Gas Absorption Rate Research Articles

THE ENHANCEMENT OF GAS ABSORPTION BY A HETEROGENEOUSLY CATALYSED CHEMICAL REACTION IN A STAGNANT LIQUID: TEMPERATURE RISE AND EFFECTIVENESS OF THE CATALYST

Abstract In the present paper a model has been developed to calculate the enhancement efficiency e of the gas absorption and the effectiveness factor η of the catalyst for a chemically reacting system consisting of a sedimented catalyst particles-containing layer of thickness γk adhering to the surface of a gas bubble situated in a stagnant liquid. This model predicts that for a heterogeneously catalysed first-order chemical reaction an increase in the thickness γk of the catalyst particles-containing layer will result in an increase of ε and a decrease of η. It has been shown that the optimum value (γk)opt of this layer can be obtained from the relation (γk) = (DAB/k 13). Further, a model is derived to calculate the steady-state temperature profile in the catalyst particles-containing layer adhering to the gas bubble surface. Both models have been applied to experimental results published in some of our previous papers. These experimental results concern the enhancement of the gas-absorption rate from a single hydrogen-containing gas bubble to a stagnant aqueous hydroxylaminephosphate-containing solution when a layer of sedimented Pd/C catalyst particles was adhered to the surface of the gas bubble. The model and the experimental results mentioned may approximately be considered as representative of slurry reactors in which finely divided catalyst particles show considerable adhesion to rising gas bubbles. KEYWORDS: AbsorptionCatalysis Additional informationNotes on contributorsO. J. WIMMERSCurrent address: Philips Research Laboratories Eindhoven, P.O. Box 80000, 5600 JA Eindhoven, The Netherlands.J.M.H. FORTUINTo whom correspondence should be addressed.

Gas absorption into a slurry accompanied by chemical reaction with solute from sparingly soluble particles

A model has been developed which represents gas absorption into a slurry accompanied by chemical reaction with solute from sparingly soluble fine particles. The rate of absorption into a slurry seemed to be higher than that into a saturated solution containing no reactive particles, as reported previously by others; but our theoretical estimates disagreed with previous results, especially under conditions of instantaneous reaction. A characteristic length determined geometrically by the size and concentration of the particles is a factor in estimating the effect of particle dissolution on the rate of gas absorption, but the mass transfer coefficient for particle dissolution need not be known.

Mixing and Mass Transfer Phenomena in Bottom-Injected Gas–Liquid Reactors

AbstractExperimental measurements of mixing time and mass transfer coefficients were undertaken in an aqueous flow model.The purpose of the work was to determine the effect of a bottom-injected gas jet, at different flowrates and for various porous plug and orifice injectors, on the mixing intensity and gas-liquid mass transfer in the bath. The measurements of mixing time were compared with calculations based on the Sahai-Guthrie equations describing the velocity field in such systems. The effect of injection conditions on the rate of mass transfer between a carbon dioxide jet and an aqueous solution of sodium hydroxide was investigated in the safne model. It was found that at low gas flowrates, porous plug injection results in much higher rates of gas absorption, probably due to the formation of finer bubbles and attendant higher interfacial area.

Mixing and Mass Transfer Phenomena in Bottom-Injected Gas–Liquid Reactors

Experimental measurements of mixing time and mass transfer coefficients were undertaken in an aqueous flow model.The purpose of the work was to determine the effect of a bottom-injected gas jet, at different flowrates and for various porous plug and orifice injectors, on the mixing intensity and gas-liquid mass transfer in the bath. The measurements of mixing time were compared with calculations based on the Sahai-Guthrie equations describing the velocity field in such systems. The effect of injection conditions on the rate of mass transfer between a carbon dioxide jet and an aqueous solution of sodium hydroxide was investigated in the safne model. It was found that at low gas flowrates, porous plug injection results in much higher rates of gas absorption, probably due to the formation of finer bubbles and attendant higher interfacial area.

OPERATION POLICIES FOR A GAS—LIQUID STIRRED TANK REACTOR

The operation of a gas-liquid stirred tank reactor is simulated, including batch operation, steady and unsteady state, continuous operation and cyclic variable volume operation. A pseudo first order reaction is considered. Analytical expressions for the enhancement factor of gas absorption rate are derived for each case, and productivity obtainable under different operation policies is evaluated. Results obtained are shown graphically for specific cases for the purpose of demonstrating the influence of some of the parameters on the system The equations as presented can be easily extended to other kinetics, and serve as a useful guide for optimum operational policies in a gas-liquid stirred tank reactor.

Rates of gas absorption from single gas bubbles

Rates of gas absorption from single gas bubbles

Estimation of rates and enhancement factors in gas absorption with zero-order chemical reaction and gas-phase mass-transfer resistances

The governing differential equation for gas absorption in laminar falling film with zero-order homogeneous chemical reaction and finite gas-phase mass transfer resistances is solved analytically by the method of separation of variables and subsequent solution with confluent hypergeometric function. The results for concentration profile, gas absorption rate, and enhancement factor are presented for various reaction rate and mass transfer resistance parameters.

