Gas-Solid Transfer

whereas voidages obtained with small spherical or cylindrical packings normally used as catalysts are less than 40% or so, which makes them impractical for countercurrent operation. However, catalysts are made in the forms of rings or saddles when very low pressure drop or countercurrent operation is desirable. 

Even when they are nominally the same type and size, packings made by different manufacturers may differ substantially in their pressure drop and mass transfer behavior, so that manufacturers data should be obtained for final design. 

Mesh or other open structures as vessel packing have attractive pressure drop and other characteristics, but each type has quite individual behavior so that it is best to consult their manufacturer s data. 

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. 

Although the phenomena are not clearcut, partial settling out of solids from the gas stream and other instabilities may develop below certain linear velocities of the gas called choking velocities. Normal pneumatic transport of solids accordingly is conducted above such a calculated rate by a factor of 2 or more because the best correlations are not more accurate. Above choking velocities the process is called dilute phase transport and, below, dense phase transport. 

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Mehta (34) has carried out a reactor network optimization study to find improved designs for the production of acrylonitrile in a collaboration between UMIST and one of its industrial partners. Most industrial installations employ fluidized-bed reactors (BP/Sohio process) with a well-mixed reaction zone. Previous process improvements have mainly resulted from better catalysts, which have produced an increase in yield from 58% to around 80%. The reaction model employed in the optimization study is taken from Ref. 81 and considers seven reactions and eight components. Air, pure oxygen, and propylene are available as raw material streams. The optimization study assumes negligible pressure drop along the reaction sections, isothermal and isobaric operation, and negligible mass gas-solid transfer effects. 

Correlation 7.181 should be used with care at low Reynolds numbers. Typical values for gas-solid transfer are 1 m mi"2 s 1 for the mass transfer coefficient and 102 W m-2 K-1 for the heat transfer coefficient. 

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. 

Gas-Solid Transfer 119 Choking Velocity 119 Pressure Drop 119... 

The IGT team also analyzed horizontal dilute-phase gas-solid transfer. They found the Yang model and a modified Hinkle analysis to work about equally well for prediction of pressure drop on coal and coal-related materials. The modified Hinkle analysis involves modification of the particle velocity developed by Hinkle. The particle velocity that gave minimum deviations between the experimental and predicted pressure drop is / ... 

For the conditions in Prob. 4-1, determine the acceleration lengths considering the two transport gas velocities. Assume the particle velocity is introduced into the system at 0.305 m/sec. 4-3 Develop a generalized numerical procedure for solution of the implicit Yang expressions in determining the pressure losses in vertical gas-solid transfer. 

V is the kinematic viscosity, u the mean gas velocity in the channel, a the thermal diffusivity, Po the gas density, Cpo the heat capacity of the gas, and its thermal conductivity. Correlations (2.1) and (2.2) indicate a strong flowrate dependence. For standard monoliths and operating conditions, Sh ranges from 0.7 to 1.6, and Nu from 0.6 to 2.7 according to the correlations above. These correlations contradict the results of Heck et al. (1974) and other earlier authors on one hand, and the results of the comparison between the Graetz-Nusselt and film models on the other hand. There are several explanations to this discrepancy. As mentioned above, wall irregularity may be invoked. However, we may also invoke a non-uniform flow distribution in the monolith sample (Martin (1978)), or the effect of the small L/Dj, ratio (less than 10) and the small diameter of the monolith sample used by Votruba et al.. Here again, we see that the gas-solid transfer process is not fully understood, and that a refined and detailed description of this process is not presently possible. Consequently, we think that the Nusselt and Sherwood numbers must be considered adjustable parameters. 

Gas—solids fluidization is the levitation of a bed of solid particles by a gas. Intense soflds mixing and good gas—soflds contact create an isothermal system having good mass transfer (qv). The gas-fluidized bed is ideal for many chemical reactions, drying (qv), mixing, and heat-transfer appHcations. Soflds can also be fluidized by a Hquid or by gas and Hquid combined. Liquid and gas—Hquid fluidization appHcations are growing in number, but gas—soHds fluidization appHcations dominate the fluidization field. This article discusses gas—soHds fluidization. 

Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO9 to develop correlations for mass-transfer coefficients [Lim et al., Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The data were correlated over a wide range of conditions with the following equation for combined natural and forced convection ... 

The above discussion relates to diffusion-controlled transport of material to and from a carrier gas. There will be some circumstances where the transfer of material is determined by a chemical reaction rate at the solid/gas interface. If this process determines the flux of matter between the phases, the rate of transport across the gas/solid interface can be represented by using a rate constant, h, so that... 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

Gases, liquids, and solids have different physical properties. A gas fills its container, so that if a certain amonnt of gas is transferred from a small container into a large one, the gas will expand to fill the new container. If there is a hole m the top of a container filled with gas, the gas will escape. A liquid keeps the same volume when transferred from one container to another, but takes the shape of the new container. On Earth, a liquid has a flat, horizontal surface. If there is a hole in its container below that surface, the liquid will spill out. A solid keeps both its shape and its volume when transferred from one container to another. 

The equations describing the possible nonreactive and/or reactive forms of energy transfer at the gas-solid interface ... 

Liquid-gas-solids mixing 275 Liquid-liquid extraction, mass transfer 599 Liquid metals, heat transfer 523 meters 269... 

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