Single-pellet Moment Technique Research Articles

Fifty Years of Moment Technique for Dynamic Analysis of Chemical Reactor Parameters

Abstract Moment technique has been extensively used for the evaluation of the rate and equilibrium parameters in chemical reactors and also in adsorption vessels, for about five decades. Adsorption and reaction rate parameters, as well as axial dispersion constants, effective diffusivities within porous catalysts and heat and mass transfer coefficients were shown to be effectively evaluated by analyzing the moments of the response peaks, which could be obtained from pulse-response experiments performed in a reaction/adsorption vessel. A detailed review of chromatographic processes, involving moment analysis of adsorption equilibrium and rate constants in fixed beds, dynamic analysis of batch adsorbers, moment analysis of fluidized bed, slurry and trickle bed reactors are reported in this manuscript. Applications of the single-pellet moment technique, which was developed for the effective investigation of intrapellet rate and equilibrium processes, by eliminating the contributions of axial dispersion and external transport parameters, are comprehensively discussed. Recent studies for the analysis of reaction rate parameters using the TAP reactor approach, use of single pellet system for the investigation of catalytic and non-catalytic solid-gas reactions and extension of the moment technique to non-linear systems opened new pathways in reaction engineering research.

Effective diffusion constant and adsorption constant of synthesized alumina, zirconia, and alumina–zirconia composite material

ABSTRACTIn this study, Al2O3, ZrO2, and Al2O3–ZrO2 composite materials were prepared with the sol–gel technique. X-ray diffraction analysis, differential scanning calorimetry–thermogravimetry, scanning electron microscopy–energy-dispersive X-ray spectrometry, nitrogen adsorption isotherm measurements, and helium pycnometry were used to characterize the resultant materials. Effective diffusion coefficients of helium and hydrogen and the adsorption equilibrium constant of hydrogen in the resultant materials were determined using single-pellet moment technique. The effective diffusivities of helium and hydrogen in both ZrO2 and Al2O3–ZrO2 composite pellets were found to be smaller than the value found for Al2O3, due to the lower tortuosity factor values of the Al2O3 pellet. It was found that hydrogen was weakly adsorbed on all resultant materials.

Determination of effective diffusivities and convective coefficients of CO2 in gypsum plasters by dynamic single pellet experiments

This paper presents the effective diffusion and convective coefficients obtained for construction gypsum, perlite, and machine plaster pellets by using a dynamic single pellet moment technique at various temperature, and at different pressure drops. The experimental studies were performed by isobaric and non-isobaric conditions across between the upper and lower surfaces of the pellets. The experimental moment values obtained from the experiments carried out were used to calculate desired coefficients such as the effective diffusivity, tortuosity factor, D parameter, and Darcy coefficient.The experimental results for CO2 diffusion in the pellets with porous at isobaric conditions showed that the effective diffusivity values for all gypsum plasters increase with increasing both pellet porosity and the temperature. It was observed that the tortuosity factor depends on macro porosity of the pellets used. The results indicated that the diffusion mechanism for all gypsum plasters is the transient regime diffusion.The effective diffusivity values decreased with increasing the pressure drop. In the range of pressure drop studied, both diffusive (at low pressure drops) and viscous (at high pressure drops) flows for CO2 diffusion in construction gypsum and perlite plasters were dominant. But, the diffusion flow type which is important for machine plaster was only the viscous flow at all pressure drops. Finally, the Darcy coefficients of the gypsum plaster pellets were calculated. It was observed that the results were in agreement with the literature results obtained for porous solids similar to porous gypsum plaster pellets used in this study.

Analysis of Diffusion and Adsorption of Volatile Organic Compounds in Zeolites by a Single Pellet Moment Technique

AbstractThe diffusion and adsorption of two common volatile organic compounds, i. e., methanol and benzene, in different zeolite pellets were studied experimentally by using the single pellet moment technique. The experiments were conducted in a one‐sided single pellet adsorption cell at different temperatures in the range between 303 and 343 K. The results showed that both volatile organic tracers were adsorbed reversibly onto all zeolite samples. The overall adsorption equilibrium constants of both volatile organic compounds decreased with increasing temperature. The adsorption of the tracers onto the zeolite samples were found to increase in the order of NaY > clinoptilolite > 4A. In the range between 303 and 343 K, the adsorption constants of benzene range from 10.51 to 5.52 for zeolite 4A, from 11.90 to 6.37 for clinoptilolite and from 20.32 to 9.82 for NaY. The adsorption constants of methanol range from 19.05 to 8.26 for zeolite 4A, from 38.40 to 9.12 for clinoptilolite and from 74.21 to 14.70 for NaY at temperatures between 303 and 333 K. The effective diffusivities for benzene varied from 2.20·10–6 to 13.01·10–6 m2/s, whereas for methanol, they varied from 9.80·10–6 to 15.60·10–6 m2/s at the temperatures studied.

