Sorption Kinetic Models Research Articles

Aging effects on cadmium transport in undisturbed contaminated sandy soil columns.

Limited information is available on the effects of contaminant aging (i.e., the contact time of Cd with the soil) on Cd transport in soils. We conducted displacement experiments in which indigenous Cd and freshly applied Cd were leached simultaneously from undisturbed samples of three Spodosol horizons. Sorption of Cd was described using Freundlich isotherms, whereas transport was described as a convection-dispersion process. Parameter optimization analysis using a mobile-immobile transport model applied to nonsorbing tracer displacement data showed that 16 to 22% of the water in the columns was immobile. The low dimensionless mass transfer coefficients in the mobile-immobile model were indicative of diffusion-limited transfer between mobile and immobile water, and hence physical nonequilibrium. A two-site kinetic sorption model could be fitted closely to breakthrough curves of the non-aged Cd for three soil horizons. No conclusive evidence was found that contaminant aging in soil affects cadmium transport. On the one hand, predictions of aged Cd leaching, using parameters estimated from displacement experiments with nonaged Cd, differed from those for the aged Cd in the E horizon. On the other hand, no meaningful differences in transport behavior between aged and non-aged Cd were found for the humus Bh and Bh/C horizons. The two-site kinetic rate coefficient alphac was found to depend on water flux, further indicating that mass transfer between sorption sites and the liquid is limited by diffusion rather than by kinetic sorption.

Modeling of Water Sorption Kinetics in Spaghetti During Overcooking

ABSTRACTThe organoleptic changes of pasta during overcooking are strongly related to the rate at which water molecules penetrate the pasta matrix once the optimal cooking conditions are reached. A model to describe water sorption kinetics during the overcooking stage is presented. The model has been developed assuming that overcooking starts once the central core disappears and that during this stage sorption kinetics are governed by the pasta matrix relaxation rate. To validate the model, water sorption tests were performed at 10–100°C. A good agreement between the model predictions and the experimental data was obtained. Based on these results, the main matrix relaxation time can be used to compare behavior during overcooking of pastas with different compositional and technological variables.

A Sorption-Kinetic Model for Surfactant-Driven Spreading of Aqueous Drops on Insoluble Liquid Substrates

Spreading of aqueous drops on hydrocarbon liquids occurs only when particular surfactants are added to the droplets above a critical concentration. For surfactant solutions of didodecyl ammonium bromide (DDAB) in water spreading over mineral oil, rates of droplet expansion are much slower than those corresponding to pure liquids spreading over immiscible liquid substrates with the same initial spreading coefficients. We present a sorption-kinetic model to explain quantitatively the spreading histories for aqueous DDAB droplets on mineral oil. Due to surfactant transport limitations, spreading occurs only when enough surfactant arrives at the dilating lens surfaces to establish a slightly positive, but near-zero spreading coefficient. We solve the convective diffusion equation for a cylindrical disk-like lens under the integral constraint of a constant surfactant adsorption density corresponding to a near-zero spreading coefficient. All observed spreading behavior is correctly portrayed by the proposed sorption-kinetic model including final equilibrium lens formation and spreading rates that are sensibly independent of drop volume, but are strongly dependent on drop surfactant concentration. Quantitative agreement is found with the experimental spreading data for a surfactant diffusion coefficient of 6×10−12 m2/s and an effective adsorption rate constant of 6.5×10−7 m/s. Both values prove physically reasonable. The sorption-kinetic model provides a new mechanism for understanding slow surfactant-driven spreading.