Design calculations for countercurrent gas-liquid reactors

A mathematical model has been developed for a countercurrent differential contactor in which a gas-liquid reaction occurs. The local mass transfer rates near the gas-liquid interface are computed from a stagnant film model that includes a second-order reaction term. The contactor model accounts for enhancement of the gas absorption rate as well as the contributions to liquid reactant conversion from both the boundary layer region and the bulk liquid. Orthogonal collocation based on Lobatto polynomials has been used to solve the nonlinear equations for both the local mass transfer rates and the macroscopic differential mass balances. Parametric studies indicate that the number of transfer units, the chemical reaction kinetics and the absorption factor all play important roles in determining reactor performance. Collocation techniques are also employed to solve the design equations that include liquid-phase axial dispersion in the countercurrent gas-liquid reactor. These techniques have been found to be sufficiently efficient and robust that they should be useful for reactor design and parameter estimation applications.

Enhancement of gas absorption rate as a function of the particle size in slurry reactors

Exact relationships are given for the enhancement of gas absorption rate as a function of particle size in a three-phase slurry reactor. The solid-liquid mass transfer in the liquid film at the gas-liquid interface is considered as a transfer through spherical surface. The solid phase is the catalyst or reactant. The enhancement of the gas absorption rate calculated by the given equations are in very good agreement with the experimental data as a function of particle size and solid phase concentration.

Nonisothermal gas absorption with chemical reaction

AbstractThe temperature rise at a gas‐liquid interface due to heat evolution and the relevant enhancement factor for gas absorption rate are analyzed for absorption, with an instantaneous irreversible reaction and with a first‐order irreversible reaction allowing for the temperature dependence of the major physicochemical properties. The analysis reveals that, unlike isothermal absorption, the film theory solutions with the replacement of any system parameters do not give a reasonable approximation to the realistic penetration theory solution, except in the case of the physical absorption regime. However, the modified Danckwerts analysis, in which the physicochemical properties are evaluated at the time‐averaged interface temperature, is shown to be useful in obtaining the approximate penetration theory solutions with satisfactory accuracy.

KINETICS OF ABSORPTION OF OXYGEN INTO AQUEOUS SOLUTIONS OF SODIUM SULPHIDE CONTAINING FINELY POWDERED ACTIVATED CARBON IN A SLURRY REACTOR

The oxidation of sodium sulphide solutions containing finely powdered activated carbon by gaseous oxygen was investigated in order to clarify the role of catalyst particles which were considerably smaller than the liquid-film thickness. Experiments were conducted in a stirred cell with an unbroken interface, at a temperature range of 288-308 K, and at atmospheric pressures. The system was found to have a complex nature, exhibiting first an initial induction, then a constant reaction rate and finally a catalyst poisoning periods. Only the constant gas absorption rate period, was analysed quantitatively and depending on the conditions, an enhancement factor of up to 12 was observed, which was, however, unaffected by the catalyst loadings exceeding a certain value. The reaction was found to be half order in oxygen and first order in sulphide ion, and had an activation energy of 23.2 kcal/mol.

KINETICS OF OXIDATION OF AQUEOUS SODIUM SULPHIDE SOLUTIONS BY GASEOUS OXYGEN IN A STIRRED CELL REACTOR

The oxidation of aqueous sodium sulphide solutions (0.13-1.00 kmol/m3) by pure oxygen at atmospheric pressure was studied in a stirred cell with an unbroken interface. The temperature ranged between 278-308 K and the pH was maintained at 13 by using 0.6 kmol/m3 sodium hydroxide. Gas absorption rate measurements were analysed using Danckwerts' plots in order to obtain reaction kinetics data. Results showed that the reaction rate followed first order kinetics with respect to both oxygen and sulphide concentrations and had an activation energy of 14.07 kcal/mol.

A Water Radiolysis Model in a Circulating Flow System with a Boiling Region and Its Application to Hydrogen Alternate Water Chemistry of Boiling Water Reactors

A gaseous mass transfer model has been proposed for quantitative evaluation of the chemical chain-back reaction system with volatile species in a boiling channel. Theoretical expression for concentration transients in liquid and vapor phases were obtained. The model was applied to water radiolysis in a boiling water reactor core channel with Bankoff's two-phase flow treatment. Hydrogen injection tests in the Oskarshamn-2 and Dresden-2 units were simulated. The calculated results showed that gas release and absorption rates in the boiling channel were not consistent with Henry's law. By using optimized parameters related to the gaseous mass transfer, calculated results agreed within a factor of 2 for lower hydrogen injection rates at the two plants. It was determined that more exact treatments are needed to determine the radiation level in the downcomer and catalytic decomposition rate of hydrogen peroxide in order to provide better evaluations of water radiolysis phenomena.

