Kinetics of adsorption on activated carbon: application of heterogeneous vacancy solution theory

The kinetics of single component adsorption on activated carbon is investigated here using a heterogeneous vacancy solution theory (VST) of adsorption. The adsorption isotherm is developed to account for the adsorbate non-ideality due to the size difference between the adsorbate molecule and the vacant site, while incorporating adsorbent heterogeneity through a pore-width-related potential energy. The transport process in the bidisperse carbon considers coupled mass transfer in both macropore and micropore phases simultaneously. Adsorbate diffusion in the micropore network is modeled through effective medium theory, thus considering pore network connectivity in the adsorbent, with the activation energy for adsorbate diffusion related to the adsorption energy, represented by the Steele 10-4-3 potential for carbons. Experimental data of five hydrocarbons, CO2 and SO2 on Ajax carbon at multiple temperatures, as well as three hydrocarbons on Norit carbon at three temperatures are first fitted by the heterogeneous VST model to obtain the isotherm parameters, followed by application of the kinetic model to uptake data on carbon particles of different sizes and geometry at various temperatures. For the hydrocarbons studied, the model can successfully correlate the experimental data for both adsorption equilibrium and kinetics. However, there is some deviation in the fit of the desorption kinetics for polar compounds such as CO2 and SO2, due to the inadequacy of the L-J potential model in this case. The significance of viscous transport in the micropores is also considered here and found to be negligible, consistent with recent molecular simulation studies. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analysis of multicomponent adsorption kinetics on activated carbon

An integrated mathematical model for the kinetics of multicomponent adsorption on microporous carbon was developed. Transport in this bidisperse solid is represented by balance equations in the macropore and micropore phases, in which gas-phase diffusion dominates the mass transfer in the macropores, with the phenomenological diffusivities represented by the generalized Maxwell-Stefan (GMS) formulation. Viscous flow also contributes to the macropore fluxes and is included in the MS expressions. Diffusion of the adsorbed phase controls the mass transfer in the micro ore phase, p which is also described in a similar way by the MS method. The adsorption isotherms are represented by a new heterogeneous modified vacancy solution theory formulation of adsorption, which has proved to be a robust method for adsorption on activated carbons. The model is applied to the coadsorption and codesorption of C2H6 and C3H8 on Ajax and Norit carbon, as well as the displacement on Ajax carbon. The effect of the viscous flow in the macropore phase is not significant for the cases studied. The model accurately predicts the overshoot behavior and rollup of C2H6 during coadsorption. The prediction for the heavier compound C3H8 is always satisfactory, though at higher C3H8 mole fraction, the overshoot extent of C2H6 is overpredicted, possibly due to neglect of heat effects.

Kinetics of reduction of FeO from slag by graphite and coal chars

The rates of reduction of FeO from iron-saturated FeO-CaO-Al2O3-SiO2 slags by graphite, coke, bituminous coal and anthracitic coal chars at temperatures in the range 1 673-1873 K have been measured using a sessile drop technique. The extents of reaction were determined using EPMA analysis of quenched samples, and on line gas analysis using a quadrupole mass spectrometer. The reaction rates have been shown to be dependent critically on carbon type. For the reaction geometry used in this investigation the reduction rates of graphite and coke are observed to be faster than with coal chars. This unexpected finding is shown to be associated with differences in the dominant chemical and mass transfer mechanisms occurring at the reaction interface. High reaction rates are observed to occur with the formation of liquid Fe-C alloy product and the associated gasification of carbon from the alloy. The rates of reduction by coal chars are determined principally by the chemical reaction at the carbon/gas interface and slag phase mass transfer.

Growth and lactic acid production in batch culture of Lactobacillus rhamnosus in a defined medium

To facilitate metabolic analysis, batch fermentations of Lactobacillus rhamnosus were carried out in a new defined medium. Biomass at 10.5 g/l and lactic acid at 67 g/l with a Y-P/S of 0.84 were achieved. The maximum specific growth rate and the average productivity were 0.49/h and 2.48 g/l.h, respectively. These are comparable to those of this organism and related organisms in complex media. Preliminary amino acid studies were also conducted, highlighting the importance of serine, asparagine, glutamine and cysteine. Kinetic analysis revealed that lactic acid production was predominantly growth-associated with growth associated and non-growth associated lactic acid constants of 0.389 mol/g-cell and 0.0025 mol/g-cell.h, respectively. Finally a kinetic model has been included to describe the fermentation of L. rhamnosus.

