Intraparticle Diffusion/Convection Models for Pressurization and Blowdown of Adsorption Beds with Langmuir Isotherm

Abstract

Intraparticle diffusion/convection and equilibrium models are used to simulate the bed dynamics of pressurization and blowdown steps of PSA processes with binary mixtures of inert and adsorbable species. The effect of the nature of the equilibrium isotherm, i.e., linear and Langmuir isotherms, is discussed. The improvement of mass transfer inside the adsorbent by increasing particle permeability or decreasing particle size is addressed. Simulation results show that using “large-pore” adsorbents, i.e., increasing permeability to cause a high intraparticle convective flow instead of decreasing particle size to reduce intraparticle mass transfer resistances, is a good choice in PSA processes.     

Modeling breakthrough and elution curves in fixed bed of inert core adsorbents: analytical and approximate solutions

A mathematical model is developed for fixed-beds packed with inert core adsorbents. New analytical solutions to predict breakthrough and elution curves are derived for linear adsorption systems coupled with axial dispersion, film mass transfer and intraparticle mass transfer. New approximate solutions are also obtained based on the assumptions of parabolic concentration profile in the adsorbent shell and the quasi-lognormal distribution for the impulse response in order to predict breakthrough and elution curves. The applicability of these approximate solutions is suggested by comparison with the new analytical solutions. The effects of the size of inert core, sample input mode, axial dispersion, film mass transfer resistance and intraparticle diffusion resistance, on the breakthrough and elution curves are discussed. The decrease of the intraparticle mass transfer resistance by using inert core adsorbents is quantitatively analyzed by introducing the parameter 1/Θ. Furthermore, an analytical expression for the resolution of two components is derived based on the quasi-lognormal distribution approximate solution; the resolution of two components is improved with the inert core adsorbent when compared with the conventional adsorbent, especially for biomacromolecules where the intraparticle diffusion rate is slow.     

Residence time distribution in a packed bed bioreactor containing porous glass particles: Influence of the presence of immobilized cells

An experimental investigation of the liquid phase residence time distribution (RTD) in a packed bed bioreactor containing porous glass particles is presented. For Re < 1, intraparticle forced convection is negligible and only diffusion, characterized by an effective diffusion coefficient, must be considered to describe the mass transfer process between the extraparticle and the intraparticle fluid phase. For Re > 1, the mass transfer rate becomes dependent on the liquid flow rate, indicating the existence of intraparticle convection. A model including axially dispersed flow for the external fluid phase and an ‘apparent’ effective diffusivity that combines diffusion and convection, predicts experimental RTD data satisfactorily. Yeast cells immobilized inside the porous glass beads did not affect the mass transfer rate at low biomass loading. At high biomass loading (0·02 g yeast cells g^?1 carrier), the mass transfer rate between the extraparticle and intraparticle fluid phase was significantly decreased. Comparison of the RTD data from experimets performed in the presence and absence of cells in the external fluid phase revealed that the mass transfer rate is influenced by the cells immobilized inside the porous particles and not by the cells present in the external fluid phase.     

The Adsorption of Pollutants by Peat,Lignite and Activated Chars

The ability of peat, lignite and activated chars made from peat and lignite to adsorb dyes and metals from wastewater and NO₂ from air was investigated. Equilibrium isotherms were determined to assess the maximum adsorption capacity of the adsorbents for the pollutants. Kinetic studies for the adsorption of dyes and metal ions onto the adsorbents were undertaken in agitated batch adsorbers. Mass transport models were tested to predict the concentration decay curves in batch adsorbers. The models tested were single resistance models based on the assumption of a single external mass transfer coefficient and two resistance models which included an internal diffusion coefficient and an external mass transfer coefficient. The surface phenomena which influence the extent and the rate of uptake have been studied. The equilibrium capacity data conform to Langmuir plots. A previously proposed model was used to evaluate the external single resistance mass transfer model and was successfully applied to predict the adsorption of metal ions in single component systems under batch conditions. It has been shown that the assumption of negligible intraparticle diffusion is valid and that external film diffusion is the rate limiting step in describing the adsorption processes at high sorbent loadings. The same type of result is not observed for the adsorption of coloured organic matter onto peat where the sorption processes cannot be successfully modelled by use of a single resistance model and a two resistance model incorporating internal diffusion is required. The surface phenomena which influence the extent and the rate of uptake of NO₂ have been studied. The type of chars produced and the activation processes affect the adsorption. As activation increases, micropore volume and surface area increase and the maximum capacity of the adsorbent increases. Surface area alone is not the only parameter which affects equilibrium uptake. © 1997 SCI.     

