Peclet number Dispersion parameter

Parameter for molecular diffusion model In a moving zone, equivalent to the reciprocal of Peclet number, dispersion number Reynolds number, Re Prandtle number, Pr Schmidt number Sc... 

The value of n is the only parameter in this equation. Several procedures can be used to find its value when the RTD is known experiment or calculation from the variance, as in /i = 1/C (t ) = 1/ t C t), or from a suitable loglog plot or the peak of the curve as explained for the CSTR battery model. The Peclet number for dispersion is also related to n, and may be obtainable from correlations of operating variables. 

Equations 8-148 and 8-149 give the fraction unreacted C /C o for a first order reaction in a closed axial dispersion system. The solution contains the two dimensionless parameters, Np and kf. The Peclet number controls the level of mixing in the system. If Np —> 0 (either small u or large [), diffusion becomes so important that the system acts as a perfect mixer. Therefore,... 

The dispersed plug flow model has been successfully applied to describe the flow characteristics in the Kenics mixer. The complex flow behavior in the mixer is characterized by the one-parameter. The Peclet number, Np, is defined by ... 

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. 

The form of the solution of the dispersion equation (11.61) depends on the sign of the determinant D = q + Pl, i.e., on the values of the characteristic parameters g and P. The latter are determined by the physical properties of the liquid and its vapor, as well as the values of the Peclet number. This allows us to use g and P as some general characteristics of the problem considered here. 

The parameter D is known as the axial dispersion coefficient, and the dimensionless number, Pe = uL/D, is the axial Peclet number. It is different than the Peclet number used in Section 9.1. Also, recall that the tube diameter is denoted by df. At high Reynolds numbers, D depends solely on fluctuating velocities in the axial direction. These fluctuating axial velocities cause mixing by a random process that is conceptually similar to molecular diffusion, except that the fluid elements being mixed are much larger than molecules. The same value for D is used for each component in a multicomponent system. 

Simulation studies are also conducted for a dispersed PFR and a recycle reactor at 260 °C, 500 psig and feed with DCPD=0.32 mol/min, CPD=0.96mol/min and ethylene=3.2mol/min. Peclet number (Pe) or the recycle ratio is selected as a variable parameter for the dispersed PFR or for the recycle reactor, respectively. Conversion approaches to that of PFR over Pe=50 as can be seen in Fig.4. It is also worth mentioning that the reactor performance is improved with recycle if the residence time is low. 

The aforementioned investigators (10-12) have derived equations relating the measured mean residence times and variances to the Peclet number or dispersion parameter for the test section. For the case where the conditions at both monitoring probes correspond to a doubly infinite pipe, it can be shown that... 

The Peclet number for axial dispersion is defined in a manner similar to the radial parameter... 

A significant merit of the dispersion model is some experimental correlations for the Peclet number. There are no such direct correlations for the parameters of the Gamma or Gaussian or other similar models. 

The only two parameters appearing in eqn. (65) are the dispersion number, DjiiL, or inverse Peclet number, and the Damkohler number, or dimensionless rate group, t/jCa," - Solutions to eqn. (65) are therefore functions only of these two groups. If term (4) in eqn. (65) is absent, then... 

The main parameter in this model characterizing the quality of the flow is the axial dispersion coefficient. The term axial is used to distinguish mixing in the direction of flow from mixing in the radial direction. Then, based on this parameter, the particle Peclet number is introduced ... 

Remember that from the nondimensional version of the advection-dispersion equation, Eq. 25-18, the Peclet Number Pe was identified as the only parameter that determines the shape of the concentration distribution in the aquifer. By introducing relative coordinates for space ( ,) and time (9) as defined in Eq. 25-16, Eq. 25-20 takes the form ... 

Although it also is subject to the limitations of a single characterizing parameter which is not well correlated, the Peclet number, the dispersion model predicts conversions or residence times unambiguously. For a reaction with rate equation rc = fcC , this model is represented by the differential equation... 

The assessment of the role of kf during protein adsorption in a fluidized bed may be performed with the help of a dimensionless transport number. Slater used the correlations provided by Rodrigues to simulate film transport limited adsorption of small ions to fluidized resins [54], In this study dimensionless groups were used to describe the influence of the system parameters particle side transport, liquid dispersion, and fluid side transport. Dispersion was accounted for by the column Peclet number analogous to Bo as introduced above and mass transport from the bulk solution to the resin was summarized in a fluid side transport number NL. 

