC MODEL WITH ON-LINE IDENTIFICATION FOR ROTARY SUGAR DRYING PROCESSES

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to replace the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.

THE EFFECT OF PROCESS CONDITIONS ON THE DRYING KINETICS AND REHYDRATION CHARACTERISTICS OF SOME MW-VACUUM DEHYDRATED FRUITS

ABSTRACT The effect of drying conditions, namely, microwave power, vacuum pressure, as well as sample geometry, on the drying kinetics and rehydration characteristics of five microwave vacuum dehydrated fruits (apple, avocado, mushroom, pear and strawberry) was studied. The investigation involved a wide range of microwave power, vacuum pressure and sample size levels. The drying rate and the rehydration ratio, a measure of rehydration characteristics, were found to depend on the drying conditions. An empirical mass transfer model, involving a characteristic parameter for each process (drying and rehydration( as a function of process variables, namely, microwave power, vacuum pressure and sample size, was also tested with the data obtained in a microwave oven equipped with vacuum apparatus. Furthermore, a comparison of rehydration properties of microwave vacuum and conventionally dehydrated products, was conducted.

MICROWAVE VACUUM DRYING KINETICS OF SOME FRUITS

ABSTRACT Microwave vacuum drying kinetics of three fruits (namely, apple, kiwi and pear) were studied by introducing an one-parameter empirical mass transfer model, involving a characteristic parameter (drying constant), as a function of process variables. The model was tested with data produced in a microwave oven equipped with vacuum apparatus, using non-linear regression analysis. The investigation involved a wide range of microwave power and vacuum pressure levels. The parameters of the model considered were found to be greatly affected by the microwave power level while vacuum pressure affected slightly the process.

Generalized scaling of spontaneous imbibition data for strongly water-wet systems

Mass transfer between fractures and matrix blocks is critical to oil recovery by waterflooding in fractured reservoirs. A scaling equation has been used for rate of oil recovery by spontaneous imbibition and presented their results as oil recovery vs. dimensionless time. Many conditions apply to this scaling equation, including identical core sample shapes and fluid viscosity ratios. Recent investigation by experiment of these two factors has resulted in a more generalized scaling equation for strongly water-wet systems with a general definition of characteristic length and a viscosity ratio term included in the definition of dimensionless time. In this paper, published data on oil recovery by imbibition have been analyzed and correlated through application of the new definition. These data sets were for different porous media, core dimensions, boundary conditions, and oil and water viscosities. All of the systems were strongly water-wet. The generalized correlation was fitted closely by an empirical mass transfer function with the new definition of dimensionless time as the only parameter.

DRYING KINETICS OF SOME FRUITS

ABSTRACT Drying kinetics of four Fruits (namely, apple, pear, kiwi and banana) were studied by introducing an one-parameter empirical mass transfer model, involving a characteristic parameter (drying constant), as a function of process variables. The model was tested with data produced in a laboratory dryer, using non-linear regression analysis. The investigation involved a wide range of characteristic dimensions of samples and air conditions (temperature, humidity, and superficial velocity). The parameters of the model considered were found to be greatly affected by sample characteristic dimension and air temperature. The model also involved the equilibrium material moisture content which was formulated in the form of the GAB equation. Its parameters were evaluated by means of non-linear regression analysis to independent experiments covering two process variables (temperature and water activity of the surrounding air).

Measurement of CO 2 diffusion coefficient and application of LIF in pressurized water

This paper deals with estimation of the diffusion coefficient in an H 2OCO 2 system under high pressure and the use of laser-induced fluorescence (LIF) for measuring CO 2 dissolution. A liquid CO 2 droplet without CO 2 clathrate was placed in the flow where the velocity profile is uniform. The diffusion coefficient is estimated by measuring the liquid CO 2 droplet-dissolution rate and using the empirical mass transfer coefficient. The measured diffusion coefficient agrees well with the Wilke-Chang equation at pressures of 29.4 and 39.2 MPa. We have used LIF for measurement of the large non-uniform, two-dimensional pH distribution induced by CO 2 dissolution. A sheet laser beam was provided by a YAG laser and the two-dimensional LIF intensity was detected by an image-intensified CCD diode-array camera.

SIMULTANEOUS HEAT and MASS TRANSFER DURING the DEEP FAT FRYING of TORTILLA CHIPS

The heating and water loss of a single tortilla chip during deep fat frying was investigated experimentally and the data were analyzed by writing two heat and mass transfer balances. the equations were solved using explicit finite difference technique. Oil uptake as a function of frying time was described by a first order exponential equation. the empirical and theoretical heat and mass transfer agreed well.The effect of oil temperature on the moisture loss and oil uptake as a function of frying time was analyzed. Moisture loss rate increased as temperature increased. the effects of temperature on oil uptake were not significant during the first 15 s of frying, however, the final oil content was higher for the tortilla chip fried at 190C than at 150C for 60 s.

