Pellet characteristic length

The Sherwood number is also known as the Nusselt number for mass transfer. Notice that the diameter of the catalyst pellet is used in the Reynolds and Sherwood numbers as the characteristic length dimension of the system. For flow... 

The characteristic length is the thickness of the equivalent slab used in the single catalyst pellet equation and it is defined as the thickness lc of the catalyst slab that gives the same external surface to volume ratio as the original pellet. For Raschig16 rings this is given by... 

A short 1 m isothermal steam reformer tube was used for this test. The reformer (3) was run under the same operating conditions as reformer (2), but with a relatively large catalyst pellet of characteristic length 0.007619 to. For Plant (3) the exit methane conversion X, the CO2 yield X, and the equilibrium values Xe and Xe for methane and carbon dioxide, respectively, are as follows. 

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

Substituting these nondimensional numbers into eqs 11-18, and after some rearrangement, the general dimensionless representation of the problem is obtained as depicted in Table 1. These equations are valid not only for spherical pellet geometry, but also for the infinite cylinder and the infinite flat plate (slab). The dimensionless numbers x, , Bim and Bib must then be calculated on the basis of the respective characteristic length, i.e. the cylinder radius or the plate thickness. Moreover, the parameter b in eqs 32 and 33 is a factor depending on the pellet geometry. It is 2 for the sphere, 1 for the cylinder, and 0 for the flat plate. 

It is worthwhile to examine how reasonably well a single characteristic length parameter describes reaction/diffusion in a finite cylinder, a very common catalyst pellet configuration. The pellet shown has a cylinder length 2xp and radius Rp. 

In gas-solid reactors when solid particles are held stationary (so-called fixed bed reactor), gas flows through a porous medium comprising macropores existing between pellets or packed solid particles and micropores within the catalyst pellets (or other porous solids). Issues such as isotropy of the porous medium, initial distribution of gases, characteristics of solid particles, ratio of characteristic length scale of solid particles and that of the reactor and so on, influence the flow within fixed bed reactors. Support screens are often used to cover the bed of solid particles to avoid fluidization and carry-over of bed particles. These reactors are extensively used in process industries. Some examples and illustrative flow simulations are discussed in Chapter 13. 

The starting point, as usual, is to nondimensionalize the problem. In the present case, this is easily done. We assume that the pellet radius R provides an appropriate characteristic length scale, tc = R, and thatthe concentration can be scaled with the surface concentration... 

A short isothermal steam reformer of one metre in length, having the same operating conditions as steam reformer II and having relatively large catalyst pellets of characteristic lengths equal to... 

What is the critical value of the intrapeUet Damkohler number for onedimensional diffusion and zeroth-order irreversible chemical reaction in catalytic pellets with spherical symmetry The radius of the sphere is used as the characteristic length in flie definition of the Damkohler number. 

The characteristic length L required to make the important spatial coordinate dimensionless is the pellet radius R, as mentioned previously in this book. Hence,... 

Step 12. Calculate the intrapellet Damkohler number, where the characteristic length is the radius of the catalytic pellet. 

Step 13. Use the analytical expression for first-order kinetics in spherical pellets to calculate the Effectiveness factor when the characteristic length is the pellet radius. 

The appropriate diffusion coefficient of reactant A2 must be modified by intrapellet porosity and tortuosity factors which summarize the internal pore structure of each catalytic pellet. For spherical catalysts, the peUet radius R is taken as the characteristic length L. 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

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