Frequency response of the adsorption vessel loaded with inert core adsorbents

An analytical solution for the frequency response of a semi-batch adsorption vessel with sinusoidal modulation of molar flow rate, loaded with inert core adsorbents is obtained for a linear isotherm coupled with intraparticle diffusion and external film diffusion. The low-frequency limiting values of the in-phase and the out-of-phase characteristic functions of the frequency response are found to be explicit functions of the size of the inert core and the external mass transfer parameter. Simulation results of the in-phase and the out-of-phase characteristic functions show that there exist a crossover frequency and overshoot of the in-phase characteristic function when external mass transfer resistance is present.     

Mass transfer kinetics in pressure swing adsorption

Many mass transfer kinetic models are used to study varying pressure steps of a pressure swing adsorption (PSA) cycle, namely pressurization and blowdown steps. It is shown that the choice of an appropriate model to account for intra-particle diffusional limitations is essential to simulate accurately PSA processes. It has been demonstrated that, besides mathematical approximations (parabolic profile within the particle), a very important factor that can affect simulation results remarkably is the correctness of the mass transfer kinetic model when regarded as being a mass balance for the adsorbent particle. In fact, neglecting intra-particle gas phase leads to erroneous simulations. Some models widely used in the literature, such as the classic linear driving force (LDF) and the solid diffusion models prove inadequate. It is recommended to use pore diffusion model as well as a new version of the solid diffusion model to get reliable predictions.     

Uranium Adsorption Properties of Hydrous Titanium Oxide Granulated with Polyacrylonitrile

Abstract

The performance of hydrous titanium oxide (HTO) adsorber granulated with polyacrylonitrile (PAN) has been studied by a batch method using natural seawater. The adsorber was classified into four classes of 24/28, 28/32, 32/35, and 35/48 mesh, and the seawater temperature was varied from 15 to 30°C. The effects of particle size and seawater temperature on the liquid film mass transfer coefficient and the intraparticle diffusion coefficient of the uranium ion were estimated. It was found that the uranium adsorption rate was dependent on both liquid film mass transfer and intraparticle diffusion for the PAN-HTO adsorber. The equilibrium adsorption capacity was in the range of 175 to 127 μg-U/g-AD at 30°C. Particle size of PAN-HTO adsorber had no distinct influence on the adsorption capacity and rates. Both adsorption capacity and rates increased with increasing seawater temperature.     

流化床用树脂基球形活性炭及其VOCs吸附性能

以聚苯乙烯树脂为原料,采用水蒸气活化、氯化锌活化及水蒸气?氯化锌协同活化方法制备了3种流化床用树脂基球形活性炭,采用固定床反应器考察了活性炭对乙酸乙酯的动态吸附行为,对比了其传质区长度,并利用Yoon?Nelson模型对实验数据进行了拟合. 结果表明,3种活性炭的摩擦磨损指数均小于0.1%,耐磨性能出色,物理、化学协同活化活性炭比表面积高达1702.49 m2/g,对二甲苯的静态吸附容量达0.86 g/g.     

余热制冷吸附床的一个新传热传质模型

在既考虑吸附剂颗粒内部的传质阻力,又考虑吸附剂颗粒之间的外部传质阻力的前提下,建立了余热吸附制冷系统中吸附床的三维非平衡传热传质数学模型,它包括加热/冷却流体传热模型、换热管传热模型、肋片传热模型、吸附剂颗粒床传热传质模型4部分;通过对模型的数值求解,获得了吸附床内部的温度演变曲线和性能指标,与实验结果基本吻合。     

Perturbation chromatography with inert core adsorbent: Moment solution for two-component nonlinear isotherm adsorption

The moment analysis is applied to study two-component perturbation chromatography with linearized nonequilibrium adsorption. General expressions for the first and second chromatographic moments of components and waves are given by taking into account axial dispersion, film mass transfer resistance, and intraparticle diffusion resistance for chromatographic column packed with inert core adsorbents. The well-known results for moment solution of the single-component case and special two-component case are extended to the general two-component case.     

等温或非等温颗粒吸附动力学模型:应用于吸附热泵(英文)

Understanding the interaction between a fluid and a solid phase is of fundamental importance to the design of an adsorption process.Because the heat effects associated with adsorption are comparatively large,the as-sumption of isothermal behavior is a valid approximation only when uptake rates are relatively slow.In this article,we propose to determine when it is needed to choose the isothermal or non-isothermal assumption according to two physical parametersα(ratio convection/capacity) andβ(quantity of energy/capacity) .The proposed problem is solved by a mathematical method in the Laplace domain.Whenα→∞(infinitely high heat transfer coefficient) or β→0(infinitely large heat capacity) ,the limiting case is isothermal.When the diffusion is rapid(α10) the kinetics of sorption is controlled entirely by heat transfer.If the adsorption process is to be used as a heat pump,it shall be represented by an isotherm model withαandβas high as possible.     

