Equilibrium Adsorption Data from Breakthrough Curves with Variable Velocity and Pressure

The adsorption of three tripeptides in an ion-exchange membrane adsorber was analyzed in single and binary solutions, with the aim of evaluating the capability of the membrane adsorber to separate triglycine (GGG) from two other tripeptides: glycine-histidine-glycine (GHG) and glycine-tyrosine-glycine (GTG). The equilibrium adsorption of single peptide solutions followed the Langmuir isotherm and GTG showed the highest adsorption affinity. The dynamic adsorption was fitted with a generalized model, which was defined using dimensionless parameters and based on the continuity equation. In general, the calculated and experimental breakthrough curves were correlated with high agreement. It was found that the axial dispersion coefficient was independent of the peptide molecule and that it increased with flow rate. The competitive adsorption between peptides in binary solutions was analyzed using the extended and modified Langmuir equations. The adsorption equilibrium data were satisfactorily fitted with the modified Langmuir isotherm for GGG/GHG solutions, while the extended Langmuir isotherm was a better fit to the data for GGG/GTG solutions. The experimental breakthrough curves of the two peptide binary mixtures were simulated using the parameters calculated from the competitive isotherms and the parameters obtained from the breakthrough curves of the single peptide solutions. The separation of GGG from the GGG/GHG mixtures was possible. The GGG recovery was higher than 35% and the GGG molar fraction in the outlet stream was higher than 0.994.

This work provides a new mass transfer model based on the Maxwell–Stefan theory, especially adapted to represent adsorbed phase multicomponent diffusion at high‐adsorbent loading. In our model—contrarily to the well‐known model developed by Krishna et al. (Chem Eng Sci. 1990;45:7:1779–1791; Gas Sep Purif. 1993;7:91–104; J Phys Chem B. 2005;109:6386–6396)—the hypothesis that the micropores are saturated does not imply a dependency between the adsorbed phase diffusion coefficients. Experimental liquid phase breakthrough curves of 2‐methylpentane (2MP), 3‐methylpentane (3MP), 2,3‐dimethylbutane (23DMB), and 2,2‐dimethylbutane (22DMB) were measured at 458 K in silicalite. The self‐diffusion coefficients and Langmuir parameters of the different species were determined using binary exchange breakthrough curves. The Maxwell–Stefan diffusion coefficients obtained for the different isomers are in the order D3MP,nc+1 > D2MP,nc+1 ≫ D23DMB,nc+1, and vary between 4 × 10−15 m2 s−1 for 3MP to 6 × 10−16 m2 s−1 for 23DMB. The 22DMB diffusion coefficient is so low that it could not be estimated (the quantity of 22DMB entering silicalite during the experiment is not significant). The model was then validated by comparing experimental breakthrough curves at different feed concentrations and simulations using the independently estimated parameters. Even though the diffusion coefficients of the different isomers vary by one order of magnitude, the agreement between simulated and experimental curves is very satisfactory, showing the good predictive power of our model. © 2010 American Institute of Chemical Engineers AIChE J, 2011

A model considering the overall axial dispersion for describing protein adsorption and breakthrough in monolithic cryogel beds has been developed. The microstructure of cryogels was characterized by tortuous capillaries with a normal diameter distribution but a constant pore wall thickness. The axial dispersion within cryogel columns was described by using the overall axial dispersion coefficient, which can be easily obtained by matching the experimental breakthrough curves without adsorption or measuring residence time distributions (RTDs). Experimental breakthrough curves of lysozyme within a metal-chelated affinity cryogel by Persson et al. (Biotechnol. Bioeng. 2004, 88, 224-236) and a cation-exchange cryogel by Yao et al. (J. Chromatogr. A 2007, 1157, 246-251) were employed as examples to test the model. The results showed that by using the axial dispersion coefficient and assuming uniform radial concentration profile at a given cross-section of the cryogel along the bed height, the model can describe the detailed behaviors of the in-bed overall axial dispersion, the in-pore mass transfer, as well as the protein adsorption and breakthrough. For a known overall axial dispersion coefficient, the lumped parameter of the mass transfer coefficient between the bulk liquid and the capillary wall can be determined by fitting the protein breakthrough curve at a known chromatographic condition. Once this parameter is determined, the model can be used to predict the protein breakthrough profiles under different conditions based on the basic physical parameters of the cryogel bed and the properties of the fluid and protein. The effective capillary diameters employed in the model are close to the actual pore sizes observed from the images by SEM. The model predictions of lysozyme breakthrough profiles at various flow rates are also in good agreement with the experimental data in both the metal-chelated affinity and cation-exchange cryogel columns.

