Plug flow, reactor model integral operation

A few reactor models have recently been proposed (30-31) for prediction of integral trickle-bed reactor performance when the gaseous reactant is limiting. Common features or assumptions include i) gas-to-liquid and liquid-to-solid external mass transfer resistances are present, ii) internal particle diffusion resistance is present, iii) catalyst particles are completely externally and internally wetted, iv) gas solubility can be described by Henry s law, v) isothermal operation, vi) the axial-dispersion model can be used to describe deviations from plug-flow, and vii) the intrinsic reaction kinetics exhibit first-order behavior. A few others have used similar assumptions except were developed for nonlinear kinetics (27—28). Only in a couple of instances (7,13, 29) was incomplete external catalyst wetting accounted for. 

The integral mode of operation has the inherent advantage that large conversions are achieved, so a high precision of chemical analysis is not required. If a plug flow model is assumed to be valid for such a reactor, a material balance for component A over a differential bed length dz gives... 

Suppose that this reactor operates in an integral mode (e.g., at an outlet fractional conversion of 0.90), and that an irreversible, first-order reaction is taking place. A rate constant can be calculated from the outlet conversion by assuming either plug-flow, complete backmixing (i.e., that the reactor is an ideal CSTR), or the dispersedplug-flow model. Calculate the values of the ratios (CSTR)/ (PFR) and (DPF)/ (PFR) for a measured outlet conversion of 0.90. 

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