Effects of Adsorbent Characteristics on Adiabatic Vacuum Swing Adsorption Processes for Solvent Vapor Recovery

The effects of the adsorbent characteristics on the performance parameters and periodic state behavior of the vacuum swing adsorption (VSA) solvent vapor recovery (SVR) processes are examined and optimized. The adsorbent characteristics studied were the adsorbent particle's porosity, density, radius and heat capacity, the packed bed void fraction, the isosteric heat of adsorption, the monolayer saturation limit of the solvent molecules on the adsorbent, the adsorbent's affinity to adsorb the solvent molecules and the mass transfer coefficient for the adsorption of the solvent molecules. It was found that the best VSA‐SVR process performances can be obtained using adsorbents characterized by the minimum possible packed bed void fraction and particle porosity, with the maximum possible adsorbent heat capacity and density, adsorption monolayer saturation capacity and mass transfer coefficient, and at intermediate adsorption affinity and isosteric heat of adsorption of the solvent molecules.     

Diffusion in liquid-filled pores of activated carbon. I. Pore volume diffusion

The adsorption isotherms on activated carbon were measured for the following six systems: benzaldehyde, phenol, and potassium chloride in water; benzene, isopropylbenzene, and phenol in cyclohexane. The systems isopropylbenzene and benzene each in cyclohexane and potassium chloride in water proved to be slightly adsorbing systems, whereas the benzaldehyde and phenol each in water were highly adsorbing systems. The rate of diffusion of the slightly adsorbing solutes was interpreted by assuming that the intraparticle diffusion was due to pore volume diffusion. The results indicated that the tortuosity factor for activated carbon is 3.5. The effective pore volume diffusivity and the tortuosity factor were not affected by the concentration of the solute, solute molecular size and the particle diameter. The external mass transfer resistance was negligible when pore volume diffusion was the controlling intraparticle diffusion mechanism.     

The Adsorption of Gold Cyanide onto Porous Adsorbents: Relation between Liquid-Phase Concentration,Suspended Solids,and Mass-Transfer Mechanisms

Abstract

Much progress has been made during the last decade on carbon-in-pulp and resin-in-pulp technology for the extraction of gold and silver from leached pulps. In this study a systematic investigation was conducted on the mass transfer of gold cyanide to activated carbon and ion-exchange resins in suspended solids under conditions of different gold solution-phase concentrations. The different mass transfer phenomena were studied by measuring the concentration profile of gold in solution. Two distinct mass transfer mechanisms have been identified: 1) at low gold solution-phase concentrations, where the rate of adsorption is controlled by film diffusion, the presence of fine inert particles had no effect on either the rate of adsorption or the equilibrium loading of gold cyanide; 2) at high gold solution-phase concentrations, where intraparticle diffusion becomes rate controlling, the inert particles affected the rate of adsorption of gold cyanide for both the adsorbents. Furthermore, the inert particles did not affect the equilibrium loading of gold at the high solution-phase concentration. It was also found that under certain conditions the silica particles in suspension enhanced the mass transfer of gold cyanide to the adsorbents. This was attributed mainly to the fact that the silica particles act as an adsorbent, thereby increasing the actual loading of gold cyanide onto the adsorbents.     

Variation of intraparticle diffusion parameter during adsorption of p‐chlorophenol onto activated carbon made from apricot stones

The adsorption of para‐chlorophenol onto an active carbon made from waste apricot stones has been studied. The batch kinetic adsorption processes have been measured for a range of system variables including agitation rate, initial concentration of para‐chlorophenol, mass of carbon and particle size of carbon. The extent of adsorption is reported as plots of solid phase concentration against the square root of time. An intraparticle diffusion parameter is used to describe the mass transfer within the adsorbent. This parameter varies with the square root of time and can be related to the type of structure which occurs within an activated carbon. A correlation is proposed relating the process variable with the intraparticle diffusion parameter in each of the three mass transfer regions. Copyright © 2003 Society of Chemical Industry     

Modelling of porous core–shell adsorbent particles with various morphologies suspended in batch adsorber from analytical solutions of diffusion equations

