Effectiveness factors significance

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

Rates and selectivities of soHd catalyzed reactions can also be influenced by mass transport resistance in the external fluid phase. Most reactions are not influenced by external-phase transport, but the rates of some very fast reactions, eg, ammonia oxidation, are deterrnined solely by the resistance to this transport. As the resistance to mass transport within the catalyst pores is larger than that in the external fluid phase, the effectiveness factor of a porous catalyst is expected to be less than unity whenever the external-phase mass transport resistance is significant, A practical catalyst that is used under such circumstances is the ammonia oxidation catalyst. It is a nonporous metal and consists of layers of wire woven into a mesh. 

II. The promotional effectiveness factor, t]p, (Chapter 11) must be significant, larger than, at least, 0.1. This requires small promotional Thiele modulus, Op, and significant dimensionless current, J, values. This implies thin (low L) catalyst films and slow kinetics of promoter destmction (low k values, Chapter 11). 

If the two competing reactions have the same concentration dependence, then the catalyst pore structure does not influence the selectivity because at each point within the pore structure the two reactions will proceed at the same relative rate, independent of the reactant concentration. However, if the two competing reactions differ in the concentration dependence of their rate expressions, the pore structure may have a significant effect on the product distribution. For example, if V is formed by a first-order reaction and IF by a second-order reaction, the observed yield of V will increase as the catalyst effectiveness factor decreases. At low effectiveness factors there will be a significant gradient in the reactant concentration as one moves radially inward. The lower reactant concentration within the pore structure would then... 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

The statistical test for the effectiveness of the factors asks the question, Has a significant amount of variance in the data set been accounted for by the factors as they appear in the model Another way of asking this is to question whether or not one or more of the parameters associated with the factor effects is significant. For models containing a Pq term, the null hypothesis to be tested is... 

The concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

However, biomagnification factors significantly different from 1 may also reflect real processes building up the effective concentrations in a given organism s tissues. Said more accurately, the chemical activity or fugacity of the compound may prove to be greater as one moves up the food chain ... 

The effectiveness factor is very low, indicating that intraparticle mass transfer resistance is very significant. The gas-liquid mass transfer resistance is also important, as expected. On the other hand, the liquid-solid mass transfer resistance is negligible. As a result, the rate of reaction in the slurry reactor is about 50 times higher than that in the trickle-bed. Therefore, in cases of such high rates of reaction, the slurry reactor is a better choice, although the gas-liquid mass transfer and the filtration of the catalyst may be a problem. 

The unexpected overlap of this problem is more surprising than significant, for the first derivative of the effectiveness factor with respect to the Thiele modulus (Figs. 8 and 9) does not stand out as of particular interest. [Note added in proof (Jan. 99). I could not have been more wrong. See p. 37, fn. 11 and reference then cited.]... 

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