Extraction equilibria modeling

One possibility for increasing the minimum porosity needed to generate disequilibria involves control of element extraction by solid-state diffusion (diffusion control models). If solid diffusion slows the rate that an incompatible element is transported to the melt-mineral interface, then the element will behave as if it has a higher partition coefficient than its equilibrium partition coefficient. This in turn would allow higher melt porosities to achieve the same amount of disequilibria as in pure equilibrium models. Iwamori (1992, 1993) presented a model of this process applicable to all elements that suggested that diffusion control would be important for all elements having diffusivities less than... 

In addition to the mechanistic simulation of absorptive and secretive saturable carrier-mediated transport, we have developed a model of saturable metabolism for the gut and liver that simulates nonlinear responses in drug bioavailability and pharmacokinetics [19]. Hepatic extraction is modeled using a modified venous equilibrium model that is applicable under transient and nonlinear conditions. For drugs undergoing gut metabolism by the same enzymes responsible for liver metabolism (e.g., CYPs 3A4 and 2D6), gut metabolism kinetic parameters are scaled from liver metabolism parameters by scaling Vmax by the ratios of the amounts of metabolizing enzymes in each of the intestinal enterocyte compart-... 

Cote, G. Jakubiak, A. Bauer, D. Szymanowski, J. Mokili, B. Poitrenaud, C. Modeling of extraction equilibrium for copper(II) extraction bypyridinecarboxylic acid esters from concentrated chloride solutions at constant water activity and constant total concentration of ionic or molecular species dissolved in the aqueous solution. Solvent Extr. 

Multiple equilibrium model, 24 131 Multiple extraction procedure (MEP), 25 869... 

The material covered in the appendices is provided as a supplement for readers interested in more detail than could be provided in the main text. Appendix A discusses the derivation of the spectral relaxation (SR) model starting from the scalar spectral transport equation. The SR model is introduced in Chapter 4 as a non-equilibrium model for the scalar dissipation rate. The material in Appendix A is an attempt to connect the model to a more fundamental description based on two-point spectral transport. This connection can be exploited to extract model parameters from direct-numerical simulation data of homogeneous turbulent scalar mixing (Fox and Yeung 1999). 

Two different approaches have been taken by researchers to determine the secondary mineralogy of CCBs (1) direct observation, which is accomplished via analysis of weathered ash materials, and (2) prediction, based on chemical equilibrium solubility calculations for ash pore-waters and/or experimental ash leachate or extractant solutions. Because the secondary phases are typically present in very low abundance, their characterization by direct analysis is difficult. On the other hand, predictions based on chemical equilibrium modelling or laboratory leaching experiments may not be reliable indicators of element leachability or accurately indicate the secondary phases that will form under field conditions (Eighmy et al. 1994 Janssen-Jurkovicova et al. 1994). 

Delmau, L.H., Bostick, D.A., Haverlock, T.J., Moyer, B.A. 2002. Caustic-side solvent extraction Extended equilibrium modeling of cesium and potassium distribution behavior. Oak Ridge National Laboratory Report. ORNL/TM-2002/116. 

Geist, A. 2008. Equilibrium model for the extraction of Am(III), Eu(III), and HN03 into DMDOHEMA in TPH. 2008. ATALANTE 2008 Nuclear Fuel Cycles for a Sustainable Future, May, Montpellier, France. 

Delmau, L. H., Bostick, D. A., Haverlock, T. J., and Moyer, B. A. Caustic-Side Solvent Extraction, Extended Equilibrium Modeling of Cesium and Potassium Distribution Behavior, Report ORNL/TM-2002/116, Oak Ridge National laboratory, Oak Ridge, TN, May 2002. 

Combination of wet chemical extraction with instrumental speciation techniques or chemical equilibrium modelling... 

Table 11.2 Results of chemical equilibrium modelling of the contribution of ferrous iron phases to the proportion of iron (in %) extracted from an anoxic freshwater sediment from the Elbe River near Hamburg (Germany) by the first two acetate buffer steps of a modified Tessier sequential extraction scheme...

It has been demonstrated that hepatic extraction ratio (ER) is also influenced by blood flow. A number of mathematical models have been proposed to explain this observation, but the simplest model, and the one that is easiest to apply to clinical practice, is the well stirred or venous equilibrium model (Equation 5.3). This model relates hepatic clearance to hepatic blood flow (Q), the fraction of drug concentration that is unbound in plasma (fu) and the intrinsic clearance of the unbound drug (Clyint) [1]. Intrinsic clearance represents the maximum clearance of drug in the absence of any restrictions caused by blood flow, binding or access to the metabolising enzymes. The model states that ... 

Figure 23 Chondrite-normalized abundances of REEs in representative harzburgites from the Oman ophiolite (symbols—whole-rock analyses), compared with numerical experiments of partial melting performed with the Plate Model of Vemieres et al. (1997), after Godard et al. (2000) (reproduced by permission of Elsevier from Earth Planet. Set Lett. 2000, 180, 133-148). Top melting without (a) and with (b) melt infiltration. Model (a) simulates continuous melting (Langmuir et al., 1977 Johnson and Dick, 1992), whereas in model (b) the molten peridotites are percolated by a melt of fixed, N-MORB composition. Model (b) is, therefore, comparable to the open-system melting model of Ozawa and Shimizu (1995). The numbers indicate olivine proportions (in percent) in residual peridotites. Bolder lines indicate the REE patterns of the less refractory peridotites. In model (a), the most refractory peridotite (76% olivine) is produced after 21.1% melt extraction. In model (b), the ratio of infiltrated melt to peridotite increases with melting degree, from 0.02 to 0.19. Bottom modification of the calculated REE patterns residual peridotites due to the presence of equilibrium, trapped melt. Models (c) and (d) show the effect of trapped melt on the most refractory peridotites of models (a) and (b), respectively. Bolder lines indicate the composition of residual peridotites without trapped melt. Numbers indicate the proportion of trapped melt (in percent). Model parameters...

In the case of Ni, the situation is even more complex since the stoichiometric equations reported in the literature differ widely depending on the diluents used, on the aqueous phase compositions, or on the extractant concentrations employed. A discrimination procedure of the equilibrium models corresponding to the back-extraction reactions has been reported previously by taking into account the expressions given in Table 37.1 and obtaining the best results with the following equation [59] ... 

It is often necessary to add user components to complete a simulation model. The design engineer should always be cautious when interpreting simulation results for models that include user components. Phase equilibrium predictions for flashes, decanters, extraction, distillation, and crystallization operations should be carefully checked against laboratory data to ensure that the model is correctly predicting the component distribution between the phases. If the fit is poor, the binary interaction parameters in the phase equilibrium model can be tuned to improve the prediction. 

Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model... 

For the previously established azophenolic crown ether extractant a predictive single stage equilibrium model (Figure 1) was constructed and validated [14]. The extent of extraction is characterised by the distribution ratios Dr and Ds for each enantiomer ... 

Bhavani, R., Neena, T. and John, W. (1994). Emulsion liquid membranes for waste-water treatment Equilibrium models for some typical metal-extractant systems. Environ. Sci. Technol., 28, 1090-8. 

Amine-anhydride reactions, equilibrium, 115 Anhydride-amine reaction, equilibrium, 115 Anhydride hydrolysis, polyimides, 58,60r,61/62 Aqueous ion extraction, kinetic model, 438-440 Aromatic polyimides applications, 67 properties, 26 structures, 27,28/ use as dielectric materials, 26... 

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