ISOTHERM EQUATION FOR WATER VAPOR ADSORPTION ONTO ACTIVATED CARBON By Shaoying Qi/

A simple isotherm model has been developed for the type-5 equilibrium adsorption systems by considering the effects of both primary and secondary adsorptive sites. The model was applied to interpret experimental data describing water vapor adsorption capacities of four activated carbon adsorbents for relative vapor pressures from 0.0 to 0.95 and temperatures between 288 and 308 K. Good agreement was observed between the model and experimental results. The isotherm parameters were found to either correlate well to the Brunauer, Emmett, and Teller specific surface area or have limited effect on describing the adsorption onto adsorbents made from the same precursor but activated with different degrees of burnout. The limiting pore volumes of the adsorbents obtained from the model based on water vapor adsorption compared favorably with those measured using volatile organic compounds. (2) (1) INTRODUCTION Equilibrium adsorption of water vapor onto microporous activated carbon adsorbents generally exhibits a type-5 isotherm according to Brunauer's classification (Adamson 1976; Basmadjian 1997). Because of the sigmoidal shape of this type of isotherm, only a few of many available isotherm models may be applied to water vapor adsorption, such as the well-known Dubinin-Serpinski (DS) equation (Dubinin 1980; Baron et a1. 1991). The original DS equation describes water vapor adsorption for the relative vapor pressure range (P/Po, where P is the actual partial pressure and Po is the saturation partial pressure of water vapor) from 0.0 to 0.6 (Cal 1995). A recent modification by Barton et al. (1992) extended the DS equation to describe the entire water vapor adsorption isotherm (Cal et al. 1997). This modified DS equation relates P/Po to the adsorption capacity of the adsorbent by an empirical four-parameter nonlinear equation. Because the adsorption capacity cannot be expressed explicitly, it is inconvenient to use the modified DS equation to determine the adsorption capacity of adsorbent for water vapor at a given P/Po. MODEL DEVELOPMENT Water vapor adsorption onto activated carbon involves primary and secondary adsorptive sites (Dubinin 1980). The primary adsorptive sites consist of oxygenated surface cornpounds capable of forming hydrogen bonds with water molecules. The secondary adsorptive sites are the previously adsorbed water molecules, which can form hydrogen bonds with the adsorbing water molecules. At low relative pressures of water vapor, adsorption occurs mainly on the primary sites. The number of available primary sites contributing to water vapor adsorption decreases with increasing water vapor pressure as water vapor adsorbs onto those sites. With further increase in water vapor pressure, adsorption occurs mainly on the secondary sites of the previously adsorbed water molecules. Therefore, it is the combination of the primary and secondary adsorptive sites that determines the change in adsorption capacity with the change in water vapor pressure. It is lEnvir. Engr., UL-I, U.S. Army Constr. Engrg. Res. Lab., Champaign, IL 61826-9005. 2Chem. Engr., UL-I, U.S. Army Constr. Engrg. Res. Lab., Champaign, IL. 'Assoc. Prof., Dept. ofCiv. Engrg., Univ. of Illinois, Urbana, IL 61801. Note. Editor: Byung R. Kim. Discussion open until April I, 1999. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this technical note was submitted for review and possible publication on March 6, 1998. This technical note is part of the Journal ofEnvironmentol Engineering, Vol. 124, No. II, November, 1998. ©ASCE, ISSN 0733-9372/98/00111130-1134/$8.00 + $.50 per page. Technical Note No. 17851. assumed that (I) the number of secondary adsorptive sites is proportional to the amount of water adsorbed or the adsorption capacity q at a specified P/Po; (2) the number of primary adsorptive sites is proportional to the remaining adsorption capacity, (qo q), where qo is the limiting adsorption capacity at P/Po approaching 1.0; and (3) the driving force for the change in adsorption capacity with the change in vapor pressure is proportional to the product of (qo q) and q. These assumptions result in a simple isotherm model in dimensionless form that follows: d (:J = k [I _(!L)] (!L) d (:J qo qo where k =a proportionality constant. Mathematically, (1) isa logistic function (Beltrami 1987). Although nonlinear, it can be integrated by separating variables to yield qo q =----~---I + exp[k(PsoIPo PlPo)] where Pso =an isotherm constant; and P = Pso at q/qo =0.5. The plot of (2) exhibits a characteristic S shape with Pso at q/ qo =0.5 as an inflection point. Comparing with the modified DS equation (Barton et a1. 1992), the simple isotherm model of (2) has the advantages of expressing q explicitly as a function of PlPo and containing three instead of four isotherm parameters. RESULTS AND ANALYSIS The experimental data of Cal (1995) for adsorption of water vapor at room temperature (25°C) onto three activated carbon-fiber cloth (ACFC) adsorbents were used to verify the isotherm model of (2). The three ACFCs, made from a crossTABLE 1. Water Vapor Adsorption Isotherm Parameters for Activated Carbon-Fiber Cloths Surface Slit-pore halfP60/PO Adsorarea" A width , Xo at qlC/o = qo bent (m/g) (nm) k 0.5 (gig) (1 ) (2) (3) (4) (5) (6) ACF-15 900 0.492 20.0 0.451 0.351 ACF-20 1,610 0.637 27.9 0.542 0.571 ACF-25 2,420 0.915 23.3 0.650 0.788 "Manufactured by American Kynol, Inc., New York. "Foster et al. (1992). ·Cal et al. 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