Dilute transport

The pressure drop in simultaneous flow of gas and solid particles is made up of contributions from each of the phases. When the particles do not interact significantly, as in dilute transport, the overall pressure drop is represented by... 

Figure 20 Predicted flow regime diagram of the industrial MIP reactor, with solids flux as a function of the imposed total pressure drop at fixed gas flow rate. The snapshots of voidage profile refer to the transition, from left to right, the dilute transport, choking transition in between with different solids inventory, to the dense fluidization (Lu et al., 2007).

In the dilute transport region in the standpipe (3-4 in Fig. 8.15), the mass balance of solids and gas requires... 

Azbel and Liapis (1983) analyzed gas/liquid systems with the assumption that the available energy at steady state is at a minimum. Reh (1971) mentioned the concept of the lowest resistance to fluid flow, and in a somewhat alternate way, the so-called minimum pressure drop was used by Nakamura and Capes (1973) in analyzing the annular structure in dilute transport risers. The instability of a uniform particle-fluid suspension was analyzed by introducing small disturbances into the system (Jackson, 1963 Grace and Tuot, 1979 Batchelar, 1988). 

According to the preceding definition, the relationship between the saturation carrying capacity K and fluid velocity Ut can be calculated, as shown in Fig. 5, which defines the transition from the PFC regime to the FD regime, that is, from fast fluidization to dilute transport, as corroborated by the experimental points (the data at high velocities was transported from Fig. 7). 

For instance, if the solids flow rate is specified at Gs = 50 kg/(m2s), choking will take place at Ug = 3.21 m/s for system FCC/air as indicated in the figure. Throughout the entire regime spectrum, only at this unique point (l/pl, K ) can both dense-phase fluidization and dilute-phase transport coexist. At velocities higher than Upt, only dilute transport can exist, shown as Mode FD in Fig. 4 at velocities lower than l/pt, only dense-phase fluidization can take place, shown as Mode PFC in Fig. 4. The transition point at l/pt identifies the unique Mode PFC/FD on the curve of Fig. 5 for the coexistence of both modes, the relative proportion of which depends on other external conditions such as the imposed pressure APimp as reported by Weinstein et al. (1983). 

The fast fluidization regime is represented by a dense region at the bottom of the riser and a dilute region above it. The inter-relationship of the fast fluidization regime with other fluidization regimes in dense-phase fluidization and with the dilute transport regime is... 

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. 

Dilute transport fluidization The gas velocity is so large that all the particles are carried out of the bed with the gas. This solid transport by gas blowing through a pipe is named pneumatic conveying. In vertical pneumatic transport, particles are always suspended in the gas stream mainly because the direction of gravity is in line with that of the gas flow. The radial particle concentration distribution is almost uniform. No axial variation of solids concentration except i the bottom acceleration section [58]. 

Flow regime Bubbling, slugging or turbulent, distinct upper interface Fast fluidization Dilute transport... 

For pneumatic conveying all the particles are evenly dispersed in the gas. This makes contacting ideal or close to ideal. The plug flow model is thus well suited for the dilute transport reactors, but has also been used for the denser fast fluidization regime neglecting gradients in the solids distribution. For first order reactions the model can be written as ... 

Transport parameters, which appear in the various forms of the infinite dilute transport equations, are the electrolyte conductivity, the ion mobility, the ion diffusion coefficient, and the ion transference number. All of these parameters can be determined from ionic equivalent conductances with units of (5-cm )/equiv) of cations and anions in solution. The ion mobility M , which appears in Equation (26.54), is related to by... 

Transport. The turbulent and advective transport of air parcels (horizontally and vertically) is often the most important factor (mixing and dilution). Transport processes show another wide range of causes, but are mainly driven by density gradient (hence, T gradients). Thus, it is clear that characteristic daily and seasonal patterns can be observed (for example, the vertical down-mixing of air in the morning after a nocturnal inversion). 

In dilute transport the gas-to-wall friction is often assumed independent of the presence of the solids and so the friction factor for the gas may be used (e.g. Fanning friction factor - see worked example on dilute pneumatic transport). 

In the high-velocity fluidized bed, the bed ean be operated in turbulent, fast fluidization, dilute transport, and downer flow regimes. In the turbulent regime, the bubble/void phase gradually becomes indistinguishable from the emulsion phase, and the particle entrainment rate increases significantly with increasing gas velocity. Upon further increase in gas velocity, the bubble/void phase eventually disappears and the gas evolves into a continuous phase in the fast... 

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