Method of electrodialysis stack testing with the feed solution concentration regulation

A technique to test electrodialysis (ED) stacks designed to desalt dilute solutions is developed. The technique permits obtaining reproducible data on laboratory and medium-scale units useful for predicting mass transfer characteristics of large ED stacks. Quasi-steady state of desalination process is the main condition to obtain such data. This state can be attained by applying recycling hydraulic modes and special devices to maintain constant pH, or pH and concentration of the feed solution. To obtain data for scaling, it is necessary to apply a fixed voltage on the stack and to use a constant flow rate of the feed solution during the experiment, the feed solution concentration may vary with the time. Specifications of the stacks studied, rational hydraulic and electrical modes of testing are considered.     

Vapour- and liquid-side volumetric mass transfer coefficients measured in distillation column. Comparison with data calculated from absorption correlations

Volumetric mass transfer coefficients in liquid and vapour phases in distillation column were measured by the method consisting of a fitting of the concentration profile of liquid phase along the column obtained by the integration of a differential model to the experimental one. The mathematical model of distillation process includes mass and energy balances and the heat and mass transfer equations. The film model flux expressions with the convective transport contributions have been considered in the transfer equations. Vapour and liquid phases are supposed to be at their saturated temperatures along the column. Effect of changes of phase flows and physical properties of phases on the mass transfer coefficients along the column and non-ideal thermodynamic behaviour of the liquid phase have been taken into account. The concentration profiles of liquid phase are measured in the binary distillation of the ethanol-water and methanol-ethanol systems at total reflux on metal Pall Rings and Intalox saddles 25 mm in the column with diameter of 150 mm. The distillation mass transfer coefficients obtained by the fitting procedure are compared with those calculated from absorption data using Onda's, Billet's and Linek's correlations. The distillation heat transfer coefficients calculated from the model assuming saturated temperatures in both phases are compared with those calculated from the Chilton-Colburn and penetration model analogy between mass and heat transfer. The results have confirmed an agreement neither between distillation and from absorption correlations calculated mass transfer coefficients nor between analogy and from enthalpy balance calculated heat transfer coefficients. Also the concentration profiles obtained by the integration of the differential model of the distillation column using the coefficients from absorption correlation have differed from the experimental profiles considerably.     

APPLICATION OF LINEARIZED MODELS OF MULTICOMPONENT MASS TRANSFER FOR CALCULATION OF EVAPORATION-CONDENSATION PROCESS IN TERNARY SYSTEMS

Results of calculations based on a linearized multicomponent mass transfer theory developed by Burghardt and Krupiczka are compared with experimental data of Modine for condensation-evaporation process in ternary systems. These data have been obtained for acetone-benzene-nitrogen and acetone-benzene-helium in a welted wall column. Models I and II, which take into account diffusional interactions of components in a mullicomponent mixture show good agreement with the experiments as well as with other calculation methods (Krishna-Standart and Toor-Stewart-Prober). When multicomponent mass transfer occurs in the presence of inert species, a straightforward Model II is recommended. Model I, which is more universal, requires some iterative calculations with respect to the sum of mass fluxes. According to theoretical considerations the latter model is limited to the case of low total mass flux. The results of calculations for the systems studied were reasonably good though the total mass fluxes were not small. The calculation procedure based on the presented linearized models are convergent to the proper solutions in contrast to the Krishna-Standart Model IV which in some cases can be unstable.     

Catalyst surface at a fractal of cost—a quest for optimal catalyst loading

Intuition tells us that any decrease in the catalytically active surface area should result in an equivalent decrease in the reaction yield and efficiency. Our findings counter this by showing that the active surface and hence the catalyst loading can be reduced drastically in the diffusion-limited heterogeneous reaction systems, while the conversion rate remains essentially unchanged by using fractals for spatial distribution of the catalyst load. The results of this study provide an unusual circumstance for optimal design of chemically active surfaces and can be used to drastically reduce cost of heterogeneous chemical and biological reactors, sensors, and electrodes of fuel cells. The proposed approach can be exploited to its fullest extent in chemical microsystems by utilizing the latest advances in our abilities to manipulate matter on the micro/nano scale.     

