Steady State Performance of Activated Carbon Contactors

1991 ◽  
Vol 23 (7-9) ◽  
pp. 1677-1686 ◽  
Author(s):  
U. K. Traegner ◽  
M. T. Suidan
Keyword(s):  
Mathematical Model ◽  
Particle Size ◽  
Activated Carbon ◽  
Steady State ◽  
Surface Diffusion ◽  
Age Distribution ◽  
Carbon Surface ◽  
Transfer Resistance ◽  
Homogeneous Surface ◽  
Component Representation

A mathematical model for the steady state adsorption of pollutants from completely mixed activated carbon contactors is derived in this paper. In order to accurately describe these processes, a sludge age distribution is incorporated for the adsorbent. The resulting mathematical model is solvable analytically using the homogeneous surface diffusion model (HSDM) as a descriptor of intraparticle mass transfer resistance. Various examples are included in this paper to illustrate the use of this new derivation. Effects of particle size, particle size distribution of commercial carbon, surface diffusion coefficients, and solids mass flow rate, on the performance of the completely mixed adsorption system are studied in detail. Examples of multicomponent, competitive adsorption as well as an equivalent single component representation of a target component are discussed.

scholarly journals A frequency quantum interpretation of the surface renewal model of mass transfer

2017 ◽  
Vol 4 (7) ◽  
pp. 170103 ◽  
Author(s):  
Chanchal Mondal ◽  
Siddharth G. Chatterjee
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Frequency Distribution ◽  
Age Distribution ◽  
Gas Absorption ◽  
Bulk Liquid ◽  
Gas Transfer ◽  
Transfer Resistance ◽  
Surface Renewal ◽  
Two Parameter

The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies or liquid elements. Assuming that surface elements of a particular age have renewal frequencies that are integral multiples of a fundamental frequency quantum, and further assuming that the renewal frequency distribution is of the Boltzmann type, performing a population balance for these elements leads to the Danckwerts surface age distribution. The basic quantum is what has been traditionally called the rate of surface renewal. The Higbie surface age distribution follows if the renewal frequency distribution of such elements is assumed to be continuous. Four age distributions, which reflect different start-up conditions of the absorption process, are then used to analyse transient physical gas absorption into a large volume of liquid, assuming negligible gas-side mass-transfer resistance. The first two are different versions of the Danckwerts model, the third one is based on the uniform and Higbie distributions, while the fourth one is a mixed distribution. For the four cases, theoretical expressions are derived for the rates of gas absorption and dissolved-gas transfer to the bulk liquid. Under transient conditions, these two rates are not equal and have an inverse relationship. However, with the progress of absorption towards steady state, they approach one another. Assuming steady-state conditions, the conventional one-parameter Danckwerts age distribution is generalized to a two-parameter age distribution. Like the two-parameter logarithmic normal distribution, this distribution can also capture the bell-shaped nature of the distribution of the ages of surface elements observed experimentally in air–sea gas and heat exchange. Estimates of the liquid-side mass-transfer coefficient made using these two distributions for the absorption of hydrogen and oxygen in water are very close to one another and are comparable to experimental values reported in the literature.

scholarly journals Adsorption Characteristics of Humic Acids by Granular Activated Carbon

1997 ◽  
Vol 15 (7) ◽  
pp. 507-516 ◽  
Author(s):  
S.H. Lin ◽  
C.M. Lin
Keyword(s):  
Activated Carbon ◽  
Humic Acid ◽  
Surface Diffusion ◽  
Humic Acids ◽  
Granular Activated Carbon ◽  
Model Parameters ◽  
Adsorption System ◽  
Transfer Resistance ◽  
Liquid Phase Mass Transfer ◽  
Continuous Adsorption

The adsorption of humic acids on granular activated carbon has been investigated. A commerically available humic acid and that extracted from the bottom sludge of a dam were employed in the studies. Both batch and continuous adsorption experiments were conducted. A simplified competitive adsorption model in conjunction with the Freundlich isotherm was employed to represent the batch multicomponent adsorption system and a homogeneous surface diffusion model utilized to describe the continuous adsorption system in a packed-bed column. The model parameters were obtained by best fit of the models to the experimental adsorption data. The results indicated that the liquid-phase mass-transfer resistance, surface diffusion coefficient and the amount of adsorption on the activated carbon decreased with increasing molecular weight of the humic acid. It was also found that the adsorption of humic acid on the activated carbon was primarily a surface diffusion-controlled process.

