Intraparticle mass and heat transfer

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

In this case the reaction rate will depend not only on the system temperature and pressure but also on the properties of the catalyst. It should be noted that the reaction rate term must include the effects of external and intraparticle heat and mass transfer limitations on the rate. Chapter 12 treats these subjects and indicates how equation 8.2.12 can be used in the analysis of packed bed reactors. 

Since the critical values of y(3 and Lw are y/3 = 4 and, Lw > 1 respectively, then referring to the results reported in Table II, it seems highly unrealistic to expect multiple steady states and periodic activity for a single catalyst particle resulting from intraparticle heat and mass transfer alone. 

Figure 13. Effectiveness factor i) as a function of the Thiele modulus . Combined effects of intraparticle heat and mass transfer on the effective reaction rate (first order, irreversible reaction in a sphere, Arrhenius number y = 20, Prater number fi as a parameter, adapted from Weisz and Hicks [110]).

Table 2 lists most of the available experimental criteria for intraparticle heat and mass transfer. These criteria apply to single reactions only, where it is additionally supposed that the kinetics may be described by a simple nth order power rate law. The most general of the criteria, 5 and 8 in Table 2, ensure the absence of any net effects (combined) of intraparticle temperature and concentration gradients on the observable reaction rate. However, these criteria do not guarantee that this may not be due to a compensation of heat and mass transfer effects (this point has been discussed in the previous section). In fact, this happens when y/J n [12]. 

The true intrinsic kinetic measurements require (1) negligible heat and mass transfer resistances by the fluids external to the catalyst (2) negligible intraparticle heat and mass transfer resistances and (3) that all catalyst surface be exposed to the reacting species. The choice of the reactor among the ones described in this section depends upon the nature of the reaction system and the type of the required kinetic data. Generally, the best way to determine the conditions where the reaction is controlled by the intrinsic kinetics is to obtain rate per unit catalyst surface area as a function of the stirrer speed. When the reaction is kinetically controlled, the rate will be independent of the stirrer speed. The intraparticle diffusional effects and flow uniformity (item 3, above) are determined by measuring the rates for various particle sizes and the catalyst volume, respectively. If the reaction rate per unit surface area is independent of stirrer speed, particle size, and catalyst volume, the measurements can be considered to be controlled by intrinsic kinetics. It is possible... 

The evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

Effective mass and heat transfer between gas and catalyst phase. Because the BSR geometry induces transition to turbulent flow at relatively low Reynolds numbers (as low as 500), mass and heat transfer between gas and catalyst phase is faster than in monolithic reactors. This is because the flow in a monolithic reactor is usually laminar. The advantage of the BSR can be exploited in processes with a large heat effect, where heat transfer through the film layer is generally more important than intraparticle heat and mass transfer. 

Inter- and intraparticle heat and mass transfer gradients are negligible. 

Several models have been proposed to describe intraparticle heat and mass transfer with heterogeneous coordination catalysts [114], but the most commonly accepted is the multigrain model (MGM) [115-126], In the MGM, the... 

Table 2.13 Conclusions on inter- and intraparticle heat and mass transfer resistances according to the MGM ...

Solution processes use autoclave, tubular, or loop reactors. As compared to slurry and gas-phase polymerization, solution processes are commonly operated at a much higher temperature to keep the polymer dissolved in the reaction medium, and at much lower average residence times (5-20 min, as opposed to 1-4 h). Since polymerization conditions are more uniform in solutions reactors - there are no inter- and intraparticle heat- and mass-transfer resistances, for instance - this configuration is commonly used for the production of EPDM rubbers with soluble Ziegler-Natta vanadium-based catalysts. Composition homogeneity is a require-... 

The MSSR presents the same advantages as BSCR, such as high efficiency of heat-and mass-transfer and minimal intraparticle diffusional resistance, and are convenient for use in batch processes. For these reasons, the slurry-agitated reactors are also suitable for kinetic studies in the laboratory. Some of their major drawbacks are large power requirement for mechanical agitation,... 

Particle Size and Desorption Rates. Bench-scale reactor studies of the desorption of toluene from single, 2- to 6-mm porous clay partides (14) showed desorption times that increased with the square of the particle radius, suggesting that diffusion controls the rate desorption. Parallel experiments performed in a small, pilot-scale rotary kiln at 300°C showed no effect of day partide size for diameters ranging from 0.4 to 7 mm. Additional single-partide studies with temperature profiles controlled to match those in the pilot-scale kiln had desorption times that were a factor of 2—3 shorter for the range of sizes studied (15). Hence, at the conditions examined, intrapartide mass transfer controlled the rate of desorption when single particles were involved and interpartide mass transfer controlled in a bed of particles in a rotary kiln. These results apply to full-scale kilns. As particle size is increased, intraparticle resistances to heat and mass transfer eventually begin to dominate. 

Here we consider a spherical catalyst pellet with negligible intraparticle mass- and negligible heat-transfer resistances. Such a pellet is nonporous with a high thermal conductivity and with external mass and heat transfer resistances only between the surface of the pellet and the bulk fluid. Thus only the external heat- and mass-transfer resistances are considered in developing the pellet equations that calculate the effectiveness factor rj at every point along the length of the reactor. 

Figures 13 and 14 refer to the situation where only intraparticlc transport effects influence the observable reaction rate. However, a similar behavior is observed if, besides intraparticle heat and mass transport processes, the heat and mass transfer between the catalyst pellet and the bulk fluid phase is also considered. More information about this situation can be found, for example, in the works of Cresswell [26], McGreavy and...

From the above it follows that in most practical situations a model, that takes into account only an intraparticle mass and an interparticle heat transfer resistance will give good results. However, in experimental laboratory reactors, which usually operate at low gas flow rates, this may not be true. In the above criteria the heat and mass transfer coefficients for interparticle transport also have to be known. These were amply discussed in Section 4.2. 

An SBC is a vertical, tubular column in which a three-phase (gas-solid-liquid) mixture is used. The slurry phase consists of FT catalysts and FT wax. The syngas flows though the slurry phase in the form of bubbles, as shown in Figure 12.12. The effective heat and mass transfer, low intraparticle diffusion, low pressure drop, and design simplicity are important advantages of this type of reactor. However, considerable problems arise in separating the liquid-phase synthesis products from the catalyst. With their attractive features, the SBC reactors are receiving extensive investment in both R D and commercialization. The concept of SBC is not new. 

The classic Thiele-Damkohler theory accounts for these effects, but is restricted to isothermal behavior and intraparticle mass transfer only by diffusion. If the reaction is highly exothermic and the particle is a poor heat conductor, the temperature in the particle center may rise above that in the contacting fluid and cause the overall rate to be higher than in the absence of heat- and mass-transfer limitations. Moreover, gas-phase reactions with change in mole number cause forced inward or outward convection that assists or counteracts reactant penetration into the particle and so enhances or depresses the rate. 

Under these circumstances, the interparticle transport resistances can be neglected. What are left are the intraparticle resistances, i.e. the heat and mass transfer effects inside the catalyst particles. Since the current case reflects the situation that few reactant and product molecules exist in an environment of solvent molecules, the simplest Fick s law approach with effective diffusion coefficients can be considered as sufficient for the description of molecular diffusion. 

Since realistic wood feedstocks are heterogeneous, the uniform entity appropriate for fundamental studies to identify improved conditions for tar formation is the single particle. In it, the intraparticle conditions can be measured and related to process conditions that can be manipulated. In addition, the effect of heat and mass transfer rates on reaction products can be determined. The findings can be rationalized to all reactors in which the studied experimental conditions prevail. The investigation of reacting single particles has proven extremely successful in the development of catalytic reactors (2) and coal pyrolysis (3,4,5). 

Reaction scheme, catalysis and kinetics, intraparticle diffusion, external heat and mass transfer rates... 

Many factors affect optimum fluidized bed reactor performance, including hydrodynamics, heat and mass transfer of interparticles and intraparticles, and complexities of reaction kinetics. The design of fluidized bed reactor processes follows the general approach for multiphase reactor processes. Krishna (1994) and Jazayeri (1995) outlined the general procedure for this process development. The design of the processes can be described by considering various factors as illustrated in Fig. 3. 

Catalyst selection should be based on catalyst reactivity, reaction selectivity, and physical properties such as particle size, density, and resistance to attrition. For process development, heat and mass transfer phenomena together with reactivity and physical properties of catalysts must be taken into account. The catalytic process begins with gas reactant transferring to the catalyst outer surface and subsequent intraparticle diffusion of the reactant through the pores of the catalyst. Reactants then absorb onto the catalyst surface and react to form product. These products desorb from the surface, and, through intraparticle diffusion, the products exit from the pores and outer catalyst surface. Consider the example of the ammoxidation of propylene to produce acrylonotrile over multicomponent molybdenum/bismuth catalysts ... 

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