Isothermal catalysts

Navler-Stokes equation, 26 Non-isothermal catalyst pellet, 156-... 

Fig. 2. Effectiveness factor as a function of Thiele modulus for an isothermal catalyst pellet.

Wheeler s treatment of the intraparticle diffusion problem invokes reaction in single pores and may be applied to relatively simple porous structures (such as a straight non-intersecting cylindrical pore model) with moderate success. An alternative approach is to assume that the porous structure is characterised by means of the effective diffusivity. (referred to in Sect. 2.1) which can be measured for a given gaseous component. In order to develop the principles relating to the effects of diffusion on reaction selectivity, selectivity in isothermal catalyst pellets will be discussed. 

In the first stage of the investigation the catalyst can be considered in the form of powder in order to derive intrinsic transient kinetics of all the relevant reactive processes. To this purpose, dynamic reactive experiments can be performed in a simple tubular fixed-bed microreactor over small quantities (50-200 mg) of finely powdered catalyst in principle, this guarantees negligible transport limitations and more controlled conditions (e.g. isothermal catalyst bed), hence enabling a direct estimation of intrinsic rate parameters by kinetic fit. Internal diffusion limitations are particularly relevant to the case of bulk (extruded) monolith catalysts, such as vanadium-based systems for NH3/urea SCR however, they... 

Fig. 9.13. Stationary-state loci for the non-isothermal catalyst pellet (a) three stationary-state branches (b) unique response (c) five stationary-state branches, appropriate to Robin boundary conditions with a < 1.

Mathematical criteria aid in understanding what reactor system features can be manipulated to achieve better isothermal control. Based on this, the following recommendations can help establish isothermal catalyst testing ... 

Further, make the same assumptions as in Appendix D of no viscous flow, no surface diffusion, an isothermal catalyst pellet and no external forces. According to the dusty gas model a force balance for component A then yields ... 

The previous discussion focused on simultaneous diffusion and reaction in isothermal catalyst pellets. Since A//, is significant for many industrially relevant reactions, it is necessary to address how heat transfer might affect solid-catalyzed... 

The FT-conversion has been conducted in a fixed bed reactor with the finely powdered catalyst (dp <0.1 mm) covering larger fused silica particles (dp = 0.25-0.4 mm) as an adhering layer, the weight ratio of catalyst to fused silica particles being 1 10. By this means a very isothermal catalyst bed was provided with highly uniform flow of the gas phase, minor pressure drop and no noticeable intraparticle resistance influence. 

Example 3.2.2. Series Solutions for Non-isothermal Catalyst Pellet - Multiple Steady States... 

The dimensionless concentration in a non-isothermal catalyst pellet[8] is governed by ... 

Isothermal Catalyst Pellets with Non-linear Kinetics... 

Other recent work in the field of optimization of catalytic reactors experiencing catalyst decay includes the work of Romero e/ n/. (1981 a) who carried out an analysis of the temperature-time sequence for deactivating isothermal catalyst bed. Sandana (1982) investigated the optimum temperature policy for a deactivating catalytic packed bed reactor which is operated isothermally. Promanik and Kunzru (1984) obtained the optimal policy for a consecutive reaction in a CSTR with concentration dependent catalyst deactivation. Ferraris ei al. (1984) suggested an approximate method to obtain the optimal control policy for tubular catalytic reactors with catalyst decay. 

The Non-isothermal Catalyst Pellets with Linear Kinetics (Non-porous Catdyst Pellet with Unimolecular Reaction)... 

Single-Bed Isothermal Catalysts. Detailed analyses of exit gases from single-bed isothermal catalysts were determined with 2 g of red bauxite at 475°C. The inlet gas contained 3.4% sulfur dioxide, 5.9% carbon monoxide, and 90.7% helium. Figure 2 (Section A) shows that the sulfur dioxide analysis decreased from 3.4 to 0.8. In other words, about 76% of the sulfur dioxide was removed in the dry state at a carbon monoxide ratio, r, of 0.87. However, when 3% water vapor was added (Section B), the sulfur dioxide in the exhaust gas increased to 1.9%, illustrating the poisoning effect of water. When water vapor flow was stopped, the sulfur dioxide exhaust analyses decreased slowly (Section... 

Probably the most widely applied criterion is the one for internal mass transfer limitations in an isothermal catalyst particle, e.g. for pore diffusion. Due to Weisz and Prater (Advances in Catalysis 6 (1954) 143) no pore diffusion limitation occurs, if the Weisz modulus... 

For a non-isothermal catalyst particle according to the Weisz-Hicks criterion no internal heat and mass transport limitations occur if... 

To avoid internal mass transfer resistances in the porous catalytic layer, its thickness, must be limited. To ensure an effectiveness factor of > 0.95 in an isothermal catalyst layer, the following criterion must be fulfilled [14] ... 

Internal effectiveness factor in isothermal catalyst layer —... 

In fluid-solid systems, the reaction takes place on the catalyst surface. Prior to this, the reactant molecules have first to reach the catalyst surface and, therefore, the rate of mass transfer is an important operational parameter (Figure 15.3). Two types of mass transfer need to be considered in fluid-solid reactions external and internal mass transfer. In particular, internal mass transfer limitations should be avoided, since they more often limit the performance of the reactor and more strongly influence the product selectivity. The internal mass transfer is characterized by an effectiveness factor, q, defined as the ratio of the observed reaction rate to that at constant concentration throughout the catalyst layer. To ensure an effectiveness factor of q > 0.95 in an isothermal catalyst layer, the following criterion must be fulfilled [16] ... 

A second application of the CPR is product enhancement for catalytic reactions, where the product spectrum is highly dependant upon catalyst temperature. In such an application, alternate channels contain a boiling heat transfer fluid to maintain an isothermal catalyst temperature. The hydrocarbon product spectrum produced by a Fischer-Tropsch catalyst is highly dependent upon catalyst temperature and rate of diffusion of reactants into the catalyst matrix. The reaction is highly exothermic and, if rates of heat removal from the catalyst are not sufficiently high, hot spots will form which result in degradation of the product spectrum. Studies have... 

Vogiatzis et al. modelled heat dispersion effects in future water-gas shift membrane reactors on an industrial scale [418]. A catalyst bed of 2-m length was assumed, which contained tubular membranes with a 4-mm outer diameter. The distance between the tubes, which was filled by the fixed catalyst bed, was only 23 mm and thus the model could be applied for systems of a smaller scale. Heat dispersion effects occurred in the reactor. Overheating of the catalyst bed by about 30 K occurred, which lead to increased conversion compared with an isothermal catalyst bed. However, the opposite effect is to be expected with an endothermic reaction, such as methane steam reforming. 

Figure 4.5.23 Effectiveness factor of a non-isothermal catalyst particle as a function of the Thiele modulus 0 (at 7 ) and the Prater number for an Arrhenius number of 20 (for solutions for other Yi x values see Weisz and Hicks, 1962 Levenspiel, 1996).

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