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Star from the general mole balance derive the differential form of PFR design equation

Star from the general mole balance derive the differential form of PFR design equation

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Answer #1

The concentration changes along the length of the reactor A differential analysis needs to be carried out for finding the differential equation

Let FA= Moles of A/ unit time entering FA+dFA= moles of A leaving.

Let differential volume be dV

Steady state mass balance reads as

Input= output + Rate loss due to Chemical Reaction

FA =FA+dFA+(-rA)dV, dV is the differential volume

FA= FAO*(1-XA) where FAO= initial moles of A, XA= conversion

-dFA= (-rA)*dV

FAO*dXA= (-rA)*dV

dV= FAO*dXA/(-rA)

Integrating

V = FAO*dXA/(-rA)

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