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.     

Modelling the solute transport under nonequilibrium conditions on the basis of mass transfer equations

A solute transport model that describes nonequilibrium adsorption in soil/groundwater systems by mass transfer equations for film and intraparticle diffusion is presented. The model is useful in cases where breakthrough curve spreading cannot be explained by dispersion only. To evaluate its validity, the model was applied to several data sets from column experiments. The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion. Furthermore, a sensitivity analysis was performed to illustrate the influence of different process and sorption parameters (pore water velocity, intraparticle mass transfer coefficient, isotherm nonlinearity) on the shape of the calculated breakthrough curves. The application of the proposed model is discussed in comparison to the widely used dispersed flow/local equilibrium model, and a relationship between both models, which is based on a lumped parameter approach, is shown.     

Characterization of metal adsorption kinetic properties in batch and fixed-bed reactors

Copper adsorption kinetic properties in batch and fixed-bed reactors were studied in this paper. The isothermal adsorption experiments showed that the copper adsorption capacity of a granular activated carbon (Filtrasorb 200) increased when ionic strength was higher. The presence of EDTA diminished the adsorption. An intraparticle diffusion model and a fixed-bed model were successfully used to describe the batch kinetic and fixed-bed operation behaviors. The kinetics became faster when the solution pH was not controlled, implying that the surface precipitation caused some metal uptake. The external mass transfer coefficient, the diffusivity and the dispersion coefficient were obtained from the modeling. It was found that both external mass transfer and dispersion coefficients increased when the flow rate was higher. Finally effects of kinetic parameters on simulation of fixed-bed operation were conducted.     

Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation processes

Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited information exists on the kinetic coupling of these processes. In this paper, a model is presented that couples nonlinear and nonequilibrium sorption (intraparticle diffusion) with biodegradation kinetics. Initially, these processes are studied independently (i.e., intraparticle diffusion, nonlinear sorption and biodegradation), with appropriate parameters determined from these independent studies. Then, the coupled processes are studied, with an initial data set used to determine biodegradation constants that were subsequently used to successfully predict the behavior of a second data set. The validated model is then used to conduct a sensitivity analysis, which reveals conditions where biodegradation becomes desorption rate-limited. If the chemical is not pre-equilibrated with the soil prior to the onset of biodegradation, then fast sorption will reduce aqueous concentrations and thus biodegradation rates. Another sensitivity analysis demonstrates the importance of including nonlinear sorption in a coupled diffusion/sorption and biodegradation model. While predictions based on linear sorption isotherms agree well with solution concentrations, for the conditions evaluated this approach overestimates the percentage of contaminant biodegraded by as much as 50%. This research demonstrates that nonlinear sorption should be coupled with diffusion/sorption and biodegradation models in order to accurately predict bioremediation and natural attenuation processes. To our knowledge this study is unique in studying nonlinear sorption coupled with intraparticle diffusion and biodegradation kinetics with natural media.     

Modelling of diffusion-limited retardation of contaminants in hydraulically and lithologically nonuniform media

A new reactive transport modelling approach and examples of its application are presented, dealing with the impact of sorption/desorption kinetics on the spreading of solutes, e.g. organic contaminants, in groundwater. Slow sorption/desorption is known from the literature to be strongly responsible for the retardation of organic contaminants. The modelling concept applied in this paper quantifies sorption/desorption kinetics by an intra-particle diffusion approach. According to this idea, solute uptake by or release from the aquifer material is modelled at small scale by a "slow" diffusion process where the diffusion coefficient is reduced as compared to the aqueous diffusion coefficient due to (i) the size and shape of intra-particle pores and (ii) retarded transport of solutes within intra-particle pores governed by a nonlinear sorption isotherm. This process-based concept has the advantage of requiring only measurable model parameters, thus avoiding fitting parameters like first-order rate coefficients.In addition, the approach presented here allows for modelling of slow sorption/desorption in lithologically nonuniform media. Therefore, it accounts for well-known experimental findings indicating that sorptive properties depend on (i) the grain size distribution of the aquifer material and (ii) the lithological composition (e.g. percentage of quartz, sandstone, limestone, etc.) of each grain size fraction. The small-scale physico-chemical model describing sorption/desorption is coupled to a large-scale model of groundwater flow and solute transport. Consequently, hydraulic heterogeneities may also be considered by the overall model. This coupling is regarded as an essential prerequisite for simulating field-scale scenarios which will be addressed by a forthcoming publication.This paper focuses on mathematical model formulation, implementation of the numerical code and lab-scale model applications highlighting the sorption and desorption behavior of an organic contaminant (Phenanthrene) with regard to three lithocomponents exhibiting different sorptive properties. In particular, it is shown that breakthrough curves (BTCs) for lithologically nonuniform media cannot be obtained via simple arithmetic averaging of breakthrough curves for lithologically uniform media. In addition, as no analytical solutions are available for model validation purposes, simulation results are compared to measurements from lab-scale column experiments. The model results indicate that the new code can be regarded as a valuable tool for predicting long-term contaminant uptake or release, which may last for several hundreds of years for some lithocomponents. In particular, breakthrough curves simulated by pure forward modelling reproduce experimental data much better than a calibrated standard first-order kinetics reactive transport model, thus indicating that the new approach is of high quality and may be advantageously used for supporting the design of remediation strategies at contaminated sites where some lithocomponents and/or grain size classes may provide a long-term pollutant source.     