The dimensionless group Del/uL is known as the dispersion number and is the parameter that measures the extent of axial dispersion. The degree to which axial dispersion influences the performance of a chemical reactor is determined by the value of the Peclet number (NPe). A high value of NPe corresponds to a slightly dispersed reactor. That is,... 

Here we have denoted y conversion, 0 Frank-Kameneckii dimensionless temperature, Da Damkohler number, Pe Peclet number for axial mass dispersion, Pe Peclet number for Sxial heat dispersion, Y dimensionless activation energy, B dimensionless adiabatic temperature rise, 3 dimensionless cooling parameter, 6 temperature of the cooling medium, A mass capacity, AT heat capacity. 

The parameter obtained after identification of the system as plug flow with axial dispersion, is the Peclet number defined from the packing height and the real fluid flow velocity ... 

Here A is the film thickness. By comparing the variance of the response obtained by this model and the one obtained for an axial dispersion model of the same system, Michell and Furzer derived the following approximate relationship between Peclet number and the parameter q ... 

Three-parameter PDE model (Van Swaaij et aL106) This model is largely used to correlate the RTD curves from a trickle-bed reactor. The model is based on the same concept as the crossflow or modified mixing-cell model, except that axial dispersion in the mobile phase is also considered. The model, therefore, contains three arbitrary parameters, two of which are the same as those used in the cross-flow model and the third one is the axial dispersion coefficient (or the Peclet number in dimensionless form) in the mobile phase (see Fig. 3-11). 

The experimental studies have shown that, in gas-liquid trickle-bed reactors, significant axial mixing occurs in both gas and liquid phases. When the RTD data are correlated by the single-parameter axial dispersion model, the axial dispersion coefficient (or Peclet number) for the gas phase is dependent upon both the liquid and gas flow rates and the size and nature of the packings. The axial dispersion coefficient for the liquid phase is dependent upon the liquid flow rate, liquid properties, and the nature and size of the packings, but it is essentially independent of the gas flow rate. 

The liquid flowing inside a MWPB can be described with a one-parameter dispersion flow model. As we show in Section 3.3, the axial mixing coefficient or, more correctly, the axial dispersion coefficient is the specific parameter for this model. Relation (3.112) contains the link between the variance of the residence time of liquid elements and the Peclet number. We can rewrite this relation so as to particularize it to the case of a MWPB. Here, we have the possibility to compute the variance of the residence time of the liquid through the stochastic model for the liquid flow developed previously in order to obtain the value of the axial dispersion coefficient ... 

Megascopic Dispersivity. The megascopic scale is the full-aquifer dispersivity whose value determines the volumetric sweep in numerical simulation blocks. Figure 3 shows the behavior of (expressed as inverse Peclet number) as a function of time for miscible displacements in a two-dimensional stochastic permeability field. The parameter V is the Dykstra-Parsons coefficient, a dimensionless measure of the spread of the permeability distribution to which the flow field was conditioned. = 0 corresponds to a... 

Though the gas phase dispersion coefficients are large and often larger than those of the liquid phase the influence of the gas phase dispersion on conversion should not be overestimated. One has to consider that it is not the dispersion coefficient itself but the Peclet number which is the governing parameter in the model equations. The Peclet number has to be formulated under consideration of the fractional gas holdup... 

There are four unknown parameters in the theoretical impulse response for porous particles, h(t) the pellet diffusion time, tdif (which contains the effective diffusion coefficient of the pair T-C, Dtc, td.fs R p/D.f( , R is the radius of the pellet equivalent sphere), the mean residence time of the carrier-gas in the interparticle space, tc (tc = v/L with the carrier gas linear interstitial velocity, v, and column length, L), Peclet number, Pe (Pe = L.v/E, with E the effective axial dispersion coefficient) and the adsorption parameter, 5q (see below). Because matching with four unknown parameters would give highly correlated parameters, it is better to determine some parameters independently,... 

Dimensional analysis of the coupled kinetic-transport equations shows that a Thiele modulus (4> ) and a Peclet number (Peo) completely characterize diffusion and convection effects, respectively, on reactive processes of a-olefins [Eqs. (8)-(14)]. The Thiele modulus [Eq. (15)] contains a term ( // ) that depends only on the properties of the diffusing molecule and a term ( -) that includes all relevant structural catalyst parameters. The first term introduces carbon number effects on selectivity, whereas the second introduces the effects of pellet size and pore structure and of metal dispersion and site density. The Peclet number accounts for the effects of bed residence time effects on secondary reactions of a-olefins and relates it to the corresponding contribution of pore residence time. 

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