Overall catalyst effectiveness factor

An overall catalyst effectiveness factor of the reaction may now be defined as the ratio of the observed effective rate, averaged over the pellet volume, divided by the intrinsic chemical rate which would be expected in absence of concentration and temperature gradients in the system (i.e. under bulk fluid phase conditions)... 

The conservation equations for mass and enthalpy for this special situation have already been given with eqs 76 and 62. As there is no diffusional mass transport inside the pellet, the overall catalyst effectiveness factor is identical to the film effectiveness factor i/cxl which is defined as the ratio of the effective reaction rate under surface conditions divided by the intrinsic chemical rate under bulk fluid phase conditions (see eq 61). For an nth order, irreversible reaction we have the following expression ... 

The first step in heterogeneous catalytic processes is the transfer of the reactant from the bulk phase to the external surface of the catalyst pellet. If a nonporous catalyst is used, only external mass and heat transfer can influence the effective rate of reaction. The same situation will occur for very fast reactions, where the reactants are completely exhausted at the external catalyst surface. As no internal mass and heat transfer resistances are considered, the overall catalyst effectiveness factor corresponds to the external effectiveness factor,... 

An overall catalyst effectiveness factor no can be derived to take into account the effective surface wetting and the external reactant supply. This factor is defined as the ratio of the actual conversion rate and that obtained without diffusion resistance. This overall effectiveness factor may be approximated by the weighted average value for the differently wetted fractions of the pellet surface (Capra et al. [8]). If the wetting situation can be simplified into one wetted and one non-wetted surface fraction, with pellet volume fractions equivalent to surface fractions, then ... 

In the case when external mass transfer is negligible, Bi is high and catalyst effectiveness factor is equal to the effectiveness factor for internal dilfusion as expressed by eq. (9.174). Thus, similar to electric circuits where the overall resistance is equal to the sum of resistances in series, it holds that... 

Heterogeneous catalytic reactors are the most important single class of reactors utilized by the chemical industry. Whether their importance is measured by the wholesale value of the goods produced, the processing capacity, or the overall investment in the reactors and associated peripheral equipment, there is no doubt as to the prime economic role that reactors of this type play in modem industry. The focus of this chapter is the design of heterogeneous catalytic reactors. Particular emphasis is placed on the concept of catalyst effectiveness factors and the implications of heat and mass transfer processes for fixed bed reactor design. 

For a PFR, c k,t) = Cf k)QKt()[-kri k)f where /7(k) is the catalyst effectiveness factor. Denoting as the overall asymptotic order for the mixture controlled by diffusion. Ho et al. showed that = ( + l)/2, a relationship similar to that in the single-reactant case. Hence diffusional falsification occurs for mixtures with n. Since > 1 in general, so n, < Gosselink and Stork " found for the HDS of a gas oil that the overall order changed from two to 1.4 in going from ground-up to 3 mm catalyst particles. Stephan et al." observed that the overall order for powder catalyst is three, vs. two for 5 mm pellets. 

Where, tIc is overall catal54ic effectiveness factor. The overall catalytic effectiveness factor for a spherical catalyst particle can be expressed as ... 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

The effect of catalyst particle size was investigated by two different catalyst particle size fractions 63-93 pm and 150-250 pm, respectively. The effect of the particle size is very clear as demonstrated by Figure 47.2. The overall hydrogenation rate was for smaller particles 0.17 mol/min/gNi while it was 0.06 mol/min/gNi, for the larger particles, showing the presence of diffusion limitation. This kind of studies can be used to determine the effectiveness factors. The conversion levels after 70 min time-on-stream were 21% and 3%, respectively, for these two cases. 

Now consider the other extreme condition where diffusion is rapid relative to chemical reaction [i.e., hT( 1 — a) is small]. In this situation the effectiveness factor will approach unity for both the poisoned and unpoisoned reactions, and we must retain the hyperbolic tangent terms in equation 12.3.124 to properly evaluate Curve C in Figure 12.11 is calculated for a value of hT = 5. It is apparent that in this instance the activity decline is not nearly as sharp at low values of a as it was at the other extreme, but it is obviously more than a linear effect. The reason for this result is that the regions of the catalyst pore exposed to the highest reactant concentrations do not contribute proportionately to the overall reaction rate because they have suffered a disproportionate loss of activity when pore-mouth poisoning takes place. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

Recall than both A and B must diffuse into the catalyst for a bimolecular reaction to occur. This can create fairly complex concentration profiles of the two reactants within the catalyst, and the overall effectiveness factor is more complex than with the assumptions above. 

