Adsorption of pollutants on to activated carbon in fixed beds

The adsorption of certain pollutants, namely phenol, p-chlorophenol, sodium dodecyl sulphate and mercuric ions, on to activated carbon has been studied using fixed bed systems. There are three main methods of contacting in solid/liquid adsorption systems, namely batch, fixed bed and fluidized bed systems. In fixed bed adsorption the adsorption rate is determined on the basis of adsorption equilibrium (unfavourable, linear, favourable or completely irreversible) and the controlling mechanism (external film mass transport, internal pore diffusion, internal solid phase diffusion or longitudinal diffusion). One or more of the previous transport mechanisms may be rate controlling depending on the solute-adsorbent system. For an adsorbent like activated carbon which is highly porous both external transport and pore diffusion will be very important. An adsorption model, based on external mass transport and internal pore diffusion, has been applied to the systems to predict theoretical breakthrough curves. These curves have then been compared with experimental data and using a ‘best fit’ technique, an effective pore diffusion coefficient can be determined for each sorbate–carbon system.     

Adsorption fixed beds modeling revisited: Generalized solutions for S-shaped isotherms

Adsorption fixed bed models are of paramount importance in chemical and environmental engineering research. Although the related literature is rich, the vast majority of models employed are either phenomenological, based on chemical reaction kinetics, or limited to systems that obey simple equilibrium isotherms (favorable, unfavorable, linear, and rectangular) combined to linear driving force (LDF) for the solid-phase mass transfer kinetics and ideal plug flow. This paper complements the existing studies by presenting and analyzing a versatile nondimensional fixed bed model equipped with diffusion-based mass transfer kinetics and nonideal flow terms and adapted to deal with S-shaped (sigmoidal) isotherms. A discussion is conducted on the rather unusual fixed bed dynamics produced by systems that follow S-shaped isotherms, a subject which has been rarely and nonsystematically discussed in the related literature. Thus, this study aims at providing better understanding of the interactions of S-shaped isotherms, mass transfer, and axial dispersion on the shape of adsorption fixed bed breakthrough curves and comes to clarify and complement previously published results, especially on the unexplored effects of the isotherms’ inflection point on the breakthrough curves.     

Adsorption of surfactants from water onto raw and HCl-activated clays in fixed beds

The removal of surfactants from water by adsorption onto raw and HCl-activated montmorillonite in fixed beds was studied. Three surfactants hexadecylpyridinium chloride (cationic), sodium dodecyl sulfate (anionic), and Triton X-102 (non-ionic) were selected in the concentration ranges lower than their critical micelle concentrations in fixed bed experiments. It was shown that the adsorption of anionic surfactant onto Ca-montmorillonite (SAz-1) decreased with increasing pH but that of cationic surfactant increased. The adsorption capacity of non-ionic surfactant was maximized at pH 7.0. For given clay, the adsorption capacities of surfactants were strongly pH-dependent. The adsorption capacity and adsorption rate of non-ionic surfactant onto SAz-1 could be largely improved after acid activation of the clay. Such an improvement was due to the fact that the dissolution of Al³⁺ or Fe²⁺ of montmorillonite occurs in acid solution. The calculated breakthrough curves in fixed bed agreed with the measured ones (standard deviation < 6%). The 50% C/C₀ breakthrough time (τ) decreased with increasing liquid flow rate. The effects of flow rate on the adsorption constant and adsorption capacity were also discussed.     

Adsorption dynamics of ethane from air in structured fixed beds with different microfibrous composites

Adsorption dynamics of ethane in two granular fixed beds and structured fixed beds with microfibrous composites was studied. 5A zeolite membrane 5A/PSSF(paper-like sintered stainless steel fiber) and microfibrous entrapped activated carbon(MEAC) composites were prepared by wet layup papermaking/sintering technique and in-situ hydrothermal method. Microfibrous composites were characterized by X-ray diffraction, scanning electron microscopy and N₂ adsorption/desorption. Structured fixed...     

Isothermal adsorption in fixed beds

Prediction of single component adsorption in a packed bed operated isothermally is accomplished through the use of a mathematical model. The model accounts for the diffusional resistance between the bulk gas and the surface of the adsorbent particles, and for the diffusional resistance within the particles. The adsorption reaction within the pores is assumed to be very rapid compared to these two rate controlling mechanisms. The model can be used for isotherms of any shape and for gaseous feeds of any concentration. The partial differential equations of the model were solved numerically. Breakthrough curves are presented for four different isotherms and for two feed concentrations. The extension of the model to handle surface diffusion is treated. The model is compared with that of Rosen ≥^{11, 20} and the differences are discussed.     

On axial dispersion in fixed beds

The primary purpose of this paper is to show that the criticisms by Tsotsas and Schlünder (1988) of an earlier paper (Gunn, 1969) are based upon elementary mathematical errors of the part of Tsotsas and Schlünder. A summary of experimental data on axial dispersion in liquids and gases shows that the dependence of the axial dispersion coefficient upon the Schmidt group predicted by Tsotsas and Schlünder is not observed despite the large number of emperical factors in their expressions. In particular, the strong dependence of the axial Peclet group upon the Schmidt group for axial dispersion in liquids predicted for Re> 1 is not observed, since the consensus of expirimental data is that for this range the dependence of Pe upon Re is slight.

The experimental dependence of Pe upon Re for different values of the Schmidt group agrees with the expressions of Gunn (1969)     

Competitive adsorption of two dissolved organics onto activated carbon—III: Adsorption kinetics in fixed beds

Adsorption breakthrough curves for bisolute systems of dissolved organics on activated carbon are measured in fixed beds.Results for strongly adsorbable species indicate that at low liquid concentrations (X<0.1 mmol/l.) only external mass transfer resistance is rate determining.However, at higher liquid concentrations internal mass transfer becomes increasingly significant. Breakthrough behaviour is predicted using alternatively three different models with different assumptions about diffusion in the liquid filled pores and diffusion on the surface in series with external film diffusion.Multi-solute adsorption equilibria are predicted from single-solute data using the ideal adsorbed solution theory developed by Myers and Prausnitz, while the single-solute equilibria are represented by Freundlich isotherms. The external mass transfer coefficient for each component is calculated by a general correlation for heat and mass transfer in fixed beds. The internal diffusion coefficient for each component is determined in batch reactor tests with the single-solute system.Systematic deviations between measured breakthrough curves and those calculated from different models using only single-solute data are observed in all experiments with mixed solutes if there is significant internal diffusional resistance and marked displacement of one component inside the carbon particles. The deviations may be due to mutual interference of diffusing molecules. A better agreement between calculated and observed breakthrough curves can be obtained using an extended model in which mixture data are required.     

Axial and radial dispersion in fixed beds

Several different methods of describing dispersion in fixed beds are defined and compared with experiment by means of a number of criteria for model validity. The principal criteria are statistical adequacy of the model when compared with experiments, consistency of bed-independent parameters when estimated from bed response, and consistency of parameters of dispersion with respect to variations in the Schmidt group and Reynolds number. THe characteristics of axial and radial dispersion for fixed beds of impermeable spheres, hollow and solid cylinders, are shown to be consistent with dispersion characteristics measured for permeable particles. The dependence of axial and radial Péclet groups for dispersion of mass upon the Schmidt and Reynolds groups is correlated throughout the range of Reynolds number by fundamentally-based equations for beds of spherical and cylindrical particles.     

Heat transfer and diffusion in fixed beds

On the basis of a set of fairly accurate frequency response measurements, various models for the dynamics of heat propagation in a fixed bed of lead balls have been examined.It has been shown that the calculated average heat transfer coefficient in the particles in the bed, depends very strongly on the type of mathematical model used. Hence, the heat loss from the bed to the surroundings, but even much more the axial dispersion in the fluid phase, have dramatic effects on the calculated heat transfer coefficient, when these physical factors are included in the mathematical model. Their significances are estimated from simple criteria developed in this paper. In general, mathematical models should be used with care when process parameters are predicted from the experiments results.As far as the frequency response characteristics are concerned, it is extremely difficult to distinguish one model from another. The residual of model fitting to the experimental frequency response remains almost the same. Therefore, systematic deviations from constancy in the evaluated process parameters have been used as a criterion for the selection of the models.     

Adsorption with axial diffusion in shallow beds

Approach to constant pattern behavior and breakthrough behavior are analyzed for adsorption in fixed beds with axial diffusion. Local equilibrium between fluid and solid phases is assumed, with concentrations related by favorable Langmuir and Freundlich isotherms. Results are presented as midheight slopes of internal and actual breakthrough curves and as breadths of actual breakthrough curves. The solutions merge smoothly with asymptotic limits appropriate for deep beds and results obtained here for very short beds. It is shown that breakthrough curves are sharper than corresponding internal breakthrough curves for beds of any length, with the difference being even more pronounced in shallow beds than in deep beds. The principal factor that determines whether or not a breakthrough curve differs significantly from the corresponding internal breakthrough curve, regardless of whether the bed is long or short or the isotherm very favorable or linear, is the breadth of the adsorption wave near the bed outlet.     

Adsorption with axial diffusion in deep beds

Breakthrough behavior is analyzed for adsorption in deep beds with axial diffusion, assuming that a constant pattern wave has developed upstream of the bed outlet. Fluid-solid equilibria are described by both Langmuir and Freundlich isotherms. Breakthrough curves are shown to be much sharper than corresponding constant pattern profiles, especially for very favorable isotherms, as the result of a change in the velocity of the fluid-phase concentration wave during breakthrough. In an appendix, a brief derivation is given of the proper boundary condition for the outlet of a fixed-bed adsorber.     

Heat transfer to submerged surfaces in coarse-grained pressurized fluidized beds and fixed beds

This contribution reports on the theory underlying a uniform representation of heat transfer to submerged surfaces in fixed bed reactors and of gas convective part of heat transfer in fluidized beds with coarse-grained bulk solids and/or at elevated pressure. Based on an analysis of the pressure drop behaviour of fixed bed percolation at different gas pressures and with different bulk solids, a new dimensionless pressure drop parameter was developed. Fixed bed heat transfer data are very well correlated by this new dimensionless number. As soon as fluid throughput is in excess of minimum fluidization velocity, the pressure drop parameter transforms into the well-known Archimedes number. These two dimensionless numbers are connected by the condition of equilibrium for pressure drop and mass of practices in a fluidized bed. This equilibrium is fulfilled as soon as fluidization commences. Up to now, the Archimedes number has been generally accepted as the significant parameter, determining the gas convective part of heat transfer in fluidized beds; however, without any physical interpretation of this parameter. Introduction of the pressure drop number, which is consistent with the Archimedes number, reduces the heat transfer behaviour to pressure drop characteristics. The usefulness of this concept is proven by the comparison of experimental results and prediction.     

Electric field phenomena in fluidized and fixed beds

Stabilization of a bed of dielectric particles against fluidization by an electric field (≥ 10³ volts/cm) is described. Glass bead and silica gel particle beds have been observed to behave as packed beds with flow rates (and pressure drops) of the fluidizing gas up to 15 times the normal incipient fluidization rate. The pressure drop at the breakup of this fixed bed was dependent on the second power of voltage, the particular bed material, and geometry of the system. Under suitable conditions 100% bed expansion without diffusive particle motion or bubble formation was obtained using silica gel particles. Comparison with iron particle bed-magnetic field effects are presented. Surface polarization charge effects are the simplest explanation of the phenomena. Several of the possible applications are suggested, such as precipitation enhancement in an aerosol filter or as a new tool for investigating aggregative fluidization.     

Limit cycles in fixed beds operated in alternating modes

Fixed beds, exchanging mass or energy with a flowing fluid according to a linear phenomenological law, are considered. When the plant is alternated periodically between two sets of operating conditions, the state of the fixed bed converges to a limit cycle. The nature of this cycle is explored for co-current and counter-current operation.     

Non-linear adsorption in fixed beds: the Freundlich isotherm

Solutions have been obtained relating the breakthrough curve to bed parameters for the case of adsorption in fixed beds where the adsorption isotherm is of the non-linear Freundlich type and where the overall rate of adsorption is controlled by the rate of mass transfer across the gas-film surrounding each particle. The solutions, which are presented in graphical form, have been obtained independently by integrating the relevant differential equations both by analogue and digital computation.     

Wall effects for the pressure drop in fixed beds

A very simple model is presented for the effect of the container wall on the pressure drop in a fluid flowing through a bed of spheres. It is based on the application of the Ergun equation to the bulk region of the bed, unaffected by the wall. Pressure loss predictions are found to correspond well to the opposing trends reported in the literature for the viscous- and inertial-flow regimes.     

Radial heat transfer to fixed beds of particles

Radial temperature distributions have been measured when air flows through a fixed bed of large particles heated at the wall. The measurements have been interpreted by two models. In the first, the axial and radial thermal conductivities are assumed constant throughout the bed, and there is a thermal resistance at the wall. In the second, thermal properties have been assumed constant in the bulk, but allowed to vary in a narrow boundary region adjacent to the wall without an additional resistance so that both temperature and temperature gradient are continuous throughout both regions. For small particles and particles of high thermal conductivity, both models interpreted the measurements equally well. For large particles of low thermal conductivity the two-region model was much better.