Metabolic and kinetic analysis of poly(3-hydroxybutyrate) production by recombinant Escherichia coli

A quantitatively repeatable protocol was developed for poly(3-hydroxybutyrate) (PHB) production by Escherichia coli XL1-Blue (pSYL107). Two constant-glucose fed-batch fermentations of duration 25 h were carried out in a 5-L bioreactor, with the measured oxygen volumetric mass-transfer coefficient (k(L)a) held constant at 1.1 min(-1). All major consumption and production rates were quantified. The intracellular concentration profiles of acetyl-CoA (300 to 600 mug.g RCM-1) and 3-hydroxy-butyryl-CoA (20 to 40 mug.g RCM-1) were measured, which is the first time this has been performed for E. coli during PHB production. The kinetics of PHB production were examined and likely ranges were established for polyhydroxyalkanoate (PHA) enzyme activity and the concentration of pathway metabolites. These measured and estimated values are quite similar to the available literature estimates for the native PHB producer Ralstonia eutropha. Metabolic control analysis performed on the PHB metabolic pathway showed that the PHB flux was highly sensitive to acetyl-CoA/CoA ratio (response coefficient 0.8), total acetyl-CoA + CoA concentration (response coefficient 0.7), and pH (response coefficient -1.25). It was less sensitive (response coefficient 0.25) to NADPH/NADP ratio. NADP(H) concentration (NADPH + NADP) had a negligible effect. No single enzyme had a dominant flux control coefficient under the experimental conditions examined (0.6, 0.25, and 0.15 for 3-ketoacyl-CoA reductase, PHA synthase, and 3-ketothiolase, respectively). In conjunction with metabolic flux analysis, kinetic analysis was used to provide a metabolic explanation for the observed fermentation profile. In particular, the rapid onset of PHB production was shown to be caused by oxygen limitation, which initiated a cascade of secondary metabolic events, including cessation of TCA cycle flux and an increase in acetyl-CoA/CoA ratio. (C) 2001 John Wiley & Sons. Inc. Biotechnol Bioeng 74: 70-80, 2001.

Discrimination of adsorption kinetic models for the description of hydrocarbon adsorption in activated carbon

Five kinetic models for adsorption of hydrocarbons on activated carbon are compared and investigated in this study. These models assume different mass transfer mechanisms within the porous carbon particle. They are: (a) dual pore and surface diffusion (MSD), (b) macropore, surface, and micropore diffusion (MSMD), (c) macropore, surface and finite mass exchange (FK), (d) finite mass exchange (LK), and (e) macropore, micropore diffusion (BM) models. These models are discriminated using the single component kinetic data of ethane and propane as well as the multicomponent kinetics data of their binary mixtures measured on two commercial activated carbon samples (Ajax and Norit) under various conditions. The adsorption energetic heterogeneity is considered for all models to account for the system. It is found that, in general, the models assuming diffusion flux of adsorbed phase along the particle scale give better description of the kinetic data.

A mechanistic model for carbon dioxide corrosion of mild steel in the presence of protective iron carbonate films - Part 3: Film growth model

A model of iron carbonate (FeCO3) film growth is proposed, which is an extension of the recent mechanistic model of carbon dioxide (CO2) corrosion by Nesic, et al. In the present model, the film growth occurs by precipitation of iron carbonate once saturation is exceeded. The kinetics of precipitation is dependent on temperature and local species concentrations that are calculated by solving the coupled species transport equations. Precipitation tends to build up a layer of FeCO3 on the surface of the steel and reduce the corrosion rate. On the other hand, the corrosion process induces voids under the precipitated film, thus increasing the porosity and leading to a higher corrosion rate. Depending on the environmental parameters such as temperature, pH, CO2 partial pressure, velocity, etc., the balance of the two processes can lead to a variety of outcomes. Very protective films and low corrosion rates are predicted at high pH, temperature, CO2 partial pressure, and Fe2+ ion concentration due to formation of dense protective films as expected. The model has been successfully calibrated against limited experimental data. Parametric testing of the model has been done to gain insight into the effect of various environmental parameters on iron carbonate film formation. The trends shown in the predictions agreed well with the general understanding of the CO2 corrosion process in the presence of iron carbonate films. The present model confirms that the concept of scaling tendency is a good tool for predicting the likelihood of protective iron carbonate film formation.