As mentioned earlier, if the rate of a catalytic reaction is proportional to the surface area, then a catalyst with the highest possible area is most desirable and that is generally achieved by its porous structure. However, the reactants have to diffuse into the pores within the catalyst particle, and as a result a concentration gradient appears between the pore mouth and the interior of the catalyst. Consequently, the concentration at the exterior surface of the catalyst particle does not apply to die whole surface area and the pore diffusion limits the overall rate of reaction. The effectiveness factor tjs is used to account for diffusion and reaction in porous catalysts and is defined as... 

It is possible to combine the resistances of internal and external mass transfer through an overall effectiveness factor, for isothermal particles and first-order reaction. Two approaches can be applied. The general idea is that the catalyst can be divided into two parts its exterior surface and its interior surface. Therefore, the global reaction rates used here are per unit surface area of catalyst. 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

When the pore-diffusion is limiting, the effectiveness factor is rj = Thiele modulus, (p = rtJ3 (k/DP) 12, m being the radius of the catalyst particle, and DP the coefficient of pore-diffusion. The overall rate of the process depends then on the reciprocal modulus,

[Pg.77]

As a consequence of diffusion there is a reduction in the reaction rate as we progress inside the catalyst with a result that the overall rate is much less than would be achieved if the reactant were at a concentration as supplied at the outer surface. Thus the catalyst regions are not effectively used and the concept of effectiveness is introduced. Effectiveness is defined as the average reaction rate, i.e., with diffusion, divided by the reaction rate if the rate of reaction is evaluated at the boundary condition value at X = 1. The effectiveness factor can be generally given by... 

From this figure, it can be concluded that the reduction of the effectiveness factor at large values of becomes more pronounced as the Biot number is decreased. This arises from the fact that the reactant concentration at the external pellet surface drops significantly at low Biot numbers. However, a clear effect of interphase diffusion is seen only at Biot numbers below 100. In practice, Bim typically ranges from 100 to 200. Hence, the difference between the overall and pore effectiveness factor is usually small. In other words, the influence of intraparticle diffusion is normally by far more crucial than the influence of interphase diffusion. Thus, in many practical situations the overall catalyst efficiency may be replaced by the pore efficiency, as a good approximation. 

Again, eq 75 cannot be used immediately to calculate the overall effectiveness factor, since the modulus fi, which is related to the unknown catalyst temperature, can only be determined when the overall efficiency has been specified (see eqs 71 and 72). Therefore, both sides of eq 74 arc multiplied by 2, resulting in an expression which relates the Weisz modulus ift to the modulus . Then, for a given value of fi, the corresponding value of ij/ is calculated, and from ij/ the unknown catalyst temperature 0S (eq 71). This temperature is substituted into eq 72 to obtain the corresponding value of the Thiele modulus <)>. Dividing ij/ by fi finally yields the overall effectiveness factor which is then plotted against i/f. 

Although multiplicities of the effectiveness factor have also been detected experimentally, these are of minor importance practically, since for industrial processes and catalysts, Prater numbers above 0.1 are less common. On the contrary, effectiveness factors above unity in real systems are frequently encountered, although the dominating part of the overall heat transfer resistance normally lies in the external boundary layer rather than inside the catalyst pellet. For mass transfer the opposite holds the dominating diffusional resistance is normally located within the pellet, whereas the interphase mass transfer most frequently plays a minor role (high space velocity). 

For the particle sizes used in industrial reactors (> 1.5 mm), intraparticle transport of the reactants and ammonia to and from the active inner catalyst surface may be slower than the intrinsic reaction rate and therefore cannot be neglected. The overall reaction can in this way be considerably limited by ammonia diffusion through the pores within the catalysts [211]. The ratio of the actual reaction rate to the intrinsic reaction rate (absence of mass transport restriction) has been termed as pore effectiveness factor E. This is often used as a correction factor for the rate equation constants in the engineering design of ammonia converters. 

When gum formation proceeds, the minimum temperature in the catalyst bed decreases with time. This could be explained by a shift in the reaction mechanism so more endothermic reaction steps are prevailing. The decrease in the bed temperature speeds up the deactivation by gum formation. This aspect of gum formation is also seen on the temperature profiles in Figure 9. Calculations with a heterogenous reactor model have shown that the decreasing minimum catalyst bed temperature could also be explained by a change of the effectiveness factors for the reactions. The radial poisoning profiles in the catalyst pellets influence the complex interaction between pore diffusion and reaction rates and this results in a shift in the overall balance between endothermic and exothermic reactions. 

---