Empirical desorption models

Models with Cellular Structure Representation, Empirical Desorption Models... 

Empirical Desorption Models. A superficial analysis of all extraction experiments may remind one of a simple desorption mechanism. Thus, some researchers chose to use an adsorption isotherm to represent natural materials extraction without any explicit concern for the actual mechanisms taking place in the host matrix. Of these. Naik. et. al. [43] used a model similar to a Langmuir like desorption isotherm. 

Geochemical models of sorption and desorption must be developed from this work and incorporated into transport models that predict radionuclide migration. A frequently used, simple sorption (or desorption) model is the empirical distribution coefficient, Kj. This quantity is simply the equilibrium concentration of sorbed radionuclide divided by the equilibrium concentration of radionuclide in solution. Values of Kd can be used to calculate a retardation factor, R, which is used in solute transport equations to predict radionuclide migration in groundwater. The calculations assume instantaneous sorption, a linear sorption isotherm, and single-valued adsorption-desorption isotherms. These assumptions have been shown to be erroneous for solute sorption in several groundwater-soil systems (1-2). A more accurate description of radionuclide sorption is an isothermal equation such as the Freundlich equation ... 

Most studies of anion competition for soil-surface sites have involved phosphate. The studies of Theng (1971), Barrow (1974), Karimian and Cox (1978), Roy, Hassett, and Griffin (1986a,b), Xie and Mackenzie (1991), and Xie, MacKenzie, and Lou (1993) revealed Mo desorption or decreased Mo sorption in the presence of phosphate. The data on anion competition of Roy et al. (1986a,b) have been modeled using various empirical sorption models (Roy et al., 1986b, 1989 Barrow, 1989). 

Equation (57) is empirical, except for the case where v = 0.5, then Eq. (57) is similar to the parabolic diffusion model. Equation (57) and various modified forms have been used by a number of researchers to describe the kinetics of solid phase sorption/desorption and chemical transformation processes [25, 121-122]. 

There are a good number of sorption/desorption isotherm models which were developed in order to reflect the actual sorption/desorption processes occurring in the natural environment. Some models have a sound theoretical basis however, they may have only limited experimental utility because the assumptions involved in the development of the relationship apply only to a limited number of sorption/desorption processes. Other models are more empirical in their derivation, but tend to be more generally applicable. 

Extensive literature has developed related to the preferential interaction of different solvents with proteins or peptides in bulk solution.156-5X1 Similar concepts can be incorporated into descriptions of the RPC behavior of peptides and employed as part of the selection criteria for optimizing the separation of a particular peptide mixture. As noted previously, the dependency of the equilibrium association constant, /CassoCji, of a peptide and the concentration of the solvent required for desorption in RPC can be empirically described1441 in terms of nonmechanistic, stoichiometric solvent displacement or preferential hydration models, whereby the mass distribution of a peptide P, with n nonpolar ligands, each of which is solvated with solvent molecules Da is given by the following ... 

The studies of Ertl and co-workers showed that the reason for self-oscillations [142, 145, 185-187] and hysteresis effects [143] in CO oxidation over Pt(100) in high vacuum ( 10 4 Torr) is the existence of spatio-temporal waves of the reversible surface phase transition hex - (1 x 1). The mathematical model [188] suggests that in each of the phases an adsorption mechanism with various parameters of CO and 02 adsorption/desorption and their interaction is realized, and the phase transition is modelled by a semi-empirical method via the introduction of discontinuous non-linearity. Later, an imitation model based on the stochastic automat was used [189] to study the qualitative characteristics for the dynamic behaviour of the surface. 

Linear stationary systems with regular fluxes are realized mostly in laboratory conditions, whereas technology deals with systems in nonsteady-state and/or random fluxes. Nevertheless, the linear stationary model is enough simple and sometimes effective for semi-empirical treatment of various experimental data (first of all adsorption-desorption) even obtained on materials obviously prepared in conditions of random fluxes. 

An empirical non-linear model was used to describe the bi-phasic nature of desorption with one fraction (labile) being released in relatively short periods of time (typically 24-100 h) and a second fraction (non-labile or irreversible) being resistant to desorption and the parameters estimated. In addition, desorption kinetics of three-month and five-month old contaminated soils showed that progressively less amount of contaminant was available for labile desorption (lower F) compared to freshly contaminated soil. 

An empirical model was used by Opdyke and Loehr [17] to describe the contaminant rate of release (ROR) similar to what we observed a relatively rapid release of the chemical followed by a much slower release of the remaining chemical. The non-linear equation used to describe this biphasic behavior during desorption was given by... 

