Model heterogeneous tube

Kaiampokis, A., Argyrakis, P., Macheras, P., A heterogeneous tube model of intestinal drug absorption based on probabilistic concepts, Pharm. Res. 1999, 16, 1764-1769. 

The model was also applied to the study of low-solubility drugs. Numerical results of the system of differential equations reported in [55] were compared to the simulations based on the heterogeneous tube. In the simulations the z variable is computed using the mean transit time of the particles, (TSi) = 24, 500 MCS, and z = tj (Tsi), expressing both t and (TSi) in MCS. The tablet was... 

Kalampokis, A., Argyrakis, P., and Macheras, P., Heterogeneous tube model for the study of small intestinal transit flow, Pharmaceutical Research, Vol. 16, No. 1, 1999, pp. 87-91. 

The microscopic understanding of tire chemical reactivity of surfaces is of fundamental interest in chemical physics and important for heterogeneous catalysis. Cluster science provides a new approach for tire study of tire microscopic mechanisms of surface chemical reactivity [48]. Surfaces of small clusters possess a very rich variation of chemisoriDtion sites and are ideal models for bulk surfaces. Chemical reactivity of many transition-metal clusters has been investigated [49]. Transition-metal clusters are produced using laser vaporization, and tire chemical reactivity studies are carried out typically in a flow tube reactor in which tire clusters interact witli a reactant gas at a given temperature and pressure for a fixed period of time. Reaction products are measured at various pressures or temperatures and reaction rates are derived. It has been found tliat tire reactivity of small transition-metal clusters witli simple molecules such as H2 and NH can vary dramatically witli cluster size and stmcture [48, 49, M and 52]. 

This study was carried out to simulate the 3D temperature field in and around the large steam reforming catalyst particles at the wall of a reformer tube, under various conditions (Dixon et al., 2003). We wanted to use this study with spherical catalyst particles to find an approach to incorporate thermal effects into the pellets, within reasonable constraints of computational effort and realism. This was our first look at the problem of bringing together CFD and heterogeneously catalyzed reactions. To have included species transport in the particles would have required a 3D diffusion-reaction model for each particle to be included in the flow simulation. The computational burden of this approach would have been very large. For the purposes of this first study, therefore, species transport was not incorporated in the model, and diffusion and mass transfer limitations were not directly represented. 

LPCVD Reactor Models. First-Order Surface Reaction. The traditional horizontal-wafer-in-tube LPCVD reactor resembles a fixed-bed reactor, and recent models are very similar to heterogeneous-dispersion models for fixed-bed reactors (21,167,213). To illustrate CVD reactor modeling, this correspondence can be exploited by first considering a simple first-order surface reaction in the LPCVD reactor and then discussing complications such as complex reaction schemes, multicomponent diffusion effects, and entrance phenomena. 

The reformer tube operation was simulated on the basis of a set of continuity-, energy- and momentum equations using one and two dimensional heterogeneous models. Intraparticle gradients in the rings were accounted for by the use of the generalized modulus concept. 

Previous one-phase continuum heat transfer models (1), (5), (10), (11), which are all based upon "large diameter tube" heat transfer data, fail to extrapolate to narrow diameter tubes. These equations systematically underpredict the overall heat transfer coefficient by 40 - 50%, on average. When allowance is made in the one-phase model for the effect of tube diameter on the apparent solid conductivity (kr>s), Eqn. (7), the mean error is reduced to 18%. However, the best predictions by far (to within 6.8% mean error) are obtained from the heterogeneous model equations. 

Recently, a novel convection-dispersion model for the study of drug absorption in the gastrointestinal tract, incorporating spatial heterogeneity, was presented [182]. The intestinal lumen is modeled as a tube (Figure 6.7), where the concentration of the drug is described by a system of convection-dispersion partial differential equations. The model considers ... 

However, these two models assume either perfect mixing conditions (well-stirred model) or no mixing at all (parallel tube model) and cannot explain several experimental observations. Therefore, other approaches such as the distributed model [268], the dispersion model [269], and the interconnected tubes model [270,271] attempt to capture the heterogeneities in flow and an intermediate level of mixing or dispersion. Despite numerous comparisons [264,265,272-... 

Chemical vapor deposition and heterogeneous catalysis share many kinetic and transport features, but CVD reactor design lags the corresponding catalytic reactor analysis both in level of sophistication and in scope. In the following we review the state of CVD reactor modelling and demonstrate how catalytic reactor design concepts may be applied to CVD processes. This is illustrated with an example where fixed bed reactor concepts are used to describe a commercial "multiple-wafers-in-tube" low pressure CVD reactor. 

In the following we present a detailed model of the commercial, multiple-wafer-in-tube reactor illustrated in Figure 2. We have selected the LPCVD as an example because of its central role in the microelectronics industry and because it nicely demonstrates the analogies to heterogeneous catalytic reactors, in particular the fixed bed reactor. 

We may first divide tubular reactors into those designed for homogeneous reactions, and therefore basically just an empty tube, and those designed for a heterogeneously catalyzed reaction, and hence to be packed with a catalyst. Both types can of course be operated adiabatically, and it was the simplest model of these that we discussed in the last chapter. If the temperature of the reactor is to be controlled this is through the wall, and the associated problems of heat transfer now arise. These include transfer at the wall and subsequent radial diffusion across the flowing reactants. In the empty tubular reactor there may be considerable variations in flow rate across the tube. For example, in the slow laminar flow the fluid... 

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