On the linear driving force model for sorption kinetics of organic compounds on suspended sediment particle

AbstractSorption kinetics of hydrophobic organic compounds on suspended sediments in the water column are analyzed using the linear driving force (LDF) model. The LDF model succinctly captures the different mass transfer resistances for uptake by aqueous suspended particles. The LDF model is appropriate for those situations where both water‐ and particle‐side processes are important. It is shown that departure from equilibrium sorption may be responsible for the near constancy in experimental sorption coefficients obtained for strongly hydrophobic compounds towards aqueous suspended particles in the sedimentary environment. The time to equilibrium for sorption diminishes with decreasing particle radius and increases with increasing compound hydrophobicity. For strongly hydrophobic compounds, the apparent partition coefficient is shown to be inversely proportional to the suspended solids concentration when sorption is far from equilibrium.

Pseudo-second order model for sorption processes

A literature review of the use of sorbents and biosorbents to treat polluted aqueous effluents containing dyes:organics or metal ions has been conducted. Over 70 systems have been reported since 1984 and over 43 of these reported the mechanism as being a pseudo-first order kinetic mechanism. Three sorption kinetic models are presented in this paper and have been used to test 11 of the literature systems previously reported as first order kinetics and one system previously reported as a second order process. In all 12 systems, the highest correlation coefficients were obtained for the pseudo-second order kinetic model. © 1999 Elsevier Science Ireland Ltd. All rights reserved.

Comparison of Kinetic and Hybrid-Equilibrium Models Simulating Colloid-Facilitated Contaminant Transport in Porous Media

The presence of colloidal particles in groundwater can enhance contaminant transport by reducing retardation effects and carrying them to distances further than predicted by a conventional advective/dispersive equation with normal retardation values. When colloids exist in porous media and affect contaminant migration, the system can best be simulated as a three-phase medium. Mechanisms of mass transfer from one phase to another by colloids and contaminants can be kinetic or equilibrium-based, depending on the sorption–desorption reaction rate between the aqueous and solid phases. When the rate of sorption between the water phase and the solid phase(s) is not much greater than the rate of change in contaminant concentration in the water phase, kinetic sorption models may better describe the phenomenon. In some cases of modeling one or more mass transfer processes, a useful simplification may be to introduce the local equilibrium assumption. In this study, the local equilibrium assumption for sorption processes on colloidal surfaces (hybrid equilibrium model) was compared with kinetic-based models. Sensitivity analyses were conducted to deduce the effect of major parameters on contaminant transport. The results obtained from the hybrid equilibrium model in predicting the transport of colloid-facilitated groundwater contaminant are very similar to those of the kinetic model, when the point of interest is not at contaminant and colloid source vicinities and the time of interest is sufficiently long for imposed sources.

The kinetics of sorption of basic dyes from aqueous solution by sphagnum moss peat

AbstractThe kinetics of sorption of three basic dyes, namely, Chrysoidine (BO2), Astrazon Blue (BB3) and Astrazone Blue (BB69) onto sphagnum moss peat have been investigated. The study focuses on the application of three sorption kinetic models for predicting the uptake of basic dyes. The sorption behaviour is found to be second order, based on the assumption of a pseudo‐second order mechanism. The rate constant of sorption, the equilibrium capacity and initial sorption rate with the effect of various peat doses and initial dye concentrations have also been predicted.

Development of a continuously stirred flow cell for investigating sorption mass transfer

This paper introduces a new reversible-flow design for a continuously stirred reactor used to study sorption mass transfer in soil and solvent systems. The stirred reactor has potential advantages over conventional packed column or batch reactors because it isolates intraparticle sorption rate limitations from advective-dispersive transport, yet allows changes to flux through the reactor for analysis of sorption kinetics under dynamic conditions. Previously, stirred reactors have often failed due to clogging of sediment on the effluent frit. The reverse-flow backwashing design allows longer life and higher confidence in maintaining mixed conditions than previous designs. Mass transfer 'rate coefficients estimated from stirred and column experiments are compared; both techniques produced results consistent with a published correlation. The data also show that fitted sorption mass transfer coefficients can be strongly dependent on the choice of equilibrium partition coefficient (i.e. batch or first-moment derived values), and that the conventional two-site sorption kinetics model fails to accurately predict sorption mass transfer in the presence of changing solvent velocity through the reactor.

