Heat and Mass Transfer in Catalytic Beds

Flow in empty tubes has a relatively narrow band of velocities—or Reynolds numbers from 2000 to 10000—wherein the character changes from laminar to turbulent. In packed beds, even the laminar flow does not mean that motion is linear or parallel to the surface. Due to the many turns between particles, stable eddies develop and therefore the difference between laminar and turbulent flow is not as pronounced as in empty tubes. 

At high velocities where turbulence dominates, the main body of flowing fluid is well mixed in the direction normal to the flow, minor differences in temperature and concentration can be neglected, and the film concept can be applied. This describes the flow as if all gradients for temperature and concentration are in a narrow film along the interface with the solid (Nernst 1904), and inside the film conduction and diffusion are the transfer mechanisms. This film concept greatly simplifies the engineering calculation of heat and mass transfer. 

The basic correlation for packed tubes is derived from those of empty tubes by properly reinterpreting some critical variables. The most important change is in the characteristic distance that is changed from the tube diameter to the particle diameter. Other corrections are also used. The transfer correlations are based on dimensional analysis, expressed as either the Nusselt-type (1930) or the Colbum-type (1933) equations. For empty tubes at high Re numbers  

For packed beds Gamson et al (1943) developed Colburn-type correlation for heat and mass from many experimental measurements for Rep 350 as  

From these unique functions of RCp the numerical value of jh and jd can be calculated. From the definitions of the Colburn factors, the transfer coefficients hg and kg can be evaluated since all other variables are physical properties, independent of flow. For correctness, the physical properties 

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