Attempts to model chemical weathering of catchments have used a variety of approaches and were originally designed to understand acidification processes. The BIRKENES code (Christophersen et al., 1982) was one of the first developed to model catchment stream chemistry. It used cation-anion charge balance, a gibbsite equilibrium solubility control for aluminum concentrations, a Gapon ion exchange for metals sorption, and rates for sulfate adsorption/ desorption in a two-reservoir model. The model was calibrated by input mass fluxes and output mass fluxes for the Birkenes catchment in Norway to provide the water flux information and to fit empirical parameters. 

IS mucn more theoretical and conceptual as it is based on physico-chemical properties and models necessary to understand the host-guest interactions which occur within a zeolite framework, i.e., the way reactions occur inside the zeolite. This involves the description of the zeolite (host) and chemical compounds (guests), as well as the characterization of the intraframework phenomena diffusion process, adsorption at specific sites, reaction mechanisms, and desorption. The aim of the consideration of the complementary theoretical knowledge is i) to interpret observations done from the retrieval and analysis of the data from the empirical knowledge base ii) to endow to the system with a detailed description of zeolite catalysis at a conceptual level, to allow the system to propose predictions and solutions for particular catalytic problem by combination of these theoretical notions. 

Two general types of models have been developed to desaibe adsorption/desorption reactions at mineral surfaces (1) empirical models that are based on the partioning relationships of a solute between the aqueous and solid phase, and (2) conceptual models for surface... 

After all parameters for the plant (Section 6.5.5) and column (Sections 6.5.6-8) models are determined, either from experimental data or from empirical correlations, the validity of the model should be checked using different experiments than those for parameter determination. Keeping in mind the separation task at hand, the position of the adsorption and desorption fronts may be taken as an indicator for the purity of the products. Therefore, the position of these fronts is often more important for process optimization than the exact height of the simulated profile. 

The previous equations describing the adsorption/desorption behavior of gases lead to models describing sink effects in indoor environments. In addition, transport of molecules within the sink material can have a major impact on desorption rates thus, models accounting for internal diffusion have been developed for indoor sinks. Models based on fundamental theories are preferred over empirical approaches, but some studies rely on experimental data to fit empirical models [21-23]. 

We must evaluate our underlying objectives in conducting sorption/ desorption research before we can evaluate the utility of kinetic approaches for this research. The perspective and rationale for the use of kinetic studies are, in turn, the bases of conceptual models against which empirical data are tested. Research objectives are often forgotten in the excitement of data acquisition and under the pressure of interpretations, but results and interpretations are only meaningful when they can be related to the questions that were being addressed. 

Laying aside, for the moment, all application problems, let us examine the inherent capabilities of kinetics. Reaction rates are the most obvious and most readily available output of these experiments. As with adsorption isotherms, empirical sorption or desorption data can simply be plotted as a function of time and the progress of the reaction can be visually examined. Such information as half-reaction time and time to establish a new equilibrium can be directly obtained from the plot. If, however, the objective of the research is to provide input for generalized sorption models, more quantita-live information will be necessary. 

Kinetic models for catalytic reactions vary widely in sophistication, generality and accuracy. The simplest, least general and easiest to obtain are the power law kinetic models which are usually strictly empirical and contain a limited number of parameters. Consequently they are valid only in a narrow region of parameters and cannot be safely extrapolated outside this region. Kinetic models which take into consideration the interaction between the gas phase and the solid surface (whether through a reduction-oxidation mechanism or an adsorption-desorption mechanism) are more difficult to formulate and usually contain a large number of parameters. However, they are certainly more reliable, general and accurate than power law kinetics. 

In our case study, the experimental observations (i.e. concentration versus time data) were used as input to the conceptualization phase of a mathematical model with two sink compartments (the so-called two-sink model). Following the above discussion, this model (schematically represented in Fig. 2.3-1) can be eonsidered as a hybrid-empirical model. Conceptually, this model describes the test chamber kinetics of a VOC for the three types of experiments which have been carried out. The adsorption-desorption kinetics is described by the rate constants k, k, k. Given that the conceptualization... 

Currently, there are numerous empirical functions of the adsorption-desorption reactions kinetics proposed for various specific conditions. As a rule, the adsorption rate is considered to be a linear function of the number of active centres on the surface of the mineral. The simplest is the single-reaction model, which assumes that the exchange is caused by the interaction of a single component i with active centres of a single type surface, is subject to the first order reactions and its rate may be presented by the following equation... 

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