Pressure Drop in a Packed Bed Reactor (PBR) Using the Ergun Equation
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A first-order, irreversible, gas-phase reaction A → B takes place in two isothermal, packed-bed catalytic reactors; they have the same diameter but different lengths (14 m and 21 m). Only A is fed to the reactors. The inlet pressure is the same for each reactor; the outlet pressure changes when particle diameter is changed with the slider, but each reactor has the same outlet pressure. As a result, the inlet molar flow rate of A is lower for the longer reactor. Show plots of conversion, pressure, reactant molar flow rate, and volumetric flow rate as a function of distance down the reactor for both reactors with buttons. The Ergun equation is used to model the pressure drop.

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: