Gas-Solid Mixtures

Gas-Solid Mixtures Carlson, Frazier, and Engdahl [Trans. Am. Soc. Mech. Eng., 70, 65-79 (1948)] describe the use of a flow nozzle and a square-edged orifice in series for the measurement of both the gas rate and the solids rate in the flow of a finely divided solid-in-gas mixture. The nozzle differential is sensitive to the flow of both phases, whereas the orifice differential is not influenced by the sohds flow. 

Farbar [Trans. Am. Soc. Mech. Eng., 75,943-951 (1953)] describes how a venturi meter can be used to measure solids flow rate in a gas-solids mixture when the gas rate is held constant. Separate calibration curves (solids flowversus differential) are required for each gas rate of interest. 

Cheng, Tung, and Soo [J. Eng. Power, 92, 135-149 (1970)] describe the use of an electrostatic probe for measurement of solids flow in a gas-solids mixture. 

Scrubbing with liquid (usually water) can enhance the collection of particles when separating gas-solid mixtures. Figure 8.11 shows three of the many possible designs for... 

Scrubbing with liquid (usually water) can enhance the collection of particles when separating gas-solid mixtures. Flotation is a gravity separation process that exploits differences in the surface properties of particles. Gas bubbles are generated in a liquid and become attached to solid particles or immiscible liquid droplets, causing the particles or droplets to rise to the surface. 

For the separation of gas-solid mixtures, preliminary design of inertial separators, cyclones, electrostatic precipitators, scrubbers and some types of filters can be carried out on the basis of collection efficiency curves derived from experimental performance. 

Tsuji et al. (1990) have modeled the flow of plastic pellets in the plug mode with discrete dynamics following the behavior of each particle. The use of a dash pot/spring arrangement to account for the friction was employed. Their results show remarkable agreement with the actual behavior of real systems. Figure 28 shows these flow patterns. Using models to account for turbulent gas-solid mixtures, Sinclair (1994) has developed a technique that could have promise for the dense phase transport. 

Current Methods. The general outline of the Kolbe-Schmitt reaction, as it is employed in the 1990s, is as follows. In the first step, phenol and hot aqueous caustic are mixed to produce the sodium phenate which is taken to dryness. Next, the phenate and dry carbon dioxide are introduced into the carbonator. Air is excluded to minimize oxidation and the formation of colored compounds. The gas—solid mixture is agitated and heated, first at low temperature, followed by several hours at higher temperatures, to complete the formation of sodium salicylate. Variations of this reaction have been noted in the literature and are still being investigated (10,11). One reported scheme produces salicylic acid or substituted salicylic acids by reaction of a granulated alkali metal salt of the respective phenolic compound with C02 in a fluidized bed at 20—130°C until at least 50—80% of the metal salt has been converted to... 

Typical fluid-bed processor elements can be seen in Figure 1. The fluidizing gas enters the bed at the bottom through an air distributor. The gas passes up through the bed of solids, causing it to fluidize. This gas/solid mixture behaves much like liquid of similar bulk density. Above the fluidized bed, a freeboard section (expansion chamber) is provided to slow down the... 

P. Maijanovic, An investigation of the behaviour of gas-solids mixture flow properties for vertical conveying in pipelines, Ph.D. Thesis, CNAA, Thames Polytechnic, London, UK, 1984. 

P. Maijanovic. Bends in gas-solids mixture flow in pipes — a view to the prediction of pressure loss, GAMM Congress, Vienna, Austria, 1988. 

D.J. Mason, A. Levy, P. Maijanovic, The influence of bends on the flow of gas-solids mixtures through pipelines, Proceedings of the 2nd Israel Conference for Conveying and Handling of Particulate Solids, Jerusalem, Israel, 1997, pp. 4.36 4.41. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

This chapter addresses the various phenomena indicated. In addition, the thermodynamic laws governing physical properties of the gas-solid mixture such as density, pressure, internal energy, and specific heat are introduced. The thermodynamic analysis of gas-solid systems requires revisions or modifications of the thermodynamic laws for a pure gas system. In this chapter, the equation of state of the gas-solid mixture is derived and an isentropic change of state is discussed. 

The analysis of a multiphase flow system is complex, in part because of the difficulties in assessing the dynamic responses of each phase and the interactions between the phases. In some special cases, the gas-solid mixture can be treated as a single pseudo-homogeneous phase in which general thermodynamic properties of a gas-solid mixture can be defined. This treatment provides an estimate for the bulk behavior of the gas-solid flow. The following treatment is based on the work of Rudinger (1980). 

Denote ap as the volume fraction of particles in a gas-solid mixture. The volume-averaged densities of both gas and particle phases are then given by... 

Example 6.2 In a gas-solid mixture, the particle density is 2,400 kg/m3 and the gas density is 1.2 kg/m3. For a particle mass fraction of 99 percent, what is the corresponding particle volume fraction What is the corresponding particle volume fraction, if the particle mass fraction is 50 percent ... 

The equation of state in an isentropic process of a gas-solid mixture can be obtained in terms of an energy conservation relationship. When applying the first law of thermodynamics to a gas-solid mixture, we have... 

Equation (6.54) accounts for the change of state in the isentropic processes of a gas-solid mixture in which the effect of a finite particle volume is considered. An example using this equation to obtain the speed of sound in a gas-solid mixture is introduced in the next section. 

Another approach for estimating am is based on the pseudothermodynamic properties of the mixture, as suggested by Rudinger (1980). The equation for the isentropic changes of state of a gas-solid mixture is given by Eq. (6.53). Note that for a closed system the material density of particles and the mass fraction of particles can be treated as constant. Hence, in terms of the case for a single-phase fluid, the speed of sound in a gas-solid mixture can be expressed as... 

Um Superficial velocity of the gas-solid mixture wM Molecular weight of a gas—particle mixture... 

It is noted from Eq. (7.78) that the maximum droplet holdup can be reached when the upward gas-solid mixture velocity Up approaches the sedimentation velocity of the droplets, assuming that no coalescence of droplets occurs. Under this condition, the collection efficiency is maximum. 

In a fully fluidized bed, the pressure drop (cross-sectionally averaged) counterbalances the weight of the pseudocontinuum of the gas-solid mixture, which yields... 

One-dimensional flow models are adopted in the early stages of model development for predicting the solids holdup and pressure drop in the riser. These models consider the steady flow of a uniform suspension. Four differential equations, including the gas continuity equation, solids phase continuity equation, gas-solid mixture momentum equation, and solids phase momentum equation, are used to describe the flow dynamics. The formulation of the solids phase momentum equation varies with the models employed [e.g., Arastoopour and Gidaspow, 1979 Gidaspow, 1994], The one-dimensional model does not simulate the prevailing characteristics of radial nonhomogeneity in the riser. Thus, two- or three-dimensional models are required. 

Leung, L. S. and Jones, P. J. (1978). Flow of Gas-Solid Mixture in Standpipes A Review. Powder Tech., 20,145. 

Assuming the riser flow to be characterized by one-dimensional steady flow and applying the two-fluid model to the flow, one can obtain the momentum equation for the gas-solid mixture as... 

The role of the pressure gradient may be shown in the momentum equation of a gas-solid mixture. Consider a steady pipe flow without mass transfer and with negligible interparticle collisions. From Eq. (5.170), the momentum equations for the gas and particle phases can be given by... 

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