Use of carbonised beet pulp carbon for removal of Remazol Turquoise Blue-G 133 from aqueous solution

Carbonised beet pulp (BPC) produced from agricultural solid waste by-product in sugar industry was used as adsorbent for the removal of Remazol Turquoise Blue-G 133 (RTB-G 133) dye in this study. The kinetics and equilibrium of sorption process were investigated with respect to pH, temperature and initial dye concentration. Adsorption studies with real textile wastewater were also performed. The results showed that adsorption was a strongly pH-dependent process, and optimum pH was determined as 1.0. The maximum dye adsorption capacity was obtained as 47.0 mg g^?1at the temperature of 25 °C at this pH value. The Freundlich and Langmuir adsorption models were used for describing the adsorption equilibrium data of the dye, and isotherm constants were evaluated depending on sorption temperature. Equilibrium data of RTB-G 133 sorption fitted very well to the Freundlich isotherm. Mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of adsorption and potential rate-controlling steps. It was found that both external mass transfer and intra-particle diffusion played an important role in the adsorption mechanisms of dye and adsorption kinetics followed the pseudo second-order type kinetic model. The thermodynamic analysis indicated that the sorption process was exothermic and spontaneous in nature.     

Experimental and modeling studies on sorption and diffusion of radium in bentonite

The sorption and desorption behavior of radium on bentonite and purified smectite was investigated as a function of pH, ionic strength and liquid to solid ratio by batch experiments. The distribution coefficients (Kd) were in the range of 10(2) to > 10(4) ml g-1 and depended on ionic strength and pH. Most of sorbed Ra was desorbed by 1 M KCl. The results for purified smectite indicated that Ra sorption is dominated by ion exchange at layer sites of smectite, and surface complexation at edge sites may increase Ra sorption at higher pH region. Reaction parameters between Ra and smectite were determined based on an interaction model between smectite and groundwater. The reaction parameters were then used to explain the results of bentonite by considering dissolution and precipitation of minerals and soluble impurities. The dependencies of experimental Kd values on pH, ionic strength and liquid to solid ratio were qualitatively explained by the model. The modeling result for bentonite indicated that sorption of Ra on bentonite is dominated by ion exchange with smectite. The observed pH dependency was caused by changes of Ca concentration arising from dissolution and precipitation of calcite. Diffusion behavior of Ra in bentonite was also investigated as a function of dry density and ionic strength. The apparent diffusion coefficients (Da) obtained in compacted bentonite were in the range of 1.1 x 10(-11) to 2.2 x 10(-12) m2 s-1 and decreased with increasing in dry density and ionic strength. The Kd values obtained by measured effective diffusion coefficient (De) and modeled De were consistent with those by the sorption model in a deviation within one order of magnitude.     

Removal of lignin and tannin colour from aqueous solution by adsorption onto activated charcoal

Sorptive uptake of lignin and tannin from an aqueous phase by activated charcoal was investigated in the laboratory. The sorption reaction was found to be of a first order. The influence on the rate of sorption of various factors, such as amount of sorbent and pH of the system, have been investigated. Sorption data fit well into the Langmuir adsorption isotherm, indicating formation of a monolayer over a homogeneous sorbent surface. Sorption capacity, rate constant, intraparticle diffusion coefficient, etc. were calculated from the sorption data. Desorption studies indicate the irreversible nature of the sorption reaction, whereas interruption studies suggest film diffusion to be rate limiting.     

