Residence time distribution Peclet number

FIG. 23-10 Residence time distributions of pilot and commercial reactors. <3 = variance of the residence time distribution, n = number of stirred tanks with the same variance, Pe = Peclet number. 

The dispersion coefficient is orders of magnitude larger than the molecular diffusion coefficient. Some rough correlations of the Peclet number are proposed by Wen (in Petho and Noble, eds.. Residence Time Distribution Theory in Chemical Tngineeiing, Verlag Chemie, 1982), including some for flmdized beds. Those for axial dispersion are ... 

Axial Dispersion and the Peclet Number Peclet numbers are measures or deviation from phig flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are fA to Ve, those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. /., 4, 53 [1972]) is... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

When a number of competing reactions are involved in a process, and/or when the desired product is obtained at an intermediate stage of a reaction, it is important to keep the residence-time distribution in a reactor as narrow as possible. Usually, a broadening of the residence-time distribution results in a decrease in selectivity for the desired product. Hence, in addition to the pressure drop, the width of the residence-time distribution is an important figure characterizing the performance of a reactor. In order to estimate the axial dispersion in the fixed-bed reactor, the model of Doraiswamy and Sharma was used [117]. This model proposes a relationship between the dispersive Peclet number ... 

Rough correlations of Peclet numbers for dispersion are given by Wen (in Petho Noble, Residence Time Distribution in Chemical Engineering, 1982)... 

Figure 17.1. Residence time distributions of some commercial and pilot fixed bed reactors. The variance, the equivalent number of CSTR stages, and the Peclet number are given for each.

Using the experimental residence time distribution data of Levenspiel and Smith in Example 8-2, determine the number of ideal tanks N, the variance, dispersion number, and Peclet number. 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

Figure 34 compares the residence time distribution in the influence zone of a single set of ring internals at location 3, which is 0.55 m downstream of tracer injection, with and without the ring set. The decrease of solids backmixing is shown by an increase of the Peclet number from 1.06 to 2.46, and from 1.97 to 3.61, when the ring set is used, for gas velocities of 1.75 and 2.62 m/s, respectively. 

The residence-time distribution in the liquid phase of a cocurrent-upflow fixed-bed column was measured at two different flow rates. The column diameter was 5.1 cm and the packing diameter was 0.38 cm. The bed void fraction was 0.354 and the mass flow rate was 50.4 g s l. The RTD data at two axial positions (which were 91 cm apart in Run 1 and 152 cm apart in Run 2) are summarized in Table 3-2. Using the method of moments, estimate the mean residence time and the Peclet number for these two runs. If one assumes that the backmixing characteristics are independent of the distance between two measuring points, what is the effect of gas flow rate on the mean residence time of liquid and the Peclet number Hovv does the measured and the predicted RTD at the downstream positions compare in both cases ... 

Schiesser and Lapidus82 showed that the jiorosity of the packings could significantly affect the residence-time distribution and, hence, the axial dispersion coefficient. This indicates the effect of static holdup on the axial dispersion. Van Swaaij et al.103 showed that the liquid-phase axial dispersion depends upon the ratio of dynamic to static liquid holdup (i.e., /ijl/ILl) as long as this ratio is approximately below 8. If > 8, the Peclet number becomes essentially... 

Table IV presents some data on liquid residence time distributions measured under conditions of hydrocracking in trickle flow. It can be seen that bed dilution with fine inert particles results in a considerable improvement in the plug-flow character of the reactor, which supports the idea that the dispersion is largely determined by the packing of fine particles. Since in the range of Re numbers of interest the Bodenstein number is approximately a constant (see Figure 4), the Peclet numbers for beds of equal length should be inversely proportional to the particle diameter. Dilution of the 1.5 mm particles with 0.2 mm particles should raise Pe by a factor of about 7, which is approximately in line with the data in Table IV.

As the Figure 8.12 reveals, the flow pattern deviates from plug flow. The residence time distribution function E(l) is calculated from the experimentally recorded responses, after which the F(t) function was obtained from integration of E(t). The experimental functions are compared to the theoretical ones. The expressions of E(t) and F(t) obtained from the analytical solution of the dynamic, non-reactive axial dispersion model with closed Danckwerts boundary conditions were used in comparison. A comparison of the results shown in Figure 8.12 suggests that a reasonable value for the Peclet number is Pe=3. 

During this residence time distribution testing, the Photo-CREC-Water I was operated in the single pass mode with no water recycling and samples taken every 10 seconds. The Peclet number assessed with this method was 30 and the number of ideal CSTR tanks was estimated as 15. Since the number of baskets in Photo-CREC-Water I is 16, this demonstrates that each basket can be viewed as a close equivalent to an ideal single mixing stage. 

If there is only one chemical reaction on the internal catalytic surface, then vai = — 1 and subscript j is not required for all quantities that are specific to the yth chemical reaction. When the mass transfer Peclet number which accounts for interpellet axial dispersion in packed beds is large, residence-time distribution effects are insignificant and axial diffusion can be neglected in the plug-flow mass balance given by equation (22-11). Under these conditions, reactor performance can be predicted from a simplified one-dimensional model. The differential design equation is... 

Convergence is obtained when the appropriate guess for d p./di at the reactor inlet predicts the correct Danckwerts condition in the exit stream, within acceptable tolerance. To determine the range of mass transfer Peclet numbers where residence-time distribution effects via interpellet axial dispersion are important, it is necessary to compare plug-flow tubular reactor simulations with and without axial dispersion. The solution to the non-ideal problem, described by equation (22-61) and the definition of Axial Grad, at the reactor outlet is I/a( = 1, RTD). The performance of the ideal plug-flow tubular reactor without interpellet axial dispersion is described by... 

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