Considering both intra-particle diffusion and film resistance for mass transfer, analytical solutions of transient concentration of adsorbate inside adsorbents with spherical, cylindrical, or slab-type particles were derived for batch adsorbers by solving governing equations using the Laplace transform. Assuming Henry's or rectangular isotherm, the average concentration inside adsorbents as well as transient bulk concentration were also obtained for the particles with or without the inert core. Computations were performed to compare the results according to the shape of adsorbents by adjusting adsorbent loading, Biot number (Bi), and inert core thickness. Regardless of particle morphologies, steady-state bulk concentration was only affected by adsorbent loading and inert core thickness, whereas the effect of Bi was confirmed from the decreasing reduction rate of adsorbate concentration with decreasing Bi. When diffusivity was dependent on time, time-decaying diffusivity caused the increase in steady-state concentration that was predicted by eigenfunction expansion. Experimental results using porous fibres by electrospinning were compared with the mathematical solution of a cylindrical adsorbent for the estimation of intra-particle diffusivity. Using the solutions of the diffusion equation model, novel core–shell cylindrical adsorbents can be designed and synthesized as core–shell fibres by electrospinning with a coaxial nozzle to save the cost of the active shell layer. Such core–shell structured fibres can be adopted as adsorbents for novel batch adsorption processes and the present modelling results can be extended to other processes like fixed bed adsorbers.     

Analysis of the constant molar flow semi-batch adsorber loaded with inert core adsorbents

An analytical solution for a constant molar flow semi-batch adsorber loaded with inert core adsorbents is obtained for the linear isotherm coupled with intraparticle diffusion and external film diffusion. The solution obtained in this study consists of two parts. One is the asymptote, to which the bulk concentration approaches as time is sufficiently large. The other is the relaxation term, which dictates how the mass in the bulk phase flows into the adsorbent within the adsorption vessel. For a given value of the inert core radius, the slope of the asymptote is a function of the equilibrium parameter only and the intercept is a function of the kinetic parameter as well as the equilibrium parameter. The intercept of the asymptote consists of two parts. One is the contribution due to the external film resistance; the other is the contribution due to the intraparticle diffusion resistance. Hence, we can obtain the information of the equilibrium constant, the film mass transfer coefficient, and the effective diffusivity from the asymptote of the solution presented in this study.     

Recovery of 1,4‐Dimethyl Piperazine from Aqueous Solutions Using Polymeric Adsorbent and Ion‐Exchange Resins

Abstract

Strong and weakly acidic ion exchange resins and polymeric adsorbents are used for recovery of 1,4‐dimethyl piperazine (DMP) from aqueous solutions. Sorption of the amine in undissociated form is the primary mechanism of uptake of DMP on the ion‐exchange resins. Equilibrium adsorption data for DMP on the resins, at various temperatures, are fitted in Langmuir adsorption isotherm. Kinetic studies show that intraparticle diffusional resistance controls the sorption of DMP into the resin matrix. A mathematical model based on intraparticle diffusion and external mass transfer is used for simulating breakthrough profiles and compared with the experimental results for a fixed bed of weakly acidic Indion‐652 resin. The DMP loaded bed of the resin was effectively regenerated with methanol.     

间歇吸附器内活性炭吸附水中微量三氯甲烷——孔扩散模型和表面扩散模型

<正> 近10多年来,各国对饮水氯化处理中的副作用研究甚多．现已发现氯化饮水中含有不同 性质的有机物约300种“’,其中三卤甲烷含量突出,而活性炭吸附是脱除其中不同性质有机物 的有效方法’‘－‘’．一般情况下,溶质在吸附剂内的扩散过程是整个吸附过程的控制步骤．但目 前文献仅限干研究活性炭吸附三卤甲烷的能力,很少涉及与吸附速率有关的有效扩散系数．     

Fast Removal of Sr(II) From Water by Graphene Oxide and Chitosan Modified Graphene Oxide

Graphene oxide is a unique material that can be used for adsorption of radioactive waste because it contains various function groups such as epoxide, carbonyl, carboxyl and hydroxyl in addition to its high specific surface area. The as-prepared GO and the modified one (GO-chitosan composite) have been prepared then characterized and used as adsorbent for radioactive metal ions [Strontium, Sr(II)]. The results showed that the prepared materials are efficient adsorbents for removal of Sr(II) from water. The effect of contact time, pH and temperature on adsorption have been studied. The results indicated that the maximum adsorption capacity was about 140 and 179.6 mg/g for GO and GO-chitosan composite respectively. It was found that pH?~?6 and temperature?~?40 °C are the best condition for removal of Sr(II) from water. Two isotherm models (Langmuir and Freundlich) and three kinetic models (Pseudo-first-order, pseudo-second-order, and intra-particle particle diffusion model) have been applied. Based on the calculated isotherm parameters (R²), it can be concluded that Langmuir model fits the adsorption equilibrium data better than Freundlich model, the results also indicated that the second order kinetic model is the best representative for adsorption of Sr(II) on GO, Chitosan and GO-Chitosan. Based on the regressions of intraparticle diffusion model, experimental data showed that the adsorption process involved intraparticle diffusion, which was not the only rate-controlling step.