Vladimír Rod

Iterative estimation of model parameters when measurements of all variables are subject to error

Abstract An iterative method is described for parameter estimation when all model variables are measured with an error. The method is based on the principle of maximum likelihood and the assumption of normally distributed errors; it leads to estimates both of model parameters and of the true values of measured variables. The iterative calculations involved utilize a standard optimization subroutine. The sequence of calculations is illustrated by a block diagram and demonstrated on two case studies.

Mass transfer cell with vibrational mixing

Abstract A new simple cell with a flat interface has been developed for mass transfer measurements in liquid—liquid systems. Mixing in both phases is performed by vibrating plates. The specific interfacial area can be varied by changing the phase volumes. Turbulence in the vicinity of an essentially flat interface can be affected independently by frequency, amplitude and the distance of the plates from the interface. The influence of these variables on the mass transfer coefficient was investigated in the n-butanol—water and cyclohexanone—water systems. The data obtained were compared with a model developed by assuming the validity of Kolmogorovs theory of local isotropic turbulence and by using the results of von Karman and Lin on the decay of turbulence behind a grid and the results of Bulicka and Prochazka on turbulence transfer across the interface. The cell is suitable for studies of mass transfer accompanied by a chemical reaction.

Break-up of a drop in a stirred tank

Abstract The drop break-up mechanism was studied in a stirred tank containing two immiscible liquids. The daughter drops formed by break-up of a single drop of known size were recorded photographically. From the experiments at constant agitator speed the following results were obtained. There is a critical drop size under which drops do not break up under given conditions. The break-up frequency increases approximately linearly with increase in drop volume. The number of daughter drops, v , is a random variable with a mean v > 2 which increases with the volume of the mother drop. The relative volume of a daughter drop has a β-distribution.

Correlation of equilibrium data in ternary liquid—liquid systems

Abstract Equilibrium data of ternary liquid—liquid systems can be correlated in the form of distribution coefficients for the individual components as functions of solute concentration. A simple form of the correlating function is proposed common to all components. The method of equilibrium calculation and the estimation of the parameters of the correlating equations are described. The proposed correlation of equilibrium data is illustrated using selected systems with open and closed binodal regions.

Unconventional extraction—stripping flowsheets for the separation of metals by liquid—liquid extraction

Abstract A general method is presented for the simultaneous calculation of the extraction and stripping sections of a liquid—liquid extraction process using various solvent flow arrangements. Flowsheets with cross-flow of solvent between the sections are compared with those of the conventional countercurrent flow arrangement. The calculations carried out indicate that the flowsheets with solvent cross-flow are more efficient, as they allow achievement of the same degree of separation with lower solvent flow rates. The advantage of this particular arrangement, which can be easily implemented with pump—mix mixer settlers, manifests itself mainly for non-linear equilibria which are common in metal extraction systems. In addition, solvent cross-flow offers the possibility of optimizing solvent flow rates and extractant concentrations in separate circulation loops.

DIFFUSIVITY DETERMINATION FROM THE RESPONSE TO INJECTION INTO LAMINAR LIQUID FLOW IN A CAPILLARY

A method for the determination of diffusivities in liquids is described; the method is based on measurements of the response to injection in a laminar flow of liquid in a capillary. By injection of δ-type, the component whose diffusivity is to be measured is introduced into the inlet part of a capillary of internal diameter 1.6 mm. The response to the injection is measured at the end of the capillary by a flow-through refractometer, the output signal of which is recorded on tape at 16-s intervals. The output signal is compared with a theroetical model of the time dependence of the response, based on Taylors analysis of the dispersion of an injected component in laminar flow. The diffusivity is calculated from one of the model parameters, which were evaluated by the method of maximum likelihood. The calibration of the instrument was performed by measuring the diffusivity of KC1 in aqueous solution. The following diffusivities at 25°C were determined: n-butanol 971 μm2/s, dioxane 1093μm2/s, caprolactame 94...

Kinetics of Metal Extraction by Chelate Formation Part II. Extraction of Cu(II) by Hydroxyoximes

Abstract The rate of extraction of copper from aqueous solutions by chelate-forming extractants was examined. Two extractants based on hydroxyoximes (salicylaldoxime dissolved in chloroform, and the commercial extraction agent LIX-64N dissolved in kerosene) were used. Experiments were carried out in a mass transfer cell with vibrational mixing of the phases. The conclusions arrived at are as follows: the model of mass transfer accompanied by a fast reversible reaction describes well the integral data obtained. The reaction rate is influenced significantly by the rate of diffusion of the extractat in the organic phase, as well as by the rate of formation of the extractable complex, and possibly also by the rate of copper diffusion towards the interface in the aqueous phase.

Mass transfer in a heterogeneous chemical reactor with two liquid phases

Abstract An important step in the design of a reactor for two liquid phases, with a rapid chemical reaction taking place in both phases, is the calculation of mass transfer rates of reaction components. Relations are presented and a calculation algorithm described which enable the determination of the interfacial molar fluxes of reaction components in systems where irreversible chemical reaction of general order proceeds at both sides of the interface.

Combination of resistances to mass transfer between a drop and an ambient liquid

Abstract A modified relationship of resistance additivity is used to express the rate of mass transfer between a drop and an ambient liquid for the case of comparable resistances at both sides of the interface. The time-varying resistance at the droplet side is expressed as a product of the limiting resistance and a correction factor. Approximate relations derived for the calculation of the correction factor are compared with accurate solutions for models of rigid, circulating and turbulent drops.

Analysis of extractor performance. III. Longitudinal mixing in the dispersed phase

Abstract Residence time distribution of the dispersed phase in column apparatusses is influenced by two different effects — backward and forward mixing. The interaction of these effects with the drop vertical velocity distribution and with the intensity of drop coalescence has been the cause of inadequate and unreliable information on this topic. A model has been developed to describe this complex phenomenon, based on statistical concepts and making use of the knowledge of the holdup profile in the column. The application of this model to data from a pilot extractor has provided data on the effects mentioned above and revealed the importance of the wetting of the column walls by the dispersed phase, of the sensitivity of coalescence intensity and of the probability of existence of a dead water region in the dispersed phase.