The Easy Way—Choose a Different Control Volume

Let s choose a different control volume over which to write the component material balance. More specifically, let s choose the control volume such that r, does not depend on V, From the above discussion, it should be clear that the new control volume must be differential in the direction of flow, since r,- varies in this direction. However, the ccaitrol volume can span the whole cross section of the reactor, normal to flow, since there are no temperature or concentration gradients normal to flow. Therefore, r,-willbeconstantover any suchcross section. 

For a tubular reactor, the control volume is a slice through the reactor perpendicular to the axis (z direction), with a differential thickness dz, as shown below. 

The inlet face of the control volume is located at an axial position, z. The molar flowrate of into the element is F, and the molar flow rate of leaving the element is Fi - - dF,-. For this element, the steady-state material balance on i is 

Design equation-ideal PFR— homogeneous reaction (molar flow rate) 

Equation (3-26) is the design equation for an ideal PFR, in differential form. This equation applies to a PFR where more than one leaetion is taking place, provided that r,- is expressed using Eqn. (1-17). 

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