Effectiveness factor exothermic reactions

The effectiveness factors of reaction I and II decrease continuously with the increase of temperature. Reaction II is exothermic (A//= - 41.15/c//mo/) and reversible, therefore the temperature has conflicting effects on its intrinsic rate of reaction. Increasing the... 

ILLUSTRATION 12.4 Effectiveness Factor Determination for a Nonisothermal Catalyst Pellet Employed to Effect an Exothermic Reaction... 

Reactions in porous catalyst pellets are Invariably accompanied by thermal effects associated with the heat of reaction. Particularly In the case of exothermic reactions these may have a marked influence on the solutions, and hence on the effectiveness factor, leading to effectiveness factors greater than unity and, In certain circumstances, multiple steady state solutions with given boundary conditions [78]. These phenomena have attracted a great deal of interest and attention in recent years, and an excellent account of our present state of knowledge has been given by Arls [45]. 

Treatment of thermal conductivity inside the catalyst can be done similarly to that for pore diffusion. The major difference is that while diffusion can occur in the pore volume only, heat can be conducted in both the fluid and solid phases. For strongly exothermic reactions and catalysts with poor heat conductivity, the internal overheating of the catalyst is a possibility. This can result in an effectiveness factor larger than unity. 

Obviously, if the reactant concentration does not go to zero at the center, the temperature difference will be less but, in many cases, it will still be quite large. Large values of this temperature difference can lead to effectiveness factors for exothermic reactions that are considerably in excess of unity. 

ILLUSTRATION 12.4 EFFECTIVENESS FACTOR DETERMINATION FOR A NONISOTHERMAL CATALYST PELLET-EXOTHERMIC REACTION... 

An exothermic first-order reaction A—h B is conducted in an FBCR, operating adiabatically and isobarically. The bed has a radius of 1.25 m and is 4 m long. The feed contains pure A at a concentration of 2.0 mol m-3, and flowing at q = 39.3 m3 s 1. The reaction may be diffusion limited assume that the relationship between r) and is 7] = (tanh The diffusivity is proportional to Tia, and Le for the particles is 0.50 mm. Determine the fractional conversion of A and the temperature at the bed outlet. How would your answer change, if (a) diffusion limitations were ignored, and (b) a constant effectiveness factor, based on inlet conditions, was assumed. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

Figure 3.6 shows that, for exothermic reactions (0 > 0), the effectiveness factor may exceed unity. This is because the increase in rate caused by the temperature rise inside the particle more than compensates for the decrease in rate caused by the negative concentration gradient which effects a decrease in concentration towards the centre of the particle. A further point of interest is that, for reactions which are highly exothermic and at low value of the Thiele modulus, the value of tj is not uniquely defined by the Thiele modulus and the parameters 0 and e. The shape of... 

In this section we have presented and solved the BVPs associated with the diffusion and reaction that take place in the pores of a porous catalyst pellet. The results were expressed graphically in terms of the effectiveness factor rj versus the Thiele modulus d> for two cases One with negligible external mass and heat transfer resistances, i.e., when Sh and Nu —> oo, and another with finite Sh and Nu values. This problem is very important in the design of fixed-bed catalytic reactors. The sample results presented here have shown that for exothermal reactions multiple steady states may occur over a range of Thiele moduli d>. Efficient numerical techniques have been presented as MATLAB programs that solve singular two-point boundary value problems. 

Construct the diagrams of the effectiveness factor and the desired yield versus the Thiele modulus of the reactant A for a first-order consecutive exothermic catalytic reaction... 

Surface reaction with diffusion and heat transfer resistance In fast exothermic reactions, in addition to grad c, also grad T (TG Ts) is present in the boundary layer between the gas bulk phase and the catalyst surface. For the outer effectiveness factor qext this means that... 

This procedure yields the curves depicted in Fig. 10 for fixed values of Bim and y. and the modified Prater number fi" as a parameter. From this figure, it is obvious that for exothermal reactions (fi > 0) and large values of the Weisz modulus, effectiveness factors well above unity may be observed. The reason for this is that the decline of the reactant concentration over the... 

However, whereas effectiveness factors above unity under nonisothcrmal conditions can be explained quite easily, the observation of multiple steady states is a new and unexpected feature. These arise at small values of provided the reaction is substantially exothermic and, additionally, has a high activation energy. This means that, for a single value of the Thiele modulus, several possible solutions for the steady state overall effectiveness factor may exist (operating points), usually up to three. The middle operating point is normally unstable. Whenever the temperature and/or the... 

Whether or not multiple steady states will appear, and how large the deviation of the effectiveness factors between both stable operating points will be, is determined by the values of the Prater and Arrhenius numbers. Effectiveness factors above unity generally occur when p > 0 (exothermal reactions). However, for the usual range of the Arrhenius number (y = 10-30), multiple steady states are possible only at larger Prater numbers (see Fig 13). For further details on multiple steady states, the interested reader may consult the monograph by Aris [6] or the works of Luss [69, 70]. 

Figure 16 shows an effectiveness factor diagram for a first order, irreversible reaction which has been calculated from eq 95 for various values of the modified Prater number / . From this figure, it can be seen that for exothermal reactions (/ > 0) effectiveness factors above unity may be observed when the catalyst operates at a temperature substantially above the bulk fluid phase temperature. This is caused by the limited heat transfer between the pellet and the surrounding fluid. The crucial parameters controlling occurrence and size of this effect are again the modified Prater number and the Arrhenius number. 

It will be clear that in case of exothermal reactions the effectiveness factor can become larger than one. This is indicated by the numerical solution for the effectiveness factor in Fig. 13 for various values of / , and ys. In these cases situations may arise that the temperature effect is counterbalanced by the concentration effects, resulting in an effectiveness factor around one. However, the temperature effect in the case of cndothcrmal reactions only adds to the lowering of the effectiveness factor by a concentration profile. 

Figure 7.9 shows the temperature and concentration profiles caused by transfer limitations in the case of an endothermic reaction. For an exothermic reaction the temperature at the external surface, T,-, increases with increasing transfer limitations. Hence the external effectiveness factor, Tie, becomes greater than 1 as soon as the decrease of the reactant concentration is compensated by the increase of the temperature. 

An experimental test to verify the absence of significant concentration gradients inside the catalyst pellet is based on the inverse proportional relation between the effectiveness factor and the pellet diameter for strong internal diffusion limitations. Hence, a measured rate which is independent of the pellet size indicates that internal diffusion limitations can be neglected. Care should be taken to avoid artifacts. External heat transfer effects also depend on pellet size and for exothermic reactions might compensate the internal diffusion limitations. If the catalyst pellet consists of a support with an non-uniformly distributed active phase, crushing and sieving to obtain smaller pellets is hazardous. 

---