Removal of nickel(II) ions from aqueous solution by biosorption in a fixed bed column: Experimental and theoretical breakthrough curves

Arsenic is a toxic element and may be found in natural as well as in industrial water; therefore, before using water for drinking purpose, its proper treatment is required. Thus, the aim of this work was to evaluate the potential of chitosan nanoparticles, in a continuous-flow method, for the removal of arsenic (III) and (V) from aqueous solutions. All experiments were conducted in fixed-bed columns. Experiments were carried out as a function of varying liquid flow rate (0.3–1.0 ml/min), initial metal concentration (0.5–1.5 mg/L), and bed height (3–9 cm) of adsorbent. The total adsorbed quantity, equilibrium uptake, and total percentage removal of arsenic ions were determined by evaluating the breakthrough curves obtained at different flow rates, initial concentrations, and bed heights. The results showed that the column performed well at the lowest flow rate. Also, column bed capacity and exhaustion time were found to increase with increasing bed height. When initial metal ion concentration was increased from 0.5 to 1.5 mg/L, the corresponding adsorption bed capacity decreased from 0.076 to 0.028 mg/g. The bed depth service time model (BDST) model was used to analyze the experimental data and the model parameters were evaluated. The calculated values of N o and K a were found to be 19.28 × 10−2 mg/L and 0.662 L/mg·min, respectively. Good agreement was found between the experimental breakthrough curves and the model predictions.

The recovery of direct dye by adsorption on cross-linked fiber (ChF-B), which we have developed, appeared technically feasible. The concentration of amino group fixed in the adsorbent phase was 3.30 mol/kg dry fiber. A typical direct dye, Brilliant Yellow (M.W.=625, divalent anion) was used in this experimental study. The breakthrough curves for adsorption of the dye were measured for different flow rates, bed heights, influent concentrations of the dye, and temperatures. The experimental breakthrough curves showed that ChF-B recovered the dye efficiently even from the hot dye solution. Axial dispersion coefficient E z (m 2 /s) in fibrous bed was measured and the following correlation for the dispersion coefficient was obtained: Ez = 5.4 × 10 −6 Re ′ 1.1 (ɛ = 0.698) Ez = 4.7 × 10 −6 Re ′ 1.2 (ɛ = 0.813) where ɛ denotes void fraction of the bed. The theoretical breakthrough curve obtained by considering the effect of axial dispersion was close to that obtained from the analytical solution for rectangular isotherm system without considering the axial dispersion in Re ′ > 0.46. The experimental breakthrough curves in pH ≤ 4 agreed well with the analytical solution. The intrafiber effective phase diffusivity of the dye at 323 K was about two times larger than that at 298 K and the bed capacity at 323 K was almost the same as that at 298 K.

The recovery of direct dye by adsorption on cross-linked fiber (ChF-B), which we have developed, appeared technically feasible. The concentration of amino group fixed in the adsorbent phase was 3.30 mol/kg dry fiber. A typical direct dye, Brilliant Yellow (M.W.=625, divalent anion) was used in this experimental study. The breakthrough curves for adsorption of the dye were measured for different flow rates, bed heights, influent concentrations of the dye, and temperatures. The experimental breakthrough curves showed that ChF-B recovered the dye efficiently even from the hot dye solution. Axial dispersion coefficient Ez (m2/s) in fibrous bed was measured and the following correlation for the dispersion coefficient was obtained: Ez = 5.4 × 10−6Re′1.1 (ɛ = 0.698) Ez = 4.7 × 10−6Re′1.2 (ɛ = 0.813) where ɛ denotes void fraction of the bed. The theoretical breakthrough curve obtained by considering the effect of axial dispersion was close to that obtained from the analytical solution for rectangular isotherm system without considering the axial dispersion in Re′ > 0.46. The experimental breakthrough curves in pH ≤ 4 agreed well with the analytical solution. The intrafiber effective phase diffusivity of the dye at 323 K was about two times larger than that at 298 K and the bed capacity at 323 K was almost the same as that at 298 K.

