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, DP is the diameter of catalyst particles, AC 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 CA is the molar concentration of reactant A, FA is the molar flow rate of A, k is a rate constant, and FA,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 Ftotal = FA,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: