The Wheeler-Jonas equation: a versatile tool for the prediction of carbon bed breakthrough times

This paper gives an overview of the recent developments in the use of the Wheeler-Jonas equation. Extensive experimental work has been done by measuring breakthrough times of different types of activated carbon beds, under different experimental conditions, for a large variety of gases and vapours. This includes the use of activated carbon fibre beds, the presence of moisture on the carbon and in the air stream, non-constant flow patterns and adsorption of chemisorbed species. In all cases the applicability of the Wheeler-Jonas has been demonstrated, i.e. one can use this equation to extrapolate single laboratory breakthrough results by simply varying the independent variables of the equation (amount of adsorbent, flow rate, inlet and breakthrough concentrations). In most cases it is even possible to perform ab initio breakthrough calculations for a well-defined carbon bed. To achieve this new supporting equations had to be derived to allow the estimation of the dependent variables, W_e (the equilibrium adsorption capacity) and k_v (the overall mass transfer coefficient), under different circumstances. In conclusion, the scope of the Wheeler-Jonas (or Reaction Kinetic) equation extends largely beyond its commonly accepted boundaries. This is primarily due to its apparent simplicity: the combination of a single capacity term and an overall kinetic effect strongly enhances its applicability to different adsorption circumstances. In this way it is far more potent than many of the more modern equations that require the exact knowledge of several, not readily available, input parameters.     

Adsorption and reaction behavior for the simultaneous adsorption of NO-NO2 and SO2 on activated carbon impregnated with KOH

This study examined the individual and simultaneous adsorption of NO_x (NO-NO₂) and SO₂ on activated carbon impregnated with KOH (KOH-IAC). For individual component adsorption, KOH-IAC showed a higher adsorption capacity in NO-NO₂ rich air than in SO₂-air. In the simultaneous adsorption of NO-NO₂-SO₂, SO₂ showed a greater adsorption affinity than NO-NO₂. The smaller the amount of NO-NO₂ adsorbed, the more SO₂ was adsorbed. XPS analysis of the adsorption of NO-NO₂ rich SO₂-air on KOH-IAC revealed that the adsorbed SO₂ was predominantly found on the external surface, producing mainly K₂SO₄ and, additionally, H₂SO₄ and K₂SO₃. Depth profile analysis showed that the amount of SO₂ adsorbed decreased regularly away from the surface, while the amount of adsorbed NO-NO₂ increased irregularly. We confirmed that the presence of the impregnant in KOH-IAC is a determining factor in the adsorption of NO-NO₂ and SO₂ by chemical reaction, clarifying the surface chemical behavior.     

Contribution of the edge effect to physical adsorption in micropores of activated carbons

The adsorption process in activated carbon micropores can be viewed as a two-dimensional condensation on micropore walls at a critical condensation pressure, p_c, which evolves into volume filling. p_c on a surface of micropore walls is calculated in respect to a critical condensation pressure on the reference nonporous surface, p_c^ref. Although theoretical treatment predicts that p_c^ref should be a parameter of adsorption isotherms, experimental isotherm equations are expressed in terms of the bulk saturation pressure, p_s. Experimental values of p_s/p_c^ref for a graphitized carbon black, which is often considered as a model of activated carbon surfaces, range from 37 to 4000 for typical adsorbates and are by no means close to unity. It is proposed that this apparent discrepancy between theory and experiments has its origin in the edge effects: carbon blacks are modeled by semi-infinite slabs, whereas the magnitudes of thickness and diameters of micropore walls are of the order of a nanometre. Factors associated with edge effects reduce the adsorption energies on surfaces of finite particles resulting in shifts of condensation pressures to higher values. For particles with diameters about 1.4 and 1.8 nm, adsorption energies decrease to ≈0.72ε₁*^∞ and ≈0.81ε₁*^∞, respectively, where ε₁*^∞ is the energy of adsorption on an infinite plane, and p_c approaches p_s. This phenomenon substantiates the application of p_s in adsorption equations and the success of the Dubinin equations probably owes much to this fact.     

