Gas-Solid Pneumatic Transfer

Before proceeding with the dilute-phase development, an explanation of the difference between the dilute phase and dense phase is in order. If one considers the vertical transport of soHds by a large quantity of gas, one finds a particular pressure drop. As the gas velocity is reduced at the same rate of transport of solids, the pressure drop decreases. This can be seen in Fig. 4-1 in going from points to point.5 on the curve. At one particular velocity of the gas a minimum pressure drop is experienced. This minimum pressure drop point may be used as the dividing point between dilute- and dense-phase transfer. Lower gas velocities produce higher pressure drops and the 

Consider the flow of solids and gas as seen in Fig. 4-2. A force balance on the particles in the differential section dL may be represented as 

At steady state, this equation can be solved for the value of Up, which results in an implicit equation. The drag coefficient ratio at various voidages is given in Example 4-1. 

Example 4-1 As noted in multiparticle flow systems, the drag coefficient is different from that for a single particle. Compute the effect of voidage on the multiparticle drag coefficient. 

Consider the voidage of 0.99,0.98,0.95, and 0.90 for a flow system. The first few values of high voidages are for dilute transport systems. 

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The book is arranged in two parts Part I deals with basic relationships and phenomena, including particle size and properties, collision mechanics of solids, momentum transfer and charge transfer, heat and mass transfer, basic equations, and intrinsic phenomena in gas-solid flows. Part II discusses the characteristics of selected gas-solid flow systems such as gas-solid separators, hopper and standpipe flows, dense-phase fluidized beds, circulating fluidized beds, pneumatic conveying systems, and heat and mass transfer in fluidization systems. 

The hydrodynamics of gas-solid transfer is complex and the literature is voluminous, as indicated by the 224-page coverage by N.P. Cheremisinoff and R. Gupta, Handbook of Fluids in Motion, Butterworth, pp. 623-847, Chapters 23-31, 1883. Equipment for pneumatic conveying is described in Section 5.2 along with some rules for calculating power requirements. Here the latter topic will be supplemented from a more fundamental point of view. 

The interphase momentum transfer term can be derived from correlation developed to model fluidization processes since the range of solids concentrations experienced in pneumatic transport systems is similar. This form has been employed by Patel and Cross [46] for modeling gas-solids fluidized beds. For solid concentrations greater than 0.2, the interphase friction coefficient, K, may be computed by using the Ergun [47] equation ... 

Mindziul and Kmiec [23 25] investigated the aerodynamics of the gas solid flow in a pneumatic flash dryer. Their mathematical model was based on the continuity equation for both the gas and the solid phase and momentum equations for the solid phase and the solid gas mixture. Heat and mass transfer were neglected. Although the drying apparatus was composed of three elements with varying cross-sectional area, one-dimensional model was solved. The effect of various empirical correlations for solid-wall friction factor has been investigated. The results... 

An interesting coupHng phenomenon occurs in a pneumatic transfer system involving a blower to move the gas-solid mixture. Doig (1975) and Leung, Wiles and... 

A model has been developed to simulate the non-suspension moving-bed type of flow in pneumatic conveying systems. The flow is modelled as two layers a dilute gas-solids mixture flowing above a dense gas-solids mixture. For each layer the conservation equations for mass, momentum and energy were solved for both the gas and solids phases. In addition mass, momentum and energy transfers between the two layers were modelled. The prediction of pressure profile and the depth of the dense layer showed good agreement with experimental observations. 

In a pneumatic conveying system, air or some other gas is used to transfer solids from one place to another. These systems are entirely enclosed, hence the product loss is small, contamination is minimized, and the problem of dust emission to the atmosphere is greatly reduced. There are many different systems only a few will be presented here. 

Blasco et al. [12] proposed two-dimensional mathematical model for the drying process of dense phase pneumatic conveying. However, heat and mass transfer were not considered and therefore their model may be used for dense phase pneumatic transport only. In their paper, both experimental and numerical predictions for axial and radial profiles for gas and solid velocity, axial profiles for solid concentration and pressure drop were presented. 

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