Washing of marine coastal sand in a batch reactor: sorption and desorption of BTEX

This study addresses the issues related to decontamination of marine beach sand accidentally contaminated by petroleum products. Sorption and desorption of BTEX (i.e., benzene, toluene, ethylbenzene, and xylene) onto the sand from Uran Beach, located near the city of Mumbai, India, were studied, and isotherms were determined using the bottle point method to estimate sorption coefficients. Alternatively, QSARs (i.e., quantitative structure activity relationships) were developed and used to estimate the sorption coefficients. Experiments for kinetics of volatilization as well as for kinetics of sorption and desorption in the presence of volatilization were conducted in a fabricated laboratory batch reactor. A mathematical model describing the fate of volatile hydrophobic organic pollutants like BTEX (via sorption and desorption in presence of volatilization) in a batch sediment-washing reactor was proposed. The experimental kinetic data were compared with the values predicted using the proposed models for sorption and desorption, and the optimum values of overall mass transfer coefficients for sorption (K(s)a(s)) and desorption (K(d)a(d)) were estimated. This was achieved by minimization of errors while using the sorption coefficients (Kp) obtained from either laboratory isotherm studies or the QSARs developed in the present study. Independent experimental data were also collected and used for calibration of the model for volatilization, and the values of the overall mass transfer coefficient for volatilization (K(g)a(g)) were estimated for BTEX. In these exercises of minimization of errors, comparable cumulative errors were obtained from the use of Kp values derived from experimental isotherms and QSARs.     

Removal of Pb(II) ions from aqueous solution and industrial effluent using natural biosorbents

Purpose

The purpose of the research is to investigate the applicability of the low-cost natural biosorbents for the removal of Pb(II) ions from aqueous solution and effluent from battery industry.

Methods

Six different biosorbents namely rice straw, rice bran, rice husk, coconut shell, neem leaves, and hyacinth roots have been used for the removal of Pb(II) ions from aqueous solution in batch process. All the biosorbents were collected from local area near Kolkata, West Bengal, India. The removal efficiency was determined in batch experiments for each biosorbent.

Results

The biosorbents were characterized by SEM, FTIR, surface area, and point of zero charge. The sorption kinetic data was best described by pseudo-second-order model for all the biosorbents except rice husk which followed intraparticle diffusion model. Pb(II) ions adsorption process for rice straw, rice bran, and hyacinth roots were governed predominately by film diffusion, but in the case of rice husk, it was intraparticle diffusion. Film diffusion and intraparticle diffusion were equally responsible for the biosorption process onto coconut shell and neem leaves. The values of mass transfer coefficient indicated that the velocity of the adsorbate transport from the bulk to the solid phase was quite fast for all cases. Maximum monolayer sorption capacities onto the six natural sorbents studied were estimated from the Langmuir sorption model and compared with other natural sorbents used by other researchers. The Elovich model, the calculated values of effective diffusivity, and the sorption energy calculated by using the Dubinin?CRadushkevich isotherm were indicated that the sorption process was chemical in nature. The thermodynamic studies indicated that the adsorption processes were endothermic. FTIR studies were carried out to understand the type of functional groups responsible for Pb(II) ions binding process. Regeneration of biosorbents were carried out by desorption studies using HNO₃. Battery industry effluents were used for the application study to investigate applicability of the biosorbents.

Conclusion

The biosorbents can be utilized as low-cost sorbents for the removal of Pb(II) ions from wastewater.     

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.     

Sorption of hydrophobic organic pollutants in saturated soil systems

Sorption equilibria and rates were characterized for a matrix of four aquifer sands and two slightly to moderately hydrophobic organic solutes (nitrobenzene and lindane), and the effects of sorption on the behavior of these solutes in saturated systems of the soils were determined. Experimental data were used to test and evaluate a variety of mathematical models for predicting contaminant fate and transport in groundwater systems.Observed equilibrium relationships between soil and solution phase solute concentrations were found to be described best by the nonlinear Freundlich isotherm model. It was further determined that the sorption process in the systems tested is rate controlled, requiring several days to approach equilibrium in completely mixed batch reactors. Subsequent modeling of solute transport in continuous flow soil column reactors was found to be most successful when rate-controlled models were used, the best results were obtained with a dual-resistance model incorporating the coupled mass transport steps of boundary-layer and intraparticle diffusion.     

