Modelling dynamic sorption

Modeling of dynamic sorption behaviour of natural gas components... 

When modeling dynamic water sorption phenomena, information about evaporation and condensation is contained in the boundary conditions that account for water exchange across membrane-gas interfaces. The rate of interfacial water exchange is determined by values of the instantaneous water content on the PEM side of the interface, Xm, and by the vapor pressure, of the adjacent gas. The deviation of these local variables from their chemical equilibrium establishes the driving force of interfacial vaporization exchange. 

Several theoretical models, such as the ion-pair model [342,360,361,363,380], the dyneuaic ion-exchange model [342,362,363,375] and the electrostatic model [342,369,381-386] have been proposed to describe retention in reversed-phase IPC. The electrostatic model is the most versatile and enjoys the most support but is mathematically complex euid not very intuitive. The ion-pair model emd dynamic ion-exchange model are easier to manipulate and more instructive but are restricted to a narrow range of experimental conditions for trtilch they might reasonably be applied. The ion-pair model assumes that an ion pair is formed in the mobile phase prior to the sorption of the ion-pair complex into the stationary phase. The solute capacity factor is governed by the equilibrium constants for ion-pair formation in the mobile phase, extraction of the ion-pair complex into the stationary phase, and the dissociation of th p ion-pair complex in the... 

The bioavailability of contaminants to wildlife and humans is also an area of critical importance, where contaminants can be taken up in pore water and by dermal contact, particle ingestion, or particle inhalation. The dynamics of sorption/desorption are not currently incorporated into exposure and risk assessment models for organic compounds, where availability, in most cases, is assumed to be 100% [224]. Recently, the following have been demonstrated and reported ... 

A tremendous amount of research has been devoted to quantifying and modeling transport processes in the vadose zone, with readily available scientific literature (journals and textbooks) extending over the last half century. Modeling is used to quantify the dynamic redistribution of chemicals along the near surface and deeper subsurface profile, which often also is subject to reactive chemical processes including sorption, dissolution or precipitation, and volatilization. 

Even a simple mathematical model for transport on colloids in an aquifer must include dynamic equations for the dissolved phase and for the colloids. The latter equation describes the migration, immobilization, and detachment of the colloids. More sophisticated models include dynamic equations for sorption and desorption of the chemical onto colloids and the stationary solid phase. 

Pressure-dependent sorption and transport properties in polymers can be attributed to the presence of the penetrant in the polymer. Crank (32) suggested in 1953 that the "non-ideal" behavior of penetrant-polymer systems could arise from structural and dynamic changes of the polymer in response to the penetrant. As the properties of the polymer are dependent on the nature and concentration of the penetrant, the solubility and diffusion coefficient are also concentration-dependent. The concentration-dependent sorption and transport model suggests that "non-ideal" penetrant-polymer systems still obey Henry s and Fick s laws, and differ from the "ideal" systems only by the fact that a and D are concentration dependent,... 

The concentration-dependent models attribute the observed pressure dependence of the solubility and diffusion coefficients to the fact that the presence of sorbed gas in a polymer affects the structural and dynamic properties of the polymer, thus affecting the sorption and transport characteristics of the system (3). On the other hand, in the dual-mode model, the pressure-dependent sorption and transport properties arise from a... 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

The comparison of kinetic sorption models presented here was made possible by the use of the mixing-cell dynamic technique, which eliminates the masking effects of hydraulic dispersion. 

Teppen et al. [89] have used a flexible model for clay minerals that allows full movement of the M-O-M bonds in the clay structure, where M represents Si, Al, or other cations in the octahedral sheet. This model was used in MD simulations of interactions of hydrated clay minerals with trichloroethene [90, 91]. The simulations suggest that at least three distinct mechanisms coexist for trichloroethene sorption on clay minerals [90], The most stable interactions of trichloroethene with clay surfaces are by full molecular contact, coplanar with the basal surface. The second type more reversible, less stable is adsorption through single-atom contact between one chlorine atom and the surface. In a third mechanism, trichloroethene interacts with the first water layer and does not interact with clay surface directly. Using MC and MD simulation the structure and dynamics of methane in hydrated Na-smectite were studied [92], Methane particles are solvated by approximately 12-13 water molecules, with six oxygen atoms from the clay surface completing the coordination shell. 

Pressure Swing Adsorption (PSA) unit is a dynamic separation process. In order to create a precise model of the process and thus an accurate design, it is necessary to have a good knowledge of the mixture s adsorption behaviour. Consequently, the dilAision rates in the adsorbent particles and the mixture isotherms are extremely vital data. This article intends to present a new approach to study the adsorption behaviour of isomer mixtures on zeolites. In a combined simulation and experimental project we set out to assess the sorption properties of a series of zeolites. The simulations are based on the configurational-bias Monte Carlo technique. The sorption data are measured in a volumetric set-up coupled with an online Near Infra-Red (NIR) spectroscopy, to monitor the bulk composition. Single component isotherms of butane and iso-butane were measured to validate the equipment, and transient volumetric up-take experiments were also performed to access the adsorption kinetics. 

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