Co-adsorption of n-butane/water vapour mixtures on activated carbon fibre-based monoliths

Water-n-butane co-adsorption experiments on Activated Carbon Fibre based Monoliths (ACFMs) under equilibrium and dynamic conditions were performed at 30 °C. ACFMs proved to be better adsorbents than active carbon particles for the dry adsorption of n-butane at low concentration levels. The presence of water vapour in the gas stream has a negligible influence on n-butane adsorption for values of relative humidity (RH) equal to or below 25%. Higher water pressures cause a significant loss of adsorption capacity in ACFMs. Equilibrium water adsorption on ACFMs can be described by the Do and Do model [Carbon 38 (2000) 767] modified in order to account for both the variable size of the water aggregates on acid centres and the variable size of the clusters detached from the aggregates and inserted into the micropores. The model results show close agreement between the amounts of active sites for adsorption calculated by the model and the number expected from subjecting the ACFMs to different pre-treatments.The equilibrium of co-adsorption of water and n-butane can be described by a pore filling concept according to which the volume occupied by both gases adsorbed together from the gas mixture is approximately equal to the volume occupied by the pure component adsorbed separately to a greater extent.Pre-moistening of the monolith has little effect on its effective n-butane adsorption capacity (breakthrough time) during dynamic adsorption experiments. For values of relative humidity equal to or below 25%, the effective n-butane adsorption capacity of the monoliths was better than that of active carbon powder. Moreover, the monoliths produced a much lower pressure drop in the system. At these conditions, adsorption efficiency for the ACFMs never showed values below 85%.     

Radial distribution of porosity in spherical activated carbon particles

The radial distribution of porosity in spherical activated carbon particles and its relationship to both activation temperature and conversion of the reaction C-CO₂ are discussed. Char spheres, obtained by pelletizing Quercus agrifolia powdered char, were activated using CO₂ as activating agent at 820 and 860 °C. For both temperatures, the gasification reaction was run until the desired conversion (30, 50 and 70%) was reached. The activation process was performed using TGA apparatus. The porosity of the samples was measured by physical adsorption of nitrogen at −196 °C. BET and Dubinin-Raduskhevich equations were used to analyse the results. From each activated carbon sphere several samples were prepared, corresponding to different layers of the sphere; an outer layer, a middle layer and the core of the particle. From these results, the radial porosity evolution as a function of activation temperature and reaction conversion was obtained and a mathematical expression that correlates pore volume evolution and reaction conversion is proposed.     

Effects of carbon surface chemistry and solution pH on the adsorption of binary aromatic solutes

Adsorption of p-cresol, nitrobenzene and p-nitrophenol on treated and untreated carbons is investigated systematically. The effects of carbon surface chemistry and solution pH are studied and discussed. All adsorption experiments were carried out in pH-controlled solutions to examine the adsorption properties of the adsorption systems where the solutes are in molecular as well as ionic forms. Using the homogeneous Langmuir equation, the single solute parameters are determined. These parameters are then used to predict the binary solute adsorption isotherms and gain further insights into the adsorption process.     

Prediction of adsorption equilibrium using a modified D-R equation: pure organic compounds on BPL carbon

A method for predicting adsorption equilibrium using a modified Dubinin-Radushkevich (D-R) equation is presented in this paper. We focus on adsorption of pure organic compounds on BPL-activated carbon. We introduce a new variable k_v, a volume adjusting coefficient, and simply use V_b, the constant molar volume of the adsorbate at its normal boiling temperature, instead of V_m, the temperature-dependent molar volume of the adsorbate at the adsorption temperature. The model parameters in the modified D-R equation for an adsorbate are predicted from V_b. Overall, the modified D-R equation gives more accurate results than the traditional one.     

Thermal modeling of activated carbon based adsorptive natural gas storage system

A homogeneous, isotropic porous matrix of activated carbon inside a portable steel cylinder is considered as the adsorption bed for natural gas (NG) which is idealized as pure methane for the purpose of simulation. The heat and fluid flow inside the porous adsorption bed are modeled using a volume averaging technique and Darcy-Brinkman formulation. The effective thermal conductivity of the activated carbon-methane system is calculated as a function of uptake according to the Luikov model. Heat generation due to the exothermic process of adsorption is considered. The governing equations are solved using an implicit finite volume method for the given boundary conditions. Three different models of adsorption are considered, namely (i) a no-flow model, (ii) flow model with uniform adsorption and (iii) a flow model with local adsorption. For each of these models, transient temperature profiles in the adsorption bed during the charging process are obtained, and the corresponding mass adsorption potentials are calculated. Parametric studies are performed to investigate the effects of gas inlet temperature and rate of charging on the maximum bed temperature and the time required to fill the cylinder.     