Absorption of carbon dioxide into aqueous methyldiethanolamine

Gas absorption rates in a laminar liquid jet were measured for carbon dioxide in methyl- diethanolamine (MDEA) solutions. It was found that for the short contact times (<0.012s) of these absorption experiments there is only a small effect of any reaction between carbon dioxide and MDEA. Solubilities and molecular diffusivities for carbon dioxide in aqueous MDEA are estimated from measurements with nitrous oxide. The absorption rate data are described well using the solubilities and diffusivities measured in this work. Solubilities were measured over the temperature range 15 to 35°C and for MDEA concentrations up to 40%. Diffusion coefficients and viscosities were measured over the same temperature range and MDEA concentrations up to 20%.

ENHANCEMENT FACTOR OF GAS ABSORPTION ACCOMPANIED BY REVERSIBLE CYCLIC CHEMICAL REACTIONS

Theoretical effect of mass transfer by reversible cyclic chemical reactions is studied in this paper. On the basis of the film theory, an analytical equation has been derived to express the enhancement factor of gas absorption with first-order reversible cyclic chemical reactions. The finite difference method has been used to study the enhancement of gas absorption with second-order reversible cyclic reactions. The results indicate that the gas absorption rate is enhanced by the forward reaction rate, while is suppressed by the backward reaction. Although the diffusivity has some effects on enhancement factor, the influence is not as much as that of reaction rate. The theoretical equations are used to predict the enhancement factors for absorptions of carbon dioxide in acidic solution and l-butene in liquid phosphoric acid.

The diffusion of CO2, CH4, C2H4, and C3H8 in polyethylene at elevated pressures

AbstractDiffusion and solubility coefficients have been determined for the CO2−, CH4−, C2H4−, and C3H8‐polyethylene systems at temperatures of 5, 20, and 35°C and at gas pressures up to 40 atm. Diffusion coefficients were obtained from rates of gas absorption in polyethylene rods under isothermal‐isobaric conditions by means of a new diffusivity apparatus. The concentration dependence of the diffusion coefficients was represented satisfactorily by Fujita's free‐volume model, modified for semicrystalline polymers, while the solubility of all the penetrants in polyethylene was within the limit of Henry's law. Semiempirical correlations were found for the free‐volume parameters in terms of physicochemical properties of the penetrant gases and the penetrant‐polymer systems. These correlations, if confirmed, should permit the prediction of diffusion and permeability coefficients of other gases and of gas mixtures in polyethylene as functions of pressure and temperature.

Gas absorption by single charged drops during their formation in a uniform electric field

A new technique for measuring gas absorption rates during the formation of liquid drops was devised. By the technique, the amount of carbon dioxide absorbed during the formation of single charged drops was measured in the presence of a uniform electric field. Also the relationships between the surface area of the drop, its volume, and the time for one cycle of the growth of the drop were obtained using a TV system. The mass transfer rates are discussed by taking account of the surface area of the drop being formed in the electric field. It is clarified that the mechanism of gas absorption during drop formation is explained satisfactorily by the surface-stretch penetration model of Angelo et al., not only for uncharged drops but also for charged drops formed in the electric field.

Leaching in a bubble‐column slurry reactor

AbstractExperimental leaching runs were carried out in a continuous concurrent laboratory size bubble column 5.2 cm in internal diameter and 2.90 m tall. The system studied was the dissolution of a synthetic covellite (CuS) in ammoniacal solution in the presence of pure oxygen. Behaviour of the column with respect to gas holdup and solids concentration profiles was measured without reaction by using nitrogen in place of oxygen. Gas holdup values were in agreement with literature results. However, solids concentration profiles for the mixed particle size solid used were of a more complex nature than those obtained for uniformly sized solids.Conversions obtained at various temperatures and gas and liquid velocities were analyzed in terms of the estimated rates of the individual rate processes occurring. From these results, gas absorption rate was clearly the controlling mechanism at high temperatures, and surface chemical reaction rate was controlling at low temperatures. Hence, the rate controlling steps can be identified in bubble column reactors from currently available literature correlations, together with independent kinetic measurements.

Statistical rate theory of interfacial transport. II. Rate of isothermal bubble evolution in a liquid–gas solution

The statistical rate theory approach is used to derive the expression for the rate of gas absorption by a liquid. This process involves two sequential rates−the rate of transport from the gas to the surface and the rate of transport from the surface to the bulk liquid. According to the statistical rate theory, the rate limiting step is the rate of transport from the surface. After deriving the rate expression for the rate limiting step, it is incorporated in an integral equation approach for predicting the rate of evolution of a bubble evolving isothermally in a liquid–gas solution. This approach accounts for the movement of the bubble boundary in the diffusion problem. Statistical rate theory leads to a complete expression for the rate of gas absorption; thus by comparing the predicted rate of bubble evolution with a set of measurements, one can investigate the validity of the statistical rate theory. This comparison is carried out and the predictions are found to be in close agreement with the experiments throughout the experimental period.

Rates of gas absorption into molten salts

Rates of gas absorption into molten salts