Peclet number NPe

It is often useful to write a model equation such as Equation 8-121 in terms of dimensionless variables. This introduces the Peclet number NPe = uL/De>1, which represents the ratio of characteristic dispersion time to characteristic convection time (residence time), and the Damkohler number,... 

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,... 

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, NPe, is defined by ... 

The dispersion number is 0.039 and the Peclet number (NPe) is 26. Figure 8-45 shows FExp(0) and FModel(0) versus 0. 

Peclet number NPe = uL/De, where u is a linear velocity, L is a linear dimension, and De is the dispersion coefficient. In packed beds, NPe = udP/De, where u is the interstitial velocity and dP is the particle diameter. 

If the reactor is modeled by a dispersion model, what is the Peclet number (NPe) ... 

The LSW theory dealing with Ostwald ripening [50,51] is, strictly speaking, valid for the case of immobile oil droplets when the molecular diffusion is the only mechanism of mass transfer. Under these circumstances, the contributions of molecular and convective diffusion are related by the Peclet number (Npe) ... 

Figure 7. Longitudinal dispersion (Dl) divided by the diffusion coefficient (Df) for tracers measured in column experiments as a function of the particle scale Peclet number (Npe). It is defined as the product of the average pore fluid velocity, u, and the grain diameter, d, divided by the free fluid diffusion coefficient, D/. The magnitude of the dispersion is independent of the pore fluid velocity (Vp) for very small Peclet numbers (or fluid velocities). Note that the effective diffusion coefficient in a porous media is smaller than the diffusion coefficient in a free fluid phase due to the tortuosity. The dispersion increases linearly with increasing flow velocity (increasing Peclet number). Modified from Appelo and Postma (1999).

Peclet-number. The Peclet number (Npe) is a dimensionless transport variable defined as (Bear 1972 Bowman and Willett 1991) ... 

Figure 13. Normalized stable isotope composition of a rock column infiltrated by a reactive fluid, (a) The solution assumes local equilibrium, with a Peclet number (Npe) of 100 and infinite Damkohler 1 number, (b) solution calculated for the case of a Peclet number of 100 and a Damkohler 1 number (No) of 1. The dimensionless parameters are given by normalized concentration c = (5, - >j )/(8j -5y ) distance z=xlL dimensionless time T =i( I 3jL) (after Bowman and Willet 1991—note that captions for their Figures 1 and 3 are switched).

The dimensionless grouping, Lu/D), appearing in equation (5-26) has commonly been used to represent the magnitude of dispersion effects, since it represents the ratio of the characteristic time constants for convective and dispersive effects. It is termed the axial Peclet number, Npe- Now equations (5-25) or (5-26) can be fit to experimental F t) data to determine the value of D or Np applicable to a given... 

The Peclet number NPe represents the effect of longitudinal backmixing. Backmixing can be neglected when the Peclet number is very large (Npe 1). In the extreme case of pure plug flow, the Peclet number Npe = when Npe = 0, the entire flow channel acts as an ideal mixer. 

NPe is known as Peclet number. When NPl, = it is ideal plug flow. The boundary conditions for the solution of Eq. (8.23) are... 

Estimate the Peclet number from Equation 8-141. If the value of NPe is 10 or greater, accept it. Otherwise, use a refinement of the theory, which accounts for the boundary conditions at the outlet, or formulate another model. 

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

As an alternative to using the computer program (PROG 16), Equation 8-162 can be expressed in a spreadsheet. Using the GOAL-SEEK command from the Tools menu (Appendix B) from the Excel spreadsheet menu to determine the Peclet number gives f(NPe) = 0. This function is incorporated in the spreadsheet. The computed Peclet number is NPe = 0.8638. 

NGf gas flow number [= xl/(/img)], dimensionless NPe Peclet number for axial dispersion (uGd0/DeE for liquid vtH/De for solids), dimensionless NKc Reynolds number (= aid2p/p in stirred tank) (= uGdcpJpL in bubble columns), dimensionless... 

Npe.s = surface Peclet number = urfDs Ds = surface diffusivity... 

Npe = bulk Peclet number For A >> 1 acts like rigid sphere ... 

L is the dimension parallel to bulk flow (length), and Npe is the Peclet number. According to Naiki (1979), the solution of Eq. 2.24 under the initial and boundary conditions (Eqs. 2.25-2.27) is... 

The first group of terms on the right-hand-side of Eq. 4 describes particle transport to a collector surface by Brownian diffusion. NPe is the Peclet number, a ratio of particle transport by fluid advection to transport by molecular or viscous processes. The term As is introduced to account for the effects of neighboring collectors or media grains on the fluid flow around a collector of interest. The results here assume Happel s model (Happel, 1958) for flow around a sphere in a packed bed 4S depends only on the porosity of the bed (Table 1). The derivation for diffusive transport is based on the early work of Levich (1962). 

Here the numerical constants employed are consistent with in BTU/h —°R, T is in °R, h is the solid-gas heat transfer coelScient [c.f. equation (7-83)], Kg the thermal conductivity of the solid phase, Npe the mass Peclet number, G the mass velocity, Cp the heat capacity, dp the particle diameter, and e is the bed porosity. The second term in brackets represents the radiative heat transfer contribution to the apparent thermal conductivity this is normally negligible for operation at less than 300-350 °C. The quantity / is a surface emissivity factor that normally can be estimated as 0 < / <0.1 (see Argo and Smith). Keep in mind that equation (7-153) is for gas flow in packed beds with Npe < 40. Other situations are discussed by both Beck, and Argo and Smith. Note also that, with the possible exception of /, there are no adjustable parameters in equation (7-153). Since the radiative contribution is normally quite small except at very elevated temperatures, a typical working form of equation (7-153) is... 

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