Models for Hydrogen Permeation

it is assumed that the H2 dissociation rate at the surface of the membranes is much higher than the bulk diffusivity of the charge carriers. The elfect of external mass transfer is also neglected. 

A schematic of the concentration profiles of various charge carriers within membranes is shown in Eig. 2.9. The protonic and electronic conductivity are presented as empirical functions of H2 partial pressure to substitute into Eq. (2.7). 

The final analytical expression for the H2 flux contained five parameters that included proton, electron and electron-hole conductivity, and their concentrations 

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Basic model for hydrogen permeation the lyer-Pickering-Zamanzadeh (IPZ) model 333... 

Liu, W. (2013) Modeling of hydrogen permeation for Ni-BZCY asymmetric membrane. /. Membr. Sci., 437,... 

Several papers have also been published in which a correlation has been sought between permeation across Caco-2 cells and physicochemical properties of the compounds. The review article by Ekins et al. (2000) discusses several studies to predict Caco-2 cell permeation. Correlations have been found with polar surface area, hydrogen bond descriptors, VolSurf, and other parameters. Van de Waterbeemd et al. (2001a) also discuss models for predicting oral absorption of compounds, including the use of Caco-2 cell lines. This paper also provides much useful information on the optimization of pharmacokinetic parameters in drug development. 

Pick M.A., Sonnenberg K. A model for atomic hydrogen-metal interactions -application to recycling, recombination and permeation. J.Nucl.Mater 1985 131 208-220. 

In the case of dense membranes, where only hydrogen can permeate (permselectivity for H2 is infinite), the permeation rate is generally much lower than the reaction rate (especially when a fixed bed is added to the membrane). Experimental conditions and/or a reactor design which diminishes this gap will have positive effects on the yield. An increase of the sweep gas flow rate (increase of the driving force for H2 permeation) leads to an increase in conversion and, if low reactant flow rates are used (to limit the H2 production), conversions of up to 100% can be predicted [55]. These models of dense membrane reactors explain why large membrane surfaces are needed and why research is directed towards decreasing the thickness of Pd membranes (subsection 9.3.2.2.A.a). 

Due to their complexity, the model equations will not be derived or presented here. Details can be found elsewhere [Adris, 1994 Abdalla and Elnashaie, 1995]. Basically mass and heat balances arc performed for the dense and bubble phases. It is noted that associated reaction terms need to be included in those equations for the dense phase but not for the bubble phase. Hydrogen permeation, the rate of which follows Equation (10-51b) with n=0.5, is accounted for in the mass balance for the dense phase. Hydrodynamic parameters important to the fluidized bed reactor operation include minimum fluidization velocity, bed porosity at minimum fluidization, average bubble diameter, bubble rising velocity and volume fraction of bubbles in the fluidized bed. The equations used for estimating these and other hydrodynamic parameters are taken from various established sources in the fluidized bed literature and have been given by Abdalla and Elnashaie [1995]. 

Nevertheless, quantitative models for oral bioavailability and blood brain barrier permeation have been derived from data sets of limited size, using different approaches [89-97] in most cases, no details of the models are provided. Lipinski s rule of five gives the recommendation that a molecular weight > 500, lipophilicity values of log P > 5, and more than five hydrogen bond donors and/or more than 10 hydrogen bond acceptors should be avoided to achieve good oral bioavailability [98], General... 

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