Development of a comprehensive free radical photopolymerization model incorporating heat and mass transfer effects in thick films

A comprehensive kinetic model describing photopolymerization is developed which allows variation of temperature, species concentrations, and light intensity through the thickness of a photopolymerized film. Heat and mass transfer effects are included, as is the generation of heat by both reaction and light absorption. In addition to initiation, propagation, and termination mechanisms, both primary radical termination and inhibition are incorporated into the model. The possible presence and diffusion of an inert solvent are also accounted for. Thus, the model is useful for examining complex polymerization kinetics and behavior in industrially and commercially important thick film photopolymerizations, such as the curing of contact lenses, dental restorative materials, photolithographic resists, and optoelectronic coatings. The comprehensive model is used to predict polymerization rate, temperature, and conversion profiles in a variety of systems. The effects of heat generation and the thermal boundary conditions are explored, with the result that heat generation in thick samples leads to greatly increased conversions approaching 100 percent. Increased temperature in these samples also may lead to the appearance of two rate maxima, with the first due to the temperature increase and the second caused by the autoacceleration process. The magnitude of the temperature increase, along with the resultant effects, is more pronounced in insulated systems.     

An analytic solution to the transient diffusion-reaction problem in particles dispersed in a slurry reactor

In this work, we present the solution of the equations that govern the reactant transport in a well mixed system that contains particles where diffusion and first-order reaction occur. The transport equations are coupled by an interfacial boundary condition that includes mass transfer resistance. The statement of the problem allows arbitrary time depending feed functions. The evaluation of the solution obtained by the Laplace method requires the solution of an eigenvalue problem. We discuss the evaluation of the solution, and typical results for three different feed functions: step, pulse and oscillatory functions are presented. The resulting equations are able to show the effect of internal and external mass transfer limitations on the particle and fluid concentrations and on kinetic experimental results.     

Modelling of batch fluidised bed drying of pharmaceutical granules

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control.     

LIQUID PHASE TRANSPORT PROPERTIES IN A HIGH PRESSURE PACKED COLUMN

A mathematical model of fluid flow and mass transfer in a packed bed was derived and used to evaluate the liquid phase axial dispersion and mass transfer coefficients under high pressure conditions. The least-squares method was used to evaluate the rate parameters from experimental breakthrough curves, and the agreement between the concentration curves predicted from rate parameters and those measured experimentally was good. Experiments were performed at 20 and 200°C with water as a solvent and nonporous soda-lime glass beads as packing. Although the axial dispersion coefficient was independent of temperature and pressure, the mass transport parameters were found to be pressure dependent.     

OXIDATION OF SULFUR DIOXIDE IN DIFFERENT TYPES OF THREE PHASE REACTORS

Five different types of three-phase reactors are compared with each other by using oxidation of sulfur dioxide on activated carbon. The kinetic measurements were carried out by changing concentrations of sulfur dioxide from 0.04 to 0.17% (volume) and those of oxygen from 2 to 21%. The reaction rate was 0.2 order with respect to sulfur dioxide and 0.5 order with respect to oxygen. The catalytic effectiveness factor and intraparticle diffusivity were evaluated by changing particle sizes of activated carbon from 0.03 to 1.6 mm. Resistances of gas-liquid, liquid-solid mass transfer and intraparticle diffusion were estimated for individual reactors. The optimum reactor was dependent on operating conditions such as gas flow rates, rotating speeds and particle sizes.     

Errors associated with swelling in the analysis of polymer-solvent diffusion measurements

Sorption curves are generated from a mathematical model which includes the influence of the polymer swelling for unsteady-state sorption of a vapor or liquid by a polymer. To investigate the simultaneous effects of the specific volumes of the polymer-penetrant pair and the difference between the final and initial equilibrium concentrations on the sorption curves, statistical experimental design approach is used. Simulation results obtained from the numerical solution of model equations are utilized to estimate the error that would occur if one simply evaluates the diffusion coefficient using the traditional formulas derived from the analytical solution of the sorption equation. An empirical expression is developed that describes the effects of the difference between the final and initial equilibrium concentrations and the specific volumes of the polymer and the penetrant on the magnitude of error in diffusivity associated with the use of one of these traditional formulas so called the initial slope method. The predictive ability of the regression model is tested by performing additional simulations not used in the regression analysis.