Thiele’s Modulus

Figure 3.4 shows the substrate concentration profile with respect to the radial distance as predicted by Eq. (3.30). For a low value of Thiele s modulus ( 0 < 1 ), the rate of the enzyme reaction is slow compared to the diffusion rate. 

Fig. 3.4 The substrate concentration profile with respect to the radial distance predicted by first-order kinetics (solid lines) and Michaelis-Menten kinetics with j3 = 5 (broken lines) for different values of Thiele s modulus ().

Figure 3.5 shows how Thiele s modulus affects the effectiveness factor for spherical immobilized particles. When 0 < 0.1, the effectiveness factor is nearly equal to one, which is the case when the rate of reaction is not slowed down by the diffusion. On the other hand, when 0 > 0.1, the effectiveness factor is inversely proportional to the Thiele s modulus. 

Fig. 3.5 Effect of Thiele s modulus on the effectiveness factor for spherical immobilized particles for first-order kinetics and Michaelis-Menten kinetics with p = 5. Thiele s modulus for first-order kinetics is...

Figure 3.5 shows the effect of the Thiele s modulus on the effectiveness factor. 

Thiele s modulus, (R/3) -Jk / Dg for first-order kinetics, (R/3) / DsK ) for Michaelis-Menten kinetics. 

As discussed above, the transport properties of porous catalyst particles of ca 3 to 100 pm are extremely important for the selectivity of catalytic reactions in which the desired initial products are liable to further reaction to undesired material. The ratio of the rate of catalytic reaction to that of transport within the pore system of catalyst particles is represented by Thiele s modulus [1], which is proportional to the pore length and to the square root of the diameter of the pores. Accordingly reducing the size of the catalyst particles is more elfective than increasing the diameter of the pores. 

The above equations can be rendered dimensionless in terms of Thiele s modulus, Biot number for mass transfer, and nondimensional time and distance, which are defined as... 

By introducing the measure h, called Thiele s modulus and defined by ... 

Two limiting cases ate interesting, depending of the range of Thiele s modulus value. 

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