Empirical models sorption processes

A number of models have been developed to reflect the actual sorption/desorp-tion processes that occur in the natural environment [1,29-33]. 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 processes. Other models are more empirical in their derivation, but tend to be more generally applicable. In the latter case, the theoretical basis is uncertain. 

Sorption is most commonly quantified using distribution coefficients (Kd), which simplistically model the sorption process as a partitioning of the chemical between homogeneous solid and solution phases. Sorption is also commonly quantified using sorption isotherms, which allow variation in sorption intensity with triazine concentration in solution. Sorption isotherms are generally modeled using the empirical Freundlich equation, S = K CUn, in which S is the sorbed concentration after equilibration, C is the solution concentration after equilibration, and Kt and 1 In are empirical constants. Kd and K are used to compare sorption of different chemicals on one soil or sorbent, or of one chemical on several sorbents. Kd and K are also commonly used in solute leaching models to predict triazine interactions with soils under various environmental conditions. 

The paper summarizes eiforts started to deliver a profound chemical base for risk assessment, namely to properly take into account the physico-chemical phenomena governing the contamination source term development in time and space. One major aspect there is the substitution of conventional distribution coefficients (IQ values) for the empirical description of sorption processes by surface complexation models, in combination with other thermodynamic concepts. Thus, the framework of a Smart Kd is developed for complex scenarios with a detailed explanation of the underl3dng assumptions and theories. It helps to identify essential processes and the associated most critical parameters, easing further refinement studies. The presented case studies cover a broad spectrum of contamination cases and successfully demonstrate the applicability of the methodology. The necessity to create a mineral-specific sorption database to support the Smart IQ approach is derived and a first prototype for such a digital database introduced, combining numeric data with a knowledge base about the relevant theories, experimental methods, and structural information. 

In the late 1990s and early 2000s certain attempts were made to expand Langmuir and Freundlich-type models to describe two- or multi-metal ions biosorption system to more accurately represent the nature of real effluents. These empirical models hardly reflect the sorption mechanism as they do not take into account all the various processes and parameters which influence the retention of metals and radionuclides by algal cells. Furthermore, a number of attempts were made to consider other mechanism in metal biosorption, e.g. ion exchange between protons in the biomass and/or complexation. Those models considered the sorbate speciation in solution pH and even electrostatic attraction however are not yet widely accepted in the scientific community... 

Modeling relaxation-influenced processes has been the subject of much theoretical work, which provides valuable insight into the physical process of solvent sorption [119], But these models are too complex to be useful in correlating data. However, in cases where the transport exponent is 0.5, it is simple to apply a diffusion analysis to the data. Such an analysis can usually fit such data well with a single parameter and provides dimensional scaling directly, plus the rate constant—the diffusion coefficient—has more intuitive significance than an empirical parameter like k. 

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]. 

Nonequilibrium sorption due to mass-transfer limitations (including slow external or internal diffusion) and sorption to two different sorbents have been incorporated into a single ADE to evaluate the conditions under which mass-transfer processes may be important [206]. Simulations with this model, using mass-transfer parameters estimated from empirical correlations, reveal nonequilibrium conditions (i.e., mass-transfer limitations) when groundwater velocities increase (such as those that might occur in a funnel-and-gate system). 

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. 

A characteristic feature associated with pore condensation is the occurrence of sorption hysteresis, i.e pore evaporation occurs usually at a lower p/po compared to the condensation process. The details of this hysteresis loop depend on the thermodynamic state of the pore fluid and on the texture of adsorbents, i.e. the presence of a pore network. An empirical classification of common types of sorption hysteresis, which reflects a widely accepted correlation between the shape of the hysteresis loop and the geometry and texture of the mesoporous adsorbent was published by lUPAC [10]. However, detailed effects of these various factors on the hysteresis loop are not fully understood. In the literature mainly two models are discussed, which both contribute to the understanding of sorption hysteresis [8] (i) single pore model. hysteresis is considered as an intrinsic property of the phase transition in a single pore, reflecting the existence of metastable gas-states, (ii) neiM ork model hysteresis is explained as a consequence of the interconnectivity of a real porous network with a wide distribution of pore sizes. 

The use of various absorbance profiles for different analyte concentrations has been applied, with activation energy independent of the amount of analyte. In this case, the main problem was due to the fact that the order of release and the activation energy were deduced from different and in many cases very short temperature ranges. Beside the ad-sorption/desorption processes, a second modeling approach based on condensation/evaporization processes have been proposed where some features of the atomization process are also interpreted - double values of the activation energy, values of E empirical relationship between Ea and Tapp (appearance) as well as the theoretical activation energies and preexponential factors. 

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