Effects of water content on reactive transport of 85Sr in Chernobyl sand columns

It is known that under unsaturated conditions, the transport of solutes can deviate from ideal advective-dispersive behaviour even for macroscopically homogeneous porous materials. Causes may include physical non-equilibrium, sorption kinetics, non-linear sorption, and the irregular distribution of sorption sites. We have performed laboratory experiments designed to identify the processes responsible for the non-ideality of radioactive Sr transport observed under unsaturated flow conditions in an Aeolian sandy deposit from the Chernobyl exclusion zone. Miscible displacement experiments were carried out at various water contents and corresponding flow rates in a laboratory model system. Results of our experiments have shown that breakthrough curves of a conservative tracer exhibit a higher degree of asymmetry when the water content decreases than at saturated water content and same Darcy velocity. It is possible that velocity variations caused by heterogeneities at the macroscopic scale are responsible for this situation. Another explanation is that molecular diffusion drives the solute mass transfer between mobile and immobile water regions, but the surface of contact between these water regions is small. At very low concentrations, representative of a radioactive Sr contamination of the pore water, sorption and physical disequilibrium dominate the radioactive Sr transport under unsaturated flow conditions. A sorption reaction is described by a cation exchange mechanism calibrated under fully saturated conditions. The sorption capacity, as well as the exchange coefficients are not affected by desaturation. The number of accessible exchange sites was calculated on the basis that the solid remained in contact with water and that the fraction of solid phase in contact with mobile water is numerically equal to the proportion of mobile water to total water content. That means that for this type of sandy soil, the nature of mineral phases is the same in advective and non-advective domains. So sorption reaction parameters can be estimated from more easily conducted saturated experiments, but hydrodynamic behaviour must be characterized by conservative tracer experiments under unsaturated flow conditions.     

Washing of Marine Coastal Sand in a Batch Reactor: Sorption and Desorption of BTEX

ABSTRACT

This study addresses the issues related to decontamination of marine beach sand accidentally contaminated by petroleum products. Sorption and desorption of BTEX (i.e., benzene, toluene, ethylbenzene, and xylene) onto the sand from Uran Beach, located near the city of Mumbai, India, were studied, and isotherms were determined using the bottle point method to estimate sorption coefficients. Alternatively, QSARs (i.e., quantitative structure activity relationships) were developed and used to estimate the sorption coefficients. Experiments for kinetics of volatilization as well as for kinetics of sorption and desorption in the presence of volatilization were conducted in a fabricated laboratory batch reactor. A mathematical model describing the fate of volatile hydrophobic organic pollutants like BTEX (via sorption and desorption in presence of volatilization) in a batch sediment-washing reactor was proposed. The experimental kinetic data were compared with the values predicted using the proposed models for sorption and desorption, and the optimum values of overall mass transfer coefficients for sorption (K_sa_s) and desorption (K_da_d) were estimated.This was achieved by minimization of errors while using the sorption coefficients (K_p) obtained from either laboratory isotherm studies or the QSARs developed in the present study. Independent experimental data were also collected and used for calibration of the model for volatilization,and the values of the overall mass transfer coefficient for volatilization (K_ga_g) were estimated for BTEX. In these exercises of minimization of errors, comparable cumulative errors were obtained from the use of K_p values derived from experimental isotherms and QSARs.     

Diffusion mechanism of lindane into wood charcoal

Abstract

The wood charcoal treated by 1N HNO₃ (WCT) was used to remove toxic chlorinated pesticide lindane (y‐HCH) residue from water by the sorption process. Using a simple first order reversible kinetics constants and half time equations, the film and pore diffusion coefficients were determined. Film diffusion was found to be rate limiting step in sorbing lindane by WCT. This was further authenticated by kinetics studies at different initial sorbate concentrations, different sorbent sizes, and different agitation speeds besides interruption test. A pore diffusion model was used to fit the data of kinetics in continuously mixed batch reactors (CMBR), and the tortuosity, external resistance, and surface diffusion effects on lindane sorption by WCT were noticed. The tortuosity values of 15 to 28 were obtained for WCT‐lindane system.     

Rate-limited mass transfer of octane, decane, and dodecane into nonionic surfactants solutions under laminar flow conditions

A key component to predicting the success of utilizing surfactants to enhance the removal of organic liquids from soil system is quantifying micellar solubilization kinetics. In this study, a flow reactor was employed to investigate the influence of surfactant ethoxylate chain length on the rates of solubilization of octane, decane, and dodecane in micellar solutions of a homologous series of purified dodecyl alcohol ethoxylates. Effluent concentration data were fit using a finite element model utilizing a linear-driving-force model to represent mass transfer at the interface. For flow rates between 0.1 and 2 ml min(-1), mass transfer coefficients ranged from 5 x 10(-8) to 7 x 10(-7)m s(-1) and did not vary in a systematic way with either solute structure or surfactant ethoxylate chain length and were lower than those found in pure water. Correlations developed for the Sherwood number based on diffusion coefficients of surfactant micelles containing organic material (organic-laden micelle) exhibit a velocity dependence similar to that found for systems based on aqueous diffusion. These results suggest that under gentle flowing conditions, the mass transfer is limited by diffusion of the organic-laden micelle. Although these trends are specific for this experimental system, the results demonstrate the importance of selecting the proper diffusion coefficient when modeling surfactant solubilization processes.     