Water Adsorption and Desorption Kinetics on Silica Insulation

Silica is an important component of thermal insulation used in aerospace transport vehicles. Although normally hydrophilic and requiring rewaterproofing after flight, silica insulation has been reported to become hydrophobic on heating and cooling in a vacuum and, therefore, potentially hydrophobic after reentry. To understand and model these processes, the rates of desorption and adsorption of water on silica were studied by thermogravimetry, Fourier transform infrared spectrometry, and X-ray photoelectron spectroscopy. Silica powders with a high surface area were heatedin vacuoin the temperature range 200–1000°C, infrared absorbance spectra were obtained at various temperatures, and surface structure was examined by X-ray photoelectron spectroscopy. A kinetic sorption model was developed based on a Langmuir rate expression. Activation energies for adsorption and desorption were determined by fitting the experimental results numerically. The study found adsorption of water on the heat-treated silica occurs within seconds, implying hydrophobicity is lost rapidly after the heat-treated silica is exposed to water.

Theoretical Treatment of Rapid Sorption Kinetics Measured in Batch Arrangement

Universal solution of a family of sorption kinetic models which are based on superposition principle has been developed to describe sorption experiments in a closed system. The models account for the interactions of a sorbate sorbent system with the apparatus which arise (i) from the mass balance condition in a closed system and (ii) from a finite rate of sorbate supply to the sorbent, the latter effect being of importance particularly in rapid nonstationary kinetic processes. Theoretical uptake curves for the intracrystalline sorption kinetics in zeolite crystals are exemplified using numerical solution of the corresponding Volterra integral equations which represent kinetic models of the overall transient sorption process in the apparatus. The approach appears to be promising for treatment of sorption kinetics in multicomponent systems.

Retardation of Tritium and Cesium in Brine‐Saturated Mudstone, Halite, and Carbonate Porous Media

AbstractBatch and column sorption/desorption experiments were conducted to quantify the retardation of tritium and cesium in brine‐saturated mudstone, halite, and carbonate rocks from Palo Duro Basin, Texas, one of the three sites originally nominated by the U.S. Department of Energy for construction of a civilian nuclear waste repository. Retardation factors (R) were determined using six different methods, including batch sorption equilibrium, fitting of two transport models, breakthrough area integration, and pore volume displacement at C/C0= 0.5, for both the sorption and desorption parts of the breakthrough curves. The breakthrough area integration method resulted in R values consistently lower than the other methods, which were in reasonable agreement. The data indicated very small retardation for cesium in all the media, except mudstone, which exhibited moderate retardation (R < 3.5). It was shown that the small extent of cesium retardation was most possibly caused by the strong competition for sorption sites of the components of the saturated brine, which were several orders of magnitude higher in concentration than cesium. Tritium breakthrough curves for all media tested were accurately simulated by the local equilibrium advection‐dispersion model (model I). With the exception of mudstone, cesium breakthrough curves were also adequately simulated by model I. The cesium breakthrough curve for mudstone exhibited considerable tailing on the desorption side of the curve, which was best described by the two‐site kinetic sorption model II. This was attributed to chemical nonequilibrium (two types of sorption sites). Predicted breakthrough curves for cesium using model I were in good to reasonable agreement with measured breakthrough curves.

Modelling nutrient uptake considering sorption kinetics: Phosphorus uptake from a one dimensional rhizosphere

Abstract A mathematical model was developed which accounts for sorption kinetics of nutrients having limited availability in soil material. Model trials in which predictions of P uptake and concentration profiles in a one dimensional simulated rhizosphere were performed. Data and parameters for the kinetic sorption of P in soil were taken from two mechanistic‐kinetic models (4,8). In addition, an apparent buffer power was defined on the basis of the mechanistic‐kinetic models (9) and was used in the uptake model as well. Predictions obtained from the uptake model based on the buffer power concept were compared to those obtained for the same soils with the kinetic sorption model. The results indicate a reduction in both the predicted uptake and concentration profiles, when sorption kinetics is accounted for.

