Development of a mathematical model for mixing index in gas- solid fluidized Bed

Abstract

Gas-solid fluidized beds have found wide industrial applications compared to fixed beds due to low pressure drop and good solid fluid mixing. Some of the important applications of gas–solid fluidized beds are in dairy, cement, food, and pharmaceutical industries for varied operations which include drying, cooling, coating and agglomeration. This permits a continuous automatically controlled operation with ease of handling and rapid mixing of solids leading to near isothermal conditions throughout the bed, thereby minimizing overheating in case of heat sensitive products. Mixing of solids is a common processing step widely used in industry. It is extensively employed in the manufacture of ceramics plastics, fertilizers, detergents, glass pharmaceuticals, processed food and cattle feed and in the powder metallurgy industry. Mixing index concept is a very much important factor in fluidization. Mixing index is the ratio of fraction of jetsam in the top portion of bed to the fraction in a well- mixed bed. Mixing index’s value from 0 to 1 corresponds to complete segregation and complete mixing respectively. A mathematical model of a real chemical process is a mathematical description which describes experimental facts and establishes relationship among the process variables. Mathematical modeling is an activity in which qualitative and quantitative representation or abstractions of the real process are carried out using mathematical symbols. In building a mathematical model, a real process is reduced to its bare essentials, and the resultant scheme is described by a mathematical formalism selected according to the complexity of the process. The resulting model could be either analytical or numerical in nature depending upon the method used for obtaining the solution. It is important that the model should also represent with sufficient accuracy qualitative and quantitative properties of the prototype process and should adequately fit the real process. For a check on this requirement, the observation made on the process should be compared with predictions derived from the model under identical ivconditions. Thus, a mathematical model of a real process is a mathematical description combining experimental facts and establishing relationships between the process and variables. Mixtures of solid particles of different sizes and/or densities tend to separate during fluidization. Particles that sink to the gas distributor are referred to as jetsam, while those that float on the fluidized bed surface are referred to as flotsam. Mixing and Segregation behavior of mixture particles is of practical importance because particle distributions in the fluidized bed influences the chemical reaction, bed expansion, and various mass and heat transfer properties in the fluidized beds. Many studies have been made in the past in order to understand the underlying mechanisms and predict the behaviour of mixing and segregation, including the investigation of factors affecting the mixing/segregation, the development of predictive empirical and theoretical correlations, as well as mathematical and numerical models. A theoretical model has been developed on the basis of “counter flow solid circulation model”. Considering both vertical and horizontal movement of the jetsam particles as some particles displace horizontally due to the bursting of bubbles, the dispersion model in the form of the differential equation is written and this is solved by finite difference method. For calculating concentration of jetsam particles and mixing index at any height of the bed, a c-language program is written. The numerical results are in satisfactory agreement with experimental data. It is observed that both the concentration of the jetsam particles and mixing index decreases with the height of particles layers in the bed (measured from the distributor). It is also observed that the unpromoted bed gives better mixing index values than promoted bed due to its greater flow area. Optimum fraction of bed materials with respect to its distribution ion the upward and downward streams during the fluidization process can be taken up to 20%. When static bed height, operating fluidization velocity and jetsam particles composition values increases, for all the cases corresponding mixing index values decreases. It is seen that mixing index values of disc promoted bed and rod promoted fluidized bed are nearly same although flow area of rod promoted fluidized bed is greater than disc promoted fluidized bed.