粉煤灰砖块对磷酸盐的吸附特性

以建筑废料粉煤灰砖块为吸附剂材料,通过静态吸附实验研究其对磷酸盐的吸附特征,以及磷酸盐初始浓度、吸附剂投加量、pH等因素对吸附反应的影响。Langmuir、Freundlich和Temkin等温模型的分析发现,Langmuir等温式方程最适合描述吸附过程,对磷酸盐的理论饱和吸附容量为44.62 mg/g。利用伪一级动力学模型、伪二级动力学模型和颗粒内扩散模型考察了吸附过程特征,其中伪二级动力学模型为最适于描述粉煤灰砖块对磷酸盐的吸附过程的动力学模型。通过颗粒内扩散模型、Bangham方程及Boyd模型对吸附动力学机理进行的探讨表明,颗粒内扩散速率不是粉煤灰砖块吸附磷酸盐反应的惟一速率控制步,膜扩散速率和颗粒内扩散速率共同影响着吸附反应速率。磷酸盐浓度较低时主要是膜扩散限制吸附反应速率,而磷酸盐浓度较高时则颗粒内扩散成为速率控制步。研究证明,粉煤灰砖块粉末作为湿地基质具有对磷酸盐很强的吸附能力,在减少了固体废弃物的数量的同时又可以实现水污染控制的目的。     

Modelling of silica diffusion experiments with 32Si in Boom Clay

A mathematical model describing the dissolution of nuclear glass directly disposed in clay combines a first-order dissolution rate law with the diffusion of dissolved silica in clay. According to this model, the main parameters describing the long-term dissolution of the glass are etaR, the product of the diffusion accessible porosity eta and the retardation factor R, and the apparent diffusion coefficient D(app) of dissolved silica in clay. For determining the migration parameters needed for long-term predictions, four Through-Diffusion (T-D) experiments and one percolation test have been performed on undisturbed clay cores. In the Through-Diffusion experiments, the concentration decrease after injection of 32Si (radioactive labelled silica) was measured in the inlet compartment. At the end of the T-D experiments, the clay cores were cut in thin slices and the activity of labelled silica in each slice was determined. The measured activity profiles for these four clay cores are well reproducible. Since no labelled silica could be detected in the outlet compartments, the Through-Diffusion experiments are fitted by two In-Diffusion models: one model assuming linear and reversible sorption equilibrium and a second model taking into account sorption kinetics. Although the kinetic model provides better fits, due to the sufficiently long duration of the experiments, both models give approximately similar values for the fit parameters. The single percolation test leads to an apparent diffusion coefficient value about two to three times lower than those of the Through-Diffusion tests. Therefore, dissolved silica appears to be strongly retarded in Boom Clay. A retardation factor R between 100 and 300 was determined. The corresponding in situ distribution coefficient K(d) is in the range 25-75 cm(3) g(-1). The apparent diffusion coefficient of dissolved silica in Boom Clay is estimated between 2 x 10(-13) and 7 x 10(-13) m(2) s(-1). The pore diffusion coefficient is in the range from 6 x 10(-11) to 1 x 10(-10) m(2) s(-1).     

A method for estimating distributions of mass transfer rate coefficients with application to purging and batch experiments

Mass transfer between aquifer material and groundwater is often modeled as first-order rate-limited sorption or diffusive exchange between mobile zones and immobile zones with idealized geometries. Recent improvements in experimental techniques and advances in our understanding of pore-scale heterogeneity demonstrate that two (or even a few) rate coefficients are insufficient in many cases. Here, we investigate a piece-wise linear model for a continuous distribution of rate coefficients, that has several advantages over previously used ‘statistical' distribution models (with functional form from gamma or lognormal PDF's): (1) distributions of arbitrary, even bimodal, shapes can be represented; (2) linear estimation methods can be applied to determine the distribution from experimental data; (3) the uncertainty in the distribution can be determined for each of its sections; and (4) the relationship between the time scales of available data and those of estimatable mass transfer processes can be investigated. A statistical model refinement algorithm is presented that reduces the number of parameters (sections of the piece-wise linear model) to the admissible minimum. We show that purging experiments allow estimation of a wider zone of the rate distribution than do batch experiments, and hence will provide predictions that are accurate over a wider range of time scales. Finally, in an application to TCE gas-purging desorption data, the piece-wise linear rate-distribution model has a higher probability of being adequate than those using a gamma or lognormal distribution or a single rate coefficient.