Methods for estimating transport resistances

Various methods are proposed to estimate the transport resistances outlined earlier. Traditionally, a, and as are obtained in terms of bubble diameter and the solid loading (aL = 6hG/db and as = 6m/ppdp here hG is the gas holdup,db is the bubble diameter, m is the catalyst loading, pp is the catalyst density, and dp is the catalyst particle diameter). For a first-order reaction, from Eq. (2-10), the global rate per unit volume of the slurry can be expressed150 as 

Satterfield150 considers a special case of the above equation, in which the gas-phase resistance is neglected (i.e., the second term on the right-hand side of the above equation is zero) and the catalyst effectiveness factor is assumed to be unity. In this case, a series of measurements of AG/R for various catalyst loadings permits a plot of AG/R versus 1/m to be established. The intercept yields the gas-liquid mass-transfer coefficient and the slope yields a combination of the intrinsic rate constant and the liquid- solid mass-transfer coefficient. 

The above method assumes that k, aL is independent of the catalyst particle loading. Chandraselcaran and Sharma,27 Joosten et al.,99 and Slcsser et al.,171 among others, have shown kbaL to be a function of solids loading and, hence, care should be exercised in making the above plots. 

Sylvester et al.173 proposed another method. They defined a series of effectiveness factors such as 

are the Damkohler numbers defined in several ways. t/0 can also be expressed as 

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