Batch adsorption model

A useful literature relating to polypeptide and protein adsorption kinetics and equilibrium behavior in finite bath systems for both affinity and ion-ex-change HPLC sorbents is now available160,169,171-174,228,234 319 323 402"405 and various mathematical models have been developed, incorporating data on the adsorption behavior of proteins in a finite bath.8,160 167-169 171-174 400 403-405 406 One such model, the so-called combined-batch adsorption model (BAMcomb), initially developed for nonporous particles, takes into account the dynamic adsorption behavior of polypeptides and proteins in a finite bath. Due to the absence of pore diffusion, analytical solutions for nonporous HPLC sorbents can be readily developed using this model and its two simplified cases, and the effects of both surface interaction and film mass transfer can be independently addressed. Based on this knowledge, extension of the BAMcomb approach to porous sorbents in bath systems, and subsequently to packed-, expanded-, and fluidized-bed systems, can then be achieved. 

Batch adsorption experiments by Yee and Fein (2002) using aqueous Cd, B. subtilis, and quartz as a function of pH showed that the thermodynamic stability constants, determined from binary systems, could successfully describe the distribution of Cd between the aqueous phase and the bacterial and mineral surfaces. The constants could also be used to estimate the distribution of mass in systems, and construct a surface complexation model. 

Modeling in multicomponent adsorption systems is an extension to that of single component adsorption. Many models have been reported in the literature for the prediction of concentration versus time decay curves in single component batch adsorption stem. However, there are very few research papers on the topic of multicCHnponent mass transport studies for liquid phase adsorption, therefore, it is a valuable contribution and novel development to adsorption research. 

The objective of the work is to present an experiment-founded adsorption model for precipitate flotation. Batch precipitate flotation of CufOH) with dodecylbenzene sulphonate (DBS) as collector, was carried out both with dissolved (DAF) and dispersed (DIS) air. The processes were considered as a succession of the dynamic equilibria taking place at the gasliquid and solidliquid interfaces. Both flotation processes were expressed quantitatively in terms of surface concentrations of Cu(OH)2 and DBS per unit surface area of the air buble, as well as the ratio of the numbers of air bubbles and solid particles (B /P ). Also the maximal concentrations of both DBS and Cu(OH)2, recoverable under the given conditions were calculated. All these values were determined by following the Cu(OH)2 and DBS recovery. The 2 flotation techniques were compared in regard to their efficiency and mechanism. Finally, the results obtained were discussed in terms of the other models for the colloid particle adsorption at the air-water interface. 

Fickian Diffusion and Linear Driving Force models are generally used to describe the transport of water vapour into the alumina particles. For isothermal adsorption of water vapour from a constant partial pressure (P ) batch adsorption system on a spherical adsorbent particle of radius Rp, the uptake profiles are given by [13] ... 

The resistance to mass transport for adsorption of water into alumina particles can be governed by diffusion of water molecules through the liquid filled pores as well as by surface diffusion of adsorbed water molecules on the pore walls. A surface excess linear driving force model [SELDF] has been successfully used to describe the adsorption of water from liquid mixtures [27]. For isothermal adsorption of water from a bulk liquid mixture from a constant water composition (xj) batch adsorption system, the uptake profile is given by ... 

By determining the bulk concentration of CH (P), the batch adsorption rate of CH using XAD-4 resin can be estimated. The adsorption rate can be modeled as follows ... 

The purpose of this article is to formulate a model which considers simultaneous diffusion and binding reaction within the immobilized adsorbent particles. The model has been developed for batch adsorption processes. It can however be easily modified to predict product adsorption in other reactor configurations. 

In this problem we will simulate a batch adsorption process that takes place with two adsorbate components. The simulation will allow us to do computational experiments with the aim of learning how the adsorption and desorption parameters affect the behavior of this process. Building the simulation will provide new experience in developing the model equations, utilizing more complex constitutive relationships, finding numerical solutions to these equations, and displaying the results graphically. 

Different batch adsorption processes were modeled using a multilayer fccdforwaKl neural network to predict water sorption [28] or adsorption of binary vapor mixtures [29]. Breakthrough parameters of an ion-exchange column [30] or a granular activated carbon fixed bed [31] were also predicted using the same kind of perceptions. 

