Rate gases/solids

In this chapter, emphasis will be given to heat transfer in fast fluidized beds between suspension and immersed surfaces to demonstrate how heat transfer depends on gas velocity, solids circulation rate, gas/solid properties, and temperature, as well as on the geometry and size of the heat transfer surfaces. Both radial and axial profiles of heat transfer coefficients are presented to reveal the relations between hydrodynamic features and heat transfer behavior. For the design of commercial equipment, the influence of the length of heat transfer surface and the variation of heat transfer coefficient along the surface will be discussed. These will be followed by a description of current mechanistic models and methods for enhancing heat transfer on large heat transfer surfaces in fast fluidized beds. Heat and mass transfer between gas and solids in fast fluidized beds will then be briefly discussed. 

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. 

A. K. Galwey, Reactions in the Sohd State, in Bamford and Tipper, eds.. Comprehensive Chemical Kinetics, vol. 22, Elsevier, 1980. Galwey, A. K., Chemistry of Solids, Chapman and Hall, 1967. Sohn, H. Y, and W. E. Wadsworth, eds.. Rate Frocesses of Extractive Metallurgy, Plenum Press, 1979. Szekely, J., J. W. Evans, and H. Y. Sohn, Gas-Solid Reactions, Academic Press, 1976. Uhmann, ed., Enzyklopaedie der technischen Chemie, Uncatalyzed Reactions with Solids, vol.. 3, 4th ed., Verlag Chemie, 1973, pp. 395-464. 

In most circumstances, it can be assumed diat die gas-solid reaction proceeds more rapidly diaii die gaseous transport, and dierefore diat local equilibrium exists between die solid and gaseous components at die source and sink. This implies diat die extent and direction of die transport reaction at each end of die temperature gradient may be assessed solely from diermodynamic data, and diat die rate of uansport across die interface between die gas and die solid phases, at bodi reactant and product sites, is not rate-determining. Transport of die gaseous species between die source of atoms and die sink where deposition takes place is die rate-determining process. 

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... 

In all of these systems, the rate of generation at the gas-solid interface is so rapid that only a small fraction is canied away from the particle surface by convective heat uansfer. The major source of heat loss from the particles is radiation loss to tire suiTounding atmosphere, and the loss per particle may be estimated using unity for both the view factor and the emissivity as an upper limit from tlris source. The practical observation is that the solids in all of these methods of roasting reach temperatures of about 1200-1800 K. 

The rates of gas-solid reaetions are surfaee area dependent, so finely-divided metals, eoal ete. may be prone to oxidation leading to spontaneous eombustion. A eombustible dust will burn mueh more rapidly than the bulk sold, and if dispersed in air eause a dust explosion (refer to Table 6.2). 

Fluid coking is very insensitive to poor gas-solids contacting, but has one problem not faced by cat cracking or hydroforming. If the heavy residual oil is fed too fast to the reactor, the coke particles will become wetted and stick together in large unfluidizable lumps. Correct control of feed rate is necessary to prevent this bogging. 

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... 

Kinetic investigations cover a wide range from various viewpoints. Chemical reactions occur in various phases such as the gas phase, in solution using various solvents, at gas-solid, and other interfaces in the liquid and solid states. Many techniques have been employed for studying the rates of these reaction types, and even for following fast reactions. Generally, chemical kinetics relates to tlie studies of the rates at which chemical processes occur, the factors on which these rates depend, and the molecular acts involved in reaction mechanisms. Table 1 shows the wide scope of chemical kinetics, and its relevance to many branches of sciences. 

The occurrence of solid clathrate solutions is clearly seen in Fig. 4, which gives a cross section of the P-T-x diagram at 60°C according to recent results.28 The two two-phase equilibria clath-rate-gas and clathrate-hydroquinone are separated by a one-phase... 

Flynn and Dickens [142] have translated the relaxation methods of fluid kinetics into terms applicable to solid phase thermogravimetry. The rate-determining variables such as temperature, pressure, gas flow rate, gas composition, radiant energy, electrical and magnetic fields are incremented in discrete steps or oscillated between extreme values and the effect on reaction rate determined. 

The above rate equations were originally largely developed from studies of gas—solid reactions and assume that particles of the solid reactant are completely covered by a coherent layer of product. Various applications of these models to kinetic studies of solid—solid interactions have been given. 

Strictly gas-phase CSTRs are rare. Two-phase, gas-liquid CSTRs are common and are treated in Chapter 11. Two-phase, gas-solid CSTRs are fairly common. When the solid is a catalyst, the use of pseudohomogeneous kinetics allows these two-phase systems to be treated as though only the fluid phase were present. All concentration measurements are made in the gas phase, and the rate expression is fitted to the gas-phase concentrations. This section outlines the method for fitting pseudo-homogeneous kinetics using measurements made in a CSTR. A more general treatment is given in Chapter 10. 

The ordinary burning of sulfur produces SO2. This is the hrst step in the manufacture of sulfuric acid. The second step oxidizes SO2 to SO3 in a gas-solid catalytic reactor. The catalyst increases the reaction rate but does not change the equilibrium compositions in the gas phase. 

Figure 11.10(b) can be modeled as a piston flow reactor with recycle. The fluid mechanics of spouting have been examined in detail so that model variables such as pressure drop, gas recycle rate, and solids circulation rate can be estimated. Spouted-bed reactors use relatively large particles. Particles of 1 mm (1000 pm) are typical, compared with 40-100 pm for most fluidizable catalysts. 

This equation gives (0) = 0, a maximum at =. /Km/K2, and (oo) = 0. The assumed mechanism involves a first-order surface reaction with inhibition of the reaction if a second substrate molecule is adsorbed. A similar functional form for (s) can be obtained by assuming a second-order, dual-site model. As in the case of gas-solid heterogeneous catalysis, it is not possible to verify reaction mechanisms simply by steady-state rate measurements. 

The rates of gas—solid reactions are surface area dependent, so finely divided metals, coal etc. may be prone to oxidation leading to spontaneous combustion. 

The CFB catalytic cracking reactor plays an important role in the petroleum industry because of its better gas-solids contact and narrow residence time distribution, but its non-uniform radial flow structure and the extensive backmixing of gas and solids lead to a lower conversion rate and poorer selectivity to desired intermediate products [14]. 

Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO2 to develop correlations for mass-transfer coefficients [Lim, Holder, and Shah, Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The mass-transfer coefficient increases dramatically near the critical point, goes through a maximum, and then decreases gradually. The strong natural convection at SCF conditions leads to higher mass-transfer rates than in liquid solvents. A comprehensive mass-transfer model has been developed for SCF extraction from an aqueous phase to CO2 in countercurrent columns [Seibert and Moosberg, Sep. Sci. Techrwl, 23, 2049 (1988) Brunner, op. cit.]. 

As well as depending on catalyst porosity, the reaction rate is some function of the reactant concentrations, temperature and pressure. However, this function may not be as simple as in the case of uncatalyzed reactions. Before a reaction can take place, the reactants must diffuse through the pores to the solid surface. The overall rate of a heterogeneous gas-solid reaction on a supported catalyst is made up of a series of physical steps as well as the chemical reaction. The steps are as follows. 

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