Steady-state permeation model

The Steady-State Permeation Model for Underground Coal Gasification... 

The steady-state permeation model of in situ coal gasification is presented in an expanded formulation which includes the following reactions combustion, water-gas, water-gas shift, Boudouard, methanation and devolatilization. The model predicts that substantial quantities of unconsumed char will be left in the wake of the burn front under certain conditions, and this result is in qualitative agreement with postburn studies of the Hanna UCG tests. The problems encountered in the numerical solution of the system equations are discussed. 

An expanded formulation of the steady-state permeation model has been presented. Two numerical problems - stiffness and an ill-conditioned boundary value problem - are encountered in solving the system equations. These problems can be circumvented by matching forward and reverse integrations at a point near the inlet (n = 0) but outside the combustion zone. The model predicts a... 

MESI operation requires processing of the whole sample to be extracted and has to reach steady-state permeation, which usually takes a long time. Thus, a new technical modification of MESI, called pulse introduction (flow injection-type) membrane extraction (PIME), has been developed, in which the sample is introduced to the membrane as a pulse pushed by a stream of eluent (usually water).55 This means that attaining a steady state is no longer crucial. PIME therefore provides not only a faster response and higher sensitivity, but also allows extraction of individual samples via discrete injections in addition to continuous on-line monitoring by sequential injection of a series of samples. Guo et al.56 described a mathematical model for the PIME permeation process, which showed that (a) there was a trade-off between the sensitivity and the time lag (the time taken to complete the permeation process) and (b) a large sample volume and a low flow rate enhance the sensitivity but also increase the time lag. 

Analysis of the effect of permeation, temperature profile and sweep gas will be proposed hereafter considering a steady-state MR modeled by a 1D, first-order model. The model can be extracted from the mass and energy balance, Equations 13.14... 

The last ten years have witnessed a number of extensive field tests of underground coal gasification (UCG) in the United States and Europe. Model development is essential to the proper understanding of these test results and to the planning of future experiments. This report will focus upon the steady-state "permeation" or "packed bed" model of in situ gasification (forward combustion mode). In this useful but idealistic model the coal bed is assumed to be uniformly permeable to reactant and product gases. 

The combined procedure described above, which uses only sorption and steady state permeation data, specifies all five of the sorption and tran rt model parameters without requiring reference to the independenfly measured time lags, Com-pariscm of tiieoretically predicted time lags with flie experimentally meaaired values provides a rigorous test of the internal consistency of the transport and sorption data as well as a check of the applicability of the partial immobSization model for description of the transient processes. 

The concentration dependent diffusion coefficient defined by Eq. (9) can be evaluated by differentiation of steady state permeation data without reference to tile partial immobilization model The concentration dependent diffusion coefficient calculated from the partial immobilization model agrees very well with values calculated in this way, and one can consider them to be essentially identical mathematically The partial inunobilization theory, therefore, serves to explain the source of the concentration dependency of Dgfr in Eq. (9). 

For mixed gas experiments, the flow rates and composition of the feed gas were controlled using electronic mass flow controllers. The total feed pressure was kept steady at 227.5 cm Hg (303 kPa) while the permeate pressure and temperature were maintained at ambient conditions (62 cm Hg and room temperature). Permeate and retentate streams, with helium as the sweep gas (on permeate side), were analyzed for gas compositions using a gas chromatograph (SRI Instruments, model 8610 C). The total steady state permeate flow rate and the gas composition of the permeate stream were used to calculate the analyte gas flux. From the flux, and the pressure differential across the membrane, the gas permeances and separation factor (ratio of permeance) can be calculated. 

Pospisil P., Wakeman R.J., Hodgson I.O.A. and Mikulasek P, 2004. Shear stress-based modelling of steady state permeate flux in microfiltration enhanced by two-phase flows, Chem. Eng. J., 97, 257-263. 

Equations (14.14) and (14.18) can be used as starting point for generating equations describing O2 and H2 permeation within single-phase perovskite membranes. Key to these equations is the nature of the boundary conditions at the feed/membrane and permeate/membrane surfaces. To this aim, one needs to address appropriate defect point thermodynamics to establish equilibrium and surface exchange relations for all potential species that can play a role during permeation. As a general rule, the law of mass action can be used to predict the concentration of ionic vacancies, protons, electrons, and electron holes in the membrane. Below we describe a series of models that can be deduced for ID steady-state permeation within perovskite and extensively other MIEC membranes. 

In our study, conunercial paratus (PERMATRAN-C Model 4/41and PERMATRAN-W Model 3/33 fiom Mocon) are used respectively to measure steady state permeation data of CO2 and water vapor. 

All the sanq)les are big enough to cover the permeation area (a circle with area of 50 cm ). Permeant CO2 (>99.99%) and carrier gas N2 (>99.998%) were provided by Praxair. Water (HPLC grade) is fi om Fisher Scientific. For both measurements, pressure for carrier gas is 45 Psi (gauge pressure) controlled by a regulator. Its flow rate is 100 seem (standard cubic centimrters per minute). For CO2 measurement, the pressure of CO2 is 15 psi (gauge pressme) by relator (also measured accurately by pressure sensor (Sensotec, model AG 300) and the flow rate is 100 seem. Usually about two days is taken to ensure steady state permeation data values. 

