Model Miyauchi

FIGURE CS5.1 Schematics of several fluidized-bed reactor models (a) Davidson model, (b) Kunii-Levenspiel model, (c) Miyauchi model, (d), (e) Fryer-Potter and Jayaraman-Kulkami-Doraiswamy models. 

FIGURE CSS.3 Parameters of the Miyauchi model. (From Doraiswarmy, L. K., 1991.)... 

Miyauchi and Vermeulen (M7, M8) have presented a mathematical analysis of the effect upon equipment performance of axial mixing in two-phase continuous flow operations, such as absorption and extraction. Their solutions are based, in one case, upon a simplified diffusion model that assumes a mean axial dispersion coefficient and a mean flow velocity for... 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

Nagata, et al. (Nl, N2), Kawamura et al. (K4), and Yagi and Miyauchi (Y2) have studied the characteristics of various impeller agitated multistaged vessels. Such vessels were assumed to be a succession of plug-flow and backmix units, whose relative sizes were a function of the impeller speed. The parameter of the model, the fraction of total volume in a plug-flow, could also be related to a dispersion coefficient. Verification of the model was then obtained with kinetic experiments. 

Groothuis and Zuiderweg (G3), and by Kramers and co-workers (K2), while qualitative experiments were carried out by Matsuzawa and Miyauchi (M3). All these methods use the homogeneous interaction model to interpret the results obtained, while generally care is taken to prevent wetting of the wall by the dispersed phase in order to avoid dead corners. 

Kasai T, Miyauchi K, Yokoyama T, Aihara K, Daida H. Efficacy of peroxisome proliferative activated receptor (PPAR)-alpha ligands, fenofibrate, on intimal hyperplasia and constrictive remodeling after coronary angioplasty in porcine models. Atherosclerosis 2005 188 274-280. 

Employing the probabilistic model developed by Tsutsui and Miyauchi (14), the following expression is derived for the local frequency distribution of bubble length (17). 

A gas bubble column is taken here as a model equipment undergoing longitudinal dispersion of the continuous phase. The theory obtained is equally applicable to a fluidized catalyst bed of good fluidity exhibiting similar flow properties. The following procedure is from Miyauchi (M27). 

For recirculation flow the Taylor dispersion mechanism was introduced by Shyu and Miyauchi (S13). Equation (4-12) is a revised result for it. For this flow regime, Ohki and Inoue (02) developed an expansion model with parameters adjusted to the data available, and also introduced the Taylor dispersion mechanism for the low-gas-velocity region of uniform bubble flow. 

The influence of longitudinal dispersion on the extent of a first-order catalytic reaction has been studied by Kobayashi and Arai (K14), Furusaki (F13), van Swaay and Zuiderweg (V8), and others. They use the one-dimensional two-phase diffusion model, and show that longitudinal dispersion of the emulsion has little effect when the reaction rate is low. Based on the circulation flow model (Fig. 2) Miyauchi and Morooka (M29) have shown that the mechanism of longitudinal dispersion in a fluidized catalyst bed is a kind of Taylor dispersion (G6, T9). The influence of the emulsion-phase recirculation on the extent of reaction disappears when the term tp defined by Eq. (7-18) (see Section VII) is greater than about 10. For large-diameter beds, where p does not satisfy this restriction, their general treatment includes the contribution of Taylor dispersion for both the reactant gas and the emulsion (M29). 

The main differences between the models lies in whether or not some fraction of the catalyst is in direct contact with the bubble gas, and in the extent of axial mixing in each phase. Properties of various models have been discussed extensively by Gilliland and Knudsen (G7) in relation to the extent of reaction in experimental fluidized bed reactors, considering that allowance for direct contact between bubble gas and a certain amount of catalyst in it is the sole way to account for the contact efficiency. Unless a fraction of the catalyst particles is assumed to be entrained in the bubble gas, the bubble size calculated to fit the reaction data is found to decrease with increasing catalyst activity at otherwise identical fluidization conditions, in which the bubble size should remain constant. Essentially the same decrease in bubble size was observed by Miyauchi and Morooka (M29) in their analysis of the data by Lewis et al. (LI 2), and by Furusaki (F14) in his fluidized bed data for the Deacon reaction. 

Thus, the general procedure described for the bubbling bed including the dilute bed (Kunii and Levenspiel, 1991) or the Miyauchi-Marooka model described in Case Stndy 11.5 can be used. Then, the porosity distribution data will be different, hi particnlar, the freeboard porosity will be higher. Strictly, new correlations for k, and are also reqnired, bnt available correlations for the bubbling bed can be used as a hrst approximation. 

As was pointed out earlier (Figure CSS.lc), it is often desirable to account for conversion in the end zones of the fluid bed. The model of Miyauchi (1974) accounts for conversion in the region... 