Sulfur vs. silica retention in oligotrophic lake sediments: Test of a simple residence time model

Limnologists have modeled solute retention (% of input) in lake sediments using the parameter: 100 k s {(z:t w +k s}−1, wherek s is an empirical mass transfer coefficient or ‘sedimentation velocity’ (m yr−1), z is lake mean depth (m), andt w is lake hydraulic residence time (yr). This flushing or residence time model was tested against sulfate and silica concentrations in lakes of the northeastern and northcentral U.S.A., using data collected during the U.S. EPA's Eastern Lake Survey. This parameter failed to predict intra-regional variations in lake sulfate at fall turnover, but was consistently negatively correlated with silica in each of the regional lake populations. However, except in the western section of the Upper Peninsula of Michigan, lake sulfate was everywhere inversely dependent on DOC [mean slope=−0.020(SE=0.03) meq mM−1]. Sulfur retention in aquatic environments appears more closely coupled to organic carbon and trophic state, than to variations in hydraulic residence time.

Fundamental aspects of high-temperature corrosion

Some recent considerations in three widely different aspects of high-temperature corrosion are summarized: 1) reactions at the metal/scale interface in support of scale growth; 2) mass transfer effects in the control of evaporation of volatile reaction products; and 3) the codeposition of multiple elements for diffusion coatings using halide-activated cementation packs. The climb of misfit edge dislocations from the metal/scale interface can achieve the annihilation of vacancies associated with scales grown by cation diffusion. For scale growth at the metal/scale interface by anion diffusion, the creation of anion vacancies occurs by the climb of misorientation dislocations. For cation-diffusing scales, a blocking of the vacancy annihilation reaction may be achieved by the specific adsorption of reactive elements at the metal/scale interface. The pinning of the interfacial misfit dislocations by segregated reactive elements can explain the changes in growth mechanism, in growth stresses, and in reaction kinetics associated with the reactive element effect for the growth of chromia scales on alloys. Although the vapor pressures of volatile species are readily calculated from available thermodynamic data, the use of these values to predict the kinetics of transport-limited evaporation has not been presented specifically for various substrate geometries and differing flow conditions. The empirical mass transfer relations are evaluated and plotted for the flat plat and tube geometries in the laminar and turbulent flow regimes. A criterion for the stability of a flat interface in selective evaporation from an alloy is still lacking. Despite the inherent difficulty to codeposit two or more elements with greatly differing thermodynamic stabilities for their halide species, cementation coating packs can be designed with selected combinations of powdered masteralloys and halide activator salts whereby elements are codeposited to yield a desirable surface composition. Selected examples for effective aluminizing/chromizing of Ni-base superalloys and for chromizing/siliconizing of steels are presented

Use of temporal moment analysis to study reactive solute transport in aggregated porous media

The paper presents an overview of the use of temporal moment analysis as a useful alternative to more complete analytical or numerical solutions of mathematical models describing adsorbing solute transport in aggregated, saturated porous media. The goal of temporal moment analysis is to derive analytical formulas for the lower-order time moments of the solute breakthrough curve, thereby yielding significant physical insight into the behavior of solute transport models. Only the bi-continuum conceptual model and one-dimensional systems are emphasized in this paper. The transfer function approach for calculating temporal moments is described and illustrated with several examples involving diffusion into spherical aggregates, first-order mass transfer, and kinetically controlled intra-aggregate adsorption. The use of moment analysis for model comparison and sensitivity analysis is discussed; in particular, the paper shows how simplified empirical first-order mass transfer models can be utilized to approximate more complex models involving diffusion into nonuniformly sized spherical aggregates.

Equilibrium and Rate Data for the Extraction of Lipids Using Compressed Carbon Dioxide

Abstract Equilibrium data are given for the solubilities in compressed C02 of the lipid components in freshly ground rape seed and of glycerol trioleate (a typical constituent of rape oil) at pressures up to 200 bar and temperatures 25 to 75C. Continuous flow tests in which a bed of ground rape seed was contacted with a stream of liquid CO2 at 25C and varied flow conditions are also reported. The results are collated in terms of an empirical mass transfer coefficient. A sharp change took place in the lipid concentration in the extractant stream leaving the bed when about 65% of the available oil had been extracted. This, and changes in the composition of the extract, are discussed, together with the use of this type of data for design purposes.