Kinetics of metal ion sorption on clinoptilolite

From an investigation into the sorption kinetics of Na+, K+, and Sr2+ ions from standard solutions on finely dispersed clinoptilolite incorporated in a highly permeable inert polyacrylamide gel we have determined the characteristic kinetic size of clinoptilolite and the diffusion coefficients for Na+, K+, and Sr2+ in the clinoptilolite microcrystallites and transport pores. Diagrams have been constructed to enable a valid selection of kinetic models for sorption of the ions from any solutions on clinoptilolite.

Evaluation of Sorption Models in the Simulation of Naphthalene Transport Through Saturated Soils

AbstractTo show the effect of sorption model selection, the one‐dimensional transport of naphthalene in two saturated porous media was simulated using numerical models, which included the processes of dispersion, advection, and sorption. Three vdifferent models describing the sorption process: (1) a local equilibrium model, (2) a first‐order kinetic sorption model, and (3) a two‐site model (a combination of equilibrium and kinetic sorption model), were examined. In addition, this study considered two types of boundary conditions: constant concentration and constant flux boundary conditions. Simulations were made for data of naphthalene transport through a laboratory soil column packed with Lincoln or Eustis soil series. Numerical simulation results show that the selection of the sorption model had significant effects on the numerical solutions. The numerical solution obtained using either the local equilibrium model or the first‐order kinetic sorption model described the experimental data very well from the Lincoln soil column. In contrast, the numerical solution obtained using the two‐site model described the experimental data for the Eustis soil better than either the equilibrium or kinetic models. Different boundary conditions had little influence on the numerical solutions. Different amounts of organic carbon in the Eustis (0.66%) and Lincoln (0.036%) soils are thought to cause the differences in breakthrough curves and the response to the sorption processes.

Field scale mass arrival of sorptive solute into the groundwater

The effect of spatial variability in sorption parameters is investigated for field scale solute transport in the unsaturated zone. The considered sorption reaction is kinetically controlled sorption‐desorption coupled with a parallel linear equilibrium isotherm. The source of solute is assumed to be distributed over a heterogeneous field where the horizontal extent of the source area is significantly larger than the depth to the ground water table. The transport model is expressed in terms of the mass flux and in dimensionless form, where the effect of equilibrium sorption is incorporated in the dimensionless parameters of the kinetic sorption model. The influence of different correlation properties between the sorption parameters and the hydraulic conductivity at saturation, Ks, on the expected field scale mass flux of solute is illustrated. The results indicate that spatially variable sorption rate coefficients with negative or no correlation to Ks may result in an earlier mass arrival and a considerably altered form of the breakthrough curve compared to the case of constant sorption parameters. In addition, a comparison between the flux‐averaged and the resident concentration models indicates that spatial variability in the sorption rate coefficients has similar effects on the temporal variation of the field‐scale resident concentration as on the field scale mass flux of solute.

Prediction of phosphate transport in small columns with an approximate sorption kinetics model