The batch adsorption is assumed to be visualized by the application of adsorption isotherm models. The different isotherms give an indication of how the contaminants from MDEA solution interact with the PAAM functional groups and distribute themselves over hydrogel surface. The equilibrium adsorption isotherms of total metal ions as well as organic acid anions were determined at 23°C. The equilibrium MDEA concentration (Ce) for varions uptake capacities of heavy metal ions and HSS anions (qe) were fitted to four standard isotherm models and it was observed that Langmuir isotherm best fitted among all. The maximum adsorption capacity (qmax) valnes obtained from the isotherm model using PAAM... 

The mass balance equations in the particle depend on the diffusion and adsorption mechanisms inside the particle. Those equations have been discussed in great details in Chapters 9, 10 and 11. In this chapter we will address a number of simple diffusion and adsorption models of which analytical solutions are feasible in order to illustrate its application in parameter determination. Other complex models can also be used with the batch adsorber method but the parameter determination must be done numerically. 

Al-Duri, B., and McKay, G., Comparison in theory and application of several mathematical models to predict kinetics of single component batch adsorption systems. Process Safety Environ. Prot., 68(4), 254-268 (1990). Chen, Y.D. Ritter, J.A., and Yang, R.T., Nonideal adsorption from multicomponent gas mixtures at elevated pressures on a 5A molecular sieve, Chem. Eng. Sci.. 45(9), 2877-2894 (1990). 

Xiu, G.H., and Wakao, N., Batch adsorption Intraparticle adsorbate concentration profile models, AlChE J., 39(12), 2042-2044(1993). 

Finally to gain a deeper understanding of the bisolute batch adsorption process, models of various significant physical phenomena taking place in the adsorber (e.g., interaction between adsorbates as well as competition) should be incorporated into the present model. Investigations of these phenomena are, however, outside the scope of the present study. 

While most of the batch unit operation models involve ordinary differential equations some unit operations like batch adsorption column encounters partial differential equations, orthogonal collocation method can be used to reduce set of partial differential equations to ordinary differential equations. 

We have developed a compact photocatalytic reactor [1], which enables efficient decomposition of organic carbons in a gas or a liquid phase, incorporating a flexible and light-dispersive wire-net coated with titanium dioxide. Ethylene was selected as a model compound which would rot plants in sealed space when emitted. Effects of the titanium dioxide loading, the ethylene concentration, and the humidity were examined in batches. Kinetic analysis elucidated that the surface reaction of adsorbed ethylene could be regarded as a controlling step under the experimental conditions studied, assuming the competitive adsorption of ethylene and water molecules on the same active site. 

Methane can be oxidatively coupled to ethylene with very high yield using the novel gas recycle electrocatalytic or catalytic reactor separator. The ethylene yield is up to 85% for batch operation and up to 50% for continuous flow operation. These promising results, which stem from the novel reactor design and from the adsorptive properties of the molecular sieve material, can be rationalized in terms of a simple macroscopic kinetic model. Such simplified models may be useful for scale up purposes. For practical applications it would be desirable to reduce the recycle ratio p to lower values (e.g. 5-8). This requires a single-pass C2 yield of the order of 15-20%. The Sr-doped La203... 

The adsorption plateaus on this solid, determined with each of the surfactants (Table II) and the individual CMC values, were used to calculate the adsorption constants input in the model. Figure 3 compares the total adsorption (sulfonate + NP 30 EO) of the pseudo-binary system investigated as a function of the initial sulfonate fraction of the mixtures under two types of conditions (1) on the powder solid, batch testing with a solid/liquid ratio, S/L = 0.25 g/cc (2) in the porous medium made from the same solid, for which this solid ratio is much higher (S/L = 4.0 g/cc). 

Abstract Removal of catechol and resorcinol from aqueous solutions by adsorption onto high area activated carbon cloth (ACC) was investigated. Kinetics of adsorption was followed by in-situ uv-spectroscopy and the data were treated according to pseudo-first-order, pseudo-second-order and intraparticle drfiusion models. It was fotmd that the adsorption process of these compotmds onto ACC follows pseudo-second-order model. Furthermore, intraparticle drfiusion is efiective in rate of adsorption processes of these compoimds. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundhch models. The fits of experimental data to these equations were examined. 

The values of solutions were adjusted with 0.1 mol/L NH OH or HNOj and measured with Metrohm Herisau E510 pH meter. A magnetic stirrer model Arex was used for stirring the adsorption batches. The concentration of solution before and after adsorption was measured by using Atomic Absorption Spectrometer (AAS) Analytika Jena. All the measurements were made under optimization of the below mentioned parameters. 

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