Adsorption of p-nitrophenol on an activated carbon with different oxidations

An activated carbon prepared from olive stones has been modified through oxidation by nitric acid or sodium hypochlorite. These treatments introduced large amounts of oxygen groups, which were characterized by mass-spectrometry, temperature-programmed desorption (DTP-MS). Both CO₂- and CO-evolving groups were created by these oxidation treatments. A part of these oxidized samples was then outgassed under vacuum up to 823 K in order to remove most of the CO₂-evolving groups from their surface. Oxidized samples have a smaller surface area than the original sample. The subsequent partial outgassing increases the surface area which, however, does not reach the value it had before oxidation. p-Nitrophenol (PNP) adsorption isotherms from aqueous solutions were determined at 298 K for the original, oxidized, and partly outgassed samples. The results confirm the presence of an intermediate plateau at low equilibrium PNP concentration (at about 10 mg/l). The relative effects of textural versus surface chemistry on PNP uptakes are then discussed. The presence of CO-evolving groups showed no influence on PNP uptakes. The conclusion is that models in which carbonylic groups are basic adsorption sites for substituted phenols can be ruled out for the entire isotherm of PNP obtained with the original carbon. These models are also unlikely for PNP adsorption on oxidized and partly outgassed samples.     

NOx adsorption-temperature programmed desorption and surface molecular ions distribution by activated carbon with chemical modification

Activated carbon, the surface of which has been modified with KOH, was used in this study. The study examined adsorption and desorption behaviors and the accompanied surface reaction mechanism as well as the distribution of molecular ions on the surface. The peaks of NO_x desorption behavior may be classified into three bond categories depending on adsorption strength. NO desorption occurs at the earliest stage as chemical adsorption occurs earlier, in a sort of competition, than physical adsorption due to strong basic OH⁻ ion of surface. It was confirmed that the adequate temperature for NO_x desorption was near 390 °C. The potassium that existed on the surface remained without being consumed even with complete desorption of NO_x.     

Controlling carbon microporosity: the structure of carbons obtained from different phenolic resin precursors

Carbons were prepared from resins synthesised using the phenolic precursors phenol, para methylphenol, para ethylphenol, para n-propylphenol, para isopropylphenol and 3,5-dimethylphenol. Loss of phenolic OH from these materials was followed using solid-state nuclear magnetic resonance. The surface areas of the carbons were determined using N₂ and CO₂ adsorption. No significant differences in the loss of phenolic OH were observed. Under the same carbonisation conditions, the para alkyl phenols gave carbons with wide micropores, while the phenol and 3,5-dimethylphenol gave carbons with narrow micropores. Grinding the cured resins prior to carbonisation was found to significantly increase the surface area of the carbons obtained, with the microporous surface area increasing rapidly with a fall in particle size, without a significant increase in burn-off. Higher carbonisation temperatures widened the micropore size distribution, as shown by fitting the CO₂ adsorption isotherm with the Dubinin-Astakhov equation. The ability to change the carbon micropore structure obtained from a simple, well defined precursor, has many potential applications in carbon molecular sieves, catalyst supports and the investigation of adsorption processes.     

Determination of pore size distribution and adsorption of methane and CCl4 on activated carbon by molecular simulation

A combined method of grand canonical Monte Carlo (GCMC) simulation and statistics integral equation (SIE) for the determination of pore size distribution (PSD) is developed based on the experimental adsorption data of methane on activated carbon at ambient temperature, T=299 K. In the GCMC simulation, methane is modeled as a Lennord-Jones spherical molecule, and the activated carbon pore is described as slit-shaped with the PSD. The well-known Steele’s 10-4-3 potential is used to represent the interaction between the fluid molecule and the solid wall. Covering the range of pore sizes of the activated carbon, a series of adsorption isotherms of methane in several uniform pores were obtained from GCMC. In order to improve the agreement between the experimental data and simulation results, the PSD is calculated by means of an adaptable procedure of deconvolution of the SIE method. Based on the simulated results, we use the activated carbon with the PSD as the prototype of adsorbent to investigate adsorption. The adsorption isotherms of methane and CCl₄ at 299 K in the activated carbon with the PSD are obtained. The adsorption amount of CCl₄ reaches 20 mmol/g at ambient temperature and pressure. The results indicate that the combined method of GCMC and SIE proposed here is a powerful technique for calculating the PSD of activated carbons and predicting adsorption on activated carbons.     