Iwai K, Maeda H, Konno T, Matsumura Y, Yamashita R, Yamasaki K, Hirayama S, Miyauchi Y. Tumor targeting by arterial administration of lipids rabbit model with VX2 carcinoma in the liver. Anticancer Res 1987 7 321-327. 

T. Furusawa, H. Nashimura, and T. Miyauchi [J. Chem. Eng. Jpn., 2,95-100 (1969)] studied stability phenomena in a single stirred-tank reactor using hydrolysis of propylene oxide as a model reaction ... 

Viscosity and elasticity are the general rheologic characteristics influencing the maintenance of the anterior chamber. Theoretically, the higher the viscosity, the better the maintenance of chamber depth at rest i.e., at zero shear rate. Based on an in-vitro study performed by Miyauchi and Iwata (1986) involving a model with different viscosity and elasticity, it was shown that the ability to maintain space in the anterior chamber is far more dependent upon the elasticity than the viscosity. 

Michel M, Dompmartin A, Moreau A, et al. (1994) Contact photosensitivity to nonoxynol used in antiseptic preparations. Photodermatol Photoimmunol Photomed 10 198-201 Mitchell JC (1965) Allergy to lichens. Arch Dermatol 92 142-146 Mitchell JC (1972) Contact dermatitis from proflavine dihydrochloride. Arch Dermatol 106 294 Miyauchi H, Horio T (1992) A new animal model for contact dermatitis the hairless guinea pig. J Dermatol 19 140-145 Moscato G, Omodeo P, et al. (1997) Occupational asthma and rhinitis caused by i,2-benzisothiazolin-3-one in a chemical worker. Occup Med (Oxf) 47 249-251 Myatt AE, Beck MH (1985) Contact sensitivity to para-chlorometaxylenol (PCMX). Clin Exp Dermatol 10 491 Nethercott JR, Lawrence MJ (1984) Airborne contact urticaria due to sodium benzoate in a pharmaceutical manufacturing plant. J Occup Med 26 734-736... 

Dilute bed region In all the models developed above, it was assumed that reaction is restricted to the bubbling bed but the data of Lewis et al. (1962) and Ean et al. (1962) show that an axial distribution of bed density exists. Eurther, it seans most likely that bubbles carry solid particles along with than through the central region of the bed and enter the dilute phase by a process of bursting on the emulsion surface (Miyauchi, 1974 ... 

Miyauchi and Furusaki, 1974). A bubble-free emulsion then flows down the bed peripherally. This situation clearly leads to some reaction in the dilute phase. An elegant model that accounts for reaction in both the bubbling and dilute regions of the bed has been proposed by Miyauchi (1974), and another by Kunii and Levenspiel (1991) (more in line with their fine particle model). 

Dispersion models for two-phase systems were proposed by Miyauchi and Vermeulen [26,27] for the case of continuous liquid-liquid contactors. For such systems, Hartland and Mecklenburgh [28] systematically developed and analyzed possible analytical solutions for a variety of limiting cases. If the mathematical treatment used for extractors is applied to BCR, the closed solutions are more complicated [29, 30] and only numerical simulations can be recommended to detect the influence of a certain parameter [30, 31]. 

Miyauchi, T. and T. Vermeulen. Diffusion and Back-Flow Models for Two-Phase Axial Dispersion. Ind. Eng. Chem. Fundam. 2 (1963) 304-310. 

Pac C, Diama M, Yasuda M, Miyauchi Y, Sakurai H (1981) Ru(bpy)3 Lmediated photoreduction of olefins with l-benzyl-l,4-dihydronicotinamide a mechanistic probe for electron-transfer reactions of NAD(P)H-model compounds. J Am Chem Soc 103 6495-6497... 

To determinate the mass transfer coefficients in a given model the experimental results have to be calculated using the same model. The method [74, 77] proper for packed bed columns for dispersion model is based on flie analytical solution of Sleicher [78], and Miyauchi and Vermeulen [79]. This solution gives the possibility to calculate the concentration profile in the packing, knowing the Bodenstein numbers and the mass transfer coefficient. Using an iteration procedure, it is possible, at given initial and end concentrations, to obtain also the respective mass transfer coefficient. The... 

Gableman, A., and Hwang, S.-T. (1999). Hollow fiber membrane contactors. J. Membr. Sci. 159, 61. Gableman, A., Hwang, S.-T., and Krantz, W. B. (2005). Dense gas extraction using a hoUow fiber membrane contactor Experimental results versus model predictions. J. Membr. Sci. 257, 11. Hestekin, J. A., Bachas, L. G., and Bhattacharyya, D. (2001). Poly(amino acid) functionalized cellulosic membranes Metal sorption mechanisms and results. Ind. Eng. Chem. Res. 40, 2668. Imai, M., Furusaki, S., and Miyauchi, T. (1982). Separation of volatile materials by gas membranes. Ind. Eng. Chem. Process Des. Dev. 21, 421. 

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