Dynamic Analysis of Diffusion and Convective Flows of Gases in Calcined Limestone Pellets

In this study, dynamic analysis of diffusion and convective flows in the pores of calcined limestone pellets, which are used for the removal of acidic gases from flue gases, has been studied using the single pellet moment technique. Experiments have been conducted in a diffusion cell by using nitrogen gas (carrier) flowing through both faces of the pellet. Prior to the diffusion experiments limestone powders were calcined in an atmosphere of N2 at 800°C. Effective diffusivity of helium has been determined by giving a pulse of helium to the upper face of the calcined limestone pellet and by comparing the response peak on the lower face of the pellet with theoretical expressions. The values of effective diffusivities increased with increasing temperature and pellet porosity. Convective flow contribution to the diffusion flux was found to increase with the increase of pressure drop across the pellet.

Dynamic Analysis of Diffusion and Adsorption of Water‐Miscible and Water‐Immiscible Organic Vapors in Soil

AbstractA dynamic analysis of the diffusion and adsorption of water‐miscible volatile organic compounds (methanol and acetone) and water‐immiscible volatile organic compounds (benzene and toluene) in a soil pellet has been performed experimentally by using the single pellet moment technique. The experiments were conducted in a one‐sided single pellet adsorption cell at a temperature of 30 °C and varying relative humidities (0, 20, and 40 %). The results obtained with dry and wet systems showed that volatile organic tracers were adsorbed reversibly onto the soil. The overall adsorption equilibrium constants of both water‐miscible and water immiscible volatile organic compounds decreased with relative humidity. The sorption of water‐immiscible VOCs (benzene) onto soil was found to be much less than that of water‐miscible VOCs (methanol). The effective diffusivity of water‐immiscible volatile organic vapor (benzene) in the soil did not show a considerable change with relative humidity. In contrast, there was an appreciable change in the effective diffusivity for water‐miscible VOCs (methanol) with moisture.

Effective Diffusivities and Convective Coefficients for CaO‐CaSO4 and CaO‐CaCl2 Pellets

AbstractDiffusion and convective flow in the pores of pellets formed by compressing mixtures of calcined limestone and CaSO4/CaCl2 powders have been studied experimentally by using the single pellet moment technique. The experiments were conducted in a diffusion cell by flowing nitrogen gas (carrier) through both faces of the pellet. Limestone powder was calcined in an atmosphere of N2 at 800 °C and mixed with CaSO4/CaCl2 for diffusion experiments. Effective diffusivity of helium has been estimated by exposing the upper face of the pellet to a pulse of and matching the response peak on the lower face of the pellet with theoretical expressions. The values of the effective diffusivities increased with temperature, but decreased with increasing CaSO4/CaCl2 content in the pellet. The convective flow contribution to the diffusion flux was found to increase with increasing pressure drop across the pellet.

Hydrogen diffusivity enhancement in alumina pellets due to impregnated palladium

Single-pellet moment technique was used for the evaluation of effective diffusivities and adsorption equilibrium constants of hydrogen, carbon dioxide, and helium in pure alumina and palladium-impregnated alumina pellets. It was found that hydrogen was strongly adsorbed on palladium of Pd-alumina pellets, and significant enhancement of hydrogen diffusivity was observed due to impregnated palladium at 40°C. On the other hand, for carbon dioxide and helium, effective diffusivities obtained in Pd-alumina pellets were smaller than the corresponding values in pure alumina due to higher tortuosity factor values of Pd-alumina pellets.