The reaction of phosphate (P) with soil is described with two processes: adsorption and diffusion precipitation. In case of small pH variations in the acid pH range (pH 4.5–6.5) P adsorption may be described with the Langmuir equilibrium or Langmuir kinetics equation. The diffusion‐precipitation process is described with an expression taking the effects of P concentration and reaction time into account. This description is based on the unreacted shrinking core model, where the metal oxides are converted into metal phosphates, and these two phases are separated by a sharp interface inside the particles. Assuming that the adsorption process is reversible and the diffusion‐precipitation process is irreversible, methods are discussed for parameter assessment of the sorption model. These methods are illustrated for a soil. The description of the experimental data is good. For an evaluation of the predictive capabilities of the sorption model, P transport in small columns is predicted, using independently assessed sorption and transport parameters. These predictions are compared to experimental data. The predicted P breakthrough curves are overall well in agreement with the experimental results obtained by percolation of a pulse of a P solution. The main difference between predicted and experimental breakthrough is observed in the sorption stage of the pulse with a feed concentration (c0) of 0.2 mol P m−3. After initial breakthrough the correspondence of the prediction and the data is good for these triplicated experiments at c0=0.2 mol/m3. At high feed concentrations (c0=3 mol/m3) only small differences between prediction and experiment are observed in the desorption stage of the concentration pulse. For experiments involving a first pulse at c0=3 mol/m3 followed by two pulses at c0=0.2 mol/m3 the same agreement of numerical and experimental breakthrough curves is found as for the experiments involving only one pulse. Because P transport involving both sorption and desorption stages was modelled reasonably for two different concentrations we conclude that the P sorption model developed describes the reactions of P with soil accurately.

Numerical modeling of sorption kinetics of organic compounds to soil and sediment particles

A numerical model is developed to simulate hydrophobic organic compound sorption kinetics, based on a retarded intraaggregate diffusion conceptualization of this solid‐water exchange process. This model was used to ascertain the sensitivity of the sorption process for various sorbates to nonsteady solution concentrations and to polydisperse soil or sediment aggregate particle size distributions. Common approaches to modeling sorption kinetics amount to simplifications of our model and appear justified only when (1) the concentration fluctuations occur on a time scale which matches the sorption timescale of interest and (2) the particle size distribution is relatively narrow. Finally, a means is provided to estimate the extent of approach of a sorbing system to equilibrium as a function of aggregate size, chemical diffusivity and hydrophobicity, and system solids concentration.

Kinetic models for hydrogen sorption and their application to the H 2-M system

Several kinetic models for the H 2-M system have been proposed and the corresponding rate equations developed. The solutions of these rate equations were compared to the experimental data for certain H 2-metal systems. These models can successfully explain the absorption/desorption kinetics of some H 2-M systems. Detailed discussions regarding the limitation of the kinetic model are also presented.

Kinetics in a chelate ion exchanger—I. Theoretical analysis

A kinetic model for sorption of metallic ions by a chelate ion exchanger is proposed in which the resistances of intraparticle diffusion and chelate complex formation reaction are both included. The Nernst-Planck equation is applied to the flux of ions in the resin particle. Analytical solutions are given for the limiting cases of diffusion control and reaction control, and numerical solutions are presented for the general case in which both resistances are significant. The analytical solution for diffusion control, which is based on the shrinking core model, gives the fractional exchange as a function of the diffusivities and valencies of the counter-ions. Uptake curves are calculated from the theoretical equations to show how the kinetics are influenced by the equilibrium constant, the diffusivity ratio of the counter-ions, the rate constant for the chelate complex formation reaction and the ionic valencies. The range in which the analytical solutions can be considered as an acceptable approximation is given.

Selective chemisorbents. Part 3: Selective binding of thiols to benzaldehyde derivatives of cellulose

Benzaldehyde derivatives of cellulose were prepared by reaction of amino derivatives of powder or bead cellulose with 4-isothiocyanato benzaldehyde in a water-dioxane-buffered neural medium. Rapid reactions of benzaldehyde cellulose derivatives with thiols (benzyl [ 35S] mercaptan, cysteine, reduced glutasthione) produced thioacetal and hemithioacetal cellulose derivatives in strongly acid (pH ≈ 0.5) and less acid or neuralmedia, respectively. Selective reaction with thiols, even in presence of other nucleophiles (benzylamine benzyl alcohol), was ensured in strongly acid medium while the presence of amine in neutral medium caused an increase of thiol sorption up 300%. The kinetics of formation of thioacetal cellulose derivatives were found to be a good model for sorption kinetics, allowing their transformation to linear form. This procedure allows a rapid estimation of carrier sorption capacity and sorption half-time.