Slurry reactors overall effectiveness

The overall rate of reaction calculated for the three-phase fluidised-bed reactor above is approximately one tenth of the rate calculated for the agitated tank slurry reactor in Example 4.6. The main reasons are the very poor effectiveness factor and the relatively smaller external surface area for mass transfer caused by using the larger particles. Even the gas-liquid transfer resistance is greater for the three-phase fluidised-bed, in spite of the larger particles being able to produce relatively small bubbles these bubbles are not however as small as can be produced... 

In order to describe the hydrogenation in slurry reactors, and as the reaction is always controlled by mass transfer [1], we must consider both the mass-transfer and the reaction steps. Thus, we must introduce the overall effectiveness factor in the expression of reaction rate [3] ... 

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

Closure After completing this chapter, the reader should be able to derive differential equations describing diffusion and reaction, discuss the meaning of the effectiveness factor and its relationship to the Thiele modulus, and identify the regions of mass transfer control and reaction rate control. The reader should be able to apply the Weisz-Prater and Mears criteria to identify gradients and diffusion limitations. These principles should be able to be applied to catalyst particles as well as biomaierial tissue engineering. The reader should be able to apply the overall effectiveness factor to a packed bed reactor to calculate the conversion at the exit of the reactor. The reader should be able to describe the reaction and transport steps in slurry reactors, trickle bed reactors, fluidized-besd reactors, and CVD boat reactors and to make calculations for each reactor. 

Ramachandran and Chaudhari [P.A. Ramachandran and R.V. Chaudhari, Can. J. Chem. Eng., 58, 412 (1980) Chem. Eng., J., 20, 75 (1980)] have shown that it is advantageous to define an overall effectiveness for the reactor in such cases. This is defined as the ratio of the actual rate of chemical reaction per unit volume of the slurry to the rate that would have prevailed it the liquid phase were in equilibrium with the inlet gas phase. Following this,... 

Combining equations (8-103) and (8-97), the overall effectiveness factor for an mth-order reaction in a slurry reactor can be obtained as... 

Table 8.1a Equations for Overall Effectiveness for a Slurry Reactor with Various Rate Equations...

Table 8.1b Overall Rate of Reaction in a Slurry Reactor without Intraparticle Diffusional Effects...

Figure 8.10 Overall effectiveness factor for a first-order reaction in a slurry reactor. [After R.V. Chaudari and P.A. Ramachandran, Amer. Inst. Chem. Eng., JL, 26, 111, with permission of the American Institute of Chemical Engineers, (1980).]...

The slurry reactor analysis given above employed the concept of an overall effectiveness factor. It is informative to break down the problem into analysis of individual phase effectiveness factors assembled together as was done for the three-phase fluid-bed model. Equating the rates of the individual steps in a manner similar to... 

The overall effect of temperature is the resultant of the increasing effect on mass transfer and the decreasing effect on solubility (see Chapter 14). However, this general conclusion should be viewed with caution because there are exceptions. An important one is hydrogen, whose solubility increases with temperature (e.g., the solubility in soybean oil increases by 60% as the temperature is raised from 20 to 100 °C (Doraiswamy and Sharma, 1984). Thus the overall effect in hydrogenation, perhaps the most frequent user of the slurry reactor, will be that the rate will increase significantly with an increase in temperature. 

Expressions for the overall rate of reaction in differentially operated slurry reactors in case of other reaction type can be found in (2l. In the same paper also diagrams are presented for overall effectiveness factors (including also intraparticle diffusion) and different kinetic models are given. 

Various factors should be considered during the scaleup of slurry reactors such as flow regime, backmixing in the different phases, temperature control, controlling regime of the overall reaction, etc. Details of the effects of various factors on scaleup are available in the literature (1,11,21,30,34). In this section, some of the factors which influence the scaleup of slurry reactors as applied to coal technology are briefly mentioned. 

Leading characteristics of five main kinds of reactors are described following. Stirred tanks, fixed beds, slurries, and three-phase fluidized beds are used. Catalyst particle sizes are a compromise between pressure drop, ease of separation from the fluids, and ease of fluidization. For particles above about 0.04 mm dia, diffusion of liquid into the pores and, consequently, accessibility of the internal surface of the catalyst have a minor effect on the overall conversion rate, so that catalysts with small specific surfaces, of the order of 1 m2/g, are adequate with liquid systems. Except in trickle beds the gas phase is the discontinuous one. Except in some operations of bubble towers, the catalyst remains in the vessel, although minor amounts of catalyst entrainment may occur. 

The LTFT tubular reactor is geared at the production of wax and under normal FT conditions, the wax is in the liquid phase and so the reactor operates as a trickle bed. The influence of liquid wax inside the catalyst particles on the overall FT activity is illustrated in the following text. It was found that periodic in situ washing of the catalyst bed with a suitable solvent, which removed the wax from the catalyst particles, immediately resulted in a large increase in conversion but the effect was short lived, as the catalyst pores were rapidly again filled with the wax produced in the FT reaction ((20), p. 199). This indicates that diffusion restrictions in the wax-filled pores lower the rate of the FT reaction. This is confirmed by the fact that the FT conversion is inversely proportional to the catalyst particle size. In the low temperature slurry-phase reactor, the catalyst particles... 

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