A model for the adsorption of single metal ion solutes in aqueous solution onto activated carbon produced from pecan shells

Adsorption isotherms for activated carbon made from pecan shells have been obtained at 25 °C and an approximate pH of 3 for a number of metal ion solutes. It was found that the Slips and Freundlich equations were satisfactory for explaining the experimental data. The correlation of metal ion adsorption with the solute parameters of metal ion electronegativity and first stability constant of the metal hydroxide was investigated. In the case of most of the metal ions studied, higher electronegativities and stability constants corresponded to the higher adsorption levels of metal ions onto the activated carbon. A correlation was developed that predicts the constants of the Freundlich equation from the selected parameters of the metal ions, and thus can predict the adsorption isotherms at constant pH. The developed correlation gives results with acceptable deviations from experimental data. A procedure is proposed for obtaining similar correlations for different conditions (temperature, pH, carbon type and dosage). The ratio of equivalent metal ions adsorbed to protons released is calculated for the studied metal ions over a range of concentrations. In most cases, particularly at low concentrations, this ratio is close to one, confirming that ion exchange of one proton with one equivalent metal ion is the dominant reaction mechanism.     

Thermal regeneration of activated carbon saturated with p-nitrophenol

Water contamination by organic compounds is an important environmental problem. Activated carbon filters are widely used to eliminate these contaminants. After exhaustion, activated carbon must be regenerated or replaced by fresh carbon. In this study thermal regeneration of saturated carbon with p-nitrophenol has been analysed. Three thermal regeneration methods have been tested: (1) pyrolysis, (2) pyrolyis-gasification and (3) direct gasification, the gasifying agents being air and CO₂. The results show that the pyrolysis treatment does not completely eliminate the contaminant from the carbon and the recovery of the initial adsorption properties is rather limited. The effect of gasification depends on both the gasifying agent and the sample (pyrolysed or saturated with PNP). CO₂-gasification yields to a complete regeneration of the adsorption characteristics in both pyrolysis-gasification and direct gasification samples. In general, air-gasification produces lower regeneration properties, although direct air-gasification sample has 87% recovery of the PNP maximum adsorption capacity. These results suggest that thermal regeneration could be carried out in a single step, simplifying the process and reducing the operation cost. Moreover, although CO₂ seems to give better recovery of the initial carbon characteristics than air, it should be noted that air is cheaper and the regeneration time is shorter.     

Adsorption of volatile organic compounds by means of activated carbon fibre-based monoliths

Activated carbon fibre monoliths (ACFMs) were prepared from the rejects of polymeric fibres (Nomex™). These were carbonised, agglomerated with a phenolic resin and steam activated at burnoff degrees between 0 and 40%. Adsorption experiments with n-butane at 30 °C show that, at high adsorbate concentrations, the amount adsorbed is a function of pore volume, but at low concentrations this mainly depends on pore size distribution. The porosity of Nomex-based ACFMs is formed by narrow micropores, which permit higher amounts of vapour to be adsorbed in low concentrations compared to monoliths prepared from different commercial activated fibres and a commercial granular activated carbon, which exhibits wider pores. The agglomeration of Nomex-fibres to form ACFMs does not cause any loss in adsorption properties with respect to non-agglomerated activated fibres. From the adsorption experiments of different vapours on a Nomex-based ACFM (40% burnoff) it was found that at high concentrations (p/p_o=1) the adsorbed volume was independent of the nature of the adsorbate and depended only on pore volume. However, at low vapor concentrations (p/p_o=0.004), the amount adsorbed depended on the adsorbate being well correlated to the molecular parachor and the polarizability of the adsorbates     

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

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)=0.85k_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)=0.56k_v (single vapor) for such.     

