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. [Pg.269]

For gas-phase reactions, (r(0) — 7 s)maxCanbesignificantwhenAradislargeandDA is high. If the reaction is endothermic, the temperature throughout the interior of the particle will be less than Tg. That will cause the actual effectiveness factor to be lower than for a catalyst particle that is isothermal at Tg. For this situation, the assumption of isothomality leads to an overestimate of t), i.e., rj (actual) < ri (isothomal). When the reaction is endothermic, the general behavior of the ri voisus (j> relationship is similar to that for the isothermal case. The effectiveness factor is 1 at voy low values of (j> and declines monotonically as the Thiele modulus increases. [Pg.337]

Figure 1 shows the dependence effectiveness factor tj = roi/ri on Thiele modulus for the selected values of parameter p and for = 2, v = 2 (sphere), yt = 7, yi = 12, 5 = 1 (endothermic reactions) and xa(1) = 1. One can find that for P

effectiveness factor rj assumes in the certain ranges of Thiele modulus values much higher than unity. This means that in the cases discussed the internal diffusion, in contrast to the classical isothermal or endothermic catalytic reactions, may considerably increase the rate of the heterogeneous autocatalytic reactions. [Pg.414]

We now know that two factors determine whether a reaction is spontaneous under a given set of conditions. The effect of one factor, the enthalpy change, is that spontaneity is favored (but not required) by exothermicity, and nonspontaneity is favored (but not required) by endothermicity. The effect of the other factor is summarized by the Second Law of Thermodynamics. [Pg.621]

Figure 4.5.15 External effectiveness factor as a function ofthe ratio ofthe (measurable) effective reaction rate to the maximum rate (complete control by external mass transfer) fora constant Arrhenius number of 20. For a Prater number jSex < 0, the reaction is endothermic, for /Sex > 0 exothermic, and for /Sex = 0 we have isothermal conditions. Arrows and dashed line indicate ignition, as explained in the text. |

In summary, the assumption of an isothermal catalyst particle is valid for many situations, e.g., most liquid-phase reactions and those gas-phase reactions where ATad is not too large and Z)A,eff is relatively low (Z)A,m/ A,eff > 10)- If the reaction is endothermic, the isothermal model can be used to estimate a maximum value of the effectiveness factor, even when ATad is large. [Pg.338]

Since the conversion rate depends on a and e, the effectiveness factor will be determined by three parameters, namely a, e and a Thiele modulus. This is illustrated in Figure 6.4 [18]. For values of a larger than zero (exothermic reaction) an increase in the effectiveness factor is found, since the temperature inside the catalyst pellet is higher than the surface temperature. For endothermic reactions (a < 0) a decrease of the effectiveness factor is observed. [Pg.118]

Theoretical work has been done on the effectiveness factor for nonisothermal particles. Fig. 3.13.1-1 shows the results of the computations by Weisz and Hicks [1962] for y = EIRT = 20. For > 0.1, that is, for sufficiently exothermic reactions, the effectiveness factor can exceed the value of 1. In such a case the temperature rise, which increases the value of the rate constant, would more than offset the decrease in reactant concentration Cas, so that fA averaged over the particle exceeds that at surface conditions. The converse is true for endothermic reactions. [Pg.224]

For an endothermic reaction there is a decrease in temperature and rate into the pellet. Hence 17 is always less than unity. Since the rate decreases with drop in temperature, the effect of heat-transfer resistance is diminished. Therefore the curves for various are closer together for the endothermic case. In fact, the decrease in rate going into the pellet for endothermic reactions means that mass transfer is of little importance. It has been shown that in many endothermic cases it is satisfactory to use a thermal effectiveness factor. Such thermal 17 neglects intrapellet mass transport that is, ri is obtained by solution of Eq. (11-72), taking C = Q. [Pg.448]

The suitability of a cycle for hydrogen production depends upon the overall thermal efficiency and operational feasibility. A highly endothermic reaction step is required in a cycle to achieve effective heat-to-chemical energy conversion. For efficient mass and momentum transfer a fluid based system is preferred [96] and, ultimately, for large-scale hydrogen production other factors such as environmental effects and cost effectiveness must also be considered. [Pg.62]

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