To boost production in a chemical plant without enlarging any of the tubular reactors, several might be arranged in parallel, as shown in Fig. P12.10. Each might be an open tube of diameter D_R and length L_R. Or, each might be a tube of those dimensions that is packed with spherical catalyst pellets of diameter d with void fraction ε. The mean velocity in an open tube and the superficial velocity in a packed tube are each denoted as v_R. The reactants are supplied by a distribution manifold and the products collected via a return manifold. It is desired to derive pressure–velocity relationships that would help in designing such systems.

(a) Modify the derivation in Example 12.3-3 as needed to find P₂ − P₁ and v_R for a tubular reactor without packing. You may assume that the flow is turbulent and that P₀ is given. (Evaluating the inlet and outlet pressures at a given branch would require analysis of the entire flow network, manifolds and reactors.)

(b) Repeat part (a) for a packed-bed reactor in which

(c) If v_R for either type of reactor is given, find the pressure change at a branch point in the return manifold. Does the pressure there in the main pipe increase or decrease in the direction of flow?

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Reactors D Figure P12.10 Tubular reactors in parallel. DR LR