10176

# Effect of Tube Diameter on Plug Flow Reactor

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.

### DETAILS

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.
, for
, for
, 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)
, reactor diameter (m)
, dynamics viscosity ()
, Reynolds number
Mass balance
, molar flow rate of reactant (mol )
, rate law constant ()
, concentration of reactant (mol )
, temperature inside reactor (K)
Energy balance
, heat transfer coefficient times area/volume ()
, coolant temperature (K)
, heat of reaction ()
, heat capacity of reactants ()

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.