Spherical Diffusion Model of Interspecies Hydrogen Transfer in Steady-State Methanogenic Reactors

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2389-2392 ◽  
Author(s):  
D. P. Smith
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Diffusion Model ◽  
Hydrogen Concentration ◽  
Hydrogen Transfer ◽  
Solution Concentration ◽  
Bulk Solution ◽  
Transfer Resistance ◽  
Concentration Difference ◽  
Spherical Diffusion

A previously developed spherical diffusion model of interspecies molecular hydrogen transfer was applied to a mathematical model of ethanol and propionate methanogenesis in a dispersed-growth, continuously stirred tank reactor (CSTR). Steady-state methanogenesis at a 0.10 day−1 space velocity required a hydrogen concentration difference of 1.12 × 10−5 aim (8.4 × 10−12 moles/cm3) between the surface of the propionate organisms and the bulk solution. The total difference in hydrogen concentration between source organism and sink organism Ihydrogenotrophic methanogenstwas 2.1 × 10−5 atm (1.6 × 10−11 moles/cm3). Steep gradients in hydrogen concentration existed only at close proximity to the bacterial spheres, with hydrogen concentration approaching bulk solution concentration at distances greater than 10 microns. Small hydrogen gradients and the bulk solution concentration prevailed through the majority of the reactor aqueous volume. Overall, the incorporation of hydrogen mass transfer resistance into the mathematical model had only a slight effect on hydrogen partial pressure, organic substrate levels, and bacterial mass concentrations predicted by the steady-state solution.

User-oriented batch reactor solutions to the homogeneous surface diffusion model for different activated carbon dosages

2009 ◽  
Vol 43 (7) ◽  
pp. 1859-1866 ◽  
Author(s):  
Qiong Zhang ◽  
John Crittenden ◽  
Kiril Hristovski ◽  
David Hand ◽  
Paul Westerhoff
Keyword(s):  
Activated Carbon ◽  
Surface Diffusion ◽  
Diffusion Model ◽  
Batch Reactor ◽  
Homogeneous Surface

Adsorption of pentachlorophenol (PCP) by activated carbon in fixed beds: application of homogeneous surface diffusion model

1998 ◽  
Vol 38 (7) ◽  
pp. 227-235 ◽  
Author(s):  
A. J. Slaney ◽  
R. Bhamidimarri
Keyword(s):  
Activated Carbon ◽  
Surface Diffusion ◽  
Diffusion Model ◽  
Freundlich Isotherm ◽  
Breakthrough Curves ◽  
Orthogonal Collocation ◽  
Homogeneous Surface ◽  
Diffusion And Convection ◽  
Film Transfer ◽  
Fixed Beds

The adsorption of pentachlorophenol (PCP) from aqueous solutions was investigated using fixed beds of activated carbon. The equilibrium behaviour was shown to fit a Freundlich isotherm with the values of parameters K and l/n of 95 and 0.180 respectively, which are comparable to those of other substituted phenolics. The surface diffusion coefficient was evaluated from batch kinetic adsorption experiments and was found to be 2.26 × 10−9 cm2s−1. The film transfer coefficient in the fixed beds was estimated using Gnielinski’s correlation. A Homogeneous Surface Diffusion Model (HSDM) was proposed to predict the PCP adsorption breakthrough curves in the fixed beds. The diffusion and convection equations were integrated using a combination of orthogonal collocation and Runge-Kutta techniques. The experimental results on the adsorption of PCP in activated carbon columns proved that the HSDM can predict the column performance satisfactorily and therefore can be used in the design of fixed beds for removal of PCP.

scholarly journals Activated Carbon/Transition Metal (Ni, In, Cu) Hexacyanoferrate Nanocomposites for Cesium Adsorption

Materials ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1253 ◽  
Author(s):  
Julien Kiener ◽  
Lionel Limousy ◽  
Mejdi Jeguirim ◽  
Jean-Marc Le Meins ◽  
Samar Hajjar-Garreau ◽  
...  
Keyword(s):  
Aqueous Solution ◽  
Particle Size ◽  
Activated Carbon ◽  
Transition Metal ◽  
Adsorption Capacity ◽  
Carbon Surface ◽  
Carbon Oxidation ◽  
Copper Hexacyanoferrate ◽  
Metal Type ◽  
Metal Hexacyanoferrate

Transition metal hexacyanoferrate/microporous activated carbon composites were obtained using a simple successive impregnation approach. The effect of metal type (nickel, indium, or copper), and the carbon oxidation on the composite characteristics (porosity, metal structure, and particle size), as well as on the removal efficiency of cesium from aqueous solution was investigated. Successful formation of the desired metal hexacyanoferrate phase was achieved and the size of the metallic nanoparticles and their dispersion in the carbon network was found to depend on the metal type, with the indium and nickel-based materials exhibiting the smallest particle size distribution (< 10 nm). Adsorption tests performed under batch conditions demonstrate that the copper hexacyanoferrate/activated carbon composite present the highest cesium removal capacity from aqueous solution (74.7 mg·g−1) among the three studied metal-based nanocomposites. The carbon oxidation treatment leads to the increase in the number of functional groups to the detriment of the porosity but allows for an improvement in the Cs adsorption capacity. This indicates that the Cs adsorption process is governed by the carbon surface chemistry and not its porosity. Moreover, combining oxidized carbon support with copper hexacyanoferrate induces the highest cesium adsorption capacity (101.5 mg·g−1). This could be related to synergistic effects through two absorption mechanisms, i.e., a cation exchange mechanism of Cs with the metallic hexacyanoferrate phase and Cs adsorption via carbon oxygen surface groups, as demonstrated using X-ray photoelectron spectroscopy (XPS) analyses.

Adsorption of Phenol on Bifunctional Resin and Granular Activated Carbon Preloaded by Tannic Acid

2011 ◽  
Vol 233-235 ◽  
pp. 765-773
Author(s):  
Zhao Yang Lu ◽  
Bi Cun Jiang ◽  
Ai Min Li ◽  
Jun Fan
Keyword(s):  
Activated Carbon ◽  
Surface Diffusion ◽  
Functional Groups ◽  
Diffusion Model ◽  
Tannic Acid ◽  
Granular Activated Carbon ◽  
Micropore Volume ◽  
Homogeneous Surface ◽  
Kinetic Tests ◽  
Almost All

For comparing the adsorption of Synthetic Organic Chemicals (SOC) competing with background pollutants between a bifunctional resin and a commercial granular activated carbon (GAC), tannic acid (TA) was preloaded to the two adsorbents at quantities of 60 and 120 μmol/g. As a result, decreases of micropores volume in the resin were 75.5 and 98.9%, while those in the GAC were only 19.0 and 30.0%, respectively. Preloading attenuated surface heterogeneities and phenol’s capacities of two adsorbents distinctly. But maximumly, 1.0 mole TA’s preloading on GAC could decline 9.23 mole phenol’s adsorption. Under the same condition, the resin’s capacity of phenol was only descended at 2.68 times, when 98.9% micropores have been blocked. In kinetic tests, blockages in the resin were misapprehended to be much lighter than those in the GAC by the Homogeneous Surface Diffusion Model (HSDM). One steady operation engineering at micropore volume 37.8% decline was introduced. The conflicts were explained by quite a number of resin’s functional groups in the macroporous and mesoporous region could attract enough phenol molecular rapidly, even if almost all micropores were blocked.

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