Adsorption dynamics of carbon dioxide in molecular sieving carbon

The sorption equilibrium isotherm of carbon dioxide at 20 °C on a commercially manufactured carbon molecular sieve has been measured with a variable volume (vacuum to high pressure) volumetric adsorption apparatus. Measurement was taken over the pressure range <10-2000 Torr and the isotherm is characterized by Dubinin-Radushkevich analysis which provides the micropore size distribution. The equilibrium information is subsequently employed to characterize the dynamics of adsorption and it is shown that the uptake of carbon dioxide is Fickian with some deviation from Fickian behavior noted at lower pressures. The derived mobility parameter agrees reasonably well with that predicted by the Darken relation over more than a 200-fold change in pressure.     

Characterization of the surfaces of single-walled carbon nanotubes using alcohols and hydrocarbons: a pulse adsorption technique

A pulse mass analyzer was used to study the vapor phase adsorption of organic compounds on single-walled carbon nanotubes and chemically modified/oxidized SWCNTs. The change in mass of a packed bed of adsorbent held at 200 °C was observed following the injection of a pulse of an organic compound from the series: ethanol, iso-propanol, cyclohexane, cyclohexene, benzene, or n-hexane. The relative strength of adsorption was obtained by the mass increase resulting from injection of the pulse and by the time required for desorption. This time was broken into the transit time to reach the end of the bed and the half-time for return from peak to baseline. Hexane was the most strongly held compound of the organic sequence. Oxidative purification of a raw nanotube sample produced a less hydrophobic surface. The effect of the purification was reversed by thermolysis at 700 °C, which removed oxygenated functional groups and increased the affinity for hydrocarbons. The amorphous carbon associated with the raw nanotube sample is a strong adsorbent for hydrocarbons. By comparison, an activated carbon had a greater affinity for hydrocarbons than any of the nanotube samples.     

Relationship between the highest occupied molecular orbital (HOMO) electron density of adsorption sites on carbon and the Freundlich exponent

This paper discusses the relationship between the electron density for various groups of phenolic compounds and their adsorption capacity on activated carbon. Chloro- and nitrophenols were used as test adsorbates, and as-received or HNO₃-modified granular activated carbon (GAC) samples were used as adsorbents. The isotherms for these systems were determined by the batch bottle technique. The highest occupied molecular orbital (HOMO) electron density at the adsorption site was estimated using the CAChE program, and a relationship between the Freundlich exponent 1/n and the HOMO density of the adsorbent was found by combining the experimental and computational results for the modified GAC. The Freundlich equation is described as: n_ads=k(C)^1/n, where n_ads, k, C, 1/n are the weight of adsorbate per weight of adsorbent (g g⁻¹), the Freundlich coefficient, the concentration of adsorbate in bulk solution (g l⁻¹), and the Freundlich exponent, respectively. The value of the Freundlich exponent 1/n for the systems investigated decreased linearly with an increase in ‘adsorbent’ HOMO density. The HOMO electron density of both the adsorbate and the adsorbent were the major factors determining the value of the Freundlich exponent, 1/n, for phenolic adsorbate-carbonaceous adsorbent systems.     

Kinetics of 1,3,6-naphthalenetrisulphonic acid ozonation in presence of activated carbon

Processes based on the simultaneous use of ozone and activated carbon have proven very effective for removing contaminants of high toxicity and low biodegradability. The present study is aimed to determine the kinetic constants involved in this purification process and their relationship with the surface chemistry of the activated carbon. For this purpose, the ozonation of 1,3,6-naphthalenetrisulphonic acid (NTS), selected as model compound, was carried out in the presence of different activated carbons. Determination of the Weisz-Prater parameter (C_WP) revealed that intraparticular diffusion limitations exist in the system for particles >500 μm. The degradation kinetics of NTS in the presence of activated carbon depends on the concentrations of both, the contaminant and the dissolved ozone, with a global reaction order of 2. The heterogeneous reaction constants were determined using a model that allowed quantification of the capacity of the activated carbon to increase the NTS degradation rate and of the chemical surface properties responsible for this increase. The basicity of the activated carbon is mainly responsible for the catalytic activity of the carbon in NTS ozonation, even though, mineral matter contributes positively to the catalytic activity.