Intraparticle peclet number

Model parameters an the Thiele modulus and the intraparticle Peclet number X=Vot/De relating the intrapordcle convective flow and the diffusive flow. 

Fig. 3.4-6 Enhancement factor l//(A) = DJD as a function of the intraparticle Peclet number A.

Figure 2 Effect of the intraparticle Peclet number on concentration profiles, =0, (left) X =10, (right).

In the above equations c is the outlet tracer concentration in the fluid phase, E is the particle porosity, e is the reactor porosity, 0=t/T (with T Sefined as the ratio between the reactor volume and the flowrate) and X=v S./D is the intraparticle Peclet number (v is the intraparticle convective velocity). °... 

One should be careful when using a measured value of the effective diffusivity by a dynamic chromatographic method for reactor design.As said before we get at a given Reynolds number an apparent effective diffusivity D (as a result of a model which does not include convective transport inside the pellet).How will the reactor design be affected by using this value for 5 instead of that of the true effective diffusivity and the intraparticle Peclet number for convection In order to answer this question let us define a quantity... 

Let us consider a situation in which the intraparticle Peclet number X=10 and the Thiele modulus is (j)=10.For a first order irreversible reaction we get E around 0.5.This means that in order to get the desired product specification the reactor should have a length two times longer than that calculated on the basis of the apparent diffusivity D. ... 

In the above equations x =z/2 (we reduced the space coordinate for the pellet by its thickness just because it is convenient for the numerical procedure developed below), T =T/Tg,f=c/c, (p = H/kg(T )/D, 3 is the Prater thermicity factor evaluated at the parlicle surface conditions,X =v /D is the mass intraparticle Peclet number and X =v /(X /p Cp ) is the thermal intraparticle Peclet number. 

A breakthrough curve with the nonretained compound was carried out to estimate the axial dispersion in the SMB column. A Peclet number of Pe = 000 was found by comparing experimental and simulated results from a model which includes axial dispersion in the interparticle fluid phase, accumulation in both interparticle and intraparticle fluid phases, and assuming that the average pore concentration is equal to the bulk fluid concentration this assumption is justified by the fact that the ratio of time constant for pore diffusion and space time in the column is of the order of 10. ... 

The gas flow velocity through the emulsion phase is close to the minimum fluidization velocity When the particles are spherical and have diameters of several tens of microns, this flow condition gives a quite small particle Peclet number, dpUmf/Dc. For example, the Peclet number is estimated as 0.1-0.01 when 122-/Lim-diam. cracking catalyst is fluidized by gas, with Umt = 0.73 cm/sec and Dq = 0.09 cmVsec and it is estimated as 0.001-0.01 for 58-/u.m-diam. particles, with Umt = 0.16 cm/sec. The mechanism of mass transfer between fluid and particles in packed beds is controlled by molecular diffusion under such low Peclet numbers, and the particle Sherwood number kfdp/Dc, is well over 10 (M24). Consequently with intraparticle diffusion shown to be negligible (M21), instantaneous equilibrium is established to be a good approximation [see Eq. (6-24)]. 

Fig.5 illustrates the PO selectivity (S) as a function of mass Peclet number. The selectivity was increased with increasing the total reaction gas flow rate (F) passing through the membrane pores, such as S= 18-41% according to F= 70-130 cmVmin at 483K, indicating an effective role of the convection flow in the membrane pores for the enhancement of S compared to intraparticle diffusion in spherical catalyst solid supports used for conventional packed bed reactors. This result experimentally proves the validity of our previous work based on the mathematical analysis [7]. 

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