A comparison of the Bond method for sizing wet tumbling ball mills with a size—mass balance simulation model

A comparison is made of the results from a ball mill model simulation with those of the conventional Bond ball mill design method, for a material whose breakage characteristics and Work Index have been determined. In order to perform the simulation, ‘normal’ values were chosen for make-up feed size distribution, mill residence time distribution, ball mix, classifier behaviour, etc. At high flow rates through a mill (low reduction ratio), it is necessary to allow for the reduction in breakage rates caused by over-filling of the mill, using an empirical mass transfer relation: filling ▪. By suitable choice of the constant in this relation, it was found possible to duplicate the variation of mill capacity with feed size and product size (in wet closed-circuit grinding) predicted by the Bond method. The simulation model is then used to predict the variation of performance with design variables not included in the Bond method.

Mass transfer in turbulent pipe flow of viscoelastic fluids

The mass transfer entry length and maximum mass transfer reduction asymptote for dragreducing viscoelastic fluids have been calculated analytically using the successive approximation technique. The eddy diffusivity of mass reported by Shulman et al. [10] and Virk's velocity profile corresponding to the maximum mass transfer reduction in turbulent pipe flow were applied to the present analysis. The mass transfer entry length for these fluids was found to be 8–40 pipe diameters depending on the Reynolds number. The predicted mass transfer rates for these fluids are in good agreement with available empirical mass transfer results, which show approximately 65–75% reduction in the mass transfer rate compared to the Newtonian values at the same Reynolds and Schmidt numbers. A comparison of these mass transfer results with available heat transfer measurements leads to the conclusion that there is no simple direct relationship between heat and mass transfer for drag-reducing viscoelastic fluids.

Experimental and Mathematical Description of Nonadsorbed Solute Transfer by Diffusion in Spherical Aggregates

AbstractDiffusion of nonadsorbed solutes (3H2O and 36Cl‐) out of two sizes of porous ceramic spheres (0.55‐ and 0.75‐cm radius) was measured. These data were analyzed to provide independent estimates of the input parameters required in two simulation models for describing solute transport in aggregated porous media with distinct mobile and stagnant pore‐water regions. Tracer‐saturated porous spheres were placed in tracer‐free 0.01N CaCl2 solution and the rate of tracer diffusion out of the porous spheres was measured by monitoring the increase in tracer concentration with time in the external electrolyte solution. Experimental results were analyzed using two mathematical models. Fick's second law, written in spherical coordinates, formed the basis for Model I. In Model II, the time‐rate of solute transfer into or out of the porous spheres was assumed to be proportional to the difference in tracer concentration inside and outside the porous spheres. The analytical solution to Model I for given initial and boundary conditions was substituted into Model II, to derive an explicit expression relating the empirical mass transfer rate coefficient (α) in Model II and known physical constants of the system. This theoretical analysis indicated that the α value is dependent upon the sphere radius, time of diffusion, volumetric water contents inside and outside the sphere, and the molecular diffusion coefficient. Over a range of experimental conditions, excellent agreement was found between measured α values and those calculated using the analytic expression developed here.

A turbulent flow theory of electrodialysis

A hydrodynamic theory is presented of desalination by electrodialysis in a parallel channel system with unobstructed fully developed turbulent flow. A set of turbulent transport equations is derived for the mean salt concentration and electric field. Closure of the set is brought about by introducing a turbulent diffusion coefficient whose behavior is assumed known from empirical mass transfer considerations, and by making two different but phenomenologically reasonable assumptions about that part of the average ion flux which is due to the correlation between the concentration and electric field fluctuations. Estimates show both assumptions to lead to sensibly the same final results. From the equations and boundary conditions it is shown that there are five parameters which govern the system performance. Four are the same as for the corresponding laminar case, while the fifth measures the thickness of the concentration diffusion sublayer, the value of which is taken to be given by semi-empirical turbulent mass transfer results for high Schmidt numbers. The thickness of this diffusion layer is found to be the critical factor governing the salt removal rate. An integral method of solution is used to obtain the distributions of salt concentration and current density. A numerical quadrature is required for the complete solution. Analytic solutions are obtained in the unpolarized and fully polarized limits. Because of the very abrupt transition between these two limits, taken together the limiting analytic solutions are adequate to describe the system performance over the entire range of operating variables. For small fractional salt removal a universal correlation for the average current density embodying the five similarity parameters of the system is suggested based on the limiting solutions. Comparison of the theory is made with the experimental results of Cowan and Brown on average limiting current density and the agreement is found to be satisfactory.