Gerry O. Wood

Affinity coefficients of the Polanyi/Dubinin adsorption isotherm equations: A review with compilations and correlations

Abstract A historical review presents the assumptions and approximations made in the Polanyi and Dubinin adsorption theories, which have defined the affinity coefficient β and proposed parameters to calculate it. A previous compilation of experimental β [Wood GO. Activated carbon adsorption capacities for vapors. Carbon 1992;30:593–599] for gases and vapors on activated carbons has been supplemented to more than double the available database. Experimental affinity coefficients reported and calculated for water vapor have also been compiled. For water vapor at relative humidity >50% on normal industrial (unacidified) activated carbons, 0.1 is a good average value of the affinity coefficient relative to that of benzene. Direct correlations of experimental affinity coefficients (other than for water) with molecular parachor, molar polarizability, and molar volume were successful ( β standard deviations of 0.09, 0.12, and 0.12, respectively). Power functions with exponents less than unity (0.9, 0.75, and 0.9, respectively) provided slightly better fits of predictions to experimental values (standard deviations of 0.08, 0.10, and 0.11, respectively). Any of these correlations can be used. Listed advantages of using molar polarization make it the correlation parameter of preference. Correlation of β with critical temperature was largely unsuccessful. No obvious effects of adsorbate polarity, adsorbent molecular sieve properties, or form of the Dubinin equations were detected for β and its correlations.

Activated carbon adsorption capacities for vapors

Abstract It is sometimes desirable to estimate the adsorption capacity of an activated carbon bed for a chemical vapor at a selected concentration. The laboratory measurement of such a capacity (one point on an adsorption isotherm) may be hindered due to toxicity, availability, cost, time, etc. Therefore, an adsorption isotherm equation with general parameters based on physical properties of the adsorbate would be very useful. Equilibrium adsorption isotherm data and affinity coefficients for wide varieties of vapors and activated carbon have been collected from reports and publications. The Dubinin/ Radushkevich equation was used for a correlation of these data based on readily available molar polarizations. The correlations for 123 affinity coefficients and 1350 adsorption capacities resulted in standard deviations of 0.18 and 0.029 g/g, respectively.

Adsorption rate coefficients for gases and vapors on activated carbons

Abstract In order to estimate carbon bed breakthrough time (service life) for a given gas or vapor which is removed from flowing air by physical adsorption, both the adsorption capacity and adsorption rate need to be known. These parameters are available for only a small number of compounds at limited sets of conditions. For 27 hydrocarbons and fluorocarbons, 165 breakthrough curves were measured and analyzed to obtain adsorption rate coefficients. Reciprocals of rate coefficients at 1 and 10% of challenge breakthrough were linear functions of reciprocals of molar polarizations. Another database of breakthrough curves for 121 compounds determined at the Lawrence Livermore National Laboratory in the 1970s was also analyzed. Effects of linear flow velocity on adsorption rate coefficients were determined. Combining these two databases of 679 breakthrough curves for 147 compounds gave correlations of reciprocal adsorption rate coefficients as functions of molar polarization, linear airflow velocity and breakthrough fraction. Only data for dry conditions and 2-cm deep beds have been considered so far.

A Review of the Wheeler Equation and Comparison of Its Applications to Organic Vapor Respirator Cartridge Breakthrough Data

This project was undertaken to study the effect of dry airflow rate and bed weight on organic vapor respirator cartridge breakthrough curves for a single vapor (acetone) and challenge concentration (1060 ppm average). Dried cartridges from a single manufactured lot were used. The data were analyzed using three applications of the Wheeler equation, including (1) varying bed weight, (2) varying residence time, and (3) fitting the breakthrough curve. These approaches are discussed and equations given. Values for the adsorption capacity (We) and the rate coefficient (kv) are presented and compared. Based on these comparisons, limitations of the Wheeler equation are discussed and guidelines given concerning its use.

Quantification and application of skew of breakthrough curves for gases and vapors eluting from activated carbon beds

Vapor and gas breakthrough curves for packed activated carbon beds are often assumed to be symmetrical, when they are actually more often skewed. This skew explains why adsorption rate coefficients calculated at differing breakthrough fractions may not agree. Three extensive databases of breakthrough curves were analyzed to quantify this skew and the effects of relative humidity (preconditioning and use) on it. Skew results for varieties of chemicals and carbons agreed well and were combined to get a quadratic expression for a defined skew parameter. This expression was combined with a previous observation of the effect of breakthrough fraction on calculated rate coefficient. The combination allows estimation of an adsorption rate coefficient at a desired breakthrough fraction from a rate coefficient known (experimentally or by calculation) at another breakthrough fraction. A sample calculation is given.

