Particle-Fluid Mass Transfer in Fixed and Fluidized Beds P. N. Dwivedi and S.
N. Upadhyay'
Department of Chemical Engineering, lnstitute of Technology, Banaras Hindu University, Varanasi-22 1005, India
Previous experimental data on mass transfer between particles and fluid in fixed and fluidized beds are reanalyzed and correlating equations are developed for the various situations.
Introduction Particle-fluid heat or mass transfer in fixed and fluidized beds is an important item of the basic information required for the design and development of various heat and mass transfer operations and chemical reactors involving a system of particles and a fluid. It has been widely investigated during the past three decades and the volume of the literature on the subject is enormous (Upadhyay and Tripathi, 1975a). Experimental measurements have been made with gases and liquids. The gas-phase mass transfer rates have been measured for the absorption of liquid vapors from the gaseous streams and evaporation of liquids from the surface of porous particles and sublimation of suitable solids into gaseous streams. In the case of liquids, most of the data have been obtained by measuring the rate of dissolution of suitable solids into a liquid stream. In a few cases the data have been obtained by measuring the rate of adsorption, ion-exchange, or crystallization or by measuring the diffusion current using a suitable electrochemical system. In most of the previous studies, the experimental results are expressed in terms of the dimensionless groups; however, in some cases the mass transfer coefficient is directly related to operating variables such as flow velocity, particle diameter, etc. The usual dimensionless groups used are the ChiltonColburn mass transfer factor (Chilton and Colburn, 1934), Sherwood number, Schmidt number, and a particle Reynolds number. In some cases, other dimensionless groups such as the particle to column diameter ratio or particle diameter to , also included bed height ratio, Archimedes number, N A ~are to improve the correlations. Further, the various conventional dimensionless terms are defined differently by research workers. The common definition for the mass transfer factor is one which includes the Schmidt group with an exponent of 2/3; however, in some cases it has been redefined with 0.58 as the exponent. The characteristic length parameter in the Reynolds and Sherwood numbers is usually the equivalent particle diameter or the hydraulic diameter for a particulate system. Occasionally it has been modified by incorporating a term known as shape factor. Similarly, the mass flow rate used is either the superficial flow rate, G, based on the empty column cross section, or the effective mass flow rate ( G I € ) through the bed. Based on these, the following three forms of particle Reynolds numbers have been used.
N R =~DpGIF
(1)
N R ~=, DpGIpt
(2)
N R ~ ,=, DpGIg (1 - t )
(3)
The first particle Reynolds number, N R ~has , been found to be successful in correlating the data for various types of packed and fluidized beds. The second Reynolds number, N R ~has ~ been , used for correlating packed bed data and was introduced by McCune and Wilhelm (1949) for correlating the liquid-phase data. The third Reynolds number, N R ~ ,has , , been
found successful in correlating the fluidized bed data and was used for the first time by Ishino and Otake (1951) for correlating liquid fluidized bed data. In one or two cases (Sengupta and Thodos, 1962a; Taecker and Hougen, 1949) the particle where A p is Reynolds number has been defined as G