The rather time- and cost-expensive preparation of primary brain microvessel endothelial cells, as well as the limited number of experiments which can be performed with intact brain capillaries, has led to an attempt to predict the blood-brain barrier permeability of new chemical entities in silico. Artificial neural networks have been developed to predict the ratios of the steady-state concentrations of drugs in the brain to those of the blood from their structural parameters [117, 118]. A summary of the current efforts is given in Chap. 25. Quantitative structure-property relationship models based on in vivo blood-brain permeation data and systematic variable selection methods led to success rates of prediction of over 80% for barrier permeant and nonper-meant compounds, thus offering a tool for virtual screening of substances of interest [119]. 

This chapter starts with a short introduction on the skin barrier s properties and the methods employed for analyzing experimental data. This is followed by an overview of several selected approaches to predict steady-state diffusion through the skin. Then a few approaches that approximate the structural complexity of the skin by predicting drug diffusion in biphasic or even multiphasic two-dimensional models will be presented. Finally, the chapter concludes with a short summary of the many variables possibly influencing drug permeation and penetration. 

Most models of the permeation of drugs through skin consider only steady-state conditions the drug amount in the donor is infinite and the concentration of accumulated drug in the acceptor is comparatively small and therefore negligible. Under these conditions the concentration-depth profile for a homogeneous membrane at time t is given by... 

Heisig M, Lieckfeldt R, Wittum G, Mazurkevich G, Lee G (1996) Non steady-state descriptions of drug permeation through stratum comeum. I. The biphasic brick-and-mortar model. Pharm Res 13 421 —426. 

Polar Cell Systems for Membrane Transport Studies Direct current electrical measurement in epithelia steady-state and transient analysis, 171, 607 impedance analysis in tight epithelia, 171, 628 electrical impedance analysis of leaky epithelia theory, techniques, and leak artifact problems, 171, 642 patch-clamp experiments in epithelia activation by hormones or neurotransmitters, 171, 663 ionic permeation mechanisms in epithelia biionic potentials, dilution potentials, conductances, and streaming potentials, 171, 678 use of ionophores in epithelia characterizing membrane properties, 171, 715 cultures as epithelial models porous-bottom culture dishes for studying transport and differentiation, 171, 736 volume regulation in epithelia experimental approaches, 171, 744 scanning electrode localization of transport pathways in epithelial tissues, 171, 792. 

In the assessment of the uptake of a chemical after dermal exposure, for instance, the dermal permeability of the skin is often estimated using the Potts-Guy quantitative structure-activity relationship (Guy Potts, 1992), which was derived from an experimental data set of in vitro measured steady-state skin permeations (Wilschut et al., 1995). Uncertainty in the use of a value for the skin permeation obtained this way comes from questions of how well a regression model based on Kow and molecular weight predicts the skin permeability of a chemical that was not in the original data set, and how representative the steady-state permeability measured in vitro is for a (possibly) non-steady-state permeability in vivo (see also IPCS, 2006b). 

Gunn and coworkers (1,2) were the first to propose a steady-state model, and their predictions agreed very well with the Hanna UCG test results. In an analysis of the different versions of permeation models that have appeared in the literature, Haynes (3) judged the steady-state model superior for most applications since reaction kinetics are taken into account and only a modest computational effort is required. Despite these desirable features, applications of the steady-state model have not been as widespread as one might anticipate. 

Despite the fact that the skin is a heterogeneous membrane, Fick s laws of diffusion have been successfully used to analyze skin permeation data. Solutions to the second law have been used in mechanistic interpretations (see later) and in considering concentration profiles within the skin. Fick s first law has been used to analyze steady-state diffusion rates and in the development of predictive models for skin permeability. 

All of these simple models have in common the fact that they are accessible to mathematical analysis, while more complex models are not. Yet whether one is dealing with idealized (analyzable) models or complex three-dimensional models, it is essential that the governing equations appropriately represent the underlying physical phenomena. To serve as a resource for this purpose, examples involving time-dependent and steady state transport, simple and facilitated diffusion, and passive permeations between regions were studied. 

The effectiveness of cisplatin depends on its ability to penetrate target tissue. Therefore, we need to estimate its penetration depth from a distributed model such as that represented by Equation 9.1. However, this is difficult to do with ovarian tumors because the permeabilities and reaction rates are not available. Hence, a first estimate is made for penetration of normal peritoneal cavity tissues by ethylenediamine-tetraacetic acid (EDTA), a molecule of molecular weight similar to that of cisplatin. The steady-state concentration profiles of EDTA should resemble those of cisplatin in normal peritoneal tissues because both compounds are cleared primarily by permeation through the fenestrated capillaries in these tissues, and the small molecular weight-related differences in P s and D should cancel out in Equations 9.5 and 9.5T By first focusing on EDTA, experimental data also become available for assessing the ability of the distributed model to account for the observed spatial dependent of concentration. 

The WK-method has clearly advantages over the static method since one can use mixtures and one operates under steady state conditions, which makes the modelling of the results easier. Moreover, one can even apply transient conditions by suddenly changing the feed gas flow from inert to a mixture or vice versa and analysing the response of the membrane to this step change. This gives sometimes nice insight in the permeation characteristics of mixtures. 

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