Estimating Service Lives of Organic Vapor Cartridges

Procedures were developed for estimating service lives of air-purifying organic vapor respirator cartridges, including methods for untested compounds and use conditions (concentration, temperature, and airflow rate). Correlations of adsorption capacities and adsorption-rate coefficients based on equilibrium and breakthrough curve data were reviewed. These correlations were combined using the Reaction Kinetic (modified Wheeler) equation to estimate breakthrough times. The proposed estimation procedure showed 95% confidence intervals of up to ±50% when no breakthrough data were assumed. It is shown how even limited breakthrough curve data for one vapor/carbon combination can be used to substantially improve accuracy of the estimation. Only dry conditions (below 50% relative humidity) have been considered so far.

Estimating Service Lives of Organic Vapor Cartridges III: Multiple Vapors at All Humidities

A widely used equation model for estimating service lives of organic vapor air-purifying respirator cartridges has been updated with more recent research results. It has been expanded to account for effects of high relative humidities. Adsorption capacity competition between water vapor and organic vapor is largely explained by mutual exclusion of adsorption volume of the activated carbon. The Dubinin/Radushkevich equation is used to describe the adsorption isotherms of both water and organic vapors. Effects of relative humidity and adsorbed water on adsorption rates are described by an empirical correlation with breakthrough times. The dynamic natures of adsorption and competition are incorporated using an expanding zone model with displaced water rollup. The complete model has been tested and verified with published and unpublished data from many sources.

Review and comparisons of D/R models of equilibrium adsorption of binary mixtures of organic vapors on activated carbons

Abstract Published models and options for predicting equilibrium adsorption capacities of multicomponent mixtures using single component Dubinin/Radushkevich isotherm equations and parameters were reviewed. They were then tested for abilities to predict total and component capacities reported for 93 binary adsorbed mixtures. The best model for calculating molar distributions was the Ideal Adsorbed Solution Theory (IAST), which balances spreading pressures. Combined with the IAST, total and component capacities were best calculated using either the Lewis or original Bering equation with the Ideal Adsorbed Solution (Raoult’s Law) assumption.

A review of the effects of covapors on adsorption rate coefficients of organic vapors adsorbed onto activated carbon from flowing gases

Abstract Published breakthrough time, adsorption rate, and capacity data for components of organic vapor mixtures adsorbed from flows through fixed activated carbon beds have been analyzed. Capacities (as stoichiometric centers of constant pattern breakthrough curves) yielded stoichiometric times τ , which are useful for determining elution orders of mixture components. Where authors did not report calculated adsorption rate coefficients k v of the Wheeler (or, more general, Reaction Kinetic) breakthrough curve equation, we calculated them from breakthrough times and τ . Ninety-five k v (in mixture)/ k v (single vapor) ratios at similar vapor concentrations were calculated and averaged for elution order categories. For 43 first-eluting vapors the average ratio (1.07) was statistically no different (standard deviation 0.21) than unity, so that we recommend using the single-vapor k v for such. Forty-seven second-eluting vapor ratios averaged 0.85 (standard deviation 0.24), also not significantly different from unity; however, other evidence and considerations lead us to recommend using k v (in mixture)=0.85 k v (single vapor). Five third- and fourth-eluting vapors gave an average of 0.56 (standard deviation 0.16) for a recommended k v (in mixture)=0.56 k v (single vapor) for such.

A review and comparison of adsorption isotherm equations used to correlate and predict organic vapor cartridge capacities

Four adsorption isotherm equations for describing measured capacities of organic vapor air-purifying cartridges were compared. Experimental breakthrough curves were measured for five organic vapors: ethanol, carbon tetrachloride, acetone, chloroform, and hexane. Plots of service life at 1% breakthrough versus bed weight (stacked cartridges) yielded capacities over concentration ranges for three brands of cartridges. The Freundlich, Langmuir, Dubinin/Radushkevich, and Hacskaylol/LeVan isotherm equations fit the capacity versus vapor concentration data equally well, except in the case of ethanol. The ethanol fit was worse for the Freundlich equation. Other characteristics of these equations were related to their usefulness for correlating service life.