Lean phase flow

The new pressure loss equation presented here is based on determining two parameters the velocity difference between gas and conveyed material and the falling velocity of the material. The advantage of this method is that no additional pressure loss coefficient is needed. The two parameters are physically clear and they are quite easily modeled for different cases by theoretical considerations, which makes the method reliable and applicable to various ap>-plications. The new calculation method presented here can be applied to cases where solids are conveyed in an apparently uniform suspension in a so-called lean or dilute-phase flow. 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

Assume that the volume of dense phase, the fraction solids in it, and the gas flow through it remain the same at all gas velocities, in which case, the lean phase alone expands and contracts to account for the variation in total volume of fluidized bed with change in gas flow rate. The dense-phase characteristics are given by the conditions at incipient fluidization. 

As discussed in Chapter 9, dense-phase fluidization other than particulate fluidization is characterized by the presence of an emulsion phase and a discrete gas bubble/void phase. At relatively low gas velocities in dense-phase fluidization, the upper surface of the bed is distinguishable. As the gas velocity increases, the bubble/void phase gradually becomes indistinguishable from the emulsion phase. The bubble/void phase eventually disappears and the gas evolves into the continuous phase with further increasing gas velocities. In a dense-phase fluidized bed, the particle entrainment rate is low and increases with increasing gas velocity. As the gas flow rate increases beyond the point corresponding to the disappearance of the bubble/void phase, a drastic increase in the entrainment rate of the particles occurs such that a continuous feeding of particles into the fluidized bed is required to maintain a steady solids flow. Fluidization at this state, in contrast to dense-phase fluidization, is denoted lean-phase fluidization. 

Subbarao, D. Chester and lean-phase behavior, Powder Technology 46, 101-107 (1986). Wallis, G. B. One-Dimensional Two-Phase Flow, p. 182. McGraw-Hill, New York, 1969. Weinstein, H., Graff, R. A., Meller, M., and Shao, M. The influence of the imposed pressure drop across a fast fluidized bed, Proc. 4th Intern. Corf. Fluidization, Kashikojima, Japan, pp. 299-306 (1983). 

Lean phase fluidization As the gas flow rate increases beyond the point corresponding to the disappearance of bubbles, a drastic increase in the entrainment rate of the particles occurs such that a continuous feeding of particles into the fluidized bed is required to maintain a steady solid flow. Fluidization at this state, in contrast to dense-phase fluidization, is generally denoted lean phase fluidization. Lean phase fluidization encompasses two flow regimes, these are the fast fluidization and dilute transport regimes. 

The fluidized bed reactors can roughly be divided into two main groups in accordance with the operating flow regimes employed. These two categories are named the dense phase and lean phase fluidized beds. 

In the entrained-flow reactor (Figure 18.11), the solid particles travel with the reacting fluid through the reactor. Such a reactor has also been described as a dilute or lean-phase fluidized bed with pneumatic transport of solids. 

Fast fluidization is characterized by a dense region at the bottom of a circulating fluidized bed, leading smoothly (without a sharp interface) into a lean region above (Li and Kwauk, 1980). In contrast, in the dilute-phase flow regime, the pressure gradient, except for an acceleration zone at the bottom, is nearly uniform. Hence the transition from fast fluidization to dilute flow can be characterized by the disappearance of the S-shaped inflection point (Li and Kwauk, 1980), or by the disappearance of nonuniform axial density profiles (Takeuchi et al., 1986). 

In conventional pneumatic transport, a minimum in the dPjdz vs. Gs curve at a fixed gas velocity is commonly used to separate dense phase flow from lean phase transport (Leung, 1980). Experimentally, internal solids circulation increases dramatically right after... 

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