Effects of humidity and soil organic matter on the sorption of chlorinated methanes in synthetic humic-clay complexes

Vapor-phase sorption is the most influential process governing the transport and the fate of volatile organic compounds in soil. To understand the influence of both soil organic content and the humidity of soil on the vapor sorption is an important process for degradation processes. The single-pellet moment technique was used to investigate sorption and diffusion of trichloromethane (TCM) and carbon tetrachloride (CTC) at varying relative humidities (0–80%) of synthetic humic-clay complex pellets consisting of clay (montmorillonite) and different amounts of organic matter (humic acid). The effective diffusivities of TCM and CTC did not show a noticeable change with moisture and humic acid content. On the other hand, with increasing humic acid content of clay at 0% relative humidity, an appreciable decrease of the equilibrium sorption constants of the tracers (TCM, CTC) was found because of the blockage of some sites of the mineral surfaces and especially micropores by the humic acid. The presence of water also reduced dramatically the sorption of TCM and CTC on synthetic humic-clay complexes. Above 20% relative humidity, the sorption coefficient of TCM and CTC varied only slightly with humic acid content. It was concluded that the sorption of TCM and CTC in synthetic humic-clay complexes was strongly effected by the moisture and humic acid content.

Single pellet reactor for the dynamic analysis of gas-solid reactions “reaction of SO 2 with activated soda”

Single-pellet moment technique which was initially proposed for the measurement of effective diffusivities in porous catalysts and adsorption rate and equilibrium constants was modified for the analysis of gas-solid reactions. In this technique dynamic version of the Wicke-Kallenbach single-pellet cell was used. A pulse of a tracer gas was introduced into stream flowing over one end face of the pellet. In the modified pulse-double response procedure, experimental moments of the response peaks of both reactant and product gases measured in both top and bottom outlet streams of the single-pellet reactor were used for the evaluation of intrapellet rate and equilibrium parameters. Application of the technique to the reaction of SO 2 with activated soda indicated that the value of Thiele modulus decreased from 6.74 to 0.33 by the increase of fractional conversion of Na 2CO 3 to Na 2SO 3 from zero to 0.63. In this range of conversion values a significant variation in pore structure and also a decrease of effective diffusivity of SO 2 from 0.045 cm 2/s to 0.025 cm 2/s was observed. A cell model which considered the changes in pore length and radius with reaction extent and variations in product layer diffusion resistance was shown to be successfully used in the analysis of experimental observations. A review of single-pellet dynamic reactor studies for catalytic and noncatalytic gas-solid reactions was also given.

Analysis of Diffusion and Sorption of Chlorinated Hydrocarbons in Soil by Single-Pellet Moment Technique

The single-pellet moment technique was shown to be a powerful method for inuestigating the diffusion and adsorption of volatile hydrocarbons in the soil. The technique was used to evaluate effective diffusivities, adsorption equilibrium, and rate constants of chlorinated hydrocarbons (monochloroethane, 1,2-dichloroethane, 1,1,1trichloroethane, and 1,1,2-trichloroethane). Results obtained in a dry system showed that adsorption rate constants of all these hydrocarbons on the soil pellet used are of the same order of magnitude (4.4-8.0 cm 3 g -1 s -1 )

Single‐pellet technique for irreversible and reversible adsorption in soil

Irreversible adsorption of some volatile organic compounds on porous solids is frequently encountered in soil as well as in gas purification and some catalytic processes. The contamination of the soil subsurface by volatile organic compounds has become an active area of environmental research. Benzene is one of the pollutants which is frequently found in the subsoil. Although transport and sorption studies for soil contaminants have recently increased, much remains to be done to achieve satisfactory understanding of soil pollution. In this work, sorption of benzene on soil was investigated using the single-pellet moment technique, and it was shown that irreversible and reversible adsorption parameters can be determined simultaneously from the same set of experimental moment values.

Dynamic analysis of viscous flow and diffusion in porous solids

In case of nonisobaric diffusion, the total flux of a gas through a porous solid is expressed in terms of the summation of diffusion and viscous flow terms. The diffusion flux is generally considered to be inversely proportional to the series combination of molecular and Knudsen resistances. On the other hand, viscous flow is expressed by the Darcy equation. In some applications with porous catalysts, diffusion with a pressure gradient is of interest. Single-Pellet moment technique is one of the fastest and most dependable methods for the measurement of intraparticle rate parameters. The method was used to determine effective diffusion coefficients, adsorption equilibrium, and the rate parameters in porous catalysts. In this work, a method is introduced for the study of relative significance of diffusion and viscous flow in porous catalysts using the single-pellet moment approach. The method allows the measurement of Darcy coefficient together with effective diffusion coefficient in a porous solid.