The present study consists of an experimental investigation of dispersion in inhomogeneous layered, isotropic porous media. Thanks to an in situ method of measuring electrical conductivity, we have studied two layered models. We examine four different layouts. The first sample has three layers of different permeabilities. The second has only two layers. Furthermore. two models with layers oriented perpendicular to the flow are considered. Besides normal "gaussian" dispersion, clear cut anomalies were observed. The experimental breakthrough curves are skewed as a consequence of tracer tailing. Tailed breakthrough curves are known from displacement in cores with local heterogeneity. Good agreement has been obtained between the experimental results and the semiphenomenological model of Coats Smith. Thus~ the mechanism involved in this anomalous dispersion is not trapping in the so-called dead end pores, but rather is due to different residence times because of permeability difference. Introduction The mixing of a tracer during flow through a porous medium involves the interplay between the two basic phenomena of dispersion, namely, molecular diffusion and mechanical (geometrical) dispersion. If two miscible fluids are in mutual contact. initially with a shaped interface, they will diffuse into one another because of random molecular motion according to the diffusion law of Fick1:: Equation (1) (Available in full paper) To account for the tortuous path of a porous medium, equation (I) was modified by Klinkenberg2, who used the analogy with electrical conductivity, thus: Equation (2) (Available in full paper) Do thereby corresponds to the bulk molecular diffusion coefficient for the fluid multiplied by the geometric factor (F Ø). The formation factor is F= σ o / σ, were σ denotes the electrical conductivity of a rock saturated with a fluid of conductivity σOØ. is the porosity of the rock. Molecular Diffusion is the dominant factor at extremely low or zero flow rate. At a higher flow rates, fluid flow plays a key role: there is a competition between the dispersive effect of the velocity gradients in the flow, and the various processes that homogenize the tracer (diffusion and transverse dispersion) across the porous media. The dimensionless Peelet number, which is the ratio of convective velocity U to the average velocity of molecular diffusion over a distance I characterizes this competition. Thus: Equation (3) (Available in full paper)

Fixed-bed column dynamics of tetracycline hydrochloride using commercial grade activated carbon: comparison of linear and nonlinear mathematical modeling studies

In this paper, we study and quantify pollutant concentrations after long-term leaching at relatively low flow rates and residual concentrations after heavy flushing of a 0.14 m3 municipal solid waste sample. Moreover, water flow and solute transport through preferential flow paths are studied by model interpretation of experimental break-through curves (BTCs), generated by tracer tests. In the study it was found that high concentrations of chloride remain after several pore volumes of water have percolated through the waste sample. The residual concentration was found to be considerably higher than can be predicted by degradation models. For model interpretations of the experimental BTCs, two probabilistic model approaches were applied, the transfer function model and the Lagrangian transport formulation. The experimental BTCs indicated the presence of preferential flow through the waste mass and the model interpretation of the BTCs suggested that between 19 and 41% of the total water content participated in the transport of solute through preferential flow paths. In the study, the occurrence of preferential flow was found to be dependent on the flow rate in the sense that a high flow rate enhances the preferential flow. However, to fully quantify the possible dependence between flow rate and preferential flow, experiments on a broader range of experimental conditions are suggested. The chloride washout curve obtained over the 4-year study period shows that as a consequence of the water flow in favoured flow paths, bypassing other parts of the solid waste body, the leachate quality may reflect only the flow paths and their surroundings. The results in this study thus show that in order to improve long-term prediction of the leachate quality and quantity the magnitude of the preferential water flow through a landfill must be taken into account.

The removal of sulfur dioxide (SO2) from simulated flue gas was investigated in a laboratory‐scale stainless steel fixed‐bed reactor using sorbents prepared from various siliceous materials, i.e., coal fly ash (CFA), oil palm ash (OPA) and rice husk ash (RHA) mixed with lime (CaO) by means of the water hydration method. Experiments were carried out with a flue gas flow rate of 150 mL/min, reaction temperature of 100 °C, and SO2 concentration of 1000 ppm. It was found that sorbents prepared from RHA have high BET surface areas and high SO2 sorption capacities, based on breakthrough curve analysis. In addition, the SO2 breakthrough curves were also described in terms of a simple first‐order deactivation model containing only two rate constants, one of which, ks, describes the surface reaction rate constant while the other, kd, describes the deactivation rate constant. The values of ks and kd obtained from the deactivation kinetics model were in good agreement with the experimental breakthrough curves and were also compared with those available in the literature.

Solute transport in heterogeneous model porous media under different flow rates: Experimental and modelling study

Biosorption of uranium(VI) from aqueous solutions by Ca-pretreated Cystoseira indica alga: Breakthrough curves studies and modeling

Fluid bed adsorption of carbon dioxide on immobilized polyethylenimine (PEI): Kinetic analysis and breakthrough behavior

Dynamic adsorption of phenolic compounds on activated carbon produced from pulp and paper mill sludge: experimental study and modeling by artificial neural network (ANN)