Lu and Wang ( 3 ) . This has the advantage that in the absence of quaternary data, the corresponding &jkl may be set to zero to obtain a better approximation than by setting (Eijkl -C i j k l ) to zero.excess Gibbs free energy i, i, k, 1, m, n, p = index representing components n = moles P =pressure R = gas constant = binary two-and three-suffix coefficient T = absolute temperature x = mole fraction y = activity coefficient In a recent article Narsimhan (18) presented a generalized expression for the minimum fluidization velocity by extending the correlation proposed by Leva, Shirai, and Wen (14) into intermediate and turbulent flow reions. Based on a similar approach by employing the &ed-bed pressure drop equation of Ergun (7), an expression for the minimum fluidization velocity quite different from that of Narsimhan has been obtained ( 2 3 ) . It is the purpose of this communication to compare these two correlations and to examine the validity and applicability of each. The generalized expression given by Narsimhan consists of three equations [Equations ( 6 ) , (9), and ( 11) in his communication (18) 1. The correlation obtained by Wen and Yu ( 2 3 ) can be represented by ( N R~)~~ = d ( 3 3 . 7 ) ' + 0.0408 N G~ -33.7 (1)For nonspherical particles, the particle diameter dp is defined as the equivalent diameter of a spherical particle with the same volume. As an approximation, the particle diameter may be calculated from the geometric mean of the two consecutive sieve openings without introducing serious errors ( 2 6 ) .The major differences between the two correlations are the minimum fluidization voidage emf and the shape factor 4%.1. Narsimhan considered that for spherical emf has the value of 0.35 and is independent of e particle diameter, provided that the wall effect can be neglected. From the literature data (16, 20, 2 4 ) , as well as trrticles from the experimental data of the present investigation ( 2 3 ) , emf for spherical particles can be shown to vary from 0.36 to 0.46. Different average values of emf have V Van Heerden, et a l . ( Z Z ) 0 Fancher and Lewis (9) o.ol -Narsimhan's correlation I 0.001 aooz 0.004 aoi aoz 03 dp (in.) 986 emf Fig. 1. Correlation of voidage shape factor function -.(1 -emf)2
The successful design of a reactor depends greatly on a knowledge of reliable rate data. It is important to make a careful study of interactions and to isolate physical effects from purely chemical processes Noncatalytic heterogeneous reactions include solidfluid, liquid-liquid, and liquid-gas systems. Here, we
Bubble size is one of the most important parameters in the design and simulation of a fluidized-bed reactor.A correlation of the bubble size and growth in fluidized beds of various diameters is developed. A maximum bubble diameter determined from the bubble coalescence is incorporated in the correlation to relate the effect of the bed diameter on the bubble size.Experimental data of bubble size reported are used to develop and test the validity of the correlation. The bubble diameters calculated using this correlation show good agreement with the observed bubble diameters.where At is the cross-sectional area of the bed, uo is the
Longitudinal liquid mixing in fluidized and fixed beds was studied using sinusoidal and pulse response techniques. The tracer used was light emissive fluorescein dye. A systematical study of liquid phase dispersion by varying particle size, fluid velocity, fraction voids, and particle density was conducted. A generalized correlation applicable to both fixed bed and fluidized bed was obtained. The application of the correlation in predicting the effect of the dispersion on reactor performance was discussed.The study of fluid mixing in a continuous flow system is of considerable importance for the design of chemical reactors. Neglecting the fluid dispersion may result in an overestimation of the conversion, the driving force, and the volume efficiency of the system. In order to estimate the dispersion coefficient in a continuous flow reactor, the dynamic response method has been generally applied. This method involves injecting a tracer into the system according to a certain function and matching the response curve with that derived from the mathematicaI model. The parameters characterizing the mixing or dispersion of the fluid in the system are then evaluated from the best fitted mathematical curve.In this work, experiments have been performed by using sinusoidal and pulse inputs of fluorescein tracer to fixed beds and fluidized beds. A systematic study of liquid phase dispersion has been conducted, particularly, the effects of particle size, fluid velocity, fraction voids, and particle density have been considered. Based on the knowledge of the ef€ect of individual factors on the dispersion coefficient and the correlations suggested by the previous investigators, a generalized correlation valid for both fixed beds and fluidized beds has been obtained. A large number of fixed bed data and fluidized bed data from literature were also incorporated into this correlation in order to confirm its validity. This work is limited to the study of liquid phase mixing in particulate systems consisting of uniform size particles. Table 1 shows a summary of the previous investigations on the longitudinal dispersion of liquid in fixed beds. Although there has been a large number of investigations on the fluid dispersion in fixed beds, only a few studies are available on the loiigitudinal dispersion of liquid in fluidized beds as shown in Table 2. The information obtained from the previous investigations on liquid mixing in fixed and fluidized beds have been fragmentary. So far no correlation that ties together the longitudinal dispersion in fixed beds with that in fluidized beds has been availabIe. The usual method of correlation of the Iongitudinal dispersion is by plotting either the Peclet number vs. the Reynolds number, or the dimensionless dispersion group, Exp/p, vs. the Reynolds, or by relating some dimensionless groups involving voidage, e. For the fixed bed, plots of the Peclet number vs. the Reynolds number has been commonly employed (10, 15, 20, 36, 37, 41, 49). However, disagreements in the magnitude of the Peclet num...
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