Electrochemical study of UNS S32550 super duplex stainless steel corrosion in turbulent seawater using the rotating cylinder electrode

The cathodic and anodic characteristics of freshly polished and pre-reduced UNS S32550 (ASTM A479) super duplex stainless steel in a filtered and conductivity-adjusted seawater have been investigated under controlled flow conditions. A rotating cylinder electrode was used together with both steady and non-steady-state voltammetry and a potential step current transient technique to investigate the electrode reactions in the fully characterized electrolyte. Both oxygen reduction and hydrogen evolution were highly irreversible and the material exhibited excellent passivation and repassivation kinetics. Relative corrosion rates were derived and the corrosion mechanism of the alloy was found to be completely independent of the mass-transfer effects, which can contribute to flow-induced corrosion.

Passive air sampling theory for semivolatile organic compounds

The mathematical modelling underlying passive air sampling theory can be based on mass transfer coefficients or rate constants. Generally, these models have not been inter-related. Starting with basic models, the exchange of chemicals between the gaseous phase and the sampler is developed using mass transfer coefficients and rate constants. Importantly, the inter-relationships between the approaches are demonstrated by relating uptake rate constants and loss rate constants to mass transfer coefficients when either sampler-side or air-side resistance is dominating chemical exchange. The influence of sampler area and sampler volume on chemical exchange is discussed in general terms and as they relate to frequently used parameters such as sampling rates and time to equilibrium. Where air-side or sampler-side resistance dominates, an increase in the surface area of the sampler will increase sampling rates. Sampling rates are not related to the sampler/air partition coefficient (K-SV) when air-side resistance dominates and increase with K-SV when sampler-side resistance dominates.

Aquatic passive sampling of herbicides on naked particle loaded membranes: Accelerated measurement and empirical estimation of kinetic parameters

Water-sampler equilibrium partitioning coefficients and aqueous boundary layer mass transfer coefficients for atrazine, diuron, hexazionone and fluometuron onto C18 and SDB-RPS Empore disk-based aquatic passive samplers have been determined experimentally under a laminar flow regime (Re = 5400). The method involved accelerating the time to equilibrium of the samplers by exposing them to three water concentrations, decreasing stepwise to 50% and then 25% of the original concentration. Assuming first-order Fickian kinetics across a rate-limiting aqueous boundary layer, both parameters are determined computationally by unconstrained nonlinear optimization. In addition, a method of estimation of mass transfer coefficients-therefore sampling rates-using the dimensionless Sherwood correlation developed for laminar flow over a flat plate is applied. For each of the herbicides, this correlation is validated to within 40% of the experimental data. The study demonstrates that for trace concentrations (sub 0.1 mu g/L) and these flow conditions, a naked Empore disk performs well as an integrative sampler over short deployments (up to 7 days) for the range of polar herbicides investigated. The SDB-RPS disk allows a longer integrative period than the C18 disk due to its higher sorbent mass and/or its more polar sorbent chemistry. This work also suggests that for certain passive sampler designs, empirical estimation of sampling rates may be possible using correlations that have been available in the chemical engineering literature for some time.

Free-Surface Aeration and Momentum Exchange at a Bottom Outlet

This study aims to provide some new understanding of the air-water flow properties in high-velocity water jets discharging past an abrupt drop. Such a setup has been little studied to date despite the relevance to bottom outlets. Downstream of the step brink, the free-jet entrains air at both upper and lower air-water interfaces, as well as along the sides. An air-water shear layer develops at the lower nappe interface. At the lower nappe, the velocity redistribution was successfully modelled and the velocity field was found to be similar to that in two-dimensional wake flow. The results highlighted further two distinct flow regions. Close to the brink (Wex < 5000), the flow was dominated by momentum transfer. Further downstream (Wex > 5000), a strong competition between air bubble diffusion and momentum exchanges took place.

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Experimental Analysis of Froude Number Effect on Air Entrainment in the Hydraulic Jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in rectangular horizontal flume with partially-developed inflow conditions. The vertical distributions of void fraction and air bubbles count rate were recorded for inflow Froude number Fr1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction Cmax increases with the increasing Fr1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was provided.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.