This Demonstration calculates the effect of tube diameter on conversion, temperature, and pressure drop for a plug flow reactor (PFR). A first-order exothermic reaction takes place in a PFR with pressure drop and heat transfer through the walls. You can vary the reactor diameter, but the total feed flow rate is kept constant by changing the number of parallel reactors ("# equivalent reactors") in order to keep the total reactor cross section constant and thus to keep the total molar feed flow rate constant. For smaller-diameter reactors, the pressure drop is higher, which increases the volumetric flow rate and reduces the residence time and thus lowers the conversion. Also, heat transfer is more efficient for smaller-diameter reactors because the surface area per volume is larger, so the temperature increases less in the reactor, and this also lowers conversion.
Ergun equation for pressure drop in a plug flow reactor
The pipe is assumed to be commercial steel. For laminar flow, the following equation is used to calculate the Darcy friction factor. For turbulent and transitional flow, Serghide's explicit solution to the Colebrook equation is used.
, pressure (N )
, fluid density ()
, cross sectional area of reactor ()
, inlet volumetric flow rate ()
, volumetric flow rate ()
, inlet molar flow rate (mol )
, ideal gas constant ()
, inlet reactor temperature (K)
, initial reactant pressure ()
, friction factor
, wall roughness (m)
, hydraulic diameter, equal to reactor diameter in absence of heating or cooling (m)