**Pressure Drop in a Packed Bed Reactor (PBR) Using the Ergun Equation**

**Details:**

The pressure decreases down the length of the reactor, and thus the volumetric flow rate increases. As a result, the concentration of the reactant decreases (in addition to the decrease due to conversion), which lowers the rate of reaction.

The Ergun equation for pressure drop in a packed bed reactor (PBR) is:

where P is pressure, z is PBR length, φ is void fraction, v is volumetric flow rate, μ is viscosity, D

_{P}is the diameter of catalyst particles, A_{C}is cross sectional area of the PBR, m is mass flow rate, B is a laminar flow term, and G is the turbulent flow term.Material balance on reactant for a first-order reaction:

where C

_{A}is the molar concentration of reactant A, F_{A}is the molar flow rate of A, k is a rate constant, and F_{A,0}is the inlet molar flow rate of A.Since the reaction is A → B, and only A is fed to the reactor, the total molar flow rate F

_{total}= F_{A,0}.Volumetric flow rate in reactor (from the ideal gas law):

where R is the ideal gas constant, and T is absolute temperature.

Conversion of reactant A: